Subbands model for semiconductors based on the Maximum Entropy Principle

Abstract

In this thesis a double-gate MOSFET is simulated with an energy-transport subband model and an energy-transport model is derived for a nanoscale MOSFET. Regarding the double-gate MOSFET the model is formulated starting from the moment system derived from the Schroedinger-Poisson-Boltzmann equations. The system is closed on the basis of the maximum entropy principle and includes scattering of electrons with acoustic and non-polar optical phonons. The proposed expression of the entropy combines quantum effects and semiclassical transport by weighting the contribution of each sub band with the square modulus of the envelope functions arising from the Schroedinger-Poisson system. The simulations show that the model is able to capture the relevant confining and transport features and asses the robustness of the numerical scheme.\\ The model for the MOSFET takes into account the presence of both 3D and 2D electron gas included along with the quantization in the transversal direction with respect to the oxide at the gate which gives raise to a sub band decomposition of the electron energy.\\ Both intra and inter scattering between the 2D and the 3D electron gas are considered. In particular, a fictitious transition from the 3D to the 2D electrons and vice versa is introduced.