Novel Solar Cell Concepts

NOVEL SOLAR CELL CONCEPTS

Dissertation zur Erlangung des akademischen Grades des Doktors der Naturwissenschaften (Dr. rer. nat.) an der Universität Konstanz Fachbereich Physik

vorgelegt von

Jan Christoph Goldschmidt Fraunhofer Institut für Solare Energiesysteme (ISE) Freiburg

September 2009 Konstanzer Online-Publikations-System (KOPS) URN: http://nbn-resolving.de/urn:nbn:de:bsz:352-opus-105444 URL: http://kops.ub.uni-konstanz.de/volltexte/2010/10544

Dissertation der Universität Konstanz Tag der mündlichen Prüfung: 16.11.2009

Referent/in: Prof. Gerhard Willeke Referent/in: Prof. Thomas Dekorsy

1

Table of contents

1

Table of contents.................................................................................................. i

2

Motivation and Introduction ............................................................................... 1 2.1

Motivation ................................................................................................. 1 2.1.1

Why it is essential to transform the global energy system?........... 1

2.1.2

Why photovoltaics?....................................................................... 1

2.1.3

Why new concepts for higher efficiencies?................................... 2

2.1.4

Photon management for full spectrum utilization ......................... 3

2.2

Main objectives of this work ..................................................................... 4

2.3

Structure of this Work ............................................................................... 5

3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts........................................................................................................................ 7 3.1

3.2

4

A short theory of solar cells....................................................................... 7 3.1.1

Thermodynamic efficiency limits ................................................. 7

3.1.2

Generating chemical energy.......................................................... 8

3.1.3

Extracting useful energy.............................................................. 10

3.1.4

The pn-structure .......................................................................... 13

Novel solar cell concepts ......................................................................... 17 3.2.1

Thermophotovoltaic Systems ...................................................... 17

3.2.2

Hot carrier solar cells .................................................................. 17

3.2.3

Tandem solar cells....................................................................... 18

3.2.4

Intermediate band-gap solar cells................................................ 18

3.2.5

Photon management .................................................................... 19

Fluorescent Concentrators................................................................................. 21 4.1

Introduction to fluorescent concentrators ................................................ 21 4.1.1

The working principle of fluorescent concentrators .................... 21

4.1.2

The factors that determine the efficiency of fluorescent concentrator systems ................................................................... 23

4.1.3

Fluorescent concentrator system design ...................................... 26

i

1 Table of contents

4.2

4.3

4.4

4.5

4.6

4.1.4

Materials for fluorescent collectors ............................................. 30

4.1.5

Fluorescence................................................................................ 31

Theoretical description of fluorescent concentrators ............................... 36 4.2.1

Maximum concentration and Stokes shift ................................... 36

4.2.2

Thermodynamic model of the fluorescent concentrator .............. 39

4.2.3

Photonic structures ...................................................................... 43

Optical characterization of fluorescent concentrator materials ................ 48 4.3.1

Photoluminescence measurements .............................................. 48

4.3.2

Characterizing the light guiding of fluorescent concentrators ............................................................................... 56

4.3.3

Measuring the angular distribution of the guided light................ 74

4.3.4

Short summary of the optical characterization ............................ 77

Simulating fluorescent concentrators....................................................... 79 4.4.1

Monte Carlo simulation............................................................... 80

4.4.2

The used model ........................................................................... 81

4.4.3

Results of simple model .............................................................. 87

4.4.4

Improvements of model............................................................... 90

4.4.5

Conclusions from simulation..................................................... 100

Fluorescent concentrator systems .......................................................... 101 4.5.1

Solar cells for fluorescent concentrator systems........................ 101

4.5.2

Systems with different materials ............................................... 103

4.5.3

Systems with silicon bottom cells ............................................. 110

4.5.4

The effect of photonic structures ............................................... 115

4.5.5

The influence of system size on collection efficiency ............... 120

The future of fluorescent concentrators ................................................. 128 4.6.1

The “Nano-Fluko” concept........................................................ 129

ii

1 Table of contents

5

Upconversion.................................................................................................. 133 5.1

Introduction to upconversion ................................................................. 133

5.2

The potential of upconversion and ways to increase upconversion efficiency ............................................................................................... 135

5.3

5.4

5.2.1

The potential of upconversion................................................... 135

5.2.2

Definition of upconversion efficiency....................................... 136

5.2.3

Upconversion efficiencies achieved so far ................................ 137

5.2.4

Spectral concentration............................................................... 137

5.2.5

An advanced system design for spectral concentration ............. 138

5.2.6

Enhancing upconversion efficiency by plasmon resonances ................................................................................. 140

Upconversion mechanisms and their theoretical description ................. 142 5.3.1

Absorption and emission........................................................... 144

5.3.2

Migration of excitation energy .................................................. 148

5.3.3

Multi-phonon relaxation............................................................ 151

5.3.4

Intensity dependence of upconversion ...................................... 152

Suitable materials for upconversion....................................................... 156 5.4.1

5.5

5.6

Theoretical aspects of the energy spectrum of trivalent erbium ....................................................................................... 157

Optical material characterization ........................................................... 161 5.5.1

Absorption measurements ......................................................... 161

5.5.2

The Kubelka-Munk theory ........................................................ 163

5.5.3

Absorption coefficient and Einstein coefficients....................... 164

5.5.4

Time-resolved photoluminescence............................................ 167

5.5.5

Intensity dependent upconversion photoluminescence.............. 176

5.5.6

Calibrated photoluminescence measurements........................... 179

5.5.7

Optical properties of luminescent nanocrystalline quantum dots (NQD)................................................................................ 185

Simulating upconversion ....................................................................... 188 5.6.1

The rate equation model............................................................ 189

5.6.2

Input parameters........................................................................ 194

iii

1 Table of contents

5.6.3 5.7

5.8

6

7

Simulation results...................................................................... 197

Upconversion systems ........................................................................... 204 5.7.1

Used solar cells and experimental setup .................................... 204

5.7.2

Applying the upconverter to the solar cell................................. 206

5.7.3

External quantum efficiency with different upconverter samples...................................................................................... 207

5.7.4

Upconversion solar cell system under concentrated sunlight...................................................................................... 211

Conclusions and outlook on the application of upconverting materials to silicon solar cells ................................................................ 220

Summary ......................................................................................................... 225 6.1

Fluorescent concentrators ...................................................................... 225

6.2

Upconversion......................................................................................... 228

Deutsche Zusammenfassung ........................................................................... 231 7.1

Fluoreszenzkonzentratoren .................................................................... 231

7.2

Hochkonversion..................................................................................... 234

8

References....................................................................................................... 237

9

Appendix......................................................................................................... 249

10

9.1

Abbreviations......................................................................................... 249

9.2

Glossary ................................................................................................. 250

9.3

Physical Constants ................................................................................. 261

Author’s Publications...................................................................................... 263 10.1 Refereed journal papers ......................................................................... 263 10.2 Conference papers.................................................................................. 264 10.3 Oral presentations .................................................................................. 267 10.4 Patents.................................................................................................... 268 10.5 Other publications.................................................................................. 269

11

Curriculum vitae ............................................................................................. 271

12

Acknowledgements ......................................................................................... 273

iv

2

Motivation and Introduction

2.1

Motivation

2.1.1

Why it is essential to transform the global energy system?

The global energy system is based on the primary energy sources oil, coal and gas predominantly. Burning these fossil fuels releases carbon dioxide and other emissions, ultimately resulting in climate change. Global climate protection is the supreme challenge that makes it necessary to transform energy systems worldwide. Also, at the local and regional levels, mining, transport, storage, and usage of fossil and nuclear fuels destroy or put at risk complete ecosystems and human health. Therefore the persisting patterns of energy usage jeopardize the natural basis of life. The global energy resources are limited and distributed unevenly. This causes geostrategic conflict and makes a forced end to our current energy usage inevitable. About two billion people have no access to modern energy sources. They are therefore cut off from any chance to overcome their poverty. All this leaves humanity with the challenge to drastically change the global energy system and to orient it towards sustainable ecological and social criteria [1]. Such criteria are the mitigation of climate change, conservation of nature and ecosystems such as oceans, rivers and soil, and the reduction of air pollution. A sufficient food supply for everybody must always be more important than energy production. Everybody should have affordable access to modern energy sources. Everybody should be able to use energy without endangering one’s health and should live without fear of risks associated with the energy system. As control over energy sources has always meant political power, reshaping our energy systems also presents a chance for more democracy and a more just distribution of power [2]. While searching for solutions, all of these criteria should be considered. There is no benefit in solving one problem while worsening another one at the same time. 2.1.2

Why photovoltaics?

An increase in energy productivity and a switch to new renewable energy sources are the two main pillars of the necessary transformation in global energy systems. Among the new renewable energy sources, solar energy has the most important role to play. The sustainably usable potential of solar energy appears to be virtually unlimited in comparison to the world energy demand. Other renewable energy sources like wind energy, water power, and biomass originate from solar energy, but their sustainably usable potential is not sufficient to meet the global energy demand [1]. The technology

1

2 Motivation and Introduction

likely to succeed in bringing solar energy to the people in developed as well as in developing countries is photovoltaics, the direct conversion of solar radiation into electric power. The modular character of the technology allows for the construction of power plants in any size. Photovoltaic devices, also known as solar cells, can serve as a power source in consumer products or be interconnected in modules as power plants of varying size: small island-systems to power houses or villages, mainly in developing countries are just as possible as grid-connected systems on residential housing in industrial countries or huge power plants in the megawatt range. The absence of moving parts makes the systems reliable and enables system lifetimes exceeding 25 years. Additionally, solar cells convert diffuse radiation into electricity as well, so they can harvest solar energy efficiently in middle and even northern Europe. Of all energy technologies, photovoltaics have the steepest learning curve. That is, no energy technology is getting cheaper faster. On average, a doubling in the cumulated installed power capacity of photovoltaic systems results in a 20% reduction in production costs. Together with the enormous market growth [3], this leads to a fast reduction in costs. Already now, levelized electricity costs from photovoltaics can compete with peak load prices in southern Europe [4]. Around 2015 or earlier, grid-parity will be reached in middle Europe [4]. Then the electricity from a roof-mounted photovoltaic system will cost about the same as the end consumer pays for electricity. However, prices are still high at the moment. To reach grid parity and to continue the expected development beyond 2015, continuous innovation is necessary. 2.1.3

Why new concepts for higher efficiencies?

Crystalline silicon is the dominant material in the production of solar cells. It is nontoxic and abundant. At the moment the material costs for silicon in the required purity dominate the costs for solar cell production. Therefore, alternative production technologies, such as thin-film solar cells or innovative silicon-wafer based concepts appear attractive. But also for new technologies, maturing production technologies will lead to a situation in which the material costs dominate. In the end, it will be the wafer, the glazing, or the substrate for thin-film technologies which sets the limit for further cost reduction. The only way to overcome this limit is to increase the efficiency of the solar cells. A higher efficiency increases the amount of electricity produced from one unit of material. This reduces the electricity costs and the amount of resources needed to meet our energy needs. Current innovations are mainly focused on production technologies. The underlying working principle of the solar cells remains unchanged. However, to achieve substantially higher efficiencies, novel solar cell concepts are needed that also address the working principle and which overcome fundamental limits.

2

2.1 Motivation

2.1.4

Photon management for full spectrum utilization

Most solar cells today are made from silicon, and therefore from one semiconductor material with one band-gap. These solar cells do not use the full solar spectrum (see Fig. 2.1). Photons which have energies below the band-gap of the semiconductor are not absorbed. The energy of photons which exceeds the band-gap is converted into heat, and is therefore lost as well [5]. As more than 55% of the energy is lost by these mechanisms, it is obvious that new concepts for higher efficiencies have to make better use of the energy contained in the solar spectrum.

Fig. 2.1:

Illustration of the principal losses incurred by a silicon solar cell. Photons with energies below the band-gap are transmitted straight through the device. Around 20% of the incident energy is lost this way. The energy of photons exceeding the band-gap is converted into heat. These thermalization losses account for around 35% of the incident energy. To achieve high efficiencies, novel concepts are needed to reduce these losses.

Several concepts are being discussed to overcome these fundamental efficiencylimiting problems. Most of these novel concepts require complex new solar cell structures and many are rather theoretical concepts than working devices. An alternative approach is photon management. Photon management means splitting or modifying of the solar spectrum before the photons are absorbed in the solar cells in such a way that the energy of the solar spectrum is used more efficiently. The solar cells themselves remain fairly unchanged, and well-established solar cell technologies can be used. This gives the concepts high realization potential. Because of these advantages, this work will deal with different concepts of photon management.

3


2.2

Main objectives of this work

The role of this work is to find and explore promising fields in the wide landscape of novel solar cell concepts. The main objectives are to increase the understanding of the concepts, investigate the materials on which the concepts are based, to realize complete systems, and to further develop the concepts to a point where their perspective and potential becomes clear. In this work, I concentrated on two concepts from the fields of photon management that appeared to be especially promising: fluorescent concentrators and upconversion. Both rely on luminescent materials. Luminescent materials absorb light independently from the direction of incidence. Therefore, in principle these concepts are able to use diffuse light as well. This is a big advantage to many other concepts for photon management, which rely on selective mirrors, filters, diffraction gratings, or similar, and which usually only work under direct sunlight. Both concepts share important aspects in theory as well as in technological issues, e.g. the need for a matrix material for the luminescent material, and they can be combined in one system as we will see later on. Fluorescent concentrators are a concept well known since the late 1970s [6, 7] to concentrate both direct and diffuse radiation without tracking systems. In a fluorescent collector, a luminescent material embedded in a transparent matrix absorbs sunlight and emits radiation with a different wavelength. Total internal reflection traps most of the emitted light and guides it to the edges of the fluorescent collector. Solar cells, optically coupled to the edges, convert this light into electricity. Fluorescent concentrators were investigated intensively in the early 1980s [8, 9]. Research at that time aimed at cutting costs by using the concentrator to reduce the need for expensive solar cells. After 20 years, there has been considerable progress in the development of solar cells and luminescent materials, and new concepts have been developed. In this work, several new ideas will be combined into one advanced concept for a fluorescent concentrator system design. The key features are a stack of different fluorescent concentrators to use the full solar spectrum, spectrally matched solar cells, and photonic structures that increase the fraction of light guided to the edges of the concentrator. To understand and to develop the different components, and finally to realize systems with all of these features is the main objective of my work on fluorescent concentrators within the frame of this PhD thesis. Upconversion of photons with energies below the band-gap is a promising approach to overcome the losses caused by the transmission of these photons [10]. An upconverter

4

2.3 Structure of this Work

generates one high-energy photon out of at least two low-energy photons. This highenergy photon can then create a free charge carrier in the solar cell. In combination with a second luminescent material, the spectral range of upconverted photons can be increased. In this work, an advanced system design for such a combination is developed. The main objectives are to characterize the materials involved, to develop a theoretical model of the upconverter and to realize systems with the relevant components.

2.3

Structure of this Work

In this chapter 2, the motivation and topic of this work is introduced. In chapter 3, I will outline fundamental theoretical concepts regarding the conversion of solar radiation into electric energy. I will restrict my presentation to very fundamental aspects that are necessary to understand how novel solar cell concepts help to increase the efficiency of solar cells and photovoltaic systems. Chapter 4 deals with fluorescent concentrators. At the beginning, I will introduce the general working principle of fluorescent concentrators and review the results achieved so far. Following this, I will present the results from optical characterization of fluorescent concentrator materials and a method to characterize the light guiding behavior of fluorescent concentrators that I developed in the context of this work. To test different hypotheses that could explain the results of the optical characterization, a Monte-Carlo simulation of the concentrator’s light guiding is developed. Finally, investigations on complete systems of fluorescent concentrators and solar cells are presented. This includes systems with different collector materials and spectrally matched solar cells, as well as systems with photonic structures that increase light guiding efficiency. Chapter 5 deals with upconversion. At the beginning, I will highlight by which mechanisms upconversion can occur and will introduce the theoretical concepts describing upconversion. I will discuss which materials are suitable as upconverter and show results of extensive optical characterization of the investigated erbium doped NaYF4. This includes absorption measurements, time and intensity resolved photoluminescence measurements, and calibrated photoluminescence measurements to directly measure upconversion efficiency. Based on the experimental results and the theory, a simulation tool that models the upconversion dynamics is developed. Finally, experimental investigations on systems with upconverting material attached to silicon solar cells will be presented.

5


Chapter 6 will summarize and conclude the results of this work, the summary can be found in German in chapter 7. The referenced publications, abbreviations, a glossary, the used physical constants, the list of the author’s publications, a CV, and the acknowledgements are located at the end of the work.

6

3

Efficiency limits of photovoltaic energy conversion and novel solar cell concepts In this chapter, I will outline fundamental theoretical concepts about the conversion of solar radiation into electric energy, in short: the theory of solar cells. In this work, solar cells are used in systems that apply photon management. The processing and optimization of the solar cells is of minor importance. Consequently, I will restrict my presentation to very fundamental aspects that are necessary to understand how novel solar cell concepts help to increase the efficiency of solar cells or photovoltaic systems. I will start from general thermodynamic considerations and will describe which conditions result in which efficiency limits. In the following, I will show how some of these limits can be overcome by novel solar cell concepts. This presentation is based on the discussions in [5, 11, 12] where detailed information can be found.

3.1

A short theory of solar cells

3.1.1

Thermodynamic efficiency limits

A photovoltaic device converts solar radiation into electric energy. Solar radiation is nothing more than heat radiation emitted by the sun. With heat, entropy is always associated, while electricity is entropy-free. Therefore, in the conversion process, the entropy must be released to the surroundings in the form of heat. This should happen at a lower temperature, so that not all the received energy is lost in this process. An idealized way of this process of receiving energy that contains entropy, dissipation of entropy, and generating entropy-free work is the Carnot cycle. With TS being the temperature of the sun and T0 the ambient temperature, the Carnot efficiency K is

K 1

T0 TS

.

(3.1)

With TS = 6000 K and T0 = 300 K this efficiency is very high and exceeds 95%. The Carnot efficiency is the fundamental limit for all thermodynamic processes, and since the limit is a direct result of the second law of thermodynamics, it cannot be overcome. However, the Carnot efficiency is a very theoretical limit. It relies on isentropic processes that generate no extra entropy. Unfortunately, these processes are infinitely slow so the working power of a Carnot engine is infinitesimally small.

7

3 Efficiency limits of photovoltaic energy conversion and novel solar cell concepts

The Carnot efficiency does not consider that energy is re-radiated from the converter to the sun. Considering the radiation emitted from the converter leads to a maximum possible efficiency of 93.3% [13]. This is the so-called Landsberg limit. A model of a solar cell system that is a little bit more realistic is an absorber that receives solar radiation and powers a heat engine that works with the Carnot efficiency. When the temperature of the absorber TA equals TS the efficiency is zero, because the absorber would emit as much energy as it receives. When TA = T0 the efficiency would be zero as well, for there would be no temperature difference to drive the heat engine. Between these extremes, for an ideal temperature an efficiency of 85.4% can be achieved [12]. This efficiency can be increased to 86.8% if an absorber for each wavelength is used, which is operated at its individual ideal temperature. Even such an ideal system suffers losses from the emission of radiation. If this emission is re-directed to another ideal system, of which the emission is again re-directed to yet another system and so on, the Landsberg limit can be reached [14]. However, this requires breaking time symmetry. For this purpose circulators are needed that accept radiation from one direction while emitting it in a different direction [12]. There are different proposals for how such a system could be realized; probably the easiest to imagine is a rotating mirror. 3.1.2

Generating chemical energy

Up to now, I have not considered the internal structure of the photovoltaic device. In a heat engine, one usually has some kind of gas that absorbs energy and performs work during expansion. Most solar cells are realized from semiconductor materials. In a semiconductor, the electrons and holes play the role of the working gas. Directly after absorption, the electrons in the conduction band and the holes in the valence band have the same energy distribution as the absorbed photons and the electron ensemble has the same temperature as the sun. In consequence, the higher energy states are relatively frequently populated. The electron ensemble cools down fast (in around 10-12 s) to the ambient room temperature by phonon interaction with the ion lattice, so that lower energy levels are now populated more frequently. The changes in the energy distribution are sketched in Fig. 3.1.

8

3.1 A short theory of solar cells

Fig. 3.1:

Directly after absorption, the electrons in the conduction band and the holes in the valence band have the same energy distribution as the absorbed photons. In 10-12 s the electrons and holes cool down to the ambient temperature. For the population of the energy levels dne/dEe and dnh/dEh this means that the population is shifted to lower energies. After the cooling, the concentration of electrons and holes is still higher than in equilibrium. To describe this non-equilibrium situation, two Fermi distributions are necessary. The idea for this picture was taken from [5].

The cooling does not change the electron or hole concentration. Therefore, the concentration of both is higher than in equilibrium with the ambient temperature. To describe this non-equilibrium situation, two (quasi-)Fermi distributions are necessary: one for the electrons in the conduction band, and one for the holes in the valence band. The Fermi energy of the electrons in the conduction band EFC can be identified as the electrochemical potential Ke of the electrons [5], and the Fermi energy of the holes in the valence band EFV can be identified as minus one times the electrochemical potential Kh of the holes. Consequently, the difference of the Fermi energies equals the sum of the electrochemical potentials: EFC - EFV = Ke + Kh = Pe + Ph =: Peh

(3.2)

Because of the opposite charges of electron and hole, the sum of their electrochemical potentials equals the sum of their chemical potentials [5]. The final consequence is that the splitting of the Fermi energies equals the chemical potential of electrons and holes. The splitting of the Fermi energies, and therefore the chemical potential, has been a result of the generation of extra carriers by photon absorption and subsequent cooling. Because of the band-gap, no complete equilibrium is reached and an electronically excited state remains: the heat or thermal energy contained in the thermal solar radiation has been converted into chemical energy.

9


It is illustrative to consider the case without a band-gap like in a metal. The absorbed photons do not generate extra free carriers, as they only excite electrons within the band to higher energies. Directly after absorption, the electron temperature is also increased, but after the cooling equilibrium is reached, because concentration had not changed. Therefore, no chemical energy is generated. 3.1.3

Extracting useful energy

As we have seen in the previous section, in a semiconductor solar energy is converted into chemical energy. This happens without any special structure, such as a pnjunction. Nevertheless, to use this energy we have to extract the electrons and holes, together with their energy from the semiconductor. In this section, I will show which aspects are important for the extraction of useful energy independent from any special structure. The chemical potential Peh is the amount of energy that can be extracted with one electron-hole pair. Therefore, multiplying this amount with the particle flux per illuminated area of extracted electron-hole pairs jeh gives the extracted power density pext: pext = jeh . Peh

(3.3)

The particle flux jeh that can be extracted from an illuminated semiconductor is given by the difference of the rates of generation geh and recombination reh (in this case the rates are defined per area): jeh = geh - reh.

(3.4)

In an idealized case, only radiative recombination occurs, so the recombination rate equals the emission of photons from the semiconductor. The number of emitted photons per time, per area, per unit solid angle, and per frequency interval is given by the generalized Planck’s law [5]

B p ,Q Q , T , P

2Q 2 n(Q ) 2 D Q c2

1 § hQ P · ¸¸ 1 exp¨¨ © k BT ¹

, (3.5)

where Qis the frequency of the photons, T the temperature of the emitter, µ the chemical potential within the emitter (which has to be identified with Peh in this case), n(Q) is the refractive index into which the emission takes place, DQ is the absorption coefficient, c the speed of light in vacuum, h the Planck constant and kB the Boltzmann

10


constant. With this definition, Bp,Q cos(T) dA dQ d: is the number of photons emitted from the surface element dA in the frequency range of Qto Q +dQ into the solid angle d: into the direction given by the polar angle T and an azimuth angle I. For the efficiency of a solar cell, especially two features of the generalized Planck’s law are important: the dependence on the chemical potential and the influence of the solid angle in which radiation is emitted. To increase the extracted power jeh*Peh a high chemical potential in the semiconductor seems beneficial. On the other hand, following equation (3.5) a high chemical potential means high emission of photons. Therefore, a high chemical potential decreases the extracted current. For a maximum chemical potential POC, all photons are emitted, so the extractable current is zero. As a result, although the chemical potential is at its maximum, no power is extracted. The contrary situation is achieved when all the electron-hole pairs are extracted. Since there are no excess carriers left in the semiconductor, the chemical potential is zero in this case. Again, the extracted power is zero. In between, there is a point where the extracted power is at its maximum (see Fig. 3.2). If the -1 in the denominator of equation (3.5) is neglected, for monochromatic irradiation and emission equations (3.4) and (3.5) can be combined to

jeh

§P · g eh const exp¨¨ eh ¸¸ . © k BT ¹

(3.6)

The structure of equation (3.6) is quite similar to that of the IV-characteristic of a pnjunction solar cell, if the electrochemical potential is identified with the voltage of the solar cell. From this derivation, it becomes clear that the exponential current voltage characteristic is not a result of the pn-junction, but a fundamental consequence of the balance between generation and recombination of electrons and holes. This is still true even when the dominant recombination mechanism is not radiative recombination. Recombination can be interpreted as a reaction with the electron and the hole being the educts. Whether such a reaction does occur is governed by the chemical potential of both in comparison to the chemical potential of the product of the reaction. In semiconductors, the chemical potential depends approximately exponentially on the concentration [15] of the electrons and holes, which is the case for most educts in chemical reactions. In a standard silicon solar cell, the current voltage characteristic is mainly determined by processes in the region close to the pn-junction. In this so-called space charge region, the recombination rate depends on the product of

11


the concentration of holes and electrons, which is again equivalent to an exponential dependency on the chemical potential of the electron-hole pairs [15]. So we can state more generally, that the extraction of useful energy is described by three cases: first, maximum extraction that reduces the chemical potential to zero; second, the maximum chemical potential in the case where there is no extraction but maximum recombination; and third, the range in between. The height of the chemical potential determines the extent of the recombination in the most cases with an approximately exponential relation and therefore the remaining number of charge carriers that can be extracted.

Fig. 3.2:

Illustration of how the extracted current jeh and the extracted power depend on the sum of chemical potentials of the electrons and holes in the semiconductor Peh [11]. At Peh = POC all photons are emitted, so the extractable current is zero. Therefore the extracted power jeh*Peh is zero as well. At Peh = 0 the extracted current is at its maximum jSC, because the radiative recombination is at its minimum. Nevertheless, because of Peh = 0 the extracted power is again zero. In between, a maximum power point (MPP) exists, at which the extracted power reaches its maximum jmpp*Pmpp (indicated as blue rectangle).

Without any special means, a semiconductor emits into a complete hemisphere. In contrast, the solid angle of the sun, from which radiation is received, is very small. Concentration with lenses or mirrors increases this solid angle. The maximum concentration is reached when radiation is received from the complete hemisphere. Equation (3.5), with T = Ts and P = 0, describes as well the absorbed photon flux

12


received from the sun and therefore the generation rate [11]. It is obvious that an expanded solid angle, from which radiation is received, increases the generation rate geh. Because the concentration of electrons and holes rises, the chemical potential is also higher with concentration. In consequence, more power jeh*Peh can be extracted and the efficiency increases. An alternative approach with the same result is to narrow the solid angle in which radiation is emitted. With a narrower solid angle of emission, the losses due to radiative recombination are smaller and the extracted current, the chemical potential, and consequently the extracted power are higher. We have seen that only from the generalized Planck’s law an exponential current/chemical potential characteristics with a maximum power point can be derived, and the effect of concentration can be explained. Now the question arises of how exactly the electrons are extracted from the semiconductor and how the chemical energy is converted into electric energy. For this purpose, electrons and holes have to be extracted at different points of the semiconductor. If these two points are connected over an electric load, the difference in the electrochemical potential of the electrons and the holes drives a current through the load and work is performed. One structure that is able to separate electrons and holes is the pn-structure of common semiconductor solar cells. 3.1.4

The pn-structure

A pn-structure consists of one p- and one n-doped region. Without illumination, in the p-doped region, the concentration of holes is higher than in intrinsic material, therefore the Fermi energy is close to the valence band edge. In the n-doped region, the electron concentration is higher and the Fermi energy is close to the conduction band edge. Illumination creates excess carriers, so both the electron and the hole concentration increases. As mentioned before, this situation is described with two Fermi distributions and therefore also two Fermi levels. This is the so-called splitting of the Fermi levels. The relative effect of the increase in charge carrier concentration is more pronounced for the minority charge carriers in each region, i.e. for the holes in the n-doped region and the electrons in the p-doped region. Consequently, the Fermi level of the majority charge carriers hardly moves, while the Fermi level of the minority charge carriers is at a distinctly different position than the common Fermi energy of the non-illuminated case. In section 3.1.2, it was shown that the Fermi level can be identified with the electrochemical potential of the respective kind of charge carrier (considering the sign of its charge). Gradients in this electrochemical potential cause the charge carriers to flow in a certain direction. For instance, the particle flux density of the electrons is [11]

13


jeh = - ne/q me grad(EFC),

(3.7)

with ne being the electron concentration, q the elementary charge and me the mobility of the electrons. The particle flux density of the holes can be calculated accordingly but the different sign of the charge must be considered. In equation (3.7), the carrier concentration plays an important role. Usually, the concentration of the majority carriers is higher by orders of magnitude than the minority carrier concentration. Therefore, the total charge current density J J = - q je + q jh,

(3.8)

can be mainly attributed to the flow of the majority charge carriers in the respective region. Additionally, at the interface between metal contact and semiconductor, a lot of recombination occurs and in the metal itself no separate Fermi levels exist. Therefore, at the contacts the charge carriers have the same concentration as under the equilibrium without illumination. Because of these two facts, only the electro-chemical potentials of the majority carriers at the contact points determine the current through an external load. The difference of these two potentials is the voltage of the solar cell Vcell that can be measured externally between the two contacts of a solar cell.

Fig. 3.3:

The pn-structure of common semiconductor solar cells under illumination. This figure shows the solar cell under short circuit conditions. Because of the short circuit, the electrochemical potentials of the majority carriers at the contact points are on the same level. The light-induced Fermi level splitting results into a large gradient of the Fermi levels across the pnjunction. This gradient causes a large current to flow. Because of their different charges, the electrons move to the contacts of the n-doped region, while the holes move to the contact of the p-doped region. The charge carriers are effectively separated. Because the external voltage is zero, no work is performed

14


If the two contacts are connected without any resistance (short circuit conditions), then the two electrochemical potentials EFC and EFV at the contact points are on the same level (see Fig. 3.3). Since the illumination has induced a splitting of the Fermi levels, a large gradient within the Fermi levels exists across the pn-junction. Following equation (3.7), this results into a large current. Further away from the junction, because of the higher charge carrier concentrations a smaller gradient of the Fermi levels is sufficient to maintain the same current. Because of their different charges, the electrons move to the contact of the n-region and the holes to the contact of the p-region. This constitutes a successful separation of electrons and holes. The resulting charge carrier density is designated short circuit current density JSC. Under short circuit conditions, no energy is extracted. As with the discussion of the chemical potential, without an external voltage, the product of current and voltage is zero. To drive a current through a load and to perform work, a voltage difference - that is a difference between the electrochemical potentials of the majority carriers at the contact points - is necessary. As visible in Fig. 3.4, this reduces the gradient of the Fermi levels within the solar cell and therefore the extracted current. If the voltage is further increased to the open circuit voltage VOC so that the gradient is zero, no current flows (Fig. 3.5).

Fig. 3.4:

Illuminated pn-structure of a solar cell under working point conditions. The electrochemical potentials of the majority carriers at the contact points determine the current through an external load. The difference of these two potentials is the voltage of the solar cell Vcell that can be measured externally between the two contacts of a solar cell. When this potential difference drives a current through the external load, work is performed. In comparison to Fig. 3.3 the internal gradient of the Fermi levels is reduced so the resulting current is smaller.

