Boundary Reflection Coefficient Research Articles

The effect of phonons-surface and grain-boundary scattering on electrical properties of metallic Ag

Explain in this study, thickness has an inverse relationship with electrical resistivity and a linear relationship with Grain boundary scattering. According to the (Fuchs-Sondheier, Mayadas-Shatzkces) model, grain boundary scattering leads To an Increase in electrical Resistivity. The surface scattering Coefficient of Ag, which Fuchs-Sondheier and Mayadas-Shatzkces measured at , Ag's grain boundary reflection coefficient , which Mayadas-Shatzkces measured at , If the concentration of material has an effect on metal's electrical properties, According to this silver is a good electrical conductor and is used frequently in electrical and electronic circuits.

Annealing Effect on Temperature Coefficient of Resistance of Microflexible Thermal Shear Stress Sensor

Knowledge of wall shear stress is of primary importance in aerodynamic and hydrodynamic designs because it determines a major part of the skin friction drag. The sensitivity of microflexible thermal shear stress sensor is positively correlated with the temperature coefficient of resistance (TCR) of thermistor film, but the TCR of thermal sensor is extremely low due to the lattice defects of deposited films. A high-sensitivity microflexible thermal shear stress sensor with TCR of 5100 ppm/°C after annealing treatment is present in this letter. The annealing effect on TCR of magnetron sputtered thermistor films was investigated. The TCR increases with increasing annealing temperature and time until annealing time exceeds 6 h. The microstructural characterization indicates that of the TCR of thermistor films is dominated by electron grain boundary scattering. The TCR improvement after annealing is attributed to the growth of grain and reduction of the grain boundary reflection coefficient.

Impact of substrates on the electrical properties of thin chromium films [Online First

Objective: We studied the impact of substrates on the electrical properties of thin chromium films. Substrates may serve many purposes, such as to define orientation, to conduct electrical current in vertical devices, as a gate in transistors, etc. The thickness range of the chromium films grown on both substrates was (3.5-70) nm. Methods and materials: We used Fuchs-Sondheimer(FS) and Mayadas-Shatzkes(MS) theories to analyze electrical resistivity data for chromium(Cr) films grown on both substrates simultaneously by thermal evaporation in vacuum, under identical deposition conditions. Results and discussion: The infinitely thick film resistivity (ρ0), conduction electron mean free path(l), specularity parameter(p), scattering power of the grain boundary(α') and grain boundary reflection coefficient(R') were found to depend upon the nature of the substrate and the binding force between them and evaporated chromium atoms. The growth and microstructure of the chromium films were examined using atomic force microscopy (AFM) and scanning electron microscopy (SEM). Conclusions: Our experimental data exactly fits with the MS theory in the entire thickness range grown for the chromium films deposited on both the substrates. Examination of film structure by SEM indicated that the films consist of grains of relatively pure chromium of different sizes, and depends upon deposition conditions and parameters, which are important factors that dictate the structural properties of the films.

Impact of substrate temperature on surface and grain boundary reflection in thin chromium nanofilms

The impact of substrate temperature on surface and grain boundary reflection is studied as a function of thickness of chromium nanofilms in the range, 10-80 nm. Substrate temperature happens to be one of the important and crucial deposition parameters, which regulates many physical properties of evaporated thin films. Hence, we have deposited the chromium nanofilms at four different substrate temperatures (Ts = 22, 100, 150 & 1800C) in order to study and analyze its effect on surface and grain boundary reflections and other electrical properties. In this work a qualitative analysis of both surface and grain boundary reflections of thin chromium nanofilms with independent variation of thickness is reported. The grain boundary reflection coefficients (R) have been calculated by estimating the resistivity data of the chromium nanofilms using Mayadas-Shatzkes and Fuchs-Sondheimer models. The substrate temperature dependent resistivity of chromium films exhibit an unusual behavior.

