Electron-hole avalanches in semiconductors

An analytical theory of the development of electron-hole avalanches in semiconductors, which qualitatively differ from the electron avalanches in gases, is proposed and the spatiotemporal distributions of the field and charge in such avalanches are determined. It is suggested to identify the onset of the avalanche-streamer transition as the moment (ta) corresponding to a 20% decrease in the impact ionization coefficient α at the avalanche center. A transcendent equation is obtained for the calculation of ta as a function of the unperturbed coefficient α(Eext) determined by the external field Eext. It is established that, as the α(Eext) value is increased in from 103 to 105 cm−1, the total number of electron-hole pairs generated by the ta moment decreases by almost three orders of magnitude.