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Mean free path
About: Mean free path is a research topic. Over the lifetime, 4412 publications have been published within this topic receiving 114418 citations.
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TL;DR: In this paper, the structure of the electronic energy bands and Brillouin zones for graphite was developed using the "tight binding" approximation, and it was found that graphite is a semi-conductor with zero activation energy, but they are created at higher temperatures by excitation to a band contiguous to the highest one which is normally filled.
Abstract: The structure of the electronic energy bands and Brillouin zones for graphite is developed using the "tight binding" approximation. Graphite is found to be a semi-conductor with zero activation energy, i.e., there are no free electrons at zero temperature, but they are created at higher temperatures by excitation to a band contiguous to the highest one which is normally filled. The electrical conductivity is treated with assumptions about the mean free path. It is found to be about 100 times as great parallel to as across crystal planes. A large and anisotropic diamagnetic susceptibility is predicted for the conduction electrons; this is greatest for fields across the layers. The volume optical absorption is accounted for.
4,395 citations
TL;DR: It is shown that electron-acoustic phonon scattering is indeed independent of n, and contributes only 30 Omega to graphene's room-temperature resistivity, and its magnitude, temperature dependence and carrier-density dependence are consistent with extrinsic scattering by surface phonons at the SiO2 substrate.
Abstract: The linear dispersion relation in graphene gives rise to a surprising prediction: the resistivity due to isotropic scatterers, such as white-noise disorder or phonons, is independent of carrier density, n. Here we show that electron-acoustic phonon scattering is indeed independent of n, and contributes only 30 Omega to graphene's room-temperature resistivity. At a technologically relevant carrier density of 1 x1012 cm-2, we infer a mean free path for electron-acoustic phonon scattering of >2 microm and an intrinsic mobility limit of 2 x 105 cm2 V-1 s-1. If realized, this mobility would exceed that of InSb, the inorganic semiconductor with the highest known mobility ( approximately 7.7 x 104 cm2 V-1 s-1; ref. 9) and that of semiconducting carbon nanotubes ( approximately 1 x 105 cm2 V-1 s-1; ref. 10). A strongly temperature-dependent resistivity contribution is observed above approximately 200 K (ref. 8); its magnitude, temperature dependence and carrier-density dependence are consistent with extrinsic scattering by surface phonons at the SiO2 substrate and limit the room-temperature mobility to approximately 4 x 104 cm2 V-1 s-1, indicating the importance of substrate choice for graphene devices.
2,947 citations
TL;DR: The mean free path of electrons in metals has been studied in this paper, where the authors show that electrons follow a straight line along the path of the electron in the metal atom.
Abstract: (2001). The mean free path of electrons in metals. Advances in Physics: Vol. 50, No. 6, pp. 499-537.
2,273 citations
TL;DR: In this paper, a model of the thermal conductivity and phonon transport in the direction perpendicular to the film plane of superlattices is established based on solving the phonon Boltzmann transport equation (BTE).
Abstract: Significant reductions in both the in-plane and cross-plane thermal conductivities of superlattices, in comparison to the values calculated from the Fourier heat conduction theory using bulk material properties, have been observed experimentally in recent years. Understanding the mechanisms controlling the thermal conductivities of superlattice structures is of considerable current interest for microelectronic and thermoelectric applications. In this work, models of the thermal conductivity and phonon transport in the direction perpendicular to the film plane of superlattices are established based on solving the phonon Boltzmann transport equation (BTE). Different phonon interface scattering mechanisms are considered, including elastic vs inelastic, and diffuse vs specular scattering of phonons. Numerical solution of the BTE yields the effective temperature distribution, thermal conductivity, and thermal boundary resistance (TBR) of the superlattices. The modeling results show that the effective thermal conductivity of superlattices in the perpendicular direction is generally controlled by phonon transport within each layer and the TBR between different layers. The TBR is no longer an intrinsic property of the interface, but depends on the layer thickness as well as the phonon mean free path. In the thin layer limit, phonon transport within each layer is ballistic, and the TBR dominates the effective thermal conductivity of superlattices. Approximate analytical solutions of the BTE are obtained for this thin-film limit. The modeling results based on partially specular and partially diffuse interface scattering processes are in reasonable agreement with recent experimental data on GaAs/AlAs and Si/Ge superlattices. From the modeling, it is concluded that the cross-plane thermal conductivity of these superlattices is controlled by diffuse and inelastic scattering processes at interfaces. Results of this work suggest that it is possible to make superlattice structures with thermal conductivity totally different from those of their constituting materials.
1,032 citations
TL;DR: In this article, the authors derived the force exerted by the impinging molecules leaving the surface depending on how they leave, assuming the usual Maxwellian distribution of velocities in the gas, the force was found to be M where M=(4π/3) Nma2cmV, N, m, a, and V being the number per unit volume, mass, radius, and mean speed of the molecules and V the speed of a droplet.
Abstract: Kinetic theory of the resistance to a sphere moving through a gas.— (1) Droplets small in comparison with the mean free path. The high degree of accuracy achieved in the experimental determination of the law of motions of droplets through gases, makes a careful theoretical examination of the problem desirable. Assuming the usual Maxwellian distribution of velocities in the gas, the force exerted by the impinging molecules is found to be M where M=(4π/3) Nma2cmV, N, m, a, and cm being the number per unit volume, mass, radius, and mean speed of the molecules and V the speed of the droplet. The force exerted by the molecules leaving the surface depends on how they leave. (1) For uniform evaporation from the whole surface, the force is -M; (2) for specular reflection of all the impinging molecules, -M; (3) for diffuse reflection with unchanged distribution of velocities, -(13/9)M; (4) for diffuse reflection with the Maxwell distribution corresponding to the effective temperature of the part of the surface they come from, -(1+9π/64)M, for a non-conducting droplet (4a), and -(1+π/8)M, for a perfectly conducting droplet (4b). Cases (1) and (2) can not be distinguished experimentally, but (2) is more probable physically. The experimental values agree with 1/10 specular reflection, case (2), and 9/10 diffuse reflection, case (4a) or (4b). For large values of l/a, the droplet behaves like a perfect conductor, case (4b). (2) Comparatively large spheres. The distribution of velocities is no longer Maxwellian because of the hydrodynamic stresses which can not now be neglected. The new law is derived (Eq. 47). The conditions at the surface of the sphere are discussed and it is shown that the diffusely reflected molecules have a Maxwellian distribution corresponding to the temperature and density of the gas, just as though they were reflected with conservation of velocity (specularly). The assumptions of Bassett are theoretically justified and a complete confirmation is obtained for the correction factor for Stokes' law [1+0.7004 (2/s-1) (l/a)] on which Millikan's conclusions are based, especially as to the percentage of specular reflection. (3) Rotating spheres are also considered in an appendix, and the values of the resistance are derived for various cases.
912 citations