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An improved analytical expression for the energy distribution function is proposed for its application to hot-carrier-related problems. The proposed energy distribution function represents an admixture of hot and cold electron populations with the cold electrons represented by a heated Maxwellian form. The inversely constructed energy distribution function agrees very well with the Monte Carlo data. The impact ionization generation rate is calculated using the Keldysh formula and shows an excellent agreement with the Monte Carlo result.

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