Investigation of the transport properties of silicon nanowires using deterministic and Monte Carlo approaches to the solution of the Boltzmann transport equation

We investigate the transport properties of silicon-nanowire FETs by using two different approaches to the solution of the Boltzmann equation for the quasi-1-D electron gas, namely, the Monte Carlo method and a deterministic numerical solver. In both cases, we first solve the coupled Schrijdinger-Poisson equations to extract the profiles of the 1-D subbands along the channel; next, the coupled multisubband Boltzmann equations are tackled with the two different procedures. A very good agreement is achieved between the two approaches to the transport problem in terms of mobility, drain-current, and internal physical quantities, such as carrier-distribution functions and average velocities. Some peculiar features of the low-field mobility as a function of the wire diameter and gate bias are discussed and justified based on the subband energy and wave-function behavior within the cylindrical geometry of the nanowire, as well as the heavy degeneracy of the electron gas at large gate biases.