Quantum hydrodynamic equations for nanostructures with spatially varying effective mass

Abstract

A recently proposed Wigner transport equation with spatially varying effective mass is applied to develop a new set of moment equations for the hydrodynamic description of quantum transport in ultrasmall semiconductor heterostructure devices. The form of the Wigner transport equation for heterostructures is presented. The moment-equation representation of the Wigner transport equation results in a set of quantum hydrodynamic equations that incorporate the principles of charge, momentum and energy conservation in the quantum domain. It is shown that the resulting momentum and energy conservation equations contain explicit quantum correction terms that are dependent on the spatial derivatives of the effective mass. These results are expected to provide a theoretical basis on which numerical simulation of quantum transport in heterostructures with nanoscale compositional changes may be performed.