Defect and grain boundary scattering in tungsten: A combined theoretical and experimental study

Several major electron scattering mechanisms in tungsten (W) are evaluated using a combination of first-principles density functional theory, a Non-Equilibrium Green's Function formalism, and thin film Kelvin 4-point sheet resistance measurements. The impact of grain boundary scattering is found to be roughly an order of magnitude larger than the impact of defect scattering. Ab initio simulations predict average grain boundary reflection coefficients for a number of twin grain boundaries to lie in the range r = 0.47 to r = 0.62, while experimental data can be fit to the empirical Mayadas-Schatzkes model with a comparable but slightly larger value of r = 0.69. The experimental and simulation data for grain boundary resistivity as a function of grain size show excellent agreement. These results provide crucial insights for understanding the impact of scaling of W-based contacts between active devices and back-end-of-line interconnects in next-generation semiconductor technology.

Resistivity scaling model for metals with conduction band anisotropy

It is generally understood that the resistivity of metal thin films scales with film thickness mainly due to grain boundary and boundary surface scattering. Recently, several experiments and ab initio simulations have demonstrated the impact of crystal orientation on resistivity scaling. The crystal orientation cannot be captured by the commonly used resistivity scaling models and a qualitative understanding of its impact is currently lacking. In this work, we derive a resistivity scaling model that captures grain boundary and boundary surface scattering as well as the anisotropy of the band structure. The model is applied to Cu and Ru thin films, whose conduction bands are (quasi-)isotropic and anisotropic respectively. After calibrating the anisotropy with ab initio simulations, the resistivity scaling models are compared to experimental resistivity data and a renormalization of the fitted grain boundary reflection coefficient can be identified for textured Ru.

Boundary Estimation of Boundary Parameters for Linear Hyperbolic PDEs

We propose an adaptive observer scheme to estimate boundary parameters in first-order hyperbolic systems of Partial Differential Equations (PDE). The considered systems feature an arbitrary number of states traveling in one direction and one counter-convecting state. Uncertainties in the boundary reflection coefficients and boundary additive errors are estimated relying on a pre-existing observer design and a novel Lyapunov-based adaptation law.

Fredholm alternative and solution regularity for time-periodic hyperbolic systems

This paper concerns linear first-order hyperbolic systems in one space dimension of the type $$ \partial_tu_j + a_j(x,t)\partial_xu_j + \sum\limits_{k=1}^nb_{jk}(x,t)u_k = f_j(x,t),\; x \in (0,1),\; j=1,\ldots,n, $$ with periodicity conditions in time and reflection boundary conditions in space. We state a non-resonance condition (depending on the coefficients $a_j$ and $b_{jj}$ and the boundary reflection coefficients), which implies Fredholm solvability of the problem in the space of continuous functions. Further, we state one more non-resonance condition (depending also on $\partial_ta_j$), which implies $C^1$-solution regularity. Moreover, we give examples showing that both non-resonance conditions cannot be dropped, in general. Those conditions are robust under small perturbations of the problem data. Our results work for many non-strictly hyperbolic systems, but they are new even in the case of strict hyperbolicity.

Thermal Behavior of Ag Micro/Nano Wires Formed by Low-Temperature Sintering of Ag Nanoparticles

Ag nanoparticles of 30 nm size were deposited onto a Si substrate to form Ag microwires. The nanoparticles were transformed into continuous Ag wires with low-temperature heat treatment at temperatures not higher than 200°C. The morphology, electrical properties, and interface of the sintered Ag nanoparticle wires are described. It is shown that the neck between the nanoparticles begins to form at 150°C, and obvious metallization was found at 170°C. The changes of the crystal structure of the Ag wires at different sintering temperatures were analyzed by x-ray diffractometry. The grain boundary resistance decreased as the crystal grain size increased above 130 nm. The corresponding resistivity of the microstructure is close to that of the bulk. Through the comparison between the Mayadas–Shatzkes’s model and experimental data, the range of the grain boundary reflection coefficient Г at different temperatures is obtained. This research lays the foundation for the study of nanoimprint lithography with a pseudoplastic metal nanoparticle fluid.

