Direct solution of the Boltzmann transport equation in nanoscale Si devices

We report the first direct numerical solution to the Boltzmann transport equation (BTE) without making any approximations about the angular shape of the distribution function or the collision integral. The mathematical and numerical techniques used for solving this problem are discussed and shown to have the correct properties for semiconductor simulation. The applications of this method are general and are demonstrated here, for both one-dimensional (50 nm n⁺-p-n⁺) and two-dimensional (50 nm ultra-thin body dual-gate nMOSFET) devices