Comparison of electron transmittances and tunneling currents in an anisotropic TiN_x/HfO_2/SiO_2/p-Si(100) metal-oxide-semiconductor(MOS) capacitor calculated using exponential- and Airy-wavefunction approaches and a transfer matrix method  

作　　者：Fatimah A.Noor Mikrajuddin Abdullah Sukirno Khairurrijal 

机构地区：[1]Physics of Electronic Materials Research Division,Faculty of Mathematics and Natural Sciences,Institut Teknologi Bandung,Jalan Ganesa 10,Bandung 40132,Indonesia

出　　处：《Journal of Semiconductors》2010年第12期28-32,共5页半导体学报（英文版）

摘　　要：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 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 TiNx metal gate increases because the electron effective mass of TiNx 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.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 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 TiNx metal gate increases because the electron effective mass of TiNx 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.

关 键 词：Airy wavefunction anisotropic MOS exponential wavefunction transfer matrix method transmittance tunneling current 

分 类 号：TN304.21[电子电信—物理电子学]