Efficient Solution of the Wigner–Poisson Equations for Modeling Resonant Tunneling Diodes

Costolanski, A. S.; Kelley, C. T.

doi:10.1109/tnano.2010.2053214

Cited by 11 publications

(8 citation statements)

References 29 publications

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“…Having determined the quantum mechanical input for the kinetic model, we are moving to the numerical solution of system (13)- (17). In recent years, several groups have been attempting to solve the Wigner-Poisson system directly (e.g., [50] and references therein). However, in most cases, such approaches have been using heuristic information for the quantum mechanical part.…”

Section: Resultsmentioning

confidence: 99%

Transport in semiconductor nanowire superlattices described by coupled quantum mechanical and kinetic models

Alvaro

Bonilla

Carretero

et al. 2013

J. Phys.: Condens. Matter

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In this paper we develop a kinetic model for the analysis of semiconductor superlattices, accounting for quantum effects. The model consists of a Boltzmann-Poisson type system of equations with simplified Bhatnagar-Gross-Krook collisions, obtained from the general time-dependent Schrödinger-Poisson model using Wigner functions. This system for superlattice transport is supplemented by the quantum mechanical part of the model based on the Ben-Daniel-Duke form of the Schrödinger equation for a cylindrical superlattice of finite radius. The resulting energy spectrum is used to characterize the Fermi-Dirac distribution that appears in the Bhatnagar-Gross-Krook collision, thereby coupling the quantum mechanical and kinetic parts of the model. The kinetic model uses the dispersion relation obtained by the generalized Kronig-Penney method, and allows us to estimate radii of quantum wire superlattices that have the same miniband widths as in experiments. It also allows us to determine more accurately the time-dependent characteristics of superlattices, in particular their current density. Results, for several experimentally grown superlattices, are discussed in the context of self-sustained coherent oscillations of the current density which are important in an increasing range of current and potential applications.

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Section: Resultsmentioning

confidence: 99%

Transport in semiconductor nanowire superlattices described by coupled quantum mechanical and kinetic models

Alvaro

Bonilla

Carretero

et al. 2013

J. Phys.: Condens. Matter

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“…The work in the current project [4][5][6] began by correcting some errors in the discretizations in the fortran codes. This led to a significant improvement in accuracy [5], which the PI improved further with a grid that was nonuniform in both space and momentum. Costolanski and the PI implemented these ideas in a matlab code.…”

Section: Resultsmentioning

confidence: 99%

“…Publications from the project include a book [16], seven journal papers [5,14,17,18,27,29,30] two Ph. D. theses [4,31], two articles in refereed proceedings [6,28], one submitted journal paper [35], and a Sandia technical report [7].…”

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confidence: 99%

Simulation of Devices with Molecular Potentials

Kelley¹

2013

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The objectives of this project were to (1) develop optimization methodology for generating the coordinate space trajectories of molecules that are undergoing conformational transformations as a result of light-induced excitations and subsequent relaxation processes and (2) develop the principal investigator's Wigner-Poisson code and extend that code to deal with longer devices and more complex barrier profiles. Over the course of the project we have produced a code for (1) using sparse interpolation and applied that code to several molecules. We have a new C++ code for (2) and have used that code for grid refinement, discretization, stability, and bifurcation studies.

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“…For example, considerable attention has been devoted to improving the numerical methods of solving the classical as well as the quantum kinetic equation. Efficient numerical schemes based on non-uniform meshes are developed for deterministic discretization method (Kim, 2007;Costolanski and Kelley, 2010;Kim and Kim, 2015;Schulz and Mahmood, 2016) or techniques based on the fast Fourier transform via the split-operator method. (Gómez et al, 2014;Spisak et al, 2015;Cabrera et al, 2015;Thomann and Borz, 2017).…”

Section: Introductionmentioning

confidence: 99%

The Effect of Elastic and Inelastic Scattering on Electronic Transport in Open Systems

Kulinowski

Wołoszyn

Radecka

et al. 2019

International Journal of Applied Mathematics and Computer Science

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The purpose of this study is to apply the distribution function formalism to the problem of electronic transport in open systems, and to numerically solve the kinetic equation with a dissipation term. This term is modeled within the relaxation time approximation and contains two parts, corresponding to elastic or inelastic processes. The collision operator is approximated as a sum of the semi-classical energy dissipation term and the momentum relaxation term, which randomizes the momentum but does not change the energy. As a result, the distribution of charge carriers changes due to the dissipation processes, which has a profound impact on the electronic transport through the simulated region discussed in terms of the current–voltage characteristics and their modification caused by the scattering. Measurements of the current–voltage characteristics for titanium dioxide thin layers are also presented, and compared with the results of numerical calculations.

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Efficient Solution of the Wigner–Poisson Equations for Modeling Resonant Tunneling Diodes

Cited by 11 publications

References 29 publications

Transport in semiconductor nanowire superlattices described by coupled quantum mechanical and kinetic models

Transport in semiconductor nanowire superlattices described by coupled quantum mechanical and kinetic models

Simulation of Devices with Molecular Potentials

The Effect of Elastic and Inelastic Scattering on Electronic Transport in Open Systems

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