Showing papers on "Mean free path published in 2006"

Lifetimes and inelastic mean free path of low-energy excited electrons in Fe, Ni, Pt, and Au: Ab initio GW+T calculations

Abstract: We present the results of the GW+ T ab initio calculations for the inelastic lifetimes and mean free path IMFP of low-energy excited electrons in Fe, Ni, Pt, and Au. For Fe and Ni we show that the T-matrix terms, incorporating the Stoner’s excitations and spin-wave emission, contribute to the IMFP of the spin-minority electrons with excitation energy below 1.2 eV, whereas the GW term dominates at higher energy. We find that the spin dependence of IMFP in Ni is governed mainly by the spin dependence of lifetimes, but in Fe it relates mainly to the spin dependence of group velocities. We show that the “random k” model of the electron decay with fixed matrix element well agrees with the GW term of the lifetimes thus showing that the energy and spin dependence of the lifetimes are determined mainly by the convolutions of densities of states. For Au the inclusion of T-matrix terms with electron-hole scattering greatly reduces the calculated IMFP, bringing them into better agreement with experimental data.

Carbon nanotube thermal transport: Ballistic to diffusive

Abstract: We propose the expression l0∕(l0+L) for the energy transmission covering both ballistic and diffusive regimes, where l0 is mean free path and L is system length. With this formula, calculations of thermal conduction in carbon nanotubes (CNTs) show: (1) Thermal conductance at room temperature is proportional to the diameter for single-walled CNTs (SWCNTs) and to the square of diameter for multiwalled CNTs. (2) Interfaces play an important role in thermal conduction in CNTs due to their symmetry of vibrational modes. (3) For CNTs in ballistic-diffusive regime, thermal conductivity κ goes as Lα. The exponent α is found to decrease with increasing temperature and is insensitive to the diameter of SWCNTs for the Umklapp process, α≈0.8 for short SWCNTs at room temperature. These results are consistent with recent experimental findings.

Anisotropic optical properties of arrays of gold nanorods embedded in alumina

Abstract: A series of thin films comprising gold nanorods embedded in an alumina matrix have been fabricated with lengths ranging from 75 to $330\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. Their optical properties, expressed in terms of extinction $\ensuremath{-}\mathrm{ln}(T)$, where $T$ is optical transmittance, have been measured as a function of wavelength, rod length, angle of incidence, and incident polarization state. The results are compared to a Maxwell-Garnett based theory modified to take into account the strongly anisotropic nature of the medium. Transverse and longitudinal plasmon resonances are observed. The interaction between the nanorods leads to the splitting of the longitudinal resonance with the longer-wavelength resonance being forbidden for direct optical observations. The shorter-wavelength resonance related to the symmetric coupling between longitudinal plasma excitations in the nanorods depends on rod length, polarization state, and angle of incidence of the probing light. The impact of electron confinement on the optical properties of the gold rods is also seen and may be incorporated into the Maxwell-Garnett theory by restricting the mean free path of the conduction electrons to produce excellent agreement between observations and the complete theory. Annealing experiments that modify the physical structure of the gold confirm this conclusion.

Thermal conductivity of composites of aligned nanoscale and microscale wires and pores

Abstract: Two-dimensional composite materials made from aligned nano- and microwires hold great promise for various applications such as thermoelectric device. Similarly, two-dimensional composites made from aligned nanoscale pores are also very important for various technologies. Phonon transport along such composites primarily involves three nondimensional parameters based on the phonon mean paths in the host medium and the wire. The first of these is the ratio of interwire distance to the phonon mean free path in the host medium, the second is the ratio of the diameter of the wire to the phonon mean free path in the host medium, and the third is the ratio of the diameter of the wire to the phonon mean free path in the wire. We develop an analytical model for the thermal conductivity in the longitudinal direction of these composites by solving the phonon Boltzmann transport equation. The analytical model includes the dependences of all three parameters and is in excellent agreement with a recently reported numerical model [Yang et al., Phys. Rev. B 72, 125418 (2005)]. Our solution shows that the scattering of phonons in the host medium at the wire interface reduces the thermal conductivity of the host medium.

