Effect of junction curvature on breakdown voltage in semiconductors

Abstract

The effect of the radius of curvature of the metallurgical junction (or junction curvature) on avalanche breakdown voltage is herein computed numerically for spherical and cylindrical p-n junctions in Ge, Si, GaAs and GaP. Three types of impurity distribution have been considered: abrupt, linearly graded and composite. For the composite distribution the space charge terminates in a graded region on one side of the junction and in a uniformly doped region on the other side. The results, which are presented graphically, show that for abrupt junctions the breakdown voltage, VB, decreases with decreasing radius of curvature, rj, the effect being larger for spherical junction than for cylindrical junction. Typically, for Si abrupt junctions with a background doping of 1015 cm-3, VB is 330 V for a plane junction, 80 V for a cylindrical junction with rj = 1 μ, and 39 V for a spherical junction with the same junction radius. For linearly graded junctions however, VB is essentially independent of rj. For composite junctions, at small impurity gradient VB is nearly equal to that of linearly graded junctions; at large impurity gradient, however, VB is determined by rj and the background doping. The results presented here can be applied to junctions formed by planar technology where the edge of the junction has cylindrical and/or spherical geometry with radius of curvature approximately equal to the junction depth. It is further suggested that the radius of curvature is an important design parameter in high power and higher frequency semiconductor devices as well as in integrated circuits. © 1966.