Overcoming the temperature effect on a single junction and intermediate band solar cells using an optical filter and energy selective contacts

Abstract

The primary purpose of the paper is to reduce the impact of ambient temperature and internally generated heat on power conversion efficiency in solar cells. To this end, we design a simple layered structure using SiO₂, Si₃N_4, and Si as an optical filter in front of the solar cell. To demonstrate the capability of the proposed structure, the Si and SiC Solar cells are considered and power conversion capabilities for these systems with and without the optical filter are evaluated. Finally, enhancement in power conversion efficiency and other characteristics of the proposed device is studied. It should mention that the Intermediate Band Solar Cells for this study are considered that be suitable cases in this field. In this case, to reduce the internally generated heat, we use a novel method for extracting the hot carrier from different energy levels by using multi-level Energy Selective Contacts. Such contacts promote Efficiency and break the Shockley–Queisser limit. Also, the proposed multilayer structure is used to reduce the effect of the ambient temperature. Using the proposed idea, it is shown that the power conversion efficiency is approximately constant for 300 to 800 °K.

Appendix: Transfer matrix method (TMM)

Using the TMM method, the reflection and transmission coefficients are calculated easily. To model the structure, a 2 × 2 boundary matrix $D_{1}$, and a 2 × 2 diffusion matrix $P_{1}$, are defined for each layer as:

$$ D_{1} = \left[ {\begin{array}{*{20}l} 1 \hfill & 1 \hfill \\ {n_{1} \cos \theta_{1} } \hfill & {n_{2} \cos \theta_{2} } \hfill \\ \end{array} } \right] $$

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$$ P_{1} = \left[ {\begin{array}{*{20}l} {e^{ - i\varphi } } \hfill & 0 \hfill \\ 0 \hfill & {e^{i\varphi } } \hfill \\ \end{array} } \right] $$

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where $n_{1}$,$n_{2}$, $\theta_{1}$, $\theta_{2}$, and $\varphi$ are refractive indices, the angle of incident and reflected components, and the propagation phase through the thin film respectively the phase is given by:

$$ \varphi = \frac{2\pi nd}{A}\cos \theta $$

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The resultant matrix is defined as follows by the product of these individual matrices.

$$ \left( {\begin{array}{*{20}l} {M_{11} } \hfill & {M_{12} } \hfill \\ {M_{21} } \hfill & {M_{22} } \hfill \\ \end{array} } \right) = D_{0}^{ - 1} \left[ {\prod\limits_{l = 1}^{N} {D_{l} P_{l} D_{l}^{ - 1} } } \right]D_{s} $$

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where the elements of the matrix for a two-layer system are written as:

$$ M_{11} = \frac{1}{2}\left( {1 + \frac{{n_{3} \cos \theta_{3} }}{{n_{1} \cos \theta_{1} }}} \right)\hbox{cos}\varphi + \frac{1}{2}i\hbox{sin}\varphi \left( {\frac{{n_{2} \cos \theta_{2} }}{{n_{1} \cos \theta_{1} }} - \frac{{n_{3} \cos \theta_{3} }}{{n_{2} \cos \theta_{2} }}} \right) $$

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$$ M_{12} = \frac{1}{2}\left( {1 - \frac{{n_{3} \cos \theta_{3} }}{{n_{1} \cos \theta_{1} }}} \right)\hbox{cos}\varphi + \frac{1}{2}i\hbox{sin}\varphi \left( {\frac{{n_{2} \cos \theta_{2} }}{{n_{1} \cos \theta_{1} }} - \frac{{n_{3} \cos \theta_{3} }}{{n_{2} \cos \theta_{2} }}} \right) $$

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$$ M_{21} = \frac{1}{2}\left( {1 - \frac{{n_{3} \cos \theta_{3} }}{{n_{1} \cos \theta_{1} }}} \right)\hbox{cos}\varphi - \frac{1}{2}i\hbox{sin}\varphi \left( {\frac{{n_{2} \cos \theta_{2} }}{{n_{1} \cos \theta_{1} }} - \frac{{n_{3} \cos \theta_{3} }}{{n_{2} \cos \theta_{2} }}} \right) $$

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$$ M_{22} = \frac{1}{2}\left( {1 + \frac{{n_{3} \cos \theta_{3} }}{{n_{1} \cos \theta_{1} }}} \right)\hbox{cos}\varphi - \frac{1}{2}i\hbox{sin}\varphi \left( {\frac{{n_{2} \cos \theta_{2} }}{{n_{1} \cos \theta_{1} }} - \frac{{n_{3} \cos \theta_{3} }}{{n_{2} \cos \theta_{2} }}} \right) $$

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The transmission and reflection coefficients are calculated as follows.

$$ T = \frac{1}{{M_{11} }} $$

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$$ R = \frac{{M_{21} }}{{M_{11} }} $$

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