ANALYTICAL EXPRESSIONS FOR THE 3-DIMENSIONAL EFFECT ON THE BREAKDOWN VOLTAGES OF PLANAR JUNCTIONS IN NONPUNCHTHROUGH AND PUNCHTHROUGH CASES

Analytical expressions are derived for the three-dimensional effect on the breakdown voltage of the planar junctions, which have the finite lateral radius of window curvature, by employing the suitable approxim ations for the electric field. The analytical results for nonpunchthro ugh and punchthrough cases are in excellent agreement with the results of the quasi-three-dimensional device simulation by MEDICI. For nonpu nchthrough case, the critical electric fields at breakdown and the bre akdown voltages are expressed successfully in a form which is normaliz ed to the parallel plane case. Also, the breakdown voltages in punchth rough case are given in terms of the punchthrough voltage and the para llel plane breakdown voltage of p+-i-n+ diodes including the lateral r adius of window curvature. The results may be applicable to the estima tion of breakdown voltages in many practical power devices.