Specularity Parameter Research Articles

Thermal conductivity of Si1−xGex/Si1−yGeysuperlattices: Competition between interfacial and internal scattering

We investigate thermal transport in Si/Ge and Si${}_{1\ensuremath{-}x}$Ge${}_{x}$/Si${}_{1\ensuremath{-}y}$Ge${}_{y}$ alloy superlattices based on solving the single-mode phonon Boltzmann transport equation in the relaxation-time approximation and with full phonon dispersions. We derive an effective interface scattering rate that depends both on the interface roughness (captured by a wave-vector-dependent specularity parameter) and on the efficiency of internal scattering mechanisms (mass-difference and phonon-phonon scattering). We provide compact expressions for the calculations of in-plane and cross-plane thermal conductivities in superlattices. Our numerical results accurately capture both the observed increase in thermal conductivity as the superlattice period increases and the in-plane vs cross-plane anisotropy of thermal conductivity. Owing to the combined effect of interface and internal scattering, an alloy/alloy superlattice has a lower thermal conductivity than bulk SiGe with the same alloy composition. Thermal conductivity can be minimized by growing short-period alloy/alloy superlattices or Si/Si${}_{1\ensuremath{-}x}$Ge${}_{x}$ superlattices with the SiGe layer thicker than the Si one.

Electron mean free path of tungsten and the electrical resistivity of epitaxial (110) tungsten films

This work describes a study of the classical electrical resistivity size effect in tungsten. The important length scale for this size effect is the isotropic average electron mean free path (EMFP), which was determined to be 19.1 nm for W at 293 K by employing density functional theory. To explore the size effect experimentally, (110) oriented epitaxial W films with thicknesses ranging from 9.8 to 299.7 nm were prepared by sputter deposition onto ($11\overline{2}0$) Al${}_{2}$O${}_{3}$ substrates at 520 \ifmmode^\circ\else\textdegree\fi{}C followed by postdeposition annealing in Ar-4$%$H${}_{2}$ at 850 \ifmmode^\circ\else\textdegree\fi{}C. Film resistivities were measured at room temperature and at liquid He temperature. The Fuchs-Sondheimer (FS) surface scattering model with a low specularity parameter ($p$ $=$ 0.11) was shown to provide a good description of the film resistivity as a function of film thickness. Further, it is shown that an upper bound to the EMFP cannot be established by fitting resistivity data to the FS model, whereas a lower bound can be assessed.

Wave packet simulations of phonon boundary scattering at graphene edges

Wave packet dynamics is used to investigate the scattering of longitudinal (LA), transverse (TA), and bending-mode (ZA) phonons at the zigzag and armchair edges of suspended graphene. The interatomic forces are calculated using a linearized Tersoff potential. The strength of a boundary scattering event at impeding energy flow is described by a forward scattering coefficient, similar in spirit to a specularity parameter. For armchair boundaries, this scattering coefficient is found to depend strongly on the magnitude, direction, and polarization of the incident wavevector, while for zigzag boundaries, the forward scattering coefficient is found to always be unity regardless of wavevector and polarization. Wave packet splitting is observed for ZA phonons incident on armchair boundaries, while both splitting and mode conversion are observed for LA and TA phonons incident on both zigzag and armchair boundaries. These simulation results show that armchair boundaries impede the forward propagation of acoustic phonon energy much more strongly than zigzag boundaries do, suggesting that graphene nanoribbons will have substantially lower thermal conductivity in armchair rather than zigzag orientation.

