A theoretical model for the HgCdTe electron avalanche photodiode

A ballistic model is presented for electron avalanche multiplication in the conduction band of HgCdTe, based upon the concept of an optical phonon limited mean free path for the electron, lambda (e). The model predicts avalanche gain as a function of applied bias voltage V, and a threshold voltage for impact ionization V(th). Impact ionization probabilities are calculated analytically using a simplified band structure model for HgCdTe and used to estimate values for the threshold energy for impact ionization. A simple ballistic model is developed to correlate the relationship between electron energy and applied bias voltage, based upon the relevant electron scattering mechanisms in HgCdTe. A comparison with published gain-voltage data suggests that the process is limited by optical phonon scattering, and the relationship between electron energy and applied bias voltage, for a uniform electric field F = V/W, across a diode depletion width W, is given by E = alpha(E)V, where alpha(E) = [lambda(e)(E)/W]. For high electron energies lambda (e)(E) is independent of E and alpha(E) depends only on the dielectric parameters of the material. Using this simple model it is easy to predict electron avalanche gain versus voltage for any parametric combination of diode geometry, bandgap, and operating temperature.