Quantum-mechanical calculation of carrier distribution in MOS accumulation and strong inversion layers

Abstract

We derive a statistical physics model of two-dimensional electron gas (2DEG) and propose an accurate approximation method for calculating the quantum-mechanical effects of metal-oxide-semiconductor (MOS) structure in accumulation and strong inversion regions. We use an exponential surface potential approximation in solving the quantization energy levels and derive the function of density of states in 2D to 3D transition region by applying uncertainty principle and Schrödinger equation in k-space. The simulation results show that our approximation method and theory of density of states solve the two major problems of previous researches: the non-negligible error caused by the linear potential approximation and the inconsistency of density of states and carrier distribution in 2D to 3D transition region.

Theory of Graphene-based Plasmonic Switch

“…where ǫ s , n(x), p(x) represent the dielectric permittivity of the semiconductor, the electron number density, and the hole number density, respectively, and N a the doping concentration of acceptor impurities. One can assume that p(x) is negligibly small in the depletion region [38]. For the low energy eigenstates strongly localized to the dielectric-semiconductor interface, the electrostatic potential energy can be well approximated by V (x) = eEx for…”

“…x > 0 with an infinite potential barrier at x = 0. In this case, the wave function can be written by Airy function with normalization constant such as Ψ n (x) = N n Ai(x n ), where the dimensionless coordinate xn = x/a + s n with s n being the n-th zero of Airy function [38]. The energy eigenvalues are given by E n = − (eEa) s n .…”