Energy-Conservation Considerations in the Characterization of Impact Ionization in Semiconductors

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Abstract
A simple expression for the ionization coefficient of charged carriers in a semiconductor as a function of electric field and lattice temperature has been developed by simultaneously fitting three physical asymptotic cases to Baraff's result. These cases are for low field (Shockley), high field (Wolff), and limitations imposed by energy conservation at high electric field or when the energy loss by phonon scattering is negligible. Given the threshold energy for ionization and the optical-phonon energy, our expression requires a single additional parameter to predict experimental results. Although the final expression is thus essentially a one-point fitting, it reproduces experimental data over as much as four decades of ionization coefficient with better accuracy than frequently used empirical two-parameter expressions. Excellent fits with much of the existing electric field dependence of the ionization coefficients for electrons and holes in Ge, Si, GaAs, and GaP were obtained. The temperature dependence was examined in the cases of GaAs and Si and excellent agreement was obtained in the case of GaAs. Some data on Si were found to be in considerable error in the sense that the data do not appear to be consistent with energy conservation.