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

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

An event bias technique for Monte Carlo device simulation

Abstract In Monte Carlo (MC) simulations of semiconductor devices it is necessary to enhance the statistics in sparsely populated regions of interest. In this work the Monte Carlo method for stationary carrier transport, known as the Single-Particle MC method, is considered. It gives a solution to the stationary boundary value problem defined by the semi-classical Boltzmann equation (BE). Using a formal approach which employs the integral form of the problem and the Neumann series expansion of the solution, the Single-Particle MC method is derived in a formal way. The independent, identically distributed random variables of the simulated process are identified. Estimates of the stochastic error are given. Furthermore, the extension of the MC estimators to the case of biased events is derived. An event bias technique for particle transport across an energy barrier is developed and simulation results are discussed

Two-dimensional Transient Wigner Particle Model

Abstract-The Wigner equation represents a convenient approach when it comes to simulate the transient behavior of a wave packet at a nanoscale regime. It is a full quantum model that can include phonon scattering terms. A two-dimensional Monte Carlo technique has been recently implemented which is based on particles sign. In this paper we show that this is an efficient approach which works in realistic time-dependent and multi-dimensional situations

Two-dimensional Transient Wigner Particle Model

Abstract-The Wigner equation represents a convenient approach when it comes to simulate the transient behavior of a wave packet at a nanoscale regime. It is a full quantum model that can include phonon scattering terms. A two-dimensional Monte Carlo technique has been recently implemented which is based on particles sign. In this paper we show that this is an efficient approach which works in realistic time-dependent and multi-dimensional situations

Two-dimensional Transient Wigner Particle Model

Abstract-The Wigner equation represents a convenient approach when it comes to simulate the transient behavior of a wave packet at a nanoscale regime. It is a full quantum model that can include phonon scattering terms. A two-dimensional Monte Carlo technique has been recently implemented which is based on particles sign. In this paper we show that this is an efficient approach which works in realistic time-dependent and multi-dimensional situations

Change-of-state Paradigms and the middle in Kinyarwanda

This paper investigates the derivational relationships among members of verbal paradigms in Kinyarwanda (Bantu JD.61; Rwanda) by pursuing two interrelated goals. First, I describe a variety of derivational strategies for marking transitive and intransitive variants in change-of-state verb paradigms. Second, I focus on the detransitivizing morpheme –ik which serves as one possible marking for intransitive members of these paradigms. Ultimately, I argue that this morpheme is a marker of middle voice, and the variety of readings which appear with this form can be subsumed under a single operation of argument suppression. Finally, I provide a discussion of reflexives and the apparent lack of a reflexive reading with –ik by arguing that this reading is blocked by either lexical reflexives or the reflexive prefix i–

Femtosecond Relaxation of Hot Electrons by Phonon Emission in Presence of Electric Field

Abstract The femtosecond relaxation of an initial distribution of electrons which interact with phonons in presence of applied electric field is studied numerically. The evolution at such a time scale cannot be described in terms of Boltzmann transport. Here, the Barker-Ferry equation is utilized as a quantum-kinetic model of the process. The integral equation The Barker-Ferry (B-F) equatio