Wigner transport in linear electromagnetic fields

Applying a Weyl-Stratonovich transform to the evolution equation of the Wigner function in an electromagnetic field yields a multidimensional gauge-invariant equation which is numerically very challenging to solve. In this work, we apply simplifying assumptions for linear electromagnetic fields and the evolution of an electron in a plane (two-dimensional transport), which reduces the complexity and enables to gain first experiences with a gauge-invariant Wigner equation. We present an equation analysis and show that a finite difference approach for solving the high-order derivatives allows for reformulation into a Fredholm integral equation. The resolvent expansion of the latter contains consecutive integrals, which is favorable for Monte Carlo solution approaches. To that end, we present two stochastic (Monte Carlo) algorithms that evaluate averages of generic physical quantities or directly the Wigner function. The algorithms give rise to a quantum particle model, which interprets quantum transport in heuristic terms

Performance Portability Study of Linear Algebra Kernels in OpenCL

The performance portability of OpenCL kernel implementations for common memory bandwidth limited linear algebra operations across different hardware generations of the same vendor as well as across vendors is studied. Certain combinations of kernel implementations and work sizes are found to exhibit good performance across compute kernels, hardware generations, and, to a lesser degree, vendors. As a consequence, it is demonstrated that the optimization of a single kernel is often sufficient to obtain good performance for a large class of more complicated operations.Comment: 11 pages, 8 figures, 2 tables, International Workshop on OpenCL 201

Non-Uniform Magnetic Fields for Single-Electron Control

Controlling single-electron states becomes increasingly important due to the wide-ranging advances in electron quantum optics. Single-electron control enables coherent manipulation of individual electrons and the ability to exploit the wave nature of electrons, which offers various opportunities for quantum information processing, sensing, and metrology. A unique opportunity offering new degrees of freedom for single-electron control is provided when considering non-uniform magnetic fields. Considering the modeling perspective, conventional electron quantum transport theories are commonly based on gauge-dependent electromagnetic potentials. A direct formulation in terms of intuitive electromagnetic fields is thus not possible. In an effort to rectify this, a gauge-invariant formulation of the Wigner equation for general electromagnetic fields has been proposed in [Nedjalkov et al., Phys. Rev. B., 2019, 99, 014423]. However, the complexity of this equation requires to derive a more convenient formulation for linear electromagnetic fields [Nedjalkov et al., Phys. Rev. A., 2022, 106, 052213]. This formulation directly includes the classical formulation of the Lorentz force and higher-order terms depending on the magnetic field gradient, that are negligible for small variations of the magnetic field. In this work, we generalize this equation in order to include a general, non-uniform electric field and a linear, non-uniform magnetic field. The thus obtained formulation has been applied to investigate the capabilities of a linear, non-uniform magnetic field to control single-electron states in terms of trajectory, interference patterns, and dispersion. This has led to explore a new type of transport inside electronic waveguides based on snake trajectories and also to explore the possibility to split wavepackets to realize edge states

Stochastic analysis of surface roughness models in quantum wires

We present a signed particle computational approach for the Wigner transport model and use it to analyze the electron state dynamics in quantum wires focusing on the effect of surface roughness. Usually surface roughness is considered as a scattering model, accounted for by the Fermi Golden Rule, which relies on approximations like statistical averaging and in the case of quantum wires incorporates quantum corrections based on the mode space approach. We provide a novel computational approach to enable physical analysis of these assumptions in terms of phase space and particles. Utilized is the signed particles model of Wigner evolution, which, besides providing a full quantum description of the electron dynamics, enables intuitive insights into the processes of tunneling, which govern the physical evolution. It is shown that the basic assumptions of the quantum-corrected scattering model correspond to the quantum behavior of the electron system. Of particular importance is the distribution of the density: Due to the quantum confinement, electrons are kept away from the walls, which is in contrast to the classical scattering model. Further quantum effects are retardation of the electron dynamics and quantum reflection. Far from equilibrium the assumption of homogeneous conditions along the wire breaks even in the case of ideal wire walls

