Enhancement of Light Extraction Efficiency of Light ...

Enhancement of Light Extraction Efficiency of Light-Emitting Diode with Hexagonal Photonic Crystal Layer Dang Hoang Long, Hyung-Ah Do, Joonmo Park, In-Kag Hwang, and Sang-Wan Ryu Department of Physics, Chonnam National University, Gwangju 500-757, Korea June-Key Lee School of Material Science and Technology, Chonnam National University, Gwangju 500-757, Korea ABSTRACT The efficiency of light emitting diode (LED) is limited because large amount of generated light is confined inside of it by total internal reflection. A photonic crystal (PC) layer embedded in LED structure substantially modifies the guiding properties inside the chip and prevents the lateral propagation of light, so that it largely increases the output power of an LED. In this paper, we present both numerical and experiment studies on the enhancement of light extraction of GaN-based light-emitting diodes (LEDs) with hexagonal PC layer. By finite difference time domain (FDTD) simulation, the PC parameters were varied in order to evaluate the enhancement. Best extraction efficiency was obtained with the lattice constant of 400 - 600 nm, the PC thickness of 150 - 200 nm and the ratio of hole radius to lattice constant of 0.3 - 0.4 for the 465 nm LED based on GaN. Furthermore, hexagonal PC GaN-based LED was fabricated using anodic aluminum oxide (AAO) method. The PC layer is located below quantum well active layer and the efficiency was improved more than 20%. It was shown that these numerical results agree reasonably well with the experimental results.

1. INTRODUCTION Light emitting diodes (LEDs) are small and convenient light sources that are used in backlight units of liquid crystal display, sign illuminations, vehicle and traffic signals and even for architectural effects in interior lighting. For these and other advanced applications, an LED with higher light output at lower power consumption is needed. However, the efficiency of these devices is limited due to the total internal reflection at the semiconductor interface and the outer medium. The critical angle of total internal reflection is low (18.4o for GaAs and 23o for GaN), so only a small fraction of light generated in the active region of LEDs can escape into the outer environment. The extraction efficiency at the semiconductor/air single interface is about ~ 1/4n2.1 Therefore, the external quantum efficiency of LEDs would be poor even if the internal quantum efficiency was close to unity. To avoid this structural problem of LEDs and to extract more light from them, there have been several approaches such as changing the LED chip shape,2 photon recycling,3 coupling to surface plasmon modes4 or roughening the Nanoengineering: Fabrication, Properties, Optics, and Devices IV, edited by Elizabeth A. Dobisz, Louay A. Eldada, Proc. of SPIE Vol. 6645, 66450G, (2007) · 0277-786X/07/$18 · doi: 10.1117/12.733722

Proc. of SPIE Vol. 6645 66450G-1

surface.5,6 It has recently been suggested that an approach using photonic crystal (PC) has been adopted to enhance light extraction efficiency dramatically. In this method, the two dimensional PC is etched into the upper cladding layer of a LED by using electron-beam lithography methods.7 The aim of this method is to avoid total internal reflection and prevent the lateral propagation of light – waveguide effect. The existence of a photonic ban gap of PC at the light emission wavelengths of an LED modifies the guiding properties and reduces the waves propagating in lateral directions relative to the LED axis.8 To achieve high light extraction of an LED, an optimized design based on the simulation on light propagation is required. The finite difference time domain (FDTD) method is a common simulation tool for calculating electromagnetic field distributions in finite structures of arbitrary geometry. In this paper, we present FDTD simulation for the enhancement of light extraction efficiency of light-emitting diodes with various photonic crystal layers. From the simulation, the optimized values of PC parameters such as lattice constant, PC thickness and the ratio of hole radius to lattice constant (r/a) were obtained for the highest light extraction efficiency. The mechanism of light extraction in a PC LED also discuss by comparing ordered and disordered PC structure. For experiment, a hexagonal PC GaN-based LED was fabricated using anodic aluminum oxide (AAO) method. The PC layer is located below quantum well active layer and the efficiency was improved more than 20%. It was shown that these numerical results agree reasonably well with the experimental results

2. FDTD SIMULATION A conventional LED structure is composed of a sapphire substrate, GaN buffer layer, n-GaN, multi-quantum well (MQW) active layer and p-GaN. A two dimensional photonic crystal is formed on the top surface of the LED to increase the light extraction efficiency. The schematic is shown in Fig. 1(a). Photonic Crystal layer

4— Active

4-

layer

Buffer layer

Substrate

(b)

side view

top view

S..... ..... 1'

800 irn

Sapphire

100011111

...... ..... ...... •.... ...... 2000 x 2000 nm

Fig. 1. (a) Schematic of LED with PC layer. (b) The simplified LED structure for simulation.


