Calculation of the diffusion curvature related avalanche breakdown in high-voltage planar p-n junctions

Avalanche multiplication calculations are performed in high-voltage planar p-n junctions to determine breakdown voltage limitations imposed by curvature effects. The issue of choice of ionization coefficient for avalanche multiplication is discussed. From the calculations, a series of design curves and equations are generated which relate the breakdown voltage and peak electric field to those of an ideal junction of the same doping profile, the critical parameters being the substrate doping concentration, the diffusion profile, and the ratio of the radius of curvature to the substrate depletion width for the ideal one-dimensional case. With appropriate distance normalization, these curves and equations can be reduced to a single curve and a single equation. The agreement between theory and experiment is consistently good provided the correct ionization coefficients are used in the theory.