Influence of correlations between scatterers on the attenuation of the coherent wave in a random medium.

Abstract: Experimental measurements of the coherent wave transmission for ultrasonic waves propagating in water through a random set of scatterers (metallic rods) are presented. Though the densities are moderate (6% and 14%) the experimental results show that the mean-free path deviates from the classical first-order approximation due to the existence of correlations between scatterers. Theoretical results for the mean free path obtained from different approaches are compared to the experimental measurements. The best agreement is obtained with the second-order diagrammatic expansion of the self-energy.

In-Plane and Out-Of-Plane Thermal Conductivity of Silicon Thin Films Predicted by Molecular Dynamics

Abstract: The thermal conductivity of silicon thin films is predicted in the directions parallel and perpendicular to the film surfaces (in-plane and out-of-plane, respectively) using equilibrium molecular dynamics, the Green-Kubo relation, and the Stillinger-Weber interatomic potential. Three different boundary conditions are considered along the film surfaces: frozen atoms, surface potential, and free boundaries. Film thicknesses range from 2 to 217 nm and temperatures from 300 to 1000 K. The relation between the bulk pho.-non mean free path (A) and the film thickness (d s ) spans from the ballistic regime (A ≥ d s ) at 300 K to the diffusive, bulk-like regime (Λ «d s ) at 1000 K. When the film is thin enough, the in-plane and out-of-plane thermal conductivity differ from each other and decrease with decreasing film thickness, as a consequence of the scattering of phonons with the film boundaries. The in-plane thermal conductivity follows the trend observed experimentally at 300 K. In the ballistic limit, in accordance with the kinetic and phonon radiative transfer theories, the predicted out-of-plane thermal conductivity varies linearly with the film thickness, and is temperature-independent for temperatures near or above the Debye's temperature.

Thermal Conductivity of Carbon Aerogels as a Function of Pyrolysis Temperature

Abstract: Amorphous carbon samples with a total porosity of about 85% were synthesized via pyrolysis of sol–gel derived resin precursors. Since the pores in the samples investigated have dimensions of a few tens of nanometers only, the gaseous contribution to the thermal conductivity is largely suppressed at ambient pressure. Values for the total thermal conductivity as low as 0.054 W·m−1·K−1 at 300°C are detected. However, the pyrolysis temperature has a great impact on the contribution of the solid backbone to the total thermal conductivity. From the same precursor a series of samples was prepared via pyrolysis at temperatures ranging from 800 to 2500°C. The thermal conductivity of this series of carbons at 300°cC under vacuum increases by a factor of about 8 if the pyrolysis temperature is shifted from 800 to 2500°C. To elucidate the reason for this strong increase, the infrared radiative properties, the electrical conductivity, the macroscopic density, the microcrystallite size, the sound velocity, and the inner surface of the samples were determined. Evaluation of the experimental data yields only a negligible contribution from radiative heat transfer and electronic transport to the total thermal conductivity. The main part of the increasing thermal conductivity therefore has to be attributed to an increasing phonon mean free path in the carbons prepared at higher pyrolysis temperatures. However, the phonon mean free path does not match directly the in-plane microcrystallite size of the amorphous carbon. Rather, the in-plane microcrystallite size represents an upper limit for the phonon mean free path. Hence, the limiting factor for the heat transport via phonons has to be defects swithin the carbon microcrystallites which are partially cured at higher temperatures.

Dynamic correlations in stochastic rotation dynamics.

