Giant Optical Pathlength Enhancement in Plasmonic

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AUTHOR SUBMITTED MANUSCRIPT - JPhysD-116442.R2

Giant Optical Pathlength Enhancement in Plasmonic Thin Film Solar Cells Using Core-shell Nanoparticles Peng Yua, b, Fanlu Zhangb, Ziyuan Lib, Zhiqin Zhongc, Alexander Govorovd, Lan Fub, Hoe Tanb,*, Chennupati Jagadishb, Zhiming Wanga,* a

Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of

China, Chengdu 610054, P. R. China. b

Department of Electronic Materials and Engineering, Research School of Physics and Engineering,

The Australian National University, Canberra, ACT 0200, Australia c

State Key Laboratory of Electronic Thin Film and Integrated Devices, University of Electronic

Science and Technology of China, Chengdu 610054, P.R. China d

Department of Physics and Astronomy, Ohio University, Athens, OH 45701, USA

*Corresponding author: [email protected]; [email protected]

Abstract In this paper, finite-difference time-domain method is adopted to investigate light scattering properties of core (metal)-shell (dielectric) nanoparticles, with varying shell thickness and refractive index. Adding a coating shell can shift the resonance to above the solar material bandgap when compared with the bare nanoparticle that has resonance out of useful solar radiation. The front-located core-shell metal-dielectric nanoparticles on the thin Si substrates demonstrate enhanced forward scatterings with suppressed backward scatterings. The fraction of light scattered into the substrate and maximum optical path length enhancement can achieve as high as 0.999 and 3133, respectively, if properly engineered, while the maximum optical path length enhancements of ideal Lambertian and dipole source are only ~100. This light scattering property can be ascribed to the constructive interference of the electric and magnetic dipoles. The giant fraction of light scattered into the substrate and maximum optical path length enhancement in core-shell plasmonic solar cells provide an insight into addressing the out-coupling and poor pathlength in thin film photovoltaic technology. Keywords: Plasmonic; Core-shell; Thin film; Solar cell; Nanoparticle

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Introduction As the efficiency of commercial photovoltaic (PV) devices approaching to the detailed balance limit [1], third generation solar cells are proposed to achieve high efficiency or cut down material consumption. Nanowire solar cells have potential to achieve nearunity light absorption above the material bandgap [2-4]. Quantum dot solar cells (QDSCs) utilize the marginal light beyond the bandgap to contribute photocurrent by introducing quantum dots within the p-n junction and the predictable efficiency can be as high as ~66% [5-7]. Perovskite solar cells attract attention with efficiency above 21% [8]. However, these novel PV devices are suffering from their intrinsic weaknesses [7, 9, 10]. Si solar cells are mainstream photovoltaic devices. The practical route to obtain cost-effective Si solar cells is to lower material consumption while maintaining high efficiency. While traditional PV devices have relied on relatively thick active layers to maximize light absorption, the thin film solar cells have a typical thickness of a few micrometers to decrease material usage, deposited on foreign substrates such as glass, ceramics, plastic, or metal for mechanical support [11, 12]. In addition, carrier diffusion path is much shorter in thin-film solar cell, which leads to a reduction of electrical loss from minority carrier recombination. However, due to relatively poor light absorption of thin-films, efficiencies of thin film solar cells are strongly limited by impaired carrier excitation, and photocurrent generation. Si is a weak absorber and thus surface texture is introduced as a light-trapping scheme in industrial fabrication. However, as the thickness goes down to a few micrometers, conventional surface texture light trapping technology is no longer compatible with it because the size of pyramids surface is usually 2-10 μm which is much larger than the typical thin film thickness of 1-2 μm [13, 14]. The metallic nanostructures, which support localized surface plasmon resonance (LSPR) and exhibit light trapping effect, have potential to concentrate and guide light to a subwavelength area, promising for enhancing the optical absorption in the thin film solar cells [15, 16]. Metal nanoparticles are extensively investigated as plasmonic enhancers to aid absorption of thin film solar cells [6, 17-23]. A nanoparticle self-assembly method provides a facile approach to cost-effective solar cell fabrication [18, 21, 24-26]. Nanosphere and multispiked nanostar are coupled to conquer the weak absorption of QDs in QDSCs [6, 17]. Arrays of Ag strips on a thin 50 nm Si film cell are able to enhance the photocurrent up to 43% [27]. Ag hemisphere can lead to a much higher scattering efficiency into substrate than its sphere counterpart [19]. Introduction of Ag nanoparticle in the cells boost the performance with an increased photocurrent of 25% and 8%, respectively [28, 29]. Moreover, nanocages [30], nanodisks [31], nanocavity [32], nanovoids [33] and nucleated nanoparticles [34] have been shown to be effective enhancers to improve the solar cell performance. Metallic nanoparticles are commonly used to boost photocurrent density by taking advantage of their near field enhancement and far field scattering coupled with solar

