Electron Reflection Coefficient Research Articles

Effects of a radial variation of surface coefficients on plasma uniformity in capacitive RF discharges

With the increasing demands toward large area plasma etching and deposition, the radial uniformity of capacitively coupled plasmas (CCPs) becomes one of the key factors that determine process performance in industrial applications. However, there is a variety of parasitic effects, e.g. electromagnetic and electrostatic edge effects, that typically lead to the formation of nonuniform radial plasma density profiles at various discharge conditions with a density peak appearing either at the center or near the edges of the electrodes. Moreover, in commercial CCPs different surface materials are in contact with the plasma at various positions as parts of boundary surfaces such as focus rings, masks, showerhead electrodes, wall and/or target materials. Via complex material specific plasma-surface interactions, the presence of such different surface materials affects plasma uniformity in a way that is typically not understood and, thus, not controlled. In this work, aided by 2d3v graphics processing unit accelerated particle-in-cell/Monte Carlo collision simulations, we study the effects of radial variations of electrode materials on the plasma via their different ion and electron induced secondary electron emission as well as electron reflection coefficients on the discharge characteristics. Based on such fundamental understanding we tailor the radial variation of boundary surface materials to improve plasma uniformity in low pressure CCPs. Such investigations are performed at different neutral gas pressures, where both center and edge high radial plasma density profiles form in the presence of radially uniform surface coefficients that resemble the presence of a single electrode material. It is demonstrated that by radially varying the surface coefficients at the grounded electrode, the radial plasma density profile can be finely adjusted and the plasma uniformity above the wafer placed at the powered electrode can be improved in both cases.

A computationally assisted technique to measure material-specific surface coefficients in capacitively coupled plasmas based on characteristics of the ion flux-energy distribution function

We present a new method for the determination of surface coefficients, more specifically the effective ion-induced secondary electron yield, γ eff, and the effective elastic electron reflection coefficient, r eff, by means of a synergistic combination of energy-selective mass spectrometry measurements and numerical particle-in-cell/Monte Carlo collisions simulations of the ion flux-energy distribution function (IEDF) in a symmetric capacitively coupled plasma (CCP). In particular, we analyze the bimodal peak structure of the IEDF, which is caused by ions crossing the sheath without collisions. The position and width of this structure on the energy scale are defined by the time-averaged sheath potential and the ion transit time through the sheath, respectively. We find that both characteristics are differently influenced by γ eff and r eff. The ion-induced secondary electrons are accelerated in the large sheath potential and mainly influence the plasma density, sheath width and, consequently, the ion transit time and in this way the bimodal peak separation. Electron reflection from the electrodes acts mainly at times of sheath collapse, where low energy electrons can reach the surfaces. Their contribution to the plasma density increase is small, however, their longer residence time in the vicinity of the electrodes modifies the space charge density and the potential gradient. Additionally, the charge balance at the electrode requires an incident electron flux that is correlated to the flux of emitted ion induced secondary electrons and reflected electrons, which is realized by a change of the electron repelling sheath voltage. As a consequence, the electron reflection coefficient mainly influences the sheath potential and, hence, the position of the bimodal peak structure. These effects allow the simultaneous in situ determination of both surface parameters. The parameter values determined for stainless steel and Al2O3 surfaces are in good agreement with literature data. Our method opens a straightforward way of obtaining γ eff and r eff under realistic plasma conditions.

Resistivity size effect in epitaxial iridium layers

The resistivity size effect in Ir is quantified with in situ and ex situ transport measurements at 295 and 77 K using epitaxial layers with thickness d = 5–140 nm deposited on MgO(001) and Al2O3(0001) substrates. Data fitting with the Fuchs–Sondheimer model of the measured resistivity ρ vs d for single-crystal Ir(001)/MgO(001) layers deposited at Ts = 1000 °C yield an effective electron mean free path λeff = 7.4 ± 1.2 nm at 295 K, a room-temperature bulk resistivity ρo = 5.2 μΩ cm, and a temperature-independent product ρoλeff = (3.8 ± 0.6)×10−16 Ω m2, which is in good agreement with first-principles predictions. Layers deposited at Ts = 700 °C and stepwise annealed to 1000 °C exhibit a unique polycrystalline multi-domain microstructure with smooth renucleated 111-oriented grains that are >10 μm wide for d = 10 nm, resulting in a 26% lower ρoλeff. Ir(111)/Al2O3(0001) layers exhibit two 60°-rotated epitaxial domains with an average lateral grain size of 88 nm. The grain boundaries cause a thickness-independent resistivity contribution Δρgb = 0.86 ± 0.19 and 0.84 ± 0.12 μΩ cm at 295 and 77 K, indicating an electron reflection coefficient R = 0.52 ± 0.02 for this boundary characterized by a 60° rotation about the ⟨111⟩ axis. The overall results indicate that microstructural features including strain fields from misfit dislocations and/or atomic-level roughness strongly affect the resistivity size effect in Ir. The measured ρoλeff for Ir is smaller than for any other elemental metal and 69%, 43%, and 25% below reported ρoλ products for Co, Cu, and Ru, respectively, indicating that Ir is a promising alternate metal for narrow high-conductivity interconnects.