Abstract: The dynamic structure factor, vorticity and entropy density dynamic correlation functions are measured for stochastic rotation dynamics (SRD), a particle based algorithm for fluctuating fluids. This allows us to obtain unbiased values for the longitudinal transport coefficients such as thermal diffusivity and bulk viscosity. The results are in good agreement with earlier numerical and theoretical results, and it is shown for the first time that the bulk viscosity is indeed zero for this algorithm. In addition, corrections to the self-diffusion coefficient and shear viscosity arising from the breakdown of the molecular chaos approximation at small mean free paths are analyzed. In addition to deriving the form of the leading correlation corrections to these transport coefficients, the probabilities that two and three particles remain collision partners for consecutive time steps are derived analytically in the limit of small mean free path. The results of this paper verify that we have an excellent understanding of the SRD algorithm at the kinetic level and that analytic expressions for the transport coefficients derived elsewhere do indeed provide a very accurate description of the SRD fluid.

Chemical disorder strength in carbon nanotubes : Magnetic tuning of quantum transport regimes

Abstract: We report on a theoretical study of quantum transport in carbon nanotubes in the presence of chemical-disorder-induced quasibound states, with a quantitative analysis of the relationship between the energy-dependent elastic mean free path and localization length. An external magnetic field applied perpendicularly to the nanotube axis is shown to induce a floating up in energy of the quasibound states, which results in giant magnetoconductance fluctuations under a Fermi level shift.

A Microscopic Analysis of Shear Acceleration

Abstract: A microscopic analysis of the viscous energy gain of energetic particles in (gradual) nonrelativistic shear flows is presented. We extend previous work and derive the Fokker-Planck coefficients for the average rate of momentum change and dispersion in the general case of a momentum-dependent scattering time τ(p) ∝ pα with α ≥ 0. We show that in contrast to diffusive shock acceleration, the characteristic shear acceleration timescale depends inversely on the particle mean free path, which makes the mechanism particularly attractive for high-energy seed particles. Based on an analysis of the associated Fokker-Planck equation we show that above the injection momentum p0, power-law differential particle number density spectra n(p) ∝ p-(1+α) are generated for α > 0 if radiative energy losses are negligible. We discuss the modifications introduced by synchrotron losses and determine the contribution of the accelerated particles to the viscosity of the background flow. Possible implications for the plasma composition in mildly relativistic extragalactic jet sources are addressed.

Heat capacity and phonon mean free path of wurtzite GaN

Abstract: The authors report lattice specific heat of bulk hexagonal GaN measured by the heat flow method in the temperature range of 20–300K and by the adiabatic method in the range of 5–70K. The best fit with the accuracy of 3% was obtained for the temperature-independent Debye temperature ΘD=365K and Einstein temperature ΘE=880K. The authors relate these temperatures to the function of density of states. Using their results for heat conduction coefficient, they established in the temperature range of 10–100K the explicit dependence of the phonon mean free path on temperature lph∝T−2. Above 100K, there is an evidence of contribution of the Umklapp processes, which limits phonon free path at high temperatures.

Vibrationally induced two-level systems in single-molecule junctions.

Abstract: A single atom or molecule with an almost transparent single conductance channel leading to a conductance near the conductance quantum 2e 2 =h�� 1G0� can be contacted to leads. Conduction electrons can pass through such junction ballistically for low bias voltages since the mean free path of the electrons is much larger than the size of the contact. However, the contact is not entirely ballistic in the sense that once the excess energy of the conduction electrons becomes equal to or larger than the energy of a local mode of the contact, the electrons can scatter inelastically by exciting a local mode. This results in the case of a perfectly transmitting single channel contact to a small decrease in the conductance, since the forward traveling electrons are backscattered due to the energy loss in the inelastic scattering process. Differential conductance (dI=dV) measurements have identified vibration modes of single molecules in an atomic contact [1]. This technique, also called point contact spectroscopy is analogous to inelastic electron tunneling spectroscopy (IETS) for single molecules [2,3], with the difference that the conductance in the latter case increases due to the opening of an additional conductance channel. In this Letter we present the observation of anomalous spikes, rather than steps, in dI=dV measurements on various single-molecule contacts. We present a model that involves two-level systems, which describes our data very well. It may be used as a new spectroscopic tool for identifying molecular vibration modes in single-molecule junctions.

