RTD relaxation oscillations and the time-dependent Wigner equation

Grubin, H. L.; Buggeln, R. C.

doi:10.1016/s0921-4526(01)01351-5

Cited by 3 publications

(4 citation statements)

References 5 publications

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“…This model should hold regardless of whether the structure has resonances or not, as it is constructed to mimic the source term in the single-particle density matrix 15,16,17,18,19,20 and Wigner function 2,3,21,22,23,24,25,26,27,28,29 formalisms, and preserve the continuity of current, state-by-state. In Sec.…”

Section: A Two-terminal Ballistic Nanostructurementioning

confidence: 99%

“…14 The purpose of this paper is to provide a simple description of the nonunitary evolution of a ballistic nanostructure's active region due to the injection of carriers from the contacts. Carrier injection from the contacts into the active region is traditionally described by either an explicit source term, such as in the single-particle density matrix, 15,16,17,18,19,20 Wigner function 2,3,21,22,23,24,25,26,27,28,29 and Pauli equation 30,31 transport formalisms, or via a special self-energy term in the ubiquitous nonequilibrium Green's function formalism. 32,33,34,35,36,37 In this work, the problem of contact-induced decoherence is treated using the open systems formalism: 38 we start with a model interaction Hamiltonian that describes the injection of carriers from the contacts, and then deduce the resulting nonunitary evolution of the active region's many-body reduced statistical operator in the Markovian approximation.…”

Section: Introductionmentioning

confidence: 99%

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Decoherence due to contacts in ballistic nanostructures

Knežević

2008

Phys. Rev. B

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The active region of a ballistic nanostructure is an open quantum-mechanical system, whose nonunitary evolution (decoherence) towards a nonequilibrium steady state is determined by carrier injection from the contacts. The purpose of this paper is to provide a simple theoretical description of the contact-induced decoherence in ballistic nanostructures, which is established within the framework of the open systems theory. The active region's evolution in the presence of contacts is generally non-Markovian. However, if the contacts' energy relaxation due to electron-electron scattering is sufficiently fast, then the contacts can be considered memoryless on timescales coarsened over their energy relaxation time, and the evolution of the current-limiting active region can be considered Markovian. Therefore, we first derive a general Markovian map in the presence of a memoryless environment, by coarse-graining the exact short-time non-Markovian dynamics of an abstract open system over the environment memory-loss time, and we give the requirements for the validity of this map. We then introduce a model contact-active region interaction that describes carrier injection from the contacts for a generic two-terminal ballistic nanostructure. Starting from this model interaction and using the Markovian dynamics derived by coarse-graining over the effective memory-loss time of the contacts, we derive the formulas for the nonequilibrium steady-state distribution functions of the forward and backward propagating states in the nanostructure's active region. On the example of a double-barrier tunneling structure, the present approach yields an I-V curve that shows all the prominent resonant features. We address the relationship between the present approach and the Landauer-Büttiker formalism, and also briefly discuss the inclusion of scattering.

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Section: A Two-terminal Ballistic Nanostructurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Decoherence due to contacts in ballistic nanostructures

Knežević

2008

Phys. Rev. B

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“…When dealing with transport in double barrier resonant tunneling diodes we have treated dissipation within the framework of the relaxation time approximation [3]. If we ignore dissipative coupling between the f Hz, k, 0L and f Hz, k, ZL spin Wigner functions, we deal with the following two coupled equations:…”

Section: The Time Dependent Spin Wigner Functionmentioning

confidence: 99%

“…We study quantum transport of barrier devices with DMS layers through implementation of the time dependent Wigner function [3]. The approach we use represents a generalization of earlier studies performed in transient Wigner function transport and involves the coupling of spin up and spin down electron and hole bands.…”

Section: Introductionmentioning

confidence: 99%

Wigner function studies of spin transport in dilute magnetic semiconductor barrier structures

Grubin

2004

SPIE Proceedings

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The spin dependent Wigner function is implemented to obtain the IV characteristics of a double barrier resonant tunneling diode with DMS layers. The structure distinguishes between spin-up and spin-down carriers, each of which experiences resonance at different magnetic field dependent bias levels. The results demonstrate the magnetic field dependence of the IV characteristics and illustrate the magnetic field dependence of relative spinup and spin-down carriers.

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Efficient Solution of the Wigner–Poisson Equations for Modeling Resonant Tunneling Diodes

Costolanski

Kelley

2010

IEEE Trans. Nanotechnology

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RTD relaxation oscillations and the time-dependent Wigner equation

Cited by 3 publications

References 5 publications

Decoherence due to contacts in ballistic nanostructures

Decoherence due to contacts in ballistic nanostructures

Wigner function studies of spin transport in dilute magnetic semiconductor barrier structures

Efficient Solution of the Wigner–Poisson Equations for Modeling Resonant Tunneling Diodes

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