A Practical Model of Hole Effective Mass of Si on Si1−x Ge x Modulated by External Electric Field and External Strain

Abstract

This paper reconsiders the mathematical formulation of the conventional nonparabolic band dispersion model of holes of Si on SiGe materials, and proposes a practical model of hole effective mass of covalent semiconductors modulated by the external electric field and external strain. This paper also discusses how the nonparabolicity of the valence band impacts the effective masses of holes 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 to enhance its usefulness. This consideration is also applied to the impact of strain on the effective mass of holes. The conventional dispersion model for the nonparabolic hole band is examined on the basis of the Hamiltonian operator representation because the insertion of perturbation energy must be validated mathematically. 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 dispersion model is reasonably valid. For example, it is anticipated that this approximation is accurate for a sub-10 nm thick Si physically confined on the SiGe layer, so this study contributes to the analysis of nano-scale devices.