Characteristics of diffused P-N junctions in epitaxial layers

A one-dimensional analysis has been made to determine properties of diffused p-n junctions in epitaxial layers with nonuniform impurity concentration. Impurity diffusion from the surface and from the substrate is assumed to have complementary error function distribution. The transcendental equations obtained by analytical integration of Poisson´s equation were evaluated numerically with the IBM 7090/94. Junction depth, impurity gradient and impurity level at the junction are given for a variety of diffusion parameters and impurity concentrations. In addition, graphs are presented, showing the relationship between reverse voltage and depletion layer thickness, capacitance per unit area, and peak electric field for the case of silicon. A comparison between the actual impurity profile and the usual linear approximation using the impurity gradient at the junction gives the range of depletion layer thickness or reverse voltage in which such an approximation is justified. Further, examples are presented of the electric field distribution in the depletion layer for several impurity concentration profiles. Calculated and experimentally determined values of some readily accessible junction characteristics show reasonably good agreement.