An analytical model of minority carrier in exponentially doped solar cell under illumination

A compact analytical model of minority carrier -concentration is presented for an exponentially-doped quasi-neutral region of Silicon solar cell. It is an iteration-free and integral-free mathematical expression that addresses the non-uniformity in doping and contribution from terrestrial solar spectrum. Due to the position dependency of transport parameters, the differential equation becomes intractable. The proposed model incorporates an elegant approximated carrier generation rate to overcome the problem and presents a new solution for minority carrier concentration by using the modified Bessel function and Hypergeometric function. The compact analytical solution is in good agreement with COMSOL drift-diffusion model and TCAD device simulator for a wide variation of doping and surface recombination velocity.