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.

1 Introduction

A quantum mechanical description of the evolution of electron ensembles in solid state materials is given by the many body Schr dinger equation for the electron ensemble. While this equation, in combination with mean field theories and the associated Poisson equation, is able to describe ballistic transport, the inclusion of scattering mechanisms on length and time scales necessary for device simulation is still an unresolved problem. Scattering of electrons with impurities and phonons leads in general to integral operators in the resulting transport equations which are completely non - local in space and time. ^[2], ^[4], ^[10] As a consequence, quantum mechanical models in device simulation usually treat quantum effects with a domain decomposition approach, modeling...