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The use of the adding-doubling method for the optical optimization of planar luminescent down shifting layers for solar cells

Sven Leyre, Jan Cappelle, Guy Durinck, Aimi Abass, Johan Hofkens, Geert Deconinck, and Peter Hanselaer

Open Access Open Access

Abstract

To enhance the efficiency of solar cells, a luminescent down shifting layer can be applied in order to adapt the solar spectrum to the spectral internal quantum efficiency of the semiconductor. Optimization of such luminescent down shifting layers benefits from quick and direct evaluation methods. In this paper, the potential of the adding-doubling method is investigated to simulate the optical behavior of an encapsulated solar cell including a planar luminescent down shifting layer. The results of the adding-doubling method are compared with traditional Monte Carlo ray tracing simulations. The average relative deviation is found to be less than 1.5% for the absorptance in the active layer and the reflectance from the encapsulated cell, while the computation time can be decreased with a factor 52. Furthermore, the adding-doubling method is adopted to investigate the suitability of the SrB4O7:5%Sm2 + ,5%Eu2 + phosphor as a luminescent down shifting material in combination with a Copper Indium Gallium Selenide solar cell. A maximum increase of 9.0% in the short-circuit current can be expected if precautions are taken to reduce the scattering by matching the refractive index of host material to the phosphor particles. To be useful as luminescent down shifting material, the minimal value of the quantum yield of the phosphor is determined to be 0.64.

© 2014 Optical Society of America

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Figures (9)
Fig. 1
Fig. 1 Encapsulation geometry used for simulations (dimensions not to scale).

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Fig. 2
Fig. 2 Transmittance spectra of Low-Iron Glass (blue) and EVA with (magenta) and without (red) uv blocker.

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Fig. 3
Fig. 3 Reflectance (red) and IQE (black) of the CIGS cell, together with the excitation (blue) and emission spectrum (magenta) of the SrB4O7:5%Sm2+,5%Eu2+ phosphor.

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Fig. 4
Fig. 4 Comparison between AD method (marks) and MC simulations (lines) of reflectance (R) and absorptance in the CIGS layer (A) of the encapsulated solar cell for an infinite solar cell, together with the incident irradiance on the cell (AM1.5 standard solar spectrum).

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Fig. 5
Fig. 5 Accuracy (red) and time computation (blue), in function of the number of incident wavelengths for the MC simulations (left) and in function of the number of channels for the AD calculations (right). The black lines denote the accuracy threshold of 1%.

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Fig. 6
Fig. 6 Relative gain in Isc by increasing the phosphor concentration in the LDS layer, with QY = 1 for the luminescent material.

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Fig. 7
Fig. 7 Relative gain in Isc by increasing the phosphor concentration under conditions of a matched refractive index for different QY values for the luminescent material.

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Fig. 8
Fig. 8 Relative gain in Isc by increasing the phosphor concentration under conditions of a matched refractive index and reduced Fresnel reflection in the multi-layer for different QY values for the luminescent material.

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Fig. 9
Fig. 9 Maximum increase of the Isc and the concentration ρ of phosphor where the maximum occurs in function of the QY of the phosphor.

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Equations (7)

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I sc = ∫ A(λ)⋅E(λ)⋅S⋅ IQE(λ)⋅ λ h⋅c ⋅e⋅dλ
s∇L(r,s)=−( μ a + μ s )L(r,s)+ μ s ∫ 4π p(s,s') L(r,s')dΩ'
s∇L(r,s)=−( μ a + μ s )L(r,s)+ μ s ∫ 4π p(s,s')L(r,s')dΩ' + w M ∑ i=1 N { μ e ( λ i )QY 1 4π ∫ 4π L(r,s', λ i )dΩ' Δλ }
R 20 (λ)= R 21 (λ)+ T 12 (λ) (E− R 10 (λ) R 12 (λ)) −1 R 10 (λ) T 21 (λ)
T 02 (λ)= T 12 (λ) (E− R 10 (λ) R 12 (λ)) −1 T 01 (λ)
R 20 c ( λ i X , λ j M )= T 12 (E− R 10 R 12 ) −1 [ R 10 ( R 12 c ( λ i X , λ j M ){ [ E− R 10 c ( λ i X , λ j M ) R 12 c ( λ i X , λ j M ) ] −1 R 10 c ( λ i X , λ j M ) T 21 c ( λ i X , λ j M ) } + T 21 c ( λ i X , λ j M ) ) + R 10 c ( λ i X , λ j M ) [ E− R 12 c ( λ i X , λ j M ) R 10 c ( λ i X , λ j M ) ] −1 T 21 ( λ i X ) ] + R 21 c ( λ i X , λ j M )+ T 12 c ( λ i X , λ j M ) [ E− R 10 ( λ i X ) R 12 ( λ i X ) ] −1 R 10 ( λ i X ) T 21 ( λ i X )
T 02 c ( λ i X , λ j M )= T 12 (E− R 10 R 12 ) −1 { R 10 R 12 c ( λ i X , λ j M ) [ E− R 10 ( λ i X ) R 12 ( λ i X ) ] −1 T 01 ( λ i X ) + R 10 c ( λ i X , λ j M ) [ E− R 12 ( λ i X ) R 10 ( λ i X ) ] −1 R 12 ( λ i X ) T 01 ( λ i X ) + T 01 c ( λ i X , λ j M ) } + T 12 c ( Δ λ i X ,Δ λ j M ) [ E− R 10 ( Δ λ i X ) R 12 ( Δ λ i X ) ] −1 T 01 ( Δ λ i X )
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