Anomalous Size Dependence of the Thermal Conductivity of Graphene Ribbons

We investigated the thermal conductivity K of graphene ribbons and graphite slabs as the function of their lateral dimensions. Our theoretical model considered the anharmonic three-phonon processes to the second-order and included the angle-dependent phonon scattering from the ribbon edges. It was found that the long mean free path of the long-wavelength acoustic phonons in graphene can lead to an unusual nonmonotonic dependence of the thermal conductivity on the length L of a ribbon. The effect is pronounced for the ribbons with the smooth edges (specularity parameter p > 0.5). Our results also suggest that, contrary to what was previously thought, the bulk-like three-dimensional phonons in graphite make a rather substantial contribution to its in-plane thermal conductivity. The Umklapp-limited thermal conductivity of graphite slabs scales, for L below ∼30 μm, as log(L), while for larger L, the thermal conductivity approaches a finite value following the dependence K(0) - A × L(-1/2), where K(0) and A are parameters independent of the length. Our theoretical results clarify the scaling of the phonon thermal conductivity with the lateral sizes in graphene and graphite. The revealed anomalous dependence K(L) for the micrometer-size graphene ribbons can account for some of the discrepancy in reported experimental data for graphene.

Application of the Surface Resistance Technique to Study the Metal|Polymer Interface: A Review Article

The use of surface resistance changes as an alternative method to study the metal|polymer interface is reviewed considering both experimental and theoretical aspects. The experimental arrangement in these investigations is, in general, one in which a polymer film is supported on a thin gold film, whose thickness is of the order of the mean free path of the conduction electrons (gold film thickness, φm ∼30 nm). Particular emphasis is laid on the effects of polymer thickness, electrolyte composition, degree of oxidation, and deactivation and reactivation processes of the polymer film on the metal film conductance. Relevant experiments, where the technique was employed to study the redox site distributions at the metal|polymer interface, during oxidation, deactivation and degradation of the polymer, were specially considered. The simple scattering model to explain surface resistance changes of a thin metal film coated with a poly(o-aminophenol) film is outlined on the basis of the specularity parameter, which represents the probability of an electron being reflected specularly or diffusely at the metal film surface. Information obtained by means of surface resistance is compared with that obtained by employing more traditional techniques such as cyclic voltammetry and rotating disc electrode voltammetry. Keywords: Degree of oxidation, Metal-polymer interface, Poly(o-aminophenol) films, Scattering model, Surface Resistance

Application of the Surface Resistance Technique to Study the Metal|Polymer Interface: A Review Article

The use of surface resistance changes as an alternative method to study the metal|polymer interface is reviewed considering both experimental and theoretical aspects. The experimental arrangement in these investigations is, in general, one in which a polymer film is supported on a thin gold film, whose thickness is of the order of the mean free path of the conduction electrons (gold film thickness, φm ∼30 nm). Particular emphasis is laid on the effects of polymer thickness, electrolyte composition, degree of oxidation, and deactivation and reactivation processes of the polymer film on the metal film conductance. Relevant experiments, where the technique was employed to study the redox site distributions at the metal|polymer interface, during oxidation, deactivation and degradation of the polymer, were specially considered. The simple scattering model to explain surface resistance changes of a thin metal film coated with a poly(o-aminophenol) film is outlined on the basis of the specularity parameter, which represents the probability of an electron being reflected specularly or diffusely at the metal film surface. Information obtained by means of surface resistance is compared with that obtained by employing more traditional techniques such as cyclic voltammetry and rotating disc electrode voltammetry. Keywords: Degree of oxidation, Metal-polymer interface, Poly(o-aminophenol) films, Scattering model, Surface Resistance

Mesoscale modeling of phononic thermal conductivity of porous Si: interplay between porosity, morphology and surface roughness

In this work we compute the effective thermal conductivity of porous Si by means of the phonon Boltzmann transport equation. Simulations of heat transport across aligned square pores reveal that the thermal conductivity can be decreased either by increasing the pore size or decreasing the pore spacing. Furthermore, by including the surface specularity parameter we show that the roughness of the pore walls plays an important role when the pore size is comparable with the phonon mean free path, because to the increase in the surface-to-volume ratio. Thanks to these results, in qualitatively agreement with those obtained with Molecular Dynamics simulations, we gained insights into the scaling of thermal properties of porous materials and interplay between disorder at different length scales. The model, being based on a flexible multiscale finite element context, can be easily integrated with electrical transport models, in order to optimize the figure of merit ZT of thermoelectric devices.

