Self-consistent three-dimensional models for quantum ballistic transport in open systems

Polizzi, Eric; Abdallah, Naoufel Ben

doi:10.1103/physrevb.66.245301

Cited by 79 publications

(54 citation statements)

References 34 publications

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“…The growing interest of the scientific community towards quantum macroscopic models arises from the fact that they are computationally less expensive than microscopic models such as the Schrödinger or Wigner equation [3,4,9,30,32,33]. Simultaneously, collisions can be modeled without the use of quantum collision operators which are difficult to handle.…”

Section: Introductionmentioning

confidence: 99%

On quantum hydrodynamic and quantum energy transport models

Degond¹,

Gallego²,

Méhats³

2007

Communications in Mathematical Sciences

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Abstract. In this paper, we consider two recently derived models: the Quantum Hydrodynamic model (QHD) and the Quantum Energy Transport model (QET). We propose different equivalent formulations of these models and we use a commutator formula for stating new properties of the models. A gauge invariance lemma permits to simplify the QHD model for irrotational flows. We finish by considering the special case of a slowly varying temperature and we discuss possible approximations which will be helpful for future numerical discretizations.Key words. Density operator, quantum Liouville equation, quantum entropy, quantum local equilibrium, Quantum Hydrodynamics, Quantum Energy Transport, commutators, gauge invariance. subject classifications. 82C10, 82C70, 82D37, 81Q05, 81S05, 81S30, 81V70. IntroductionThis paper is the continuation of series of works investigating the properties and numerical approximations of quantum hydrodynamics and diffusion models based on the entropy principle. The growing interest of the scientific community towards quantum macroscopic models arises from the fact that they are computationally less expensive than microscopic models such as the Schrödinger or Wigner equation [3,4,9,30,32,33]. Simultaneously, collisions can be modeled without the use of quantum collision operators which are difficult to handle. The modeling of both quantum effects and collisions is particularly important for semiconductor devices where the active zone is small (sometimes less than 100 nanometers) and quantum effects are dominant while the access zones are constituted of electron reservoirs in which collisions are predominant and drive the system towards thermodynamic equilibrium. An example of such a device is the resonant tunneling diode [7] which constitutes a good candidate for testing models since it can be approximated by a one dimensional device.The route which has been usually followed for the derivation of quantum hydrodynamics and diffusion models consists in incorporating some "quantum" correction terms, often based on the Bohm potential, into classical fluid models. This Bohm potential appears naturally in the fluid formulation of the Schrödinger equation for a single particle evolving in an external potential V . One obtains this formulation through the use of the Madelung Transform, which consists in writing the wave function into an exponential form ψ = √ ne iS/ , where n is the density of mass, S is the phase and denotes the scaled Planck constant. Inserting this Ansatz in the Schrödinger equation, taking the real part and the gradient of the imaginary part, we recover the "Madelung equations" consisting in a pressureless Euler system involving an additional potential, called the Bohm potential

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Section: Introductionmentioning

confidence: 99%

On quantum hydrodynamic and quantum energy transport models

Degond¹,

Gallego²,

Méhats³

2007

Communications in Mathematical Sciences

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“…2 Our simulator includes a full three-dimensional ͑3D͒ treatment of electrostatics, and is based on real space nonequilibrium Green's function ͑NEGF͒ technique within the nearest neighbor -orbital approximation. 17,18 To model the vacancy, we set the on-site potential to 10 6 eV at the carbon vacancy site, which ensures that a channel electron is effectively repelled from the location of the vacancy. 19 We find that the vacancy creates a localized state in the band gap and a reduction of the transmission probability in both the conduction and valence bands.…”

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confidence: 99%

Influence of defects on nanotube transistor performance

Neophytou

Kienle

Polizzi

et al. 2006

Applied Physics Letters

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We study the effect of vacancies and charged impurities on the performance of carbon nanotube transistors by self-consistently solving the three-dimensional Poisson and Schrödinger equations. We find that a single vacancy or charged impurity can decrease the drive current by more than 25% from the ballistic current. The threshold voltage shift in the case of charged impurities can be as large as 40mV.

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“…The potential at the top nsensitive to the local electron charge, and is solely determined by the applied voltage biases found that C G < C Q when V GS > 0.28V so the QCL is not achieved at the the SiO 2 layer [7][8][9][10][11][12]. …”

Section: International Journal Of Advanced Engineering Research and Smentioning

confidence: 99%