15


Fig. 3.5:

Illuminated pn-structure under open circuit conditions. At the open circuit voltage VOC the gradients of the electrochemical potentials across the pnjunction are zero and no current is flowing.

The maximum efficiency of a solar cell with one pn-junction has been calculated in [16] and also in [11]. Under the assumption that only radiative recombination occurs, the efficiency limit is 33% for an optimum band-gap of 1.3 eV under illumination with non-concentrated light and an AM1.5g spectral distribution. The band-gap of silicon is 1.12eV and therefore the achievable efficiency is very close to the optimum value. Experimentally, an efficiency of 24.7% [17] has been reached so far for a silicon solar cell under non-concentrated sunlight. These values are considerably lower than the efficiency limits presented in the beginning of this chapter. The reason for this is that energy is lost in the cooling of the electrons and that photons are transmitted that have an energy below the band-gap, as it was visualized in Fig. 2.1. For a silicon solar cell, about 20% of the incident energy is lost because low-energy photons are not absorbed. The thermalization losses are specified to be around 35% of the incident energy. This value is calculated under the assumption that all electrons thermalize to the energy of the band-gap. As we have seen in this chapter, the energy distribution of the electrons has an average above the band-gap (Fig. 3.1). However, it is not the band-gap that determines the voltage, but the splitting of the Fermi levels. Additionally, to extract current, the voltage must be reduced in order to enable a current flow. So even under idealized conditions, the unavoidable losses are even higher. In conclusion, the band-gap that played an important role in converting heat into chemical energy is also a source of fundamental losses. Therefore, most novel concepts deal with the question of how these losses associated with the band-gap can be overcome.

16

3.2 Novel solar cell concepts

3.2

Novel solar cell concepts

3.2.1

Thermophotovoltaic Systems

A system design that resembles the idealized system, with an absorber that powers a Carnot engine (section 3.1.1), is the thermophotovoltaic system [18, 19]. In a thermophotovoltaic system, the sun heats an absorber. The heated absorber then radiates energy to a solar cell. A filter can be placed between absorber and solar cell that transmits only monochromatic radiation and is reflective otherwise. In this way, the solar cell is illuminated monochromatically. With the right band-gap, the solar cell converts the monochromatic radiation very efficiently. The radiation that is reflected by the filter heats the absorber and therefore is not lost. Also the photons emitted from the solar cell are either reflected back to the solar cell, or transmitted by the filter and used by the absorber. Since the photons emitted from the solar cell are not lost, it is not necessary to operate the solar cell at its maximum power point. The solar cell can be operated with a higher voltage close to open circuit conditions [11]. In consequence, the efficiency limit of 85.4% presented in section 3.1.1 can be achieved theoretically. In practice the achieved efficiencies are very low and no system has been commercialized yet [20]. The reasons for this, among others, are that very high concentration is needed and that very high absorber temperatures are necessary for reasonable efficiencies, posing a serious challenge for material development. 3.2.2

Hot carrier solar cells

Another system design that avoids thermalization losses is the hot carrier cell. The idea is to extract the energy of the hot electron and hole ensembles before they cool down by interacting with the lattice [12, 21]. As mentioned before, the time scale in which thermalization usually takes place is 10-12s and is therefore very short. Since the carriers have a finite velocity, they hardly can travel a reasonable distance to the contacts in this time. Therefore, phonon interaction must be slowed down in a hot carrier solar cell. There are possibilities discussed to achieve this by nano-structuring the device such that the phonon spectrum is modified and a phonon bottleneck created [22]. In the metal contact, the charge carriers are thermalized at the lattice temperature. Therefore the charge carriers in the metal must be prevented from interacting with the hot carriers in the solar cell. This could be achieved with energy-selective contacts, through which the hot carriers are extracted [21]. It becomes clear that the hot carrier solar cell is a very demanding system design. Accordingly, no hot carrier solar cells have yet been successfully realized.

17


3.2.3

Tandem solar cells

In contrast to the rather theoretical aforementioned concepts, tandem solar cells are an already established concept to reduce the band-gap associated losses. The general idea is to combine solar cells with different band-gaps in one stack, such that each solar cell uses a different part of the solar spectrum efficiently. The solar cell with the highest band-gap must be placed on top of the stack. It absorbs all high-energy photons and transmits the photons with energies below its band-gap. Under the top cell, the solar cell with the second highest band-gap is placed and so on. Theoretically, a stack of an infinite number of solar cells could reach a maximum efficiency of 86.8% for direct sunlight [12]. In practice, three to four different solar cells are stacked on top of each other. With a system of three solar cells, the highest confirmed efficiency of 41.1% for a photovoltaic system was reached under 454 suns concentration [23]. Such tandem cells are usually made by growing several solar cells made from III-V compound semiconductors on top of each other. Therefore the solar cells are forced to be connected in series, with a tunnel diode between each pair of cells. Since in a series connection, the current through all cells must be the same, the cell with the lowest current limits the performance of the stack. Another disadvantage of this concept is that the needed cell structures are very complex and expensive to fabricate. Therefore, tandem solar cells are only used in conjunction with concentrating systems in terrestrial applications. 3.2.4

Intermediate band-gap solar cells

In a tandem solar cell, stacking different solar cells on top of each other creates different energy thresholds for the absorption of photons. An alternative approach realizes different energy thresholds within one solar cell by creating an intermediate band [24, 25]. The general idea is that a half-filled band located between valence and conduction bands creates the opportunity for lower energy photons to be absorbed. An electron can reach the conduction band by the absorption of two photons using the intermediate band as stepping-stone. On the other hand, the high-energy photons do not lose most of their energy due to thermalization as they only thermalize to the conduction band edge. A problem is that the intermediate band also creates more opportunities for recombination losses, so in practice no improvement of the solar cell performance has yet been achieved with this concept.

18

3.2 Novel solar cell concepts

3.2.5

Photon management

Most of the presented novel concepts require complex new solar cell structures. An alternative approach is photon management. Photon management means splitting or modifying the solar spectrum before the photons are absorbed in the solar cells, such that the energy of the solar spectrum is used more efficiently. The solar cells themselves remain fairly unchanged, and well-established solar cell technologies can be used giving the concepts high realization potential. Because of these advantages, this work will deal with different concepts of photon management. 3.2.5.1

Spectrum splitting

The high efficiencies of tandem solar cells show that by utilizing different parts of the solar spectrum with different solar cells high efficiencies can be achieved. In tandem solar cells the transmission of the upper cells determines which spectrum is used by the lower solar cells. Using selective mirrors, filters, diffraction gratings, prism etc. the solar spectrum can be split and the different parts of the spectrum can be directed to different solar cells in a more active way. The advantage is that the stack configuration of tandem solar cells is avoided. This results into a greater freedom in the choice of material from which the solar cells are produced and a greater freedom in the way the solar cells are interconnected, and a series connection is no longer inevitable. However, most of these concepts are very complex and use only direct radiation. A special way to realize spectrum splitting is the concept of fluorescent concentrators [7], which will be discussed in detail in the following chapter 4. Fluorescent concentrators combine spectrum splitting with concentration and are able to utilize diffuse light as well. However, we will also see in this work that fluorescent concentrators are better suited to reduce cost via concentration and the use of cheap materials than to achieve high efficiencies. 3.2.5.2

Quantum cutting

We have seen before that the energy of the incident photons in excess of the conduction band edge is transformed into heat. These losses could be reduced significantly, if more than one free charge carrier was generated by a high-energy photon. The idea of quantum cutting, which is sometimes called down conversion as well, is to transform one high-energy photon into two lower energy photons, which still have sufficient energy to generate free carriers. A system of one single junction solar cell and a quantum cutting material with one intermediate level has a theoretical efficiency limit of 39.6% [26]. The problem of this concept is that some kind of luminescent material that performs the down conversion has to be placed in front of

19


the solar cell. Any parasitic absorption or reflection of this material affects the solar cells performance negatively. 3.2.5.3

Upconversion

Upconversion of photons with energies below the band-gap is a promising approach overcoming the losses due to the transmission of these photons. An upconverter generates one high-energy photon out of at least two low-energy photons. For most materials, this involves an intermediate energy level, which is excited by the absorption of the first photon. From this level, a higher excited state can be reached after the absorption of the second photon. If the electron returns directly to the ground state via radiative recombination, one high-energy photon is emitted. Depending on the energy levels involved, this high-energy photon can create a free charge carrier in the solar cell. An additional upconverter pushes the theoretical efficiency limit for a silicon solar cell with an upconverter illuminated by non-concentrated light up to 40.2% [10]. A big advantage of upconversion is that the upconverter can be placed at the back of the solar cell, as the sub-band-gap photons are transmitted through the solar cell. In this configuration, the upconverter does not interfere negatively with the solar cell performance. All improvements are real gain, since they come on top of the original performance of the solar cell. Upconversion can be used in conjunction with classical silicon solar cells. Therefore, upconversion addresses the fundamental problem of transmission losses, while still retaining the advantages of silicon photovoltaic devices. The concept of upconversion will be investigated in detail in chapter 5 of this work.

20

4

Fluorescent Concentrators This chapter deals with fluorescent concentrators. At the beginning, I will introduce the general working principle of fluorescent concentrators and review the results achieved so far. In the following, I will present the results from optical characterization of fluorescent concentrator materials and a method to characterize the light guiding behavior of fluorescent concentrators that I developed in the context of this work. Based on the optical characterization a Monte-Carlo simulation of the concentrator’s light guiding is developed. Finally, experimental results are presented of a complete system of fluorescent concentrators and solar cells. This includes systems with different collector materials and spectrally matched solar cells, as well as systems with photonic structures that increase light collection efficiency.

4.1

Introduction to fluorescent concentrators

4.1.1

The working principle of fluorescent concentrators

Fluorescent concentrators are a special type of light concentrating device. The underlying principle was first used in scintillation counters [27, 28] and then their application to concentrate solar radiation was proposed in the late 1970s [6, 7]. In a fluorescent collector, a luminescent material embedded in a transparent matrix absorbs sunlight and emits radiation with a different wavelength. Total internal reflection traps most of the emitted light and guides it to the edges of the collector (Fig. 4.1). Solar cells optically coupled to the edges convert this light into electricity. Different configurations are possible as well: The luminescent material can be applied in a film on a transparent slab [29] and solar cells can also be coupled to the bottom of the collector [30]. The fluorescent concentrator has many different names, e.g. luminescent collector or organic solar concentrator. All kinds of luminescent materials can be used in a fluorescent concentrator: fluorescent materials that show a Stokes shift of the emission to longer wavelengths; phosphorescent materials; upconverters that emit one high-energy photon after the absorption of at least two low-energy photons; and quantum-cutting materials that emit two low-energy photons after the absorption of one high-energy photon.

21

4 Fluorescent Concentrators

Fig. 4.1:

Principle of a fluorescent concentrator. A luminescent material in a matrix absorbs incoming sunlight (E1) and emits radiation with a different energy (E2). Total internal reflection traps most of the emitted light and guides it to solar cells optically coupled to the edges. Emitted light that impinges on the internal surface with an angle steeper than the critical angle șc is lost due to the escape cone of total internal reflection. A part of the emitted light is also reabsorbed, which can be followed by re-emission.

This work is based on fluorescent materials. Therefore, I will use the term fluorescent concentrator for the overall concept. For clarity, fluorescent collector will identify the collector plate without attached solar cells and fluorescent concentrator system will refer to a system constructed from a collector plate with solar cells attached. In graphs the abbreviation fluko will be used to describe collector or concentrator systems, whereas the meaning will be clear from the context. Fluorescent concentrators are able to concentrate both direct and diffuse radiation. A geometric concentration is achieved, if the area of the solar cell at the edges is smaller than the illuminated front surface of the collector, i.e. when the area from which light is collected is larger than the solar cell area. If the solar cell is illuminated with a higher intensity than it would be in direct sunlight, a real concentration is achieved. For real concentration, high geometric concentration, as well as high collection efficiency is necessary. The ability to concentrate diffuse radiation presents a great advantage for the application of fluorescent concentrators in temperate climates, such as in middle Europe, or in indoor applications with relatively high fractions of diffuse radiation. Additionally, fluorescent concentrators do not require tracking systems that follow the path of the sun, in contrast to concentrator systems that use lenses or mirrors. This facilitates, for instance, the integration of fluorescent concentrators in buildings.

22

4.1 Introduction to fluorescent concentrators

Fluorescent concentrators were investigated intensively in the early 1980s [8, 9]. Research at that time aimed at cutting costs by using the concentrator to reduce the need for expensive solar cells. After 20 years of progress in the development of solar cells and luminescent materials, and with new concepts, several groups such as those of Refs. [20, 30-46] are currently reinvestigating the potential of fluorescent concentrators. 4.1.2

The factors that determine the efficiency of fluorescent concentrator systems

Several factors determine the efficiency of a fluorescent concentrator system. Most of these factors are wavelength dependent. By integrating over the respective relevant spectrum, a description of the overall system efficiency with a set of efficiencies for individual processes is possible [47, 48]. The important parameters are:

Ktrans,front

Transmission of the front surface in respect to the solar spectrum

Kabs

Absorption efficiency of the luminescent material due to its absorption spectrum with respect to the transmitted solar spectrum

QE

Quantum efficiency of the luminescent material

Kstok

“Stokes efficiency”; (1-Kstok) is the energy loss due to the Stokes shift

Ktrap

Fraction of the emitted light that is trapped by total internal reflection

Kreabs

Efficiency of light guiding limited by self-absorption of luminescent material, (1-Kreabs) is the energy loss due to reabsorption

Kmat

“Matrix efficiency”; (1-Kmat) is the loss caused by scattering or absorption in the matrix.

Ktref

Efficiency of light guiding by total internal reflection

Kcoup

Efficiency of the optical coupling of solar cell and fluorescent collector

Kcell

Efficiency of the solar cell under illumination with the edge emission of the fluorescent collector

The overall system efficiency can be calculated from the single parameters via

K system K transK abs QEK stokK trapK reabsK matK tref K coupK cell . Several aspects are of importance for the different efficiencies:

23

(4.1)


The transmission of the front surface is determined by its reflection R(Oinc). This is usually the Fresnel reflection, which is

RO

§ nOinc 1 · ¨¨ ¸¸ © nOinc 1 ¹

2

(4.2)

for normal incidence and the surface between a medium with refractive index of one and a medium with refractive index n(Oinc). The reflection of typical materials is in the range of 4% for one surface. Special layers or structures applied to the front can reduce or increase reflection. Interestingly, an antireflection coating that reduces the Fresnel reflection does not affect the total internal reflection. This can be understood by considering that total internal reflection is an effect strongly linked to refraction. Total internal reflection occurs when the light from inside the high index material impinges on the surface with an angle sufficiently shallow that the light would be refracted back into the medium again. As the antireflection coating does not change the refraction, total internal reflection is not affected either. The absorption spectrum Abs(Oinc) determines the absorption efficiency. A large fraction of the solar spectrum is lost, because many luminescent materials only absorb a narrow spectral region. The absorption range of typical fluorescent organic dyes is only about 200 nm in width. The quantum efficiency QE of the luminescent material is defined as the ratio of emitted photons to the number of the absorbed photons. For organic dyes the fluorescent quantum efficiency can exceed 95%. The energy of the emitted photons is usually different from the energy of the absorbed photons. For most luminescent materials, a Stokes shift to lower energy occurs. This means that the emitted photons possess less energy than the absorbed ones. Therefore the wavelength of the emitted photons Oemit is different from the wavelength of the incident photons Oinc. As we will see in section 4.2, this Stokes shift is of critical importance to the ability of the fluorescent concentrator to concentrate light. The luminescent material emits light isotropically in a first approximation. All light that impinges on the internal surface with an angle smaller than the critical angle Tc(Oemit) leaves the collector and is lost (Fig. 4.1). The critical angle is given by

§

1

·

¸¸ . T c O arcsin¨¨ n O emit ¹ ©

24

(4.3)


This effect is also called the escape cone of total internal reflection. The light which impinges with greater angles is totally internally reflected. Integration gives a fraction

Ktrap O

1 nOemit

2

(4.4)

of the emitted photon flux that is trapped in the collector [49]. For PMMA (Polymethylmethacrylate) with n = 1.5, this results in a trapped fraction of around 74%, which means that a fraction of 26% is lost after every emission process. The 26% account for the losses through both surfaces. An attached mirror does not change this number, as with a mirror the light leaves the collector through the front surface after being reflected. The absorption spectrum and the emission spectrum overlap. For principal reasons, absorption must be possible in the spectral region where emission occurs. Therefore, part of the emitted light is reabsorbed. Again, the energy loss due to a quantum efficiency smaller than one occurs, and again radiation is lost into the escape cone. Realistic matrix materials are not perfectly transparent. They absorb light and they scatter light so it leaves the collector. Total internal reflection is a loss-free process. However, the surface of the fluorescent collector is not perfect. Minor roughness at the surface causes light to leave the collector, because locally the light hits the uneven surface with a steep angle. Fingerprints and scratches can seriously harm the efficiency of the light guiding. The fluorescent collector and the solar cell have to be optically coupled. Otherwise, reflection losses occur at the interface between collector and air and again at the interface air to solar cell. However, the optical coupling can also cause losses: Light can be scattered away from the solar cell or parasitic absorption can occur. Finally, the solar cell has to convert the radiation it receives from the collector into electricity. Again, a whole set of parameters determine this process, ranging from reflection and transparency losses, to thermalization and electrical losses. This description is not very relevant for actually calculating the efficiency of fluorescent concentrator systems, because some of the involved efficiencies are neither easy to calculate nor directly accessible by measurement. Nevertheless, this description illustrates very well the effects that affect the efficiency of fluorescent concentrator systems.

25


4.1.3

Fluorescent concentrator system design

Many system designs have been proposed for efficient and economic fluorescent concentrator systems. Probably the most fundamental one was the concept to stack several collector plates [7]. With different dyes in each plate, different parts of the spectrum can be utilized (see Fig. 4.2). At each fluorescent collector, a solar cell can be attached, which is optimized for the spectrum emitted from the collector. With this spectrum splitting, high efficiencies can be achieved in principle. The stack design with the matched solar cells at the edges provides a high degree of freedom for cell interconnection. Therefore, there is no forced series connection like in tandem cell concepts, which causes current limitation problems. Additionally, no tunnel diodes are necessary.

Fig. 4.2:

Concept of stacked fluorescent concentrators, as presented in [7]. (a) The different collectors C1-C3 are connected with different solar cells S1-S3. In each collector, a different dye is incorporated. The absorption and emission (shaded) spectra of the different dyes are shown in (b). With a proper alignment of the absorption and emission properties, the recycling of photons lost from one collector in another collector is possible. It is important that an air gap between the different collectors is maintained so that each spectral range of light is guided in one collector by total internal reflection and does not get lost in adjacent collectors.

The possibilities to realize systems in this configuration were limited during the first research campaign in the 1980s because the range of solar cell materials with different band-gaps was very limited. The situation has improved considerably in the interim, so in Chapter 4.5 a detailed investigation of stack systems with spectrally matched solar cells will be presented.

26


Fig. 4.2 shows mirrors at some of the edges of the collector plate as well. If some edges are not covered with solar cells, but with reflectors, the geometric concentration is increased. This can be beneficial for the costs of the fluorescent concentrator system, as solar cells are usually the most expensive component of the system. However, the reflection on mirrors is not free of losses. Therefore, it should be kept to a minimum and the emitted light should reach the solar cells with as few reflections on mirrors as possible. For this purpose, an isosceles and rectangular triangular shape of the fluorescent collector is beneficial [7]. With solar cells at the hypotenuse and the two other sides covered with mirrors, only two reflections are necessary at most until the emitted light hits a solar cell. A reflector underneath the collector increases the collection efficiency as well. It reflects transmitted light back into the collector and creates a second chance for absorption. When a white reflector instead of a mirror is used, light can also be scattered and redirected towards the solar cells. Both for reflectors underneath the collector and for mirrors at the edges, it is beneficial to maintain an air gap between collector and reflector. In this configuration, the reflection of the reflector comes on top of total internal reflection. However, with an air gap the diffuse reflector does not change the direction of light emitted into the escape cone to directions that are subject to total internal reflection. The reason for this is that due to refraction, the light that leaves the collector is already distributed over a complete hemisphere, even before it hits the diffuse reflector. This is not changed by diffuse reflection. So consequently, when the light enters the collector again, it is refracted into exactly the angles of the escape cone. Another idea to increase the geometric concentration was proposed in [50]. The angular range of the edge emission of the fluorescent concentrator is limited by the critical angle of total internal reflection. Therefore, a further concentration is possible until the divergence reaches the full hemisphere. Compound parabolic concentrators, which are attached to the edges, are one possibility for this purpose. As mentioned before, no luminescent materials that are active in the infrared and show high quantum efficiency, high stability, and broad absorption have been developed so far. Therefore, a range of designs were proposed to utilize the infrared radiation. The infrared light transmitted through the collector could be used by a thermal collector. It was also suggested to use an upconverter to convert the transmitted radiation into light that could be collected by the fluorescent collector [48]. The transmitted light can also be used to grow plants in a greenhouse [51]. Another option will be investigated in this work: the bottom of the fluorescent collector can be covered with silicon solar cells (or

27


another low band-gap material), while solar cells made from a high band-gap material are attached to the edges (Section 4.5.3). In this way, spectrum splitting is achieved. High-energy photons are absorbed in the fluorescent collector and a large fraction of their energy is used by the solar cells at the edges. The remaining photons are not lost, but utilized by the silicon solar cells. Besides the losses due to an incomplete utilization of the full solar spectrum, the escape cone of total internal reflection is the most important loss mechanism. The loss of around 26% does not only occur once, but after every reabsorption and re-emission. However, the Stokes shift between absorption and emission opens the opportunity to reduce these losses significantly: a selective reflector, which transmits all the light in the absorption range of the luminescent material and reflects the emitted light, would trap nearly all the emitted light inside the collector [52]. As we will discuss in section 4.2, it is not possible to trap all the light inside the collector due to fundamental reasons. The concept is illustrated in Fig. 4.3.

Fig. 4.3:

A selective reflector, realized as a photonic structure, reduces the escape cone losses. The photonic structure acts as a band stop reflection filter. It allows light in the absorption range of the dyes to enter the collectors, but reflects light in the emission range.

In [34] hot mirrors were proposed to serve as selective reflectors and in [30] photonic structures. In this work, photonic structures and their effect on fluorescent concentrators will be investigated in detail. Sections 4.2 and 4.2.3 document theoretical considerations and in section 4.5.4 experimental results are presented.

28


An alternative to selective reflectors is to modify the emission characteristic of the dyes in such a way that emission occurs predominantly into favorable directions. This can be achieved with an orientation of dye molecules which show a distinct angular characteristic in their emissions depending on their position. This can be achieved with liquid crystals and an efficiency increase has been reported [38]. However, this approach requires the production of new collector plates and was therefore beyond the scope of this PhD thesis. The presented ideas can be combined into an advanced concept for a fluorescent concentrator system design. The key features are a stack of different fluorescent concentrators to use the full solar spectrum, spectrally matched solar cells, and photonic structures that increase the fraction of light guided to the edges of the concentrator. To understand and to realize the different components and finally systems with all these features has been the main objective of my work on fluorescent concentrators within the frame of this PhD thesis.

Fig. 4.4:

Advanced fluorescent concentrator system design. The full spectrum can be used with a stack of fluorescent collectors with different dyes. The stack configuration allows for ‘‘recycling’’ of emitted photons that are lost in one collector but can be absorbed in another one. The escape cone of total internal reflection is a principal efficiency-limiting problem. A photonic structure helps to minimize these losses. The photonic structure acts as a band-stop reflection filter. It allows light in the absorption range of the dyes to enter the concentrator, but reflects light in the emission range. Therefore a larger amount of light is trapped in the concentrator and guided to the solar cells at the edges.

29


4.1.4

Materials for fluorescent collectors

Many of the parameters described in the section 4.1.2 are related to the materials used for the fluorescent collector, and especially to the luminescent material. Therefore, a lot of research has been conducted to find materials for efficient fluorescent collectors.

Fig. 4.5:

A selection of fluorescent concentrator materials, based on organic dyes that were produced during the first research campaign in the 1980s and that are still among the most efficient fluorescent concentrator materials.

Organic dyes were the dominant luminescent material in the first research campaign in the 1980s [8, 9, 29, 47, 51, 53-56]. They were applied both distributed in a transparent matrix material and as a thin layer on a transparent slab of material. The research of this time resulted in fluorescent dyes with high fluorescent quantum efficiencies above 95% and good stability. Fig. 4.5 shows a photograph of a selection of fluorescent concentrator materials produced during that time. Today, these fluorescent dyes are commercially available and therefore also used in recent works [37, 39, 40, 57, 58]. Until now, the highest reported efficiencies as presented in this work and in [40, 46] were reached with systems based on organic dyes. However, high quantum efficiency is only achieved in the visible range of the spectrum, while efficiency remains low in the infrared. In [47] it is shown that these low quantum efficiencies have fundamental reasons that are difficult to overcome. Another problem of the organic dyes is the large overlap between absorption and emission spectra. This results in reabsorption and re-emission with the associated losses. Research has therefore been conducted to increase the Stokes shift of the organic dyes. One option is to use energy transfer from one absorbing dye to another emitting dye [59, 60]. Another option is to use phosphorescence instead of

30


fluorescence [60]. Phosphorescence is associated with a larger Stokes shift, but also with lower quantum efficiency (see section 4.1.5). There have also been attempts to increase overall efficiency by bringing metal nanoparticles close to the dyes, in order to increase absorption and luminescence due to plasmonic resonances [61, 62]. Because of the instability of organic materials, especially under ultraviolet radiation, inorganic materials have been investigated as well. Promising inorganic materials are glasses and glass ceramics doped with rare earth ions like ND3+ and Yb3+, or other metal ions like Cr3+ [63-66]. The advantages to these approaches are high stability and a high refraction index of the glasses, which increases the trapped fraction of light. One big disadvantage is the narrow absorption bands of the luminescent materials. Additionally, these material systems turned out to be quite complex and costly to fabricate. With the development of nanotechnology, luminescent nanocrystalline quantum dots (NQD) have become of interest for luminescent concentrators. The most frequently used materials are CdS, CdSe and ZnS quantum dots [41, 42, 67-69]. One big advantage of the NQD is that absorption and emission properties can be tuned by the size and composition of the nanocrystals. Additionally, the NQD feature a broad absorption range. However, the achieved quantum efficiencies are lower than those of organic dyes, especially if the NQD are incorporated into polymer matrixes. This work focuses on system designs and not on materials development. Therefore, it was sufficient to use old material produced in the first research campaign in the 1980s at Fraunhofer ISE [8, 47, 51, 53, 55]. The fluorescent collectors consist of PMMA (Polymethylmethacrylate) doped with organic dyes produced from BASF [9]. The used dyes are perylene derivates. The precise chemical structures, however, were not published by BASF. Despite the age of the samples, excellent results could be achieved from this material, as we will see in this work. 4.1.5

Fluorescence

This work will be based on fluorescent organic dyes. Therefore, a short introduction into fluorescence will be given in this section, which is based mainly on [70]. The emission of a photon due to the transition of an electronic system from a higher energetic state to a lower energetic state is called luminescence. If the excitation is the result of the absorption of another photon, the luminescence is called photoluminescence. Fluorescence is a special form of photoluminescence. In the case of fluorescence, the photon is emitted directly after absorption and the energy of the emitted photons is lower than the energy of the absorbed photon. The difference

31


between the energy of absorption and emission is called the Stokes shift. Phosphorescence is a different type of photoluminescence, characterized by a time delay between absorption and emission.

Fig. 4.6: Energy diagram that illustrates the three processes involved in fluorescence: absorption of a photon, vibrational relaxation, and emission of a photon. The excitation usually starts from the electronic ground state (S0) and the lowest vibrational level (v0=0). The absorption of a photon excites the molecule to higher electronic and vibrational levels. Vibrational relaxation to the lowest vibrational level of the excited electronic state occurs before emission of a photon and the return of the molecule to the ground state. The vibronic transitions during absorption and emission happen so fast that the nuclear distances of the atoms in the molecule cannot adjust. That is why the transitions are represented as vertical lines. The probability of a transition is determined by the overlap of the vibrational wave function (Franck-Condon principle).

32


In organic fluorescent dyes, the fluorescence is caused by the transitions between electronic states of rather complex organic molecules. The energy states of the molecule are determined by its electronic states, the vibrational modes of the molecule, and by its rotational modes. The electronic state determines the distribution of negative charge and the overall molecular geometry. The different electronic states depend on the total electron energy and the symmetry of various electron spin states. Each electronic state is further subdivided into a number of vibrational and rotational energy levels. The difference in energy between two neighboring electronic states usually corresponds to the energy of photons in the ultraviolet and visible spectral range. For comparison, the difference of the vibrational states corresponds to the near-infrared and the difference of the rotational states to the far infrared and the microwave range. In the frame of this work, only the electronic states and the vibrational modes are relevant. Fluorescence involves three important processes: absorption of a photon, vibrational relaxation, and emission of a photon. They are illustrated in Fig. 4.6. At room temperature, most molecules are in their ground state (S0) and also at the lowest vibrational level (v0=0). In consequence, most excitation processes originate from this level. The excitation by an incoming photon happens in femtoseconds (10 -15s), which is the time necessary for a photon to travel the distance of a single wavelength. For most organic molecules, the ground state is an electronic singlet state, which means that all electrons are spin-paired (have opposite spins). Normally, the excitation of a molecule takes place without a change in electron spin-pairing, so the excited state is also a singlet (S1). Light in the visible or ultraviolet range usually excites higher vibrational levels of the excited electron level (v1>0). After the absorption of the photon several processes can occur, but most likely is relaxation to the lowest vibrational energy level of the first excited state (v1=0). This process is called vibrational relaxation. This relaxation takes picoseconds or less. The excess vibrational energy is dissipated as heat. Because of this relaxation, emission spectra are generally independent of the excitation wavelength, which is known as the Kasha rule. However, there are also materials that show exceptions to this rule. After a relatively long period of nanoseconds, a photon is emitted and the molecule returns to its ground state. As mentioned before, the excitation started from the ground state to higher vibrational levels of the excited electronic state, and then energy was dissipated as heat during relaxation. Finally, during emission of the photon the molecule does not necessarily return directly into the ground state and the lowest

33


vibrational level. It is likely that directly after the emission the molecule is at a higher vibrational level of the electronic ground state and relaxes subsequently to lower vibrational levels. In consequence, the energy of the emitted photon is lower than that of the absorbed photon, which results in the Stokes shift. During absorption and emission, the electronic energy and the vibrational energy change simultaneously. Those simultaneous changes are called vibronic transitions. The probability of the vibronic transitions, and therefore the shape of the absorption and the emission spectra, is determined by the overlap of the vibrational wave functions of the states involved in the transition: the larger the overlap, the more likely is the transition (see also Fig. 4.6). This rule is also known as the Franck-Condon principle.

Fig. 4.7:

Jablonski Energy Diagram showing the different energy states of a molecule and the possible transitions between them. In addition to Fig. 4.6, internal conversion from higher excited singlet states (S2), intersystem crossing to triplet states (T1), and phosphorescence are depicted as well.

