Energy transport in semiconductor devices

Abstract

The modelling, analysis and numerical approximation of energy-transport models for semiconductor devices are reviewed. The derivation of the partial differential equations from the semiconductor Boltzmann equation is sketched. Furthermore, the main ideas for the analytical treatment of the equations, employing thermodynamic principles, are given. A new result is the proof of the weak sequential stability of approximate solutions to some time-dependent energy-transport equations with physical transport coefficients. The discretization of the stationary model using mixed finite elements is explained, and some numerical results in two and three space dimensions are presented. Finally, energytransport models with lattice heating or quantum corrections are reviewed.

Hybrid OpenMP-CUDA parallel implementation of a deterministic solver for ultrashort DG-MOSFETs

“…Notwithstanding, the performance is still not competitive with respect to macroscopic, hence lower dimensional, models which possess an intermediate accuracy, like: driftdiffusion (Ben Abdallah et.al., 2004), energy-transport (Ungel, 2010), moment-like (Ringhofer et al, 2001), maximum-entropy-principle (Camiola et al, 2013;Mascali and Romano, 2012), or spherical harmonics expansion (SHE) models (Hong et al, 2011;Rupp et al, 2011Rupp et al, , 2012.…”

A hierarchy of hydrodynamic models for silicon carbide semiconductors

“…Recently, this methodology as been applied to SiC [9] obtaining a closed set of balance equation of hyperbolic-type. The aim of this paper is to obtain, from this hydrodynamic model, simpler transport models, such as the energy transport and the drift-diffusion ones which are useful to devise efficient numerical schemes [10].…”

Asymptotic Behavior of the Solution to a 3-D Simplified Energy-Transport Model for Semiconductors

“…Then the model (1.1)-(1.3) can be changed into the following model for the electron density n(x,t), the electron temperature θ(x,t) and the electric field E(x,t): j· n| ∂Ω = 0, ∇θ · n| ∂Ω = 0, E· n| ∂Ω = 0, (1.8) where n denotes the exterior unit normal vector on ∂Ω, and the initial datum n 0 (x) satisfies the following condition Before we exposit our results, we review the energy-transport model in the literature. The common form for energy-transport model [4] is…”