Ij. Kkim et al., ANALYTICAL EXPRESSIONS FOR THE 3-DIMENSIONAL EFFECT ON THE BREAKDOWN VOLTAGES OF PLANAR JUNCTIONS IN NONPUNCHTHROUGH AND PUNCHTHROUGH CASES, I.E.E.E. transactions on electron devices, 41(9), 1994, pp. 1661-1665
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.