Consideration of isotropic scattering of radiation in the single-phase Stefan problem for the medium with semitransparent boundaries

The single-phase Stefan problem is solved by the methods of numerical design for the semitransparent gray crystalline medium with consideration of bulk isotropic scattering. Dependence of radiation scattering albedo on boundary reflection coefficient is shown. The conditions of phase process, obtained through solving the problem, allow the development of both efficient materials for heat protection and better methods of melting for the semitransparent materials, depending on the optical properties of boundaries.

The electron scattering at grain boundaries in tungsten films

The impact of electron scattering at grain boundaries in polycrystalline tungsten (W) thin films is studied with a unique approach. Two nominally 300nm-thick films, a (110)-oriented epitaxial and a (110)-textured polycrystalline W film, were prepared in identical fabrication conditions except for the substrates, i.e., Al2O3 substrate for the epitaxial film and thermally oxidized Si substrate for the polycrystalline film. The significantly larger dimension of the film thickness than the electron mean free path in W allows the contribution of surface scattering to be negligible, and the additional resistivity for the polycrystalline W film relative to the epitaxial film is attributed to grain boundary scattering. The Mayadas–Shatzkes (MS) grain boundary scattering model is employed for quantitative analyses, with the grain boundary reflection coefficient determined to be 0.42±0.02 and 0.40±0.02 at 293K and 4.2K, respectively, using the measured lateral grain size of 119±7nm. Based on the grain boundary reflection coefficient determined in this study and the surface scattering coefficient (p=0.11) of the Fuchs–Sondheimer model given elsewhere, the resistivity of W lines having line-widths less than 10nm is predicted to be lower than that of Cu lines.

Laser-pulled ultralong platinum and gold nanowires

We report the preparation and characterization of single platinum and gold nanowires with lengths up to 5 millimeters. Quartz-sealed platinum and gold nanowires are fabricated by drawing a short piece of the corresponding microwire using a highly reproducible laser pulling procedure. Bare metal nanowires are prepared by hydrofluoric (HF) acid etching of the quartz encapsulation. We show that these nanowires have cylindrical shape and taper down to an observed diameter as small as 10 nm for platinum and 40 nm for gold, yielding exceptionally high aspect ratios. X-ray diffraction (XRD) analysis indicates that both the gold and platinum nanowires exhibit a significant preference for development of the {111} crystal face in the axis normal to the nanowire length, whereas the {200} crystal face is nearly absent in this axis which is supported by Transmission Electron Microscopy (TEM) analysis. Quartz-sealed nanowires can be easily manipulated and arranged into complex patterns with an increasing number of contact points. Electrical properties of single nanowires were measured at nearly 0.5 mm lengths at room temperature. Each of the samples tested was found to have a resistivity approaching the bulk metal value and high observed current densities before wire failure. The grain boundary reflection coefficient was calculated on single laser-pulled nanowires to be R = 0.616 for gold and R = 0.259 for platinum.

(Invited) Carrier Transport through Grain Boundaries in Highly Transparent Conductive Ga-Doped ZnO Films

Polycrystalline Ga-doped ZnO films (GZO) with different thicknesses ranging from 70 to 500nm were deposited by ion plating with DC arc discharge at a glass substrate temperature of 200°C. The dominant role of grain boundary scattering in carrier transport in the films is demonstrated by varying the film thickness and grain size. With increasing film thickness, the grain size increases and alignment of the c-axis between the columnar grains is improved. A comparison of Hall mobility and optical mobility shows that for GZO films with thicknesses of above 100nm, carrier transport is mainly limited by grain boundary scattering, whereas for GZO films with thicknesses of less than 100nm, both intragrain scattering and grain boundary scattering are the mechanisms limiting carrier transport. By comparing a grain-size-effect theory with the electrical resistivity data, we obtained that grain boundary reflection coefficients deceases with increasing the grain size.

