Efficient calculation of ionization coefficients in silicon from the energy distribution function

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Abstract
A method for calculating impact ionization coefficients by solving the Boltzmann transport equation is presented. The distribution function is taken to be expressible as a Legendre polynomial expansion, which is substituted into a Boltzmann equation that incorporates the effects of nonparabolic band structure, deformation-potential phonon scattering, and impact ionization. The resulting Boltzmann equation can be expressed in a linear form, and solved using sparse-matrix difference-differential methods. Ionization coefficients are obtained directly from the distribution function. Calculated values for the ionization coefficients agree very well with experiment for electrons in silicon.