The R-σ Method for Nanoscale-Device Analysis

This paper describes part of an investigation that aims at consistently incorporating quantum corrections into the transport model, for applications to advanced solid-state devices. The task is carried out in two steps. The first one derives two equations in which the dynamics of the dispersion of the single-particle wave function is accounted for in addition to that of the expectation value of position. The model is founded on an approximate description of the wave function that eliminates the need of the Ehrenfest approximation. The second step is based on the Lagrangian form of the single-particle equations and incorporates such an extended dynamics into the statistical framework. The theory is suitable for different levels of applications: the first step is applicable to the single-particle ballistic dynamics; the second, after a suitable generalization of the collision terms, to the solution of the Boltzmann equation by the Monte Carlo or other methods, and to the solution of the continuity equations in the position-dispersion space. The paper shows the formalism of the single-particle dynamics and provides some examples of its application to typical test cases, along with comparisons with the corresponding solutions of the Schrödinger equation. The derivation of the balance equations for the collective transport is discussed as well.