Modeling hole effective mass of Si modulated by external field

This paper reconsiders the mathematical formulation of the conventional nonparabolic valence band dispersion model for Si, and discusses how the nonparabolicity of the valence band and the external electric field impact the effective masses (so-called curvature mass) of holes. Basically, the conventional model for band nonparabolicity does not include the external potential effect as a perturbation. Accordingly, this paper examines whether this perturbation can be implemented in the conventional energy dispersion model for convenience. The dispersion model for the nonparabolic band is examined on the basis of the Hamiltonian operator representation because the insertion of perturbation must be validated physically and mathematically. In the following discussion, we focus on the low-dimensional hole system with insulator barrier confinement, so this study is also applicable to nano-scale device analyses. Here we propose an analytical expression for the effective mass of holes including band nonparabolicity.