Journal of Statistical Physics

, Volume 139, Issue 2, pp 280–306 | Cite as

Diffusive Limit of the Two-Band k⋅p Model for Semiconductors

  • Luigi Barletti
  • Giovanni Frosali


We derive semiclassical diffusive equations for the densities of electrons in the two energy bands of a semiconductor, as described by a k⋅p Hamiltonian. The derivation starts from a quantum kinetic (Wigner) description and resorts to the Chapman-Enskog method as well as to the quantum version of the minimum entropy principle. Four different regimes are investigated, according to different scalings of the k⋅p band-coupling and band-gap parameters with respect to the scaled Planck constant.


Quantum drift-diffusion k⋅p model Quantum entropy principle 


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Authors and Affiliations

  1. 1.Dipartimento di Matematica “U. Dini”Università di FirenzeFirenzeItaly
  2. 2.Dipartimento di Matematica Applicata “G. Sansone”Università di FirenzeFirenzeItaly

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