Analytical model of non-uniformly doped silicon solar cell for all illumination condition

Abstract

A mathematical model of a non-uniformly doped silicon solar cell for all illumination condition has been developed. The drift-diffusion equation has been solved under low injection approximation for the derivation of the model. The model is iteration-free and integration-free, so it offers an elegant way to study the wide variation of several transport parameters, their individual contributions and interdependence. This analytical expression can successfully describe the mobility and lifetime variation, variation of surface recombination, positional dependence of parameters, effect of biasing, the contribution from dark and light response, and the response from standard terrestrial solar spectrums. For the validation of the derived model, a COMSOL Finite Element Model of solar cell has been developed. Along with that, a physically-based (TCAD) model in Silvaco/ATLAS is constructed for checking the results. The proposed model is in good agreement with both of the numerical models. The model is further improved so that the same model can also analyze the effect of individual wavelength, the addition of multiple emitter/base layers, and the inclusion of other non-uniform doping variation. The solution even works for non-Silicon photovoltaic materials, when the material properties are tailored properly. All the aforementioned effects and transport physics have been aggregated in a compressed expression, but with an added complexity of Bessel and Hypergeometric function. This analytical model can be helpful in optimizing solar cell designs by providing direct relationship of the physics with the device dimensions.