A new look at impact ionization-Part I: A theory of gain, noise, breakdown probability, and frequency response

Impact ionization in thick multiplication regions is adequately described by models in which the ionization coefficients are functions only of the local electric field. In devices with thin multiplication lengths, nonlocal effects become significant, necessitating new models that account for the path that a carrier travels before gaining sufficient energy to impact ionize. This paper presents a new theory that incorporates history-dependent ionization coefficients, and it is shown that this model can be utilized to calculate the low-frequency properties of avalanche photodiodes (APD's) (gain, noise, and breakdown probability in the Geiger mode) and the frequency response. A conclusion of this work is that an ionization coefficient is not a fundamental material characteristic at a specific electric field and that any experimental determination of ionization coefficients is valid only for the particular structure on which the measurement was performed.