Efficient wave-function matching approach for quantum transport calculations

Sørensen, Henrik Rokkjær; Hansen, Per Christian; Petersen, Dan; Skelboe, Stig; Stokbro, Kurt

doi:10.1103/physrevb.79.205322

Cited by 55 publications

(41 citation statements)

References 29 publications

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“…In such a device, only the atoms facing the gate electrode will be strongly influenced, and this explains why in Ref. 26 we found that the transport in the device was dominated by tunneling even though the nanotube was 110 Å long, and thus longer than the graphene junctions studied in this paper. Thus, to obtain efficient gating of a nanotube, the gate electrode must wrap around the tube.…”

Section: B Transistor Characteristicsmentioning

confidence: 77%

Semiempirical model for nanoscale device simulations

et al. 2010

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We present a semiempirical model for calculating electron transport in atomic-scale devices. The model is an extension of the extended Hückel method with a self-consistent Hartree potential that models the effect of an external bias and corresponding charge rearrangements in the device. It is also possible to include the effect of external gate potentials and continuum dielectric regions in the device. The model is used to study the electron transport through an organic molecule between gold surfaces, and it is demonstrated that the results are in closer agreement with experiments than ab initio approaches provide. In another example, we study the transition from tunneling to thermionic emission in a transistor structure based on graphene nanoribbons.

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Section: B Transistor Characteristicsmentioning

confidence: 77%

Semiempirical model for nanoscale device simulations

et al. 2010

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“…In order to evaluate the transport properties of the device we use the Landauer-Büttiker approach together with the wave function matching method [49,50] which requires a numerical solution of the scattering problem. A low temperature ∼ 0K and a source-drain bias within the linear response regime are assumed.…”

Section: B Conductancementioning

confidence: 99%

Imaging snake orbits at graphene n−p junctions

Kolasiński¹,

Mreńca-Kolasińska²,

Szafran³

2017

Phys. Rev. B

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We report on the observation of magnetoresistance oscillations in graphene p-n junctions. The oscillations have been observed for six samples, consisting of single-layer and bilayer graphene, and persist up to temperatures of 30 K, where standard Shubnikov-de Haas oscillations are no longer discernible. The oscillatory magnetoresistance can be reproduced by tight-binding simulations. We attribute this phenomenon to the modulated densities of states in the n-and p-regions. p-n junctions are among the basic building blocks of any electronic circuit. The ambipolar nature of graphene provides a flexible way to induce p-n junctions by elec-trostatic gating. This offers the opportunity to tune the charge carrier densities in the n-and p-doped regions independently. The potential gradient across a p-n interface depends on the thickness of the involved insula-tors and can also be modified by appropriate gate voltages. Due to the high electronic quality of present day graphene devices a number of transport phenomena in pnp or npn junctions have been reported, such as ballistic Fabry-Pérot oscillations 1-3 and so-called snake states 4,5 , both of which depend on characteristic length scales of the sample. Here we report on the discovery of yet another kind of oscillation, which does not depend on any such length scale. The oscillations occur in the bipolar regime, in the magnetic field range where Shubnikov-de Haas oscillations are observed in the unipolar regime. These novel oscillations in the bipolar regime are governed by the unique condition that the distance between two resistance minima (or maxima) in gate voltage space is given by a constant filling factor difference of ∆ν = 8. The features are remarkably robust: they occur in samples with one and two p-n interfaces; in single and bilayer graphene; up to temperatures of 30 K (where Shubnikov-de Haas oscillations have long disappeared); over a large density range; for interface lengths ranging from 1 µm to 3 µm and in both pnp and npn regimes. The oscillations have been observed in a magnetic field range of B = 0.4 T up to B = 1.4 T. Their periodicity does not sample name A B C D E F sample width W (µm) 1.3 1.4 1.1 0.9 3 1.2 sample length L (µm) 3.0 1.4 1.0 2.3 3 2.8 top gate length L TG (µm) 1.1 0.7 0.55 1.2 1.0 1.0 distance to top gate (nm) 23 44 28 57 35 25 number of graphene layers 2 1 2 2 2 2 junction type npn pn npn pn npn npn TABLE I. Characteristics of samples A-F match the periodicity of the aforementioned snake states. In this paper we address this phenomenon and suggest a model which can qualitatively explain the oscillations. Measurements were performed on six samples in total , which all consist of a graphene flake encapsulated between two hexagonal boron nitride (h-BN) flakes on a Si/SiO 2 substrate. They all show similar behavior. This paper focuses on measurements performed on one sample (sample A), with the device geometry sketched in Fig. 1a. Specifications of the other five samples are summarized in table I. The bilayer graphene (BLG) flake was e...

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“…The calculation of contact self-energies using iterative and direct approaches (as used here) is already well established in literature. [29,[36][37][38] Nonetheless, we will detail the procedure here. Our reasons for this are twofold; (1) our basis, being non-orthogonal, introduces additional complexity that, to our knowledge, has not been previously described for the direct approach, and (2) our numerical approach avoids some numerical errors in calculating the self-energies directly.…”

Section: Contact Self-energiesmentioning

confidence: 99%

Scalable atomistic simulations of quantum electron transport using empirical pseudopotentials

Put

Fischetti

Vandenberghe

2019

Computer Physics Communications

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The simulation of charge transport in ultra-scaled electronic devices requires the knowledge of the atomic configuration and the associated potential. Such "atomistic" device simulation is most commonly handled using a tight-binding approach based on a basis-set of localized orbitals. Here, in contrast to this widelyused tight-binding approach, we formulate the problem using a highly accurate plane-wave representation of the atomic (pseudo)-potentials. We develop a new approach that separately deals with the intrinsic Hamiltonian, containing the potential due to the atomic configuration, and the extrinsic Hamiltonian, related to the external potential. We realize efficient performance by implementing a finite-element like partitionof-unity approach combining linear shape functions with Bloch-wave enhancement functions. We match the performance of previous tight-binding approaches, while retaining the benefits of a plane wave based model. We present the details of our model and its implementation in a full-fledged self-consistent ballistic quantum transport solver. We demonstrate our implementation by simulating the electronic transport and device characteristics of a graphene nanoribbon transistor containing more than 2000 atoms. We analyze the accuracy, numerical efficiency and scalability of our approach. We are able to speed up calculations by a factor of 100 compared to previous methods based on plane waves and envelope functions. Furthermore, our reduced basis-set results in a significant reduction of the required memory budget, which enables devices with thousands of atoms to be simulated on a personal computer.

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Efficient wave-function matching approach for quantum transport calculations

Cited by 55 publications

References 29 publications

Semiempirical model for nanoscale device simulations

Semiempirical model for nanoscale device simulations

Imaging snake orbits at graphene n−p junctions

Scalable atomistic simulations of quantum electron transport using empirical pseudopotentials

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