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cell active layers both in organic and inorganic solar cells [35]. Previous studies incorporating pure metallic nanoparticles in thin film solar cells have mainly focused on achieving large resonant scattering cross sections. Although these pure metallic nanoparticles have large scattering cross section, they also introduce useless backward scattering. In most plasmonic solar cell case, nanoparticles are located on the front of the substrate and thus the plasmonic source with suppressed backward scattering and enhanced forward scattering are favored. Core-shell nanoparticles, combine an optical signature with other physical properties, are particularly useful for plasmonic solar cells [36, 37]. The core-shell nanoparticle not only exhibits double plasmonic resonance spectra in two different regions of the electromagnetic spectrum [38], but also provides optimal spacing, chemical isolation [39]. Recently, it is demonstrated the core (metal)shell (dielectric) nanoparticles can support simultaneously both electric and magnetic resonances, and when the resonances are properly engineered, azimuthally symmetric unidirectional scattering can be achieved [36, 40]. The plasmonic core (metal)-shell (dielectric) nanoparticles (with coatings made of SiO2, Ag2S, TiO2, etc.) are primarily used in organic solar cells with shell serving as a chemical or electrical isolation to inhibit unwanted charge recombination, e.g. dye-sensitized solar cells and perovskite solar cells [38, 39, 41-43]. Core (SiO2)-shell (Au) plasmonic nanoparticles in PbS colloidal quantum dot solar cell demonstrate a 35% enhancement in photocurrent in the performance-limiting near-infrared spectral region [44]. Wei Zhang et al. attribute the enhancement of perovskite-based solar cells employing core (Au)−shell (SiO2) to reduced exciton binding energy with the incorporation of the metal nanoparticles, rather than enhanced light absorption [42]. However, the properties of core (metal)-shell (dielectric) that demonstrates zero backward scattering and enhanced forward scattering are overlooked in PV devices. This paper investigates plasmonic solar cells based on core (metal)-shell (dielectric) nanoparticle, illustrated conceptually in figure 1a. The proposed structure includes a Ag core and an external coating dielectric layer with refractive index n and thickness t. By varying the adjustable parameters t and n, one can optimize such nanocrystals and receive engineered optical characteristics. In the properly-designed nanocrystals, light scattering is highly directional towards the solar-cell device and, simultaneously, the system exhibits a highly-enlarged optical path length. Potential usages of the core-shell nanocrystals designed by us are useful in solar cells and photodetectors.

Method Full-wave finite-difference time-domain (FDTD) simulations and online multilayered nanoparticle toolkit are employed to evaluate the properties of nanoparticles and nanoparticles on the silicon substrate [45]. The normalized scattering (absorption) cross section, Qscat (Qabs) is defined as scattering (absorption) cross section divided by its geometrical cross section, illuminated by a linearly polarized (along z) plane wave. A built-in analysis group is surrounded around the core-shell nanoparticle and a total-field


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scattered-field (TFSF) source is used. Perfectly matched layer (PML) and periodic boundaries are adopted for simulation. We use override mesh 0.5 nm for the core-shell nanoparticles and an auto mesh generation method is used in other simulation region. We decrease the mesh size and increase the PML layers until the results are convergent. The refractive index of Ag and crystalline Si in the simulation is modelled using fitted optical data from Ref. [46]. A factor determining the light trapping ability in plasmonic solar cells is the fraction of light scattered into the underneath substrate, fsub, defined as the power scattered into the Si substrate divided by total scattered power. The light absorption is exponential in planar PV devices with the intensity of the incident illumination decays from front surface of the Si substrate, as defined in eq. 1:

E  E0e L

(1)

