Cascade Capture of Electrons by Ionized Impurities

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Abstract
An improved theory of cascade capture by ionized impurities in semiconductors has been developed which retains the basic features of Lax's "giant trap" theory, but which uses a distribution function rather than a trajectory description. Assuming infrequent acoustic-phonon transitions, the classical Boltzmann equation describing the capture process near a single ionized impurity is converted into an integral equation for the distribution function in terms of total energy alone. This equation, which treats transitions between free and bound states identically to transitions between two bound states, is then transformed into a closely related integral equation for the "sticking probability." Numerical solution of the latter yields cross sections which are substantially larger than those previously found and which are in good agreement with recent experimental values for the shallow donors in Ge.

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