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ABSTRACT We use the Wigner Monte Carlo approach.•We evolve a Gaussian wave packet in a previously calculated self-consistent electrostatic potential.•We decompose the potential into a classical and quantum part.•We compare the full Wigner... more
ABSTRACT We use the Wigner Monte Carlo approach.•We evolve a Gaussian wave packet in a previously calculated self-consistent electrostatic potential.•We decompose the potential into a classical and quantum part.•We compare the full Wigner Monte Carlo method and the potential decomposition technique to the benchmark solutions of the discretized Schrödinger equation.
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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... more
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.
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... e − ∫ t0 0 ν(xb(y))dyΓ(xb(t0),k1,kb(t0))e − ∫ t1 0 ν(x1(y))dyA(x1(t1),k1(t1)) Due to θD only that part of a Newton's trajectory which belongs to D contributes to 〈A〉1. The series (6) is the main entity of the stochastic... more
... e − ∫ t0 0 ν(xb(y))dyΓ(xb(t0),k1,kb(t0))e − ∫ t1 0 ν(x1(y))dyA(x1(t1),k1(t1)) Due to θD only that part of a Newton's trajectory which belongs to D contributes to 〈A〉1. The series (6) is the main entity of the stochastic approach. Following the MC theory, numerical trajectories are ...
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A theoretical analysis of the Monte Carlo (MC) method for both semiclassical and quantum device simulation is presented. A link between physically-based MC methods for semiclassical transport calculations and the numerical MC method for... more
A theoretical analysis of the Monte Carlo (MC) method for both semiclassical and quantum device simulation is presented. A link between physically-based MC methods for semiclassical transport calculations and the numerical MC method for solving integrals and integral equations is established. The integral representations of the transient and the stationary Boltzmann equations are presented as well as the respective conjugate equations. The structure of the terms of the Neumann series and their evaluation by MC integration is discussed. Using this formal approach the standard MC algorithms and a variety of new algorithms is derived, such as the backward and the weighted algorithms, and algorithms for linear small-signal analysis. Applying this theoretical framework to the Wigner-Boltzmann equation enables the development of particle models for quantum transport problems.
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Research Interests: Distributed Computing, Computational Complexity, Kinetics, Modeling, Integer quantum hall effect, and 13 moreTrajectory, Variance, Grid, Parallel Algorithm, Gaussian distribution, Three Dimensional, Initial Condition, Electric Field, Spatial Dependence, Monte Carlo Method, Variance Reduction Techniques, Kinetic Equation, and Electron-phonon interaction
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... of the truncated Wigner potential [7], V + w (k) = Max(0,Vw(k)), which is positive definite and thus amenable to a probabilistic inter-pretation. Expressing the Liouville operator in (1) as a total time derivative and writing the... more
... of the truncated Wigner potential [7], V + w (k) = Max(0,Vw(k)), which is positive definite and thus amenable to a probabilistic inter-pretation. Expressing the Liouville operator in (1) as a total time derivative and writing the operators on the right hand side explicitly gives [dfw ...
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ABSTRACT A thermal simulation module, based on the solution of the coupled Heat Flow, Poisson, and Current Continuity Equations, has been developed and implemented in the ‘atomistic’ simulator GARAND to investigate the impact of self... more
ABSTRACT A thermal simulation module, based on the solution of the coupled Heat Flow, Poisson, and Current Continuity Equations, has been developed and implemented in the ‘atomistic’ simulator GARAND to investigate the impact of self heating on FinFET DC operation. A progressive study of coupled electro-thermal simulation for FinFETs is presented. A new approximate formula for the reduced thermal conductivity due to phonon-boundary scattering in the fin is presented which considers both the fin height and the fin width, and is both position and temperature dependent. Simulation results for a SOI FinFET and a bulk FinFET example are compared and analysed.
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ABSTRACT A Monte Carlo analysis of the evolution of an electron interacting with phonons is presented in terms of a Wigner function. The initial electron state is constructed by a superposition of two wave packets and a pronounced... more
ABSTRACT A Monte Carlo analysis of the evolution of an electron interacting with phonons is presented in terms of a Wigner function. The initial electron state is constructed by a superposition of two wave packets and a pronounced interference term. The results show that phonons effectively destroy the interference term. The initial coherence in wave vector distribution is pushed towards the equilibrium distribution. Phonons hinder the natural spread of the density with time and advance it towards a classical localization. The decoherence effect due to phonons, which brings about the transition from a quantum to a classical state, is demonstrated by the purity of the state, which decreases from its initial value of 1, with a rate depending on the lattice temperature.