Stochastic treatment of electron multiplication without scattering in dielectrics

By treating the emission of optical phonons as a Markov process, a simple analytic method is developed for calculating the electronic ionization rate per unit length for dielectrics. The effects of scattering from acoustic and optical phonons are neglected. The treatment obtains universal functions in recursive form, the theory depending on only two dimensionless energy ratios. A comparison of the present work with other numerical approaches indicates that the effect of scattering becomes important only when the electric potential energy drop in a mean free path for optical-phonon emission is less than about 25% of the ionization potential. A comparison with Monte Carlo results is also given for Teflon.