Numerical simulation of evolution of electron-hole avalanches and streamers in silicon in a uniform electric field

Numerical simulation of origination and evolution of streamers in Si is performed for the first time. It is assumed that an external electric field E0 is constant and uniform, the avalanche and streamer are axially symmetric, and background electrons and holes are absent. The calculations have been performed in the context of the diffusion-drift approximation with impact and tunneling ionization, Auger recombination, and electron-hole scattering taken into account. The most realistic values of the ionization and recombination rates, diffusion coefficients, and drift mobilities of electrons and holes have been used. It is shown that the features of evolution of avalanches and streamers are generally consistent with the result obtained previously for a hypothetic semiconductor with equal kinetic coefficients for electrons and holes. Asymmetry of these coefficients (mostly, the impact-ionization coefficients) manifests itself only at the initial stage of evolution. However, with time, two exponentially self-similar streamers are formed, differing only in the sign of charge of fronts and directions of their propagation. Empirical dependences of the main parameters of streamers on E0 in the range of 0.34-0.75 MV/cm have been derived for this most important stage of evolution.