Comparison of tunneling currents in graphene nanoribbon tunnel field effect transistors calculated using Dirac-like equation and Schr&#246;dinger&#39;s equation

Endi Suhendi; Lilik Hasanah; Dadi Rusdiana; Fatimah A. Noor; Neny Kurniasih; Khairurrijal

doi:10.1088/1674-4926/40/6/062002

Journals >Journal of Semiconductors >Volume 40 >Issue 6 >Page 062002 > Article

Journal of Semiconductors
Vol. 40, Issue 6, 062002 (2019)

Comparison of tunneling currents in graphene nanoribbon tunnel field effect transistors calculated using Dirac-like equation and Schrödinger's equation

Endi Suhendi¹, Lilik Hasanah¹, Dadi Rusdiana¹, Fatimah A. Noor², Neny Kurniasih³, and Khairurrijal²

Author Affiliations

¹Physics of Electronic Material Research Division, Universitas Pendidikan Indonesia, Bandung 40154, Indonesia

²Physics of Electronic Material Research Division, Institut Teknologi Bandung, Bandung 40132, Indonesia

³Earth Physics and Physics of Complex Systems Research Division, Institut Teknologi Bandung, Bandung 40132, Indonesia

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DOI: 10.1088/1674-4926/40/6/062002 Cite this Article

Endi Suhendi, Lilik Hasanah, Dadi Rusdiana, Fatimah A. Noor, Neny Kurniasih, Khairurrijal. Comparison of tunneling currents in graphene nanoribbon tunnel field effect transistors calculated using Dirac-like equation and Schrödinger's equation[J]. Journal of Semiconductors, 2019, 40(6): 062002 Copy Citation Text

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Abstract

The tunneling current in a graphene nanoribbon tunnel field effect transistor (GNR-TFET) has been quantum mechanically modeled. The tunneling current in the GNR-TFET was compared based on calculations of the Dirac-like equation and Schrödinger's equation. To calculate the electron transmittance, a numerical approach-namely the transfer matrix method (TMM)-was employed and the Launder formula was used to compute the tunneling current. The results suggest that the tunneling currents that were calculated using both equations have similar characteristics for the same parameters, even though they have different values. The tunneling currents that were calculated by applying the Dirac-like equation were lower than those calculated using Schrödinger's equation.

$ H = {v_{\rm F}}\left[ \!\!\!{\begin{array}{*{20}{c}} 0 & { - i\hbar {\partial _{ z}} - \hbar {\partial _{ x}}}\\ { - i\hbar {\partial _{\rm z}} + \hbar {\partial _{ x}}} & 0 \end{array}}\!\!\! \right]. $

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$\begin{array}{*{20}{c}} {{\psi _1} = \frac{1}{\sqrt 2 }\left( \!\!\!\!{\begin{array}{*{20}{c}} 1\\ \frac{\left| {E - {V_1}} \right|}{E - {V_1}}{{\rm e}^{i{\theta _1}}} \end{array}}\!\!\!\! \right){{\rm e}^{i{k_1}z + i{k_{\rm n}}x}} + \frac{B_1}{\sqrt 2}\left(\!\!\!\! {\begin{array}{*{20}{c}} 1\\ { - \frac{{\left| {E - {V_1}} \right|}}{{E - {V_1}}}{{\rm e}^{ - i{\theta _1}}}} \end{array}} \!\!\!\!\right){{\rm e}^{ - i{k_1}z + i{k_n}x}},\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} & {} & {z \leqslant 0}\\ {{\psi _{\rm S,C,D}} = \frac{{{A_{\rm S,C,D}}}}{{\sqrt 2 }}\left(\!\!\!\! {\begin{array}{*{20}{c}} 1\\ {\frac{{\left| {E - {V_{\rm S,C,D}}} \right|}}{{E - {V_{\rm S,C,D}}}}{{\rm e}^{i{\theta _{\rm SCD}}}}} \end{array}} \!\!\!\!\right){{\rm e}^{i{k_{\rm SCD}}z + i{k_n}x}} + \frac{{{B_{\rm S,C,D}}}}{{\sqrt 2 }}\left(\!\!\!\! {\begin{array}{*{20}{c}} 1\\ { - \frac{{\left| {E - {V_{\rm S,C,D}}} \right|}}{{E - {V_{\rm S,C,D}}}}{{\rm e}^{ - i{\theta _{\rm SCD}}}}} \end{array}} \!\!\!\!\right){{\rm e}^{ - i{k_{\rm SCD}}z + i{k_{\rm n}}x}}\,\,\,} & {} & {0 < z \leqslant 2L}\\ {{\psi _2} = \frac{{{A_2}}}{{\sqrt 2 }}\left(\!\!\!\! {\begin{array}{*{20}{c}} 1\\ {\frac{{\left| {E - {V_2}} \right|}}{{E - {V_2}}}{{\rm e}^{i{\theta _2}}}} \end{array}}\!\!\!\! \right){{\rm e}^{ - i{k_2}z + i{k_{\rm n}}x}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} & {} & {z > 2L,} \end{array}$

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