Avalanche breakdown as a nonlinear wave

It is shown without assuming the special form of the ionization rate that the breakdown process of an avalanche diode propagates as a nonlinear wave with the wave velocity exceeding the carrier velocity under the boundary condition of a constant external current. A new nonlinear LC transmission line is constructed from the equivalent circuit representation of the avalanche breakdown. It is found from computer simulations that solitary waves propagate along the nonlinear transmission line showing soliton-like nature.