Analytical model of open circuit voltage of a schottky barrier solar cell for all levels of injection

Abstract

Today’s research works surrounding Solar cells revolve around finding out different ways to improve efficiency. Open Circuit Voltage is now considered as an important parameter in determining efficiency of Solar Cell. In this work, analytical modeling of open circuit voltage (VOC) is performed for Schottky Barrier (SB) Solar Cell and mathematical expression for VOC is derived for all levels of injection of carriers. No analytical work for finding open circuit voltage of SB solar cell for all levels of injection has been done previously. Some of the works attribute to analytical modeling of open circuit voltage of SB Solar Cell for special cases of low and high level of injection. This work is valid for all levels of injection and it has tracked down the previous results for low and high level of injection by applying necessary assumptions. Mathematical expressions obtained after applying necessary assumptions are then compared with previous mathematical modeling of low and high level of injection. Mathematical expression of VOC for low and high level of injection is found same to those obtained by works done previously. For finding out this mathematical representation of open circuit voltage second order differential equation is required to be solved to obtain excess minority carrier hole concentration in depletion and neutral region of a n-type SB Solar Cell. Proper boundary conditions are applied in evaluating constants of the solution of the differential equation. Effect of doping concentration, Metal work function, effective surface recombination velocity at the n-n+ interface and thickness of semiconductor on VOC has been studied. Variation of VOC with doping concentration and metal work function has been explained. Both Si and GaAs are considered as semiconductors and different metals are used. Comparison of VOC for different levels of injection as function of doping concentration has been performed. With the increase of doping concentration and metal work functions VOC increases for different levels of injection. For changing level of injection from low to all level it has been found that Voc increases by around 0.1 volt for a certain metal and while changing level of injection from all level to high level around 0.1 volt increase of VOC occurs for a certain metal. While changing doping level from 1014 to 1017 range, Voc increases about 0.1-0.25 volt for various metal combinations. Using GaAs instead of Si means increase of about 0.2 volt in VOC. Increase of metal work function indicates increase in VOC. The variation of VOC is less prominent among various levels of injection while using n-GaAs instead of n-Si as semiconductor. Increase of effective surface recombination velocity Seff and thickness of the semiconductor L does not imply significant change in VOC. With increase of Seff, VOC decreases slightly for all level and low level of injection. With increase of L, VOC remains almost constant under all level and low level of injection. High level of injection indicates slight increase of VOC with Seff and L. In the end comparisons of low level and high level of injection has been performed while using current analytic model with the previous result obtained for low and high level of injection.