On the physical understanding of the kT-layer concept in quasi-ballistic regime of transport in nanoscale devices

The aim of this paper is to establish a well-defined theoretical background in which the kT-layer concept and the empirical expression of the backscattering coefficient introduced by Lundstrom and co-workers to describe the role of scattering in nanoscale devices under high-field conditions and quasi-ballistic transport regime are derived analytically. To this purpose, one-dimensional (1-D) Boltzmann transport equation is solved in the framework of a "relaxation length" approximation, leading to a set of drift-diffusion like transport equations. This set of equations is then solved in a template 1-D structure (with a linear potential-energy profile), leading to an analytical expression for the backscattering coefficient, which is equal, in the limit of low- and high-electric fields, to the formulas proposed by Lundstrom et al. This approach allows us to identify the exact assumptions and qualitative validity limits of these formulas.