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Photonic light-trapping versus Lambertian limits in thin film silicon solar cells with 1D and 2D periodic patterns

Angelo Bozzola, Marco Liscidini, and Lucio Claudio Andreani

Open Access Open Access

Abstract

We theoretically investigate the light-trapping properties of one- and two-dimensional periodic patterns etched on the front surface of c-Si and a-Si thin film solar cells with a silver back reflector and an anti-reflection coating. For each active material and configuration, absorbance A and short-circuit current density Jsc are calculated by means of rigorous coupled wave analysis (RCWA), for different active materials thicknesses in the range of interest of thin film solar cells and in a wide range of geometrical parameters. The results are then compared with Lambertian limits to light-trapping for the case of zero absorption and for the general case of finite absorption in the active material. With a proper optimization, patterns can give substantial absorption enhancement, especially for 2D patterns and for thinner cells. The effects of the photonic patterns on light harvesting are investigated from the optical spectra of the optimized configurations. We focus on the main physical effects of patterning, namely a reduction of reflection losses (better impedance matching conditions), diffraction of light in air or inside the cell, and coupling of incident radiation into quasi-guided optical modes of the structure, which is characteristic of photonic light-trapping.

© 2011 Optical Society of America

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Figures (11)
Fig. 1
Fig. 1 Short-circuit current density Jsc for c-Si (indirect band-gap), a-Si, CdTe and CuIn1−xGaxSe2 (CIGS, direct band-gap, taking x = 0.08) as a function of thickness, under AM1.5 solar spectrum [3]. Solid lines refer to the single pass case, while dashed lines refer to the Lambertian light-trapping limit denoted as LLα in this paper [9]. In both cases reflection losses are not considered.

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Fig. 2
Fig. 2 Scheme of silicon PV cells patterned with a simple 1D photonic lattice (a) and with a square 2D lattice (b).

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Fig. 3
Fig. 3 (a) Multilayer subdivision of PV cells along z (the unit cell volume used for A calculation is enclosed with dash line). (b) Convergence of the calculated absorbance (main panel) and Jsc (inset) as a function of the number NPW of plane waves involved in the calculation.

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Fig. 4
Fig. 4 Contour plot of short-circuit current density Jsc as a function of etching depth h and ratios b/a and r/a (in %) for c-Si PV cells patterned with a simple 1D lattice (a) and square 2D lattice (b). For both patterns the thickness d=1μm and the optimal period a=600 nm.

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Fig. 5
Fig. 5 Calculated optical spectra (for unpolarized light) for c-Si PV cells patterned with optimal 1D simple lattice (d=1 μm, a=600 nm, h=240 nm, b/a=0.3): reflectance Rn=0 and contributions from diffraction in air ∑n≠0 Rn (a), absorbance A (b) and absorption enhancement F (c). Calculated optical spectra (for unpolarized light) for c-Si PV cells patterned with optimal 2D square lattice (d=1 μm, a=600 nm, h=190 nm, r/a=0.33): reflectance Rn=0 and contributions from diffraction in air ∑n≠0 Rn (d), absorbance A (e) and absorption enhancement F (f). For absorbance the Lambertian limits LL0 and LLα are reported, together with single pass (SP) absorption with and without reflection losses. The thin grey lines refer to the calculated data, while the thick black lines are the corresponding smoothed quantities.

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Fig. 6
Fig. 6 Spectral contributions dJsc/dE to short-circuit current density Jsc for c-Si PV cells patterned with optimized 1D and square 2D square lattices. Thickness d=1μm, optimal period a=600 nm.

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Fig. 7
Fig. 7 (a) Calculated short-circuit current densities Jsc for c-Si PV cells patterned with optimized 1D and square 2D lattices varying the thickness d of the starting active material’s slab. (b) Jsc for optimal configurations as a function of period a and thickness d.

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Fig. 8
Fig. 8 Contour plot of short-circuit current density Jsc as a function of etching depth h and ratios b/a and r/a (in %) for a-Si PV cells patterned with a simple 1D photonic lattice (a) and square 2D lattice (b). For both patterns the thickness d=300 nm and the optimal period a=300 nm.

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Fig. 9
Fig. 9 Calculated optical spectra (for unpolarized light) for a-Si PV cells patterned with optimal 1D simple lattice (d=300 nm, a=300 nm, h=210 nm, b/a=0.55): reflectance Rn=0 and contributions from diffraction in air ∑n≠0 Rn (a), absorbance A (b) and absorption enhancement with respect to single pass absorption without reflection losses, F (c). Calculated optical spectra (for unpolarized light) for a-Si PV cells patterned with optimal 2D square lattice (d=300 nm, a=300 nm, h=215 nm, b/a=0.4): reflectance Rn=0 and contributions from diffraction in air ∑n≠0 Rn (d), absorbance A (e) and absorption enhancement with respect to single pass absorption without reflection losses, F (f). For absorption the Lambertian limits LL0 and LLα are reported, together with single-pass absorption with and without reflection losses.

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Fig. 10
Fig. 10 Spectral contributions dJsc/dE to short-circuit current density Jsc for a-Si PV cells patterned with optimized 1D and square 2D lattices. The thickness d=300 nm, the optimal period a=300 nm.

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Fig. 11
Fig. 11 (a) Calculated short-circuit current densities Jsc for a-Si PV cells patterned with optimized 1D and square 2D lattices varying the thickness d of the starting active material’s slab. (b) Jsc for optimal configurations as a function of period a and thickness d.

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Equations (9)

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F F S i = 1 − π r 2 a 2                     F F A R C = π r 2 a 2 .
J ( V ) = J s c − J 0 [ e e V K B T − 1 ] ,
J s c = e ∫ E g ∞ A ( E ) d 𝒩 d E I Q E ( E ) d E ≡ e ∫ E g ∞ A ( E ) d 𝒩 d E d E ≡ ∫ E g ∞ d J s c ( E ) d E d E ,
E ( ρ , z ) = ∑ n = 0 N P W − 1 E ˜ ( G n , z ) e i ( k / / + G n ) ⋅ ρ ,
A + R + T + ∑ n ≠ 0 R n + ∑ n ≠ 0 T n = 1 ,
4 n 2 α d ≪ 1 ,
A s p ( E ) = 1 − e − α ( E ) d .
A L L 0 ( E ) = 1 − e − 4 n 2 α ( E ) d ,
F ( E ) = A ( E ) A s p ( E ) = A ( E ) 1 − e − α ( E ) d ,
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