Semiempirical closed-form models for the inversion-layer centroid of a p-MOS including quantum effects

We have studied the importance of the average inversion-layer penetration, which is termed the inversion-layer centroid, to the depletion and inversion charge of a general p-MOS structure. From the quantum theory, and using the Luttinger Hamiltonian, which takes into account the main features of the valence band (degeneracy at k = 0, split-off influence and warping in the k_x-k_y plane), we self-consistently solve the Poisson and Schrodinger equations and thus obtain the hole distribution under various doping levels and external applied voltages. In this way we can numerically determine the centroid and we compare it with the usual empirical expressions. Furthermore, we propose new closed-form expressions to model the centroid for a wide range of technological variables. We also study the influence of the centroid on the surface potential, depletion charge and inversion charge, showing the way in which classical expressions should be modified to take the centroid into account and to model these magnitudes more accurately.