Voltage- and temperature-dependent gate capacitance and current model: application to ZrO2 n-channel MOS capacitor

Based on the energy-dispersion relation in each region of the gate-dielectric-silicon system, a tunneling model is developed to understand the gate current as a function of voltage and temperature. The gate capacitance is self-consistently calculated from Schrodinger and Poisson equations subject to the Fermi-Dirac statistics, using the same band structure in the silicon as used for tunneling injection. Franz two-band dispersion is assumed in the dielectric bandgap. Using a Wentzel-Kramer-Brillouin (WKB)-based approach, direct and Fowler-Nordheim (FN) tunneling and thermionic emission are considered simultaneously. The model is implemented for both the silicon conduction and valence bands and both gate- and substrate-injected currents. ZrO₂ NMOSFETs were studied through temperature-dependent C_g-V_g and I_g-V, simulations. The extracted band gaps and band offsets of the ZrO₂- and interfacial-Zr-silicate-layer are found to be comparable with the reported values. The gate currents in ZrO₂-NMOSCAPs are found to be primarily contributed from the silicon conduction band and tunneling appears to be the most probable primary mechanism through the dielectric. Oscillations of gate currents and kinks of gate capacitance were observed near the flat-band in the experiments. These phenomena might be caused by the interface states.