Breakdown voltage analysis of planar p-n junctions taking into account the radius of curvature of the corners in the patterning mask

The breakdown voltages of planar p-n junctions have been studied with respect to cylindrical or spherical junction curvature. However, in practical planar p-n junctions for high voltage, the radius of curvature of the corners in the patterning mask, which affects the actual three-dimensional junction curvature, must also be considered. A new simple one-dimensional numerical analysis method is proposed. For this method Poisson's equation has been reduced to a one-dimensional form in a polar coordinate system with two poles, and solved only for the surface of the depletion layer. To verify the method, an accurate three-dimensional numerical analysis for electrostatic potential distribution was also performed. Good agreement was found between the numerical breakdown voltages using this method and experimental data.