Approximations of Quantum Corrected Energy-Transport Model with Non-parabolic Energy Relaxation Time

摘要

An energy transport model coupled with the density gradient method as quantum mechanical corrections has been proposed and numerically investigated. We called it quantum corrected energy-transport model, QCET model. This model used a parabolic approximation for the energy relaxation time but this is often inadequate to describe advanced semiconductor phenomena. In this paper we extend the QCET model to consider the non-parabolic band diagrams in the sense of Kane. We get explicit expressions of energy relaxation time involving the non-parabolic band effects. An adaptive algorithm for solving this model is applied to solve the problem. Numerical simulations on diodes with the length down to 30 nm using this model have been performed and adaptive meshes are given to demonstrate the accuracy and efficiency of the algorithm. It shows that the energy-band non-parabolicity effect is significant for nano-scale semiconductor devices.