Where E0 is the incident intensity that enters the material, which is equal to 1 in our simulation, L is optical pathlength and α is the absorption coefficient corresponding to the wavelength λ. Thus the L can be defined in eq.2: (2) L   ln E /  The decayed intensity is different between a flat solar cell and a flat solar cells with plasmonic enhancers after same length penetration. For the maximum relative optical path length enhancement factor, dop, it is determined by eq. 3:

dop  Lmax / Lbare  ln Emin / ln Ebare

(3)

where Emin is the maximum electric field intensity after coupling core-shell or bare nanoparticle; Ebare is the electric field in planar device. It is worth noting that only when the electric field intensities are monitored after same penetration length the eq. 3 validates. Based on the maximum relative optical path length enhancement factor, dop, a maximum light enhancement can be determined by eq. 4 [47]:

2dop / (1  f sub )

(4)

Results and Discussion Per Mie theory, a particle’s scattering and absorption properties rely on its composition, shape, size and surrounding environment. To compare the absorption and scattering properties difference between the core-shell nanoparticle and bare nanoparticle, the Qabs and Qscat are plotted in figure 1(a) and (b). As the size increases, the Qscat will increase and the Qabs will decrease, leading to a large scattering efficiency (Qscat/ Qabs). However, the scattering peak of 320 nm Ag nanoparticle results from dipole resonance shifts to regions beyond 1100 nm, which is useless for solar cell application. The core-shell nanoparticle that has same size with that of a bare Ag nanoparticle can alleviate the red shift of dipole resonance and fasten it within the near-infrared region where Si absorbs weakly. Multiple peaks are evident in the core-shell case due to the excitation of higher order resonances (e.g. quadruple and octupole moments), as shown in figure 1(b). The core-shell nanoparticle demonstrates strong Qscat preserved over a wide spectral range

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than the bare nanoparticle. The maximum Qscat of 80 nm and core-shell nanoparticle locates at ~381 nm and ~1061 (labelled as P) nm, indicating a strong scattering around their resonant frequencies. However, their scattering features are totally different: the 80 nm sphere at 381 nm presents a symmetry in the backward and forward directions. Spherical symmetry of the silver sphere does not guarantee azimuthally symmetric scattering because only electric response dominants in the sphere [36]. After coated with a dielectric layer, the core shell nanoparticle shows enhanced forward scattering with vanished backscattering which originates from the destructive interference of electric and magnetic dipolar resonances that coexist with the same strength within the particle itself, as compared in figure 1(c) [36]. The scattering of a multilayered sphere can be solved by Mie theory [48]. The effective electric dipolar polarizability α1𝑒 and magnetic dipolar polarizability α1𝑚 can be expressed as: 3i 3i (5) 1e  2 a1 , 1m  2 b1 2k 2k where a1 and b1 are Mie scattering coefficients, which correspond to electric and magnetic dipole moments, respectively, and k is the angular wavenumber in the background material. The core-shell nanoparticle can be considered as a combination of geminate orthogonal electric and magnetic dipole when taking first order electric and magnetic eigenmodes of the core-shell nanoparticle into account. The two modes can be superimposed spectrally with same strength due to the orthogonality by tailoring the radius aspect ratio and coating refractive index n. In the core (Ag, 80 nm)-shell (t=60, n=3.2 nm) case, the Qscat value from a1 and b1 contribution is 6.55 and 6.66 at point P, respectively. As a result, the core-shell nanoparticle is able to achieve enhanced forward scattering with suppressed backward scattering because of the constructive and destructive interference of the electric and magnetic dipoles, respectively. To further evaluate the scattering efficiency, the scattering-to-absorption cross sections (S= Qscat/Qabs) between the core-shell and bare nanoparticle are compared in figure 1(d). The scattering efficiency of core-shell nanoparticle outperforms that of the bare nanoparticle with maximum S approaching to ~500 preserved over a broadband spectral range, meaning that the beneficial light scattering enhancement exceeds the punitive absorption significantly. Since absorption in a metal nanoparticle will simply create heat and the energy will be lost, the large S of core-shell nanoparticle indicates the heat loss can be neglected.


