J. Semicond. > 2010, Volume 31 > Issue 12 > 124002

SEMICONDUCTOR DEVICES

Comparison of electron transmittances and tunneling currents in an anisotropic TiNx/HfO2/SiO2/p-Si(100) metal–oxide–semiconductor (MOS) capacitor calculated using exponential- and Airy-wavefunction app

Fatimah A. Noor, Mikrajuddin Abdullah, Sukirno and Khairurrijal

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DOI: 10.1088/1674-4926/31/12/124002

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Abstract: 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-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 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.

Key words: Airy wavefunctionanisotropic MOSexponential wavefunctiontransmittancetunneling current

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    Received: 18 August 2015 Revised: 30 July 2010 Online: Published: 01 December 2010

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      Fatimah A. Noor, Mikrajuddin Abdullah, Sukirno, Khairurrijal. Comparison of electron transmittances and tunneling currents in an anisotropic TiNx/HfO2/SiO2/p-Si(100) metal–oxide–semiconductor (MOS) capacitor calculated using exponential- and Airy-wavefunction app[J]. Journal of Semiconductors, 2010, 31(12): 124002. doi: 10.1088/1674-4926/31/12/124002 ****F A Noor, M Abdullah, Sukirno, Khairurrijal. Comparison of electron transmittances and tunneling currents in an anisotropic TiNx/HfO2/SiO2/p-Si(100) metal–oxide–semiconductor (MOS) capacitor calculated using exponential- and Airy-wavefunction app[J]. J. Semicond., 2010, 31(12): 124002. doi:  10.1088/1674-4926/31/12/124002.
      Citation:
      Fatimah A. Noor, Mikrajuddin Abdullah, Sukirno, Khairurrijal. Comparison of electron transmittances and tunneling currents in an anisotropic TiNx/HfO2/SiO2/p-Si(100) metal–oxide–semiconductor (MOS) capacitor calculated using exponential- and Airy-wavefunction app[J]. Journal of Semiconductors, 2010, 31(12): 124002. doi: 10.1088/1674-4926/31/12/124002 ****
      F A Noor, M Abdullah, Sukirno, Khairurrijal. Comparison of electron transmittances and tunneling currents in an anisotropic TiNx/HfO2/SiO2/p-Si(100) metal–oxide–semiconductor (MOS) capacitor calculated using exponential- and Airy-wavefunction app[J]. J. Semicond., 2010, 31(12): 124002. doi:  10.1088/1674-4926/31/12/124002.

      Comparison of electron transmittances and tunneling currents in an anisotropic TiNx/HfO2/SiO2/p-Si(100) metal–oxide–semiconductor (MOS) capacitor calculated using exponential- and Airy-wavefunction app

      DOI: 10.1088/1674-4926/31/12/124002
      • Received Date: 2015-08-18
      • Accepted Date: 2009-11-17
      • Revised Date: 2010-07-30
      • Published Date: 2010-11-25

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