Piecewise analytic solution of the charge carrier transport equation for nondegenerate semiconductors

摘要

We present an alternative to conventional finite difference solutions to the transport equations for electrons and holes in nondegenerate semiconductor devices. The equations are solved using piecewise analytic methods in which the electric field is approximated by a linear function in a series of relatively large subintervals, and the continuity and current density equation is solved by transforming it into Weber’s equation. Carrier concentrations are expressed as a linear combination of Weber parabolic cylinder functions in each interval. Selfconsistency is obtained by iterative corrections with Gummel’s method. Computational results are presented for an abrupt P‐N+ junction. It is believed that this method is particularly efficient for moderate bias conditions and especially in modeling heterojunction solar photovoltaic devices.