Showing papers on "Mean free path published in 2013"

Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance.

Abstract: Little is known about the mean free path spectra of lattice vibrations—known as phonons—that carry heat in non-metallic solids. Regner et al . demonstrate a technique that enables measurement of these spectra over an unprecedented range, enabling a more complete pi…

Dicalcium nitride as a two-dimensional electride with an anionic electron layer

Abstract: The ionic crystal Ca2N is shown to be an electride in terms of [Ca2N]+·e−, with diffusive two-dimensional transport in dense electron layers. The physical properties of electrides — ionic crystals in which electrons behave as anions — significantly depend on the topology of the confining cavity for anionic electrons. Thus, an essential step towards practical electride applications is to discover new confinement spaces with unique topologies. Confined two-dimensional electron layers have previously been achieved by artificially fabricating hetero-interface structures usually of semiconducting materials. Here the authors extend the range of materials demonstrating such behaviour to an electride, dicalcium nitride (Ca2N). This compound has ideal properties for electron confinement: a layered structure with appropriate interlayer spacing and a chemistry that allows for loosely bound electron layers without electron trapping. By providing a new material image for electrides, this work should lead to a series of two-dimensional electrides with unique physical properties. Recent studies suggest that electrides—ionic crystals in which electrons serve as anions—are not exceptional materials but rather a generalized form, particularly under high pressure1,2,3. The topology of the cavities confining anionic electrons determines their physical properties4. At present, reported confining sites consist only of zero-dimensional cavities or weakly linked channels4. Here we report a layered-structure electride of dicalcium nitride, Ca2N, which possesses two-dimensionally confined anionic electrons whose concentration agrees well with that for the chemical formula of [Ca2N]+·e−. Two-dimensional transport characteristics are demonstrated by a high electron mobility (520 cm2 V−1 s−1) and long mean scattering time (0.6 picoseconds) with a mean free path of 0.12 micrometres. The quadratic temperature dependence of the resistivity up to 120 Kelvin indicates the presence of an electron–electron interaction. A striking anisotropic magnetoresistance behaviour with respect to the direction of magnetic field (negative for the field perpendicular to the conducting plane and positive for the field parallel to it) is observed, confirming diffusive two-dimensional transport in dense electron layers. Additionally, band calculations support confinement of anionic electrons within the interlayer space, and photoemission measurements confirm anisotropic low work functions of 3.5 and 2.6 electronvolts, revealing the loosely bound nature of the anionic electrons. We conclude that Ca2N is a two-dimensional electride in terms of [Ca2N]+·e−.

Direct Measurement of Room-Temperature Nondiffusive Thermal Transport Over Micron Distances in a Silicon Membrane

Abstract: The "textbook" phonon mean free path of heat carrying phonons in silicon at room temperature is ∼40 nm. However, a large contribution to the thermal conductivity comes from low-frequency phonons with much longer mean free paths. We present a simple experiment demonstrating that room-temperature thermal transport in Si significantly deviates from the diffusion model already at micron distances. Absorption of crossed laser pulses in a freestanding silicon membrane sets up a sinusoidal temperature profile that is monitored via diffraction of a probe laser beam. By changing the period of the thermal grating we vary the heat transport distance within the range ∼1-10 μm. At small distances, we observe a reduction in the effective thermal conductivity indicating a transition from the diffusive to the ballistic transport regime for the low-frequency part of the phonon spectrum.

Direct Measurement of Room-Temperature Nondiffusive Thermal Transport Over Micron Distances in a Silicon Membrane

Abstract: The "textbook" phonon mean free path of heat carrying phonons in silicon at room temperature is ∼40 nm. However, a large contribution to the thermal conductivity comes from low-frequency phonons with much longer mean free paths. We present a simple experiment demonstrating that room-temperature thermal transport in Si significantly deviates from the diffusion model already at micron distances. Absorption of crossed laser pulses in a freestanding silicon membrane sets up a sinusoidal temperature profile that is monitored via diffraction of a probe laser beam. By changing the period of the thermal grating we vary the heat transport distance within the range ∼1-10 μm. At small distances, we observe a reduction in the effective thermal conductivity indicating a transition from the diffusive to the ballistic transport regime for the low-frequency part of the phonon spectrum.

