Formulation of a phase space exponential operator for the Wigner transport equation accounting for the spatial variation of the effective mass

Schulz, Lukas

doi:10.1007/s10825-020-01551-0

Cited by 10 publications

(7 citation statements)

References 32 publications

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“…ρ denotes the statistical density, q represents the elementary charge, and B describes the static conduction band, as well as effects of the externally applied bias [13] comprised by the function V and is defined according to…”

Section: Fundamentalsmentioning

confidence: 99%

Efficiency Analysis of Discontinuous Galerkin Approaches for the Application Onto Quantum-Liouville Type Equations

Ganiu,

Schulz

2023

Preprint

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The simulation of nano devices is computationally inefficient with current algorithms. The discontinuous Galerkin approach has been demonstrated in the field of computational fluid dynamics to deliver high order accuracy and efficiency due to its reliance on matrix-vector multiplications. The discontinuous Galerkin approach was previously successfully used in conjunction with the Finite Volume technique to solve the Liouville-von Neumann equation in center-mass coordinates and thus simulate nano devices. To exploit its full potential regarding high performance computing, this work aims to substitute the aforementioned Finite Volume technique with the discontinuous Galerkin method. To arrive at the said formalism, a Finite Element method is implemented as an intermediate step.

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Section: Fundamentalsmentioning

confidence: 99%

Efficiency Analysis of Discontinuous Galerkin Approaches for the Application Onto Quantum-Liouville Type Equations

Ganiu,

Schulz

2023

Preprint

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“…Damodaran et al investigated a quantum well modulationdoped FET for use as a quantum dot memory device Reproduced from [355]. CC BY 4.0.…”

Section: Other Types Of Fets and Diodesmentioning

confidence: 99%

“…Schulz et al introduced a numerical approximation technique for the Wigner transport equation (including the spatial variation of the effective mass) and applied it to simulating a resonant tunneling diode with different material systems using a GaAs/Al x Ga 1−x As structure [355], see figure 20.…”

Section: Other Types Of Fets and Diodesmentioning

confidence: 99%

Computational perspective on recent advances in quantum electronics: from electron quantum optics to nanoelectronic devices and systems

Weinbub

Kosik

2022

J. Phys.: Condens. Matter

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Quantum electronics has significantly evolved over the last decades. Where initially the clear focus was on light-matter interactions, nowadays approaches based on the electron's wave nature have solidified themselves as additional focus areas. This development is largely driven by continuous advances in electron quantum optics, electron based quantum information processing, electronic materials, and nanoelectronic devices and systems. The pace of research in all of these areas is astonishing and is accompanied by substantial theoretical and experimental advancements. What is particularly exciting is the fact that the computational methods, together with broadly available large-scale computing resources, have matured to such a degree so as to be essential enabling technologies themselves. These methods allow to predict, analyze, and design not only individual physical processes but also entire devices and systems, which would otherwise be very challenging or sometimes even out of reach with conventional experimental capabilities. This review is thus a testament to the increasingly towering importance of computational methods for advancing the expanding field of quantum electronics. To that end, computational aspects of a representative selection of recent research in quantum electronics are highlighted where a major focus is on the electron's wave nature. By categorizing the research into concrete technological applications, researchers and engineers will be able to use this review as a source for inspiration regarding problem-specific computational methods.

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“…The drain-source bias is kept constant U DS = 1 V Fig. 13 Electron densities n(z, x, t) at different times scheme with respect to the -direction as described in [24] is adopted. THz oscillations of the current density are observed as previously described by [45][46][47].…”

Section: Resonant Algaas/gaas Tunneling Diodementioning

confidence: 99%

“…[14,[17][18][19][20][21][22]. In [23,24], the approach has been analyzed with regard to plane wave functions spanning the numerical basis, which become particular important when multiband transport has to be considered or the spatially varying effective mass has to be taken into account.…”

Section: Introductionmentioning

confidence: 99%

Subdomain-based exponential integrators for quantum Liouville-type equations

2021

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In order to describe quantum mechanical effects, the use of the von-Neumann equation is apparent. In this work, we present a unified numerical framework so that the von-Neumann equation in center-of-mass coordinates leads to a Quantum Liouville-type equation when choosing a suitable basis. In particular, the proposed approach can be related to the conventional Wigner equation when a plane wave basis is used. The drawback of the numerical methods is the high computational cost. Our presented approach is extended to allow reducing the dimension of the basis, which leads to a computationally efficient and accurate subdomain approach. Not only the steady-state behavior is of interest, but also the dynamic behavior. In order to solve the time-dependent case, suitable approximation methods for the time-dependent exponential integrator are necessary. For this purpose, we also investigate approximations of the exponential integrator based on Faber polynomials and Krylov methods. In order to evaluate and justify our approach, various test cases, including a resonant tunnel diode as well as a double-gate field-effect transistor, are investigated and validated for the stationary and the dynamic device behavior.

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Formulation of a phase space exponential operator for the Wigner transport equation accounting for the spatial variation of the effective mass

Cited by 10 publications

References 32 publications

Efficiency Analysis of Discontinuous Galerkin Approaches for the Application Onto Quantum-Liouville Type Equations

Efficiency Analysis of Discontinuous Galerkin Approaches for the Application Onto Quantum-Liouville Type Equations

Computational perspective on recent advances in quantum electronics: from electron quantum optics to nanoelectronic devices and systems

Subdomain-based exponential integrators for quantum Liouville-type equations

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