Abstract: Analytical expressions of electron transmittance and tunneling current in an anisotropic TiN_x/HfO₂/SiO₂/p-Si(100) metal–oxide–semiconductor (MOS) capacitor were derived by considering the coupling of transverse and longitudinal energies of an electron. Exponential and Airy wavefunctions were utilized to obtain the electron transmittance and the electron tunneling current. A transfer matrix method, as a numerical approach, was used as a benchmark to assess the analytical approaches. It was found that there is a similarity in the transmittances calculated among exponential- and Airy-wavefunction approaches and the TMM at low electron energies. However, for high energies, only the transmittance calculated by using the Airy-wavefunction approach is the same as that evaluated by the TMM. It was also found that only the tunneling currents calculated by using the Airy-wavefunction approach are the same as those obtained under the TMM for a range of oxide voltages. Therefore, a better analytical description for the tunneling phenomenon in the MOS capacitor is given by the Airy-wavefunction approach. Moreover, the tunneling current density decreases as the titanium concentration of the TiN_x metal gate increases because the electron effective mass of TiN_x decreases with increasing nitrogen concentration. In addition, the mass anisotropy cannot be neglected because the tunneling currents obtained under the isotropic and anisotropic masses are very different.

Key words: Airy wavefunction, anisotropic MOS, exponential wavefunction, transmittance, tunneling current