Showing papers on "Mean free path published in 2001"

Phonon heat conduction in a semiconductor nanowire

Abstract: A model for phonon heat conduction in a semiconductor nanowire with dimensions comparable to the phonon mean free path is developed. It is based on the solution of Boltzmann’s equation, which takes into account (i) modification of the acoustic phonon dispersion due to spatial confinement, and (ii) change in the nonequilibrium phonon distribution due to partially diffuse boundary scattering. Numerical simulation is performed for a silicon nanowire with boundaries characterized by different interface roughness. Phonon confinement and boundary scattering lead to a significant decrease of the lattice thermal conductivity. The value of this decrease and its interface roughness and temperature dependence are different from the predictions of the early models. The observed change in thermal resistance has to be taken into account in simulation of deep-submicron and nanometer-scale devices.

Ballistic-Diffusive Heat-Conduction Equations

Abstract: We present new heat-conduction equations, named ballistic-diffusive equations, which are derived from the Boltzmann equation. We show that the new equations are a better approximation than the Fourier law and the Cattaneo equation for heat conduction at the scales when the device characteristic length, such as film thickness, is comparable to the heat-carrier mean free path and/or the characteristic time, such as laser-pulse width, is comparable to the heat-carrier relaxation time.

Compressible Magnetohydrodynamic Turbulence in Interstellar Plasmas

Abstract: Radio wave scintillation observations reveal a nearly Kolmogorov spectrum of density fluctuations in the ionized interstellar medium. Although this density spectrum is suggestive of turbulence, no theory relevant to its interpretation exists. We calculate the density spectrum in turbulent magnetized plasmas by extending the theory of incompressible magnetohydrodynamic (MHD) turbulence given by Goldreich & Sridhar to include the effects of compressibility and particle transport. Our most important results are as follows: 1. Density fluctuations are due to the slow mode and the entropy mode. Both modes are passively mixed by the cascade of shear Alfven waves. Since the shear Alfven waves have a Kolmogorov spectrum, so do the density fluctuations. 2. Observed density fluctuation amplitudes constrain the nature of MHD turbulence in the interstellar medium. Slow mode density fluctuations are suppressed when the magnetic pressure is less than the gas pressure. Entropy mode density fluctuations are suppressed by cooling when the cascade timescale is longer than the cooling timescale. These constraints imply either that the magnetic and gas pressures are comparable or that the outer scale of the turbulence is very small. 3. A high degree of ionization is required for the cascade to survive damping by neutrals and thereby to extend to small length scales. Regions that are insufficiently ionized produce density fluctuations only on length scales larger than the neutral damping scale. These regions may account for the excess of power that is found on large scales. 4. Provided that the thermal pressure exceeds the magnetic pressure, both the entropy mode and the slow mode are damped on length scales below that at which protons can diffuse across an eddy during the eddy's turnover time. Consequently, eddies whose extents along the magnetic field are smaller than the proton collisional mean free path do not contribute to the density spectrum. However, in MHD turbulence eddies are highly elongated along the magnetic field. From an observational perspective, the relevant length scale is that transverse to the magnetic field. Thus, the cutoff length scale for density fluctuations is significantly smaller than the proton mean free path. 5. The Alfven mode is critically damped at the transverse length scale of the proton gyroradius and thus cascades to smaller length scales than either the slow mode or the entropy mode.

Compressible MHD Turbulence in Interstellar Plasmas

Abstract: Radio-wave scintillation observations reveal a nearly Kolmogorov spectrum of density fluctuations in the ionized interstellar medium. Although this density spectrum is suggestive of turbulence, no theory relevant to its interpretation exists. We calculate the density spectrum in turbulent magnetized plasmas by extending the theory of incompressible MHD turbulence given by Goldreich & Sridhar to include the effects of compressibility and particle transport. Our most important results are as follows. (1) Density fluctuations are due to the slow mode and the entropy mode. Both modes are passively mixed by the cascade of shear Alfven waves. Since the shear Alfven waves have a Kolmogorov spectrum, so do the density fluctuations. (2) Observed density fluctuation amplitudes imply either that the magnetic and gas pressures are comparable, or that the outer scale of the turbulence is very small. (3) A high degree of ionization is required for the cascade to survive damping by neutrals and thereby to extend to small lengthscales. Regions that are insufficiently ionized produce density fluctuations only on lengthscales larger than the neutral damping scale. These regions may account for the excess of power that is found on large scales. (4) Both the entropy mode and the slow mode are damped on lengthscales below that at which protons can diffuse across an eddy during the eddy's turnover time. Consequently, eddies whose extents along the magnetic field are smaller than the proton collisional mean free path do not contribute to the density spectrum. However, in MHD turbulence eddies are highly elongated along the magnetic field. From an observational perspective, the relevant lengthscale is that transverse to the magnetic field. Thus the cut-off lengthscale for density fluctuations is significantly smaller than the proton mean free path.

