Analysis of a diffusive effective mass model for nanowires

Clément Jourdana (1, 2) , Nicolas Vauchelet (3, 4)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 IMATI - Istituto di Matematica Applicata e Tecnologie Informatiche
3 LJLL - Laboratoire Jacques-Louis Lions
4 BANG - Nonlinear Analysis for Biology and Geophysical flows

We propose in this paper to derive and analyze a self-consistent model describing the diffusive transport in a nanowire. From a physical point of view, it describes the electron transport in an ultra-scaled confined structure, taking in account the interactions of charged particles with phonons. The transport direction is assumed to be large compared to the wire section and is described by a drift-diffusion equation including effective quantities computed from a Bloch problem in the crystal lattice. The electrostatic potential solves a Poisson equation where the particle density couples on each energy band a two dimensional confinement density with the monodimensional transport density given by the Boltzmann statistics. On the one hand, we study the derivation of this Nanowire Drift-Diffusion Poisson model from a kinetic level description. On the other hand, we present an existence result for this model in a bounded domain.

Mots clés: Hamiltonian's spectrum; drift-diffusion system; relative entropy method; diffusive limit; Hamiltonian's spectrum.

Domaines: Equations aux dérivées partielles [math.AP]

Clément Jourdana, Nicolas Vauchelet. Analysis of a diffusive effective mass model for nanowires. Kinetic and Related Models , 2011, 4 (4), pp.1121-1142. ⟨10.3934/krm.2011.4.1121⟩. ⟨hal-00593984⟩