Comparison of electron transmittances and tunneling currents in an anisotropic TiNx/HfO2/SiO2/p-Si（lO0） metal-oxide-semiconductor （MOS） capacitor calculated using exponential- and Airy-wavefunction approaches and a transfer matrix method

Analytical expressions of electron transmittance and tunneling current in an anisotropic TiNx/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-wavefimction approaches and the TMM at low electron energies. However, for high energies, only the transmit- tance 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 all range of oxide voltages. Therefore, a better analytical description for t