Effective Potentials and Quantum Fluid Models: A Thermodynamic Approach

Abstract

We present a thermodynamic approach to introducing quantum corrections to the classical transport picture in semiconductor device simulation. This approach leads to a modified Boltzmann equation with a quantum corrected force term and to quantum corrected fluid, or quantum hydrodynamic models. We present the quantum interaction of electrons with a gate oxide barrier potential and quantum hydrodynamic simulations of a resonant tunneling diode as application examples.

Quantum and Coulomb Effects in Nano Devices

“…This involves successive solution of a heat equation for which the Green's function is well known, giving (see Ref. [61] for the details)…”

Quantum corrections to semiclassical transport in nanoscale devices using entropy principles

“…Quite a lot of attention has been paid to the quantum mechanical modeling of free (collisionless) transport. Efforts here include the direct solution of the Schrödinger equation [2], [11], macroscopic moment equations (quantum hydrodynamic models) [9], [10], and extensions of semiclassical Monte Carlo methods, either directly [13], [8] or via effective potential approaches [6], [1], [12]. Comparably little work has been done on the inclusion of quantum effects into collision operators.…”

Low-momentum classical mechanics with effective quantum potentials

“…Apart from more pragmatic purposes, effective quantum potentials have also attracted attention as an attempt to return to phase space and classical statistical mechanics. For a general introduction on the subject of effective potentials, the reader can see the works [4,5] as well as the references therein.…”

“…Recently [5,6], a new effective quantum potential has been proposed and applied [7] to model nano-MOSFETs of 25nm. The advantage of the new method over the previous ones like is that it does not require the introduction of a fitting parameter to be adjusted at the beginning of the simulations.…”

“…The derivation of the effective potential comes from the fact that the Wigner-Bloch and quantum Boltzmann equations should have identical stationary solutions. The details on the derivation can be found in [5,6]. The effective quantum potential introduced in [5,6] depends in a nontrivial way on momentum.…”