A computational approach for investigating Coulomb interaction using Wigner-Poisson coupling.

Entangled quantum particles, in which operating on one particle instantaneously influences the state of the entangled particle, are attractive options for carrying quantum information at the nanoscale. However, fully-describing entanglement in traditional time-dependent quantum transport simulation approaches requires significant computational effort, bordering on being prohibitive. Considering electrons, one approach to analyzing their entanglement is through modeling the Coulomb interaction via the Wigner formalism. In this work, we reduce the computational complexity of the time evolution of two interacting electrons by resorting to reasonable approximations. In particular, we replace the Wigner potential of the electron-electron interaction by a local electrostatic field, which is introduced through the spectral decomposition of the potential. It is demonstrated that for some particular configurations of an electron-electron system, the introduced approximations are feasible. Purity, identified as the maximal coherence for a quantum state, is also analyzed and its corresponding analysis demonstrates that the entanglement due to the Coulomb interaction is well accounted for by the introduced local approximation.

Complex Systems in Phase Space.

The continued reduction of semiconductor device feature sizes towards the single-digit nanometer regime involves a variety of quantum effects. Modeling quantum effects in phase space in terms of the Wigner transport equation has evolved to be a very effective approach to describe such scaled down complex systems, accounting from full quantum processes to dissipation dominated transport regimes including transients. Here, we discuss the challanges, myths, and opportunities that arise in the study of these complex systems, and particularly the advantages of using phase space notions. The development of particle-based techniques for solving the transport equation and obtaining the Wigner function has led to efficient simulation approaches that couple well to the corresponding classical dynamics. One particular advantage is the ability to clearly illuminate the entanglement that can arise in the quantum system, thus allowing the direct observation of many quantum phenomena.

ReaxFF Reactive Molecular Dynamics Study of Orientation Dependence of Initial Silicon Carbide Oxidation.

We analyze the early stage of the highly anisotropic silicon carbide oxidation behavior with reactive force field molecular dynamics simulations. The oxidation of a-, C,- m-, and Si-crystallographic faces is studied at typical industry-focused temperatures in the range from 900 to 1200 °C based on the time evolution of the oxidation mechanism. The oxide thicknesses and the growth rates are obtained from these simulation results. In addition, an investigation of the silicon and carbon emission is performed with respect to various orientations in order to support further development of macroscopic physical models that aim to predict initial silicon carbide oxidation.

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. Here we explore non-uniform magnetic fields, which offer unique mechanisms for single-electron control. 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 [M. Nedjalkov et al., Phys. Rev. B, 2019, 99, 014423]. However, the complexity of this equation requires the derivation of a more convenient formulation for linear electromagnetic fields [M. 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 the exploration of a new type of transport inside electronic waveguides based on snake trajectories and the possibility of splitting wavepackets to realize edge states.

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

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.

Gate-controlled electron quantum interference logic.

Inspired by using the wave nature of electrons for electron quantum optics, we propose a new type of electron quantum interference structure, where single-electron waves are coherently injected into a gate-controlled, two-dimensional waveguide and exit through one or more output channels. The gate-controlled interference effects lead to specific current levels in the output channels, which can be used to realize logic gate operations, e.g., NAND or NOR gates. The operating principle is shown by coherent, dynamic Wigner quantum electron transport simulations. A discussion of classical simulations (Boltzmann) allows to outline the underlying process of interference. Contrary to other electron control approaches used for advanced information processing, no magnetic or photonic mechanisms are involved.

Electron evolution around a repulsive dopant in a quantum wire: coherence effects.

We present an analysis of the quantum processes involved in the electron evolution around a repulsive dopant in a quantum wire. The quantum electron behavior has been studied by using a Wigner function approach. The Wigner phase space description allows the treatment of both classical and quantum evolution in the same framework, enabling ease of highlighting the effects of coherence. While the former is governed by a force, which is the first derivative of the dopant potential, the latter accounts for the entire potential, namely all derivatives in the corresponding Taylor expansion take part in the interaction. This gives rise to processes of tunneling and non-locality of the action of the potential. The complicated interplay of these quantum effects with the boundary conditions associated with the wire affects the physical observables like electron and current densities and in particular can give rise to an increase of the total current.

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.