On fluid/wall slippage

Abstract: Certain (non polymeric) fluids show an anomalously low friction when flowing against well chosen solid walls. We discuss here one possible explanation, postulating that a gaseous film of small thickness h is present between fluid and wall. When h is smaller than the mean free path l of the gas (Knudsen regime) the Navier length b is expected to be independent of h and very large (microns).

Theory of thermal conduction in thin ceramic films

Abstract: The theory of heat conduction in ceramics by phonons, and at high temperatures also by infrared radiation, is reviewed. The phonon mean free path is limited by three-phonon interactions and by scattering of various imperfections. Point defects scatter high-frequency phonons; extended imperfections, such as inclusions, pores, and grain boundaries, affect mainly low-frequency phonons. Thermal radiation is also scattered by imperfections, but of a larger size, such as splat boundaries and large pores. Porosity also reduces the effective index of refraction. For films there are also external boundaries, cracks, and splat boundaries, depending on the method of deposition. Examples discussed are cubic zirconia, titanium oxide, and uranium oxide. Graphite and graphene sheets, with two-dimensional phonon gas, are discussed briefly.

Sub-Continuum Simulations of Heat Conduction in Silicon-on-Insulator Transistors

Abstract: The temperature rise in sub-micrometer silicon devices is predicted at present by solving the heat diffusion equation based on the Fourier law. The accuracy of this approach needs to be carefully examined for semiconductor devices in which the channel length is comparable with or smaller than the phonon mean free path. The phonon mean free path in silicon at room temperature is near 300 nm and exceeds the channel length of contemporary transistors. This work numerically integrates the two-dimensional phonon Boltzmann transport equation (BTE) within the silicon region of a silicon-on-insulator (SOI) transistor. The BTE is solved together with the classical heat diffusion equation in the silicon dioxide layer beneath the transistor. The predicted peak temperature rise is nearly 160 percent larger than a prediction using the heat diffusion equation for the entire domain. The disparity results both from phonon-boundary scattering and from the small dimensions of the region of strongest electron-phonon energy transfer. This work clearly shows the importance of sub-continuum heat conduction in modern transistors and will facilitate the development of simpler calculation strategies, which are appropriate for commercial device simulators.

Scattering optics of foam

Abstract: The multiple scattering of light by aqueous foams is systematically studied as a function of wavelength, bubble size, and liquid fraction. Results are analyzed in terms of the transport mean free path of the photons and an extrapolation length ratio for the diffuse photon concentration field. The wavelength dependence is minimal and may be attributed entirely to the wavelength dependence of the refractive index of water rather than thin-film interference effects. The transport mean free path is found to be proportional to the bubble diameter and the reciprocal of the square root of liquid fraction. The extrapolation length ratio varies almost linearly with liquid fraction between the values for water-glass-air and air-glass-air interfaces.

Spin valve sensor having a nonmagnetic enhancement layer adjacent an ultra thin free layer

Abstract: A spin valve device includes a non-magnetic enhancement layer adjacent an ultra thin free layer The thickness of the free layer may be less than the mean free path of a conduction electron through the free layer The GMR ratio is significantly improved for free layer thicknesses below 50 Å The enhancement layer allows electrons to travel longer in their spin state before encountering scattering sites The electronic properties of the enhancement layer material can be matched with the adjacent free layer without creating a low resistance shunt path Because the free layer may be made ultra thin and the enhancement layer is formed of a nonmagnetic material, less magnetic field is required to align the free layer, allowing for improved data density Also, the enhancement layer allows for effective bias point control by shifting sensor current density distribution

Measurement of ballistic phonon conduction near hotspots in silicon

Abstract: The Fourier law for lattice heat conduction fails when the source of heat is small compared to the phonon mean free path. We provide experimental evidence for this effect using heating and electrical-resistance thermometry along a doped region in a suspended silicon membrane. The data are consistent with a closed-form two-fluid phonon conduction model, which accounts for the severe departure from equilibrium at the hotspot. The temperature rise exceeds predictions based on the Fourier law by 60% when the phonon mean free path is a factor of 30 larger than the resistor thickness. This work is improving the constitutive modeling of heat flow in deep-submicron transistors.

