LANDAUER BUTTIKER FORMALISM PDF

In mesoscopic physics , ballistic conduction ballistic transport is the transport of charge carriers usually electrons in a medium, having negligible electrical resistivity caused by scattering. Without scattering, electrons simply obey Newton's second law of motion at non-relativistic speeds. For a given particle, a mean free path can be described as being the average length that the electron can travel freely, i. The mean free path can be increased by reducing the number of impurities in a crystal or by lowering its temperature. Ballistic transport is observed when the mean free path of the electron is much longer than the dimension of the medium through which the electron travels.

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In mesoscopic physics , ballistic conduction ballistic transport is the transport of charge carriers usually electrons in a medium, having negligible electrical resistivity caused by scattering. Without scattering, electrons simply obey Newton's second law of motion at non-relativistic speeds.

For a given particle, a mean free path can be described as being the average length that the electron can travel freely, i. The mean free path can be increased by reducing the number of impurities in a crystal or by lowering its temperature. Ballistic transport is observed when the mean free path of the electron is much longer than the dimension of the medium through which the electron travels.

The electron alters its motion only upon collision with the walls. This is because there is an energy to be paid to extract the electron from the medium work function. Ballistic conduction is the unimpeded flow of charge, or energy-carrying particles, over relatively long distances in a material.

Normally, transport of electrons or holes is dominated by scattering events, which relax the carrier momentum in an effort to bring the conducting material to equilibrium.

Thus, ballistic transport in a material is determined by how ballistically conductive that material is. Ballistic conduction differs from superconductivity due to the absence of the Meissner effect in the material. A ballistic conductor would stop conducting if the driving force is turned off, whereas in a superconductor current would continue to flow after the driving supply is disconnected. Ballistic conduction is typically observed in quasi-1D structures, such as carbon nanotubes or silicon nanowires , because of extreme size quantization effects in these materials.

Ballistic conduction is not limited to electrons or holes but can also apply to phonons. It is theoretically possible for ballistic conduction to be extended to other quasi-particles, but this has not been experimentally verified. In terms of scattering mechanisms, optical phonon emission normally dominates, depending on the material and transport conditions.

There are also other scattering mechanisms which apply to different carriers that are not considered here e. To get these characteristic scattering rates, one would need to derive a Hamiltonian and solve Fermi's golden rule for the system in question. In , Rolf Landauer proposed that conduction in a 1D system could be viewed as a transmission problem. For the 1D graphene nanoribbon field effect transistor GNR-FET on the right where the channel is assumed to be ballistic , the current from A to B, given by the Boltzmann transport equation , is.

The contacts have a multiplicity of modes due to their larger size in comparison to the channel. Conversely, the quantum confinement in the 1D GNR channel constricts the number of modes to carrier degeneracy and restrictions from the energy dispersion relationship and the Brillouin zone. For example, electrons in carbon nanotubes have two intervalley modes and two spin modes.

Since the contacts and the GNR channel are connected by leads, the transmission probability is smaller at contacts A and B ,. Therefore, even in the case of a perfect ballistic transport, there is a fundamental ballistic conductance which saturates the current of the device with a resistance of approximately Ballistic conduction enables use of quantum mechanical properties of electron wave functions.

Ballistic transport is coherent in wave mechanics terms. Phenomena like double-slit interference , spatial resonance and other optical or microwave -like effects could be exploited in electronic systems at nanoscale in systems including nanowires and nanotubes.

The widely encountered phenomenon of electrical contact resistance or ECR, arises as an electric current flowing through a rough interface is restricted to a limited number of contact spots.

The size and distribution of these contact spots is governed by the topological structures of the contacting surfaces forming the electrical contact. In particular, for surfaces with high fractal dimension contact spots may be very small. Electrical contacts resulting in ballistic electron conduction are known as Sharvin Contacts.

When the radius of a contact spot is larger than the mean free path of electrons, the contact resistance can be treated classically.

A comparison with light provides an analogy between ballistic and non-ballistic conduction. Ballistic electrons behave like light in a waveguide or a high-quality optical assembly.

Non-ballistic electrons behave like light diffused in milk or reflected off a white wall or a piece of paper. Electrons can be scattered several ways in a conductor. Electrons have several properties: wavelength energy , direction, phase, and spin orientation.

Different materials have different scattering probabilities which cause different incoherence rates stochasticity. Some kinds of scattering can only cause a change in electron direction, others can cause energy loss. Consider a coherent source of electrons connected to a conductor.

Over a limited distance, the electron wave function will remain coherent. You still can deterministically predict its behavior and use it for computation theoretically. But there is still almost no energy loss. Like monochromatic light passing through milk, electrons undergo elastic interactions.

Information about the state of the electrons at the input is then lost. Transport becomes statistical and stochastic. From the resistance point of view, stochastic not oriented movement of electrons is useless even if they carry the same energy — they move thermally. If the electrons undergo inelastic interactions too, they lose energy and the result is a second mechanism of resistance.

Electrons which undergo inelastic interaction are then similar to non-monochromatic light. As mentioned, nanostructures such as carbon nanotubes or graphene nanoribbons are often considered ballistic, but these devices only very closely resemble ballistic conduction. Their ballisticity is nearly 0. The dominant scattering mechanism at room temperature is that of electrons emitting optical phonons.

Such a transport regime has been found to depend on the nanoribbon edge structure and the electron energy. It is often incorrectly thought that Si nanowires are quantum confined ballistic conductors. There are major differences between carbon nanotubes which are hollow and Si nanowires which are solid. However it is still possible to observe ballistic conduction in Si nanowires at very low temperatures 2—3 K.

Isotopically pure diamond can have a significantly higher thermal conductivity. See List of thermal conductivities. Heat conduction can experience ballistic thermal transport when heating size is larger than phonon mean free paths. Ballistic thermal transport has been observed in multiple materials systems [8]. From Wikipedia, the free encyclopedia. Movement of charge carriers with negligible scattering.

This article may require cleanup to meet Wikipedia's quality standards. The specific problem is: article was merged and the lede needs to be reviewed for duplicate material Please help improve this article if you can. March Learn how and when to remove this template message. Main article: Landauer formula. JSAP International. Electronic Transport in Mesoscopic Systems.

New York: Cambridge University Press. Physical Review B. Bibcode : PhRvB.. Time-dependent resonant tunneling". Extreme Mechanics Letters. Applied Physics Letters. Bibcode : ApPhL.. Nature Nanotechnology.

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Coherent Electronic Transport: Landauer-Büttiker Formalism

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Ballistic conduction

Control of Magnetotransport in Quantum Billiards pp Cite as. After presenting the general framework, we focus on the linear response regime of transport. Skip to main content. This service is more advanced with JavaScript available. Advertisement Hide.

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