Effect of adiabatic cooling on the fitted parallel mean free path of solar energetic particles

Abstract: The focused transport equation without adiabatic energy loss is widely used to model solar energetic particles' (SEP) interplanetary propagation by fitting spacecraft data. We incorporate the adiabatic energy loss effect, provided by the divergence of the solar wind flows, into the focused transport equation. The equation is then solved numerically using a time-backward stochastic integration method. We show the comparison between solutions of focused transport equations with and without energy loss. We found the effect of adiabatic cooling is significant on the time profile of the intensity of SEPs. It is also shown that without energy loss, for gradual events, we can only fit the initial phase of SEP events. However, with energy loss, we can fit the entire ( initial and decaying) phases. In addition, the values of the mean free path obtained by fitting the SEP events with energy loss is always smaller than that without. The results suggest that including adiabatic cooling effect is another way to partially fix the solar energetic particle mean free paths' "too small'' problem discussed by Bieber et al. ( 1994), i.e., the mean free paths obtained by fitting transport equation to observation data are much larger than the quasi-linear theory results.

Nonlinear electrical properties of three-terminal junctions

Abstract: The authors report on room-temperature electrical measurements of three-terminal junctions made from a semiconductor heterostructure. The correlation between the junction size of the devices and the voltages needed to be applied in order to observe the electrical characteristics of three-terminal ballistic junctions is studied. The authors show that the ballistic behavior of electron transport can be observed in a three-terminal junction with a junction size of a few micrometers, much larger than the mean free path of electrons in the material. The results are explained in terms of a bias-induced enhancement of the electron mean free path in the system.

Electromagnetic field correlations near a surface with a nonlocal optical response

Abstract: The coherence length of the thermal electromagnetic field near a planar surface has a minimum value related to the nonlocal dielectric response of the material. We perform two model calculations of the electric energy density and the field’s degree of spatial coherence. Above a polar crystal, the lattice constant gives the minimum coherence length. It also gives the upper limit to the near field energy density, cutting off its 1/z3 divergence. Near an electron plasma described by the semiclassical Lindhard dielectric function, the corresponding length scale is fixed by plasma screening to the Thomas–Fermi length. The electron mean free path, however, sets a larger scale where significant deviations from the local description are visible.

Atomic oxygen recombination on quartz at high temperature: experiments and molecular dynamics simulation.

Abstract: A joint experimental and theoretical approach has been developed to study oxygen atom recombination on a β-quartz surface. The experimental MESOX setup has been applied for the direct measurement of the atomic oxygen recombination coefficient γ at TS = 1000 K. The time evolution of the relative atomic oxygen concentration in the cell is described by the diffusion equation because the mean free path of the atoms is less than the characteristic dimension of the reactor. The recombination coefficient γ is then calculated from the concentration profile obtained by visible spectroscopy. We get an experimental value of γ = 0.008, which is a factor of about 3 less than the γ value reported for O recombination over β-cristobalite. The experimental results are discussed and compared with the semiclassical collision dynamics calculations performed on the same catalytic system aimed at determining the basic features of the surface catalytic activity. Agreement, both qualitative and quantitative, between the experime...

Relativistic Solar Protons on 1989 October 22: Injection and Transport along Both Legs of a Closed Interplanetary Magnetic Loop

Abstract: Worldwide neutron monitor observations of relativistic solar protons on 1989 October 22 have proven puzzling, with an initial spike at some stations followed by a second peak, which is difficult to understand in terms of transport along a standard Archimedean spiral magnetic field or a second injection near the Sun. Here we analyze data from polar monitors, which measure the directional distribution of solar energetic particles (mainly protons) at rigidities of � 1‐3 GV. This event has the unusual properties that the particle density dips after the initial spike, followed by a hump with bidirectional flows and then a very slow decay. The spectral index, determined using bare neutron counters, varies dramatically, with energy dispersion features. The density and anisotropy data are simultaneously fit by simulating the particle transport for various magnetic field configurations and determining the best-fit injection functionneartheSun.ThedataarenotwellfitforanArchimedeanspiralfield,amagneticbottleneckbeyondEarth,or particle injection along one leg of a closed magnetic loop. A model with simultaneous injection along both legs of a closed loop provides a better explanation: particles moving along the near leg make up the spike, those coming from thefarlegmakeupthehump,bothlegscontributetothebidirectional streaming,andtrappingintheloopaccountsfor the slow decay of the particle density. Refined fits indicate a very low spectral index of turbulence, q < 1, a parallel mean free path of 1.2‐2.0 AU, a loop length of 4:7 � 0:3 AU, and escape of relativistic protons from the loop on a timescale of 3 hr. The weak scattering is consistent with reports of weak fluctuations in magnetic loops, while the low q-value may indicate a smaller correlation length as well.

