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

This paper (i) examines through numerical solutions of the coupled coo rdinate representation Liouville and Poisson equations, the use of the Bohm quantum potential to represent the equilibrium distribution of d ensity and energy in quantum feature size structures; (ii) discusses t he development of the nonequilibrium quantum hydrodynamic (QHD) equati ons with dissipation through the truncation of the quantum distributio n function; and (iii) compares select results of the QHD equations inc orporating the Bohm potential to the exact Liouville equation solution s. The broad conclusion of the study is that for structures of current interest such as HEMTs, only quantum mechanical solutions, or the inc orporation of the quantum potential as a modification of the classical equations will permit representative solutions of such critical featu res as the sheet charge density.