Electron scattering at surfaces and grain boundaries in Cu thin films and wires

The electron scattering at surfaces, interfaces, and grain boundaries is investigated using polycrystalline and single-crystal Cu thin films and nanowires. The experimental data is described by a Fuchs--Sondheimer (FS) and Mayadas--Shatzkes (MS) model that is extended to account for the large variation in the specific resistivity of different grain boundaries as well as distinct top and bottom surfaces with different scattering specularity $p$. Textured polycrystalline Cu(111) thin films with thickness $d$ $=$ 25--50 nm are deposited on a stack of 7.5-nm Ta on SiO${}_{2}$/Si(001). Subsequent annealing results in small-grain (SG) thin films with an average grain size $\overline{D}$ that increases from 90 to 120 nm with increasing $d$. Corresponding large-grain (LG) thin films with $\overline{D}$ $=$ 160--220 nm are obtained by depositing 100--200-nm-thick films, followed by an in-situ anneal and a subsequent etch to match the thickness of the SG samples. Nanowires are fabricated from the SG and LG thin films using a subtractive patterning process, yielding wire widths of 75--350 nm. Single-crystal and LG layers exhibit a 18--22$%$ and 10--15$%$ lower resistivity than SG layers, respectively. The resistivity decrease from SG to LG Cu nanowires is 7--9$%$. The thickness and grain size dependence of the resistivity of polycrystalline and single-crystal Cu layers is well described by an exact version of the existing FS $+$ MS model but is distinct from the commonly used approximation, which introduces an error that increases with decreasing layer thickness from 6.5$%$ for $d$ $=$ 50 nm to 17$%$ for $d$ $=$ 20 nm. The case of nanowires requires the FS $+$ MS model to be extended to account for variation in the grain boundary reflection coefficient $R$, which effectively increases the overall resistivity by, for example, 16$%$ for 50 \ifmmode\times\else\texttimes\fi{} 45 nm${}^{2}$ wires. The overall data from single and polycrystalline Cu layers and wires yields $R$ $=$ 0.25 \ifmmode\pm\else\textpm\fi{} 0.05, and $p$ $=$ 0 at Cu-air and Cu-Ta interfaces.

Electrical properties and reduced Debye temperature of polycrystalline thin gold films

The temperature-dependent electrical properties of four suspended polycrystalline thin gold films with thicknesses of 20.0, 23.0, 36.0 and 54.0 nm have been measured in the temperature range 100–310 K. The measured results show that the electrical resistivity of the films significantly increases while the corresponding temperature dependence decreases compared with bulk gold. The significantly increased electrical resistivity indicates that grain boundary scattering dominates over surface scattering in the studied films. However, fixing the Debye temperature to the bulk value will lead to an erroneous temperature dependence of resistivity. Taking into account the reduced characteristic Debye temperature along with the surface and grain boundary scattering, the electrical properties of the films can be well described in the whole temperature range. The extracted grain boundary reflection coefficient is 0.3 ± 0.03, within the range of the previous reported values, 0.1–0.45. The films' characteristic Debye temperatures decrease from the bulk value of 165 K to between 83 and 121 K and tend to increase with increasing film thickness. This tendency coincides with the previous studies on thin gold, copper, platinum, silver films or wires, and cobalt/nickel superlattices. The possible mechanism responsible for the reduced Debye temperature is phonon softening at the surfaces, grain boundaries, disorder, defects and impurities, part of which has been demonstrated in other studies.

Optical metrology of Ni and NiSi thin films used in the self-aligned silicidation process

The thickness-dependent optical properties of nickel metal and nickel monosilicide (NiSi) thin films, used for self-aligned silicidation process, were characterized using spectroscopic ellipsometry. The thickness-dependent complex dielectric function of nickel metal films is shown to be correlated with the change in Drude free electron relaxation time. The change in relaxation time can be traced to the change in grain boundary (GB) reflection coefficient and grain size. A resistivity based model was used as the complementary method to the thickness-dependent optical model to trace the change in GB reflection coefficient and grain size. After silicidation, the complex dielectric function of NiSi films exhibit non-Drude behavior due to superimposition of interband absorptions arising at lower frequencies. The Optical models of the complete film stack were refined using x-ray photoelectron spectroscopy, Rutherford backscattered spectroscopy, and x-ray reflectivity (XRR).