Mean free path spectra as a tool to understand thermal conductivity in bulk and nanostructures

Abstract: A rigorous derivation is given for the thermal conductivity accumulation function and mean free path (MFP) spectrum of an isotropic bulk material. The key physical insight is to express the kinetic theory integral in terms of MFP rather than frequency. Extending this framework to incorporate boundary scattering in nanostructures leads to an integral equation that transforms a material's bulk MFP spectrum into the size-dependent thermal conductivity of the nanostructure. The kernel of this transform represents the boundary scattering rule for the particular type of nanostructure. The principal benefit of this transform is that it requires only a single function, the material's bulk MFP spectrum, or equivalently its accumulation function. Explicit knowledge of the material's dispersion relation and frequency-dependent bulk MFPs is not needed, nor is a summation over polarizations, because the bulk MFP spectrum already contains this information in exactly the form required to evaluate boundary scattering. The utility of this framework is demonstrated through a case study of six models for the phonon thermal conductivity of silicon: three analytical, one gray, and two numerical.

Ballistic InAs nanowire transistors.

Abstract: Ballistic transport of electrons at room temperature in top-gated InAs nanowire (NW) transistors is experimentally observed and theoretically examined. From length dependent studies, the low-field mean free path is directly extracted as ∼150 nm. The mean free path is found to be independent of temperature due to the dominant role of surface roughness scattering. The mean free path was also theoretically assessed by a method that combines Fermi’s golden rule and a numerical Schrodinger–Poisson simulation to determine the surface scattering potential with the theoretical calculations being consistent with experiments. Near ballistic transport (∼80% of the ballistic limit) is demonstrated experimentally for transistors with a channel length of ∼60 nm, owing to the long mean free path of electrons in InAs NWs.

Observation of room-temperature ballistic thermal conduction persisting over 8.3 µm in SiGe nanowires.

Abstract: SiGe nanowires exhibit ballistic thermal conduction at room temperature with a long phonon mean free path.

Universal phonon mean free path spectra in crystalline semiconductors at high temperature

Abstract: Thermal conductivity in non-metallic crystalline materials results from cumulative contributions of phonons that have a broad range of mean free paths. Here we use high frequency surface temperature modulation that generates non-diffusive phonon transport to probe the phonon mean free path spectra of GaAs, GaN, AlN, and 4H-SiC at temperatures near 80 K, 150 K, 300 K, and 400 K. We find that phonons with MFPs greater than 230 ± 120 nm, 1000 ± 200 nm, 2500 ± 800 nm, and 4200 ± 850 nm contribute 50% of the bulk thermal conductivity of GaAs, GaN, AlN, and 4H-SiC near room temperature. By non-dimensionalizing the data based on Umklapp scattering rates of phonons, we identified a universal phonon mean free path spectrum in small unit cell crystalline semiconductors at high temperature.

Linear magnetoresistance in topological insulator thin films: Quantum phase coherence effects at high temperatures

Abstract: In addition to the weak antilocalization cusp observed in the magnetoresistance (MR) of topological insulators at low temperatures and low magnetic fields, we find that the high-field MR in Bi2Te2Se is linear in field. At fields up to B = 14 T, the slope of this linear-like MR is nearly independent of temperature over the range T = 7 to 150 K. We find that the linear MR arises from the competition between a logarithmic phase coherence component and a quadratic component. The quantum phase coherence dominates up to high temperatures, where the coherence length remains longer than the mean free path of electrons.

Magnetoresistance measurements of a superconducting surface state of in-induced and Pb-induced structures on Si(111).

