6533b7d6fe1ef96bd1266eca

RESEARCH PRODUCT

Multi-Scale Modeling of Quantum Semiconductor Devices

Anton ArnoldAnsgar Jüngel

subject

PhysicsOpen quantum systemsymbols.namesakeSemiconductor device modelingInelastic collisionsymbolsWigner distribution functionBoundary value problemStatistical physicsSemiconductor process simulationQuantumSchrödinger's cat

description

This review is concerned with three classes of quantum semiconductor equations: Schrodinger models, Wigner models, and fluid-type models. For each of these classes, some phenomena on various time and length scales are presented and the connections between micro-scale and macro-scale models are explained. We discuss Schrodinger-Poisson systems for the simulation of quantum waveguides and illustrate the importance of using open boundary conditions. We present Wigner-based semiconductor models and sketch their mathematical analysis. In particular we discuss the Wigner-Poisson-Focker-Planck system, which is the starting point of deriving subsequently the viscous quantum hydrodynamic model. Furthermore, a unified approach to derive macroscopic quantum equations is presented. Two classes of models are derived from a Wigner equation with elastic and inelastic collisions: quantum hydrodynamic equations and their variants, as well as quantum diffusion models.

yearjournalcountryeditionlanguage
2006-10-14
https://doi.org/10.1007/3-540-35657-6_12