Model-comparison study of quasi-ballistic electron transport in nanoscale semiconductor devices

We compare two relaxation time approximation (RTA) models of the 1-D Boltzmann transport equation, one of Sano and the other of Gnani et ah. Using an asymmetric parabola to approximate the potential-energy profile, we determine semi-analytically the distribution function at the virtual source (VS). We consider three different forms of energy dependence of the relaxation time (RT). The backscattering coefficient and ballistic efficiency are calculated and compared for each RTA model. We find that the VS model is strictly applicable only to the case of a constant mean-free-path.