Wigner paths for electrons interacting with phonons

Pascoli, M.; Bordone, Paolo; Brunetti, Rossella; Jacoboni, Carlo

doi:10.1103/physrevb.58.3503

Cited by 40 publications

(30 citation statements)

References 15 publications

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“…Equation (4) manifests the nonlocal nature of the electronphonon interaction: the classical trajectories are generalized by Wigner paths [8]. The basic differences between (1) and the Boltzmann equation are introduced by the time integration on the right hand side and by the cosine function which replaces the energy conserving δ function.…”

Section: Kinetic Modelsmentioning

confidence: 99%

Ultrafast Wigner transport in quantum wires

et al. 2006

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Two quantum-kinetic models, governing the transport of an initial highly non-equilibrium carrier distribution generated locally in a nanowire, are explored. Dissipation processes due to phonons govern the carrier relaxation, which at early stages of the evolution is characterized by the lack of energy conservation in the collisions. The models are analyzed and approached numerically by a backward Monte Carlo method. The basic difference between them is in the way of treatment of the finite collision duration time. The latter introduces quantum effects of broadening and retardation, ultrafast spatial transfer and modification of the classical trajectories, which are demonstrated in the presented simulation results.

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Section: Kinetic Modelsmentioning

confidence: 99%

Ultrafast Wigner transport in quantum wires

et al. 2006

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“…30,61 It has been shown that a ballistic evolution of a ␦-like contribution to the Wigner function carries its value following a classical trajectory. 27 The action of the Wigner potential operator is interpreted as scattering, which, along with the scattering by the phonons, links pieces of classical trajectories to Wigner paths.…”

Section: B Particle Modelsmentioning

confidence: 99%

Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices

et al. 2004

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Small semiconductor devices can be separated into regions where the electron transport has classical character, neighboring with regions where the transport requires a quantum description. The classical transport picture is associated with Boltzmann-like particles that evolve in the phase-space defined by the wave vector and real space coordinates. The evolution consists of consecutive processes of drift over Newton trajectories and scattering by phonons. In the quantum regions, a convenient description of the transport is given by the Wigner-function formalism. The latter retains most of the basic classical notions, particularly, the concepts for phase-space and distribution function, which provide the physical averages. In this work we show that the analogy between classical and Wigner transport pictures can be even closer. A particle model is associated with the Wigner-quantum transport. Particles are associated with a sign and thus become positive and negative. The sign is the only property of the particles related to the quantum information. All other aspects of their behavior resemble Boltzmann-like particles. The sign is taken into account in the evaluation of the physical averages. The sign has a physical meaning because positive and negative particles that meet in the phase space annihilate one another. The Wigner and Boltzmann transport pictures are explained in a unified way by the processes drift, scattering, generation, and recombination of positive and negative particles. The model ensures a seamless transition between the classical and quantum regions. A stochastic method is derived and applied to simulation of resonant-tunneling diodes. Our analysis shows that the method is useful if the physical quantities do not vary over several orders of magnitude inside a device.

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“…For any given basis {ln)} in the space of the electron states the coefficients [7] fnn' (r, p) i dr'e -ip'r'/h (r + r'/2l,)(,,lrr'/2). (3) they constitute a unitary transformation and connect the generalized WF to the density matrix '} t) and viceversa.…”

Section: Transfer Coefficients Approachmentioning

confidence: 99%

“…After a formal integration with respect to time and a transformation back to the Schr6dinger picture, the following integral equation for the WF is obtained [3]: =fo) + f (4) where '-(He_/i). In Eq.…”

Section: P(n{nq}nt{nqmentioning

confidence: 99%

“…In this paper we discuss the concept of Wigner paths (WP's), recently introduced by the authors [3,4], which overcome the theoretical problems discussed above, and which can be used also when the coupling of the carrier with phonons and/or with an arbitrary potential profile is present. WP's are based on the linearity of the evolution equation for the WF and are independent of the quantum state of the system; each WP describes the evolution of a -like contribution to the WF, and contains "ballistic flights" and "scattering events" in strict analogy with carriers paths in semiclassical transport.…”

Section: Introductionmentioning

confidence: 99%

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Wigner Paths Method in Quantum Transportwith Dissipation

et al. 2001

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The concept of Wigner paths in phase space both provides a pictorial representation of the quantum evolution of the system of interest and constitutes a useful tool for numerical solutions of the quantum equation describing the time evolution of the system. A Wigner path is defined as the path followed by a “simulative particle” carrying a σ-contribution of the Wigner function through the Wigner phase-space, and is formed by ballistic free flights separated by scattering processes (both scattering with phonons and with an arbitrary potential profile can be included), as for the case of semiclassical particles. Thus, the integral transport equation can be solved by a Monte Carlo technique by means of simulative particles following classical trajectories, in complete analogy to the “Weighted Monte Carlo” solution of the Boltzmann equation in the integral form.

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Wigner paths for electrons interacting with phonons

Cited by 40 publications

References 15 publications

Ultrafast Wigner transport in quantum wires

Ultrafast Wigner transport in quantum wires

Unified particle approach to Wigner-Boltzmann transport in small semiconductor devices

Wigner Paths Method in Quantum Transportwith Dissipation

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