On the choice of appropriate ionization coefficients for breakdown voltage calculations

It is shown that normalized breakdown voltages of planar cylindrical junctions are independent of the doping profiles of the junctions and the ionization coefficients used, when the normalization is carried out with respect to plane-parallel breakdown voltage and expressed as a function of normalized radius of curvature rj/Wc, Wc being the depletion layer width on the lightly doped side of the plane-parallel junction at breakdown. It is thus shown that curvature-limited breakdown-voltage calculations can be simplified and that the exact doping profiles and the ionization coefficients need be considered only in the one-dimensional analysis for calculating the plane-parallel breakdown voltage and depletion-layer width on the lightly doped side at breakdown. © 1987.