Broadband omnidirectional antireflection coatings for metal-backed solar cells optimized using simulated annealing algorithm incorporated with solar spectrum

Yin-Jung Chang; Yu-Ting Chen

doi:10.1364/OE.19.00A875

Optics Express
Vol. 19,
Issue S4,
pp. A875-A887
(2011)
•https://doi.org/10.1364/OE.19.00A875

Broadband omnidirectional antireflection coatings for metal-backed solar cells optimized using simulated annealing algorithm incorporated with solar spectrum

Yin-Jung Chang and Yu-Ting Chen

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Yin-Jung Chang and Yu-Ting Chen, "Broadband omnidirectional antireflection coatings for metal-backed solar cells optimized using simulated annealing algorithm incorporated with solar spectrum," Opt. Express 19, A875-A887 (2011)

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Abstract

Broadband omnidirectional antireflection (AR) coatings for solar cells optimized using simulated annealing (SA) algorithm incorporated with the solar (irradiance) spectrum at Earth’s surface (AM1.57 radiation) are described. Material dispersions and reflections from the planar backside metal are considered in the rigorous electromagnetic calculations. Optimized AR coatings for bulk crystalline Si and thin-film CuIn_1–xGa_xSe₂ (CIGS) solar cells as two representative cases are presented and the effect of solar spectrum in the AR coating designs is investigated. In general, the angle-averaged reflectance of a solar-spectrum-incorporated AR design is shown to be smaller and more uniform in the spectral range with relatively stronger solar irradiance. By incorporating the transparent conductive and buffer layers as part of the AR coating in CIGS solar cells (2μm-thick CIGS layer), a single MgF₂ layer could provide an average reflectance of 8.46% for wavelengths ranging from 350 nm to 1200 nm and incident angles from 0° to 80°.

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Fig. 1 Two-dimensional structure and the associated transmission-line network for the reflectance calculation of a general solar cell with a backside metal.

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Fig. 2 Calculated reflectance R(λ, θ) (averaged over TE and TM polarization) of a polished crystalline Si substrate with an SA-optimized three-layer AR coating given in Table 1 for (a) λ = [400, 750] nm, θ = [40°, 80°] and (b) λ = [400, 1100] nm, θ = [0°, 80°].

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Fig. 3 Calculated angle-averaged reflectance spectrum of an SA-optimized AR coating for metal-backed Si solar cells with (a) and without (b) the solar spectrum consideration. The Si layer is assumed 300 μm in thickness and the incident angle θ ranges from 0° to 80°. The electromagnetic model is shown as an inset; ARC: antireflection coating, PEC: perfect electric conductor.

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Fig. 4 Calculated angle-averaged (θ = [0°, 80°]) reflectance spectrum for CIGS solar cells with (a) and without (b) the solar spectrum consideration. The CIGS layer has a thickness of 2 μm. The electromagnetic model is shown as an inset; ARC: antireflection coating, PEC: perfect electric conductor.

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Fig. 5 The reflectance R(λ, θ) averaged over TE and TM polarization of (a) a single MgF₂ layer and (b) a two-layer AR coating for CIGS solar cells. The CIGS structure is shown in the inset of Fig. 4.

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Tables (4)

Table 1 Comparisons Between Layer Thickness (in nm) and Average Reflectance R _ave (Averaged over Incident Angles, Wavelengths, and Polarization) for a Three-Layer AR Coating on Top of a Polished Crystalline Si Substrate Obtained Using a Genetic Algorithm [8] and the Present SA Algorithm

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Table 2 Refractive Index n and Thickness t (in nm) of Individual Layers in SA-Optimized AR Coatings for Bulk Crystalline Si Solar Cells with Back Reflectors*

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Table 3 Layer Thickness (in nm) and Average Reflectance R _ave of an SiO₂/TiO₂ Double-Layer AR Coating for Metal-Backed 300-μm-Thick Crystalline Si Solar Cells

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Table 4 Refractive Index n and Layer Thickness t (in nm) of Individual Layers in SA-Optimized AR Coatings for CuIn_1−xGa _x Se₂|_x=0.31 Solar Cells*

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Equations (11)

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{\underline{X}}_{k + 1} = {\underline{X}}_{k} + r \underset{͇}{V} {\underline{e}}_{u}^{T},

v_{u}^{'} = {\begin{array}{l} v_{u} [1 + c_{u} (\frac{n_{acpt}^{(u)} / N_{S} - 0.6}{0.4})] & if n_{acpt}^{(u)} > 0.6 N_{S}, \\ v_{u} {[1 + c_{u} (\frac{0.4 - n_{acpt}^{(u)} / N_{S}}{0.4})]}^{- 1} & if n_{acpt}^{(u)} > 0.4 N_{S}, \\ v_{u}, & otherwise, \end{array}

