Avalanche Breakdown Calculations for a Planar p-n Junction

A mathematical analysis is presented on the avalanche breakdown voltage of a planar p-n junction. This analysis takes into consideration junction curvature, as encountered near a diffusion mask edge. Three different impurity atom profiles are considered: abrupt, linearly graded, and diffused. For an asymmetrical abrupt structure, it is shown that regions of junction curvature exhibit either an increase or a decrease in avalanche breakdown voltage. It is also shown that similar regions in a linearly graded junction exhibit a combination of these abrupt junction mechanisms; thereby, their breakdown voltage is little influenced by junction curvature. In addition, the diffused planar junction can be designed to exhibit nearly the same breakdown voltage as a corresponding mesa structure, or, instead, it can be designed to exhibit a substantially lower avalanche breakdown voltage.