34


Several other relaxation pathways compete with the fluorescence emission. They are illustrated in Fig. 4.7. One process is that the excited state energy is dissipated nonradiatively as heat. Alternatively, intersystem crossing can occur, which causes phosphorescence. During intersystem crossing the energy is transferred from the electronic singlet state to a triplet state. Because spin conversion is necessary for this transition, it is relatively unlikely. The transition from the excited triplet state to the singlet ground state by emission of a photon is forbidden by spin selection rules. However, due to several effects it becomes possible, but rate constants remain small. In consequence, the excited triplet state can be long-lived and the emission can occur long after the absorption of a photon. As discussed extensively e.g. in [47], the non-radiative processes become more likely for a small energy difference between ground state and excited state, while the radiative transitions become less frequent. In consequence, the quantum efficiency of dyes emitting at longer wavelengths and especially in the infrared is lower for principal reasons. 4.1.5.1

Angular anisotropy of fluorescence

When a fluorescent molecule absorbs an incident photon, the excitation arises from an interaction between the oscillating electric field of the incoming radiation and the transition dipole moment created by the electronic state of the molecular orbitals. The molecules preferentially absorb photons that have an electric field vector aligned parallel to the molecule’s absorption transition dipole moment. The fluorescence emission occurs in a plane that is defined by the direction of the emission transition dipole moment. The directions of the transition dipole moments are determined by the molecular structure. Because of changes in the molecular structure due to the excitation, the directions of absorption and emission can differ. Rotation of the molecule further depolarizes the emission in respect to the excitation vector. The molecule’s size and the rigidity of the molecule’s environment therefore determine how strongly the direction of the emission is coupled to the direction of excitation. In the case of fluorescent concentrators, the light impinges from one direction onto the fluorescent concentrator. Therefore the polarization vectors are aligned in one plane. The matrix material of fluorescent concentrators, in which the molecules are embedded, is a rather rigid polymer. In consequence, an angular anisotropy of the emission remains, which is subsequently reduced by reabsorption.

35


4.2

Theoretical description of fluorescent concentrators

4.2.1

Maximum concentration and Stokes shift

The ability to as well concentrate diffuse radiation sets the fluorescent concentrator apart from all other types of concentrators. Systems utilizing only geometrical optics cannot concentrate diffuse light. For a discussion of this difference, the concept of étendue and its links with entropy are very helpful. Therefore, I will briefly introduce the concept of étendue at this point. The étendue dH of a light beam being received from a solid angle d: by an infinitesimal surface element dA can be defined as

dH

cos T d: dA ,

(4.5)

with ș being the angle between the surface normal of dA and the incident light. The definition of étendue usually does not consider the refractive index and is therefore, strictly speaking, only useful for systems in vacuum. In media with a refractive index unequal to one, the changes of the solid angle due to refraction have to be considered. To calculate the étendue H from the perspective of an extended receiving system, an integration must be performed over the receiving area Ainc and over the solid angle :inc from which radiation is received:

³ ³ cosT d:dA .

H

Ainc : inc

(4.6)

The étendue can also be calculated from the perspective of an emitting system. In this case, the integration has to be performed over the emitting area Aemit and over the solid angle :emit in which radiation is emitted. For light incident from a cone, with șinc being half of the opening angle, and a flat, not tilted illuminated area Ainc (see Fig. 4.8) the étendue can be calculated to be

H

S sin 2 T inc Ainc .

(4.7)

From the definition and this result, the étendue can be understood as a measure of how “spread out” a light beam is in terms of angular divergence and illuminated or emitting area.

36

4.2 Theoretical description of fluorescent concentrators

Fig. 4.8:

Illustration of the conservation of étendue. The étendue is a measure of how “spread out” a light beam is in terms of angular divergence and illuminated or emitting area. In a system utilizing only geometrical optics, the étendue cannot be decreased. That is, if the area from which light is emitted Aemit is smaller than the receiving area Ainc, the angular divergence of the emitted light must be larger than the divergence of the incoming light.

The étendue is closely linked to entropy. If an optical system increases the étendue, entropy is generated. Following Markvart in [71], if Hinc is the étendue of the incident beam and Hemit the étendue of the emitted beam, the entropy per photon V that is generated is

V

k B ln

H emit . H inc

(4.8)

A conservative system does not generate entropy, so in a conservative system the étendue is constant. If there are no other sources of entropy, the étendue cannot be reduced, because the entropy cannot decrease. That is, any concentration with geometrical optics that decreases the illuminated area must increase the angular divergence. Because for diffuse radiation angular divergence is already at its maximum, diffuse radiation cannot be concentrated with a system using only geometrical optics. As a fluorescent concentrator is able to concentrate diffuse radiation, there must be another source of entropy. This source of entropy can be found in the Stokes shift. The dissipation of part of the excitation energy as heat generates entropy and leads to photon emission at longer wavelengths. Therefore, the extent of the Stokes shift determines the maximum concentration that is achievable with a fluorescent concentrator.

37


This relationship between Stokes shift and concentration has been theoretically described in [72]. The theoretical model considers two distinct photon fields: one that is incident on the fluorescent collector and one that is emitted from the collector. The entropy change 'V1 associated with the loss of a photon from the incident Bose field is 2 · § 8S n 2Q inc ¸, 'V 1 k B ln¨1 2 ¨ c F ¸ p ,Q ,inc ¹ ©

(4.9)

where Fp,Q, inc is the flux of photons (i.e. photons per unit time) per unit area, per unit bandwidth, and per 4S solid angle of the incident field. The other parameters are the frequency of the photon Qinc, the speed of light c, and the refractive index n [72]. The emission of a photon with the frequency Qemit increases the entropy of the emitted field. Additionally, due to the Stokes shift the energy h (Qinc - Qemit) is dissipated as heat at the ambient temperature T. The entropy generated from these two processes is

'V 2

2 § 8S n 2Q emit ¨ k B ln 1 2 ¨ c F p ,Q , emit ©

· hQ inc Q emit ¸ , ¸ T ¹

(4.10)

with the parameters defined for the emission corresponding to the parameters of the incident field. According to the second law of thermodynamics, it must be

'V 1 'V 2 t0 .

(4.11)

In the argument of the logarithm in (4.9) and (4.10) the 1 can be neglected under illumination with sunlight and for frequencies in the visible spectral range. With this approximation and the equations (4.9)-(4.11), the concentration ratio C can be calculated to be

C:

Fp ,Q ,emit Fp ,Q ,inc

2 § hQ inc Q emit · Q emit ¸¸ . d 2 exp¨¨ kB T Q inc ¹ ©

(4.12)

Fig. 4.9 illustrates these results. The maximum possible concentration has been calculated with equation (4.12) for three different wavelengths of the incident light. It becomes obvious that from an entropic point of view, higher concentrations can be achieved for shorter wavelengths than for longer wavelengths. For short wavelengths, the maximum concentration is very high and constitutes no practical limit. For longer

38


wavelengths, however, a sufficiently large Stokes shift is necessary in order to avoid limitations for principal reasons. The fact that there is a maximum concentration has one more consequence: When the maximum concentration is reached, increasing the collector area will not increase the output at the edges of the concentrator. Already before the maximum concentration is reached, increasing the collector area of a large concentrator will not increase the output in the same way as increasing the area of smaller collector. In consequence, the light collection efficiency of fluorescent collectors decreases with increasing size.

Fig. 4.9:

4.2.2

Illustration of the maximum concentration from an entropic point of view. For short wavelengths, very high concentrations are theoretically possible. For longer wavelengths, a large Stokes shift is necessary to avoid limitations. Thermodynamic model of the fluorescent concentrator

The picture of an incident and an emitted light field that was introduced by Yablonovitch in [72] has been subsequently developed into a thermodynamic model of fluorescent concentrators e.g. [41-43, 73, 74]. This model was successfully used to describe fluorescent concentrators based on luminescent quantum dots. To include the more complex spectral characteristics of organic materials, a stack of different materials and features like diffuse reflectors and photonic structures proved to be difficult. Therefore, I will not use this model to actually calculate characteristics of any system presented in this work, but will rely on ray tracing simulations that will be

39


presented in chapter 4.4. Nevertheless, I will attempt to present a phenomenological thermodynamic model in this section, which brings together the main ideas of different theoretical discussions, that offers valuable insight into the working principles of fluorescent concentrators, and will be helpful later on in this work. The incident light field with the intensity Binc excites the ensemble of fluorescent molecules in the collector out of equilibrium with the ambient temperature T. Because of the fast thermal equilibration among the vibrational substates of the electronically excited state, the electrons cool down very fast to the ambient temperature. But as the molecule remains nonetheless in an electronically excited state, the electrons have a chemical potential µ > 0, just as in an illuminated semiconductor. The chemical potential is a measure of how many fluorescent molecules are excited. Similar to the discussion in section 3.1, the emission of the ensemble of the fluorescent molecules is described by the generalized Planck’s law. The number of emitted photons per time, per area, per unit solid angle, and per frequency interval is

B p ,Q , emit Q emit , T , P

2Q emit n 2 D Q emit c2 2

1 § hQ P · ¸¸ 1 exp¨¨ emit © k BT ¹

, (4.13)

where DQemit is the absorption coefficient. Part of the emitted light is lost due to the escape cone of total internal reflection, but most of the light is trapped and guided in the collector to its edges. In consequence, the molecules are illuminated not only by the incident field but also by the emitted and trapped light. The higher the combined intensity Bint is at a point of the collector, the higher is the chemical potential, and in turn also the emission of light. The chemical potential is not constant throughout the collector. For instance, close to the front surface, the chemical potential is higher because the fluorescent molecules are excited from the full incident field. Further away from the surface, part of the incident light has been absorbed and therefore intensity is lower.

40


Fig. 4.10: Illustration of the main ideas of the thermodynamic model. Incident radiation with the intensity Binc excites the ensemble of fluorescent molecules in the fluorescent collector. The fraction of excited molecules is described by the chemical potential µ of the molecule ensemble. The fluorescent molecules emit radiation with the intensity Bemit which depends on the chemical potential. The trapped fraction of the emitted light and the incident light combine to the internal intensity Bint. This internal intensity again determines the chemical potential. As the internal intensity is not constant throughout the collector, the chemical potential varies as well. This picture can explain why there is a maximum possible concentration. The larger the collector is, the more photons from the incident field are collected. Thus, the intensity of the trapped light field that travels towards the edges also increases. This increases the chemical potential, and consequently, the emission of light as well. The maximum concentration is reached when the chemical potential has become so high that the emitted light lost in the escape cone equals the incident field. The limit obtained from this consideration is stricter than the limit presented in equation (4.12) [72]. The link of the maximum concentration with the Stokes shift and the problematic of reabsorption can be understood considering a simple model system that features an absorption region and an emission region (see Fig. 4.11) [30]. The absorption coefficient Dabs in the absorption region is much higher than in the emission region with an absorption coefficient Demit.

41


Fig. 4.11: Idealized model of the absorption and emission characteristics of a fluorescent concentrator [30]. In the absorption region the absorption coefficient Dabs is high, while in the emission region the coefficient Demit is much smaller. Following Kirchoff’s law, the emission coefficient equals the absorption coefficient. Nevertheless, emission in the emission region is much higher, because the generalized Planck’s law favors emissions at lower energies. A bandstop reflection filter that reflects in the emission region can increase efficiency and the maximum possible concentration considerably. As described by Kirchoff’s law, the absorption and emissions coefficients are equal. In spite of Dabs>Demit, the emission in the emission region is much larger than in the absorption region, because of the energy dependency of the generalized Planck’s law, which states that in this regime the emission at lower energies is considerably more likely than at higher energies. Hence, the larger the Stokes shift, that is the bigger the energy difference E2 - E1, the less frequent is the emission in the absorption range relative to the emission in the emission range. With less light being emitted in the absorption range, reabsorption becomes less likely. Because each reabsorption and reemission again causes escape cone losses, with less reabsorption the escape cone losses are reduced as well. Less escape cone losses mean that a higher internally guided field and a higher chemical potential is possible until the emitted light lost in the escape cone equals the incident field. In consequence, a higher maximum concentration is possible.

42


Because absorption and emission are linked by Kirchhoff’s law, it is not possible to eliminate reabsorption entirely. Additionally, without reabsorption the excitation of the molecules would be completely independent from the emitted light. This would allow for an infinite concentration, which is a clear contradiction of the second law of thermodynamics. However, it is possible to reduce the escape cone losses and therefore to increase the maximum possible concentration with the addition of a band stop filter. The band stop filter should reflect in the emission range, but should transmit in the absorption range. The desirable reflection band is sketched in Fig. 4.11. Like this, only the small amount of light emitted in the absorption region can be subjected to escape cone losses. Again, this means that a higher internally guided field and a higher chemical potential is possible until the emitted light lost in the escape cone equals the incident field. In [30] it was shown that the maximum efficiency of a fluorescent concentrator system with such a band stop filter equals the Shockley-Queisser limit of a solar cell with a bandgap similar to that of the cut-off wavelength E2 of the band stop filter. 4.2.3

Photonic structures

The term photonic structure describes optical elements that show distinct energy or angular selective characteristics and rely on structures in the order of magnitude of the wavelength of the considered light. As described in the introduction and the previous section, spectrally selectively reflective structures have the potential to increase the efficiency of fluorescent concentrators significantly. Later on in this work, we will also see how such structures can be used for photon management in the context of upconversion. The structures used in this work were obtained from external sources. Nevertheless, I will give a short theoretical introduction of the source of their unique properties, which is mainly based on the work presented in [75]. Photonic crystals are a special type of photonic structure. In a photonic crystal, the refractive index varies periodically. The period length of this variation must be on the order of magnitude of the wavelength of the light that should be affected. The number of directions in which the refractive index is varied determines the periodicity of the photonic crystal (Fig. 4.12). For instance, in a one-dimensional photonic crystal the refractive index varies only in one direction, while it is constant in the other two directions. Such a 1D crystal can be described as planes with different refractive indices stacked upon each other.

43


Fig. 4.12: Photonic crystals with different dimensions. In these examples two different refractive indices n1 and n2 are ordered in one to three different directions, resulting in 1D – 3D photonic crystals. For a photonic crystal, the periodic variation of the refractive index is important. They can be formed with more than two different refractive indices as well, and also the function describing the spatial distribution can be varied. The concept underlying this picture was taken from [76]. Photonic crystals show exceptional optical properties, including the spectral and angular selectivity, necessary for the concepts presented in this work. Natural examples of photonic crystals are found in butterfly wings, in the sting of the sea mouse, or in the iridescent play of colors in several gems. Bykov described photonic crystals in 1972 for the first time [77]. In 1987 Yablonovitch [78] and John [79] independently calculated their optical properties. A summary of the field of photonic crystals can be found in [76]. In a classical crystal, the periodic potential of the crystal ions interacts with the electrons. In a photonic crystal, it is the refractive index, and consequently the dielectric function, that varies periodically. The periodic variation of the dielectric function affects the propagation of electromagnetic waves in a similar way, as the periodic potential in a crystal lattice affects the electron motion. Consequently, in analogy to the electronic band structure, a band structure for the photons in a photonic crystal can be calculated. The band structure is obtained from the dispersion relation of the photons under the influence of diffraction in the photonic crystal with a periodic dielectric function. The band structure describes the allowed and forbidden energy states of the photons. Like in a semiconductor with an electronic band-gap, bands of forbidden energy states that form a photonic band-gap can occur in a photonic crystal. In the energy range of the photonic band-gap, no propagation of light within the photonic crystal is possible. Therefore, a photonic crystal with a photonic band-gap is completely reflective for light in the respective energy range. One can distinguish between a complete band-gap and a pseudogap. In a complete band-gap the

44


propagation of light is forbidden in all crystallographic directions, whereas in a pseudogap the propagation of light is only forbidden in certain crystallographic directions. A common representation of the band structure shows the allowed energy regions in the momentum-space reduced to the first Brillouin zone. An example for a photonic band structure is given in Fig. 4.13. The band structure diagram shows a closed path in the Brillouin zone that includes all points of high symmetry.

Fig. 4.13: Band structure (left) and first Brillouin zone (right) of a face centered cubic (fcc) photonic crystal (opal) with a lattice constant a [80]. The band structure is plotted against the normalized frequency a/O The band structure is scalable with the frequency. A photonic crystal with twice the lattice constant will show the same characteristic for half the frequency of the light. In the band structure a complete band (red) and one exemplary pseudogap in *–L direction (blue) are shown. The band structure was calculated using the MIT photonic bands program [81] for an inverted opal with the refractive index contrast 3.5:1. 4.2.3.1

One-dimensional photonic crystals

In this work, mainly one-dimensional photonic crystals were used. A structure that can be classified as a 1D photonic crystal, but that has been known considerably longer than the idea of photonic crystals, is the distributed Bragg reflector (DBR). A DBR consists of two layers, A and B, with the refractive index nA and nB that are ordered periodically in the scheme ABAB… This structure shows a high reflectance for normal incidence at the wavelength O0, if the thicknesses of the layers dA and dB fulfill the condition that

di

O0 4 ni

, i=A,B.

45

(4.14)


Every surface in this structure reflects light. Because of the special thickness of each layer, the reflected light interferes constructively for light with the wavelength O0. The result is high reflectance for this special wavelength. More layers increase the reflectance. The structure of the DBR and its reflection characteristic are visualized in Fig. 4.14. Not only light with the design frequency Q0 = c/O0 experiences constructive interference and therefore high reflection, but also all odd multiples of this frequency 3Q0 , 5Q0 , 7Q0 and so on. They are called the harmonic reflection peaks. The applications in this work require high reflection in a single spectral region and high transmission otherwise. Therefore the harmonic reflections are detrimental.

Fig. 4.14: Refractive index profile (left) and reflection spectrum (right) of a distributed Bragg mirror. The presented profile is designed for high reflection at O0 = 1000nm [75]. Reflection peaks occur for the design frequency Q0 and the odd multiples of this frequency 3Q0 , 5Q0 , 7Q0 and so on. The problem of the harmonics can be overcome by non-binary refractive index profiles. A sinusoidal refractive index profile shows no harmonics. Only a single reflection peak remains, but this peak usually features some side lobes. Such structures are called Rugate filters. Optimized Rugate filters [82] show only one single reflection peak for a certain wavelength and almost no other reflections. The characteristics of an optimized Rugate filter are shown in Fig. 4.15. Such optimized Rugate filters that were produced at the company mso-jena [83] were used throughout this work as photonic structures.

46


Fig. 4.15: Refractive index profile (left) and calculated reflection spectrum (right) of an optimized Rugate filter [75]. This filter shows only a single reflectance peak and very low reflection otherwise.

4.2.3.2

Two- and three-dimensional photonic structures

No two-dimensional photonic crystals were used in this work, but a special type of 3D photonic crystal was tested as a band reflection filter on a fluorescent concentrator system. The investigated 3D photonic crystal was an opal. The opal consists of spheres ordered in a closest package. Opals can be produced by a self-organizing process [84]. First, monodisperse spheres are produced with colloidal chemistry. Common sphere materials are PMMA or SiO2. Subsequently, the dispersed colloids can be assembled into ordered structures by different techniques, including vertical deposition by lifting the substrate out of suspension of dispersed colloids, or the slow drying of a colloidal dispersion on a flat substrate. The advantage of the opal structure is that it has the potential to be easy to produce on a large scale. On the other hand, the ordering in these colloidal crystals critically determines their properties. The higher the ordering, the more distinct is the Bragg reflectance and the lower is the rate of diffuse scattering.

47


4.3

Optical characterization of fluorescent concentrator materials

In this chapter, I will discuss different optical methods for characterizing fluorescent concentrator materials and the results obtained. I will start with photoluminescence measurements. The fluorescence of the dyes is the fundamental property that enables the construction of fluorescent concentrators. Additionally, the photoluminescence spectrum will be important for a correct interpretation of the following measurements, the simulation of fluorescent collector and complete systems, and for the design of fluorescent concentrator systems. Secondly, I will present measurements performed with spectrophotometers. This includes classical reflection and transmission measurements. However, the interpretation of the results is not trivial for samples that show fluorescence and have light guiding properties. Additionally, the most interesting characteristic to be tested is the ability of the collectors to guide light to their edges, where the solar cells are mounted. This ability depends on a large set of parameters, such as the absorption and the quantum efficiency of the dyes, the optical properties of the matrix material, the surface quality, and geometric dimensions of the collector plate. Hence, measurements of absorption spectra and the photoluminescence alone are not sufficient to assess the spectral collection efficiency. Therefore, I will present a novel method to determine this ability spectrally resolved with transmission, reflection measurements using a spectrophotometer and an integrating sphere, and with one measurement where the sample is mounted in the center of the integrating sphere. Finally, I will present a method for measuring the angular distribution of the light guided in the fluorescent collector. 4.3.1

Photoluminescence measurements

The photoluminescence (PL) spectrum is a very fundamental property of the fluorescent material. In this work, I measured the photoluminescence directly on samples of the materials from which the fluorescent collectors were realized. That is, I investigated PMMA samples that were doped with different organic dyes. As mentioned before, these materials were produced during the first research campaign in the 1980s at our institute and were stored in the dark since. The investigated samples were 2 cm x 2 cm in size. Measuring the fluorescence directly on the later collector material has the advantage that the PL spectrum is determined under realistic conditions. The energy states, and therefore the PL spectrum depend e.g. on the

48

4.3 Optical characterization of fluorescent concentrator materials

chemical surroundings of the dyes. Additionally, a rigid environment affects the vibrational levels differently than a liquid solvent. Therefore, only measurements on the used material system yield data that are actually relevant for the fluorescence concentrator systems, be they for simulation purposes or for system design (e.g. the question which solar cell should be attached to the edges). When measuring the PL on the collector material, several issues have to be taken into account. Because the collector should preferably absorb the incoming light completely, the dye concentration is relatively high. Hence, reabsorption will occur and alter the shape of the PL spectrum. Therefore, to investigate the effect of reabsorption was one objective of the PL measurements. Related to the question of reabsorption is the difference between the spectrum that could be measured at the edges of the fluorescent collector and at its front or back surface. The spectrum at the edges will illuminate the solar cells and is therefore relevant for the system design. The spectrum emitted at the back or the front has experienced less reabsorption, because the path length through the collector is considerably shorter. In consequence, it is more similar to the spectrum actually emitted from the dye and thus important e.g. for determining the input data for the collector simulation. In conclusion, the PL spectrum was measured both at the edges and at the back of the collector (see Fig. 4.16). Another important question was whether the PL spectrum is really independent from the excitation wavelength. In following measurements of the collection efficiency (section 4.3.2), and also on fluorescent concentrator systems (section 4.5), a wavelength dependency occurred, and the question arose whether this could be linked to a wavelength dependency of the PL spectrum. Therefore PL spectra were measured with two different excitation wavelengths. 4.3.1.1

Setup for photoluminescence measurements

The samples were illuminated with monochromatic light. For this purpose, a manually operated monochromator with a single grating was used to select single wavelengths from the light of a Xenon lamp. Because the monochromator was originally designed for the NIR, the second order peak was used for the illumination of the samples. Peaks of higher order were blocked with a Schott WG360 filter. The excitation peak was around 10 nm wide (FWHM). The emitted light was collected with a collimator and guided to spectrometer with an optical fiber. The collimator was placed either at one edge of the sample (position 1) or at the back (position 2), see also Fig. 4.16. The PL spectra were measured with a MCDP 1000 diode array spectrometer from Otsuka.

49


Fig. 4.16: Setup for the photoluminescence measurements. The samples were illuminated with monochromatic light. The emitted light was collected with a collimator and guided to a spectrometer with an optical fiber. The collimator was placed either at one edge of the sample (position 1) or at the back (position 2.) The PL spectra were measured with a MCDP 1000 diode array spectrometer from Otsuka. 4.3.1.2

Results of photoluminescence measurements

Fig. 4.17 shows a comparison between the normalized PL spectra measured at the edge (position 1) and at the back (position 2) of a collector made from the material BA241. Furthermore, also the absorption spectrum is shown, which will be discussed in the following section. The sample was 2 cm x 2 cm in size and 3.2 mm thick. The excitation was at Oinc= 490 nm. During the measurement at the back, a Schott OG 530 filter was placed between sample and collimator to block the excitation peak. The transmission of the filter was taken into account in the data analysis. The spectrum measured at the back is somewhat similar to a mirrored spectrum of the absorption. This is expected from theory. Usually the vibrational levels in the electronically excited state are quite similar to the vibrational level of the ground state, both in the energy spacing and in the shape of the wave functions. Therefore, the overlap between the lowest vibrational level (v0=0) in the electronic ground state (S0), from which the excitation starts, and the higher vibrational levels (v1>0) of the electronically excited state (S1) is quite similar to the overlap of the lowest vibrational level (v1=0) of the electronically excited state (S1) and the higher vibrational levels (v0>0) of the electronic ground state (S0) (see also Fig. 4.6). Therefore, the PL spectrum should have the mirrored shape of the absorption spectrum. This is also known as the mirror rule [70].

50


In the spectrum measured at the edge, the peak that is visible in the back measurement at Oemit= 546 nm appears only as a little kink in the falling edge of the peak at Oemit= 575 nm. This is the effect of reabsorption. The dye shows significant absorption at 546 nm already. As the light has to travel some distance from the excitation in the middle of the sample to the edge, most of the light emitted at this wavelength is absorbed and emitted at different wavelengths. The differences at higher wavelengths are considered to be measurement artifacts. The background noise level was considerably higher relative to the PL spectrum in the measurements at the back and occurred to be increasing at longer wavelengths. Because of the normalization, this background appears amplified.

Fig. 4.17: Comparison between the normalized PL spectra measured at the edge (position 1) and at the back (position 2) of a collector made from the material BA241. Also the absorption spectrum is shown. The spectrum measured at the back is reasonably similar to a mirrored spectrum of the absorption. The reason behind this is the similarity between the vibrational levels in the electronically excited state to the vibrational level of the electronic ground state. The spectrum measured at the edge shows the effect of re-absorption: the peak that is visible in the back measurement at 546 nm appears only as a little kink in the falling edge of the peak at 575 nm, because the dye already shows significant absorption at 546 nm. Fig. 4.18 shows a comparison of the normalized PL spectra measured at the edge for two different excitation wavelengths for three different materials. The samples were excited at Oinc= 490 nm and at Oinc= 440 nm. No significant differences are visible for the different excitation wavelengths.

51


Fig. 4.18: Comparison of the normalized PL spectra measured at the edge for two different excitation wavelengths for three different materials. No significant differences are visible for the different excitation wavelengths. In Fig. 4.19, the normalized PL spectra measured at the back of three samples made from the material BA241 are presented. The samples are made from the exact same material, but two samples were thinned to a thickness of 2 mm and 1 mm, respectively. The excitation was at Oinc= 490 nm. Again, the excitation peak was blocked with a Schott OG530 filter between sample and collimator. The relative height of the peaks at Oemit= 546 nm and Oemit= 575 nm changes considerably with the thickness. For the thickest sample, both peaks have nearly the same height, but the peak at Oemit= 575 nm is still a little bit higher. With decreasing thickness, the Oemit= 546 nm peak rises and is clearly the highest peak at 1 mm thickness. Again, this is a clear sign of the reabsorption. From the measurements we can conclude two things: first, in the spectrum emitted from the dye, the peak at Oemit= 546 nm peak is much more pronounced than the Oemit= 575 nm. Second, the distance, in which nearly all the light emitted at the shorter wavelengths is reabsorbed, is only a few millimeters.

52


Fig. 4.19: PL spectra measured at the back of three samples made from the same material BA241, but with three different thicknesses. The excitation was at Oinc= 490 nm. The spectra were normalized such that the peaks at Oemit= 546 nm have the same heights. The relative height of the peaks at Oemit= 546 nm and Oemit= 575 nm changes considerably with the thickness. For the thickest sample, both peaks have nearly the same height. With decreasing thickness, the Oemit= 546 nm peak becomes relatively higher and is clearly the highest peak at 1 mm thickness. This is a clear hint that re-absorption changes the shape of the spectrum within a few millimeters. The dependence of the excitation wavelength on the PL spectrum was measured as well at the back. Fig. 4.20 shows the results for the 3.2 mm thick sample made from BA241. The samples were excited at Oinc= 490 nm and at Oinc= 440 nm. Again, the excitation peak was blocked with a filter between the sample and the collimator. A Schott OG530 filter was used during excitation with Oinc= 490 nm and a GG455 filter for the Oinc= 440 nm measurement. The transmission spectra of the filters were considered in the evaluation of the data.

53


Fig. 4.20: Comparison of the normalized PL spectra measured at the back for two different excitation wavelengths, at Oinc= 490 nm and Oinc= 440 nm. The measured sample was made from BA241 and 3.2 mm thick. The relative height of the peaks at Oemit= 546 nm and Oemit= 575 nm changes considerably with the excitation. Clear differences between the two measurements are visible. Part of these differences can be attributed to the fact that the total height of the signal was considerably lower during excitation with Oinc= 440 nm, for the absorption at Oinc= 440 nm is lower than at Oinc= 490 nm. In consequence, after normalization of the spectra, the Oinc= 440 nm spectrum shows a higher background that again increases to longer wavelengths. Independent from the background, the relative peak heights change significantly with the excitation wavelength. The nearly similar heights of the peaks at Oemit= 546 nm and Oemit=575 nm change to a clear domination of the Oemit=546 nm peak under excitation with Oinc= 440 nm. Several effects could explain this correlation between shorter wavelength excitation and shorter wavelength emission. One factor could be the lower absorption for the Oinc= 440 nm excitation. With strong absorption, most of the light is absorbed and therefore emitted close to the front. With less absorption, the absorption and consequently the emission profile is more evenly distributed over the depths of the collector. Hence, on average the emitted light has to travel only a shorter distance to the back and the detector. This would result in lower re-absorption and therefore a relatively higher peak at Oemit=546 nm, because this peak is strongly influenced by reabsorption. If this effect was dominant, the differences between the two excitations

54


should be less pronounced for the thinner samples. Fig. 4.21 shows the results of the same measurement for the 1 mm thick BA241 sample. Although the effects of the background are even stronger, it is still visible that the relative peak heights change considerably. Under excitation with Oinc= 440 nm, the peak at Oemit=570 nm is hardly visible. Therefore, the different absorption cannot be the only factor. Another explanation could be that the excitation at Oinc= 440 nm excites higher energy levels, from which direct transitions to the ground state are also possible. These higher energy levels could be either higher vibrational states of the first electronically excited level that show a large overlap with states of the electronic ground state, or higher electronically excited levels (S2). From Fig. 4.21 it appears reasonable that most of the first emission actually involves these higher energy states, and that the peak at Oemit=570 nm is only the result of re-absorption and subsequent emission, at least for excitation at Oinc= 440 nm. The different possibilities will be discussed again in detail in the simulation chapter (4.4), where the different assumptions will be tested in a Monte-Carlo model.

Fig. 4.21: Comparison of the normalized PL spectra measured at the back for different excitation wavelengths, at Oinc= 490 nm and Oinc= 440 nm. measured sample was made from BA241 and 1 mm thick. Also for thickness, the relative height of the peaks at Oemit=546 nm Oemit=575 nm changes considerably with the excitation.

55

two The this and


4.3.2

Characterizing the light guiding of fluorescent concentrators

The development of new material systems for fluorescent concentrators requires the testing of a wide range of materials with a fast method. The most important characteristic to be tested is the ability of the collectors to guide light to their edges, where the solar cells are mounted. For the construction of advanced systems with several collectors in one stack, such as in [40, 46, 85], this information is required with spectral resolution. In this work, the spectrally resolved information about the ability of the fluorescent collector to guide light to the edges will be designated “spectral collection efficiency” KS(Oinc). It is defined as the ratio of the number of photons that leave the collector through the edges Nedge(Oinc) under monochromatic excitation with Oinc, to the number of photons incident Ninc(Oinc):

K S Oinc :

N edge Oinc N inc Oinc

(4.15)

Several parameters determine this spectral collection efficiency, such as the absorption and the quantum efficiency of the dyes, the optical properties of the matrix material, the surface quality, and the geometric dimensions of the collector plate. Hence, measurements of the absorption spectra and the photoluminescence alone are not sufficient to assess the spectral collection efficiency. In this section, I present a method to determine the spectral collection efficiency with transmission, reflection and centermount measurements using a spectrophotometer and an integrating sphere. The method was developed during the work for this PhD-thesis and represents considerable progress to existing methods. Moreover, additional information such as the escape cone losses can be obtained from the measurements. First, I will briefly discuss alternative methods. Then I will discuss the important features of the used spectrophotometer. Subsequently, I will introduce the concept of the method and show qualitative results. Reasonably similar samples can be compared without requiring any corrections. For fully quantitative results on an absolute scale, for samples with large Stokes shifts and/or very different properties, additional corrections must be applied. Therefore, I will discuss the necessary corrections and compare the results with EQE measurements. In the last part, I will present which information in addition to the spectral collection efficiency can be obtained with the method.

