Electron-hole avalanches with constant ionization coefficients

An exact formula for a solution of the space-time partial differential equations is described for ionization coefficients which are constant in the avalanche zone. The solution, which exhibits a spatially varying conduction current, is exponentially increasing in time. For comparison, the initial value solution was computed numerically by the method of characteristics. After about one transit time, this numerical solution settles down to the exponential time behavior and the spatial distribution of the exact solution.