Electron energy distribution functions in low-pressure inductively coupled bounded plasmas

Abstract: The electron energy distribution function (EEDF) in a low-pressure inductively coupled plasma confined between two infinite plates separated by 10cm is investigated using a one-dimensional particle-in-cell simulation including Monte Carlo collisions. At low pressure, where the electron mean free path is of the order of or greater than the system length, the EEDF is close to Maxwellian, except for its tail, depleted at high energy. We give clear evidence that this depletion is mostly due to the high-energy electrons escaping to the walls. As a result of the EEDF nonlocality, the break energy, for which the depletion of the Maxwellian starts, is found to track the plasma potential. At a higher pressure, the electron mean free paths of the various elastic and inelastic collisions become shorter than the system length, resulting in a loss of nonlocality and the break energy of the distribution function moves to energies lower than the plasma potential.

Photon diffusion coefficient in scattering and absorbing media

Abstract: We present a unified derivation of the photon diffusion coefficient for both steady-state and time-dependent transport in disordered absorbing media. The derivation is based on a modal analysis of the time-dependent radiative transfer equation. This approach confirms that the dynamic diffusion coefficient is given by the random-walk result D = cl(*)/3, where l(*) is the transport mean free path and c is the energy velocity, independent of the level of absorption. It also shows that the diffusion coefficient for steady-state transport, often used in biomedical optics, depends on absorption, in agreement with recent theoretical and experimental works. These two results resolve a recurrent controversy in light propagation and imaging in scattering media.

An investigation into the structural features and thermal conductivity of silicon nanoparticles using molecular dynamics simulations

Abstract: Th es tructural features and thermal conductivity of silicon nanoparticles of diameter 2–12 nm are studied in a series of molecular dynamics simulations based on the Stilling–Weber (SW) potential model. The results show that the cohesive energy of the particles increases monotonically with an increasing particle size and is independent of the temperature. It is found that particles with a diameter of 2 nm have a heavily reconstructed geometry which generates lattice imperfections. The thermal conductivity of the nanoscale silicon particles increases linearly with their diameter and is two orders of magnitude lower than that of bulk silicon. The low thermal conductivity of the smallest nanoparticles is thought to be the result of particle boundary and lattice imperfections produced during fabrication, which reduce the phonon mean free path (MFP). Finally, it is found that the influence of the temperature on the thermal conductivity decreases significantly as the temperature increases. Again, this is thought to be the result of a reduced phonon MFP at elevated temperatures. (Some figures in this article are in colour only in the electronic version)

The Ion-Matter Interaction with Swift Heavy Ions in the Light of Inelastic Thermal Spike Model

Abstract: A description of the inelastic thermal spike model is presented in order to correlate the energy deposited by swift heavy ions to the nanometric matter transformation induced in inorganic metallic and insulating materials. Knowing that insulator is more sensitive than metallic material and that amorphous material is in general more sensitive than a crystalline one, it appears evident that the electron–phonon coupling constant g plays a key role. It will be shown that in metallic material we are able to describe different phenomena with the same value of g: for example, track formation with defect annealing or sputtering of atoms. In insulators the emphasis is made on results obtained for amorphizable materials like SiO2 quartz and for non-amorphizable ionic crystals like CaF2. Assuming that tracks result from a transient thermal process, a quantitative development of the model is proposed using the electron–atom mean free path λ (inversely proportional to the square root of g) as a free parameter. With this parameter it is possible to quantitatively describe track radii in a wide range of ion velocities — whatever the bonding character of the crystal is — assuming specific criteria: tracks may result from a rapid quenching of a cylinder of matter in which the energy deposited on the lattice has overcome either the energy necessary to reach a quasi-molten phase in the case of amorphizable materials or the vaporization energy in the case of non-amorphizable materials. The evolution of the λ parameter of the considered insulator decreases versus the band gap energy. In this model, velocity effect, and a link between track formation and sputtering of atoms is established for amorphizable insulators while open questions appear for ionic crystals.

