Small-signal impedance of avalanching junctions with unequal electron and hole ionization rates and drift velocities

A small-signal analysis of an avalanching semiconductor junction is presented for unequal electron and hole ionization rates and saturated drift velocities. The model consists of a thin ionization layer in a thicker depletion layer. The ionization rates are assumed independent of distance in the ionization layer and zero elsewhere. This analysis is an improvement of Read´s, and is sufficiently realistic to predict most of the small-signal characteristics shown by the computer analysis of Misawa. The linearized differential equations describing the ionization layer are solved with the ionization rates perturbed by the ac electric field. The ac junction impedance is calculated from the solutions of the differential equations. Although the small-signal analysis does not predict the conversion efficiency of an avalanche diode oscillator, it does predict the threshold conditions for oscillation. It may also help predict the conditions for maximum efficiency through knowledge of the input power and the Q of the diode at the onset of oscillation.