Epitaxial Ag(001) grown on MgO(001) and TiN(001): Twinning, surface morphology, and electron surface scattering

Epitaxial Ag(001) layers were deposited on MgO(001) in order to study electron surface scattering. X-ray reflection indicates 3D layer nucleation with a high rms surface roughness of 1.0 nm for a layer thickness d = 3.5 nm. X-ray diffraction shows that {111} twins form at d < 11 nm, followed by 2nd generation twinning for 11 nm < d < 120 nm. Increasing the growth temperature from 25 to 150 °C suppresses 2nd generation twinning and reduces the twin density by 2 orders of magnitude. In situ deposition of epitaxial 2.5-nm-thick TiN(001) underlayers prior to Ag deposition results in twin-free single-crystal Ag(001) with 10 × smoother surfaces for d = 3.5 nm. This is attributed to a better wetting on the higher energy TiN(001) than MgO(001) surface, resulting in the absence of 3D nuclei with exposed {111} facets, which facilitate twin nucleation. The twinned Ag/MgO layers have a higher resistivity ρ than the single crystal Ag/TiN layers at both 298 and 77 K, due to electron scattering at grain and twin boundaries. The ρ for single-crystal Ag layers increases with decreasing d, which is well explained with known surface scattering models and provides specularity parameters for the Ag-vacuum and the Ag-air interfaces of p = 0.8 ± 0.1 and 0.4 ± 0.1, respectively. A comparison with corresponding epitaxial Cu(001) layers shows that ρAg < ρCu for d > 50 nm, consistent with known bulk values. However, ρAg > ρCu for d < 40 nm. This is attributed to the larger electron mean free path for electron-phonon scattering and a correspondingly higher resistivity contribution from surface scattering in Ag than Cu. In contrast, air exposure causes ρAg < ρCu for all d, due to diffuse scattering at the oxidized Cu surface and the correspondingly higher Cu resistivity.

Ocular Biocompatibility of Nitinol Intraocular Clips

To evaluate the tolerance and biocompatibility of a preformed nitinol intraocular clip in an animal model after anterior segment surgery. Yucatan mini-pigs were used. A 30-gauge prototype injector was used to attach a shape memory nitinol clip to the iris of five pigs. Another five eyes received conventional polypropylene suture with a modified Seipser slip knot. The authors compared the surgical time of each technique. All eyes underwent standard full-field electroretinogram at baseline and 8 weeks after surgery. The animals were euthanized and eyes collected for histologic analysis after 70 days (10 weeks) postsurgery. The corneal thickness, corneal endothelial cell counts, specular microscopy parameters, retina cell counts, and electroretinogram parameters were compared between the groups. A two sample t-test for means and a P value of 0.05 were use for assessing statistical differences between measurements. The injection of the nitinol clip was 15 times faster than conventional suturing. There were no statistical differences between the groups for corneal thickness, endothelial cell counts, specular microscopy parameters, retina cell counts, and electroretinogram measurements. The nitinol clip prototype is well tolerated and showed no evidence of toxicity in the short-term. The injectable delivery system was faster and technically less challenging than conventional suture techniques.

AppGen

We present AppGen , an interactive system for modeling materials from a single image. Given a texture image of a nearly planar surface lit with directional lighting, our system models the detailed spatially-varying reflectance properties (diffuse, specular and roughness) and surface normal variations with minimal user interaction. We ask users to indicate global shading and reflectance information by roughly marking the image with a few user strokes, while our system assigns reflectance properties and normals to each pixel. We first interactively decompose the input image into the product of a diffuse albedo map and a shading map. A two-scale normal reconstruction algorithm is then introduced to recover the normal variations from the shading map and preserve the geometric features at different scales. We finally assign the specular parameters to each pixel guided by user strokes and the diffuse albedo. Our system generates convincing results within minutes of interaction and works well for a variety of material types that exhibit different reflectance and normal variations, including natural surfaces and man-made ones.