Abstract: In situ micro-four-point-probe conductivity measurements in ultrahigh vacuum revealed that the Si(111)-striped incommensurate-Pb surface showed the superconductivity transition at 1.1 K. Both of the hexagonal and rectangular phases of Si(111)√[7]×√[3]-In surface showed superconductivity at 2.4 and 2.8 K, respectively. By applying magnetic field perpendicular to the surface, the upper critical field was deduced to be 0.1-1 T. The derived Ginzburg-Landau coherence length of the Cooper pairs was several tens of nm, which was much smaller than the Pippard's coherence length estimated from the band structures. The short coherence length is determined by the carrier mean free path.

Gallium arsenide thermal conductivity and optical phonon relaxation times from first-principles calculations

Abstract: In this paper, thermal conductivity of crystalline GaAs is calculated using first-principles lattice dynamics. The harmonic and cubic force constants are obtained by fitting them to the force-displacement data from density functional theory calculations. Phonon dispersion is calculated from a dynamical matrix constructed using the harmonic force constants and phonon relaxation times are calculated using Fermi's Golden rule. The calculated GaAs thermal conductivity agrees well with experimental data. Thermal conductivity accumulations as a function of the phonon mean free path and as a function of the wavelength are obtained. Our results predict a significant size effect on the GaAs thermal conductivity in the nanoscale. Relaxation times of optical phonons and their contributions from different scattering channels are also studied. Such information will help the understanding of hot phonon effects in GaAs-based devices.

Turbulent pitch-angle scattering and diffusive transport of hard-X-ray producing electrons in flaring coronal loops

Abstract: Recent observations from {\em RHESSI} have revealed that the number of non-thermal electrons in the coronal part of a flaring loop can exceed the number of electrons required to explain the hard X-ray-emitting footpoints of the same flaring loop. Such sources cannot, therefore, be interpreted on the basis of the standard collisional transport model, in which electrons stream along the loop while losing their energy through collisions with the ambient plasma; additional physical processes, to either trap or scatter the energetic electrons, are required. Motivated by this and other observations that suggest that high energy electrons are confined to the coronal region of the source, we consider turbulent pitch angle scattering of fast electrons off low frequency magnetic fluctuations as a confinement mechanism, modeled as a spatial diffusion parallel to the mean magnetic field. In general, turbulent scattering leads to a reduction of the collisional stopping distance of non-thermal electrons along the loop and hence to an enhancement of the coronal HXR source relative to the footpoints. The variation of source size $L$ with electron energy $E$ becomes weaker than the quadratic behavior pertinent to collisional transport, with the slope of $L(E)$ depending directly on the mean free path $\lambda$ again pitch angle scattering. Comparing the predictions of the model with observations, we find that $\lambda \sim$$(10^8-10^9)$ cm for $\sim30$ keV, less than the length of a typical flaring loop and smaller than, or comparable to, the size of the electron acceleration region.

Turbulent pitch-angle scattering and diffusive transport of hard X-ray-producing electrons in flaring coronal loops

Abstract: Recent observations from RHESSI have revealed that the number of non-thermal electrons in the coronal part of a flaring loop can exceed the number of electrons required to explain the hard X-ray-emitting footpoints of the same flaring loop. Such sources cannot, therefore, be interpreted on the basis of the standard collisional transport model, in which electrons stream along the loop while losing their energy through collisions with the ambient plasma; additional physical processes, to either trap or scatter the energetic electrons, are required. Motivated by this and other observations that suggest that high-energy electrons are confined to the coronal region of the source, we consider turbulent pitch-angle scattering of fast electrons off low-frequency magnetic fluctuations as a confinement mechanism, modeled as a spatial diffusion parallel to the mean magnetic field. In general, turbulent scattering leads to a reduction of the collisional stopping distance of non-thermal electrons along the loop, and hence to an enhancement of the coronal hard X-ray source relative to the footpoints. The variation of source size L with electron energy E becomes weaker than the quadratic behavior pertinent to collisional transport, with the slope of L(E) depending directly on the mean free path λ associated with the non-collisional scattering mechanism. Comparing the predictions of the model with observations, we find that λ ~ (108-109) cm for ~30 keV, less than the length of a typical flaring loop and smaller than, or comparable to, the size of the electron acceleration region.

