Shallow p-n Junctions Under Discrete Impurities in Semiconductor Devices

We investigate the influence of the discrete nature of impurities on ensemble-average device characteristics of shallow junctions, in which the spatial distribution of impurities is strongly nonuniform. A general scheme of how to simulate the device characteristics averaged over random, yet nonuniform impurity configurations is presented. It is shown that under the framework of device simulations in which the Poisson equation is coupled self-consistently with the transport equations, the usual jellium impurity density is replaced by the average effective impurity density so that the self-consistent Hartree potential properly takes into account the long-range potential fluctuations induced by impurities. The present scheme is applied to the drift–diffusion (DD) simulations of cylindrical diodes with shallow junctions and we show that the ensemble-average current densities of n+-p-n+ diodes could differ by orders of magnitude from those predicted by the conventional simulation with the jellium impurity density.