Quantum mechanical modeling of capacitance and gate current for MIS structures using zirconium dioxide as the gate dielectric

Self-consistent numerical calculations were conducted to study the gate tunneling current and capacitance of metal-insulator-silicon (MIS) structures using zirconium dioxide as the gate insulator layer. Quantum mechanical (QM) simulation of the capacitance-voltage (C-V) characteristics was also performed for analyzing the electrical thickness, dielectric constant, and the interface trap density level of the zirconium dioxide layer. For gate current analysis, both the bulk high-κ layer and interfacial silicate layer were considered in the simulation. In the open-boundary system, the quantum transmitting boundary method (QTBM) was used to connect the propagating waves in the metal gate with the stationary waves at the silicon surface. The complex eigenvalues, or the lifetimes of the quasi-bound states, were calculated to obtain the gate current density. It is shown that the simulated gate current agrees with the experimental measurements obtained from aluminum gate/zirconium dioxide/n-type silicon (Al/ZrO₂/n-Si) MIS devices with equivalent oxide thickness (EOT) of ∼2.5 nm.