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4.3.2.1

Common methods to determine the spectral collection efficiency

In the past, measurements on systems consisting of a fluorescent collector with a solar cell attached to its edges were used to determine the collection efficiency of fluorescent concentrators, e.g. [41]. From external quantum efficiency (EQE) measurements, the spectral collection efficiency KS(Oinc) can be determined, if the EQE of the solar cell in use is known. However, the results are sensitive to the optical coupling of solar cell and fluorescent concentrator. For the comparison of different samples, the varying properties of the solar cells add uncertainty. Moreover, this method is quite laborious and therefore not very well suited to test a wide range of material. Usually, the excitation during the EQE measurements is point like. This is a problem, because the collection efficiency is strongly dependent on the position, as I will show in chapter 4.5. So also the relevance of the EQE based method is limited. I first presented my method in [32]. In the meantime Currie et al. presented a method that used an integrating sphere as well [60]. In their method, the samples are placed inside an integrating sphere and two measurements are performed. In the second measurement, the emission from the edges is blocked with ink or tape. However, in that case obtaining the information necessary for the corrections is not possible. Additionally, with black edges, no further use of the samples is possible and therefore also no direct comparison with system measurements can be performed. 4.3.2.2

Working principle of a spectrophotometer

In this work, the spectral collection efficiency is determined with three measurements with an integrating sphere and a spectrophotometer. A Cary500i UV-Vis-NIR Spectrophotometer from Varian Inc. was used for the reflection and transmission measurements. For the centermount measurements, the samples were placed inside the integrating sphere. Therefore, a larger Cary5000i UV-Vis-NIR Spectrophotometer from the same company was used. Fig. 4.22 shows the schematic setup of the spectrophotometers. The spectrophotometers contain several different light sources, in order to cover a wide spectral range. A double-monochromator selects a specific excitation wavelength Oinc. The monochromatic beam is split by a reflecting chopper into a sample beam and a reference beam. The sample beam interacts with the sample, and depending on the measurement, different fractions of light reflected, transmitted or absorbed and re-emitted from the sample are collected from the integrating sphere and detected.

57


Fig. 4.22: Setup of a spectrophotometer. A double-monochromator selects a specific excitation wavelength. The monochromatic beam is split by a reflecting chopper into a sample beam and a reference beam. The sample beam interacts with the sample, and depending on the measurement, different fractions of light reflected, transmitted or absorbed and re-emitted are collected from the integrating sphere and detected. For reflection measurements, the sample is mounted tilted by an angle D=4° so that the direct reflection does not leave the sphere, but is also detected. The detection does not discriminate different wavelengths. That is, photons with all wavelengths are detected. In consequence, all data is given as a ratio of the number of photons (regardless of which wavelength) detected under the monochromatic excitation with Oinc to the number of photons incident at the wavelength Oinc. The reference beam enters the integrating sphere without interacting with the sample. The signal recorded during the measurement is the ratio of the signal from the sample beam and the signal from the reference beam. In this way, fluctuations of the excitation intensity are compensated. Additionally, a baseline correction was performed for all measurements. The reference beam enters the integrating sphere without interacting with the sample. The signal recorded during the measurement is the ratio of the signal from the sample beam and the signal from the reference beam. This compensates for fluctuations in the excitation intensity. Additionally, a baseline correction was performed for all measurements. These baseline corrections take into account the varying sensitivity of the setup for different wavelengths. The baseline corrections will be discussed in more detail in section 4.3.2.4. Because of the fluorescence and the Stokes shift, the case is a little bit more complex than for standard measurements.

58


The detection does not discriminate between different wavelengths. This means that photons with all wavelengths are detected. In consequence, all data is given as a ratio of the number of photons detected, regardless of their wavelength Nmes(Oinc) under excitation with Oinc, to the number of photons incident Ninc(Oinc). The number of photons detected Nmes(Oinc) can be described as

N mes Oinc

³ N O , O dO

mes all wavelengths

(4.16)

inc

with Nmes(OOinc) being the number of photons that have a wavelength Othat are detected under excitation with Oinc. So finally, the recorded data can be expressed as

Datames Oinc 4.3.2.3

³ N O , O dO

mes all wavelengths

inc

N inc Oinc

(4.17)

The general concept of measuring the light guiding

For the first measurement, the sample is located at the transmission sample port of the integrating sphere of the spectrophotometer (Fig. 4.23a). I will designate the result of this measurement Tmes(Oinc). The second measurement is performed with the sample at the reflection port (Fig. 4.23b), giving Rmes(Oinc). For the third measurement, the sample is placed inside the integrating sphere with a centermount (Fig. 4.23c), from which one obtains Cmes(Oinc). Fig. 4.24 shows the data from all three measurements for one sample. The sample was made from the already introduced material BA241, 3.2 mm thick and 2 cm x 2 cm in size. In figure Fig. 4.24, the transmission drops in the absorption range of the dye at around 500 nm. The reflection is roughly 8% over a broad spectral region, which corresponds to the Fresnel reflection at the front and back surface. The reflection appears to be higher in the absorption region of the dye. This is because the reflection measurement also detects light that is emitted into the escape cone of total internal reflection and leaves the sample at its front surface. The centermount measurement shows that parasitic absorption in the matrix material is low, but that losses occur in the absorption region of the dye.

59


Fig. 4.23: Three measurements are performed with an integrating sphere setup to determine the spectral collection efficiency KS(Oinc) of the fluorescent concentrator. At first, standard transmission Tmes(Oinc) (a) and reflection Rmes(Oinc) measurements (b) are performed. The light that is detected is shown as bold arrows, the light not detected as thinner arrows. As the sample is outside the integrating sphere during the first two measurements, especially light that leaves the fluorescent concentrator at the edges is not detected. The third measurement is performed with the sample mounted in the center of the integrating sphere (c). This measurement yields CmesOinc), which is one minus the total absorption Absmes(Oinc).

Fig. 4.24: The data collected with the transmission, reflection and centermount measurements of a sample from the material BA241. From this data, the spectral collection efficiency is calculated. The effect of the dye’s absorption is clearly visible in the transmission and centermount measurements. The increased reflection is a result of the dye’s emission into the escape cone of total internal reflection.

60


From this data, one can determine the spectral collection efficiency KS(Oinc), which is the fraction of photons that leaves the collector at the edges in respect to the number of photons incident. With the sample inside the integrating sphere during the third measurement, all photons are detected that are not absorbed and their energy transformed into heat. This measurement therefore yields Cmes(Oinc)= 1 - Absmes(Oinc).

(4.18)

Of particular interest is the fact that the light leaving the edges is also detected. In contrast, during the first two measurements, the sample is outside the integrating sphere. Hence, light that leaves the collector sample at its edges is not detected. For standard transmission T and reflection R measurements, 1 – T - R yields the absorption Abs of the sample. However, this is not true in our case, because the light that leaves the collector at the edges KS(Oinc) is neither absorbed nor detected in Tmes(Oinc) or Rmes(Oinc). It has to be considered additionally. Therefore, it is 1 - Tmes(Oinc) - Rmes(Oinc) - KS(Oinc) = Absmes(Oinc).

(4.19)

Combining equation (4.18) and (4.19) the spectral collection efficiency can be calculated with

KS(Oinc) = Cmes(Oinc) - Tmes(Oinc) - Rmes(Oinc) .

(4.20)

I performed these measurements on samples from more than 20 different materials, a task that would have meant tremendous effort with other methods. All samples were 2 cm x 2 cm in size. Fig. 4.25 shows the spectral collection efficiency for a representative set of samples with relatively high efficiencies. The figure shows the efficiency of two samples with the same dye but different thickness (BA241 3.2mm and 8.3mm). With increasing thickness, Ks(Oinc) increases up to a maximum spectral collection efficiency of 60% for specific wavelengths. In a thicker sample, more light is absorbed. Another effect that might contribute to the increase in efficiency is that fewer reflection events at the surfaces are needed in a thicker sample before the light reaches the edges. Fig. 4.25 also shows the results for samples with different dyes. In order to compare different materials, the geometric dimensions of the samples must be the same, as KS(Oinc) is dependent upon size and the ratio between length and thickness. As mentioned before, all samples were 2 cm x 2 cm in size and these samples were all 3.1 mm thick. A trend becomes obvious that collection efficiency decreases for materials that are active at longer wavelengths.

61


Fig. 4.25: The spectral collection efficiency Ks(Oinc) of a representative set of different materials. All samples were 2 cm x 2 cm. The figure shows the efficiency of two samples with the same dye but different thickness (BA241 3.2mm and 8.3mm). With increasing thickness, Ks(Oinc) increases as well. The spectral collection efficiency reaches up to 60%. The graph also shows the results for samples with different dyes. These samples were all 3.1 mm thick. Collection efficiency tends to decrease for materials that are active at longer wavelengths. Fig. 4.25 shows a spectral collection efficiency of 1-2% in the spectral region above 600 nm for the thinner BA241 sample. This can be considered an artifact from the uncertainties of the measurement in combination with the performed calculations. To obtain the data, several sets of spectral data have to be added or subtracted from each other. A small relative error in the transmission or centermount measurements that show high signals in this region could lead to that 1% absolute error. Nevertheless, the collection efficiency in the absorption region of the dye is of primary interest. In that region, relative errors remain small. In the presented way, the method is already a fast and easy way to assess and compare the ability of concentrators made from different materials. As we will see later on in this work (chapter 4.5), I also fabricated complete fluorescent concentrator systems with attached solar cells from materials tested with this method [46]. Indeed, the samples that had been the most promising ones based on the results of the new method also achieved the highest system efficiencies. The spectral information obtained

62


proved to be very helpful for the decision regarding which materials should be combined in one stack. However, the results are not yet fully quantitative, and care must be taken when comparing samples with significantly differing properties. This is especially true when the materials are active in very different regions of the spectrum and for large Stokes shifts, as I will show in the next section. 4.3.2.4

Correcting for Stokes shift effects

The spectral data presented in the previous section was obtained from measurements with a spectrophotometer and an integrating sphere. While obtaining these measurements, a standard baseline correction is performed. For the transmission measurement, the signal with no sample is recorded as 100% baseline. The signal during each measurement of a sample is then compared to the baseline signal to obtain the transmission data. For the baseline of the reflection measurements, the signal with a standard reference is recorded. The reflection of this standard reference is known, so by comparing the signal with the sample to the baseline and taking into account the reference’s reflection, the reflection data of the sample can be obtained. The reflection of the fluorescent concentrator has both specular and diffuse parts. I chose a diffuse standard reference made from Polytetrafluoroethylene (PTFE). The standard baseline corrections are usually completely sufficient. However, a problem occurs when investigating fluorescent concentrators. Because of the Stokes shift, the emitted light has a different wavelength Oemit than the light impinging on the sample with a wavelength Oinc. On the other hand, the baseline value used for the calculation of the result is, by default, the value for the wavelength of the incident light. Under standard conditions, the resulting data is calculated via Data(Oinc)=Signal(Oinc)/Baseline(Oinc).

(4.21)

With this standard procedure, the signal from the emitted light with Oemit would be divided by a baseline value for a different wavelength Oinc: Data’(Oinc)=Signal(Oemit)/Baseline(Oinc).

(4.22)

Therefore, we must correct the outcome of the standard procedure via Datacorr O Data ' Oinc

BaselineOinc BaselineOemit

Signal Oemit BaselineOinc BaselineOinc BaselineOemit

to obtain the correct data.

63

Signal Oemit BaselineOemit

(4.23)


Fig. 4.26: This graph highlights the problems associated with the Stokes-shift and the baseline correction. It shows 1 - Tmes(Oinc) - Rmes(Oinc) of the sample BA241 3.2mm, which one could call “apparent absorption”. This data indicates very well in which spectral region the dye absorbs. The graph also presents the photoluminescence spectrum recorded at the edges of the fluorescent concentrator. The excitation was at 497 nm. Additionally, the baseline scans for transmission and centermount measurements and the baseline scan for the reflection measurement divided by the reflection of the standard reference are shown. It becomes obvious that calculating the data with the baseline value for the wavelength of the absorbed light leads to mistakes, as the baseline is different in the absorption and emission regions. As we can see from Fig. 4.26, light is not emitted at a single wavelength Oemit, but over a whole wavelength range. Consequently, we need the weighted average value for the baseline in the emission range of the dye. This can be calculated by

³ PLO BaselineO dO

Baselineav

Emission Range

(4.24)

³ PLO dO

Emission Range

and finally the correction is

64

,


Datacorr Oinc Data ' Oinc

BaselineOinc . Baselineav

(4.25)

In the case of the reflection measurements, the measured baseline divided by the reflection of the standard reference must be used instead of only the baseline in this correction. 4.3.2.5

Calculating the emitted fraction

The correction of the data need only be applied to the part of the light that has been emitted by the dye, as this is the only part for which a Stokes shift occurs. Consequently, it is necessary to separate in the measurement data the fraction that is transmitted or reflected without interaction with the dye from the fraction which has interacted with the dye and stems from an emission process. For the reflection measurement, a good assumption is that the diffuse fraction results primarily out of the approximately isotropic emission process. Therefore, we should be able to calculate the fraction of emitted light detected during the reflection measurement Remit(Oinc) from measurements of the diffuse reflection Rdiffuse(Oinc). I checked this hypothesis by measuring the diffuse reflection from a reference sample without a dye Rdiffuse,ref(Oinc). Indeed, the diffuse reflection independent of the dye was very small. So Remit (Oinc) determined via Remit(Oinc) = Rdiffuse(Oinc) - Rdiffuse, ref(Oinc)

(4.26)

is very close to Rdiffuse(Oinc). The results of the calculation of the emitted fraction can be seen in Fig. 4.27. In a similar way, the fraction of emitted light detected during the reflection measurement Temit(Oinc) can be calculated from the diffuse fraction of the transmitted light of the sample (see also Fig. 4.27). I determined this diffuse fraction through a comparison of the direct transmission with the total transmission measured with the integrating sphere. The case is a little bit more complicated for the emitted fraction detected during the centermount measurement. As given in equation (4.18), the data of the centermount measurement Cmes(Oinc) is equal to 1 - Absmes(Oinc). The absorption of the matrix material Absmatrix(Oinc) and the absorption of the dye Absdye(Oinc) contribute to the total absorption. A part of the absorbed light is re-emitted and leaves the sample, which is the fraction Cemit(Oinc) that we need. Cmes(Oinc) can be expressed as

Cmes Oinc 1 Absmatrix Oinc Absdye Oinc Cemit Oinc

65

(4.27)


The term 1 - Absmatrix(Oinc) can be identified with the data obtained from a centermount measurement of a reference sample Cref(Oinc), which yields the expression

Cemit Oinc Cmes Oinc Cref Oinc Absdye Oinc

(4.28)

to calculate the emitted fraction. The absorption of the dye Absdye(Oinc), which is needed for this calculation, can be derived from the already available data via Absdye Oinc Tref Oinc Tmes Oinc Temit Oinc Rref Oinc Rmes Oinc Remit Oinc

(4.29)

Please note that for calculating the emitted fraction in the centermount measurement, to which we wish to apply the correction, Absdye(Oinc) must be calculated with the uncorrected Temit(Oinc) and Remit(Oinc). Fig. 4.27 shows the emitted fractions for the different measurements. The absorption of the dye is shown in Fig. 4.32 and will be discussed in more detail in a following section.

Fig. 4.27: The fraction of photons which is emitted by the dye inside the collector and detected during the three measurements. Please note that all data is given relative to the number of photons incident on the sample. The presented correction must be applied to these data. One can see that the emitted fraction is lower for the transmission measurement than for the reflection measurement. More light is absorbed, and consequently emitted, close to the front surface. To be detected in the transmission measurement, this emitted light must traverse the fluorescent collector. Along the way, reabsorption reduces the amount that actually leaves the collector. These losses do not occur in the same strength for the light to be detected during the reflection measurement. Hence, the emitted and detected fraction is higher in the reflection measurement.

66


4.3.2.6

Calculating the corrected spectral collection efficiency

With all this corrected data, the correct spectral collection efficiency KS(Oinc) can be calculated with equation (4.20). Having calculated all the emitted fractions, there is also a faster way:

Ks , corr Oinc Cemit , corr Oinc Temit , corr Oinc Remit , corr Oinc

(4.30)

A comparison between the corrected and the uncorrected data is shown in Fig. 4.28. The effect should be more pronounced for larger Stokes shifts or spectral regions, where the baseline varies more strongly.

Fig. 4.28: Comparison of the spectral collection efficiency with and without the described correction. With the correction, the values are higher than without. This can be explained as follows: in the emission region of the dye, the sensitivity of the detector in the integrating sphere is lower than in the absorption region. This is why the baseline is lower in the emission region, as can be seen in Fig. 4.26. This has not been taken into account in the uncorrected measurement and is now corrected. 4.3.2.7

Comparison between spectral collection efficiency and external quantum efficiency measurements

To test the new method, I compared the results with external quantum efficiency measurements (EQE). The EQE was measured for a system with a 2 cm x 2 cm fluorescent concentrator (BA241, 3.2mm thick) with four attached GaInP solar cells. The solar cells and the complete systems of fluorescent collector and solar cells will be

67


discussed in detail in chapter 4.5. At this point, I will treat the EQE measurement simply as an alternative method to determine the spectral collection efficiency. In contrast to chapter 4.5, I placed a black absorber underneath the fluorescent concentrator. In this way, light that has passed the collector is absorbed and cannot enter the collector again. The EQE measurement gives the ratio of electrons collected at the contacts of the solar cells to the photons impinging on the system. I denote the result of the EQE measurement of the system of fluorescent collector and solar cell EQEsystem(Oinc). The spectral collection efficiency KS(Oinc) is the result of optical measurements. To compare both results, one has to calculate which result of the external quantum efficiency one could expect based on the optical measurements. This “predicted” value is denoted EQEsystem,optical (Oinc). In our case, the solar cells are illuminated by the light emitted from the dye molecules (Fig. 4.29). So one has to take into account the average external quantum efficiency encountered by the emitted light. The resulting relation is

EQEsystem, optical Oinc K s Oinc ³

PLO ' EQEcell O ' dO '

³ PLO ' dO '

.

(4.31)

Fig. 4.29: The external quantum efficiency EQEcell(Oinc) of one GaInP solar cell and the photoluminescence spectrum PL(Oemit) of the dye BA241.

68


Fig. 4.30 shows the measured EQEsystem(Oinc) of the system in comparison to the EQEsystem,optical(Oinc) calculated with equation (4.31) from the optically measured spectral collection efficiency. Apparently, the measured EQEsystem(Oinc) is considerably lower than the one calculated from the optical measurement. There is yet another effect that must be considered: The external quantum efficiency depends on the position of the measurement spot on the fluorescent concentrator, as we will see in chapter 4.5. Losses like re-absorption of the emitted light by the dye and parasitic absorption in the matrix material depend on the length of the path of the emitted light within the concentrator. Therefore, the distance of the excitation spot from the solar cells at the edges affects the measured efficiency significantly. As the dyes emit the light approximately isotropically, the average distance to the solar cell is important and not the direct way (see Fig. 4.31).

Fig. 4.30: Comparison of the measured EQEsystem(Oinc) of the system in comparison to the EQEsystem,optical(Oinc) calculated from the optically measured spectral collection efficiency. Also, the measured EQEsystem,corr(Oinc) scaled by a factor of 1.13 to consider the position dependency of the EQE is shown. The scaled EQEsystem,corr(Oinc) and EQEsystem,optical(Oinc) from the optical measurement agree very well, considering uncertainties of the measurements and the corrections applied.

69


Fig. 4.31: Illustration of the average distance of the excitation spot from the solar cells at the edges. Because the dye emits isotropically, the average distance is considerably longer than the direct path to the closest solar cell. The average distance is longest in the middle of the sample. For a 2 cm x 2 cm sample the average distance from the center is 1.12 cm. Close to the corner it is about 0.7 cm and even directly at a corner the average distance is still 0.56 cm. The presented EQEsystem(Oinc) was measured in the middle of the sample where efficiency is the lowest with an excitation point of a few mm. For an excitation in the middle of the sample, the average distance in the horizontal direction to a solar cell at one of the edges is about 1.12 cm [45]. The data presented in [45] shows that for 44% of the area of the fluorescent concentrator, the average path is between 0.98 cm and 1.12 cm. For this 44% we can use the EQEsystem(Oinc) measured in the middle to be a good estimate for the local EQE. Another 34% have an average path between 0.84 cm and 0.98 cm. As we ill see in chapter 4.5, the EQE in the absorption region of the dye in 0.5 cm distance to the solar cell (direct way) is about 16% higher than in 1 cm (direct way) distance. Therefore, it is reasonable to expect a 16% higher efficiency for the aforementioned 34% fraction of the area. The remaining 22% have a shorter average distance to a solar cell. The measured EQE in 0.25 cm distance (direct way) was 34% higher than in 1 cm distance. A weighted average with these values yields a correction factor of 1.13 to consider the position dependency of the EQE measurement. An accordingly scaled graph of EQEsystem,corr(Oinc) is also shown in Fig. 4.30. The agreement with the EQEsystem,optical derived from the optical measurement is much better than without the scaling.

70


The remaining differences are small, and the agreement very good considering the measurement uncertainty of about 1-2% absolute for the individual optical measurements and of 3% relative for the measurement of the EQE. Naturally, the corrections applied add uncertainty as well. Especially critical is the influence of the photoluminescence spectra. As we have seen before, the spectrum is heavily influenced by re-absorption. In addition to the effects discussed in section 4.3.1, we have to consider also a position dependency. Due to re-absorption, the spectrum leaving the edges also depends on how close the excitation was to the edges. If the peak at shorter wavelengths is not fully lost due to re-absorption, additional wavelength dependencies will occur. All this is a bigger problem for the EQE measurement than for the optical method: The baseline of the optical system does not vary strongly in the emission range, while the EQE decreases strongly above 600 nm. Considering the complexity, the last correction for the position dependency of the EQE has to be considered as fairly rough. Nonetheless, the satisfactory agreement between measured EQEsystem,corr(Oinc) and EQEsystem,optical(Oinc) from the optical measurement achieved in spite of all these problems can be seen as a good validation of the method proposed. Furthermore, it has become obvious that determining the spectral collection efficiency via the electrically measured EQE contains a considerable amount of uncertainties and problems and requires significant corrections. Consequently, the proposed new method provides more reliable results. 4.3.2.8

Collateral information from the measurements

Much data has been measured and calculated to determine the corrected spectral collection efficiency. This data can be used to gain some additional information about the fluorescent collector. One byproduct of the correction presented in the previous section was the fraction of the incident light that is absorbed by the dye Absdye(Oinc) (Fig. 4.32). This result could not be derived simply via 1-T(Oinc)-R(Oinc) because some of the absorbed light is reemitted. The absorption coefficient of the dye inside the host material could give information on whether the dye was affected by the embedding process. It also presents valuable input data for simulations of the fluorescent concentrators, e.g. [86]. Care must be taken, because the data is given as the fraction of the light incident on the concentrator. So to calculate the absorption coefficient, the reflection at the front surface must be taken into account (see also section 4.4.2.2).

71


Fig. 4.32: The fraction of the incident light which is absorbed by the dye within the material BA241. The slab was 3.2 mm thick. The correction does not affect the absorption data significantly. Another very important result which can be directly derived from the generated data is the escape cone loss. As I already showed in Fig. 4.1, emitted light that impinges on the surface with angles steeper than the critical angle Tc is lost, due to the escape cone of total internal reflection. In section 4.3.2.5 I have calculated the emitted fraction detected during the centermount measurement Cemit(Oinc), which corresponds to the total amount of light emitted in any direction. I also calculated the fraction of light emitted and detected during the reflection measurement Remit(Oinc) and the transmission measurement Temit(Oinc). This corresponds to the fraction of light lost due to the escape cone through the front and the back surface. So via

EscapeOinc

Remit Oinc Temit Oinc Cemit Oinc

(4.32)

one can calculate the fraction that is lost due to the escape cone of total internal reflection. The results can be seen in Fig. 4.33.

72


Fig. 4.33: The fraction of emitted light that is lost due the escape cone of total internal reflection. The value predicted theoretically under ideal conditions is 26%. Interestingly, the escape cone losses are not constant. They tend to be lower for smaller wavelengths. This is surprising considering the results of the photoluminescence measurements. There, under excitation with shorter wavelengths shorter wavelengths were also emitted. These shorter wavelengths are more prone to re-absorption, which would increase the escape cone losses. A possible explanation for this occurrence could be that for higher energy photons that are absorbed, more thermal relaxation occurs before a new photon is emitted. More entropy is generated and more information from the incoming photon is lost. This results in the emission characteristic becoming increasingly isotropic. Without this angular randomization, light is emitted more frequently into unfavorable directions with higher escape cone losses [47]. Consequently, more thermalization would mean lower escape cone losses. However, this explanation has to be confirmed by wavelength dependent measurements of the angular characteristics of the emitted light. Another issue is the total height of the escape cone losses. In our results, the losses peak at around 28% in the region with relevant absorption. This could be considered well in agreement with the theoretical prediction of 26%. However, the lower values are below the theoretical value. One explanation could be in the experimental setup: for practical reasons, the openings in the integrating sphere during reflection and transmission measurements are slightly smaller than the samples. Therefore, part of the light being lost into the escape cone is not detected in these measurements.

73


Consequently, the escape cone losses might be underestimated. This could also explain the slight overestimation of the spectral collection efficiency visible in Fig. 4.30. However, the quantification of this effect is not straightforward. A first estimation is that the fraction of the losses that could not be measured is, in any case, smaller than the fraction of the covered area. The reason for this assumption is that the escape cone losses predominantly occur close to the excitation and in the covered areas outside the openings, there is no excitation. 4.3.3

Measuring the angular distribution of the guided light

The escape cone losses depend on the angle under which emitted light impinges onto the internal surface. Furthermore, photonic structures show a pronounced angular characteristic. Therefore, to be able to understand the effect of the photonic structure on light guiding in the collector, it is interesting to investigate the angular distribution of the light that is trapped in the collector and subsequently guided to the edges. As we will see, the complex angular characteristic is also a benchmark whether the different models describing fluorescent concentrators are able to explain the lightguiding well. 4.3.3.1

Setup

To measure the angular characteristic of the guided light, I realized a setup that was first described by Zastrow in [47]. Fig. 4.34 presents a sketch of the experimental setup. An index-matched half cylinder is optically coupled to the edge of the concentrator such that at this edge no total internal reflection occurs. If the cylinder is large in comparison to the thickness of the concentrator, the light impinges on the outer surface of the cylinder perpendicularly. The light leaves the cylinder without significant refraction and the intensity is measured at every angle T. The half cylinder is made from PMMA and is 2 cm thick. The surroundings of the half cylinder are covered with blinds, so only light leaving the concentrator directly into the half cylinder is detected. The blind thickness is 0.5 cm, so the last 0.5 cm of the collector remains unilluminated.

74


Fig. 4.34: Experimental setup to measure the angular distribution of the light that is coupled out at the edges of the fluorescent concentrator. A PMMA half cylinder is optically coupled to one edge to avoid internal reflection and refraction. 4.3.3.2

Results

I measured the angular distribution on a 5 cm x 5 cm sample from the material BA241. The thickness was 3.2 mm. The measurement was repeated three times and the average calculated. The standard deviation is shown as error bars. The result is shown in Fig. 4.35.

Fig. 4.35: Measured angular distribution of the light which is coupled out at the edges of a 5 x 5 x 0.3 cm3 fluorescent concentrator made from BA241.

75


4.3.3.3

Discussion

As shown in Fig. 4.35, the intensity drops significantly at angles T § 50° and 130°, which correspond to the critical angle of total internal reflection. Between T § 50° and 130° the light is guided to the edges by total internal reflections. The few photons detected beyond these angles, in expression with T < 50° or T > 130° must have been emitted close to the edge of the concentrator and therefore could reach the cylinder without a reflection at the top or the back surface of the fluorescent concentrator. All this is well in accordance with the simple picture of isotropically emitting dyes and total internal reflection. However, the angular distribution shows an unexpected anisotropic dip around

T = 90°. This dip is also visible in measurements of [47] but was neglected as a measurement artifact at that time. My co-authors and I investigated this interesting feature in [44].

Fig. 4.36: The path of different rays in the fluorescent concentrator. Ray a) is detected with an angle Tslightly less than 90°. Directly before this ray leaves the collector it traverses through the bottom area of the concentrator. At the bottom, only a minor amount of light is emitted, because of the absorption/emission profile in the concentrator. In contrast, ray b) passes through the top section last. That is, many photons are detected with an angle slightly larger than 90°. Rays with angles significantly different from 90°, such as ray c), pass several times through the collector. Therefore no large differences between angles significantly smaller and greater than 90° occur.

76


Ray tracing simulations with a model developed by Liv Prönneke [44] and by the independent model presented in this work in chapter 4.4 showed both that the assumed angular emission characteristic changes the angular distribution, but that an anisotropic characteristic prevails independent from the angular emission characteristic. Therefore, an explanation must be found in more fundamental properties of the collector. Here, help comes from the thermodynamic model presented in 4.2.2. As mentioned before, because of the absorption of the incoming light in the concentrator, the intensity of the incoming light drops with increasing distance from the front surface. Thus, the chemical potential also decreases and less light is emitted further away from the front surface. Now one has to consider that light detected at different angles experiences different light paths. The different paths are illustrated in Fig. 4.36. Light detected with an angle slightly greater than 90° originates partly from the area close to edge and close to the front surface, an area were a high flux of light is emitted. In contrast, the light which is detected with angles slightly smaller than 90° stems either from regions where less light is emitted (close to the bottom of the concentrator) or has to travel longer distances in the concentrator, which means higher re-absorption losses. Light that is detected with angles significantly different from 90° has on average traveled several times through the collector. It originates both from the top and the bottom regions. Therefore, no big differences are obvious between angles significantly smaller and larger than 90°. However, angles above 90° remain slightly more frequent. In conclusion, it is the spatial distribution of the absorption of the incident light and the resulting re-emission profile that is responsible for the anisotropy in the angular distribution. 4.3.4

Short summary of the optical characterization

Optical methods offer powerful tools to characterize fluorescent collectors. With photoluminescence measurements I could show the strong effects of re-absorption and a dependence of the luminescence spectrum on the wavelength of the excitation light. I presented a novel method to determine the spectral collection efficiency of fluorescent concentrator systems. Only three optical measurements with a photospectrometer and an integrating sphere are necessary to determine the ability of the concentrator to guide light to its edges. A comparison with results from external quantum efficiency measurements on a system with fluorescent concentrator and attached solar cells showed good agreement. From the measurements, additional relevant data, such as the absorption of the dyes in use and the fraction of light lost into the escape cone, could be derived. Especially in the escape cone measurements, an interesting wavelength dependency occurred.

77


Measurements of the angular distribution of the guided light showed interesting features. These can be explained by the absorption profile within the fluorescent collector and are rather independent from the emission profile of the dye. Unfortunately, it is therefore difficult to derive the emission’s angular characteristics from these measurements. To explain the different measurement results, I offered several models and hypothesizes. To test these different models, a Monte-Carlo based simulation will be presented in the next chapter.