Gerüste für Mikro- und Nanoelektronische Bauelemente-Simulation

Abweichender Titel laut Übersetzung der Verfasserin/des VerfassersZsfassung in dt. SpracheHerangehensweisen für Softwaregerüste, welche die zunehmend herausfordernden Aufgaben von Mikro- und Nanoelektronischer Bauelemente-Simulation bewältigen, werden untersucht. Im Besonderen fokussieren sich die entwickelten Herangehensweisen auf die Schlüsselanforderungen, die für heutige Forschungssimulationssoftware von höchster Bedeutung sind, wie Wiederverwendbarkeit, Flexibilität, Bedienbarkeit, Wartbarkeit und Erweiterbarkeit. Forschungssoftware erfährt neue Herausforderungen primär durch die schnell voranschreitenden Entwicklungen in physikalischer Modellierung. Simulationswerkzeuge sind typischerweise einen Schritt hinter der Entstehung von zukünftigen Bauelementen, im Sinne der Vorhersage der Eigenschaften von zukünftigen Bauelementen durch heutige Werkzeuge. Forschungsmodellierungssoftwareprojekte - insbesondere im Bereich der Mikro- und Nanoelektronischen Bauelemente-Simulation - versuchen diese Herausforderungen alleine zu bewältigen, demnach opfern sie wertvolle Ressourcen für die Entwicklung von nichtmodellierungsbezogenen Aspekten, was einen signifikanten Verlust von Synergieeffekten mit sich bringt. An den Universitäten werden primär hochspezialisierte Simulationswerkzeuge, basierend auf monolithischem Softwaredesign und in einer quelltext-geschlossenen Art, implementiert, um einen Vorteil gegenüber Konkurrenten zu haben. In dieser Arbeit werden Softwareentwicklungsaspekte bezüglich der Entwicklung von Gerüsten untersucht, insbesondere liegt der Fokus auf der Verbesserung der Verfügbarkeit von öffentlich zugänglichen Simulationswerkzeugen, relevant für das Gebiet der Mikro- und Nanoelektronischen Bauelemente-Simulation. Die Vorteile von frei verfügbaren Simulationsquelltexten und der Entkopplung von Implementierungen in wiederverwendbaren Bibliotheken werden ausgearbeitet. Die entwickelten Herangehensweisen ermöglichen die Umhüllung von bereits verfügbaren Funktionalitäten in wiederverwendbare Komponenten. Im Konkreten werden ein Bauelemente-Simulationsgerüst, ein Komponentenausführungsgerüst und ein Interaktivsimulationsgerüst untersucht. Während ein Bauelemente-Simulationsgerüst die Berechnung von Bauelemente-Characteristika ermöglicht, erlaubt ein Komponentenausführungsgerüst die Ausführung einer Menge von Komponenten auf hochgradig parallelen Berechnungszielen. Interaktiv-Simulationsgerüste stellen einen Hochbedienbarkeitszugang durch modulare grafische Benutzeroberflächen bereit. Herausforderungen und Anforderungen werden behandelt wie auch konkrete Herangehensweisen in der Form von entwickelten Softwarewerkzeugen, welche frei unter quelltext-offenen Lizenzen zugänglich sind. Anwendungsbeispiele unterstreichen die Machbarkeit der aufgezeigten Herangehensweisen. Die entwickelten Gerüste dienen als moderne und langfristige Simulationsplattformen, welche Wiederverwendbarkeit, Flexibilität, Bedienbarkeit, Wartbarkeit und Erweiterbarkeit fördern; all jene Aspekte sind im Speziellen in dem sich schnell entwickelnden Bereich der Mikro- und Nanoelektronischen Bauelemente-Simulation wichtig.Approaches for software frameworks, tackling the increasingly challenging tasks of micro- and nanoelectronics device simulations, are investigated. In particular, the developed approaches focus on the key requirements defined to be most important for today's research simulation software, those being reusability, flexibility, usability, maintainability, and expandability. Research software experiences new challenges primarily due to the fast pacing developments in physical modeling. Simulation tools are typically one step behind the evolution of future devices, in the sense that today's tools have to predict the properties of tomorrow's devices. Research modeling software projects - especially in the area of micro- and nanoelectronics device simulation - attempt to tackle these challenges on their own, thus sacrificing valuable resources for the development of non-modeling related aspects, which introduces a significant loss of synergy effects. In universities, primarily highly specialized simulation tools based on monolithic software design are implemented in a closed-source manner to uphold an advantage over competitors. In this work, software engineering aspects related to developing frameworks are investigated, particularly focusing to improve the availability of publicly accessible simulation tools relevant to the field of micro- and nanoelectronics device simulation. The advantages of freely accessible simulation source code as well as of decoupling implementations into reusable libraries are elaborated. The developed approaches enable to wrap already available functionality into reusable components. More concretely, a device simulation framework, a component execution frame work, and an interactive simulation framework is investigated. Where a device simulation framework allows to compute the device characteristics, a component execution framework enables to execute a set of components on highly parallel computing targets. Interactive simulation frameworks provide a high-usability access via modular graphical user interfaces. Challenges and requirements are highlighted as well as concrete approaches in form of developed software tools which are freely available under open source licenses. Application examples underline the feasibility of the depicted approaches. The developed frameworks serve as modern and long-term simulation platforms, favoring reusability, flexibility, usability, maintainability, and expandability; all of those aspects are particularly important in the fast developing area of micro- and nanoelectronics device simulation.12

