Breakdown voltages of germanium plane-cylindrical junctions

The breakdown voltages of planar n-p diodes in germanium have been found to be consistently lower than those on mesa diodes having the same impurity gradient and junction depth. The measurements were made on circular diodes having a radius of ten mils and junction depths ranging from three-quarter micron to one micron. The lowering of the breakdown voltage in the planar diodes is accounted for by the geometry of the n-p junction. The diffused layer takes the form of an oblate spheroid and the breakdown voltage is determined by the curvature of the junction at the edge of the diode. Since the diameter of the diodes is much greater than the junction depth the oblate spheroid has been approximated by a flat junction with cylindrical edges, and the theoretical values for the breakdown voltage of the cylindrical region have been computed using Miller's ionization data and the solution to Poisson's equation in cylindrical coordinates. The results of the computation show that for shallow junctions ≤ 10 µ the breakdown voltage of the cylindrical region is considerably smaller than Miller's value for body breakdown, and for a junction depth of 0.1 microns the breakdown voltage can be reduced by an order of magnitude. The measured values of breakdown voltage on planar diodes are in good agreement with the theoretical predictions.