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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 simple Laplace Potential. (a) Schematic of a simple Laplace potential profile with a bias of 0.3 V across the GNR channel. (b) The resulting DOS(E) versus E with red arrow indicating the new addition of DOS(E) due to the upward movement of valence band-edge by 0.3 eV. (c) T(E) versus E. Results for U = 0 and that calculated by TB-π are also included for comparison.
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Figure 5: The DOS(E) and T(E) of a simple Laplace Potential. (a) Schematic of a simple Laplace potential profile with a bias of 0.3 V across the GNR channel. (b) The resulting DOS(E) versus E with red arrow indicating the new addition of DOS(E) due to the upward movement of valence band-edge by 0.3 eV. (c) T(E) versus E. Results for U = 0 and that calculated by TB-π are also included for comparison.

Mentions: To apply the NEGF-TBDE to more realistic transport situations, one needs to solve the NEGF-TBDE under bias potentials. For a Laplace potential (with a bias of 0.3 V), as shown in Figure 5a, the DOS(E) and T(E) for the W14 GNR are shown in Figure 5b,c, respectively. The corresponding TB-π results and that of TBDE model with U = 0 are also included for reference. As shown in Figure 5a, the 0.3 V bias is achieved by shifting the conduction and valence bands upwards relative to those at the drain. As the highest valence band-edge (Ev) (at source) shifted up by 0.3 eV, the onset of DOS(E) for E < 0 also creeped up into the original forbidden zone (with U = 0) by about 0.3 eV as indicated by arrow in Figure 5b. The positions of the DOS(E) associated with the higher subbands have also moved up the energy scale relative to those for U = 0. However, the onset of DOS(E) for E > 0 has not been affected significantly by the Laplace setup because the lowest conduction band-edge, which is at the drain, is still intact at E = Eg/2. Although the forbidden zone for DOS(E) has narrowed as indicated in Figure 5b, the forbidden zone for T(E) has actually widen, as shown in Figure 5c, with the onset of non-zero T(E) for E > 0 receding upwards by about 0.3 eV as indicated by the arrow, but unchanged T(E) for E < 0. This is because from carriers are only unhindered source-to-drain only at E >Eg/2 + 0.3 eV and E <Eg/2. The newly addition of DOS(E) at the source-side valence has no state of comparable E to connect to in the channel and drain and hence does not contribute to T(E).


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 simple Laplace Potential. (a) Schematic of a simple Laplace potential profile with a bias of 0.3 V across the GNR channel. (b) The resulting DOS(E) versus E with red arrow indicating the new addition of DOS(E) due to the upward movement of valence band-edge by 0.3 eV. (c) T(E) versus E. Results for U = 0 and that calculated by TB-π are also included for comparison.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3368727&req=5

Figure 5: The DOS(E) and T(E) of a simple Laplace Potential. (a) Schematic of a simple Laplace potential profile with a bias of 0.3 V across the GNR channel. (b) The resulting DOS(E) versus E with red arrow indicating the new addition of DOS(E) due to the upward movement of valence band-edge by 0.3 eV. (c) T(E) versus E. Results for U = 0 and that calculated by TB-π are also included for comparison.
Mentions: To apply the NEGF-TBDE to more realistic transport situations, one needs to solve the NEGF-TBDE under bias potentials. For a Laplace potential (with a bias of 0.3 V), as shown in Figure 5a, the DOS(E) and T(E) for the W14 GNR are shown in Figure 5b,c, respectively. The corresponding TB-π results and that of TBDE model with U = 0 are also included for reference. As shown in Figure 5a, the 0.3 V bias is achieved by shifting the conduction and valence bands upwards relative to those at the drain. As the highest valence band-edge (Ev) (at source) shifted up by 0.3 eV, the onset of DOS(E) for E < 0 also creeped up into the original forbidden zone (with U = 0) by about 0.3 eV as indicated by arrow in Figure 5b. The positions of the DOS(E) associated with the higher subbands have also moved up the energy scale relative to those for U = 0. However, the onset of DOS(E) for E > 0 has not been affected significantly by the Laplace setup because the lowest conduction band-edge, which is at the drain, is still intact at E = Eg/2. Although the forbidden zone for DOS(E) has narrowed as indicated in Figure 5b, the forbidden zone for T(E) has actually widen, as shown in Figure 5c, with the onset of non-zero T(E) for E > 0 receding upwards by about 0.3 eV as indicated by the arrow, but unchanged T(E) for E < 0. This is because from carriers are only unhindered source-to-drain only at E >Eg/2 + 0.3 eV and E <Eg/2. The newly addition of DOS(E) at the source-side valence has no state of comparable E to connect to in the channel and drain and hence does not contribute to T(E).

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