Abstract
Approximate equations for cylindrical breakdown voltages of planar pn junctions are proposed and verified. The equations show good agreement with the Baliga's results for $r_{j}/Wpp{\leqq}0.3$ and with numerical results for $r_{j}/Wpp{\geqq}0.3$ within 1% error. Sensitivity of the breakdown voltage with respect to the doping concentrations is successfully derived using the approximate equations. The sensitivity formula can be utilized in the area of tolerance design of power semiconductor devices.