Improved approximate analytic charge distributions for abrupt p-n junctions

Abstract
Poisson’s equation is solved approximately in abrupt nondegenerate semiconductor pn heterojunctions and homojunctions by using the Thomas‐Fermi dielectric function to describe free‐carrier (Debye) screening with the approximation of a local screening length function. Analytic forms are presented for the electrostatic charge distribution and electrostatic potential, which illustrate features not predicted by the usual Schottky theory. Charge density and space‐charge capacitance are shown to change with applied voltage in agreement with exact numerical calculations.