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.

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References

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  1. E. Hecht, Optics (Pearson Education, 2002).
  2. H. A. Macleod, Thin-Film Optical Filters (Taylor and Francis Group, 2010).
  3. M. Born and E. Wolf, Principles of Optics (Pergamon Press Ltd., 1980).
  4. C. C. Katsidis and D. I. Siapkas, “General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference,” Appl. Opt. 41(19), 3978–3987 (2002).
    [Crossref] [PubMed]
  5. E. Centurioni, “Generalized matrix method for calculation of internal light energy flux in mixed coherent and incoherent multilayers,” Appl. Opt. 44(35), 7532–7539 (2005).
    [Crossref] [PubMed]
  6. J. S. C. Prentice, “Coherent, partially coherent and incoherent light absorption in thin-film multilayer structures,” J. Phys. D Appl. Phys. 33(24), 3139–3145 (2000).
    [Crossref]
  7. M. C. Troparevsky, A. S. Sabau, A. R. Lupini, and Z. Zhang, “Transfer-matrix formalism for the calculation of optical response in multilayer systems: from coherent to incoherent interference,” Opt. Express 18(24), 24715–24721 (2010).
    [Crossref] [PubMed]
  8. R. Siegel, “Net radiation method for transmission through partially transparent plates,” Sol. Energy 15(3), 273–276 (1973).
    [Crossref]
  9. R. Santbergen, J. M. Goud, M. Zeman, J. A. M. van Roosmalen, and R. J. C. van Zolingen, “The AM1.5 absorption factor of thin-film solar cells,” Sol. Energy Mater. Sol. Cells 94(5), 715–723 (2010).
    [Crossref]

2010 (2)

M. C. Troparevsky, A. S. Sabau, A. R. Lupini, and Z. Zhang, “Transfer-matrix formalism for the calculation of optical response in multilayer systems: from coherent to incoherent interference,” Opt. Express 18(24), 24715–24721 (2010).
[Crossref] [PubMed]

R. Santbergen, J. M. Goud, M. Zeman, J. A. M. van Roosmalen, and R. J. C. van Zolingen, “The AM1.5 absorption factor of thin-film solar cells,” Sol. Energy Mater. Sol. Cells 94(5), 715–723 (2010).
[Crossref]

2005 (1)

2002 (1)

2000 (1)

J. S. C. Prentice, “Coherent, partially coherent and incoherent light absorption in thin-film multilayer structures,” J. Phys. D Appl. Phys. 33(24), 3139–3145 (2000).
[Crossref]

1973 (1)

R. Siegel, “Net radiation method for transmission through partially transparent plates,” Sol. Energy 15(3), 273–276 (1973).
[Crossref]

Centurioni, E.

Goud, J. M.

R. Santbergen, J. M. Goud, M. Zeman, J. A. M. van Roosmalen, and R. J. C. van Zolingen, “The AM1.5 absorption factor of thin-film solar cells,” Sol. Energy Mater. Sol. Cells 94(5), 715–723 (2010).
[Crossref]

Katsidis, C. C.

Lupini, A. R.

Prentice, J. S. C.

J. S. C. Prentice, “Coherent, partially coherent and incoherent light absorption in thin-film multilayer structures,” J. Phys. D Appl. Phys. 33(24), 3139–3145 (2000).
[Crossref]

Sabau, A. S.

Santbergen, R.

R. Santbergen, J. M. Goud, M. Zeman, J. A. M. van Roosmalen, and R. J. C. van Zolingen, “The AM1.5 absorption factor of thin-film solar cells,” Sol. Energy Mater. Sol. Cells 94(5), 715–723 (2010).
[Crossref]

Siapkas, D. I.

Siegel, R.

R. Siegel, “Net radiation method for transmission through partially transparent plates,” Sol. Energy 15(3), 273–276 (1973).
[Crossref]

Troparevsky, M. C.

van Roosmalen, J. A. M.

R. Santbergen, J. M. Goud, M. Zeman, J. A. M. van Roosmalen, and R. J. C. van Zolingen, “The AM1.5 absorption factor of thin-film solar cells,” Sol. Energy Mater. Sol. Cells 94(5), 715–723 (2010).
[Crossref]

van Zolingen, R. J. C.

R. Santbergen, J. M. Goud, M. Zeman, J. A. M. van Roosmalen, and R. J. C. van Zolingen, “The AM1.5 absorption factor of thin-film solar cells,” Sol. Energy Mater. Sol. Cells 94(5), 715–723 (2010).
[Crossref]

Zeman, M.

R. Santbergen, J. M. Goud, M. Zeman, J. A. M. van Roosmalen, and R. J. C. van Zolingen, “The AM1.5 absorption factor of thin-film solar cells,” Sol. Energy Mater. Sol. Cells 94(5), 715–723 (2010).
[Crossref]

Zhang, Z.

Appl. Opt. (2)

J. Phys. D Appl. Phys. (1)

J. S. C. Prentice, “Coherent, partially coherent and incoherent light absorption in thin-film multilayer structures,” J. Phys. D Appl. Phys. 33(24), 3139–3145 (2000).
[Crossref]

Opt. Express (1)

Sol. Energy (1)

R. Siegel, “Net radiation method for transmission through partially transparent plates,” Sol. Energy 15(3), 273–276 (1973).
[Crossref]

Sol. Energy Mater. Sol. Cells (1)

R. Santbergen, J. M. Goud, M. Zeman, J. A. M. van Roosmalen, and R. J. C. van Zolingen, “The AM1.5 absorption factor of thin-film solar cells,” Sol. Energy Mater. Sol. Cells 94(5), 715–723 (2010).
[Crossref]

Other (3)

E. Hecht, Optics (Pearson Education, 2002).

H. A. Macleod, Thin-Film Optical Filters (Taylor and Francis Group, 2010).

M. Born and E. Wolf, Principles of Optics (Pergamon Press Ltd., 1980).

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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)

Equations on this page are rendered with MathJax. Learn more.

{ 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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