Analytical solution for the avalanche breakdown voltage of p+–n junctions and schottky diodes. Anomalous behaviour of low energy bandgap high-mobility semiconductors

A new analytical expression for the avalanche breakdown voltage of p+–n and Schottky diodes as a function of the net doping concentration has been derived based on a power function approximation for the charge carrier ionization rates. The breakdown voltage decreases with increasing doping concentration, N, until a minimum is reached corresponding to a doping concentration Nmin. Further increase of N leads to an anomalous behaviour: The breakdown voltage increases with N exceeding Nmin. Normally this effect cannot be measured because the tunneling mechanism dominates the breakdown characteristic in this doping region. The observation is limited therefore to low energy bandgap high-mobility semiconductors; e.g. InSb which is discussed in detail. For this semiconductor the minimum avalanche breakdown voltage has been calculated to be Umin = 1.2 V occurring at a corresponding doping concentration Nmin = 0.7 × 1013 cm−3. The temperature dependence resulting from this model shows anomalous behaviour in the doping range N > Nmin: The breakdown voltage decreases with increasing temperature. This is known from published measurements.