TRANSPORT VIA THE LIOUVILLE EQUATION AND MOMENTS OF QUANTUM DISTRIBUTION-FUNCTIONS

This paper (i) examines through numerical solutions of the coupled coordinate representation Liouville and Poisson equations, the use of the Bohm quantum potential to represent the equilibrium distribution of density and energy in quantum feature size structures; (ii) discusses the development of the nonequilibrium quantum hydrodynamic (QHD) equations with dissipation through the truncation of the quantum distribution function; and (iii) compares select results of the QHD equations incorporating the Bohm potential to the exact Liouville equation solutions. The broad conclusion of the study is that for structures of current interest such as HEMTs, only quantum mechanical solutions, or the incorporation of the quantum potential as a modification of the classical equations will permit representative solutions of such critical features as the sheet charge density.