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Quantum transport simulations of graphene nanoribbon devices using Dirac equation calibrated with tight-binding π-bond model.

Chin SK, Lam KT, Seah D, Liang G - Nanoscale Res Lett (2012)

Bottom Line: The approach has the advantage of the computational efficiency of the Dirac equation and still captures sufficient quantitative details of the bandstructure from the tight-binding π-bond model for graphene.We demonstrate how the exact self-energies due to the leads can be calculated in the NEGF-Dirac model.We apply our approach to GNR systems of different widths subjecting to different potential profiles to characterize their device physics.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institute of High Performance Computing, A*STAR, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore. chinsk@ihpc.a-star.edu.sg.

ABSTRACT
We present an efficient approach to study the carrier transport in graphene nanoribbon (GNR) devices using the non-equilibrium Green's function approach (NEGF) based on the Dirac equation calibrated to the tight-binding π-bond model for graphene. The approach has the advantage of the computational efficiency of the Dirac equation and still captures sufficient quantitative details of the bandstructure from the tight-binding π-bond model for graphene. We demonstrate how the exact self-energies due to the leads can be calculated in the NEGF-Dirac model. We apply our approach to GNR systems of different widths subjecting to different potential profiles to characterize their device physics. Specifically, the validity and accuracy of our approach will be demonstrated by benchmarking the density of states and transmissions characteristics with that of the more expensive transport calculations for the tight-binding π-bond model.

No MeSH data available.


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The DOS(E) and T(E) of a rectangular barrier. (a) Schematic of a rectangular barrier of height 0.1 eV across the W14 GNR channel. (b) The DOS(E) with red arrow indicating region of reduced DOS(E) due to the introduction of the barrier at channel. The region near E = Eg/2 (as indicated) is magnified as inset with DOS(E) in log-scale. Two discrete bound states, created by the inverted well at valence band-edge, as shown in (a). (c) The T(E) with red arrow indicates the receding T(E) away from Eg/2 due to the 0.1 eV barrier. Results for U = 0 and that calculated from TB-π are also included for comparison.
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Figure 6: The DOS(E) and T(E) of a rectangular barrier. (a) Schematic of a rectangular barrier of height 0.1 eV across the W14 GNR channel. (b) The DOS(E) with red arrow indicating region of reduced DOS(E) due to the introduction of the barrier at channel. The region near E = Eg/2 (as indicated) is magnified as inset with DOS(E) in log-scale. Two discrete bound states, created by the inverted well at valence band-edge, as shown in (a). (c) The T(E) with red arrow indicates the receding T(E) away from Eg/2 due to the 0.1 eV barrier. Results for U = 0 and that calculated from TB-π are also included for comparison.

Mentions: Next, we subjected the W14 GNR to a rectangular barrier of 0.1 eV in the channel as shown in Figure 6a. The resulting DOS(E) and T(E) are shown in Figure 6b,c, respectively, with that of TB-π model and U = 0 included for comparison. As expected, the onset of both DOS(E) at the conduction and valence ranges have not changed because the lowest Ec and highest Ev, at -Eg/2, and Eg/2, respectively, have not been changed by the introduction of the barrier potential compared to that of U = 0. However, it is observed that the magnitude of DOS(E) just above E = Eg/2 was reduced significantly due to the lost of states in the channel region dominated by the barrier. The inverted well of depth 0.1 eV at the channel valence band-edge is expected to accommodate some discrete bound states. However, the DOS(E) associated with them may be too sharp to be captured, or partially captured by the E grids being used. This expectation is borne out by the inset of Figure 6b, which shows the log-scale of the DOS(E) in the vicinity of E = -Eg/2. Two discrete bound states, with the heights of their DOS(E) partially captured, are discernible within the inverted well energy range of within 0.1 eV above -Eg/2. As for T(E), the carriers are unhindered source-to-drain only for E >Eg/2 + 0.1 eV and E < -Eg/2 eV and hence those boundaries marked the onset of T(E), as shown in Figure 6c. The bound states created by the inverted well in the channel region do not contribute to T(E) as there are no states of comparable energies both at the source and drain to connect to them.


