Extension of analytical model for conduction band nonparabolicity to transport analysis of nanoscale metal-oxide-semiconductor field-effect transistor

Abstract

This paper reconsiders the mathematical formulation for the conventional nonparabolic band model and discusses how the nonparabolicity of the conduction band impacts the effective masses of electrons that are confined within the barriers. Since the conventional simplified model for band nonparabolicity does not include the external potential effect as a perturbation, it is examined whether this perturbation can be implemented into the conventional model for usefulness. When the perturbation energy is smaller than the unperturbed energy, the insertion of the perturbation energy term into the conventional expression for the nonparabolic band model is reasonably valid. It is demonstrated that this approximation is actually accurate given a sub-10-nm-thick Si layer surrounded by an SiO2 layer. A major part of this discussion is focused on the low-dimensionality electron system confined with insulator barriers so this study contributes to the analysis of future electron devices. To support this consideration, this paper proposes an analytical expression for the conduction-band effective mass of electrons including the term of band nonparabolicity.