78

4.4 Simulating fluorescent concentrators

4.4

Simulating fluorescent concentrators

For a full understanding of fluorescent concentrators, it is helpful to be able to test the different hypotheses of how a fluorescent concentrator works and which effects are important. Therefore, a simulation model based on Monte Carlo methods was developed in the context of this work. The development of this model was a joint project of the University of Ulm and the Fraunhofer Institute for Solar Energy Systems. I developed the physical model of the relevant processes in the fluorescent collector and generated the input data from different measurements; Marion Bendig from the University of Ulm implemented that model with efficient algorithms within the frame of her master’s Thesis [87]. In her work, many details on the simulation and the Monte Carlo method can be found. Several works have investigated fluorescent concentrators using Monte Carlo methods and ray tracing. One of the first works is the dissertation of Heidler [88]. Heidler modeled absorption of the dye, isotropic emission, total internal reflection, and reabsorption. The model was even capable of simulating a diffuse back reflector and stack configurations. Simulated collection efficiencies exceeded experimental data by 15% on average due to the idealized conditions of the model. However, good agreement between the simulated and measured edge emission spectrum was achieved. Recently, new attempts for simulating fluorescent concentrators have been made [30, 35, 89-92]. Kennedy et al. [90, 91] use a simple model describing absorption of the dye, emission, total internal reflection, and re-absorption to calculate the relative Jsc of solar cells coupled to one edge of the collector and to predict the emitted spectrum leaving at the bottom of the collector. The Jsc values were overestimated by about 10%, but again the emitted spectra agreed well with predictions. Burgers [92] used a quite similar model. He determined relevant parameters, like the dye concentration or the quantum efficiency by fitting the model to measured data. He also included mirrors at the collector edges. With his model, he achieved good agreement between EQE measurements and the simulation-based predictions. In [30, 35] a highly idealized model was presented, that for the first time included a photonic structure. This idealized model is currently being further developed by Liv Prönneke to describe more realistic systems; first results have been published in [44]. In all the previous works, only minor testing of the simulation results against spectrally resolved experimental data, such as reflection and emission measurements, was performed. The angular distribution of the light was neglected as well. Therefore in this work, the simulated data shall be tested against a range of experimental data to

79


verify the different assumptions on the working principle of fluorescent collectors. The model uses efficient algorithms, which allows for the calculation of complex systems with high accuracy. First results derived with this model were published in [86], where all coauthors who contributed to the model are listed. In this work, I present results that were achieved with a slightly refined model and more accurate input data. First, I will present the Monte Carlo method shortly and will give an overview of the model. In the following, I will document the input data and how the data was derived. Then I will compare results from a simple method and with experimental data. Subsequently, I will show which modifications of the simple model increase agreement with experimental data. 4.4.1

Monte Carlo simulation

The Monte Carlo method uses random numbers for the numerical solution of mathematical problems. Early works on this method are from Metropolis and S. Ulam [93]. At this point, I will only give a very short introduction. Comprehensive presentations can be found in [94, 95]. The term Monte Carlo describes a large set of different methods used in many different applications. Many methods follow a pattern that could be described with three steps [96]: 1.

Generate inputs randomly using a certain specified probability distribution.

2.

Perform a deterministic computation using the inputs.

3.

Aggregate the results of the individual computations into the final result.

A classical example is to determine the area of a circle, inscribed into a square, by shooting randomly onto the square and then counting the holes in the circle. By comparing to the total number of shots, the area fraction of the circle can be estimated, and as the area of the square is known, the area of the circle can be calculated (and the value of the number S). The pattern of the three steps is present in this example: the random shooting corresponds to the generating of random input. The determination whether the hole is in or outside the circle corresponds to the deterministic computing and the division by the total number of shots and multiplying with the area of the square corresponds to the computation of the final result. The underlying reason, why this method works can be found in the central limit theorem. The central limit theorem states, in simple words, that the sum of large number of random variables is asymptotically normally distributed. Let X be the quantity to be calculated and m a random variable with the expectation value E(m)=X.

80


Additionally, m1, m2, m3,…mN are N independent variables, which have the same distribution as m. According to the central limit theorem

¦

N i 1

mi

is asymptotically

normally distributed and, which is important, the expectation value is

E ¦i 1 mi N

NX

.

(4.33)

The expected deviation of the sum of the random variables from NX decreases with a

1/ N

law with increasing number of variables N. Therefore the value of X can be

estimated by simulating N realizations of m and calculating the mean average. In our example, for the bullet holes in the circle, the expectation value is similar to the area fraction of the circle (without that this fraction would be known before the experiment). Shooting holes corresponds to simulating the random variables, e.g. in the first round of ten shots five are in and five are out, in the second round eight are in and two are out etc. Following the central limit theorem, the mean average of all rounds will be close to the area fraction of the circle. With more rounds, the precision increases, but for doubled accuracy the number of rounds needs to be quadrupled. For the simulation of fluorescent collectors, the simulated quantities do not follow normal distributions. For instance the penetration depth of the incident radiation follows the exponential Lambert-Beers relation. That is, it is more likely that an incident photon is absorbed close to the surface than close to the back. To sample these random variables with the help of a uniformly distributed random variable y, the inversion method was applied. If m is the random variable with the cumulative distribution function P(x), which gives the probability that mx, than m can be sampled by m=P-1(y). In this relation, P-1(y) is the inverse function of P(x). Obviously, certain requirements for monotony have to be fulfilled for P(x). 4.4.2

The used model

4.4.2.1

Considered processes

In the standard configuration, the model considers wavelength dependent reflection, refraction, total internal reflection, absorption in the PMMA matrix and absorption in the dye. After absorption in the dye the probability of the emission is determined by the dye’s quantum efficiency and the emission wavelength is determined by the photoluminescence spectrum of the dye. Fig. 4.37 shows the process diagram of the simulation.

81


Fig. 4.37: Process diagram of the simulation model

82


The model calculates the reflection of the light at all boundaries with the help of the Fresnel equations:

Rs

§ sin D in D out · ¨¨ ¸¸ , D D sin in out ¹ ©

(4.34)

Rp

§ tan D in D out · . ¨¨ ¸¸ © tan D in D out ¹

(4.35)

2

2

The light is assumed to be unpolarized, so the average value

R

Rs R p

(4.36)

2

was used. The incident and outgoing angle, Din and Dout, were determined by Snell’s law of refraction

sin D in sin D out

n2 n1

.

(4.37)

In this relation n1 is the refractive index of the medium from which the light is incident, and n2 the refractive index of the medium the light enters. For the surrounding a refractive index of 1 was assumed. The refractive index of the fluorescent collectors was calculated using the Cauchy equation [97]

nO c1

c2 .

O2

(4.38)

In this equation, the material constants for PMMA are c1=1.49 and c2=0.004 µm2. Total internal reflection occurs for angles Din bigger than the critical angle Dc, with

sin D c

n2 . n1

(4.39)

The presented relationships were transformed into forms that allowed fast computation prior to implementation, e.g. trigonometric functions are very time consuming in calculations, while scalar products can be processed fast. Therefore mathematical

83


relationships were used to replace trigonometric functions by terms using scalar products. If an incident ray is still in the collector after the previous events, its mean free path is calculated. The relation that determines the free path length 'w can be derived from the Lambert-Beer characteristic with the help of the inversion method. The relation is

'w

ln 1 y

D total O

(4.40)

[87]. In this relation, y is a random variable sampled with a uniform distribution in the interval [0,1). The Dtotal is the sum of the absorption coefficient of the dye Ddye and the absorption coefficient of the PMMA matrix DPMMA. If the ray is absorbed before it hits a boundary of the concentrator, the probability that the ray is absorbed by the dye is Ddye/Dtotal and the probability that the ray is absorbed by the PMMA DPMMA/Dtotal. If the ray is absorbed by the dye, the probability that an emission occurs is given by the quantum efficiency QE. The wavelength of the emission is sampled according to the photoluminescence spectrum. In the standard model the direction of the emission is distributed isotropically. After any emission, reflection or refraction event, after which the ray is still in the collector, the calculation process is repeated. During the calculations, many different data of the rays are collected and aggregated to give meaningful output values. 4.4.2.2

Input data

For a wavelength dependent simulation, the absorption spectrum of the dyes and the PMMA matrix, as well as the photoluminescence spectrum of the dyes must be known. These data were taken from the optical characterization presented in chapter 4.3. To test the simulation, the material properties of BA241 were chosen to be investigated, as for this material the most extensive experimental data was available. In section 4.3.2.8, the fraction of the incident light that is absorbed by the dye AbsdyeOinc was calculated. AbsdyeOinc represents the number of photons absorbed by the dye divided by the number of photons incident on the collector slab. However, only the photons that enter the collector can be absorbed. Therefore, to determine the absorption coefficient DOinc the reflection of the front surface RfrontOinc must be taken into account, as only the fraction of (1-Rfront) enters the slab. It is

84


Absdye Oinc · 1 § ¸, D Oinc ln¨¨1 1 R front Oinc ¸ d ¹

©

(4.41)

with d being the thickness of the fluorescent collector. It must be said that this relation is only an approximation. In spectral regions with low absorption light might pass the collector and might be reflected at the back surface. In consequence, this light would get a second chance to be absorbed and the inserted thickness of the collector would be inappropriate. However, only around 4% of the transmitted light is reflected back into the collector and the effect is only important in regions of low absorption, so this can be considered a minor uncertainty which is in the magnitude of the uncertainties for AbsdyeOinc . The front reflection RfrontOinc was determined from the reflection measurements of the reference sample. In the spectral regions above 350 nm, where the absorption of the reference is low, RfrontOinc was assumed to be half the reference reflection. In the region where reference shows relevant absorption (GSA ESA SE IE MPZ @N ETU ( N , D) .

(5.59)

For most involved processes the rate of change is the product of the probability W for the relevant transition and the occupation

* N . The probabilities for the different

transitions are described by several matrixes. The matrix GSA describes the ground state absorption, ESA the excited state absorption, SE the spontaneous emission, IE the stimulated emissions and MPZ the multi-phonon relaxation. Additionally, the vector ETU, which is a function of the occupation

* N and the distance of the ions D,

describes the change in occupation due to energy transfer. The different matrixes are explained with more detail in the following sections.

189

5 Upconversion

5.6.1.1

Ground state and excited state absorption

Ground state and excited state absorption are stimulated processes. In section 5.3.1 it was shown that it is possible to describe as well the absorption processes with the Einstein coefficient Aij for the spontaneous emission. Equation (5.13) gave the probability for an absorption event depending on the spectral energy density u(Z) with which the ion interacts. In the presented experiments, the upconverter was excited by incident radiation that had a certain irradiance. Therefore, the model shall also work with spectral irradiance IQ(Z) instead of with the spectral energy density. These two quantities can be easily converted into each other via

u (Z )

n IQ (Z ) , c

(5.60)

with c being the speed of light in vacuum and n the refractive index. The model assumes monochromatic excitation with the angular frequency Z, which corresponds to a wavelength of 1523 nm. The model assumes that the transitions from level 1 to 2, 2 to 4, and 4 to 6 are directly excited by this excitation. Therefore the probability of ground state and excited state absorption can be described by the following combined matrix

GSA ESA

§ g1 A21 ¨ ¨ g2 ¨ g1 ¨ g A21 2 2 ¨ 2 S cn 0 I ¨ 3 Q !Z 21 ¨ 0 ¨ ¨ 0 ¨ 0 ¨¨ ©

0

0

0

g2 A42 g4 0 g2 A42 g4 0

0

0

0

0

0 g4 A64 0 g6 0 0 g4 A64 0 g6

· 0 0¸ ¸ ¸ 0 0¸ ¸ 0 0¸ 0 0¸ ¸ 0 0¸ ¸ 0 0 ¸¸ ¹

(5.61)

. The Einstein coefficients used were taken from Table 5.1 in section 5.5.3 with the experimentally determined Einstein coefficients.

190

5.6 Simulating upconversion

5.6.1.2

Spontaneous emission

The probability of spontaneous emission is given directly by the Einstein coefficients. The model only considers the transitions from which emission was observed in the photoluminescence measurements. The matrix SE is therefore:

§ 0 A21 ¨ ¨ 0 A21 ¨0 0 ¨ 0 ¨0 ¨ 0 ¨0 ¨0 0 ©

SE

5.6.1.3

A31

A41

A51

A 61

0

0

A52

A62

A31

0

0

0

0

A41

0

0

0

0 A51 A52

0

0

0

0 A61

· ¸ ¸ ¸ ¸. ¸ ¸ ¸ A62 ¸¹

(5.62)

Stimulated emission

Stimulated emission is the inverse process of absorption. From equation (5.14) it can be simply derived that the probability for the stimulated emission can be described via

IE

5.6.1.4

§ 0 A21 ¨ ¨ 0 A21 2 2 0 S c n ¨¨ 0 I 3 Q 0 ¨0 !Z 21 ¨0 0 ¨ ¨0 0 ©

0 0 0 A42 0 0 0 A42 0 0 0

0

· ¸ ¸ ¸ ¸. ¸ ¸ ¸ 0 A64 ¸¹ 0 0 0 0 0

0 0 0 A64 0

(5.63)

Multi-phonon relaxation

In section 5.3.3 it was already discussed how the probability for multi-phonon relaxation depends on the energy difference between the involved levels. Accordingly, the matrix describing the probability for phonon relaxation between the different neighboring levels is

MPZ

§ 0 e ( N!Z 21 ) ¨ ¨ 0 e ( N!Z 21 ) ¨ 0 0 WMPZ (0) ¨ ¨0 0 ¨ 0 0 ¨ ¨0 0 ©

0

0 0

( N!Z 32 )

0 0 0

e e ( N!Z32 ) 0 0

e ( N!Z 43 ) e ( N!Z 43 ) 0

e ( N!Z54 ) e ( N!Z54 )

0

0

0

191

· ¸ ¸ ¸ ¸ ¸ ¸ e ( N!Z 65 ) ¸ e ( N!Z 65 ) ¸¹ 0 0 0 0

(5.64)

5 Upconversion

The quantities WMPZ(0) and N are material constants of the crystal. They have not yet been determined for the investigated erbium doped NaYF4. Therefore they were treated as free parameter of the model during simulation. 5.6.1.5

Energy transfer

Energy transfer is the dominant upconversion mechanism [116]. The energy is transferred from one excited sensitizer ion to the acceptor ion. Following equation (5.28), the overlap of the two involved line form factors determines how likely the energy transfer is. This means that the two transitions involved must be in resonance. Fig. 5.29 indicates which transitions are in sufficient resonance and are therefore considered in the model. The transitions can occur as well in the opposite direction. This is the so-called cross-relaxation that empties higher excited levels and can therefore be considered a loss mechanism in the context of upconversion. Crossrelaxation between the indicated transitions is considered as well in the model.

Fig. 5.29: For energy transfer to take place, the two involved transitions must be in resonance to each other. Four different energy transfer transitions that show sufficient resonance are included in the model. These transitions are shown as colored arrows in the figure. Two arrows of the same color indicate that these two transitions are in resonance. The transition can occur as well in the opposite direction. This is the already mentioned cross-relaxation that empties higher excited levels.

192


The vector ETU that describes the energy transfer upconversion and the crossrelaxation is composed of four single vectors that each describe one specific transition:

* ETU ( N , D)

ET 1 ET 2 ET 3 ET 4 ,

(5.65)

In section 5.3.2.2, the probability for energy transfer due to dipole-dipole interaction was derived. By combining equation (5.28) for the probability with the equations (5.19) and (5.20), which establish a link between the dipole matrix elements and the Einstein coefficients for spontaneous emission, the following expression can be derived

WddET

3! Sc 6 9 1 AJ c J AJ c J g A (Z ) g S (Z ) dZ . 6 4 2 4 ZT n n 2 D 6 A A S S ³

(5.66)

In this expression, ZT is the angular frequency of the transition and D the average distance between the ions. The term 9/(n(n2+2)4) stems from the consideration of the change of the local electric field due to the crystal. J’A und JA are the quantum numbers of the total angular momentum for the start and end state of the acceptor ion, while J’S und Js are the respective quantum numbers for the sensitizer ion. The line factors of the transitions are given by gA(Z) and gS(Z). The rate, by which the occupation changes, is the product of the presented probability times the occupation of both starting levels involved. Additionally, the inverse processes must be considered as well. In the following equations, KET1-KET4 represent the different overlap integrals of the line form factors. For a better traceability, the Einstein coefficients were written in the form Axy and Ayx to indicate into which direction the transitions occur. However, independent of the order of the indices Axy=Ayx. In consequence, the vectors describing the different transitions are

ET 1

3! Sc 6 9 6 2 4 Z 21 n n 2 4

§ A21 A24 N 2 2 A12 A42 N1 N 4 · ¨ ¸ ¨ 2 A21 A24 N 2 2 2 A12 A42 N1 N 4 ¸ ¨ ¸ 0 1 ¨ ¸ K ET 1 ¨ A21 A24 N 2 2 A12 A42 N1 N 4 ¸ D6 ¨ ¸ 0 ¨ ¸ ¨ ¸ 0 © ¹ .

193

(5.67)

5 Upconversion

ET 2

ET 3

ET 4

5.6.2

3! Sc 6 9 6 2 4 Z 42 n n 2 4

0 § · ¨ ¸ 2 ¨ A42 A46 N 4 A24 A64 N 2 N 6 ¸ ¨ ¸ 0 1 ¨ ¸ K 2 ET 2 D6 ¨ 2 A42 A46 N 4 2 A24 A64 N 2 N 6 ¸ ¨ ¸ 0 ¨ ¸ 2 ¨ A A N A A N N ¸ 42 46 4 24 64 2 6 © ¹

3! Sc 6 9 6 2 4 Z 21 n n 2 4

§ A21 A46 N 2 N 4 A12 A64 N1 N 6 · ¸ ¨ ¨ A21 A46 N 2 N 4 A12 A64 N1 N 6 ¸ ¸ ¨ 0 1 ¸ ¨ K ET 3 D6 ¨ A21 A46 N 2 N 4 A12 A64 N1 N 6 ¸ ¸ ¨ 0 ¸ ¨ ¨ A A N N A A N N ¸ 12 64 1 6 ¹ © 21 46 2 4

(5.69)

3! Sc 6 9 4 Z 636 n n 2 2 4

§ A31 A36 N 3 2 A13 A63 N1 N 6 · ¨ ¸ ¸ ¨ 0 ¨ ¸ 2 1 ¨ 2 A31 A36 N 3 2 A13 A63 N1 N 6 ¸ K ET 4 ¸ ¨ D6 0 ¸ ¨ 0 ¸ ¨ ¨ A A N 2A A N N ¸ 31 36 3 13 63 1 6 ¹ ©

(5.70)

(5.68)

Input parameters

Inserting all described matrixes in equation (5.59) results in a set of differential equations. This set was solved with the software program MatLab©. The dynamics of the occupation and photo luminescence are modeled. After a certain time, the resulting values reach equilibrium. In the following, these equilibrium values will be presented. Where possible, the model’s parameters were determined experimentally, i.e. the different Einstein coefficients were determined from the determination of the absorption coefficient (see section 5.5.3) and the angular frequencies of the different transitions were determined from the photoluminescence measurements (see section 5.5.5). For the energy transfer, the distance between the ions is important. It was calculated that the density of the Er3+ ions in the NaYF:20% is 2.1027 m-3 and therefore the distance to the closest neighboring ion 7.9.10-10 m.

194


Several coefficients could not be determined theoretically or experimentally in the scope of this work and were therefore treated as free parameters of the model. This affects especially the parameters governing multi-phonon relaxation and energy transfer. These parameters were adjusted such that the relative heights of the different photoluminescence peaks were reproduced. The adjustment was performed for the data set of relative peak heights at an irradiance of 2000 Wm-2 as they are presented in Fig. 5.20. The influence of the parameters and the adjustments will be discussed in the following. Quite independently of the chosen parameters, the model tends to overestimate the occupation of the higher levels 4 to 6. A possible explanation is that the stimulated processes are overestimated. The reason is that for the stimulated processes the model assumes exact the same energy distance between levels 2 to 4 and 4 to 6 as between level 1 and 2. In reality, these transitions do not have exactly the same energy. Therefore, the transitions between the upper levels will not be stimulated as effectively with the incident 1523 nm radiation than the transition between the ground state 4I15/2 and the first excited state 4I13/2. To allow for these differences, the stimulated processes between the higher levels were damped by a factor of 106. In expression, the Einstein coefficients A42 and A64 in the matrix ESA for the excited state absorption and in the IE matrix for the stimulated emission were divided by 106. This does not mean that the determined Einstein coefficients are wrong by this factor, but that the model is too simple at this point, because it does not involve energy levels with a certain energy width. Additionally, the Einstein coefficients for all transitions involving the highest two levels were adjusted manually. Without this adjustment, it was not possible to reach the experimentally observed relative peak heights. In section 5.5.3 the Einstein coefficients had been determined from reflection measurements (see Fig. 5.12). For the higher energy transitions a high background signal is present in the reflection measurements. Although the estimated background was subtracted, some background signal may have remained to distort the results for the Einstein coefficients involving the higher energy levels. Good results were achieved, when the experimentally determined values for the Einstein coefficients for the highest two levels were divided by a factor of 5.9. Table 5.4 displays the Einstein coefficients used in the simulation.

195

5 Upconversion

Table 5.4: Einstein coefficients for the spontaneous emission used in the simulation model. The columns indicate the level from which the emission occurs and the rows the final state after the emission. Values that are not bold are different from the experimentally determined values given in section 5.5.3. Those values were obtained by dividing the experimentally determined values by a factor of 5.9. The values indicated with an * were divided by a factor of 106 before they were used in the matrixes for excited state absorption and for stimulated emission to account for the energy mismatch of the corresponding transitions in respect to the 1523 nm excitation (here the values are shown without the damping factor applied). [s-1] 4

I15/2

4

I13/2

4

I11/2

4

I13/2

4

87

105 4.8

I11/2

4

4

14

97

171

1.5*

19

45

0.09

4.1

15

0.8

5.6*

4

I9/2

4

4

F9/2

I9/2

S3/2

0.56

F9/2

The multi-phonon relaxation is described by an exponential relation in the form

WMPZ ,if

WMPZ (0) expN !Z if .

(5.71)

Reasonable results were achieved with an WMPZ(0) of 108 s-1 and a N of 1020 J-1. However, better relative heights between the neighboring levels were achieved when individual matrix entries were chosen for two transitions. Multi-phonon relaxation from level 4S3/2 to level 4F9/2 was amplified by a factor of 18 in relation to the values calculated with equation (5.71), while the transitions from level 4S3/2 to level 4F9/2 were damped by multiplying by a factor of 0.38. A possible explanation as to why these alterations are necessary, might be that the equation (5.71) is a very simple empirical model that does not describe the full complexity of the multi-phonon interaction. Table 5.5 displays the values for the KETi that describe the strength of the different energy transfer processes. The order of magnitude of the presented values was taken from [118], for the exact values care has been taken to reflect the different energy match between the involved transitions, i.e. the better the match the higher the factor.

196


Table 5.5: Different KETi values used in the simulation that describe the strength of the different energy transfer processes. The order of magnitude of the presented values was taken from [118]. The individual values reflect the different energy match between the involved transitions, i.e. the better the match the higher the factor. Overlap integral [J-1]

³g 5.6.3

A

(Z ) g S (Z ) dZ

KET1

KET2

KET3

KET4

2.2.1022

3.3.1022

2.4.1022

1.6.1022

Simulation results

The simulation was performed for different excitation intensities. Fig. 5.30 shows the luminescence from transitions from the different excited levels to the ground state in dependence on the excitation intensities. Several features are visible that agree nicely with the experimental results and the theoretical expectations on a qualitative level. For all transitions the luminescence increases with increasing irradiance. Thereby, the luminescence from the two levels 4S3/2 and 4F9/2 that are populated dominantly by three photon processes increases with a steeper slope than the luminescence from the levels that are populated by two photon processes. This is in perfect agreement with the theoretical expectation and with the experimental observation as well. Another interesting feature of the experiment is reproduced: for an irradiance of around 900 W/m2, the two curves for the luminescence from level 4I9/2 and level 4F9/2 intersect. This intersection appears as well in the experimental data presented in Fig. 5.22. However, here the differences to the experiments become visible as well. In the experimental data, the intersection occurs at an irradiance two orders of magnitude higher. Possible explanations for these differences might be that the irradiance in the model is the irradiance directly at the upconverter ion. Effects of reflection from the powder, absorption by other ions that reduce the effective irradiance on ions further into the material etc. are not taken into account. Furthermore, the laser beam profile is not homogeneous and therefore certain areas are illuminated with considerably lower intensity. In consequence, the experimental values must be considered an average over the luminescence at many different irradiance levels that are lower than the given maximum irradiance on the surface of the sample. So in conclusion, the agreement with the experiment can be considered to be fairly good.

197

5 Upconversion

Fig. 5.30: Photoluminescence from the different excited levels to the ground state as simulated with the presented model. The results agree very well with theoretical expectations and experimental observations. This includes the steeper slope for luminescence from levels populated by three photon processes and the intersection of curves from different levels that was observed experimentally as well. The presented results were obtained by adjusting numerous free parameters. Therefore, the quality of the model and the question to which extent it describes all relevant processes accurately must remain somewhat unanswered, as flaws of the model might have been obscured by the possibility to make the results fit by adjusting free parameters. At this point more experimental input would be desirable that could be used both as input parameters or to test the model against. For example time-resolved photoluminescence measurements of every level under direct excitation of this level would yield another direct way to determine the Einstein coefficients for spontaneous emission. Nevertheless, the model is still very useful to investigate the influence of single parameters and therefore to enhance the understanding of the upconversion dynamics, as we will see in the following section.

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5.6.3.1

The influence of multi-phonon relaxation

On the one hand, multi-phonon relaxation is an important loss mechanism by which excitation energy is dissipated as heat. On the other hand, multi-phonon relaxation critically determines the relative occupation of neighboring levels that have a small energy gap between them. Fig. 5.31 shows the relative occupation of the higher excited states in dependence on the strength of the multi-phonon relaxation represented by WMPZ(0).

Fig. 5.31: Relative occupation of the higher excited states in dependence on the strength of the multi-phonon relaxation represented by WMPZ(0). For most states the occupation decreases with higher multi-phonon relaxation because more electrons return to the lower states by multi-phonon relaxations. The level 4I9/2 is populated exclusively by multi-phonon relaxation from higher levels. Its population shows a maximum for medium strength of the relaxation. As multi-phonon relaxation is a loss mechanism, it is not surprising to see that for the most levels occupation decreases with increasing strength of the relaxation. Interestingly, the occupation of level 4I11/2 shows a pronounced maximum at medium strength of the multi-phonon relaxation. This level is populated exclusively by multiphonon relaxation from higher levels. Therefore, the occupation of this level benefits from higher multi-phonon relaxation at first. Fig. 5.32 shows, how the multi-phonon relaxation influences the intensity dependence of the luminescence of the 4I9/2 level.

199

5 Upconversion

Fig. 5.32: Normalized luminescence from level 4I9/2 to the ground state in dependence on the multi-phonon relaxation. The luminescence of the individual levels was normalized to their value at 200 Wm-2 to compare the different intensity dependencies. With higher multi-phonon relaxation, the relative increase of the luminescence with increasing irradiance is more pronounced than for lower multi-phonon relaxation. Interestingly, the relative increase of the luminescence with increasing irradiance is more pronounced for higher multi-phonon relaxation than for lower multi-phonon relaxation. Fig. 5.32 shows the dependency for the most important luminescence from level 4I9/2 to the ground state, but the qualitatively same behavior was observed as well for the other transitions. In section 5.3.4, the intensity dependence of the luminescence was investigated with a simple theoretical model. In that simple model, the saturation of the increase in luminescence with increasing irradiance was the result of stronger stimulated emission. The stimulated emission depends on the overall occupation of the higher levels. With multi-phonon relaxation the overall occupation is lower. Therefore, the saturation effect kicks in at higher irradiances. In consequence, the normalized relative occupation should grow roughly the same as with lower multi-phonon relaxation for low irradiances and then should show less signs of saturation for higher irradiances. That is exactly what can be seen in the simulated curves in Fig. 5.32.

200


5.6.3.2

Simulating the effect of plasmon resonance

It was already discussed in section 5.2.6 that external concentration by lenses or mirrors could be complemented by an internal, local intensity increase due to plasmon resonance in metal nanoparticles in order to achieve higher efficiencies. The potential of this concept will be assessed with the help of the simulation tool in this section. The concept is to achieve an enhancement of photon absorption by designing the nanoparticles in such a way that the plasmons show resonance at the energy of the low energy photons, which should be absorbed. That is, the transitions 4I15/2 to 4I13/2 and 4 I13/2 to 4I9/2 are amplified. Fig. 5.33 shows a simulation result of how a gold nanoparticle with a 40 nm radius changes the distribution of the squared absolute value of the electric field normalized to the squared absolute value of the incident electric field in its near field under illumination with 1523 nm irradiation. This simulation was performed by Florian Hallermann at RWTH Aachen. The direction of incidence is from the bottom of the graph in positive y-direction and the polarization is in the xy-plane. The metal nanoparticle does not increase the electric field everywhere, but there are areas with higher and areas with lower electric field. Ten different levels of amplification and attenuation respectively were defined and the relative frequency Fi of each level in the volume around the gold nanoparticle was determined. In Fig. 5.34 the resulting frequency distribution of the irradiance in the volume around the metal nanoparticles is shown for the assumption of a 2000 Wm-2 irradiance on the particle. Results are shown for particle radii of 20, 40 and 60 nm. The frequency distributions show a peak around the initial irradiance of 2000 Wm-2 and a longer tail reaching to higher irradiances. Fig. 5.34 shows the upconversion luminescence in dependence of the irradiance as well. The upconversion luminescence is the sum over all luminescence curves that represent emission of photons that can be used by a silicon solar cell, which were presented in Fig. 5.30. For each level of irradiance Ii the upconversion luminescence PLUC,i(Ii) was determined. Therefore the effective upconversion luminescence could be determined via

PLUC

¦ F PL I i

UC , i

i

201

i

.

(5.72)

5 Upconversion

Fig. 5.33: The distribution of the squared absolute value of the electric field normalized to the squared absolute value of the incident electric field around a gold nanoparticle with a radius of 40 nm under illumination with 1523 nm radiation. The direction of incidence is from the bottom of the graph in positive y-direction and the polarization is in the xy-plane. In certain areas the electric field is increased, while in different areas the electric field decreases due to the metal nanoparticle. This simulation was performed by Florian Hallermann at RWTH Aachen.

Fig. 5.34: Relative frequency distribution of the irradiance in the volume around the gold nanoparticles for an irradiance of 2000 Wm-2 at 1523 nm for particle radii of 20, 40 and 60 nm. The frequency distributions show a peak around the initial irradiance of 2000 Wm-2 and a longer tail reaching to higher irradiances. The figure shows the upconversion luminescence dependent on the irradiance as well. The upconversion luminescence is the sum over all luminescence curves, presented in Fig. 5.30, that represent emission of photons that can be used by a silicon solar cell.

202


For all particle sizes, the upconversion luminescence is increased. The relative increase is 7% for the 20 nm particle, 11% for the 40 nm particle and 16% for the 60 nm particle. These are promising values that underline the potential to increase upconversion efficiency by the application of metal nanoparticles. It will be interesting to investigate even bigger particle sizes in future. On the other hand, the effect of the nanoparticles on the emission must still be investigated. This effect could by itself increase efficiency. The direct enhancement of the emission of the upconverted photons could be achieved by designing the nanoparticles so they support plasmons that are in resonance with the high-energy transitions from the 4I11/2 or 4I9/2 levels of the trivalent levels back to the ground level. However it must be clarified whether the particles that increase absorption have negative effects on the emission and vice versa. To investigate the effect of the metal nanoparticles on the emission, it must be known how the plasmons couple with the emission transitions and how this affects the corresponding Einstein coefficients. With the altered coefficients, the model should be able to demonstrate the effect of the particles on the emission. However, these analyses were beyond the scope of this work.

