Multiple uniform layer approximation in analysis of negative resistance in p-n junction in breakdown

A simplified analytical method of calculating high-frequency, small signal negative resistance of p-n junctions in breakdown is presented. The negative resistance can lead to microwave oscillations in Impact Avalanche Transit Time (IMPATT) diodes. The method consists in subdividing the entire space charge region into several uniform layers, each of which has constant avalanche multiplication (including zero), and connecting the analytical solutions of the successive layers (multiple uniform layer approximation). The simplest case of the approximation, in which there is only one constant-avalanche region and one or two avalanche-free drift regions, is used to investigate how the small signal characteristics change with width and position of the avalanche region. From the behavior of the small signal negative
Q
, it is expected that for low bias currents the oscillator performance improves when the avalanche region becomes relatively shorter, when its position moves from the center to the edge of the space charge region, and when the total space charge layer becomes wider. In materials with larger ionization rates, a negative resistance of a given quality (
Q
) is obtained at lower breakdown voltage and bias current.