New model for capacitance-voltage analysis of metal semiconductor contacts

Abstract

A new numerical model for capacitance-voltage analysis of metal-semiconductor contacts has been developed and used to simulate on various experimental results. The model is based on self-consistency between Poisson's equation and Schrodinger's equation for the numerical simulation of lD MIS structure. Poisson's equation has been solved in the combined oxide-semiconductor region using Finite Difference method with non-uniform mesh size and boundary value technique. Doolittle's decomposition technique has been used to the tri-diagonal coefficient matrix to speed up the Poisson solver. Eigen states, as well as the eigen energies are calculated from the solution of ID Schrodinger's equation. To make the Schriidinger solver numerically efficient and easy to program, Green's function formalism has been used which uses retarded Green's function to find eigen energy and eigen states of any ID quantum well structures using open. boundary condition. Interface trap charge distribution in accordance with the Fermi - Dirac statistics has been included in the CV curve considering both donor and acceptor type of trap states. It has been observed that simulated C-V is sensitive to the variation of unintentionally formed interfacial layer thickness. Numerical results show that C-V curves are rather sensitive to the degree and details of the interface trap distributions. Non-unifrom doping is also responsible for the non-ideal effects in the C2 vs Vg curves apart from interfacial trap states distribution. A simple technique to extract doping profile from experimental C-V curves has been developed. Results showed excellent agreement with experimentally determined doping profile. Several C-V curves are simulated for different types of doping profiles and doping profiles are extracted from them subsequently to illustrate the robustness of the technique. An easy technique to extract interface trap state distribution within the bandgap from low or high frequency C-V curves has also been developed.