Semiclassical hydrodynamics of a quantum Kane model for semiconductors

• DOI: 10.48550/arxiv.1402.3429
• Publication Date: 2014-01-01
• Authors: Luigi Barletti; G. Borgioli; Giovanni Frosali
• Keywords: Semiclassical physics; Hamiltonian (control theory)

In this paper we derive a semiclassical hydrodynamic system for electron densities and currents in the two energy bands of semiconductor. We use Wigner equation with k.p Hamiltonian BGK dissipative term to construct first moment equations. The closure is obtained using Maximum Entropy Principle, by minimizing Gibbs free-energy functional under suitable constraints. prove that constraint equations can be uniquely solved, i.e. local equilibrium state parametrized density velocity field. Some BGK-like models are proposed mimic quantum interband migration.