Proceedings of the 24th High Performance Computing Symposium (HPC 2016)

International audienc

Investigating Quantum Coherence by Negative Excursions of the Wigner Quasi-Distribution

Quantum information and quantum communication are both strongly based on concepts of quantum superposition and entanglement. Entanglement allows distinct bodies, that share a common origin or that have interacted in the past, to continue to be described by the same wave function until evolution is coherent. So, there is an equivalence between coherence and entanglement. In this paper, we show the relation between quantum coherence and quantum interference and the negative parts of the Wigner quasi-distribution, using the Wigner signed-particle formulation. A simple physical problem consisting of electrons in a nanowire interacting with the potential of a repulsive dopant placed in the center of it creates a quasi two-slit electron system that separates the wave function into two entangled branches. The analysis of the Wigner quasi-distribution of this problem establishes that its negative part is principally concentrated in the region after the dopant between the two entangled branches, maintaining the coherence between them. Moreover, quantum interference is shown in this region both in the positive and in the negative part of the Wigner function and is produced by the superposition of Wigner functions evaluated at points of the momentum space that are symmetric with respect to the initial momentum of the injected electrons

Accelerating Flux Calculations Using Sparse Sampling

The ongoing miniaturization in electronics poses various challenges in the designing of modern devices and also in the development and optimization of the corresponding fabrication processes. Computer simulations offer a cost- and time-saving possibility to investigate and optimize these fabrication processes. However, modern device designs require complex three-dimensional shapes, which significantly increases the computational complexity. For instance, in high-resolution topography simulations of etching and deposition, the evaluation of the particle flux on the substrate surface has to be re-evaluated in each timestep. This re-evaluation dominates the overall runtime of a simulation. To overcome this bottleneck, we introduce a method to enhance the performance of the re-evaluation step by calculating the particle flux only on a subset of the surface elements. This subset is selected using an advanced multi-material iterative partitioning scheme, taking local flux differences as well as geometrical variations into account. We show the applicability of our approach using an etching simulation of a dielectric layer embedded in a multi-material stack. We obtain speedups ranging from 1.8 to 8.0, with surface deviations being below two grid cells (0.6⁻3% of the size of the etched feature) for all tested configurations, both underlining the feasibility of our approach