Simulation of avalanche multiplication of electrons in photodetectors with blocked hopping conduction

The avalanche electron multiplication in a silicon structure with blocked hopping conduction is simulated for the photon-counting mode. The acceleration of an electron in an electric field that is linearly dependent on the coordinate, the elastic scattering of electrons by longitudinal acoustic phonons, the inelastic scattering of electrons by intervalley phonons, and the ionization of impurity centers are taken into account when considering the motion of an electron. A simple algorithm making it possible to calculate directly the coordinates of all ionized centers in an avalanche and the probability of N electrons leaving the avalanche if a single electron has entered the multiplication region is suggested. It is shown that this probability is at its maximum in the vicinity of 〈N〉 (the mean value of the leaving-probability function), which is consistent with experimental data.