Intrinsic Quantum Excitations of Low Temperature Glasses

Abstract: Several puzzling regularities concerning the low temperature excitations of glasses are quantitatively explained by quantizing domain wall motions of the random first order glass transition theory. The density of excitations agrees with experiment and scales with the size of a dynamically coherent region at T(g), being about 200 molecules. The phonon coupling depends on the Lindemann ratio for vitrification yielding the observed universal relation l/lambda approximately 150 between phonon wavelength lambda and mean free path l. Multilevel behavior is predicted to occur in the temperature range of the thermal conductivity plateau.

Theory of collision-dominated dust voids in plasmas.

Abstract: A dust void, i.e., the dust-free region in a dusty plasma, results from the balance of the electrostatic and plasma (such as the ion drag) forces acting on a dust particle. The properties of dust voids depend on the ratio of the void size to the mean free path of plasma ions colliding with neutral species of a weakly ionized plasma. For many plasma-processing and plasma-crystal experiments, the size of the void is much larger than the ion-neutral mean free path. The theory and numerical results are presented for such a collisional case including the situations in which the plasma is quasineutral in the void region or the plasma quasineutrality is violated, as well as the case in which the ion ram pressure is insignificant.

Molecular simulations of sound wave propagation in simple gases

Abstract: Molecular simulations of sound waves propagating in a dilute hard sphere gas have been performed using the direct simulation Monte Carlo method. A wide range of frequencies is investigated, including very high frequencies for which the period is much shorter than the mean collision time. The simulation results are compared to experimental data and approximate solutions of the Boltzmann equation. It is shown that free molecular flow is important at distances smaller than one mean free path from the excitation point.

Propagation of single-cycle terahertz pulses in random media.

Abstract: We describe what are to our knowledge the first measurements of the propagation of coherent, single-cycle pulses of terahertz radiation in a scattering medium. By measuring the transmission as a function of the length L of the medium, we extract the scattering mean free path lsω over a broad bandwidth. We observe variations in ls ranging over nearly 2 orders of magnitude and covering the entire thin sample regime from L/ls≪1 to L/ls∼10. We also observe scattering-induced dispersive effects, which can be attributed to the additional path traveled by photons scattered at small angles.

On the temperature profile and heat flux in the solar corona: Kinetic simulations

Abstract: In the solar corona the collisional mean free path for a thermal particle (electrons or protons) is of the order of 10 2 to 10 4 times the typical scale of variation H of macroscopic quantities like the density or the temperature. Despite the relative smallness of the ratio =H, an increasingly large number of authors have become convinced that the heat flux in such a plasma cannot be described satisfactorily by theories which suppose that the local particle velocity distribution functions are close to Maxwellian. We address this question through kinetic simulations of the low solar corona by assuming that non thermal velocity distribution functions are present at the base of the corona. In particular, we show that if one assumes that the electron velocity distribution functions at the base of the corona have suciently strong suprathermal power law tails, the heat flux may flow upwards, i.e. in the direction of increasing temperature. Using kappa velocity distribution functions as prototypes for non thermal velocity distributions, we nd that the heat conduction can be properly described by the classical Spitzer &H ¨ (1953) law provided the kappa index is> 5. This value is much smaller than the value previously found by Dorelli & Scudder (1999). In addition we show that, unless extremely strong power law tails are assumed near the base of the corona (i.e. <4), a local heating mechanism (e.g. waves) is needed to sustain the temperature gradient between the base of the corona and the coronal temperature maximum.

Effect of Trapped Ions on Shielding of a Charged Spherical Object in a Plasma

Abstract: Summary form only given, as follows. The problem of electrostatic shielding around a small spherical collector immersed in plasma, and the related problem of electron and ion flow to the collector, date to the origins of plasma physics. The earliest work by Langmuir was motivated by probe theory, but more recently there has been considerable interest in connection with the physics of "dust grains" in plasma. Theoretical analyses of these problems have generally been based on the assumption that collisions can be neglected, since the mean free path is typically long compared to shielding length scales, i.e. the Debye length lambda-D. However, investigators beginning with Bernstein and Rabinowitz (1959) have speculated that negative-energy trapped ions, created by occasional collisions, might be important. We have performed an analytic calculation of the density of both trapped and untrapped ions, self-consistent with a calculation of the potential. We show that under typical conditions for dust grains immersed in a discharge plasma, trapped ions dominate the shielding cloud in steady state, even in the limit of very long mean free path. In fact, the density of trapped ions in steady state is independent of the mean free path, as pointed out by Goree (1992). The problem depends mainly on two dimensionless parameters, Tn/Te and a/lambda-D, where Tn is the neutral molecule temperature, Te is the electron temperature, and a is the grain radius. The trapped ion density near the grain can be many times larger than the untrapped density in the regime a/sup /spl and//2/lambda-D/sup /spl and//2<

