Gate capacitance of deep submicron MOSFETs with high-K gate dielectrics

We study gate capacitance of deep submicron MOSFETs with high-K gate dielectrics. Schrödinger’s equation is solved by applying an open boundary condition at silicon-gate dielectric interface. Self-consistent numerical results reveal that accounting for wave function penetration into the gate dielectric causes the carrier distribution to be shifted closer to the gate dielectric. This effect increases with increasing gate voltage and also increases with the decreasing conduction band offset of the gate dielectric material with silicon. Gate capacitance calculated from conventional modeling is found to be independent of dielectric materials for a given equivalent oxide thickness (EOT). But our study shows that when wave function penetration into the gate dielectric is considered, gate capacitance for a given EOT increases with a decrease in the conduction band offset. Effects of substrate doping density on gate capacitance are found to be negligible when wave function penetration effects are incorporated.