Deterministic solution of the 1D Boltzmann transport equation: Application to the study of current transport in nanowire FETs

In this work we investigate the ballistic ratio and the backscattering coefficient in nanowire FETs operating under quasi-ballistic conditions. Starting from general expressions of the current–voltage characteristics worked out in a previous paper, we extract the above parameters and their functional dependence on inversion-layer charge and device length. The computation is based on a rigorous analytic solution of the BTE and on a numerical solution of the coupled Schrödinger–Poisson equations, by which multiple subbands are taken into account. We propose three different definitions of the ballistic ratio, clarify their meaning and compute their values against the gate voltage and the device length. As opposed to most phenomenological treatments addressing this subject for 2D nanoscale MOSFETs, the strength of our approach is that the aforementioned parameters can be computed from the knowledge of the scattering probabilities, without introducing any major simplifying assumptions.