The plasma-sheath transition with a constant mean free path model and the applicability of the Bohm criterion

Abstract: The fluid model for positive ions is used together with the assumption of a constant ion mean free path to examine the structure of the plasma-wall sheath at low and medium pressures in plasmas where ionization is by electron impact and the ion temperature is set to zero. It is shown that in the near collisionless regime there is the same structure as was found with the constant collision frequency for momentum transfer model with the Bohm speed playing the same role and similar scaling of the transitional layer. At higher pressures there is again no transitional layer, only plasma joining smoothly to a collisional sheath, thus the Bohm criterion has no significance, but the scaling is with a different exponent than for the mobility case. No fundamental differences are found between the two models. An expression is derived to describe the boundary between the parameter region where the Bohm criterion applies and that where it does not.

Target-vapour interaction and atomic collisions in pulsed laser ablation

Abstract: Numerical solution of the Boltzmann equation with a relaxation collision term is used to study gas-dynamic flows formed under nanosecond pulsed laser ablation. Atoms ejected from the surface of a target are assumed to have a Maxwell velocity distribution corresponding to the surface temperature and the saturated vapour pressure. The surface temperature is obtained from a transient heat transfer equation in the condensed phase. Atomic collisions in the ablation plume orient atoms towards the surface normal and speed up the plume expansion from the target. Atoms backscattered in the gas phase, stick to the target surface and cause back condensation of the vapour at later stages. When the mean free path is much less than the plume dimension, a Knudsen layer, a hydrodynamic flow region, and a low-density tail may be distinguished in the gas phase. The present numerical simulation is in good agreement with the analytical quasi-steady Mott-Smith approach to the Knudsen layer in the case of evaporation and at the early stages of condensation. Comparison with experiment reveals that the model underestimates both the width of the ablated material angular distribution and the amount of high-energy atoms. The difference increases with the laser fluence and may be caused by lateral expansion of the plume, by vapour acceleration due to laser radiation absorption or probably by non-thermal evaporation effects.

Asymptotic-Preserving (Ap) Schemes for Multiscale Kinetic Equations: a Unified Approach

Abstract: Kinetic equations have scalings, characterized by the mean free path, that lead to various different limiting behaviors, such as the Euler and Navier-Stokes approximations. Based on our previous studies on these issues, here we present a unified approach to develop asymptotic-preserving scheme for multiscale kinetic equations that allows the treatment of different length scales in a robust way. Our scheme works for both the rarefied and hydrodynamic (Euler and Navier-Stokes) regimes with a uniform accuracy. The idea is to use the even and odd-parity formulation. Our approach covers a large class of kinetic and transport equations.

Wetting layer carrier dynamics in InAs/InP quantum dots

Abstract: The electronic coupling between InAs/InP quantum dot (QD) array and its wetting layer (WL) is studied by continuous wave and time resolved photoluminescence. The carrier dynamics is explained by the existence of two regimes in the WL: at low QD density the carrier dynamics is dominated by the diffusion and at high density when the distance between QDs is comparable to the carrier mean free path in the WL the quantum capture into QDs dominates. From the identification of these two regimes the carrier mean free path in the WL is estimated to about 30 nm.

Cosmic ray transport in anisotropic magnetohydrodynamic turbulence

Abstract: Observations of interstellar turbulence imply that the power spectrum of the wave turbulence must be highly anisotropic This anisotropy has to be included when transport of high energy cosmic rays in the Galaxy is discussed Here we evaluate the relevant cosmic ray transport parameters in the presence of anisotropic plasma wave turbulence, consisting of a mixture of shear Alfven waves and fast magnetosonic waves By averaging the respective Fokker-Planck coefficient over the par- ticle pitch-angle we calculate the momentum and spatial diffusion coefficients for different anisotropy parameters For strongly perpendicular turbulence (Λ � 1) we obtain that the momentum diffusion coefficient is proportional to Λ −1/2 � ln � −1 + ln Λ 1/2 � , whereas for strongly parallel turbulence (Λ � 1) the momentum diffusion coefficient is a constant We also calculate the anisotropy dependence of the spatial diffusion coefficient and the parallel mean free path for the mixed turbulence For all coefficients we discuss the rigidity dependence for different cosmic ray particles

Diffusion approximation in heterogeneous media

Abstract: We investigate the behaviour of the solutions of kinetic equations as a parameter related to both the mean free path and a characteristic length of heterogeneities goes to 0. We obtain in the limit a diffusion equation for the macroscopic density which combines the homogenization effects to the diffusion approximation. In particular the limit equation contains drift terms related to the behaviour of the kernel of the collision operator.

