Diffused Junction Depletion Layer Calculations

Abstract

Depletion layer properties have been calculated for diffused junctions in silicon and germanium as a function of reverse voltage and of diffusion parameters for the gaussian and the complementary error function distributions. These results bridge the gap between the linearly graded behavior generally exhibited by suck junctions at low voltage and the step behavior exhibited at high voltage. For total depletion layer thickness and capacitance, the transition from graded to step junction behavior extends over about one decade of voltage. For depletion layer thickness on a single side of the junction, it extends over several decades. Depletion layer thickness and peak electric field are presented graphically as a function of voltage for a variety of junction depths and impurity concentration functions. The ranges for which the. step and graded junction approximations are valid are apparent from these charts. The results were obtained by an analytical integration of Poisson's equation, and a subsequent use of the IBM 704 for a numerical evaluation of the transcendental equations obtained.