Figure 1. Normalized absorption (a) and scattering (b) cross-section spectra of bare Ag nanospheres with 80, 320 nm diameter and a core (Ag, 80 nm)-shell (t=60 nm, n=3.2) nanoparticle. For practical applications, it is essential to achieve zero backward scattering when the n > 2.5 and thus Si, CdSe, InP, TiO2, Cinnabar, GaAs, GaP and Ge are ideal candidates. (c) Angular scattering of the 80 nm Ag sphere (red plot) and core (Ag, 80 nm)-shell (t=60, n=3.2 nm) nanoparticle at plasmon wavelength (381 and 1061 nm, respectively) in xz plane; The Y-axis value is square of the scattering electric field intensity. (d) Calculated scattering-to-absorption cross section (S) between the 80 nm Ag sphere (red plot) and core (Ag, 80 nm)-shell (t=60, n=3.2 nm) nanoparticle; the inset is a schematic unit cell in simulation. According to the Mie theory, the scattering performance of the core shell nanoparticle will be influenced by the coating shell due to the fact that the effective permittivity of the surrounding environment change and size increase. In the practical application, particles are usually placed on top of a substrate. Peng Yu et al. have shown that the core-shell nanoparticle demonstrates a better performance when surface plasmon is located in front of a solar cell [37]. Therefore, we compare the bare Ag nanoparticles with Ag nanoparticles coated with different t and n located on the front side of Silicon substrates. In this case, a large amount of light scattered into the underneath Si is critical for achieving high efficiency solar cells. The coating thickness and refractive index have different scattering patterns when compared nanoparticles without coating, as shown in figure 2. The fsub of a paralleled electric point dipole and bare Ag nanoparticle

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are also shown in figure 2(a). As can be seen in figure 2(a) and (b), the core-shell nanoparticle is able to achieve nearly perfect forward light scattering (fsub= ~1) accompanied by a peak. The peak and dip can be attributed to constructive plasmon and destructive Fano resonance, respectively [37]. The Fano resonance gives rise to dips, which is inherent in the metal nanostructures and metamaterials [49]. When the interference wavelength is lower than the plasmon resonance, a phase difference π is generated compared to the incident field, and thus lead to a destructive interference. For wavelengths longer than the resonance wavelength, the light is scattered preferentially towards the Si medium, keeping in phase with the incident field and thus give rise to a constructive interference. As disclosed in the Fig. 2, as the t and n increases, the amplitude of peaks decreased and dips increased, indicating that the Fano resonance becomes evident with increasing dielectric coating thickness and refractive index [50]. The fsub maximizes at t=30 and n=2.2, respectively due to the matching degree of orthogonal electric and magnetic dipole by changing the t and n. Although the Fano resonance leads to a useless backward scattering, the ultimate efficiency of large size nanoparticles still outperform that of the small one [37]. It is worth noting that one may argue that the core-shell nanoparticles have better scattering properties than that of the bare Ag nanoparticle because of the increased size of the shells. However, according to Ref. [19], the fsub is impaired as the size increases.

Figure 2. Fraction of light scattered into the Silicon substrate with coating thickness (a) and coating refractive index (b) change. For practical application consideration, a 400 nm lattice constant is adopted and the core diameter is set to be 120 nm; the n in (a) is set as 3.2 and t in (b) is 20 nm; a parallel electric dipole and a bare 120 nm sphere are plotted for comparison. When the thickness of PV devices decreases to a few microns, a thin slab can efficiently collect generated carrier while long wavelength photons are not absorbed resulting in impaired photocurrent, as shown in Fig. 3(a). A thick film is able to absorb nearly all of the incident light but long pathlength aggravates the likelihood of carrier recombination before collection and leads to reduced current, as shown in Fig. 3(b). Therefore, there is a trade-off for a given material and it leads to an optimum thickness to obtain maximum efficiency. In order to increase the absorption within the thin film, one needs


to increase the optical path. We calculate the relative optical path length enhancement factor dop to explain how core-shell nanoparticle aids the optical pathlength enhancement, as illustrated in Fig. 3(c). The bare nanoparticle and core-shell nanoparticle can both improve the dop, but the core-shell nanoparticle demonstrates a distinct improvement when compared with that of the bare one as the n or t changes, as shown in Fig. 3(d) and (e). For example, the dop for bare nanoparticle at 588 nm is ~1.24 while for core-shell nanoparticle with 10 nm coating is 3.59 which exceeds the value of electric point dipole and Lambertian scatter [19]. This again justify the extraordinary forward scattering properties of the core-shell nanoparticle. As n increases, the dop becomes more evident in near-infrared region where Si absorbs weakly, meaning that core-shell nanoparticles are ideal candidates to boost the light harvesting of Si thin film solar cells.