In FDTD, we must choose a reasonable grid size for a meaningful result.9 However, the number of grids for a real LED is so large (~1010) that the simulation requires too much memory and computation time. Therefore, a FDTD simulation for any realistic LED device is a numerical challenge. To solve the problem, we need to find a sensible truncation scheme to reduce the payload of computation without hampering the underlying physics. Our simplified LED structure used for simulation is illustrated in Fig. 1(b). We ignored the electrode and the insulating layer in the LED, and detailed structure of quantum well active region. To reduce the size of the calculation region, we considered a sample LED with a smaller size than a real device, i.e., LED area of 2000×2000 nm. This is too small when compared with the actual size of the LED, so some finite-size effects can occur such as edge emission that might influence the accuracy of our simulation. To deal with the finite-size effects and the reduced size of our simulation, perfect mirrors were placed at four lateral sides of the structure. This corresponds to an infinite size of LED. By this way, the finite-size effect is neglected completely. The light source was regarded as a polarized dipole and was placed in the middle of the MQWs at a depth of 200 nm from the top GaN surface. The center wavelength of the dipole source was 465nm and the spectral width (as a full width half maximum) was 10nm. Absorption coefficient of GaN was assumed 300 cm-1, which corresponded to the photon lifetime of 320 fs.10 Then the extracted light was measured by computing the Poynting vectors at the surfaces surrounding all sides of the LED. At the spatial boundaries of the calculation domain, the electromagnetic wave should satisfy the condition such as non-reflection continuation of the structure inside the calculation region. To meet this requirement, a perfectly matched layer (PML) was introduced outside the LED.11

3. RESULTS AND DISCUSSION. The light extraction efficiencies were calculated for PC LEDs with various photonic crystal structures. The photonic crystal was comprised of hexagonally arranged air holes with GaN as a matrix. The efficiency of PC LED was simulated and compared with that of normal LED without PC. The extraction enhancement was calculated by a ratio (EPC – Eo)/Eo, where EPC and Eo were total light extraction energies with and without PC, respectively. To find the optimal design of an LED for high enhancement of light extraction, we concentrated on studying in detail the photonic crystal geometries and three photonic crystal parameters were considered. First, the lattice constant of the PC was varied and the light extraction efficiency was simulated. Then, the PC thickness and the ratio of hole radius to lattice constant (r/a) was varied and the effect on the light extraction was calculated. After defining the optimal design, a disordered PC LED was generated and simulated. By comparing ordered and disordered PC, the results showed that the mechanism for improved light extraction of LED was mainly due to scattering. Finally, we show the experiments on hexagonal PC GaN-based LED that fabricated using anodic aluminum oxide (AAO) method. It was shown that these numerical results are good agreement with the experimental results. First, we simulated PC LEDs with different of lattice constant. The thickness of the PC was fixed at 200 nm and the ratio r/a was 0.3. For comparison, the lattice constant parameters were varied from 100 nm to 700 nm. Fig. 2 describes the integrated total energy outputs versus time for the LEDs both with and without the PC. This figure also shows the


emitted energy from the single dipole source with time. The emitted energy from a dipole source has a Gaussian profile and its peak time was 200 fs after the start of radiation. The width of the source was 67 fs as in full width at half maximum. The generated photon energy was considered to contribute to LED efficiency only when it was extracted before the photon lifetime. After the lifetime, we assumed that all the photon energy in the LED chip was absorbed. So, even though the FDTD simulation calculated the energy extraction after the lifetime, we ignored the extraction after it. According to these results, the total energy outputs for the LED with PC increased faster than the LED without PC and hence, in sense, PC could enhance efficiency of the LED. To acknowledge this more clearly, the enhancement of light extraction efficiency was plotted as a function of lattice constant in Fig. 3(a). All the PC LEDs showed higher extraction efficiency than normal LED. The extraction enhancement increased with the pattern periodicity and reached maximum at 400 - 600 nm while it decreased for larger pattern periodicity. 1 .0

0.8

0.6

> w

0.4

0.2

>< io

0.0 200

400

600

800

1000

1200

Time (s)

Fig. 2. Integrated total energy emitted from LED with and without PC. The lattice constant was varied from 100 nm to 700 nm for LED with PC.

