Simulation of Electron Transmittance and Tunneling Current in a Metal-Oxide- Semiconductor Capacitor with a High-K Dielectric Stack of HfO2 and SiO2 Using Exponential- and Airy-Wavefunction Approaches and a Transfer Matrix Method

Analytical expressions of electron transmittance and tunneling current in a metal-oxide-semiconductor (MOS) capacitor with a high dielectric constant (high-K) oxide stack of HfO2 and SiO2 and a negative bias applied to the metal gate were derived. Exponential- and Airy-wavefunction approaches were employed in deriving analytically the electron transmittance and tunneling current. A numerical approach based on a transfer matrix method was used as a standard to evaluate the analytical approaches. It was found that the transmittances obtained under the exponential- and Airy-wavefunction approaches and the TMM are matching for low electron energies, while for higher energies only the transmittances calculated by employing the Airy- wavefunction approach is the same as those computed by using the TMM. It was also found that the tunneling currents calculated by using the exponential- and the Airy-wavefunction approaches and the TMM are equal for low oxide voltages (lower than 0.5 V), while for higher oxide voltages only the tunneling currents computed under the Airy-wavefunction approach fit those obtained under the TMM. Therefore, the Airy-wavefunction approach provides a better analytical model to tunneling processes in the MOS capacitor.