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Time domain simulation of tandem silicon solar cells with optimal textured light trapping enabled by the quadratic complex rational function

H. Chung, K-Y. Jung, X. T. Tee, and P. Bermel

Open Access Open Access

Abstract

Amorphous silicon/crystalline silicon (a-Si/c-Si) micromorph tandem cells, with best confirmed efficiency of 12.3%, have yet to fully approach their theoretical performance limits. In this work, we consider a strategy for improving the light trapping and charge collection of a-Si/c-Si micromorph tandem cells using random texturing with adjustable short-range correlations and long-range periodicity. In order to consider the full-spectrum absorption of a-Si and c-Si, a novel dispersion model known as a quadratic complex rational function (QCRF) is applied to photovoltaic materials (e.g., a-Si, c-Si and silver). It has the advantage of accurately modeling experimental semiconductor dielectric values over the entire relevant solar bandwidth from 300—1000 nm in a single simulation. This wide-band dispersion model is then used to model a silicon tandem cell stack (ITO/a-Si:H/c-Si:H/silver), as two parameters are varied: maximum texturing height h and correlation parameter f. Even without any other light trapping methods, our front texturing method demonstrates 12.37% stabilized cell efficiency and 12.79 mA/cm2 in a 2 μm-thick active layer.

© 2014 Optical Society of America

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Figures (10)
Fig. 1
Fig. 1 Cross section of a-Si/c-Si tandem solar cell. It is contacted with indium tin oxide on the front, and silver in the back, and encapsulated with glass. The randomly textured front surface is shown from two different perspectives. Note that the same textured surface on the ITO and a-Si is also applied to the top of the c-Si layer. The minimum glass thickness of 1500 nm is used only in simulation. Experimental thicknesses are greater, but Fig. 4 shows that this only has a minor effect on the absorption spectrum.

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Fig. 2
Fig. 2 Dispersion curve fittings of photovoltaic materials using the QCRF model. The solid lines and symbols indicate the results of the QCRF model and the experimental data of dispersive material, respectively: (a) Real part of relative permittivity of a-Si. (b) Imaginary part of relative permittivity of a-Si. (c) Real part of relative permittivity of c-Si. (d) Imaginary part of relative permittivity of c-Si. (e) Real part of relative permittivity of silver.

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Fig. 3
Fig. 3 The theoretical and simulated absorption rates of 300 nm thick a-Si, the former being obtained from Eq. (3) combined with literature data from ref. [36], and the latter being obtained from our QCRF model. The root mean square error from comparing the two data sets is 3.97%.

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Fig. 4
Fig. 4 The left figure indicates the experimental absorption rate for a 1500 nm thick c-Si solar cell. It is adapted from recently published research [38]. The right figure indicates the absorption rate obtained by the simulation.

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Fig. 5
Fig. 5 (a) Contour plot showing calculated short-circuit current density as a function of maximum texturing height and correlation factor for 2D solar cells, using TM-polarized light incident at normal incidence. Note that the optimal performance is expected to occur at f = 0.975, ln(1 − f) = −3.689 and h = 1000 nm in 2-D structure. (b) The optimized 2D geometry used to generate our contour plot.

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Fig. 6
Fig. 6 Random surface texturing algorithm represented in terms of correlation factor (f).

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Fig. 7
Fig. 7 Efficiency versus thickness of (left) indium-tin oxide and (right) a-Si. Each red dot corresponds to a single 3-D FDTD simulation and is projected from a higher-dimension manifold of design space onto the axes displayed, in order to identify the optimal values for these individual parameters. Note that each simulation is performed in a flat solar cell structure without texturing.

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Fig. 8
Fig. 8 Contour plot showing silicon tandem cell efficiency versus texturing height and the correlation factor. Note that the optimal performance is predicted to occur when f = 0.999 and h = 1158 nm, as explained in the text.

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Fig. 9
Fig. 9 Light absorption rate of the optimized tandem silicon solar cell with two reference absorption curves that are obtained from a flat structure and a totally random structure for normal incidence. (a) Light absorption in the a-Si layer. (b) Light absorption in the a-Si layer. (c) Normalized light absorption in the c-Si layer with rest of light filtered by the a-Si layer and by subtraction of the first reflected light at the SiO2 layer. (d) Total light absorption in both layers.

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Fig. 10
Fig. 10 Optimal random surface texturing in a tandem cell application shown from two different perspectives.

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Equations (9)

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ε r , QCRF ( ω ) = A 0 + A 1 ( j ω ) + A 2 ( j ω ) 2 1 + B 1 ( j ω ) + B 2 ( j ω ) 2 ,
r ( λ ) = ρ 1 + ∑ n = 1 ∞ τ 1 τ 1 ′ ( ρ 1 ′ ) n − 1 ρ 2 n e − j ω t = ρ 1 + τ 1 τ 1 ′ ρ 2 − 1 e j ω t − ρ 1 ′
t ( λ ) = τ 1 τ 2 ∑ n = 0 ∞ ( ρ 2 ρ 1 ′ ) n e − j ω t = τ 1 τ 2 1 − ρ 2 ρ 1 ′ e − j ω t ,
Z n + 1 = f * Z n + 1 − f 2 * r n ,
Z n + 1 = w ( n , N ) * Z n + ( f − w ( n , N ) ) * Z N − n − 1 + 1 − f 2 * r n ,
w ( n , N ) = f − ( f / 2 ) * exp ( − ( N − 2 * n + 2 ) ) ,
Z i + 1 , j + 1 = w ( i , N i ) * Z i , j + 1 + ( f / 2 − w ( i , N i ) ) * Z N + 2 − i , j + 1 + w ( j , N j ) * Z i + 1 , j + ( f / 2 − w ( j , N j ) ) * Z i + 1 , N + 2 − j + 1 − f 2 * r n ,
w ( i , N i ) = f / 2 − ( f / 4 ) * exp ( − ( N i − 2 * i + 2 ) ) , w ( j , N j ) = f / 2 − ( f / 4 ) * exp ( − ( N j − 2 * j + 2 ) ) .
f 2 D = f 3 D ( N Δ y 2 D / Δ y 3 D ) ,
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