Epitaxial TiN(001) wetting layer for growth of thin single-crystal Cu(001)

Single-crystal Cu(001) layers, 4-1400 nm thick, were deposited on MgO(001) with and without a 2.5-nm-thick TiN(001) buffer layer. X-ray diffraction and reflection indicate that the TiN(001) surface suppresses Cu-dewetting, yielding a 4 × lower defect density and a 9 × smaller surface roughness than if grown on MgO(001) at 25 °C. In situ and low temperature electron transport measurements indicate that ultra-thin (4 nm) Cu(001) remains continuous and exhibits partial specular scattering at the Cu-vacuum boundary with a Fuchs-Sondheimer specularity parameter p = 0.6 ± 0.2, suggesting that the use of epitaxial wetting layers is a promising approach to create low-resistivity single-crystal Cu nanoelectronic interconnects.

複数光源イメージスキャナによる形状，色および光沢の推定

複数光源イメージスキャナによる形状，色および光沢の推定

Electronic Transport Properties and Growth Mechanisms of Ni-Fe/Au/Co/Au Multilayers from In Situ Conduction Measurements

In the following we present the role of surface scattering at Au/Co and Au/Ni–Fe interfaces in Ni–Fe/Au/Co/Au multilayers deposited in different temperatures. Specularity parameter, which describes the electron scattering, is calculated from fitting in situ collected conductance data with the Fuchs–Namba– Tesanovic model. Application of the parallel resistors model enabled to depict changes between Au/Co and Au/Ni–Fe interfaces within multilayers for each repetition. The correlation between enhanced grain boundary scattering for higher deposition temperatures and surface roughness of Ni–Fe/Au/Co/Au multilayers is found.

Effect of O2 adsorption on electron scattering at Cu(001) surfaces

The electrical resistance of epitaxial Cu(001) sequentially increases, decreases, and again increases when exposed to 10−3–105 Pa s of O2. This is attributed to partial specular surface scattering for smooth clean Cu(001) and for the surface with a complete adsorbed monolayer, but diffuse scattering at partial coverage and after chemical oxidation. A model relates the surface coverage to the specularity parameter and finds adatom and advacancy scattering cross-sections of 0.8±0.2 and 0.06±0.03 nm2, which are qualitatively validated by nonequilibrium ab initio transport simulations. The rates for resistance change are proportional to the O2 partial pressure.

Thermoelectric and structural characterizations of individual electrodeposited bismuth telluride nanowires

The thermoelectric properties and crystal structure of individual electrodeposited bismuth telluride nanowires (NWs) were characterized using a microfabricated measurement device and transmission electron microscopy. Annealing in hydrogen was used to obtain electrical contact between the NW and the supporting Pt electrodes. By fitting the measured Seebeck coefficient with a two-band model, the NW samples were determined to be highly n-type doped. Higher thermal conductivity and electrical conductivity were observed in a 52 nm diameter monocrystalline NW than a 55 nm diameter polycrystalline NW. The electron mobility of the monocrystalline NW was found to be about 19% lower than that of bulk crystal at a similar carrier concentration and about 2.5 times higher than that of the polycrystalline NW. The specularity parameter for electron scattering by the NW surface was determined to be about 0.7 and partially specular and partially diffuse, leading to a reduction in the electron mean-free path from 61 nm in the bulk to about 40 nm in the 52 nm NW. Because of the already short phonon mean-free path of about 3 nm in bulk bismuth telluride, diffuse phonon-surface scattering is expected to reduce the lattice thermal conductivity of the 52–55 nm diameter NWs by only about 20%, which is smaller than the uncertainty in the extracted lattice thermal conductivity based on the measured total thermal conductivity and calculated electron thermal conductivity. Although the lattice thermal conductivity of the polycrystalline NW is likely lower than the bulk values, the lower thermal conductivity observed in this polycrystalline sample is mainly caused by the lower electron concentration and mobility. For both samples, the thermoelectric figure of merit (ZT) increases with temperature and is about 0.1 at a temperature of 400 K. The low ZT compared to that of bulk crystals is mainly caused by a high doping level, suggesting the need for better control of the chemical composition in order to improve the ZT of the electrodeposited NWs. Moreover, bismuth telluride NWs with diameter less than 10 nm would be required for substantial suppression of the lattice thermal conductivity as well as experimental verification of theoretical predictions of power factor enhancement in quantum wires. Such stringent diameter requirement can be relaxed in other NW systems with longer bulk phonon mean-free path or smaller effective mass and thus longer electron wavelength than those in bulk bismuth telluride.

