On the Physically Based Compact Gate C –V Model for Ultrathin Gate Dielectric MOS Devices Using the Modified Airy Function Approximation

The exponent of the modified Airy function solution of the quantized energy levels in the MOS potential well, which is used in the physically based quantum-mechanical compact gate C-V model of Li et al., has been found to be dependent on the barrier height at the Si-dielectric interface and the substrate doping density. The physical origins of this dependence are discussed. An empirical equation that considers these effects is proposed for lambda. Comparison with the experimental C-V data of MOS devices with high-k gate dielectrics shows that inclusion of these effects in the compact C-V model of Li et al. is necessary for the accurate simulation of MOS field-effect transistors with high- gate dielectrics.