Phonon Heat Conduction in Corrugated Silicon Nanowires Below the Casimir Limit

Abstract: The thermal conductance of straight and corrugated monocrystalline silicon nanowires has been measured between 0.3 K and 5 K. The difference in the thermal transport between corrugated nanowires and straight ones demonstrates a strong reduction in the mean free path of the phonons. This averaged mean free path is remarkably smaller than the smaller diameter of the nanowire, evidencing a phonon thermal transport reduced below the Casimir limit. Monte Carlo simulations highlight that this effect can be attributed to significant multiple scattering of ballistic phonons occuring on the corrugated surfaces. This result suggests an original approach to transforming a monocrystalline material into a phonon glass.

Phonon Heat Conduction in Corrugated Silicon Nanowires Below the Casimir Limit

Abstract: The thermal conductance of straight and corrugated monocrystalline silicon nanowires has been measured between 0.3 K and 5 K. It is demonstrated that the corrugation strongly reduces the thermal transport by reducing the mean free path of the phonons. The experimental averaged mean free path is remarkably smaller than the smaller diameter of the nanowire, evidencing a phonon thermal transport reduced below the Casimir limit. Monte Carlo simulations highlight that this effect can be attributed to significant multiple scattering of ballistic phonons occurring on the corrugated surfaces. This result suggests an original approach to transforming a monocrystalline material into a phonon glass.

Transition between Saturation Regimes of Gyrokinetic Turbulence

Abstract: A gyrokinetic model of ion temperature gradient driven turbulence in magnetized plasmas is used to study the injection, nonlinear redistribution, and collisional dissipation of free energy in the saturated turbulent state over a broad range of driving gradients and collision frequencies. The dimensionless parameter L(T)/L(C), where L(T) is the ion temperature gradient scale length and L(C) is the collisional mean free path, is shown to parametrize a transition between a saturation regime dominated by nonlinear transfer of free energy to small perpendicular (to the magnetic field) scales and a regime dominated by dissipation at large scales in all phase space dimensions.

Position-dependent diffusion of light in disordered waveguides

Abstract: Summary form only given. Diffusion is a statistical description of random walk of a classical particle, and the diffusion constant D0 is the only parameter in the diffusion equation. For light as well as for other kinds of waves, this is an approximation, because the interference of partial waves is ignored [1]. Such interference is essential to Anderson localization. Proper account of the interference effects in random samples of finite size [2] and/or with absorption [3] results in spatial variation of the diffusion coefficient D(r) in the self consistent theory (SCT) of localization.To observe position-dependent diffusion, disordered waveguide structures were fabricated with the silicon on insulator wafer (see Fig. 1a). The patterns were written by electron beam lithography and etched in an inductive coupled reactive ion etcher. The waveguides contained 2D random arrays of air holes that scattered light, and the scattering length was varied by the hole size and filling fraction. The waveguide walls were made of photonic crystals that had complete bandgap in 2D, so that light could not escape laterally. However, light will leak out of the plane while being scattered by the air holes. This vertical leakage can be described by an effective absorption or dissipation. The relevant parameters are the diffusive absorption length ha0 and the transport mean free path . The localization length h is determined by and the waveguide width W. Light from a CW laser source was injected into the waveguide from one end, and transported through the random medium. Spatial distribution of light intensity on the sample surface was imaged onto a camera by an objective lens. After entering the random medium, light is attenuated due to competing effects of backscattering and dissipation. I(y, z) was integrated along the transverse y-direction to determine the variation of intensity along the axial z-direction (parallel to the waveguide axis).Fig. lb shows the measured light intensity I(z) inside the ensembles of random waveguides of different width W (blue). The values of ξ and ξασ are obtained by fitting the most diffusive sample (W = 60 μm, longest ξ) with SCT (red dashed line) [2,3]. Using these values, SCT successfully predicts I(z) for all other samples. D(z) corresponding to red curves in Fig. lb are plotted in Fig. lc, showing a suppression of diffusion in the middle of the sample with increase ξασ/ξ (decrease of W) as predicted by SCT.

