Negative resistance and filamentary currents in avalanching silicon p+-i-n+junctions

Space-charge effects in avalanching p⁺-i-n⁺diodes give rise to a current-controlled bulk negative resistance. It is shown that this negative resistance gives rise to an instability which tends to lead to the formation of current filaments. A steady state can be found in which the generation of carriers in the filament by impact ionization is balanced by radial diffusion of carriers. We present the results of approximate numerical calculations of filament current-density profiles and total filament current as a function of applied voltage. The total filament current is a decreasing function of the applied voltage; thus, the diode exhibits a quasistatic negative external resistance. It is suggested that this negative resistance may be used to interpret observed sub-transit-time oscillations of p⁺-i-n⁺structures.