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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 total computing time for calculating a series of (E) for all relevant modes in - 1 ≤ E ≤ 1 eV with 0.001 eV spacing using analytic (○) and iterative (Δ) methods in the TBDE model for different GNR width. The iterative method takes about 40 × longer than that of analytic method. Included for comparison is the total time to calculate the corresponding surface Green's functions calculated using iterative method in the TB-π model (◊).
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Figure 2: The total computing time for calculating a series of (E) for all relevant modes in - 1 ≤ E ≤ 1 eV with 0.001 eV spacing using analytic (○) and iterative (Δ) methods in the TBDE model for different GNR width. The iterative method takes about 40 × longer than that of analytic method. Included for comparison is the total time to calculate the corresponding surface Green's functions calculated using iterative method in the TB-π model (◊).

Mentions: In the past, (6)-(13) are evaluated iteratively to calculate , and hence Σ[s, d] [13,17]. In this study, we have shown that (6)-(13) can be solved analytically for the Dirac form in (2) and that significant computational saving and accuracy can therefore be achieved by directly using (18) instead of numerically iterating (6)-(13). Figure 2 shows that the total computing time to calculate all the relevant modes of (E) for E ∈ [-1,1] eV with spacing of 0.001 eV via analytical, i.e., (17), and iterative means, i.e., (6)-(13) for a range of GNR width on a typical duo core PC using MATLAB. The time needed to calculate using the iterative method is about 40× larger than that of the analytic method over the entire range of the GNR width considered. In general, it is observed that the computing time increases with the GNR width for both analytical and iterative methods because the number of modes also increases with the width. (See Table 1.) Figure 2 also shows, as a comparison, the corresponding total computing time for calculating the all relevant surface Green's functions (via iterative method) for the same set of GNR width in TB-π model. This time is much larger than that of the TBDE, between about 100× (at 1.1 nm width) and 455× (for 3.8 nm width) that of the analytic method of TBDE. Therefore the computational saving from using our analytic results for the surface Green's function, (17), is compelling. The computing saving will be even more apparent in more realistic quantum transport calculations in which the NEGF and Poisson equation are solved iteratively to achieve self-consistent solutions.


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 total computing time for calculating a series of (E) for all relevant modes in - 1 ≤ E ≤ 1 eV with 0.001 eV spacing using analytic (○) and iterative (Δ) methods in the TBDE model for different GNR width. The iterative method takes about 40 × longer than that of analytic method. Included for comparison is the total time to calculate the corresponding surface Green's functions calculated using iterative method in the TB-π model (◊).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 2: The total computing time for calculating a series of (E) for all relevant modes in - 1 ≤ E ≤ 1 eV with 0.001 eV spacing using analytic (○) and iterative (Δ) methods in the TBDE model for different GNR width. The iterative method takes about 40 × longer than that of analytic method. Included for comparison is the total time to calculate the corresponding surface Green's functions calculated using iterative method in the TB-π model (◊).
Mentions: In the past, (6)-(13) are evaluated iteratively to calculate , and hence Σ[s, d] [13,17]. In this study, we have shown that (6)-(13) can be solved analytically for the Dirac form in (2) and that significant computational saving and accuracy can therefore be achieved by directly using (18) instead of numerically iterating (6)-(13). Figure 2 shows that the total computing time to calculate all the relevant modes of (E) for E ∈ [-1,1] eV with spacing of 0.001 eV via analytical, i.e., (17), and iterative means, i.e., (6)-(13) for a range of GNR width on a typical duo core PC using MATLAB. The time needed to calculate using the iterative method is about 40× larger than that of the analytic method over the entire range of the GNR width considered. In general, it is observed that the computing time increases with the GNR width for both analytical and iterative methods because the number of modes also increases with the width. (See Table 1.) Figure 2 also shows, as a comparison, the corresponding total computing time for calculating the all relevant surface Green's functions (via iterative method) for the same set of GNR width in TB-π model. This time is much larger than that of the TBDE, between about 100× (at 1.1 nm width) and 455× (for 3.8 nm width) that of the analytic method of TBDE. Therefore the computational saving from using our analytic results for the surface Green's function, (17), is compelling. The computing saving will be even more apparent in more realistic quantum transport calculations in which the NEGF and Poisson equation are solved iteratively to achieve self-consistent solutions.

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