Hole confinement and energy subbands in a silicon inversion layer using the effective mass theory

We present a study of the main features of a two-dimensional hole gas confined near a Si-SiO₂ heterointerface. Starting from the framework of the effective mass theory, we were able to separate the Luttinger Hamiltonian into two 3 X 3 matrices using a semiaxial approximation and still retaining the warped shape of the isoenergetic surfaces in the k_x-k_y plane and the coupling of heavy, light, and split-off holes. This allows us to solve iteratively and simultaneously the Schrodinger and Poisson equations in the case of an inversion layer of holes in a P-channel metal-oxide-semiconductor structure for different applied gate biases. We have obtained the energy subbands and the main characteristics of the inversion layer. The form of the energy subbands suggests that the use of parabolic bands should be seriously questioned, and that even the use of a unique effective mass in each subband is not a realistic assumption. Furthermore, our results show that the character of the subbands becomes mixed as k_∥ separates from zero, and that the complete dispersion characteristics must be considered in hole studies.