Efficient Simulation and Analysis of Quantum Ballistic Transport in Nanodevices With AWE

Huang, Jun; Chew, Weng Cho; Tang, Min; Jiang, Lijun

doi:10.1109/ted.2011.2176130

Cited by 12 publications

(6 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A similar procedure has been applied recently in Ref. 45 for the current flow through ballistic nanodevices but in the absence of magnetic field. After solution of the quantum scattering problem we evaluate the conductance by the Landauer-Büttiker formula…”

Section: Modelmentioning

confidence: 99%

Wave-function description of conductance mapping for a quantum Hall electron interferometer

Kolasiński

Szafran

2014

Phys. Rev. B

View full text Add to dashboard Cite

Scanning gate microscopy of quantum point contacts (QPC) in the integer quantum Hall regime is considered in terms of the scattering wave functions with a finite-difference implementation of the quantum transmitting boundary approach. Conductance (G) maps for a clean QPC as well as for a system including an antidot within the constriction are evaluated. The step-like locally flat G maps for clean QPCs turn into circular resonances that are reentrant in external magnetic field when the antidot is introduced to the constriction. The current circulation around the antidot and the spacing of the resonances at the magnetic field scale react to the probe approaching the QPC. The calculated G maps with a rigid but soft antidot potential reproduce the features detected recently in the electron interferometer [F. Martins et al. Nature Sci. Rep. 3, 1416].

show abstract

Section: Modelmentioning

confidence: 99%

Wave-function description of conductance mapping for a quantum Hall electron interferometer

Kolasiński

Szafran

2014

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…In our simulation, the device parameters are L g = 10 nm, L s = L d = 4 nm, W ch = 5 nm, and W ox = 1 nm; doping density is N + = 10 26 /m 3 ; the relative permittivity of silicon is 11.9; and relative permittivity of the silicon dioxide is 3.8. Other parameters can be found in [7].…”

Section: Simple Heterogeneous Poisson Problemmentioning

confidence: 99%

“…is N + = 10 26 /m 3 ; the relative permittivity of silicon is 11.9; and relative permittivity of the silicon dioxide is 3.8. Other parameters can be found in [7].…”

Section: Complex Poisson Problem With Dirichlet Boundary Conditionmentioning

confidence: 99%

“…An accurate and efficient solution of Poisson equation is critical in various areas. For example, in design optimization of nanodevices where quantum effects are significant, a widely used scheme is to solve the coupled Schrödinger-Poisson system self-consistently [6,7], in which Poisson equation is solved repeatedly, and concomitantly with the Schrödinger's equation. As such, the computational load for solving Poisson equation is always of concern.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Novel Efficient Numerical Solution of Poisson's Equation for Arbitrary Shapes in Two Dimensions

Chew

Jiang

2016

Commun. Comput. Phys.

Self Cite

View full text Add to dashboard Cite

We propose a novel efficient algorithm to solve Poisson equation in irregular two dimensional domains for electrostatics. It can handle Dirichlet, Neumann or mixed boundary problems in which the filling media can be homogeneous or inhomogeneous. The basic idea of the new method is solve the problem in three steps: (i) First solve the equation ∇ · D = ρ. The inverse of the divergence operator in a restricted subspace is found to yield the electric flux density D by a fast direct solver in O(N ) operations. The D so obtained is nonunique with indeterminate divergence-free component. Then the electric field is found by E = D/ǫ. But ∇ × E = 0 for electrostatic field; hence, E is curl free and orthogonal to the divergence free space. (ii) An orthogonalization process is used to purify the electric field making it curl free and unique. (iii) Then the potential φ is obtained by solving ∇φ = −E or finding the inverse of the gradient operator in a restricted subspace by a similar fast direct solver in O(N ) operations. Treatments for both Dirichlet and Neumann boundary conditions are addressed. Finally, the validation and efficiency are illustrated by several numerical examples. Through these simulations, it is observed that the computational complexity of our proposed method almost scales as O(N ), where N is the triangle patch number of meshes. Consequently, this new algorithm is a feasible fast Poisson solver.

show abstract

“…In the effective mass approximation, 4,8 the self-energy matrices can be obtained for the whole energy band once the eigenmodes of the leads are solved. 10 Beyond the effective mass approximation, such as the ab initio methods 11 and the empirical tight-binding approaches, 9 however, the self-energy matrices must be evaluated for each energy point individually, further increasing the computational burden. The tight binding models will be the focus of this work, as they are well-suited for nanodevice modeling due to limited-range interactions and reasonably sized basis sets.…”

Section: Introductionmentioning

confidence: 99%

Methods for fast evaluation of self-energy matrices in tight-binding modeling of electron transport systems

Huang

Chew

et al. 2012

Journal of Applied Physics

Self Cite

View full text Add to dashboard Cite

Simulation of quantum carrier transport in nanodevices with non-equilibrium Green's function approach is computationally very challenging. One major part of the computational burden is the calculation of self-energy matrices. The calculation in tight-binding schemes usually requires dealing with matrices of the size of a unit cell in the leads. Since a unit cell always consists of several planes (for example, in silicon nanowire, four atomic planes for [100] crystal orientation and six for [111] and [112]), we show in this paper that a condensed Hamiltonian matrix can be constructed with reduced dimension ($1=4 of the original size for [100] and $1=6 for [111] and [112] in the nearest neighbor interaction) and thus greatly speeding up the calculation. Examples of silicon nanowires with sp 3 d 5 s Ã basis set and the nearest neighbor interaction are given to show the accuracy and efficiency of the proposed methods. V

show abstract

Efficient Simulation and Analysis of Quantum Ballistic Transport in Nanodevices With AWE

Cited by 12 publications

References 16 publications

Wave-function description of conductance mapping for a quantum Hall electron interferometer

Wave-function description of conductance mapping for a quantum Hall electron interferometer

A Novel Efficient Numerical Solution of Poisson's Equation for Arbitrary Shapes in Two Dimensions

Methods for fast evaluation of self-energy matrices in tight-binding modeling of electron transport systems

Contact Info

Product

Resources

About