Transverse acoustic impedance of normal liquid 3He with 4He coating

We measured the transverse acoustic impedance of the normal liquid 3He at 16 MHz and 10 bar with and without 4He layers plated on a wall in the temperature range of 500 to 3 mK. The real component of the impedance gradually increased with cooling in the high-temperature hydrodynamic region and saturated in the low-temperature collisionless region. In the crossover region around 20 mK, the real component had a steep increase and the imaginary component was minimum. Overall change in the temperature dependence became smaller by 4He coating and we can obtain the specularity parameter S of the wall by fitting the temperature dependence of the experimental impedance to the theory.

Accurately estimating reflectance parameters for color and gloss reproduction

A new method is described to estimate diffuse and specular reflectance parameters using spectral images, which overcomes the dynamic range limitation of imaging devices. After eliminating the influences of illumination and camera on spectral images, reflection values are initially assumed as diffuse-only reflection components, and subjected to the least squares method to estimate diffuse reflectance parameters at each wavelength on each single surface particle. Based on the dichromatic reflection model, specular reflection components are obtained, and then subjected to the least squares method to estimate specular reflectance parameters for gloss intensity and surface roughness. Experiments were carried out using both simulation data and measured spectral images. Our results demonstrate that this method is capable of estimating diffuse and specular reflectance parameters precisely for color and gloss reproduction, without requiring preprocesses such as image segmentation and synthesis of high dynamic range images.

Modeling heat transfer in Bi 2Te 3–Sb 2Te 3 nanostructures

Bi 2Te 3–Sb 2Te 3 nanostructures are gaining importance for use in thermoelectric applications following the finding that the Bi 2Te 3–Sb 2Te 3 superlattice exhibits a figure of merit, ZT = 2.4, which is higher than conventional thermoelectric materials. In this paper, thermal transport in the cross-plane direction for Bi 2Te 3–Sb 2Te 3 nanostructures is simulated using the Boltzmann transport equation (BTE) for phonon intensity. The phonon group velocity, specific heat, and relaxation time are calculated based on phonon dispersion model. The interfaces are modeled using a combination of diffuse mismatch model (DMM), and the elastic acoustic mismatch model (AMM). The thermal conductivity for the Bi 2Te 3–Sb 2Te 3 superlattice is compared with the experimental data, and the best match is obtained for specularity parameter, p, of 0.9. The present model is extended to solve for thermal transport in 2-D nanowire composite in which Sb 2Te 3 wires are embedded in a host material of Bi 2Te 3. Unlike in bulk composites, the results show a strong dependence of thermal conductivity, temperature, and heat flux on the wire size, wire atomic percentage, and interface specularity parameter. The thermal conductivity of the nanowire is found to be in the range of 0.034–0.74 depending on the atomic percentage and the value of p.

Lattice thermal conductivity of Si nanowires: Effect of modified phonon density of states

We investigate the size-dependent lattice thermal conductivity of silicon (Si) square cross-sectional and cylindrical nanowires. The calculation includes the modifications of the phonon density of states and group velocities due to phonon confinement. The decrease in phonon density of states and group velocities results in further thermal conductivity reduction in Si nanowires. By using suitable values of interface specularity parameters, the calculated thermal conductivities of Si square cross-sectional and cylindrical nanowires are found to be in good agreement with molecular dynamics and experimental results, respectively.

Phonon backscattering and thermal conductivity suppression in sawtooth nanowires

The effect of surface roughness on phonon transport in a nanowire has often been described by treating the surface as flat with a specularity parameter (p) in the range between 0 and 1. A lower thermal conductivity limit is approached at p=0 for diffuse surface. It is demonstrated here by Monte Carlo simulation that sawtooth roughness on a nanowire can cause phonon backscattering and suppress the thermal conductivity below the diffuse surface limit. The backscattering effect can be accounted for only by a negative p if the detail of the surface roughness is ignored.