T_{0} = {\bar{Δ C}}^{(+)} {[ln \frac{m_{2}}{m_{2} χ + (χ - 1) m_{1}}]}^{- 1},

Z_{0, i} = {\begin{matrix} ω μ_{0} / κ_{i} & TE wave \\ κ_{i} / (ω ɛ_{0} ɛ_{i}) & TM wave, \end{matrix}

κ_{i} = \frac{2 π}{λ} \sqrt{ɛ_{i} - ɛ_{a} {sin}^{2} θ},

Γ (λ, θ) = \frac{Z_{L, 0^{+}} - Z_{0, a}}{Z_{L, 0^{+}} + Z_{0, a}},

Z_{in, i} = Z_{0, i} (\frac{1 + Γ_{i, i + 1} e^{- j 2 κ_{i} t_{i}}}{1 - Γ_{i, i + 1} e^{- j 2 κ_{i} t_{i}}}),

Γ_{i, i + 1} = \frac{Z_{in}, i + 1 - Z_{0}, i}{Z_{in}, i + 1 + Z_{0}, i} .

C (\underline{X}) = \frac{1}{2 Δ λ Δ θ} \int_{Δ λ} \int_{Δ θ} w (λ) [{| Γ_{TE} (λ, θ) |}^{2} + {| Γ_{TM} (λ, θ) |}^{2}] d θ d λ

w (λ) = I_{λ} / \int_{Δ λ} I_{λ} d λ,

R_{θ - ave} (λ) = \frac{1}{2 Δ θ} \int_{Δ θ} [{| Γ_{TE} (λ, θ) |}^{2} + {| Γ_{TM} (λ, θ) |}^{2}] d θ,

Algorithm	TiO₂ (nm)	SiO₂ (nm)	Porous SiO₂ (nm)	R _ave (%)
Genetic Algorithm	45	120	200	4.90
Simulated Annealing	56.81	122.88	373.14	3.54

	1-layer	2-layer	3-layer	4-layer	5-layer	6-layer
n ₁	1.9734	1.3349	1.0925	1.0500	1.0500	1.0500
n ₂	-	2.4611	1.5454	1.1793	1.1880	1.4553
n ₃	-	-	2.6599	1.6305	2.6309	1.0923
n ₄	-	-	-	2.6600	1.5105	2.4363
n ₅	-	-	-	-	2.6599	1.3961
n ₆	-	-	-	-	-	2.6592
t ₁	74.29	134.21	231.30	273.42	279.47	297.72
t ₂	-	58.47	108.21	151.58	165.93	26.12
t ₃	-	-	53.88	101.79	9.02	96.14
t ₄	-	-	-	54.48	66.13	15.61
t ₅	-	-	-	-	56.97	60.48
t ₆	-	-	-	-	-	58.85
R _ave(%) 400 nm −1100 nm, 0°–80°	17.20	9.56	6.59	5.46	5.38	5.34
R _ave(%) 400 nm −1000 nm, 0°–80°	13.24	5.37	2.39	1.41	1.31	1.26

	0° – 60°	0° – 70°	0° – 80°	0° – 90°
SiO₂ (nm)	102.82	105.60	108.44	109.90
TiO₂ (nm)	49.38	49.56	49.89	50.11
R _ave (%)	7.90	8.90	11.30	17.24

	1-layer	2-layer	3-layer	4-layer	5-layer
n ₁	1.3461	1.1126	1.0505	1.0500	1.0500
n ₂	-	1.5037	1.2453	1.1643	1.1628
n ₃	-	-	1.6528	1.4079	1.3933
n ₄	-	-	-	1.7842	1.7515
n ₅	-	-	-	-	1.9994
t ₁	122.71	205.12	304.23	296.52	294.98
t ₂	-	100.20	143.06	150.42	147.56
t ₃	-	-	88.39	114.94	110.00
t ₄	-	-	-	80.25	92.02
t ₅	-	-	-	-	73.04
t _ZnO	351.06	346.77	281.31	277.81	200.05
t _CdS	42.58	42.93	41.82	43.02	42.82
R _ave(%)	8.46	5.30	4.18	3.31	3.26

Algorithm	TiO₂ (nm)	SiO₂ (nm)	Porous SiO₂ (nm)	R _ave (%)
Genetic Algorithm	45	120	200	4.90
Simulated Annealing	56.81	122.88	373.14	3.54

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Equations (11)

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