The Quantum Hydrodynamic Model for Semiconductor Devices.

Resolvent estimates for Douglis–Nirenberg systems

“…The parameter ν 0 is proportional to the strength of this interaction, and τ figures as a relaxation time. For derivations of the model, we refer to [5,11].…”

Existence of weak solution and semiclassical limit for quantum drift-diffusion model

“…Quantum macroscopic models, including the quantum hydrodynamic models, quantum energy transport models and quantum drift diffusion models, were introduced recently to simulate the miniaturized semiconductor devices where the quantum effects contribute the leading role, [7,5,8], etc. We refer to the references [3,19,16,11] for semiconductor physics and modelling.…”

The quantum hydrodynamic model for semiconductors in thermal equilibrium

“…Recently, various so-called Quantum Hydrodynamic (QHD) models were used in semiconductor simulations [3]. These models are dispersively regularized versions of the classical hydrodynamic model for semiconductors, where the scaled Planck constant δ plays the role of the dispersivity.…”

“…These models are dispersively regularized versions of the classical hydrodynamic model for semiconductors, where the scaled Planck constant δ plays the role of the dispersivity. Using QHD models it was possible to simulate typical quantum effects in semiconductors, like resonant tunneling and negative differential resistance [3].…”

“…The equations of the QHD model are obtained by adding quantum correction terms to the equations of the classical hydrodynamic model for semiconductors. On the derivation of QHD models see [3,4,5,6] and references therein. Denoting by n, J, V , p, C the electron density, electron current density, electric potential, pressure and doping profile of the semiconductor, the equations of the isothermal (p(n) = n) or isentropic (p(n) = n α , α > 1) QHD model read n t + div J = 0,…”