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

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

Impact of self-heating on the statistical variability in bulk and SOI FinFETs

In this paper for the first time we study the impact of self-heating on the statistical variability of bulk and SOI FinFETs designed to meet the requirements of the 14/16nm technology node. The simulations are performed using the GSS ‘atomistic’ simulator GARAND using an enhanced electro-thermal model that takes into account the impact of the fin geometry on the thermal conductivity. In the simulations we have compared the statistical variability obtained from full-scale electro-thermal simulations with the variability at uniform room temperature and at the maximum or average temperatures obtained in the electro-thermal simulations. The combined effects of line edge roughness and metal gate granularity are taken into account. The distributions and the correlations between key figures of merit including the threshold voltage, on-current, subthreshold slope and leakage current are presented and analysed

One-Dimensional Multi-Subband Monte Carlo Simulation of Charge Transport in Si Nanowire Transistors

In this paper, we employ a newly-developed one-dimensional multi-subband Monte Carlo (1DMSMC) simulation module to study electron transport in nanowire structures. The 1DMSMC simulation module is integrated into the GSS TCAD simulator GARAND coupling a MC electron trajectory simulation with a 3D Poisson-2D Schrödinger solver, and accounting for the modified acoustic phonon, optical phonon, and surface roughness scattering mechanisms. We apply the simulator to investigate the effect of the overlap factor, scattering mechanisms, material and geometrical properties on the mobility in silicon nanowire field-effect transistors (NWTs). This paper emphasizes the importance of using 1D models that include correctly quantum confinement and allow for a reliable prediction of the performance of NWTs at the scaling limits. Our simulator is a valuable tool for providing optimal designs for ultra-scaled NWTs, in terms of performance and reliability

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

A Multi-Scale Simulation Study of the Strained Si Nanowire FETs

In this work, we study 2.1nm-diameter uniaxial strained Si gate-all-around nanowire field-effect transistors, focusing on the electron mobility and the variability due to random discrete dopants (RDDs). Firstly, we extract the electron effective masses under various strains from Density Functional Theory (DFT) simulations. Secondly, we present the impact of the strain on the electron mobility in the Si nanowire using the Kubo-Greenwood formalism with a set of multi-subband phonon, surface roughness, and ionized impurity scattering mechanisms. Finally, we perform quantum transport simulations to investigate the effect of RDD on the threshold voltage and ON-state current variation

Mobility of circular and elliptical si nanowire transistors using a multi-subband 1d formalism

We have studied the impact of the cross-sectional shape on the electron mobility of n-type silicon nanowire transistors (NWTs). We have considered circular and elliptical cross-section NWTs including the most relevant multisubband scattering processes involving phonon, surface roughness, and impurity scattering. For this purpose, we use a flexible simulation framework, coupling 3D Poisson and 2D Schrödinger solvers with the semi-classical Kubo-Greenwood formalism. Moreover, we consider cross-section dependent effective masses calculated from tight binding simulations. Our results show significant mobility improvement in the elliptic NWTs in comparison to the circular one for both 100 and 110 transport directions

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