A deterministic solution of the Boltzmann transport equation for a one-dimensional electron gas in silicon nanowires

This paper presents a new deterministic approach to the solution of the Boltzmann Transport Equation (BTE) for a one-dimensional electron gas (1DEG) in a silicon nanowire MOSFET. Quantum confinement is taken into account by solving the 2D Schroedinger equation in every cross section. The set of equations is completed with the 3D Poisson equation. At present, only acoustic and optical-phonon scattering are accoounted for in the model which, however, is sufficient to demonstrate the validity of the numerical and algorithmic approach. The form factors are computed consistently with the wave functions given by the transverse Schroedinger equation. One of the advantages of this method is that accurate distribution functions on a wide energy range are obtained with a reasonable numerical efficiency, as long as the number of subbands is not too large.