On analytical solution of the near isotropic approximation to the Boltzmann equation for hot electrons in a semiconductor base in an electric field

• W. Cox ^[1]
  1. [1] Department of Mathematics & Physics, University of Aston, Reino Unido
• Localización: Compel: International journal for computation and mathematics in electrical and electronic engineering, ISSN 0332-1649, Vol. 4, Nº 4, 1985, págs. 183-193
• Idioma: inglés
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• Resumen

  • The near isotropic approximation to the Boltzmann equation in the presence of a constant electric field is considered, with collision integral appropriate to hot electron transport in a parabolic band homogenous semiconductor. A parabolic equation for the symmetric part of the distribution function is obtained and its analytical solutions are investigated. By a choice of energy variables as canonical coordinates, the equation is reduced to a separable form which may be solved in terms of confluent hypergeometric functions. These solutions are not compatible with the type of boundary conditions required for the semiconductor problem when expressed in terms of the energy variables. However, when the original space and velocity variables are used, boundary conditions appropriate to a semi‐infinite semiconductor may be accommodated.