Causes of phase variations in the air–ice boundary reflection coefficient in the microwave range

We study phase variations in the coefficient of reflection from a flat air-ice boundary at the ice melting point. The measurements were performed by different methods at frequencies 3.3, 6, 13, and 32 GHz. The experimental data were compared with simple theoretical models. It was found that ice wettening in thin layers leads to a phase variation in the reflection coefficient by up to a few ten degrees with satisfactory agreement between the experiment and the theory. However, anomalies of the transmission properties of the samples unexplainable in terms of the model of effective dielectric permittivity of the melting layers were observed in a narrow temperature range before the ice destruction.

Factors Affecting ENSO’s Period

Abstract Accurately capturing the observed mean period of ENSO in general circulation models (GCMs) is often challenging, and it is therefore useful to understand which parameters and processes affect this period. A computationally efficient simulation-based approach is used to extract both the dominant eigenvalues and corresponding eigenvectors of the linearized model from the Zebiak–Cane intermediate-complexity model of ENSO without having to directly construct the linearization. The sensitivity of the period to a variety of parameters is examined, including atmosphere–ocean coupling, atmospheric heating parameterization, thermocline depth zonal profile, western boundary reflection coefficient, atmospheric and ocean wave speeds or Rossby radii of deformation, ocean decay time, and the strength of the annual cycle. In addition to the sensitivity information, the spatial structures of the main fields (SST, thermocline thickness, and more) that are involved in period changes are obtained to aid in the physical interpretation of the sensitivities. There are three main time lags that together compose one-half of a model ENSO period: the Rossby-plus-Kelvin wave propagation time for a wind-caused central Pacific disturbance to propagate to the western ocean and back, SST dynamics that determine the lag between eastern ocean thermocline anomalies and eastern ocean SST anomalies, and the “accumulation” lag of integrating a sufficient delayed wave signal arriving from the western ocean to cancel the eastern ocean anomalies. For any of the parameter changes considered, the eigenvector changes show that the largest contributor to the period change is from changes to the last of these three mechanisms. Physical mechanisms that affect this accumulation delay are discussed, and the case is made that any significant change to ENSO’s period is in turn likely to involve changes to this delay.

Sound propagation in two-axis underwater channel based on beam-displacement ray-mode theory

Sound propagation in a deep ocean two-axis underwater channel is often complex and difficult to simulate between surface channel and sound fixing and ranging (SOFAR) channel. The beam-displacement ray-mode (BDRM) theory is a normal mode method for propagation modeling in horizontally stratified shallow water. An improved method for computing the upper boundary reflection coefficient in the BDRM is proposed and applied to calculate the acoustic fields of a two-axis underwater channel. Transmission losses in the two-axis underwater channel are calculated in the new BDRM. The corresponding results are in good agreement with those from the Kraken code, and furthermore the computed speed of the new BDRM excels the other methods.

Analysis of the size effect in electroplated fine copper wires and a realistic assessment to model copper resistivity

The size effect in electroplated copper wires has been widely studied recently. However, there is no consensus on the role of various scattering mechanisms. Therefore, an in-depth analysis to reveal the origin of the size effect is needed. In this article, we study the resistivity of fine copper wires whose feature sizes shrink in two dimensions. It is shown that the residual resistivity (at 5 K) increases with decreasing wire width or height and the temperature-dependent resistivity slightly deviates from that of bulk copper. This is mainly attributed to surface scattering rather than grain boundary scattering. In fact, the influence of grain boundary scattering in these well annealed copper wires is relatively small. In addition, for copper wires with a constant height, a linear dependence of the copper resistivity on 1/width (w) or 1/cross-sectional area (A), namely ρ=ρic+c*∕w (or ρ=ρic+c**∕A), is derived from the classic surface and grain boundary scattering models and validated experimentally. In this simple description, the contributions of different scattering mechanisms, such as surface reflectivity, p, and grain boundary reflection coefficient, R, defect and impurity density, combine together in parameters of ρic and c* (or c**). Especially, c* is a good indicator of scattering strength, from which one can quantitatively analyze the impact of nonsurface scattering contribution with a reference slope of c*=32.14.