Formulation of minority carrier density of a non-uniformly doped n-Si schottky barier diode

Abstract

A Schottky barrier diode (SBD) is a majority carrier device when the barrier height is low. On the other hand, in a high barrier SBD both minority and majority carrier currents contribute to the total diode current. A good number of works have been done considering minority carrier current for uniformly doped Silicon SBD. But, no work has been reported for SBD with non-uniformly doped semiconductor. When the SBD is not uniformly doped, the differential equation obtained using drift and diffusion current equation is not analytically tractable. In this work, the doping density is considered to be non-uniform and solution for minority carrier density has been obtained based on some assumption. From minority carrier profile, important performance parameters like storage time and injection ratio are obtained. The analysis shows that both the parameters depend upon peak doping density Nd0, logarithmic slope of doping density α, minority carrier current density Jp, width of the n-region W and the effective surface recombination velocity Sef. It is observed that storage time τs increases with decrease in Nd0 and increase in α, Jp and W. τs also increases very slowly with Sef. Injection ratio γ increases with decrease in Nd0 and increase in α, Jp, W and Sef. It is seen that low storage time can be obtained by reducing the length of n region and by increasing the peak doping density. Injection ratio can be decreased by increasing peak doping density and decreasing length of n region.