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5 Upconversion

5.7

Upconversion systems

In the optical measurements, the upconverter NaYF4 : 20 % Er3+ showed a high upconversion efficiency of up to 10.2%. In this section, it is investigated as to how this high efficiency can be transferred to a solar cell system. At first, spectrally resolved measurements of the external quantum efficiency will be presented and compared to the results of the optical measurements. Prior to this work, comparable investigations have been performed by Shalav and Richards [107] and by Strümpel [144]. However, these investigations relied only on the excitation with coherent laser illumination. While the dominant upconversion mechanisms in erbium do not need coherence, this is disadvantageous for two reasons: First, other upconversion mechanisms, which occur under coherent illumination, might influence the experiments. Second, the illumination with a single wavelength does not reflect the situation of the later application, where the material will be illuminated with the broad spectrum of the sun. With a broad spectrum, e.g. photons of different energies might be combined to one high-energy photon. The only experiments performed without laser illumination [125] were restricted to the visible range of the spectrum on organic materials, and are therefore of minor significance for application on silicon solar cells. Therefore, at the end of this chapter additional first measurements of solar cell upconverter systems under concentrated sunlight illumination will be presented. 5.7.1

Used solar cells and experimental setup

A bifacial back junction rear side contacted silicon solar cell served as the basis for an upconversion photovoltaic device. The solar cell is designed as a concentrator solar cell and is therefore very well suited to be operated under high irradiances that are beneficial for the upconversion efficiency. The active area of the solar cell is 4.5 x 4.5 mm2. Details on the solar cells’ processing and characterization can be found in [145]. This solar cell has both n- and p-contacts on the rear. Under AM1.5G illumination on the grid-free planar side, the solar cell exhibits around 19 % efficiency. Without an upconversion layer, no spectral response could be measured at wavelengths between 1400 nm and 1600 nm. The solar cell was operated upside down, i.e. it was illuminated from its rear. In this configuration, various upconverters could be attached to the former front side and the contacting of the solar cell was not hindered by the application of the upconverter. To avoid total internal reflection of light in the infrared that should reach the upconverting material, the grid-free side of the solar cell was not textured. On the other hand, having

204

5.7 Upconversion systems

all contact fingers on the front causes serious shading losses. The geometric coverage of the grid fingers amounts to roughly 60 % of the active cell area. This cell design is therefore not suited to reach the highest efficiencies, but it is a convenient test device for the experiments. Fig. 5.35 shows the schematic setup for the external quantum efficiency (EQE) measurements. During the measurements, the solar cell was placed on a measurement chuck. The measurement chuck has an opening for the upconverter and other optical materials. The chuck is coated with gold to achieve a high reflection in the infrared.

Fig. 5.35: Schematic graph of the experiment for EQE measurements of a solar cell with upconversion in the IR spectral region. The upconverter is attached to the planar grid-free side of a bifacial silicon solar cell. The same tunable IR-laser as for the optical characterization was used to illuminate the solar cell upconverter systems. Due to different geometrical properties of the experimental setup, higher irradiances for the excitation compared to the optical measurement were possible. The external quantum efficiency of the solar cell upconverter systems was measured in the range of 1430 nm to 1630 nm with an irradiance of 1090 Wm-2. The excitation beam was chopped with low 9 Hz because of the long lifetime of the excitation of the energy levels from the trivalent erbium (see section 5.5.4). Additionally, a continuous bias illumination of 0.04 suns was applied.

205

5 Upconversion

The short-circuit current of the solar cell due to upconverted photons ISC,UC(Oinc,I) under excitation with a wavelength Oinc and an irradiance I was measured using a lockin amplifier 7265 from signal recovery. The external quantum efficiency was obtained as the ratio of the short-circuit current of the upconversion system and the short-circuit current ISC,ref(Oinc,I) of a germanium reference cell illuminated under the same conditions. The external quantum efficiency of the germanium cell EQEref(Oinc) is known from different measurements with standard solar cell characterization equipment. So the EQE of the upconversion solar cell system EQEUC(Oinc,I) can be calculated by

EQEUC (Oinc , I )

EQEref (Oinc )

I SC ,UC (Oinc , I ) . I SC , ref (Oinc , I )

(5.73)

The uncertainty of the EQEref(Oinc) in the IR spectral region from the calibration of the setup is lower than 3 %, but it is still the dominating error. The statistical errors of both short-circuit currents calculated from 25 measurement points at the same Oinc and I are typically much lower. 5.7.2

Applying the upconverter to the solar cell

Since NaYF4 : 20 % Er3+ is a microcrystalline powder, some kind of binding agent is needed to apply the upconverter to the solar cell. Two different binding agents were tested in this work: the silicone gel Sylgard 184 and zapon varnish. The silicone acts as a transparent matrix material, in which particles of the upconverter material are dispersed. Samples with different weight concentrations of the upconverter in the silicone and two different thicknesses (approximately 1.5 mm and 3.0 mm) were produced. Silicone is well suited for low weight concentration of the upconverter in the mixture. At high upconverter concentrations, processing of the silicone/upconverter mixture is difficult and the optical quality poor. Additionally, silicon shows quite strong absorption in the spectral region around 1500 nm to 1600 nm, which is disadvantageous as this is the absorption range of the NaYF4 : 20 % Er3+. In contrast, zapon varnish is more like glue that connects and stabilizes the particles of the powder and is therefore applicable for very high upconverter concentrations. The upconverter powder was mixed with zapon varnish. Subsequently, the samples were dried at room temperature. The obtained samples vary in their geometrical properties

206


like thickness and shape, but not much in the concentration of the upconverter in the mixture, which is close to 100 %. The various solidified powder upconverter/binding agent mixtures were optically connected with a refractive index matching liquid to the silicon solar cell, and the EQEUC(Oinc,I) was measured. 5.7.3

External quantum efficiency with different upconverter samples

The EQEUC(Oinc,I) was measured for various upconverter samples. Fig. 5.36 shows the EQEUC(Oinc,I) for the best samples with silicone and zapon varnish. The best silicone sample was 3.0 mm thick and had a weight concentration of 25 % of the upconverter in the silicone. The best sample made from zapon varnish was roughly 0.9 mm thick and had an upconverter concentration of almost 100 %. Both systems were measured with an irradiance of 1090 Wm-2. The EQEUC(Oinc,I) of the best silicone sample peaks only at 0.11 %. This low efficiency can be partly attributed to the overall low upconverter concentration in this sample. Furthermore, the unwanted absorption of the silicone in the absorption region of the erbium further reduces efficiency. The zapon varnish sample shows much higher efficiencies. The EQEUC(Oinc,I) peaks at 0.34 % at a an incident wavelength of 1522 nm. Just as for the optical efficiency, a normalized quantum efficiency EQEUC,norm(Oinc,I) can be calculated by dividing the efficiency by the irradiance. This makes values obtained at different irradiances more comparable. With an irradiance of 1090 Wm-2 the EQEUC,norm(Oinc,I) is 0.03 cm2W-1 and therefore 2.2 times higher than best value known so far that was measured by Richards [107]. A strong oscillation is visible in the EQEUC(Oinc,I) signal. The oscillation is caused by oscillations in the transmission of the silicon solar cell as plotted in Fig. 5.37. These oscillations are very likely the result of interference effects within the cell. The transmission in the spectral region of 1430 nm to 1630 nm varies between 25 % and 45 % with a period length of approximately 2.5 nm. Due to this variation in the transmission, the EQEUC(Oinc,I) varies by two effects: first, more or less photons impinge on the upconverter and therefore less photons can be converted. Second, since upconversion is a non-linear process, the efficiency is increasing with increasing photon flux and decreasing when the photon flux is lower.

207

5 Upconversion

Fig. 5.36: EQE measurement of a silicon solar cell with two different upconverter samples optically coupled to its back: one sample with the upconverter immersed in silicone with a relatively low concentration of the upconverter in the silicone, and one sample with the upconverter glued together with zapon varnish with a relatively high concentration of the upconverter in the mixture. The sample with the high upconverter concentration shows a much higher efficiency. This is attributed to the higher upconverter concentration and also to some unwanted absorption in the silicone. The strong oscillations in the EQEUC are caused by the oscillating transmission of the silicon solar cell (see Fig. 5.37)

Fig. 5.37: Transmission of the silicon solar cell in the IR spectral region. Very likely interference effects within the cell cause the strong oscillations.

208


5.7.3.1

Comparison to optical measurements

Fig. 5.38 shows the EQEUC(Oinc,I) divided by the transmission Tcell(Oinc) of the solar cell. However, this division only eliminates the first effect, but the effect caused by the non-linear upconversion efficiency remains. Hence, the effect of the solar cell’s transmission can not be fully eliminated. Nevertheless, a similarity of the EQEUC(Oinc,I) divided by the transmission of the solar cell to the optically determined KUC(Oinc,I) from Fig. 5.24 becomes visible.

Fig. 5.38: The EQEUC(Oinc,I) divided by the transmission of the silicon solar cell Tcell in comparison to the integrated optical efficiency presented already in Fig. 5.24. By dividing the electrical measurement by the solar cells transmission the strong oscillations in the signal can be partly eliminated. In this way, the substructure formed by the sub energy levels of the Er3+ is visible in both measurements that are well in agreement. The quantum efficiency at 1522 nm is 0.7 % for the EQEUC(Oinc,I)/Tcell(Oinc). This is the quantum efficiency for the photons that actually reached the upconverter. This quantum efficiency reflects the efficiencies of the several involved processes: the quantum efficiency of the upconversion, the efficiency by which upconverted photons reach the solar cell, and the utilization of the upconverted photons by the solar cell. The dominant peak of the upconversion emission is at 980 nm. The external quantum efficiency of the solar cell EQEcell(O) at 980 nm is roughly 50 %. Therefore, the optical upconversion efficiency is estimated to be 1.4 %. At around 1522 nm the silicon solar cell transmits roughly 40 % of the light. Therefore the actual irradiance impinging on the upconverter is 440 Wm-2. The optical

209

5 Upconversion

upconversion efficiency KUC(Oinc,I) at this irradiance is 1.9 % at the lower limit (see section 5.5.6). That means that the results from the electrical measurement are a little bit lower than that what would be expected from the optical measurements. This could be the result of additional optical losses. For instance, the upconverted light will impinge from all angles onto the silicon surface, resulting in reflection losses especially for shallow angles of incidence. Furthermore, there is scattering and parasitic absorption within the upconverter and in the zapon varnish. Moreover, there will be electrical losses due the inhomogeneous illumination of the solar cell. Taking these losses into account, one can state that the optical and the electrical measurements are very well in agreement. 5.7.3.2

Intensity dependence of EQE

Fig. 5.39 shows the EQEUC(Oinc,I) and the EQEUC,norm(Oinc,I) for different irradiances at a wavelength of 1522 nm of the incident photons. While the EQEUC(Oinc,I) increases with increasing irradiance, the EQEUC,norm(Oinc,I) slightly decreases. This means that the EQEUC(Oinc,I) grows a little bit less than linearly with the irradiance, which would have been the expectation for a perfect two photon process and a three level system. Already in the optical measurements the characteristic exponents had been lower than the theoretical expectations (Fig. 5.22) and saturation effects had occurred for higher irradiances. Therefore this result is well in agreement with the optical measurements.

Fig. 5.39: The EQEUC(Oinc,I) of the solar cell/upconverter device increases with higher irradiances. The EQEUC,norm(Oinc,I) defined as the ratio of EQEUC and irradiance, however, is slightly decreasing. This means that the EQEUC(Oinc,I) grows a little bit less than linearly with the irradiance.

210


5.7.3.3

Time-resolved solar cell response

Besides the spectrally resolved features, it is interesting as well, whether the timeresolved features of the optical measurement could also be found in the response of the solar cell upconverter system. The upconversion solar cell response under excitation with 1522 nm was measured as a function of time using a Tektronix TDS3034 digital oscilloscope. Fig. 5.40 shows the time-resolved response. It exhibits a very slow decay. A single-exponential fit holds a decay time constant of 17.9 ms. Because the response of a silicon solar cell is magnitudes faster, this time constant has to be attributed to the luminescence decay of the upconversion layer. The time constant of 17.9 ms is slightly larger than the 13 ms as reported in section 3 for the state 4I11/2, which is responsible for the dominant 980 nm luminescence. Bearing in mind that the 4I11/2 decay was observed optically after pulsed excitation into the 4F3/2 level whereas the solar cell response decay followed a continuous wave excitation of the transition 4I15/2 Æ 4I13/2 Æ 4I9/2 and supposedly a multi-phonon relaxation 4I9/2 Æ 4I11/2, the agreement is reasonable.

Fig. 5.40: The solar cell short-circuit current shows a build-up and decay pattern as observed for E-NaYF4: 20% Er3+. The decay time constant of 17.9 ms was obtained by a single-exponential fit. 5.7.4

Upconversion solar cell system under concentrated sunlight

The spectrally resolved measurements presented in the previous section are well suited to investigate the spectral behavior of the upconverter. However, the later application will be under continuous illumination with a broad spectrum. Therefore, the best

211

5 Upconversion

upconverter/solar cell device based on the zapon bound upconverter was measured under concentrated white light to determine the short circuit current ISC. 5.7.4.1

Experimental setup and method

Fig. 5.41 shows a schematic of the experimental setup. Several lenses concentrate the light of a sun simulator onto the solar cell. To increase the relative impact of the upconversion layer, a polished silicon wafer with a thickness of 160 µm blocks most of the light that can be used directly by the silicon solar cell, but transmits the far IR photons suitable for upconversion. However, a part of the light that can be used directly by the silicon solar cell is still transmitted. This light has the function of a bias illumination that ensures that the solar cell is operated under sufficient illumination conditions to be able to make efficient use of the upconverted photons. In this configuration, the benefit of the upconversion due to a raised short-circuit current ISC is much more easily detectable than under full AM1.5 sun illumination.

Fig. 5.41: Schematic of the setup to measure the IV-characteristic of solar cells under concentrated white light. With lenses, the light of a Xe-lamp is concentrated on the solar cell. A polished silicon wafer serves as a long pass filter (see Fig. 5.42). The measurement chuck can be cooled and its position fixed with a vacuum exhaust.

212


The optical properties of the used silicon wafer are plotted in Fig. 5.42. Below a wavelength of 1180 nm, the transmission decreases from roughly 53 % to 0 % at wavelengths shorter than 930 nm. Therefore, some photons usable by a silicon solar cell are transmitted and induce a small offset current. The solar cells were mounted on the same measurement chuck as described in the previous chapter for the measurements of the external quantum efficiency. The chuck was cooled to keep the solar cell temperature near standard conditions. However, as the upconverter was mounted underneath the solar cell, the full solar cell did not have direct thermal contact with the cooled chuck. Therefore, an unavoidable inhomogeneous temperature profile might have been present in the solar cell during the measurements.

Fig. 5.42: Optical properties of the polished silicon wafer used as long pass filter. Above 1200 nm it shows no significant absorption. In this spectral region, the reflection is around 47 %. This means 53 % of the photons suitable for upconversion are transmitted. Between 930 nm and 1150 nm some photons are transmitted that can produce free carriers in a silicon solar cell. The concentration of the light was measured with a calibrated back contact Si solar cell designed for concentrated light, similar to the cells used in the silicon solar cell upconverter device. With the ISC of the reference cell under concentration and the ISC under one sun the concentration of the impinging light can be calculated. With two different settings of the lenses, two different concentration levels were reached. These concentration levels were 147±2 and 242±6 suns. In the calculation of these results, the mismatch between the AM1.5 norm spectrum and the spectrum of the Xe-lamp

213

5 Upconversion

modified by the transmission of the lenses has been taken into account. The light spot is not fully homogeneous. Therefore the concentration level varies slightly with the exact position of the solar cell. To make sure that observed differences are due to real effects and not due to different positions of the device, every measurement was repeated 5-6 times and for each repetition the solar cell was removed and mounted again to cover the fluctuation due to different positions in the determined uncertainty as well. The given uncertainty is the uncertainty of the average value of the repeated measurements. The additional silicon wafer transmits roughly 53.5 % in the spectral area below the band-gap of silicon. Therefore, one can state that the effective concentration level of the light impinging on the silicon solar cell/upconverter system corresponds to a concentration of 79±1 and 129±3 below the band-gap of silicon. However, these concentration levels can only be used as a rough orientation, as the spectral region below the band-gap of the silicon was not considered in the determination of the concentration level with silicon solar cells. Therefore, for efficiency calculations, exact photon fluxes in the relevant spectral regions will be used later on. These photon fluxes could be calculated from the measurement of a relative spectrum of the Xe lamp and the presented determination of the concentration levels with the silicon solar cells. NaYF4 : 20 Er3+ is a good diffuse reflector as well. Therefore, photons with energies slightly above the band-gap of silicon could be reflected by the upconverting powder and absorbed by the silicon solar cell. In this case, the application of the upconverter would increase solar cell efficiency without any significant upconversion taking place. Therefore, the ISC was measured from the silicon solar cell with a diffuse reflector without upconverting properties optically coupled to the back of the solar cell. For this purpose, polytetrafluorethylene (PTFE, also known as Teflon) was used, which is a very good reflector and often used as reflection standard. A comparison of the reflectivity of PTFE and a thick, approximately 0.9 mm, layer of the NaYF4 : 20 Er3+ solidified with zapon varnish dried on an optical glass is plotted in Fig. 5.43.

214


Fig. 5.43: Comparison of the reflectance of the NaYF4 : 20 % Er3+ solidified with zapon varnish on an optical glass and the reflectance of PTFE. The upconverter sample shows some absorption peaks at wavelengths of the transitions between the energy levels and reflects overall roughly 10 % less than PTFE. It is obvious that the reflection of the PTFE is higher than that of the upconverter sample. Therefore, a short-circuit current measured with upconverter that exceeds the current measured with PTFE back reflector should be a clear sign of a positive effect of upconversion that proves that efficiency can be increased by the application of an upconverter in comparison to a simple back reflector design. To extract the extra current due to the upconverter ISC,UC the average of the shortcircuit current measurements with PTFE reflector ISC,PTFE is subtracted from the average of the measurements with upconverter attached to the silicon solar cell ISC,Zap :

I SC ,UC 5.7.4.2

I SC ,Zap I SC , PTFE .

(5.74)

Results

Table 5.6 shows the different measured and calculated short-circuit current values. Fig. 5.44 visualizes the results. For ISC,PTFE and ISC,Zap the uncertainties of the average values as determined from the repeated measurements are listed as uncertainties. The uncertainty of ISC,UC was calculated with Gaussian error propagation from these values. The relative error of ISC,UC is quite high, as ISC,UC itself is quite small but the result of the subtraction of two relatively big values. In Fig. 5.44 the uncertainties of the concentration are shown as well. This uncertainty reflects the uncertainty of the average value determined from the repeated measurements of the concentration level.

215

5 Upconversion

Fig. 5.44: Extra short-circuit current due to the upconverter ISC,UC and the spectrally integrated external quantum efficiency of the silicon solar cell upconverter device EQEUC,device()p,cell) at two different concentration levels. This is the first time a significant effect of an upconverter on the short-circuit current of a silicon solar cell was measured under white light illumination. Both extra current and EQEUC,device()p,cell) show a trend of increasing with higher concentration. This fact supports the conclusion that the observed effect is due to upconverted photons as this is the kind of non-linear behavior which is expected from upconverting material. Despite all uncertainties, a significant increase of the short-circuit current due to the upconverter was observed. For instance, at 129x concentration the short circuit current with white PTFE reflector was 3.26 r 0.07 mA. This current was increased by 0.69 r 0.08 mA to 3.95 r 0.04 due to the addition of the upconverting layer. To my best knowledge, this is the first time that such an increase in short-circuit current due to upconversion has been measured on a silicon solar cell under white light. From the short-circuit current measurements a spectrally integrated external quantum efficiency of the solar cell/upconverter device EQEUC,device()p,cell) can be calculated via

EQEUC , device () p , cell )

I SC ,UC . q ) p , cell

(5.75)

In this equation q is the elementary chargeand)p,cell is the photon flux impinging on the solar cell in the absorption range of the upconverter. For calculating this photon flux, the transmission of the additional silicon wafer, the area of solar cell of 4.5 x 4.5 mm2, the concentration level and the changes in the spectrum due to the addition of lenses were taken into account. This flux critically depends on which

216


spectral range is chosen to be the absorption range of the upconverter. Therefore the calculations were performed for three different absorption ranges: a narrow range from 1480-1630 nm, in which the upconverter shows significant response (see Fig. 5.24), a medium range from 1460-1600 nm, which includes as well the spectral ranges in which the upconverter shows very little response, and a very wide range from 14301630 nm. The corresponding photon fluxes and the resulting efficiencies are listed in Table 5.6. The EQEUC,device()p,cell) for the medium absorption range is plotted as well in Fig. 5.44. The theoretical expectation is that the integrated quantum efficiency increases with increasing irradiance because of the non-linearity of the upconversion. Unfortunately, experimental uncertainty is quite high for the higher concentration measurement, mainly due to a smaller illumination spot with higher inhomogeneity with a resulting higher sensitivity to the solar cell position. Nevertheless, a clear trend that both the extra current and the EQEUC,device()p,cell) increase with increasing irradiance is visible. This agreement with the theoretical expectation supports the conclusion that the observed effect is due to upconversion. For further evidence measurements should be performed with a larger set of concentration levels. It is an interesting question, how the upconversion efficiencies under white light illumination compare to those measured with monochromatic laser excitation. For this purpose, it has to be considered that only roughly 40 % of the photons impinging on the solar cell are transmitted through the cell (see Fig. 5.37). The photon flux impinging on the upconverter )p,abs,UC is estimated to be

) p ,abs ,UC

) p ,cellTcell ,

(5.76)

This result can only be an estimate, because the upconverter is optically coupled to the solar cell, while the transmission measurements were performed with the silicon solar cell in air. In consequence the reflection from the grid-free surface is present in the transmission data, but will be less pronounced in the data of the system measurements. Nevertheless, the estimate should be reasonable because most of the overall reflection is due to the unchanged reflection of the grid, which covers nearly 60% of the front surface, while the grid-free surface was equipped with an antireflection coating and therefore has low reflection. Additionally, it has to be taken into account that the EQE of the solar cell EQEref(Oinc) is only 50% at 980 nm, where the dominating peak of the upconversion emission occurs. In consequence, the optical measurement equivalent efficiency of the upconversion KUC,converter()p,abs,UC) can be estimated to be:

KUC , converter () p , abs ,UC )

I SC ,UC , q ) p , abs ,UC EQEref (980 nm)

217

(5.77)

5 Upconversion

Table 5.6: Summary of the results of the measurements under concentrated white light Concentration onto the solar cell upconverter device

79r1

129r3

ISC,PTFE [mA]

1.67 r 0.02

3.26 r 0.08

ISC,Zap [mA]

1.99 r 0.02

3.95 r 0.04

ISC,UC [mA]

0.33 r 0.03

0.69 r 0.08

1430-1630 nm

(3.62 r 0.04)1017

(5.78 r 0.13)1017

1460-1600 nm

(2.53 r 0.03)1017

(4.04 r 0.09)1017

1480-1580 nm

(1.80 r 0.02)1017

(2.88 r 0.06)1017

1430-1630 nm

0.57 r 0.05

0.77 r 0.09

1460-1600 nm

0.81 r 0.07

1.07 r 0.13

1480-1580 nm

1.14 r 0.09

1.49 r 0.19

1430-1630 nm

2.8 r 0.2

3.7 r 0.5

1460-1600 nm

4.1 r 0.3

5.3 r 0.7

1480-1580 nm

5.7 r 0.5

7.5 r 0.9

2.6-5.3

3.7-7.4

[suns]

Photon flux )p,cell [s-1] With UC absorption range

EQEUC,device()p,cell) [%] With UC absorption range

KUC,converter()p,abs,UC [%] With UC absorption range

KUC,converter(Oinc,)p,abs,UC) measurements [%]

from

optical

218


At a concentration of 129 suns, an optical measurement equivalent upconversion efficiency KUC,converter()p,abs,UC) of 5.3 r0.7 % is reached under the assumption of a medium absorption range of the upconverter. To achieve the same photon flux impinging on the upconverter under laser illumination at 1523 nm as it was impinging in the absorption range of the upconverter during the concentrated white light measurement, a laser irradiance of 1047 Wm-2 is necessary. As can be seen in Fig. 5.26, at this irradiance the lower limit is 3.7 % and the upper limit 7.4 % in the optical measurements. The optical measurement equivalent upconversion efficiency KUC,converter()p,abs,UC) lies perfectly between these limits. This is true as well for the lower concentration level. This result is more special than it appears on first sight. For one, based on the spectral measurements in the absorption range of the upconverter there are wavelengths with associated upconversion efficiency considerably below the peak values. Furthermore, the solar cell only utilizes photons that actually reach the solar cell. This corresponds to the conditions for the lower limit, while the upper limit was based on the assumption that more photons are emitted than detected because of optical losses in the upconverter powder. These two facts would make efficiencies under white light illumination considerably below the lower limit reasonable. In contrast, upconversion efficiencies under white light illumination appear to be at the same height or even higher than under monochromatic excitation. This result can be partly attributed to the uncertainty of determining the photon flux that actually reaches the upconverter. On the other hand, efficiencies are so high that there must be effects that positively influence the efficiency under white light. One possible positive effect is that the energy gaps between the energy levels involved in the upconversion process are not centered on exactly the same energy. Therefore, illumination with slightly different photon energies may enhance the probability of an upconversion process. Additionally, during the experiments with the white light the upconverter is illuminated on a larger area and not with a small spot like with the laser. With only a small area illuminated, a considerable part of the excitation energy could migrate to non-illuminated areas by radiative and non-radiative processes. As excitation intensity in these regions is low, the dissipated energy hardly contributes to upconversion and therefore this dissipation constitutes a loss mechanism. These losses should be reduced under larger area white light illumination. Due to the special definition of upconversion quantum efficiency, the achieved quantum efficiency of around 5% means that 10% of the photons incident in the absorption range of the upconverter were used. This quite positive finding supports the hope that upconverters can successfully enhance silicon solar cell efficiencies.

219

5 Upconversion

5.8

Conclusions and outlook on the application of upconverting materials to silicon solar cells

In this work several promising results were obtained that constitute significant progress in the field of upconversion research. This includes progress in the theoretical modeling, the investigation of the time dynamics of erbium doped NaYF4, calibrated optical measurements that showed up to 10% upconversion efficiency and measurements of complete systems of silicon solar cells and upconverter. Record efficiencies were achieved and for the first time a positive effect of an upconverting layer on the short-circuit current of a silicon solar cell could be demonstrated under white light illumination. Nevertheless, significant challenges remain to be solved until upconversion can be applied successfully to increase silicon solar cell efficiencies. Fig. 5.45 shows the EQE of a silicon concentrator solar cell as used in this work measured with standard solar cell characterization equipment, and the additional response in the spectral range around 1500 nm due to the additional upconversion layer as it was presented in Fig. 5.36 in section 5.7.3. Two facts are obvious from this figure: first, the utilization of the spectrum is still incomplete and the achieved efficiency due to the upconverter is too low to have a significant positive effect on the overall solar cell performance. Furthermore, these efficiencies were achieved under high concentration conditions.

Fig. 5.45: EQE of a silicon concentrator solar cell as used in this work measured with standard solar cell characterization equipment and the additional response in the spectral range around 1500 nm due to the additional upconversion layer as it was presented in Fig. 5.36 in section 5.7.3.

220

5.8 Conclusions and outlook on the application of upconverting materials to silicon solar cells

On the other hand, with spectral concentration a concept was presented, and for the first time a design for its realization introduced, that could positively solve these issues. In combination with a luminescent material, the spectrum could be utilized more completely and additional internal concentration could be achieved. The promising upconversion efficiency of 5%, representing 10% photon utilization, was achieved under white light illumination at a concentration level of 129 suns. This concentration level was calculated from reference measurements with a silicon solar cell and served to calibrate the overall irradiance. If the photon flux in the absorption range of the upconverter from 1460-1600 nm is considered, the effective concentration is about 5.7 times higher because of the differences in the Xe-lamp spectrum modified by the transmission of the lenses in comparison to the AM1.5 norm spectrum. Therefore the effective concentration level for the upconverter is about 735 suns. On the other hand, in the spectral range between the band-gap of silicon and 1460 nm, there are around 13 times more photons than in the absorption range of the upconverter. Therefore spectral concentration could yield an internal concentration factor of around 10, assuming a quantum efficiency of 80% of the luminescent nanocrystalline quantum dots (NQD). Additionally, the NQD could be incorporated into a fluorescent concentrator as discussed in section 5.2.5. This could yield an additional concentration of at least a factor of 10. Therefore, an overall internal concentration of a factor of 100 should be possible. In consequence, high enough concentration levels for high upconversion efficiencies should be achievable with low external concentration factors of around 10, and in any case with higher concentrating systems. However, considerable progress in the field of luminescent NQD and especially in their incorporation into transparent matrix materials is necessary to make this concept possible. Moreover, the investigated solar cell/upconverter system structures can be further developed in addition to the concept of spectral concentration to achieve efficiencies well beyond the level of today. One issue is the optimization of the upconverter material itself. For instance it will be interesting to investigate whether replacing Y by La, Gd, or Lu in the NaYF4 host lattice can increase upconversion efficiencies because the maximum phonon energy and thus the unwanted non-radiative decay is reduced. Until now, an unexplored possibility is the use of neodymium instead of erbium. Neodymium features energy levels suitable for upconversion for an excitation at around 1650 nm [146]. This would be advantageous because lower energy photons could be used and a larger number of photons could contribute to spectral concentration. Additionally, neodymium features larger absorption cross sections. On

221

5 Upconversion

the other hand, energy levels in between the levels involved in the upconversion could induce losses. Finally, the solar cell itself has to be optimized to make the best use of the upconverted light. A first step is to have aligned contacts on both surfaces of the solar cell, to reduce the shading losses in comparison with the solar cell used in this study. Another important issue is the optical coupling of the solar cell and the upconverter to achieve high transmission of light in both directions. Accordingly, specially adapted antireflection coatings have to be developed. To convert the light emitted from the upconversion system efficiently, the solar cell must possess a bifacial layout with high rear side efficiency. Under illumination from the back, most electron-hole pairs are generated close to the back surface of the crystalline silicon solar cell. To achieve high rear side efficiency, a high diffusion length of the generated free carriers is necessary so they can reach the p/n-junction close to the front. In consequence, n-type silicon would be a good choice, as n-type silicon shows significantly higher diffusion lengths than the common p-type silicon [147]. A possible design is shown in Fig. 5.46.

Fig. 5.46:

Design for a solar cell optimized for the application of an upconverter. The main features are: n-type material to achieve a high rear side efficiency, adapted anti-reflection coatings for high transmission, both for the upconvertible light and the upconverted light, and an aligned contact grid design on back and front surface to avoid shading losses.