Parallel Diffusion of Charged Particles in Strong Two-dimensional Turbulence

Abstract: Computation of charged-particle orbits shows that large-amplitude two-dimensional magnetic turbulence supports diffusive transport of charged test particles parallel to the mean magnetic field. This stands in sharp contrast to scattering in the quasi-linear approximation, for which we show quite generally that the two-dimensional scattering rate vanishes. We also demonstrate that at large amplitude, two-dimensional turbulence makes important contributions to the parallel mean free path of particles in mixtures of two-dimensional and slab turbulence. This raises important questions regarding cosmic-ray mean free paths that had been thought to be settled based on quasi-linear theory.

Lattice Boltzmann Modeling of Subcontinuum Energy Transport in Crystalline and Amorphous Microelectronic Devices

Abstract: Numerical simulations of time-dependent energy transport in semiconductor thin films are performed using the lattice Boltzmann method applied to phonon transport. The discrete lattice Boltzmann method is derived from the continuous Boltzmann transport equation assuming first gray dispersion and then nonlinear, frequency-dependent phonon dispersion for acoustic and optical phonons. Results indicate that a transition from diffusive to ballistic energy transport is found as the characteristic length of the system becomes comparable to the phonon mean free path. The methodology is used in representative microelectronics applications covering both crystalline and amorphous materials including silicon thin films and nanoporous silica dielectrics. Size-dependent thermal conductivity values are also computed based on steady-state temperature distributions obtained from the numerical models. For each case, reducing feature size into the subcontinuum regime decreases the thermal conductivity when compared to bulk values. Overall, simulations that consider phonon dispersion yield results more consistent with experimental correlations.

Electrical conduction mechanisms in thermally evaporated tungsten trioxide(WO3) thin films

Abstract: Thin films of amorphous tungsten trioxide, a-WO3, have been thermally evaporated onto glass substrate held at 350K. Annealing at 723K caused the formation of polycrystalline tungsten trioxide, c-WO3, with a monoclinic structure. The dark DC electrical conductivity of both a-WO 3 and c-WO3 was studied over a temperature range from 298 to 625K in two environmental conditions (air and vacuum). A simple Arrhenius law, a polaron model and a variable range hopping model have been used to explain the conduction mechanism for a-WO3 films. Using the variable range hopping model, the density of localized states at the Fermi level, N(EF), was found to be 1.08 × 1019eV -1cm-3. The mechanism of electrical conduction in c-WO3 films is explained by means of the Seto model. The Seto model parameters were determined as the energy barrier (Eb ≤ 0.15eV), the energy of trapping states with respect to the Fermi level (Et ≤ 0.9eV) and the impurity concentration (ND ≤ 4.05 × 1015eV-1cm-3). The thickness dependence of resistivity of c-WO3 films has been found to decrease markedly with increasing film thickness, which is explained on the basis of the effective mean free path model. Using this model, the mean free path of electrons in c-WO 3 films was evaluated. The temperature dependence of the thermoelectric power for a-WO3 films reveals that our samples are n-type semiconductors.