Figure 3. Schematic of absorption depth and carrier collection for different wavelengths of incident light and film thicknesses: (a) Light absorption in a thin slab; (b) Light absorption in a thick device. (c) Illustration of pathlength enhancement and carrier collection in core-shell assisted thin film. Relative optical path length enhancement factor of the bare and core-shell nanoparticle, dop as the t (d) and n (e) change. The black and red value in parenthesis are variable and fsub, respectively. Once the dop is determined, the maximum pathlength can be calculated by eq.4, as shown in Fig. 4(a). As compared in Ref. [19], the Lambertian scatter and ideal dipole have maximum pathlength enhancement ~100, which demonstrate better maximum pathlength enhancement than that of the spheres (the value for spheres is ~10). The maximum pathlength enhancement of bare spheres is confirmed in Fig. 4(a). However, the maximum pathlength enhancements at wavelengths that have maximum fsub demonstrate value above 100, exceeding Lambertian scatter and ideal dipole. The core-

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shell nanoparticle (t=30 nm; n=3.2) shows a maximum pathlength enhancement as high as ~3133. The extraordinary pathlength enhancement results from the perfect fsub. Figure 4(b) plots the influence of core-shell (t=20 nm; n=3.2) nanoparticle on absorption properties of blue, green, red and infrared light, excluding the parasitic absorption in core-shell nanoparticle. As discussed above, the thin film will suffer from destructive interference when wavelengths below the resonance wavelength. However, the light absorption enhancement in red and near-infrared region is significantly boosted. Although suffered from destructive Fano resonance, the weighted solar spectrum with absorption profile is boosted when compared with that of the flat cell and cell with bare nanoparticle and thus gives rise to photocurrent enhancement [37].

Figure 4. (a) Maximum path length enhancement for core-shell nanoparticles in figure 3. (b) Nanoparticle absorption profile for different wavelengths of light. To provide an intuitively interpretation into the enhanced scattering and suppressed backward scattering, we plot the near and far-field image from the 20 nm coating coreshell (n=3.2) for illustration, as shown in figure 5. When the incident wavelength satisfies either the zero-backward condition or the maximum forward condition, the field is primarily concentrated around the core-shell nanoparticle, as shown in Fig. 5(b). In fact, 99.6% of the scattered energy in the plane is radiated into the Si substrate and only 0.4% is remained in the backward. However, the bare particle demonstrates a strong backward scattering with 25.5% backward scattering power, as shown in Fig. 5(a). The near-field reveals that the concentrated light around bare particle is mainly concentrated within the backward zone.


Figure 5. Calculated distribution of the total near-field intensity (logarithmic scale) and far-field intensity (square scale) around the bare (a) and core-shell particles (b).

Conclusion In conclusion, we have investigated the light trapping ability of core-shell nanoparticles on Si thin films. They demonstrate enhanced forward scattering with suppressed backward scattering when they are front-located on the Si substrate. The fraction of light scattered into the substrate can achieve as high as 0.999 and maintain a high value within broadband spectra. As the coating thickness and refractive index increase, the maximum relative optical path length enhancement factor increase dramatically at the

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long wavelength where Si thin film solar cells absorbs weakly. In thin film solar cell technology, the cell needs to be significantly thinner than the minority carrier diffusion while a significant fraction of long wavelength solar radiation is not absorbed. The coreshell nanoparticles can be synthesized and to be placed on the surface of the Si solar cell (rear or front side). The thickness of coating shells can be governed in the range of tens to several hundred nanometers by changing the concentration of the sol-gel precursor or reactive time [51]. Fabrication of solar cells with plasmonic core-shell nanoparticles can be achieved by a facile method with drop casting. This work provides a new insight for addressing this issue by using core-shell nanoparticle with perfect forward scattering while getting rid of backward scattering.

Acknowledgments Authors appreciate the financial supports by the National Program on Key Basic Research Project (973 Program) No. 2013CB933301, National Natural Science Foundation of China No. 11305029. Australian Research Council is acknowledged for the financial support.

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