Simple model for carrier densities in the depletion region of p-n junctions

By applying the concepts of carrier velocity saturation, and electron-hole pair generation and recombination, in concert with the standard textbook derivation of the p-n abrupt junction diode equations, an analytic expression is found for the magnitude of the carrier densities near and through the depletion region of abrupt p-n junctions. The analytic expression is useful for determining carrier-density or recombination-dependent processes within the depletion region. The derivation is based on the assumption that electrons and holes pass through the depletion region at the saturation velocity. The analytic expression is compared to S-PISCES 2B simulation in a specific silicon-p-n junction. The model is called VESAT to indicate its dependence on carrier velocity saturation