Heat transport by long mean free path vibrations in amorphous silicon nitride near room temperature

Abstract: We present measurements of thermal transport in 500-nm-thick, 35-$\ensuremath{\mu}$m-wide, and 806-$\ensuremath{\mu}$m-long micromachined suspended silicon nitride (Si-N) bridges over the temperature range of 77 to 325 K. The measured thermal conductivity of Si-N (for material grown by low-pressure chemical vapor deposition in two different furnaces) deviates somewhat from previously reported measurements and also shows surprising dependence on surface variation at these relatively high temperatures. Addition of discontinuous gold films causes the thermal conductance of Si-N bridges to drop through the entire measured temperature range, before rising again when thicker, continuous films are added. Similar effects occur when continuous but very low-thermal-conductivity alumina films are deposited. The reduction in thermal conductance upon modification of the Si-N surface is strong evidence that vibrational excitations with long mean free paths carry significant heat even at these high temperatures. By measuring a series of film thicknesses the surface-scattering effects can be mitigated, and the resulting experimental values of the thermal conductivity of alumina and Au thin films compare very well to known values or to predictions of the Wiedemann-Franz law. We also present a modified model for the phonon mean free path in thin-film geometries, and use it along with atomic force microsope scans to show that a very small population of phonons with mean free path on the order of 1 $\ensuremath{\mu}$m and wavelength much longer than the expected thermal wavelengths carry up to $50%$ of the heat in Si-N at room temperature.

Phonon surface scattering controlled length dependence of thermal conductivity of silicon nanowires

Abstract: We present a kinetic model to investigate the anomalous thermal conductivity in silicon nanowires (SiNWs) by focusing on the mechanism of phonon–boundary scattering. Our theoretical model takes into account the anharmonic phonon–phonon scattering and the angle-dependent phonon scattering from the SiNWs surface. For SiNWs with diameter of 27.2 nm, it is found that in the case of specular reflection at lateral boundaries, the thermal conductivity increases as the length increases, even when the length is up to 10 μm, which is considerably longer than the phonon mean free path (MFP). Thus the phonon–phonon scattering alone is not sufficient for obtaining a normal diffusion in nanowires. However, in the case of purely diffuse reflection at lateral boundaries, the phonons diffuse normally and the thermal conductivity converges to a constant when the length of the nanowire is greater than 100 nm. Our model demonstrates that for observing the length dependence of thermal conductivity experimentally, nanowires with smooth and non-contaminated surfaces, and measuring at low temperature, are preferred.

Monte Carlo simulation of phonon transport in silicon including a realistic dispersion relation

Abstract: Thermal conductivities in bulk Si and Si films are analyzed using a Monte Carlo method to solve the phonon Boltzmann transport equation. By taking into account the realistic phonon dispersion relation calculated from the adiabatic bond charge model along with pure diffuse boundary scattering based on Lambert's law, simulated results that were in good agreement with the experimental ones were obtained. In addition, it was found that the approximated dispersion curves fitted along the [100] direction underestimate the density of states for mobile phonons, which results in a smaller specific heat and a longer phonon mean free path. The resulting impact on the simulation of heat transfer in nanostructures is discussed.

