A Finite Volume Method for the Multi Subband Boltzmann Equation with Realistic 2D Scattering in Double Gate MOSFETs (Communications in Computational Physics, 2011)
We propose a deterministic solver for the time-dependent multi-subbandBoltzmann transport equation (MSBTE) for the two dimensional (2D) electron gas indouble gate metal oxide semiconductor field effect transistors (MOSFETs) with flaredout source/drain contacts. A realistic model with six-valleys of the conduction bandof silicon and both intra-valley and inter-valley phonon-electron scattering is solved.We propose a second order finite volume method based on the positive and flux conservative(PFC) method to discretize the Boltzmann transport equations (BTEs). Thetransport part of the BTEs is split into two problems. One is a 1D transport problem inthe position space, and the other is a 2D transport problem in the wavevector space. Inorder to reduce the splitting error, the 2D transport problem in the wavevector spaceis solved directly by using the PFC method instead of splitting into two 1D problems.The solver is applied to a nanoscale double gate MOSFET and the current-voltage characteristicis investigated. Comparison of the numerical results with ballistic solutionsshow that the scattering influence is not ignorable even when the size of a nanoscalesemiconductor device goes to the scale of the electron mean free path.