The first application of upconversion will be in concentrator modules using crystalline silicon solar cells. A first reason for this assumption has been discussed extensively in this work: the solar cells and hence the upconverter system is illuminated with higher intensities in concentrator modules. Because of the non-linear characteristic of the

222

5.8 Conclusions and outlook on the application of upconverting materials to silicon solar cells

upconverter this results into higher upconversion efficiencies and the positive effect of the upconverter is more pronounced. But there are additional reasons: the specific costs per area can be higher than in large-area modules. Furthermore, processing of the solar cells and assembly of the concentrator modules have more elements of a pick-andplace-technology. This resembles modern lighting technology, which involves as well luminescent material and structures that are related to the proposed upconversion system. Today’s concentrator technology is dominated by expensive multi-junction solar cells based on III-V semiconductors. Applying the upconverting systems will help to narrow the efficiency gap between silicon solar cells and the multi-junction cells, while maintaining the cost advantage of silicon solar cells. As there will be internal concentration onto the upconverter, the upconverter will not cover the whole area and therefore only little amounts of upconverter material are necessary, hence material costs will be reasonably low. Therefore the cost efficiency is critical determined by how much extra processing costs occur. These could be kept low, if the addition of the upconverter system is incorporated into the cell production and the module assembly. For instance, photonic structures made from silicon alloy could simultaneously provide surface passivation on the solar cell and therefore no extra processing step would be required, or the matrix material with the embedded luminescent materials could provide the mechanical interconnection of the cell to the module and would therefore replace the glue in current modules. In consequence, it is likely that the achievable efficiency increase will be high enough to justify the additional costs for an upconversion system. The application of upconversion is not limited to crystalline silicon solar cells. Because it only requires adding an optically active layer system to solar cells without influencing the electrical properties, upconversion can be applied to nearly all existing or emerging solar cell technologies. If high enough internal concentration were reached, thin-film photovoltaics could be an attractive surrounding for the application of upconversion. Micro-crystalline silicon solar cells, for instance, show low current densities due to incomplete absorption of light at longer wavelengths. On the one hand, this is a challenge for the use of the upconverter radiation. On the other hand, a larger amount of unused photons is available for upconverting in a broader spectral range. This will provide for a higher flux of unconvertible photons, which is advantageous because of the non-linear behavior of the upconversion efficiency. Furthermore, the relative increase in current due to the upconverter could be higher. In consequence, upconversion has the potential to lower costs for different kinds of photovoltaic technologies and therefore will potentially find widespread application throughout photovoltaics.

223

6

Summary

Most solar cells today are made from silicon. However, silicon solar cells do not use the full solar spectrum. They do not absorb photons with energies below the band-gap of silicon, and they convert the energy of photons which exceeds the band-gap into heat instead of electricity. Several concepts are discussed to overcome the resulting fundamental efficiency limits. One especially promising concept is photon management. Photon management means the splitting or modifying of the solar spectrum before the photons are absorbed in the solar cells in such a way that the energy of the solar spectrum is used more efficiently. Photon management has the advantage that the solar cells themselves remain fairly unchanged and well-established solar cell technologies can be used. Therefore, photon management has a high potential for realization. In this thesis, I explored concepts to increase the efficiency of photovoltaic systems with the means of photon management. I concentrated on two related concepts using luminescent materials that feature many advantages: first, fluorescent concentrators with photonic structures, and second, upconversion of sub-band-gap photons. For both concepts, this work comprises theoretical models and simulation tools that highlight the important mechanisms and processes, help the general understanding of the concepts and allow one to draw new conclusions on general working principles. The experimental work ranged from basic material investigations, for which new methods were developed and new experimental setups realized, to the fabrication and characterization of complete photovoltaic systems, for which record efficiencies were achieved. Finally, based on the findings of this work, new system designs were developed in both fields that constitute real conceptual progress, documented in granted patents and pending patent applications.

6.1

Fluorescent concentrators

Fluorescent concentrators are a well-known concept to concentrate both diffuse and direct light without tracking. A fluorescent concentrator consists of a slab of a transparent matrix material doped with a luminescent material. The luminescent material absorbs incoming radiation and subsequently emits radiation with a longer wavelength. Most of the emitted radiation is trapped by total internal reflection and guided to solar cells mounted at the edges of the fluorescent concentrator. A stack of different fluorescent concentrators with different luminescent materials can use a wide

225

6 Summary

spectral range. Such a configuration can be used to split the solar spectrum, because the different fluorescent concentrators each collect different fractions of the spectrum. In combination with spectrally adapted solar cells, each fraction can be converted by solar cells that are the most efficient in that spectral range. In this work, I presented entropic considerations that show that the maximum achievable concentration depends on the Stokes shift between absorbed and emitted radiation. Because of the energy dependence, the imposed fundamental limit could become critical for fluorescent concentrators operating in the infrared. Therefore during the development of NIR emitting materials for fluorescent concentrators, care must be taken to achieve large enough Stokes shifts. I presented a thermodynamic model of fluorescent collectors, in which the chemical potential of the excited dye molecules is an important parameter. The chemical potential determines the emission of radiation through the generalized Planck’s law. The chemical potential and consequently the emission of light are not constant throughout the cross-section of the collector, because of the absorption profile in the collector. This was found to be the main source for the asymmetric angular distribution of the light leaving the edges of the collector, which has been determined experimentally in this work. I developed a new method to determine the spectral collection efficiency of fluorescent collectors. Only three optical measurements with a photospectrometer and an integrating sphere are necessary to determine the ability of the concentrator to guide light to its edges. This method constitutes a fast and easy way to scan reasonably similar samples to find the one, which is best suited for application in fluorescent concentrator systems. For fully quantitative results on an absolute scale, for samples with large Stokes shifts and/or very different properties, additional corrections must be applied. For the investigated samples, the spectral collection efficiency reached values above 60% in the absorption region of the used dye. A comparison with results from external quantum efficiency measurements on a system with fluorescent collector and attached solar cells showed good agreement. The information necessary for the correction can also be used to derive additional relevant data, such as the absorption of the dyes in use and the fraction of light lost into the escape cone. Photoluminescence measurements showed that the photoluminescence spectrum of the dyes in the concentrators depends on the excitation wavelengths. However, due to re-absorption of emitted light no differences are present in the spectrum of the light that leaves the concentrators at the edges.

226

6.1 Fluorescent concentrators

A simulation tool for the light-guiding properties of the fluorescent collector was developed, which is based on Monte-Carlo methods. This tool allows testing different hypotheses that could explain the results of the optical characterization. The shape of the photoluminescence spectrum emitted by the dye and the angular distribution of this emitted light proved to be very important for the properties of the collector. In contrast, scattering and the dependence on the excitation wavelength of the photoluminescence spectrum were found to be of minor importance. The model should be further developed to include wavelength dependent emission anisotropy. With such an amendment the simulation could be used for the optimization of key parameters of fluorescent concentrator systems. For the realization of fluorescent concentrator systems, specially adapted solar cells made from GaInP and GaAs were produced. These materials were chosen because their band-gap and therefore the resulting solar cell characteristics fitted nicely to the emission of the used luminescent materials. The solar cells have special geometries and adapted antireflection coatings. With these solar cells and different fluorescent collector materials, several different systems were realized. I demonstrated that the collection efficiency of fluorescent concentrator systems can be increased by two independent measures. First, the combination of different dyes enlarges the used spectral range. In this way, a high efficiency of 6.9% was achieved. Second, photonic structures that act as a bandstop reflection filter in the emission range of the dye reduce the escape cone losses and therefore increase the collection efficiency of the overall system. The system efficiency could be increased by 20% with a commercially available filter. With the achieved efficiency of 3.1% and the concentration ratio of 20, the realized fluorescent concentrator system produces about 3.7 times more power than the used GaInP solar cell had produced on its own. The detailed analysis of size effects showed that photonic structures are especially beneficial for larger systems. With the achieved efficiencies, it is obvious that fluorescent concentrators are no highefficiency approach. Hence, in practical applications the achieved concentration ratio and the resulting cost reduction potential will be important. To make fluorescent concentrators commercially attractive, system sizes and efficiency have to be increased. One important issue is to extend the used spectral range into the infrared. One concept that might help to increase concentration levels and light guiding efficiency is the novel “Nano-Fluko” concept presented in this work.

227

6 Summary

6.2

Upconversion

Photon upconversion of sub-band-gap light is a promising approach to overcome the fundamental problem of sub-band-gap losses while still retaining the advantages of silicon photovoltaic devices. An upconverter generates one high-energy photon out of at least two low-energy photons. Several mechanisms cause upconversion, of which excited state absorption (ESA) and energy transfer upconversion (ETU) are the most frequent ones. The involved processes can be theoretically described with the help of Einstein coefficients. The derived model allows theoretically predicting the intensity dependence of the upconversion luminescence. At low excitation irradiance, the upconversion luminescence from one level obeys a power law with a characteristic exponent k, which reflects the number of photons necessary to populate this level. For higher irradiance the increase in luminescence saturates because stimulated emission processes and population of higher levels become more important. The Einstein coefficients can be determined from absorption coefficient data, with the help of the Judd-Ofelt theory. In this work, erbium doped microcrystallineE-NaYF4 was investigated as an upconverter material. This material was only available as microcrystalline powder, which makes absorption measurements difficult. Therefore, the Kubelka-Munk theory was applied to derive the absorption coefficient of the material from reflection measurements on samples of various thicknesses. With the combination of these theories, the Einstein coefficients could be estimated that served as input for further theoretical modeling. Based on the obtained Einstein coefficients and the according theory, a simulation tool that models the upconversion dynamics was developed. The model includes ground state and excited state absorption, energy transfer and multi-phonon relaxation. The model is capable of reproducing qualitatively experimental results such as the dependence of the upconversion luminescence on the irradiance. The model can be used to study the effect of different parameters, such as the multi-phonon relaxation, on the upconversion dynamics. It was found that multi-phonon relaxation critically determines the relative occupation of the different levels and also affects the dependence on the irradiance. The effect of plasmon resonance in metal nanoparticles on the upconversion was investigated using the model. The intensity distribution around a gold nanoparticle of 60 nm radius was found to increase upconversion luminescence by 16% in comparison to the case without the particle. Time-resolved photoluminescence measurements yielded first insights into the time dynamics of the involved processes. Long time constants were found for the excitation

228

6.2 Upconversion

decay of two energy levels that are most important for the upconversion for silicon solar cells. The time constants depend on the erbium upconverter concentration. From this dependence it could be concluded that energy transfer plays a very important role in the luminescence dynamics, and therefore most likely for upconversion as well. Intensity dependent photoluminescence measurements showed an increase of photoluminescence intensity with increasing irradiance following a power law as predicted from theory. With calibrated photoluminescence measurements it was possible to directly determine the upconversion efficiency. Spectrally resolved measurements showed an active and efficient spectral range from 1480-1580 nm. Integrated upconversion efficiency increased with increasing irradiances to 10.2 % at the upper limit at an irradiance of 1880 Wm-2 at a wavelength of 1523 nm. Because at least two low-energy photons are necessary to generate one high-energy photon, this means that more than 20% of the incident photons contributed to the generation of upconverted photons. Normalized to the excitation irradiance, this is the highest upconversion efficiency achieved so far. The E-NaYF4:20% Er3+ was applied to bifacial silicon concentrator solar cells in different binding agents. External quantum efficiency measurements of the complete system showed very good agreement with the optical measurements. The efficiency of the complete system peaks at 0.34% in the upconversion regime at an incident wavelength of 1522 nm and an irradiance of 1090 Wm-2. Normalized to the intensity, this is again the highest measured value. These experiments were carried out under monochromatic laser excitation. However, solar cells are used in sunlight. Therefore, measurements under concentrated white light were performed as well. For the first time in the context of upconversion for silicon solar cells, a positive effect of an upconverting layer on the current could be measured under white light. Very interestingly, the achieved efficiencies for a broader spectral range are at the same level as the peak values under monochromatic excitation. This means that there must be mechanisms that influence upconversion efficiency positively under white light excitation. The better excitation of all involved transitions with slightly different energies and a larger illuminated area could be possible explanations. The positive results under white light illumination promise that upconversion can be applied to enhance silicon solar cell efficiencies. On the other hand, prior to an industrial application, the used spectral range and the achieved efficiencies must be increased considerably. The presented concept of spectral concentration might help to achieve this goal: a luminescent material absorbs in a wide spectral range and emits in

229

6 Summary

the absorption range of the upconverter. This increases efficiency by two mechanisms: first, more photons are used, and second the photon flux in the absorption range of the upconverter is increased, increasing the upconversion efficiency. For the realization of this concept, I developed a system design that combines spectral concentration with geometric concentration by a fluorescent concentrator. Therefore the high concentration levels needed for sufficient upconverter efficiencies can be achieved internally without high external concentration. The application of spectrally selective, reflective photonic structures, avoids re-absorption losses and the solar cell is equipped with a good back-reflector. For the realization of this concept, progress in the implementation of luminescent nanocrystalline quantum dots is necessary. Further fields for optimization are the silicon solar cells, which should be adapted to make better use of the upconverter light, and the upconverter itself, where new materials might boost efficiency. In conclusion, new insights were gained and significant progress was achieved in the two investigated fields, fluorescent concentrators and upconversion. This progress opens a positive perspective for the application of photon management. Nevertheless, considerable efforts are still necessary until these concepts can fulfill their promise to reduce solar electricity costs and to help the widespread dissemination of photovoltaics.

230

7

Deutsche Zusammenfassung

Die meisten Solarzellen werden heutzutage aus kristallinem Silizium hergestellt. Diese Solarzellen nutzen die im Sonnenspektrum enthaltene Energie aber nur unvollständig aus. Photonen mit einer Energie unterhalb der Bandlücke werden nicht absorbiert. Bei Photonen mit Energien oberhalb der Bandlücke geht der Teil der Energie, der die Bandlücke übersteigt, als Wärme verloren. Es gibt mehrere Konzepte, wie diese prinzipiellen Verluste reduziert werden können. Besonders vielversprechend ist dabei der Ansatz des Photonen-Managements. Photonen-Management zielt darauf, den Wirkungsgrad von Solarzellensystemen zu erhöhen, indem das Sonnenspektrum aufgeteilt oder verändert wird, bevor das Sonnenlicht von Solarzellen absorbiert wird. Der Vorteil dieses Ansatzes ist es, dass die eigentlichen Solarzellen im Wesentlichen unverändert verwendet werden können und deshalb auf etablierte Solarzellentechnologien zurückgegriffen werden kann. Im Vergleich zu anderen Ansätzen hat das Photonen-Management deshalb ein hohes Realisierungspotenzial. In dieser Arbeit habe ich zwei verwandte Konzepte des Photonen-Managements untersucht: Fluoreszenzkonzentratoren mit photonischen Strukturen und die Hochkonversion von Photonen mit Energien unterhalb der Bandlücke von Silizium. Diese Konzepte verbindet, dass lumineszente Materialien zum Einsatz kommen. Für beide Konzepte wurden theoretische Modelle aufgestellt sowie Simulationsprogramme entwickelt. Mit diesen Modellen konnten die wesentlichen Wirkmechanismen untersucht und das Verständnis vertieft werden. Die experimentellen Arbeiten reichten von der Untersuchung wesentlicher Materialeigenschaften bis zur Realisierung und Charakterisierung kompletter Solarzellensysteme. Für die experimentellen Untersuchungen wurden zum Teil neue Methoden entwickelt und neue Versuchsaufbauten realisiert. Aufbauend auf den Ergebnissen dieser Arbeiten wurden in beiden Gebieten konzeptionell weiterführende Ansätze für neue Systemarchitekturen entwickelt. Diese wurden zum Teil bereits patentiert bzw. sind Gegenstand laufender Patentanmeldungen.

7.1

Fluoreszenzkonzentratoren

Fluoreszenzkonzentratoren sind ein bekanntes Konzept, um diffuses und direktes Sonnenlicht zu konzentrieren, ohne dass dazu das Photovoltaiksystem der Sonne nachgeführt werden muss. Fluoreszenzkonzentratoren bestehen aus einem transparenten Material, in welches ein lumineszentes Material eingebracht wurde. Das

231

7 Deutsche Zusammenfassung

lumineszente Material absorbiert einfallende Strahlung und emittiert anschließend Strahlung mit einer etwas größeren Wellenlänge. Der Großteil der emittierten Strahlung wird durch Totalreflexion im Konzentrator gefangen und zu Solarzellen an den Seitenflächen geleitet. In einem Stapel mit unterschiedlichen Fluoreszenzkonzentratoren kann das Sonnenspektrum aufgeteilt werden und jeder Teil des Spektrums kann zu Solarzellen geleitet werden, die für diesen Bereich besonders effizient sind. In dieser Arbeit habe ich entropische Überlegungen präsentiert, die zeigen, dass die maximal erreichbare Konzentration eines Fluoreszenzkonzentrators von der StokesVerschiebung zwischen einfallender und emittierter Strahlung abhängt. Die sich daraus ergebene prinzipielle Grenze kann für Konzentratoren, die im nahen Infrarot aktiv sind, zu einem begrenzenden Faktor werden. Deshalb ist es wichtig, bei der Entwicklung der dafür notwendigen Materialien auf eine möglichst große StokesVerschiebung zu achten. Fluoreszenzkonzentratoren lassen sich mit Hilfe eines thermodynamischen Modells beschreiben, in dem das chemische Potenzial der angeregten Farbstoffmoleküle ein wesentlicher Faktor ist. Dieses bestimmt über das verallgemeinerte Planck’sche Strahlungsgesetz die Emission von Strahlung. Das chemische Potenzial ist über den Querschnitt durch den Konzentrator nicht konstant. Dadurch wird nahe der Oberfläche mehr Licht emittiert. Mit Hilfe dieses Modells konnte die Winkelverteilung des Lichtes, das den Fluoreszenzkonzentrator an den Kanten verlässt, erklärt werden. Diese war im Rahmen dieser Arbeit experimentell bestimmt worden und hatte eine unerwartete Asymmetrie gezeigt. Im Rahmen dieser Arbeit entwickelte ich eine neue Methode, um die Seitenleiteffizienz, also die Fähigkeit der Fluoreszenzkonzentratoren Licht zu ihren Seitenflächen zu leiten, spektral aufgelöst zu bestimmen. Dafür sind lediglich drei Messungen mit einem Photospektrometer und einer Ullbricht-Kugel notwendig. Mit dieser Methode können ähnliche Materialien sehr einfach bezüglich ihrer Eignung für einen Einsatz in Fluoreszenzkonzentratoren miteinander verglichen werden. Für eine vollständig quantitative Bestimmung der Seitenleiteffizienz, für Proben mit einer sehr großen Stokes-Verschiebung und zum Vergleich von Proben mit sehr unterschiedlichen Eigenschaften müssen die Ergebnisse noch einer Korrektur unterzogen werden. Die für die Korrektur notwendigen Daten können außerdem benutzt werden, um noch weitere Eigenschaften der Konzentratoren zu bestimmen. Dazu zählen die Absorption der verwendeten Farbstoffe und der Anteil des Lichtes, der durch den Verlustkegel der Totalreflexion verloren geht. Die untersuchten Materialien erreichten Seitenleiteffizienzen von bis zu 60%. Die Ergebnisse der neuen

232

7.1 Fluoreszenzkonzentratoren

Methode zeigten eine gute Übereinstimmung mit Messungen der externen Quanteneffizienz an Systemen aus Fluoreszenzkonzentratoren und Solarzellen. Photolumineszenzmessungen zeigten, dass das Photolumineszenzspektrum von der Anregungswellenlänge abhängt. Durch den Einfluss von Reabsorption ist allerdings bei dem Licht, das den Kollektor an den Seiten verlässt, kein Einfluss der Anregungswellenlänge mehr festzustellen. Um die unterschiedlichen Hypothesen zu überprüfen, die zur Erklärung der Ergebnisse der optischen Charakterisierung dienten, wurde eine Simulation der Lichleiteigenschaften der Fluoreszenzkonzentratoren entwickelt. Es zeigte sich, dass die Form des Photolumineszenzspektrums und die Winkelcharakteristik der Emission die Lichtleiteigenschaften erheblich beeinflussen. Im Gegensatz dazu spielten Streuung und die Wellenlängenabhängigkeit der Photolumineszenz nur eine untergeordnete Rolle. Wahrscheinlich lässt sich die Übereinstimmung mit den Messergebnissen noch weiter verbessern, indem eine Wellenlängenabhängigkeit der Winkelcharakteristik der Abstrahlung berücksichtigt wird. Damit sollte das Modell sehr gut für die Optimierung von Fluoreszenzkonzentratorsystemen einsetzbar sein. Zur Realisierung von Systemen aus Solarzellen und Fluoreszenzkonzentratoren wurden Solarzellen aus GaInP und GaAs hergestellt. Die Bandlücken dieser Materialien ermöglichen eine besonders effiziente Ausnutzung der von den Fluoreszenzkonzentratoren geführten Strahlung, welche im sichtbaren Spektralbereich liegt. Die Solarzellen besaßen spezielle geometrische Abmessungen und angepasste Antireflexionsschichten. Aus diesen Solarzellen wurde mit unterschiedlichen Fluoreszenzkonzentratormaterialien eine Vielzahl von Systemen realisiert. Dabei ließ sich der Wirkungsgrad der Systeme mit zwei unabhängigen Ansätzen signifikant steigern: Die Kombination unterschiedlicher Materialien vergrößerte den ausgenutzten Spektralbereich, so dass ein Wirkungsgrad von 6.9% erreicht wurde. Zum anderen reduzieren photonische Strukturen mit spektral selektiv reflektierenden Eigenschaften die Strahlungsverluste durch den Verlustkegel der Totalreflexion. Dadurch ließ sich der Systemwirkungsgrad um 20% steigern. Mit dem für das untersuchte System erzielten Wirkungsgrad von 3.1% und der hohen 20fachen Konzentration lieferte dieses System aus Fluoreszenzkonzentrator und Solarzelle das 3.7fache der Leistung, welche die verwendete GaInP Solarzelle alleine geliefert hätte. Eine detailliert Untersuchung größenabhängiger Effekte zeigte, dass photonische Strukturen insbesondere für größere Systeme sinnvoll sind. Mit den erzielten Wirkungsgraden sind Fluoreszenzkonzentratoren kein HocheffizienzAnsatz. Für praktische Anwendungen sind daher die erreichbare Konzentration und

233


das sich daraus ergebende Kostensenkungspotenzial interessant. Um Fluoreszenzkonzentratoren kommerziell interessant zu machen, müssen deshalb die Systemgrößen und der Wirkungsgrad weiter gesteigert werden. Außerdem muss der genutzte Spektralbereich ins Infrarote ausgedehnt werden. Ein Ansatz der evt. helfen könnte, die Konzentration und die Wirkungsgrade zu steigern, ist das “Nano-Fluko“konzept, das ich in dieser Arbeit präsentiert habe.

7.2

Hochkonversion

Die Hochkonversion von Photonen mit Energien unterhalb der Bandlücke von Silizium ist ein vielversprechender Weg auch die Energie dieser Photonen nutzbar zu machen und gleichzeitig die Vorteile von Siliziumsolarzellen zu erhalten. Hochkonverter erzeugen ein hochenergetisches Photon aus mindestens zwei Photonen mit niedrigerer Energie. Die wichtigsten Hochkonversionsmechanismen sind die Absorption eines Photons durch ein Atom, das sich bereits in einem angeregten Zustand befindet und die Energietransfer-Hochkonversion. Die an der Hochkonversion beteiligten Prozesse lassen sich mit Hilfe der Einsteinkoeffizienten beschreiben. Ein daraus abgeleitetes theoretisches Modell erlaubte eine qualitative Vorhersage der Intensitätsabhängigkeit der Hochkonversion. Bei niedrigen Anregungsintensitäten hängt die Intensität der Hochkonversionslumineszenz über ein Potenzgesetz von der Anregungsintensität ab. Der Exponent wird dabei durch die Anzahl der für den Hochkonversionsprozess notwendigen Photonen bestimmt. Bei höheren Anregungsintensitäten flacht sich der Verlauf ab, insbesondere weil angeregte Niveaus verstärkt durch stimulierte Emission entvölkert werden. Mit Hilfe der Judd-Ofelt Theorie lassen sich die Einsteinkoeffizienten aus dem Absorptionskoeffizienten eines Materials berechnen. In dieser Arbeit wurde Erbium dotiertes, mikrokristallines E-NaYF4 als Hochkonverter untersucht. Dieses Material ist nur als mikrokristallines Pulver verfügbar. Deshalb wurde die Kubelka-Munk Theorie angewendet, um aus Reflexionsmessungen den Absorptionskoeffizienten zu bestimmen. Durch die Kombination dieser Theorien konnten die Einsteinkoeffizienten abgeschätzt werden. Diese dienten dann im Weiteren als Eingangsparameter für die Simulation der Hochkonversionsdynamik. Mit Hilfe der experimentell bestimmten Einsteinkoeffizienten und der vorgestellten Theorie wurde ein auf Ratengleichungen basierendes Simulationsmodell der Hochkonversionsdynamik entwickelt. Das Modell berücksichtigt Absorption im Grundzustand und in den angeregten Zuständen, Energietransfer und Multi-Phononen-Übergänge. Das Model ist in der Lage, die experimentell gefundene Abhängigkeit der

234

7.2 Hochkonversion

Hochkonversionslumineszenz von der Anregungsintensität qualitativ zu reproduzieren. Außerdem kann das Modell eingesetzt werden, um die Wirkung der unterschiedlichen Einflussgrößen genauer zu untersuchen. So bestimmt die Stärke der Multi-Phononen-Übergänge sehr stark die relative Besetzung der einzelnen Energieniveaus, sowie den Verlauf der Hochkonversionslumineszenz in Abhängigkeit von der Anregungsintensität. Das Modell konnte dazu eingesetzt werden, die Wirkung von Plasmonenresonanz in Metall-Nanopartikeln zu untersuchen auf die Hochkonversion zu untersuchen. Ein Gold–Nanopartikel mit 60 nm Radius erhöhte die Hochkonversionslumineszenz um 16% im Vergleich zum Fall ohne Partikel. Mit Hilfe von zeitaufgelösten Photolumineszenzmessungen konnten erste experimentelle Einblicke in die zeitliche Dynamik der Photolumineszenz einzelner Übergänge gewonnen werden. Aus der Abhängigkeit der charakteristischen Zeitkonstanten von der Konzentration des Erbium Hochkonverters konnte geschlossen werden, dass Energietransfer maßgeblich die Dynamik der Lumineszenz bestimmt. Intensitätsabhängige Messungen der Hochkonversionslumineszenz zeigten einen Anstieg der Intensität der Hochonversionslumineszenz bei höheren Anregungsintensitäten. Dieser Anstieg folgte einem Potenzgesetz, wie auch von der Theorie erwartet worden war. Mit kalibrierten Photolumineszenzmessungen war es möglich, die Effizienz der Hochkonversion direkt zu messen. Spektral aufgelöste Messungen zeigten einen aktiven Spektralbereich von 1480-1580 nm. Die integrierte Hochkonversionseffizienz steigt mit der Anregungsintensität an. Bei einer Anregung mit 1880 Wm-2 bei einer Wellenlänge von 1523 nm wurde eine Hochkonversionseffizienz von 10.2% erreicht. Weil mindestens zwei niederenergetische Photonen notwendig sind, um ein hochenergetisches Photon zu erzeugen, bedeutet dieser Wert, dass mehr als 20% der einfallenden Photonen genutzt wurden. Normiert auf die Bestrahlungsdichte der Anregung ist dies die höchste jemals gemessene Hochkonversionseffizienz. Das E-NaYF4 :20% Er3+ wurde mit Hilfe unterschiedlicher Bindemittel auf bifaciale Silizium Solarzellen aufgebracht. Die Solarzellen sind für den Einsatz in Konzentratorsystemen optimiert. Messungen der externen Quanteneffizienz (EQE) zeigten sehr gute Übereinstimmung mit den spektral aufgelösten optischen Messungen. Die EQE des Systems erreichte einen Spitzenwert von 0.34% bei einer Wellenlänge von 1522 nm und einer Bestrahlungsstärke von 1090 Wm-2. Normiert auf die Bestrahlungsstärke ist auch dies der höchste jemals gemessene Wert. Diese Experimente wurden unter Anregung mit monochromatischer Laserstrahlung durchgeführt. Solarzellen werden aber normalerweise mit dem kontinuierlichen

235


Sonnenspektrum bestrahlt. Deshalb wurden auch Experimente unter Anregung mit weißem Licht durchgeführt. Zum ersten Mal im Kontext von Hochkonversion für Siliziumsolarzellen konnte dabei ein positiver Effekt des Hochkonverters auf den Kurzschlussstrom der Solarzelle gezeigt werden. Interessanterweise waren die gemessenen Hochkonversionseffizienzen für eine Anregung mit einem breiten Spektrum auf der Höhe der besten Werte unter monochromatischer Anregung. Eine bessere Anregung aller beteiligten Übergänge, deren Energien sich teilweise leicht unterscheiden, sowie die größere bestrahlte Fläche könnten hierfür Erklärungen sein. Die positiven Resultate insbesondere unter Anregung mit weißem Licht lassen eine Anwendung von Hochkonvertern zur Effizienzsteigerung von Siliziumsolarzellen realistisch erscheinen. Allerdings ist bis jetzt der ausgenutzte Spektralbereich zu klein und die erzielten Wirkungsgrade noch zu niedrig. Hier könnte der Ansatz der spektralen Konzentration Abhilfe schaffen. Dabei absorbiert ein lumineszentes Material Photonen aus einem breiten Spektralbereich und emittiert Photonen im Absorptionsbereich des Hochkonverters. Dies erhöht die Hochkonversionseffizienz über zwei Mechanismen: Erstens werden mehr Photonen ausgenutzt, und zweitens erhöht sich die Photonenflussdichte im Absorptionsbereich des Hochkonverters. Aufgrund der nichtlinearen Intensitätsabhängigkeit steigt dadurch die Hochkonversionseffizienz. Im Rahmen dieser Arbeit habe ich ein Konzept vorgestellt, wie ein solches System realisiert werden kann. In diesem Konzept werden spektrale Konzentration und geometrische Konzentration mit Hilfe eines Fluoreszenzkonzentrators miteinander kombiniert. Dadurch lassen sich die für hohe Hochkonversionswirkungsgrade notwendigen hohen Intensitäten ohne aufwendige externe Konzentration mit Linsen oder Spiegeln erreichen. Zusätzlich verhindern spektral selektiv reflektierende Strukturen Reabsorptionsverluste, und die Solarzelle erhält trotz bifacialen Designs einen guten Rückseitenreflektor. Für die Realisierung des Konzeptes ist aber noch wesentlicher Fortschritt in der Entwicklung lumineszenter Nanokristalle und deren Einbettung notwendig. Das Gesamtsystem lässt sich außerdem noch durch die Optimierung der Solarzellen verbessern. Eventuell lassen sich auch Fortschritte durch die Verwendung neuer Hochkonvertermaterialien erzielen. Zusammenfassend wurden in den beiden untersuchten Gebieten, Fluoreszenzkonzentratoren und Hochkonversion, neue wichtige Erkenntnisse gewonnen und konzeptioneller Fortschritt erzielt. Dieser Fortschritt eröffnet Perspektiven für eine erfolgreiche Anwendung der Konzepte. Allerdings ist noch umfangreiche Forschung notwendig, bis diese ihr Versprechen erfüllen können, zu einer weiteren Verbreitung der Photovoltaik beizutragen.