Broadband mean free path of diffuse light in polydisperse ensembles of scatterers for white light-emitting diode lighting

Abstract: We study the diffuse transport of light through polymer slabs containing TiO2 scattering particles. The slabs are diffuser plates typical of a commercial white light-emitting diode (LED) module (Fortimo). We have measured the diffuse transmission and reflection properties over a broad wavelength range (470–840 nm) from which we derive the transport mean free path using the theory of light diffusion. With increasing scatterer density, the mean free path becomes shorter. The mean free path increases with wavelength; hence, blue light is scattered more strongly than red light. To interpret the results, we propose an ab initio model without adjustable parameters for the mean free path by using Mie theory. We include inhomogeneous broadening as a result of the size distribution of the scattering particles as measured by dynamic light scattering. Surprisingly, the calculated mean free path decreases with wavelength, at variance with our experiments, which is caused by particles with radii R in excess of 0.25 μm. Close inspection of the scatterers by electron microscopy reveals that large particles (R>0.4 μm) consist of clusters of small particles (R<0.13 μm). Therefore, we have improved our model by only taking into account the individual scatterers within the clusters. This model predicts mean free paths in good agreement with our experimental results. We discuss consequences of our results to white LED lighting modules.

Surface excitations in electron spectroscopy. Part I: dielectric formalism and Monte Carlo algorithm

Abstract: The theory describing energy losses of charged non-relativistic projectiles crossing a planar interface is derived on the basis of the Maxwell equations, outlining the physical assumptions of the model in great detail. The employed approach is very general in that various common models for surface excitations (such as the specular reflection model) can be obtained by an appropriate choice of parameter values. The dynamics of charged projectiles near surfaces is examined by calculations of the induced surface charge and the depth- and direction-dependent differential inelastic inverse mean free path (DIIMFP) and stopping power. The effect of several simplifications frequently encountered in the literature is investigated: differences of up to 100% are found in heights, widths, and positions of peaks in the DIIMFP. The presented model is implemented in a Monte Carlo algorithm for the simulation of the electron transport relevant for surface electron spectroscopy. Simulated reflection electron energy loss spectra are in good agreement with experiment on an absolute scale. Copyright © 2012 John Wiley & Sons, Ltd.

Experimental observation of a fundamental length scale of waves in random media.

Abstract: Waves propagating through a weakly scattering random medium show a pronounced branching of the flow accompanied by the formation of freak waves, i.e., extremely intense waves. Theory predicts that this strong fluctuation regime is accompanied by its own fundamental length scale of transport in random media, parametrically different from the mean free path or the localization length. We show numerically how the scintillation index can be used to assess the scaling behavior of the branching length. We report the experimental observation of this scaling using microwave transport experiments in quasi-two-dimensional resonators with randomly distributed weak scatterers. Remarkably, the scaling range extends much further than expected from random caustics statistics.

Analytical model for the radio-frequency sheath.

Abstract: A simple analytical model for the planar radio-frequency (rf) sheath in capacitive discharges is developed that is based on the assumptions of a step profile for the electron front, charge exchange collisions with constant cross sections, negligible ionization within the sheath, and negligible ion dynamics. The continuity, momentum conservation, and Poisson equations are combined in a single integro-differential equation for the square of the ion drift velocity, the so called sheath equation. Starting from the kinetic Boltzmann equation, special attention is paid to the derivation and the validity of the approximate fluid equation for momentum balance. The integrals in the sheath equation appear in the screening function which considers the relative contribution of the temporal mean of the electron density to the space charge in the sheath. It is shown that the screening function is quite insensitive to variations of the effective sheath parameters. The two parameters defining the solution are the ratios of the maximum sheath extension to the ion mean free path and the Debye length, respectively. A simple general analytic expression for the screening function is introduced. By means of this expression approximate analytical solutions are obtained for the collisionless as well as the highly collisional case that compare well with the exact numerical solution. A simple transition formula allows application to all degrees of collisionality. In addition, the solutions are used to calculate all static and dynamic quantities of the sheath, e.g., the ion density, fields, and currents. Further, the rf Child-Langmuir laws for the collisionless as well as the collisional case are derived. An essential part of the model is the a priori knowledge of the wave form of the sheath voltage. This wave form is derived on the basis of a cubic charge-voltage relation for individual sheaths, considering both sheaths and the self-consistent self-bias in a discharge with arbitrary symmetry. The externally applied rf voltage is assumed to be sinusoidal, although the model can be extended to arbitrary wave forms, e.g., for dual-frequency discharges. The model calculates explicitly the cubic correction parameter in the charge-voltage relation for the case of highly asymmetric discharges. It is shown that the cubic correction is generally moderate but more pronounced in the collisionless case. The analytical results are compared to experimental data from the literature obtained by laser electric field measurements of the mean and dynamic fields in the capacitive sheath for various gases and pressures. Very good agreement is found throughout.

