A Stochastic Approach for Investigation Ultrafast Phenomena in Semiconductors

2002 Mathematics Subject Classification: 65C05In this paper a stochastic approach is proposed for investigation the ultrafast evolution of electrons interacting with phonons in the presence of an applied electric field. The quantum-kinetic equation describing the above ultrafast phenomena contains polynomial non-linearity which allows to use the link between non-stationary iterative processes and the branching stochastic processes. The considered stochastic approach relies on the numerical Monte Carlo (MC) theory as applied to the integral form of the quantum-kinetic equation and estimates the electron energy distribution using statistical averages over long evolution times. The numerical tests were performed for GaAs material parameters. The numerical results for the electron energy distribution function in the case of a non-linear electron quantum transport is compared with the obtained results in the linear case.Supported by Center of Excellence BIS-21 grant ICA1-2000-70016 and by the NSF of Bulgaria under Grants # I 811/98 and # MM 902/99

Studien zur Lokalisation: Teil: 2.: Verbgebundene Lokalisation vs. Lokalisation von Propositionen

Der vorliegende Aufsatz gliedert sich in zwei Unterabschnitte. In Abschnitt I geht es um verbgebundene, von der Valenz geforderte Lokalisation. Die einzelsprachlichen Beispiele zeigen, daß es sich konstant um Verben der Position oder Positionsveränderung (Bewegungs - und Transferverben) handelt, die lokale Relationen wie LOK (Ortsruhe), SOURCE oder GOAL fordern. Unter Bezugnahme auf die Erkenntnisse zur Dimension der PARTIZIPATION (H. Seiler/W. Premper 1991) können die Varianten, wie sie in der einzelsprachlichen Kodierung zu beobachten sind, zwischen den Polen zentralisiert und dezentralisiert (peripher) angeordnet werden . Dies bedeutet, daß lokale Relationen (als verbgebundene Entitäten) einerseits am Partizipatum selbst und andererseits im Bereich der Partizipanten in Gestalt verschiedener grammatischer Relationen in Erscheinung treten können. Im ersteren Fall kann die Inkorporation einer lokalen Ergänzung ins Partizipatum als optimal zentralisiert betrachtet werden, während eine Kodierung als Präpositionalphrase das andere Extrem darstellt. Dazwischen liegt eine Kodierung als "Subjekt"- bzw. "Objekt"-Relation, für die sich, wie auch für die anderen Fälle, eine Reihe von Beispielen finden lassen. Somit schwankt die Skala der Kodierungsmöglichkeiten für verbgebundene lokale Relationen zwischen Inkorporation und Präpositional-/Postpositionalphrasen, was letztlich eine Differenzierung in markierte und unmarkierte, im letzteren Falle gar prototypische Instanzen bedeutet. Im II . Abschnitt geht es darum, so weit dies möglich erscheint, Varianten zu beschreiben, die funktional die Aufgabe einer Situierung einer Gesamtproposition bewerkstelligen

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

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

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

Number-Phase Wigner Representation for Efficient Stochastic Simulations

Phase-space representations based on coherent states (P, Q, Wigner) have been successful in the creation of stochastic differential equations (SDEs) for the efficient stochastic simulation of high dimensional quantum systems. However many problems using these techniques remain intractable over long integrations times. We present a number-phase Wigner representation that can be unraveled into SDEs. We demonstrate convergence to the correct solution for an anharmonic oscillator with small dampening for significantly longer than other phase space representations. This process requires an effective sampling of a non-classical probability distribution. We describe and demonstrate a method of achieving this sampling using stochastic weights.Comment: 7 pages, 1 figur

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

Manufacturing and characterization of femtosecond laser-inscribed Bragg grating in polymer waveguide operation in an IR-A wavelength range

Optical sensors, such as fiber Bragg gratings, offer advantages compared to other sensors in many technological fields due to their outstanding characteristics. This sensor technology is currently transferred to polymer waveguides that provide the potential for cost-effective, easy, and flexible manufacturing of planar structures. While sensor production itself, in the majority of cases, is performed by means of phase mask technique, which is limited in terms of its degrees of freedom, other inscription techniques enable the manufacture of more adaptable sensor elements for a wider range of applications. In this article, we demonstrate the point-by-point femtosecond laser direct inscription method for the processing of polymer Bragg gratings into waveguides of the epoxy-based negative photoresist material EpoCore for a wavelength range around 850 nm. By characterizing the obtained grating back-reflection of the produced sensing element, we determined the sensitivity for the state variables temperature, humidity, and strain to be 45 pm/K, 19 pm/%, and 0.26 pm/με, respectively. Individual and more complex grating structures can be developed from this information, thus opening new fields of utilization