236

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248

9

Appendix

9.1

Abbreviations

Variable

Meaning

Al

Aluminum

AM

Air mass

EQE

External quantum efficiency

e

Electron

ESA

Excited state absorption

ETU

Energy transfer upconversion

Fluko

Fluorescent collector or fluorescent concentrator system

FWHM

Full width half maximum

GaAs

Gallium Arsenide

GaInP

Gallium Indium Phosphide

GSA

Ground state absorption

h

Hole

IR

Infrared

NQD

Nanocrystalline quantum dot

PL

Photoluminescence

PTFE

Polytetrafluoroethylene

PMMA

Polymethylmethacrylate

Si

Silicon

SR

Spectral response

sr

Steradiant

UV

Ultraviolet

249

9 Appendix

9.2

Glossary

Variable

Unit

a

m 2

Meaning Lattice constant 2

A

m or cm

Area

Ainc

m2 or cm2

Area that receives radiation

Aemit

m2 or cm2

Area that emits radiation

Aij

s

-1

Einstein coefficient of spontaneous emission between the two energy levels i and j

Absdye

Fraction of incident radition that is absorbed by the dye

Absmes

Fraction of incident radiation that is absorbed (and not emitted again)

Absmatrix

Fraction of incident radition that is absorbed by the matrix

DDQ DO

m-1 or cm-1

Absorption coefficient

Dabs

m-1 or cm-1

Absorption coefficient in the absorption region of the fluorescent collector

Ddye

m-1 or cm-1

Absorption coefficient of the dye

Demit

m-1 or cm-1

Absorption coefficient in the emission region of the fluorescent collector

DPMMA

m-1 or cm-1

Absorption coefficient of the PMMA

D

°

Angle

Din

°

Angle of incident ray in refraction event

Dout

°

Angle of outgoing ray in refraction event

250

9.2 Glossary

Variable

Unit

Meaning

%

W/(m2 sr)

Radiant intensity, defined as radiant energy per unit time, per unit surface area (on which radiation incidents), per unit solid angle

%inc

W/(m2 sr)

Incident intensity

%int

W/(m2 sr)

Intensity inside a medium

Bp,Q

1/(s m2 sr Hz)

Number of emitted/incident photons per time, per area, per unit solid angle, and per frequency interval

B12

m3/(Js2)

Einstein coefficient for the absorption

Cmes

Fraction of incident radition that is detected in centermount measurements

F

Free parameter used in different settings

d

m or cm

Thickness, Thickness of the layer i

D

m

Distance

E

J or eV

Energy

EC

J or eV

Lowest energy in the conduction band

EF

J or eV

Fermi level

EFC

J or eV

Fermi energy of the electrons in the conduction band

EFV

J or eV

Fermi energy of the holes in the valence band

Ei

J or eV

Energy state i

Eg

J or eV

Band-gap energy

EQE

External quantum efficiency

251

9 Appendix

Variable

Unit

Meaning

EQEsystem(Oinc)

External quantum efficiency of system of fluorescent collector with attached solar cells

EQEsystem,optical(Oinc)

External quantum efficiency of system of fluorescent collector with attached solar cells calculated from optical measurements

EQEUC(Oinc,I)

External quantum efficiency of a system of solar cell and upconverter

EQEUC,norm(Oinc,I)

W-1m2

External quantum efficiency of a system of solar cell and upconverter normalized to the irradiance of the excitation

EQEUC,device()p,cell)

Spectrally integrated external quantum efficiency of the solar cell/ upconverter device

E(m)

Expectation value of the random variable m

H

Étendue

Hinc

Étendue of incident beam

Hemit

Étendue of emitted beam

f

Oscillator strength

Fp,Q, emit

Flux of photons (i.e. photons per unit time) per unit area, per unit bandwidth, and per 4S solid angle of the incident/emitted field.

Fi

Relative frequency of the irradiance level i

FF

Fill factor

Fp,Q, inc

)

W

Radiant flux

) p

1/s

Photon flux

)p,UC(OUC)

1/s

Flux of upconverted photons with a wavelength ,OUC

252

9.2 Glossary

Variable

Unit

Meaning

)p,inc(Oinc)

1/s

)pcell

1/s

Photon flux impinging on the solar cell in the absorption range of the upconverter

)p,abs,UC

1/s

Photon flux impinging on the upconverter cell in the absorption range of the upconverter

Incident flux of photons with a wavelength

Oinc.

gi

Degeneracy factor of energy level i

g(Z)

Line form factor

gA(Z), gS(Z)

Line form factor of the transition in the acceptor ion, respectively the sensitizer ion

gem(Z), gabs(Z)

Line form factor of the emission, respectively the sensitizer transition

geh

1/(s cm2)

J H0

Generation rate of electron-hole pairs, per area Anisotropy coeeficient

J

Hamiltonian that describes the coulombic interaction between the nucleus and the inner electrons with the valence electrons Hamiltonian that describes the influence of the electric field of the crystal

Hcf

J

Hee

J

Hamiltonian that describes the coulombic repulsion between the electrons

HES

J

Hamiltonian that describes electrostatic coupling of two ions

HIon

J

Hamiltonian that describes an ion in a crystal

253

9 Appendix

Variable

Unit

Meaning

HIon, free

J

Hamiltonian that describes a free ion

Hint

J

Hamiltonian that describes interaction of two ions

HSO

J

Hamiltonian that describes the spin-orbit interaction

K

Efficiency

Kabs

Absorption efficiency of the luminescent material due to its absorption spectrum with respect to the transmitted solar spectrum

Kcell

Efficiency of the solar cell under illumination of the edge emission of the fluorescent collector

Kcoup

Efficiency of the optical coupling of solar cell and fluorescent collector

Kmat

“Matrix efficiency”, (1-Kmat) is the loss caused by scattering or absorption in the matrix.

Kreabs

Efficiency of light guiding limited by selfabsorption of luminescent material, (1-reabs) is the energy loss due to re-absorption

Krel

Relative efficiency of upconversion processes

KS(O)

Spectral collection efficiency

Kstok

“Stokes efficiency”, (1-Kstok) is the energy loss due to the Stokes shift

Ktrans,front

Transmission of the front surface in respect to the solar spectrum

Ksystem

System efficiency

254

9.2 Glossary

Variable

Unit

Meaning

Ktrap

Fraction of the emitted light that is trapped by total internal reflection

Ktref

Efficiency of light guiding by total internal reflection

KUC,spectral(Oin,OUC,I)

Spectral upconversion quantum efficiency at a certain luminescence wavelength OUC under the excitation with a wavelength Oinc and an irradiance I

KUC(Oinc,I)

Integrated upconversion efficiency

KUC,norm(Oinc,I)

W-1m2

Integrated upconversion efficiency normalized to the irradiance of the excitation

K e

J or eV

Electro-chemical potential of electrons

K h

J or eV

Electro-chemical potential of holes

,

W m-2

Irradiance, defined as radiant energy per unit time, per unit surface area on which radiation incidents

Icell

W m-2

Irradiance on the solar cell

Iexc

W m-2

Irradiance of excitation radiation photoluminescence measurements

Ii

W m-2

Irradiance of irradiance level i

IPL

W m-2

Emittance of sample in photoluminescence measurements

IUC

W m-2

Irradiance on the upconverter

W m-2 Hz-1

Spectral irradiance, defined as radiant energy per unit time, per unit surface area on which radiation incidents, per unit frequency bandwidth

IQ(Z)

255

in

9 Appendix

Variable

Unit

Meaning

I+, I-,

W m-2

Irradiance in z-direction and in the opposite direction

,

A

Current

Imes

A

Measured current

ISC

A

Short-circuit current

ISC,PTFE

A

Short-circuit current measured with a PTFE reflector attached to the back of the solar cell

ISC,ref

A

Short-circuit current of the reference solar cell

ISC,UC

A

Part of the short circuit current which is due the upconverted photon

ISC,Zap

A

Short-circuit current measured with the upconverter attached to the back of the solar cell

je, jh, jeh

1/(s cm2)

Particle flux per area, of electrons, holes, and electron-hole pairs

J

mA/cm2

Current density

Jsc

mA/cm2

Short circuit current density

ji

kg·m2s-1

Total angular momentum of a single electron

J

kg·m2s-1

Total angular momentum of a system of electrons

ki

Summation index giving the multipol order k of the transition in the ion i.

li

Orbital angular momentum of a single electron

256

9.2 Glossary

Variable

Unit

Meaning Orbital angular momentum of a system of electrons

L

O

m or nm

Wavelength of light

Oemit

m or nm

Wavelength of emitted light

Oinc

m or nm

Wavelength of incident light

O0

m or nm

Design wavelength for photonic structure Characteristic exponent that defines the power law characteristic

m me, mh

m2/Vs

Mobility of electrons, holes

M

W m-2

Emittance, defined as radiant energy per unit time, per unit surface area from which radiation is emitted

P

J

Chemical potential

Pe, Ph, Peh

J

Chemical potentials of the electrons, holes, and the sum of chemical potential of electrons and holes

Cm

Dipole matrix elements of a transition between the levels i and j, respectively for the absorption and emission transition

(1) (1) Pij(1) , P abs , Pem

n, n(O),n(Q)

Refractive index

ne, nh

1/m3

Charge carrier concentration of electrons, holes

1

1/m3

Concentration of optically active ions

1L

Number of ions being in a certain state i

257

9 Appendix

Variable

Unit

Meaning Vector that describes the occupation of energy levels. The single elements of the vector give the relative occupation of the specific level, i.e. the fraction of ions of a large ion ensemble that is excited to this state.

* N

Q

Hz

Frequency

QincQemit

Hz

Frequency of an incident/emitted photon

pext

W/m2

Extracted power density

PLUC

a.u.

Intensity of upconversion luminescence

Q

J

Radiant energy Quantum efficiency of the luminescent material

QE

ș

°

Angle, in most contexts the polar angle in polar coordinates

șc

°

Critical angle of total internal reflection

șinc

°

Half of the opening angle of the cone, from which radiation is received

șemit

°

Half of the opening angle of the cone, in which radiation is emitted

reh.

1/(s cm2)

Recombination rate of electron-hole pairs, per area

R

Reflection coefficient

Rmes

Fraction of incident photons that is detected during the reflection measurement Reflection coefficient of infinite thick layer

R

Ui

s

-1

Rate coefficient

258

9.2 Glossary

Variable

Unit

Meaning

sO

m-1 or cm-1

Scattering coefficient

si

Js

Spin angular momentum of a single electron

S

Js

Spin angular momentum of a system of electrons Singlet state of a molecule with number i

Si

V

JK

Entropy per photon

t

s

Time

7

K

Temperature

7S

K

Temperature of the sun

7

K

Ambient temperature

7A

K

Absorber temperature

-1

T

Transmission

Tcell

Transmission of the solar cell

Tmes

Fraction o f incident photons that is detected in the transmission measurement

WWup

s

Decay / Build-up time constant

u(Z)

J/(m3 Hz)

Spectral energy density

U(t)

Tensor operator of rank t

vi

Number of the vibrational state of the electron state with number i

V

V

Voltage

VOC

V or mV

Open circuit voltage

Vcell

V or mV

Voltage than can be measured externally at the solar cell

259

9 Appendix

Variable

Unit

Meaning

W12

1/s

Probability that an electron is excited into the higher level by the absorption of a photon

W21

1/s

Probability that an electron returns from an excited state to the ground state by either spontaneous emission or stimulated emission of a photon

Wmig

1/s

Probability for excitation energy migration by emission and absorption of a photon.

WET

1/s

Probability for energy transfer

Ȧ

1/s

Angular frequency

:

Solid angle

:emit

Solid angle from in which radiation is emitted

:inc

Solid angle from which radiation is received

ȍt

Judd-Ofelt intensity parameters.

260

9.3 Physical Constants

9.3

Physical Constants

Variable

Value

Unit

Meaning

c

299 792 458

m/s

Speed of light in vacuum

H0

8.854 187 817…u10-12

F/m

Permittivity of vacuum

h

6.626076u10-34

м=h/2S

1.054572u10-34

Js

Planck constant

kB

1.380 6504u10-23

J/K

Boltzmann constant

m0

9.109 382 15u10-31

kg

Electron rest mass

q

1.602 176 462(63)u10-19

C

Elementary charge

261

10

Author’s Publications

10.1

Refereed journal papers

J. C. Goldschmidt, M. Peters, M. Hermle, and Stefan W. Glunz, Characterizing the light guiding of fluorescent concentrators, Journal of Applied Physics 2009, 105, p. 114911-1 – 114911-9. J. C. Goldschmidt, M. Peters, A. Bösch, H. Helmers, F. Dimroth, S.W. Glunz, und G. Willeke, Increasing the efficiency of fluorescent concentrator systems, Solar Energy Materials & Solar Cells, 2009, 93, p. 176-182. M. Peters, J. C. Goldschmidt, P. Löper, B. Bläsi, und A. Gombert, The effect of photonic structures on the light guiding efficiency of fluorescent concentrators, Journal of Applied Physics, 2009, 105, p. 014909-1 - 014909-10. M. Peters, J. C. Goldschmidt, T. Kirchartz, B. Bläsi, The photonic light trap – Improved light trapping in solar cells by angularly selective filters, Solar Energy Materials & Solar Cells, 2009, 93, p. 1721-1727 J. C. Goldschmidt, M. Peters, L. Prönneke, L. Steidl, R. Zentel, B. Bläsi, A. Gombert, S. Glunz, G. Willeke and U. Rau, Theoretical and experimental analysis of photonic structures for fluorescent concentrators with increased efficiencies, Physica Status Solidi A, 2008, 205(12), p. 2811-2821. B. Ahrens, P. Löper, J. C. Goldschmidt, S. Glunz, B. Henke, P. Miclea and S. Schweizer, Neodymium-doped fluorochlorozirconate glasses as an upconversion model system for high efficiency solar cells, Physica Status Solidi A, 2008, 205(12), p. 2822-2830. A. Goetzberger, J. C. Goldschmidt, M. Peters and P. Löper, Light trapping, a new approach to spectrum splitting, Solar Energy Materials & Solar Cells, 2008, 92, p. 1570-1578. Submitted M. Peters, J. C. Goldschmidt and B. Bläsi, Comparison of the principle efficiency limits for concentration and angular confinement in photovoltaic converters, submitted to Progress in Photovoltaics, 24.8.2009.

263

10 Author’s Publications

B. Groß, G. Peharz, G. Siefer, M. Peters, T. Gandy, J. C. Goldschmidt, J. Benick, S. W. Glunz, A. W. Bett, and F. Dimroth, Four-junction spectral beam splitting photovoltaic receiver with high optical efficiency, submitted to Progress in Photovoltaics, 15.10.2009. In preparation S. Fischer, J. C. Goldschmidt1, P. Löper, M. Hermle, S. Glunz, K. Krämer, D. Biner Detailed experimental analysis of upconversion to enhance solar cell efficiencies, to be submitted in January 2010.

10.2

Conference papers

J. C. Goldschmidt, S. Fischer, P. Löper, M. Peters, L. Steidl, M. Hermle, S. W. Glunz, Photon management with luminescent materials, 21th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2009), 2009, Rauris, Salzburg, Austria. Löper, P., M. Künle, A. Hartel, J. C. Goldschmidt, M. Peters, S. Janz, M. Hermle, S. W. Glunz, M. Zacharias, Silicon quantum dot superstructures for all-silicon tandem solar cells, 21th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2009), 2009, Rauris, Salzburg, Austria. M. Peters, J.C. Goldschmidt, B. Bläsi, Photonic Structures and Solar Cells, 21th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2009), 2009, Rauris, Salzburg, Austria. J. C. Goldschmidt, P. Löper, S. Fischer, S. Janz, M. Peters, S. W. Glunz, G. Willeke, E. Lifshitz, K. Krämer, D. Biner, Advanced upconverter systems with spectral and geometric concentration for high upconversion efficienciesm, in Proceedings IUMRS International Conference on Electronic Materials, 2008, Sydney, Australia, p. 307-311 Digital Object Identifier 10.1109/COMMAD.2008.4802153. J. C. Goldschmidt, M. Peters, F. Dimroth, S. W. Glunz and G. P. Willeke, Efficiency enhancement of fluorescent concentrators with photonic structures and material combinations, in Proceedings of the 23rd European Photovoltaic Solar Energy Conference, 2008, Valencia, Spain, p. 193-197. P. Löper, J. C. Goldschmidt, M. Peters, D. Biner, K. Krämer, O. Schultz, S. W. Glunz, J. Luther, Upconversion for silicon solar cells: Material and system characterization, in Proceedings of the 23rd European Photovoltaic Solar Energy Conference, 2008, Valencia, Spain, p. 173-180.

264

10.2 Conference papers

M. Peters, J. C. Goldschmidt, P. Loeper, B. Bläsi and G. Willeke. Lighttrapping with angular selective filters, in Proceedings of the 23rd European Photovoltaic Solar Energy Conference, 2008, Valencia, Spain, p. 353-357. S. Fischer, J. C. Goldschmidt, P. Löper, S. Janz, M. Peters, S. W. Glunz, A. Kigel, E. Lifshitz, K. Krämer, Material characterization for advanced upconverter systems, in Proceedings of the 23rd European Photovoltaic Solar Energy Conference, 2008, Valencia, Spain, p. 620-623. C. Ulbrich, S. Fahr, M. Peters, J. Üpping, T. Kirchartz, C. Rockstuhl, J. C. Goldschmidt, P. Löper, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau. Directional selectivity and light-trapping in solar cells, in Photonics for Solar Energy Systems II, Strasbourg, France, SPIE, 2008, p. 70020A-11. M. Peters, J. C. Goldschmidt, P. Löper, L. Prönneke, B. Bläsi, and A. Gombert, Design of photonic structures for the enhancement of the light guiding efficiency of fluorescent concentrators, in Photonics for Solar Energy Systems II, Strasbourg, France, SPIE, 2008, p. 70020V-11. M. Bendig, J. Hanika, H. Dammertz, J. C. Goldschmidt, M. Peters and M. Weber. Simulation of fluorescent concentrators, in IEEE/EG Symposium on Interactive Ray Tracing, 2008, Los Angeles, California, USA, p. 93-98. J. C. Goldschmidt, P. Löper, M. Peters, A. Gombert, S. W. Glunz, G. Willeke Progress in photon management for full spectrum utilization with luminescent materials, in Proceedings of 20th Workshop on Quantum Solar Energy Conversion (QUANTSOL 2008), 2008, Bad Gastein, Salzburg, Austria. M. Peters, J. C. Goldschmidt, P. Löper, C. Ulbrich, T. Kirchartz, S. Fahr, B. Bläsi, S. W.Glunz, A. Gombert. Photonic structures for the application on solar cells, in Proceedings of 20th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2008), 2008, Bad Gastein, Salzburg, Austria. M. Peters, J. C. Goldschmidt, P. Löper, B. Blaesi and A. Gombert, Photonic crystals for the efficiency enhancement of solar cells, in EOS Topical Meeting on Diffractive Optics, 2007, Barcelona, Spain. J. C. Goldschmidt, M. Peters, P. Löper, O. Schultz, F. Dimroth, S. W. Glunz, A. Gombert, G. Willeke, Advanced fluorescent concentrator system design, in Proceedings of the 22nd European Photovoltaic Solar Energy Conference, 2007, Milan, Italy, p. 608-612.

265


P. Löper, J. C. Goldschmidt, M. Peters. D. Biner, K. Krämer, O. Schultz, S.W. Glunz, J. Luther, Efficient upconversion systems for silicon solar cells, in Proceedings of the 22nd European Photovoltaic Solar Energy Conference, 2007, Milan, Italy, p. 589-594. M. Peters, J. C. Goldschmidt, P. Löper, A. Gombert and G. Willeke, Application of photonic structures on fluorescent concentrators, in Proceedings of the 22nd European Photovoltaic Solar Energy Conference, 2007, Milan, Italy, p. 177-181. J. C. Goldschmidt, M. Peters, P. Löper, S. W. Glunz, A. Gombert, G. Willeke, Photon management for full spectrum utilization with fluorescent materials, in Proceedings of 19th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2007), 2007, Bad Hofgastein, Salzburg, Austria. J. C. Goldschmidt, S. W. Glunz, A. Gombert and G. Willeke, Advanced fluorescent concentrators, in Proceedings of the 21st European Photovoltaic Solar Energy Conference, 2006, Dresden, Germany, p. 107-110. J. C. Goldschmidt, S. W. Glunz, A. Gombert, G. Willeke, Advanced Fluorescent Concentrators, in Proceedings of 18th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2006), 2006, Rauris, Salzburg, Austria. J. C. Goldschmidt, O. Schultz and S. W. Glunz, Predicting multi-crystalline silicon solar cell parameters from carrier density images, in Proceedings of the 20th European Photovoltaic Solar Energy Conference, 2005, Barcelona, Spain, p. 663-666. O. Schultz, S. W. Glunz, J. C. Goldschmidt, H. Lautenschlager, A. Leimenstoll, E. Schneiderlöchner, G. P. Willeke, Thermal oxidation processes for high-efficiency multicrystalline silicon solar cells, in Proceedings of the 19th European Photovoltaic Solar Energy Conference, 2004, Paris, France, WIP-Munich, ETA-Florence, p. 604607. J. C. Goldschmidt, K. Roth, N. Chuangsuwanich, A. B. Sproul, B. Vogl and A. G. Aberle. Electrical and optical properties of polycrystalline silicon seed layers made on glass by solid-phase crystallization, in Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion, 2003, Osaka, Japan, p. 1206-1209. K. Roth, J. C. Goldschmidt, T. Puzzer, N. Chuangsuwanich, B. Vogl and A. G. Aberle, Structural properties of polycrystalline silicon seed layers mad on glass by solid-phase crystallisation, in Proceedings of the 3rd World Conference on Photovoltaic Energy Conversion, 2003, Osaka, Japan, p. 1202-1205.

266

10.3 Oral presentations

10.3

Oral presentations

J. C. Goldschmidt, S. Fischer, P. Löper, M. Peters, L. Steidl, M. Hermle, S. W. Glunz, Photon management with luminescent materials, 21th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2009), 2009, Rauris, Salzburg, Austria J. C. Goldschmidt, M. Peters, F. Dimroth, S. W. Glunz and G. P. Willeke, Efficiency enhancement of fluorescent concentrators with photonic structures and material combinations, 23rd European Photovoltaic Solar Energy Conference, 2008, Valencia, Spain. J. C. Goldschmidt, P. Löper, S. Fischer, S. Janz, M. Peters, S. W. Glunz, G. Willeke, E. Lifshitz, K. Krämer, D. Biner, Advanced Upconverter Systems with Spectral and Geometric Concentration for high Upconversion Efficiencies, IUMRS International Conference on Electronic Materials, 2008, Sydney, Australia. J. C. Goldschmidt, „Neuartige Solarzellenkonzepte“ oder „Wie man Photonen managt?“, 83. Stipendiatenseminar der Deutschen Bundesstiftung Umwelt, Deutsche Bundesstiftung Umwelt, Roggenburg, Germany, 9.–13.06.2008 J. C. Goldschmidt, P. Löper, M. Peters, A. Gombert, S. W. Glunz, G. Willeke, Progress in photon management for full spectrum utilization with luminescent materials, 20th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2008). 2008, Bad Gastein, Salzburg, Austria J. C. Goldschmidt, Novel solar cell concepts – How to manage photons, Ornstein Colloquium, Utrecht University, The Netherlands, 15.11.2007 J. C. Goldschmidt, Neuartige Solarzellenkonzepte, 79. Stipendiatenseminar der Deutschen Bundesstiftung Umwelt, Deutsche Bundesstiftung Umwelt, Benediktbeuren, Germany, 5.–9.11.2007 J. C. Goldschmidt, M. Peters, P. Löper, S. W. Glunz, A. Gombert, G. Willeke, Photon management for full spectrum utilization with fluorescent materials, 19th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2007), 2007, Bad Hofgastein, Salzburg, Austria. J. C. Goldschmidt, S. W. Glunz, A. Gombert and G. Willeke, Advanced fluorescent concentrators, 21st European Photovoltaic Solar Energy Conference, 2006, Dresden, Germany.

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J. C. Goldschmidt, Neuartige Solarzellenkonzepte, 68. Stipendiatenseminar der Deutschen Bundesstiftung Umwelt, Deutsche Bundesstiftung Umwelt, Papenburg, Germany, 11.-16.6.2006 J. C. Goldschmidt, S. W. Glunz, A. Gombert, G. Willeke, Advanced Fluorescent Concentrators, 18th Workshop on Quantum Solar Energy Conversion - (QUANTSOL 2006), 2006, Rauris, Salzburg, Austria. J. C. Goldschmidt, Solarzellen: Alte Rekorde und neue Konzept, Graduiertenkolleg – Nichtlineare Optik und Ultrakurzzeitphysik, Technische Universität Kaiserslautern, Germany, 11.1.2006 J. C. Goldschmidt, O. Schultz and S. W. Glunz, Predicting multi-crystalline silicon solar cell parameters from carrier density images, 20th European Photovoltaic Solar Energy Conference, 2005, Barcelona, Spain.

10.4

Patents

J. C. Goldschmidt, P. Löper and M. Peters, Solarelement mit gesteigerter Effizienz und Verfahren zur Effizienzsteigerung, Deutsches Patent, 10 2007 045 546.3, granted A. Goetzberger, J. C. Goldschmidt, M. Peters and P. Löper, Photovoltaik-Vorrichtung und deren Verwendung, pending J. C. Goldschmidt, M. Peters, M. Hermle, P. Löper, B. Bläsi, Lumineszenzkollektor mit mindestens einer photonischen Struktur mit mindestens einem lumineszenten Material sowie diesen enthaltendes Solarzellenmodul, pending M. Peters, J. C. Goldschmidt, B. Bläsi, Kombination aus Konzentrator und winkelselektiven Filter für hocheffiziente Photovoltaik-Systeme, pending M. Peters, B. Bläsi, J. C. Goldschmidt, Hubert Hauser, Martin Hermle, Pauline Voisin Strukturierungskonzept für effizientes Lighttrapping in Siliziumsolarzellen, pending M. Hermle, B. Bläsi, M. Peters, H. Hauser, J.C. Goldschmidt, Solarzelle und Verfahren zu deren Herstellung, pending

268

10.5 Other publications

10.5

Other publications

J. C. Goldschmidt, M. Peters, F. Dimroth and S. W. Glunz, Zurück in die Zukunft - mit neuen Konzepten erlebt eine alte Konzentratortechnologie ihre Renaissance. Erneuerbare Energien, 2008. Nov 2008: p. 48-52. F. Creutzig and J. C. Goldschmidt (Editors), Energie, Macht, Vernunft - der umfassende Blick auf die Energiewende. Taschenbuch ed. 2008, Aachen: Shaker Media. p. 352. ISSBN 3868580700 J. C. Goldschmidt, Einfluss von inhomogenen Materialeigenschaften auf die Effizienz multikristalliner Silizium-Solarzellen, Diplomarbeit, Fakultät für Mathematik und Physik, 2005, Universität Freiburg: Freiburg. p. 92. J. C. Goldschmidt, Seeding Layers on Textured Glass Substrates for Crystalline Silicon Thin-Film Solar Cells, Bachelor Thesis, Key Centre for Photovoltaic Engineering, Bachelor for Photovoltaic Engineering, University of New South Wales, November 2002, p. 54 M. Peters, A. Bielawny, B. Bläsi, R. Carius, S.W. Glunz, J.C. Goldschmidt, H. Hauser, M. Hermle, T. Kirchartz, P. Löper, J. Üpping, R. Wehrspohn, G. Willeke Photonic Concepts for Solar Cells, in Physics of Nanostructured Solar Cells, V. Badescu, Editor, Nova Science, to be published in 2010

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11

Curriculum vitae Jan Christoph Goldschmidt born 3rd of July 1979 in Schlüchtern Education

1985-1998

Primary school, Gymnasium, Abitur (1,0)

10/1999-02/2005

Albert-Ludwigs-Universität Freiburg Major subject: Physics/Diploma Minor subjects: Micro-systems Engineering, and Seminconductor Physics and Technology

02/2002-11/2002

University of New South Wales in Sydney (UNSW), Australia Research project on silicon thin-film solar cells

03/2004-02/2005

Diploma thesis at Fraunhofer Institute for Solar Energy Systems (ISE) on high-efficiency multi-crystalline silicon solar cells

02/2005

Diploma (very good)

08/2005-09/2009

PhD thesis at Fraunhofer ISE/ University of Konstanz Scholarships Studienstiftung des deutschen Volkes Deutscher akademischer Austauschdienst (DAAD) Heinrich Böll Stiftung Deutsche Bundesstiftung Umwelt (DBU) Work experience

08/1998-08/1999

Community service at Diakoniekrankenhaus Freiburg

06/2001-01/2002

Research assistant at Fraunhofer ISE

04/2003-02/2004

Research assistant at Fraunhofer ISE

04/2005-06/2005

Internship at McKinsey&Company Inc.

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12

Acknowledgements

I would like to thank Prof. Dr. Gerhard Willeke for the supervision and advancement of this PhD thesis. I thank Prof. Dr. Thomas Dekorsy for being the second assessor of this thesis. I am very thankful to Dr. Stefan W. Glunz for the great opportunity to work in his group and later his department, for his inspiring enthusiasm, his motivation, and his support. I thank Dr. Martin Hermle and Dr. Oliver Schultz-Wittmann, who became my group leaders, for their feedback, support, and encouragement. It was a great honor and privilege to work together with Prof. Dr. Adolf Goetzberger. I am thankful for the chance to learn from his experience. His creativity is tremendously inspiring, and his humor made the collaboration very enjoyable. My master students Philipp Löper and Stefan Fischer contributed significantly to this thesis. Furthermore, it was a great pleasure to work together with them. My colleague Marius Peters joined me in the quest to enhance solar cell efficiencies by photon management. This has been a great collaboration, which resulted in many interesting discussions, a huge amount of new ideas, and great fun as well. Many students supported this work during their internships or their time as student research assistant, by performing measurements, by cycling to the hardware store to buy equipment, by proof reading this thesis etc. I am thankful for the support of Michael Rauer, Anna Walter, Katarzyna Bialecka, Janina Löffler, Rena Gradmann, Tim Rist, Wesley Dopkins, and Marcel Pinyana. I am thankful to all my colleagues with whom I shared an office, for the friendly atmosphere and the great fun we had together. I would like to especially mention Elisabeth Schäffer and Thomas Roth, with whom I shared an office for the longest period. Additional to discussion on all kind of subjects, I profited a great deal from their knowledge and support in many areas. I would also like to mention my old friend Tobias Kalden, who showed that music and solar energy perfectly match, and with whom I had many ice cream breaks during his part time job at ISE. Many more colleagues at Fraunhofer ISE contributed to this work. I am especially thankful to Armin Bösch, Henning Helmers, and the team of the III-V solar cell group,

273

12 Acknowledgements

who provided me with the III-V solar cells used in this work; to Benedikt Bläsi and Andreas Gombert, from whom I learned a lot about optics, to Prof. Wittwer, Armin Zastrow and Franz Brucker, who shared their knowledge from the early Fluko-research period with me; to Jochen Hohl-Ebinger and Holger Seifert, who contributed to various calibration efforts; and to the team of the mechanical workshop, who did a great job in producing all the special components for the measurement setups. I am grateful for all the collaborations with many colleagues from outside the Fraunhofer ISE, with whom I had very fruitful discussions and who supported this work by various means. I would like to mention Bernd Ahrens, Prof. Dr. Gottfried Bauer, Marion Bendig, Daniel Biner, PD Dr. Rudolf Brüggemann, Dr. Andreas Büchtemann, Florian Hallermann, Prof. Dr. Karl Krämer, Ariel Kigel, Prof. Dr. Efrat Lifshitz, Prof. Dr. Andries Meijerink, Liv Prönneke, Lorenz Steidl, and all the other colleagues of the “Nano”-projects. I gratefully acknowledge the scholarship support from the Deutsche Bundesstiftung Umwelt, and the ideational support from the Heinrich-Böll Stiftung and the German National Academic Foundation. I thank my friends for the distraction from my work, for enduring me being late at the mensa and for their support. I am very thankful to all my family for supporting me through my studies and this PhD work and especially my parents, whose gracious support and encouragement through all these years made all this possible. Finally, I would like to thank my wonderful wife Berit Lange. Not only had she the calm hand that I lacked, when soldering contacts to solar cells, but she gave me great support of all kinds through all this work.

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