Quantum transport simulations of graphene nanoribbon devices using Dirac equation calibrated with tight-binding π-bond model.

Chin SK, Lam KT, Seah D, Liang G - Nanoscale Res Lett (2012)

The DOS(E) and T(E) of a rectangular barrier. (a) Schematic of a rectangular barrier of height 0.1 eV across the W14 GNR channel. (b) The DOS(E) with red arrow indicating region of reduced DOS(E) due to the introduction of the barrier at channel. The region near E = Eg/2 (as indicated) is magnified as inset with DOS(E) in log-scale. Two discrete bound states, created by the inverted well at valence band-edge, as shown in (a). (c) The T(E) with red arrow indicates the receding T(E) away from Eg/2 due to the 0.1 eV barrier. Results for U = 0 and that calculated from TB-π are also included for comparison.
© Copyright Policy - open-access
Related In: Results  -  Collection

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Figure 6: The DOS(E) and T(E) of a rectangular barrier. (a) Schematic of a rectangular barrier of height 0.1 eV across the W14 GNR channel. (b) The DOS(E) with red arrow indicating region of reduced DOS(E) due to the introduction of the barrier at channel. The region near E = Eg/2 (as indicated) is magnified as inset with DOS(E) in log-scale. Two discrete bound states, created by the inverted well at valence band-edge, as shown in (a). (c) The T(E) with red arrow indicates the receding T(E) away from Eg/2 due to the 0.1 eV barrier. Results for U = 0 and that calculated from TB-π are also included for comparison.
Mentions: Next, we subjected the W14 GNR to a rectangular barrier of 0.1 eV in the channel as shown in Figure 6a. The resulting DOS(E) and T(E) are shown in Figure 6b,c, respectively, with that of TB-π model and U = 0 included for comparison. As expected, the onset of both DOS(E) at the conduction and valence ranges have not changed because the lowest Ec and highest Ev, at -Eg/2, and Eg/2, respectively, have not been changed by the introduction of the barrier potential compared to that of U = 0. However, it is observed that the magnitude of DOS(E) just above E = Eg/2 was reduced significantly due to the lost of states in the channel region dominated by the barrier. The inverted well of depth 0.1 eV at the channel valence band-edge is expected to accommodate some discrete bound states. However, the DOS(E) associated with them may be too sharp to be captured, or partially captured by the E grids being used. This expectation is borne out by the inset of Figure 6b, which shows the log-scale of the DOS(E) in the vicinity of E = -Eg/2. Two discrete bound states, with the heights of their DOS(E) partially captured, are discernible within the inverted well energy range of within 0.1 eV above -Eg/2. As for T(E), the carriers are unhindered source-to-drain only for E >Eg/2 + 0.1 eV and E < -Eg/2 eV and hence those boundaries marked the onset of T(E), as shown in Figure 6c. The bound states created by the inverted well in the channel region do not contribute to T(E) as there are no states of comparable energies both at the source and drain to connect to them.

Bottom Line: The approach has the advantage of the computational efficiency of the Dirac equation and still captures sufficient quantitative details of the bandstructure from the tight-binding π-bond model for graphene.We demonstrate how the exact self-energies due to the leads can be calculated in the NEGF-Dirac model.We apply our approach to GNR systems of different widths subjecting to different potential profiles to characterize their device physics.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institute of High Performance Computing, A*STAR, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore. chinsk@ihpc.a-star.edu.sg.

ABSTRACT
We present an efficient approach to study the carrier transport in graphene nanoribbon (GNR) devices using the non-equilibrium Green's function approach (NEGF) based on the Dirac equation calibrated to the tight-binding π-bond model for graphene. The approach has the advantage of the computational efficiency of the Dirac equation and still captures sufficient quantitative details of the bandstructure from the tight-binding π-bond model for graphene. We demonstrate how the exact self-energies due to the leads can be calculated in the NEGF-Dirac model. We apply our approach to GNR systems of different widths subjecting to different potential profiles to characterize their device physics. Specifically, the validity and accuracy of our approach will be demonstrated by benchmarking the density of states and transmissions characteristics with that of the more expensive transport calculations for the tight-binding π-bond model.

No MeSH data available.


Related in: MedlinePlus