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Optical model for multilayer structures with coherent, partly coherent and incoherent layers

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Abstract

We present a novel approach for modeling the reflectance, transmittance and absorption depth profile of thin-film multilayer structures such as solar cells. Our model is based on the net-radiation method adapted for coherent calculations and is highly flexible while using a simple algorithm. We demonstrate that as a result arbitrary multilayer structures with coherent, partly coherent and incoherent layers can be simulated more accurately at much lower computational cost.

©2013 Optical Society of America

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Figures (4)

Fig. 1
Fig. 1 Schematic multilayer structure, with numbering convention of interfaces, layers and electric field strength.
Fig. 2
Fig. 2 Simulated (area) and measured (symbols) R, A and T of a 1 μm ZnO:Al film on glass. The inset shows T in more detail. (a) single coherent simulation (b) average of three coherent simulations (the inset shows the individual simulations with φ = 0°, 120° and 240° and their average).
Fig. 3
Fig. 3 Deviation from the exact solution as a function of the number of coherent simulations averaged. The existing method of averaging with random φ (red line) and our new method of averaging with equidistant φ (green line) are compared.
Fig. 4
Fig. 4 (a) Absorptance and (b) absorption depth profile for of the absorber layer of an a-Si:H solar cell for various degrees of absorber layer coherence, indicated by visibility V. The lines represent V = 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0.

Equations (8)

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{ E ia = τ i1 E (i1)d E ib = r i> E ia + t i< E ic E ic = τ i E (i+1)b E id = t i> E ia + r i< E ic .
τ i = e i δ i ,
δ i =2π N i d i /λ ,
P i =( E i H i * ) ,
E i = E ia + E ib = E ic + E id ,
H i = N 0 N i1 ( E ia E ib )= N 0 N i ( E id E ic ) ,
R=1 P 1 A i = P i P i+1 T= P I .
δ i (t)=2π N i d i /λ+φ(t) .
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