Analysis of MOS Device Capacitance-Voltage Characteristics Based on the Self-Consistent Solution of the Schrödinger and Poisson Equations

ABSTRACTThe one-dimensional Schridinger and Poisson equations have been numerically solved in metal-oxide-semiconductor devices using a three-point finite difference scheme with a non-uniform mesh size. The capacitance-voltage characteristic of the structure has been calculated via this self-consistent approach and results have been compared with data obtained from the resolution of Poisson equation using different approximated methods based on the Boltzmann statistic with and without a first order quantum effect correction or the exact Fermi-Dirac statistic. The present work permits to evaluate and quantify the errors made by these approximations in determining the thickness of ultra-thin oxides.