A stochastic invariant imbedding approach to avalanche noise in semiconductors

The multiplication statistics in an avalanche region in semiconductors by impact ionization are treated stochasticly by means of the invariant imbedding technique. An explicit result is obtained for the variance of the process for arbitrary ionization coefficients. A simple formula is derived for the determination of the spectral density of the fluctuations, caused by multiplication statistics. Formulae will be given for the mean and the variance of both electrons and holes. An exact result is obtained for a linear spatial dependency of the ionization coefficients.