Physics Department, University of Pavia, Italy Lucio Claudio Andreani, Angelo Bozzola, Piotr Kowalczewski, Marco Liscidini EMRS-Lille, Symposium Y, Photonic structures for light trapping in thin-film solar cells Outline 1.Introduction 2.Photonic lattices: ordered, disordered, hybrid 3.Electro-optical modelling 4.Conclusions Goals: a)to determine the best photonic structures for light trapping, taking the Lambertian limit as a reference; b)to determine the efficiency limits and the optimal thickness of thin-film crystalline silicon solar cells, taking into account nonradiative (bulk and surface) recombination. Silicon film: single-pass absorption Silicon film: Lambertian light trapping E. Yablonovitch, J. Opt. Soc. Am. 72, 899 (1982): thick solar cells (d ), weak absorption d1 light path enhancement by 4n 2 (LL0 limit) M.A. Green, Progr. Photovolt: Res. Appl. 10, 235 (2002): thick solar cells (d ), arbitrary absorption light path enhancement smaller than 4n 2 (LL limit) Reference works for Lambertian limits to light trapping: (rather a benchmark than a limit) Light trapping: order vs. disorder a hot topic X. Meng et al., OE 20, A465 (2012) C. Battaglia et al., ACS Nano (2012), DOI /nn300287j E. Martins et al., Nature Commun. 4, 2665 (2013). DOI: /ncomms3665 K.X. Wang et al., Nano Letters (2012), DOI /nl204550q Nanocavities (ordered) Pyramids (random) a-Si Quasi-random structure Ordered 1D or 2D photonic lattice Theoretical approach Optical problem: calculate short-circuit current density j sc, assuming 100% collection probability of e-h pairs: Calculation of absorption by Rigorous Coupled Wave Analysis [Whittaker & Culshaw, PRB 60, 2610 (1999); Liscidini et al., PRB 77, (2008)] N.b. we neglect parasitic absorption in the TCO Electrical problem: Carrier collection, I-V curves, efficiency Simulations with analytic modelling and with Silvaco-ATLAS Absorbance spectrumPhoton fluxSpectral contribution to j sc Outline 1.Introduction 2.Photonic lattices: ordered, disordered, hybrid 3.Electro-optical modelling 4.Conclusions A.Bozzola et al, OpEx 20, A224 (2012); Progr. Photov. Res. Appl. (2013). DOI: /pip.2385 P. Kowalczewski et al., Opt. Letters 37, 4868 (2012); OpEx 21, A808 (2013) Optimization of a 2D PhC pattern in c-Si Silicon thickness d=1000 nm, optimal a=600 nm Reference structure: no pattern, antireflection coating J sc =14.6 mA/cm 2 Optimal configuration: a=600 nm, r/a=0.33, h=190 nm J sc =22.0 mA/cm 2 best configuration has shallow etching depth S. Zanotto, M. Liscidini and LCA, Optics Express 18, 42604274 (2010) A. Bozzola, M. Liscidini and LCA, Opt. Express 20, A224 (2012) J SC vs. film thickness with 1D and 2D PhCs can be further improved using correlated disorder: Progr. Photov. Res. Appl. (2013), DOI: /pip.2385 Engineering Gaussian disorder at rough interfaces Topography of rough TCO substrateModel with 1D Gaussian disorder Model: Gaussian random surface I. Simonsen, Eur. Phys. J. Special Topics 181, 1 (2010); V. Freilikher, E. Kanzieper, and A. Maradudin, Phys. Rep. 288, 127 (1997). Validation: good agreement with 2D scattering properties (isotropic). See Opt. Letters 37, 4868 (2012). Disorder leads to increase and smoothing of absorption Photogeneration rate in ordered vs. disordered photonic structures: can be explained by Diffusion Diffraction Rough interface vs. Lambertian limit Gaussian disorder ( =300 nm, l c =160 nm) Gaussian disorder approaches Lambertian limit in a wide range of thicknesses wide spectrum of Fourier components Optimization of real substrates but increasing RMS height may lead to poor Si-material growth (cracks). Optimal compromise has to be found. P. Kowalckzewski, M. Liscidini, LCA, Opt. Letters 37, 4868 (2012) Hybrid structure: rough+grating (combination of disorder + order) P. Kowalckzewski, M. Liscidini, LCA, Opt. Express 21, A808 (2013) Lambertian limit is approached with moderate (80 nm) Outline 1.Introduction 2.Photonic lattices: ordered, disordered, hybrid 3.Electro-optical modelling 4.Conclusions A. Bozzola et al., J. Appl. Phys. 115, (2014); P. Kowalczewski et al., J. Appl. Phys. 115, (2014) Light harvesting + electronic transport Optical calculation yields spatial profile of photogenerated carriers Electronic transport is treated by solving drift-diffusion equations with generation and recombination terms, either with analytical model or by finite-element method (Silvaco-ATLAS) Generation rate profile for a Lambertian scatterer is analytically known Analytic model + Silvaco/ATLAS simulations Thin-film silicon solar cells can be more efficient than bulk ones with comparable material quality, provided light trapping close to Lambertian limit is implemented. This follows from gaining in open-circuit voltage V oc as the thickness is reduced: for a given material quality, carrier collection benefits from reduced thickness. But how are these results affected by surface recombination? Optimal region for high efficiency Efficiency J. Appl. Phys. 115, (2014); 115, (2014) L n =232 m, L p =23 m Efficiency as a function of thickness and material quality For any given material quality, thin-film solar cells with optimal thickness can outperform bulk ones. For high-quality material (c-Si), the optimal thickness is ~30 m and the conversion efficiency can be > 20% Effect of surface recombination Thin-film solar cells can still outperform bulk ones when surface recombination is present, provided SR velocity is smaller than a critical value S~10 3 cm/s [S