A Coherent Extension of the Transport Equations in Semiconductors Incorporating the Quantum Correction: Part II – Collective Transport

The aim of this investigation is to consistently incorporate quantum corrections in the transport model for applications to nanoscale semiconductor devices. This paper is made of two parts. In Part I, a set of two semiclassical equations were derived, 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 for the Ehrenfest approximation. This leads to a set of two Newton-like single-particle equations for position and dispersion. Here, in Part II, it is shown that the Lagrangian form of the single-particle equations naturally lends itself to the incorporation of such extended dynamics into the statistical framework. The theory is suitable for different levels of applications: description of the single-particle ballistic dynamics, solution of the generalized Boltzmann equation by Monte Carlo or other methods, and solution of the continuity equations in the position-dispersion space.