Generalized Drude model: Unification of ballistic and diffusive electron transport

Abstract: For electron transport in parallel-plane semiconducting structures, a model is developed that unifies ballistic and diffusive transport and thus generalizes the Drude model. The unified model is valid for arbitrary magnitude of the mean free path and arbitrary shape of the conduction band edge profile. Universal formulas are obtained for the current-voltage characteristic in the nondegenerate case and for the zero-bias conductance in the degenerate case, which describe in a transparent manner the interplay of ballistic and diffusive transport. The semiclassical approach is adopted, but quantum corrections allowing for tunneling are included. Examples are considered, in particular the case of chains of grains in polycrystalline or microcrystalline semiconductors with grain size comparable to, or smaller than, the mean free path. Substantial deviations of the results of the unified model from those of the ballistic thermionic-emission model and of the drift-diffusion model are found. The formulation of the model is one-dimensional, but it is argued that its results should not differ substantially from those of a fully three-dimensional treatment.

Generalized Drude model: unification of ballistic and diffusive electron transport

Abstract: For electron transport in parallel-plane semiconducting structures, a model is developed that unifies ballistic and diffusive transport and thus generalizes the Drude model. The unified model is valid for arbitrary magnitude of the mean free path and arbitrary shape of the conduction band edge profile. Universal formulas are obtained for the current-voltage characteristic in the nondegenerate case and for the zero-bias conductance in the degenerate case, which describe in a transparent manner the interplay of ballistic and diffusive transport. The semiclassical approach is adopted, but quantum corrections allowing for tunnelling are included. Examples are considered, in particular the case of chains of grains in polycrystalline or microcrystalline semiconductors with grain size comparable to, or smaller than, the mean free path. Substantial deviations of the results of the unified model from those of the ballistic thermionic-emission model and of the drift-diffusion model are found. The formulation of the model is one-dimensional, but it is argued that its results should not differ substantially from those of a fully three-dimensional treatment.

Ion acoustic instability driven by a temperature gradient in laser-produced plasmas

Abstract: The return current instability excited in laser-produced plasmas by a temperature gradient has been studied using a nonlocal theory of electron transport. The transport model is applicable for an arbitrary ratio of the temperature inhomogeneity scale length to the collisional mean free path. It is demonstrated that nonlocal thermal effects have a significant impact on the ion acoustic instability growth rate, threshold and angular distribution of excited waves that can be important for the interaction of smoothed laser beams with a plasma. A nonlinear dependence of the return current instability growth rate on the gradient length has been discovered. The particularly important example of ion acoustic instability due to inhomogeneous plasma heating as a result of inverse bremsstrahlung absorption in a hot spot has been considered.

Viscosity and Mean Free Path of Very Diluted Solutions of 3He in 4He

Abstract: We have measured the laminar friction of various diluted 3 He- 4 He mixtures, of natural 4 He and of isotopically pure 4 He on an oscillating sphere below 1 K. For 3 He concentrations x 3 ranging from 10 −2 to 10 −4 we find a reduction of the drag above 0.5 K when compared to the pure liquid and a large enhancement below, which is almost independent of x 3 . At low concentrations 5·10 −5 >x 3 ≥5·10 −7 the drag becomes proportional to x 3 which implies a transition from a hydrodynamic to a ballistic regime. This is confirmed by deducing the mean free path of the 3 He atoms from the data. The temperature dependence of the drag in the ballistic regime, however, is found to be proportional to T and therefore different from the expected T 1/2 behaviour.

Spin-dependent scattering in transition metals

Abstract: The spin-dependent electron inelastic mean free path (IMFP) in transition metals is studied in the energy range 5–50 eV above the Fermi level. It is shown that the spin-dependent IMFP is simply related to the number of holes in both d spin subbands, whatever the detail of the d-band structure. This analysis allows us to disentangle the different scattering channels. Many experimental determinations of the spin-dependent part of the electron scattering cross section, from several teams, are analyzed in the framework of this model. The strong energy dependence of the exchange matrix element is clearly evidenced.

Study of the ordinary size effect in the electrical conductivity of Bi nanowires

Abstract: The temperature dependence of the electrical conductivity of a cylindrical nanowire is investigated. The calculations are performed for thin wires with an ellipsoidal Fermi surface, based on the Fuchs-Sondheimer boundary scattering theory given for thin metallic films with spherical Fermi surfaces. It is seen that the conductivity depends on the process of scattering of the carrier on the surface, and on the thickness of the wire for wires with diameters smaller than the carrier's mean free path. The temperature dependence of the electrical resistivity of a Bi nanowire is calculated and compared with the experimental results reported by Gurvitch, where good agreement is observed.