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Asymptotic analysis of the high field semiconductor Boltzmann equation

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  • Stichel, P.C.
  • Strothmann, D.

Abstract

We present an asymptotic analysis for long times and large distances of the linear semiconductor Boltzmann equation for a given strong electric field, slowly varying in real space. By means of singular perturbation techniques, using the multiple scale formalism we show that the initial-value and the boundary-value problem lead to different asymptotic evolution equations. For the initial value problem we derive Thornber's augmented drift-diffusion equation. In case of the boundary value problem Thornber's equation describes only the hot part of the asymptotic distribution function. The cold part, staying in thermal equilibrium with the lattice at the boundary, is described asymptotically by means of a new evolution equation. In this way we solve the well known inconsistency problem occuring if Thornber's equation is applied to an equilibrium situation in the presence of large built-in fields.

Suggested Citation

  • Stichel, P.C. & Strothmann, D., 1994. "Asymptotic analysis of the high field semiconductor Boltzmann equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 202(3), pages 553-576.
    • Handle: RePEc:eee:phsmap:v:202:y:1994:i:3:p:553-576
    DOI: 10.1016/0378-4371(94)90479-0
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