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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

引用

Journal of Semiconductors 2010年第12期31卷 28-32页

作者： Fatimah A.Noor Mikrajuddin Abdullah Sukirno Khairurrijal Physics of Electronic Materials Research Division Faculty of Mathematics and Natural SciencesInstitut Teknologi BandungJalan Ganesa 10Bandung 40132Indonesia

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

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