Simple analytical forms of the perpendicular diffusion coefficient for two-component turbulence. i. magnetostatic turbulence

Abstract: We explore perpendicular diffusion based on the unified nonlinear transport theory. We derive simple analytical forms for the perpendicular mean free path and investigate the influence of different model spectra. We show that for cases where the field line random walk is normal diffusive, the perpendicular diffusion coefficient consists of only two transport regimes. Details of the spectral shape are less important, especially those of the inertial range. Only the macroscopic properties of the turbulence spectrum control the perpendicular diffusion coefficient. Simple formulae for the perpendicular diffusion coefficient are derived which can easily be implemented in solar modulation or shock acceleration codes.

Multiscale electronic transport in Li(1+x)Ni(1/3-u)Co(1/3-v)Mn(1/3-w)O2: a broadband dielectric study from 40 Hz to 10 GHz.

Abstract: This work is the first detailed study concerning the multiscale electronic transport and its temperature dependence in the LiNi1/3Co1/3Mn1/3O2 (NMC) family, high-capacity electrode materials for lithium ion batteries. Powders with two different mean cluster sizes (3 μm and 10 μm) but the same particle sizes (0.4 to 1.3 μm) were measured. The detailed formula of the studied compound is Li1.04Ni(2+)0.235Ni(3+)0.09Mn(4+)0.315Co(3+)0.32O2. Different electrical relaxations are evidenced, resulting from the polarizations at the different scales of the powder architecture. When the frequency increases, three dielectric relaxations are detected in the following order due to: (a) space-charge polarization (low-frequency range) owing to the interface between the sample and the conductive metallic layer deposited on it; (b) polarization of NMC clusters (micronic scale) induced by the existence of resistive junctions between them; and (c) polarization of NMC particles (at sub-micronic scale) induced by resistive junctions between them. High interatomic level conductivity of about 20 S m(-1) was evidenced and attributed to the contribution of the extended states and to a Brownian motion of the charge carriers with mean free path similar to the lattice constant. The ratio between sample and local conductivity is more than 10(5). The large conductivity drop of 3 to 4 orders of magnitude is observed from the particle to the cluster scale. A very large number of charge carriers are blocked by the interparticle junctions within the clusters. The conductivity drop from the cluster to the sample scale is comparatively very small, owing to the dense architecture of the NMC sample in which the spherical clusters are very piled up on each other.

Ion–Neutral Collision Modeling Using Classical Scattering With Spin-Orbit Free Interaction Potential

Abstract: A particle-in-cell Monte Carlo collision model is developed to explore dominant collisional effects on high-velocity xenon ions incident to a quiescent xenon gas at low neutral pressures. The range of neutral pressure and collisionality examined are applicable for electric propulsion as well as plasma processing devices; therefore, the computational technique described herein can be applied to more complex simulations of those devices. Momentum and resonant charge-exchange collisions between ions and background neutrals are implemented using two different models, classical scattering with spin-orbit free potential and variable-hard-sphere model, depending on the incident particle energy. The primary and charge-exchange ions are tracked separately, and their trajectories within a well-defined “Test Cell” domain are determined. Predicted electrode currents as a function of the Test Cell pressure are compared with electrode currents measured in an ion gun experiment. The simulation results agree well with the experiment up to a Test Cell pressure corresponding to a mean free path of the Test Cell length and then start to deviate with increasing collisionality at higher pressures. This discrepancy at higher pressures is likely due to the increasing influence of secondary electrons emitted from electrodes due to the high-velocity impacts of heavy species (i.e., beam ions and fast neutrals created by charge-exchange interaction) at the electrode surfaces.