To find the dependence of enhancement of extraction efficiency on the thickness of the PC, the thickness of the PC was changed from 50 nm to 250 nm. In this simulation, we set the lattice constant as 300 nm and the ratio r/a as 0.3. Fig. 3(b) showed the simulation result, that is, the enhancement as a function of the thickness of the PC. The enhancement value almost increases linearly. It means that the thickness of the PC is greater, and the enhancement of light extraction efficiency is greater. However, it is very difficult to achieve a large thickness for the PC in the experiment. Normally, this value is smaller than 200 nm, so the PC thickness of 150 – 200 nm is a good choice.


(b)

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60 40 20 100 200 300 400 500 600 700

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100

150

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80 60 40 20 0

0.1

0.2

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0.5

Ratio r/a

Fig. 3. The enhancement of light extraction efficiency as a function of (a) the lattice constant and (b) the PC thickness and (c) the ratio r/a

And in final step to find optimal design of a PC LED, we selected the thickness of the PC of 200 nm and lattice constant of 300 nm and then varied the value of ratio r/a between 0.1 and 0.5. The r/a of 0.5 means that the holes meet each other. It was expected that the enhancement of light extraction by the PC would be low when r/a is too small or too large because the index contrast is small in both cases. Fig. 3(c) again affirmed this guess. The maximum value of enhancement was attained at the ratio r/a of 0.3 - 0.4. To understand clearly the mechanism for improved light extraction of LED, disordered PC was generated and simulated. First, disordered PC with random hole radius was studied. To describe the degree of disorder, radius disorder parameter δr was defined. The disordered PC pattern was generated from the order PC with a pattern periodicity of 300 nm and a hole radius of 0.3a. The radius of each hole was altered by the amount randomly chosen between – δra and δra. So, the degree of disorder increase with δr. Secondly, the disordered PC with random hole position was generated while the hole radius was kept 0.3a. Position disorder parameter δp was defined that each hole is moved along random direction with the amount randomly chosen between 0 and δpa. The disordered PC patterns with various δr and δp were generated and simulated with the LED structure. Figure 4 shows the dependence of extraction enhancement on disorder parameters. Because the disordered PC pattern changes randomly even though it has the same δr or δp, the simulation was done three times for one disorder parameter and the average value was displayed. As illustrated in this figure, the extraction enhancement changed only a little, even increased slightly, with the increased disorder. And standard deviation of the extraction efficiency increased for larger disorder parameters. This results suggest that the dominant mechanism for improved LED using PC is scattering.


(b)

(a)

100

80

Enhancement (%)

Enhancement (%)

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60 40 20 0

0.00

0.05

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80 60 40 20 0

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0.00 0.05 0.10 0.15 0.20 0.25 0.30

Random parameter δ r

Random parameter δp

Fig. 4. The enhancement of light extraction efficiency as a function of random parameter (a) δr and (b) δp

For experiment, we fabricated hexagonal PC GaN-based LED using anodic aluminum oxide (AAO) method. The PC was located 2 µm below the QW active layer with the thickness of 0.3 µm, the lattice constant of 180nm and the hole size of 140nm. The PC and normal LEDs were operate under dc bias condition at room temperature. Fig 5 describe the output-current (L-I) characteristics of two LEDs – with and without PC. This results shows that the light output power of the LEDs with PC is higher then that of the LED without PC. The efficiency of PC LED was improved more than 20% compared with normal LEDs. All our simulation and experiment results demonstrated that PC could enhance efficiency of the LED. These results

Light Intensity (mW)

are reasonable and in good agreement with experiments in other published papers.12,13

15

10

5

0

normal LED PC LED

0

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Current (mA) Fig. 5. The light output–current (L–I) characteristics of LEDs with and without PC

4. CONCLUSION. We have presented FDTD simulation to calculate the light extraction efficiency of the light-emitting diode with a


hexagonal photonic crystal layer. The design parameters of the PC were varied and the optimized values were simulated. The best extraction efficiency was obtained with a lattice constant of 400 – 600 nm, PC thickness of 150 – 200 nm and r/a of 0.3 - 0.4. With the optimized PC structure, the extraction efficiency increased as much as 120% compared to the LED without the PC layer. A disordered PC LED also was simulated and compared with order PC LED. The results showed that scattering was the dominant mechanism for the enhanced extraction efficiency of LED. Furthermore, hexagonal PC GaN-based LED was fabricated using anodic aluminum oxide (AAO) method. The PC layer is located below quantum well active layer and the efficiency was improved more than 20%. It was shown that these numerical results agree reasonably well with the experimental results.

ACKNOWLEDGMENTS This work was supported by Center for Photonic Materials and Devices at Chonnam National University

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