Determination of mean free path for energy loss and surface oxide film thickness using convergent beam electron diffraction and thickness mapping: a case study using Si and P91 steel

Abstract: Determining transmission electron microscope specimen thickness is an essential prerequisite for carrying out quantitative microscopy. The convergent beam electron diffraction method is highly accurate but provides information only on the small region being probed and is only applicable to crystalline phases. Thickness mapping with an energy filter is rapid, maps an entire field of view and can be applied to both crystalline and amorphous phases. However, the thickness map is defined in terms of the mean free path for energy loss (lambda), which must be known in order to determine the thickness. Convergent beam electron diffraction and thickness mapping methods were used to determine lambda for two materials, Si and P91 steel. These represent best- and worst-case scenario materials, respectively, for this type of investigation, owing to their radically different microstructures. The effects of collection angle and the importance of dynamical diffraction contrast are also examined. By minimizing diffraction contrast effects in thickness maps, reasonably accurate (+/-15%) values of lambda were obtained for P91 and accuracies of +/-5% were obtained for Si. The correlation between the convergent beam electron diffraction-derived thickness and the log intensity ratios from thickness maps also permits estimation of the thickness of amorphous layers on the upper and lower surfaces of transmission electron microscope specimens. These estimates were evaluated for both Si and P91 using cross-sectional transmission electron microscopy and were found to be quite accurate.

Thermal conductivity of small nickel particles

Abstract: The thermal conductivity of nanoscale nickel particles due to phonon heat transfer is extrapolated from thin film results calculated using nonequilibrium molecular dynamics (NEMD). The electronic contribution to the thermal conductivity is deduced from the electrical conductivity using the Wiedemann–Franz law. Based on the relaxation time approximation, the electrical conductivity is calculated with the Kubo linear-response formalism. At the average temperature of T=300 K, which is lower than the Debye temperature ΘD=450 K, the results show that in a particle size range of 1.408–10.56 nm, the calculated thermal conductivity decreases almost linearly with decreasing particle size, exhibiting a remarkable reduction compared with the bulk value. The phonon mean free path is estimated, and the size effect on the thermal conductivity is attributed to the reduction of the phonon mean free path according to the kinetic theory.

Size-dependent resistivity of nanometric copper wires

Abstract: Higher electrical resistivity is observed in metals when dimensions approach the mean free path of the electrons. The effects of electron scattering at surfaces and at grain boundaries are then becoming substantial. This issue has been extensively studied on thin films but rarely on wires, where both small dimensions (width and height) influence the resistivity increase. In this study, copper wires having variable width and height down to $100\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ are investigated. An alternative approach is suggested in which the resistivity of such wires at different temperatures is compared to that of films having thickness that is equal to the height of the wires. The main outcome is a reliable model that overcomes the well-known difficulty of separating the contribution of surfaces to the resistivity from that of grain boundaries. It is shown that when both width and height of the wire are larger than one third of the mean free path, its resistivity exhibits a filmlike behavior with a separate contribution to the resistivity of each small dimension. The scattering of electrons at the surfaces of the investigated wires was best described by a zero specularity parameter, indicating the importance of this effect for the resistivity increase in small wires.

Deformation Potential Carrier-Phonon Scattering in Semiconducting Carbon Nanotube Transistors

Abstract: Theoretical calculations of carrier transport in single-walled carbon nanotubes are compared with recent experiments. Carrier-phonon scattering is accounted for using the deformation potential approximation. Comparing with experiments, a deformation potential coupling constant of 14eV is determined for semiconducting carbon nanotubes. Theory is shown to closely predict the low-field mobility, on conductance, and on resistance of field-effect transistors as a function of induced nanotube charge density, diameter, and temperature. Results indicate that the device conductance is reduced as multiple subband channels conduct due to strong intersubband scattering. Comparison with experiment allows identification of the mean free path (Lm) in semiconducting carbon nanotubes. As the device turns on, Lm is found to increase significantly. When the device is in the on state, the mean free path (Lm-ON) varies linearly with tube diameter and inversely with temperature. Intersubband scattering is found to strongly decrease Lm-ON when a few subbands are occupied. When 3 subband channels are considered at room temperature, Lm-ON decreases from 570nm to 200nm for a 4nm diameter tube when intersubband scattering is included. Since the subband spacing increases with decreasing tube diameter, the effects of intersubband are reduced for smaller diameters.