Comparison of mechanical, optical and electronic transport properties of ‎isotropic and anisotropic borophosphene

In this research, mechanical, optical and electronic transport properties of two phases of graphene-like borophosphene are investigated using density functional theory. Graphene-like borophosphene, a honeycomb structure with equal ratio of boron and phosphorus atoms, is introduced in two isotropic and anisotropic phases. For this purpose, band structure, partial density of states, Young’s modulus, Poisson ratios, dielectric function, and current-voltage characteristics are calculated and compared. The results show that the anisotropic phase of graphene-like borophosphene is semimetal and the isotropic phase is a semiconductor with a direct energy gap of 0.9 eV. Moreover, the Young’s modulus has the highest values for both phases in the zigzag and armchair directions of crystal, and the Poisson ratio has the lowest values in these two directions. Besides, optical properties of these two structures include electron energy loss spectroscopy, refractive index, extinction coefficient, optical conductivity and reflection coefficient for parallel and perpendicular polarization of electric fields respect to the sheets are computed by real and imaginary parts of dielectric function using random phase approximation. Plasmon’s energies are obtained 2.24 and 8.88 eV in the armchair direction and 9.01 eV in the zigzag direction for the anisotropic phase and for the isotropic phase, 3.38 and 9.12 eV are obtained in both directions. Both phases are transparent respect to visible light polarized in the perpendicular direction to the crystal, and the reflection and absorption are zero. Due to the selective transmission / absorption / reflection of the electromagnetic wave in the crystals, this material is suggested as a suitable candidate in the fabrication of nano optoelectronic devices. Furthermore, Ohmic behavior is observed in current-voltage characteristics of the isotropic phase after the threshold bias voltage of 0.9 V. As a result of the high Fermi velocity of charge carriers in the anisotropic phase of borophosphene ( ), this material can be used in nanoelectronic devices.

Resistivity Size Effect in Epitaxial Rh(001) and Rh(111) Layers

Rh(001) and Rh(111) layers with thickness d = 8-181 nm are sputter deposited onto MgO(001) and Al2O3(112̅0) substrates and their resistivity ρ measured in situ and ex situ at room temperature and 77 K in order to quantify the resistivity size effect. Rh(001) layers are epitaxial single crystals and show a resistivity increase with decreasing d that is well described with the classical Fuchs and Sondheimer model, indicating an effective electron mean free path λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</sub> = 9.5 ± 0.8 nm at 295 K. Rh(111) layers exhibit an epitaxial microstructure with two 60°-rotated domains with a lateral width of 19 ± 2 nm, as determined from the X-ray coherence length. The grain boundaries between the domains cause a thickness-independent resistivity contribution Δρ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gb</sub> = 0.74 and 0.59 μΩcm at 295 and 77 K, indicating an electron reflection coefficient R = 0.16 ± 0.03 for a boundary characterized by a 60° rotation about the (111) axis. Air exposure causes a nearly negligible (<; 6%) resistivity increase which suggests a possible reduction in the surface scattering specularity by Δp <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> = -0.3 ± 0.2 during surface oxidation. The overall results yield a temperature-independent product of the bulk resistivity times the electron mean free path ρ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> λ = (4.5 ± 0.4) × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-16</sup> Ωm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . This is 1.4 times larger than previously predicted from first principles, but 33%, 55%, 63%, and 11% smaller than for Cu, W, Co, and Ru, respectively, suggesting great promise for Rh as an alternative metal for narrow interconnects.

Characteristics of Ag thin films sputter deposited using Ar or Kr gas under different pressure

Recently, we found that Ag thin films with low electrical resistivity could be produced by DC sputtering using Kr gas, whose atomic mass is closer to that of Ag than Ar gas is. In contrast, sputtering using Ar caused trapping of Ar atoms in the film, leading to higher resistivity. In addition, the films sputtered using Kr gas had a much larger crystallite size than those sputtered using Ar gas. In the present study, we clarified the relation between the resistivity and crystallite size by data fitting using an equation proposed in the literature. Ag thin films with a thickness of 150 nm were deposited on glass substrates via DC magnetron sputtering in Ar or Kr gas at a pressure of 2 mTorr. The sputtering voltage was varied from 300 to 1000 V. By fitting the experimental data, we found that the model curves reproduced the experimental results for films sputtered in either Ar or Kr gas, and the electron reflection coefficient at the grain boundaries was the same for both types of film. Thus, the resistivity depends on the crystallite size, and the electron scattering behavior is basically the same for both films. Therefore, it is considered that the main reason for the lower resistivity of the film produced by sputtering in Kr is enhanced grain growth due to suppression of energetic neutral Kr bombardment of the film surface. Although it is known that the Ar gas pressure affects the characteristics of thin films, the effects of pressure have not been well investigated for Kr gas. In the present study, we examined the effect of the Kr gas pressure on the resistivity and crystallite size for sputtered Ag films. The results indicated that there was no significant effect.

Effect of high temperature annealing on resistivity and temperature coefficient of resistance of sputtered platinum thin films of SiO2/Pt/SiOx interfaces

The influence of high temperature annealing up to 800∘C on electrical resistivity and temperature coefficient of resistance of magnetron sputtered platinum films were investigated experimentally and theoretically. Highly adherent platinum films were manufactured on silicon oxide interfaces without using additional adhesion layers like titanium or tantalum. Such platinum films can be extremely useful for the fabrication of microelectromechanical sensors. X-ray diffraction studies exhibit grain sizes in the range of 39 nm for the as-deposited case to 162 nm after annealing at 800 ∘C. Thereby film resistivity values decrease from 16.8 ± 0.4 µΩ cm to 12.7 ± 0.2 µΩ cm and temperature coefficient of resistance values increase from 2180 ppm/K to 2810 ppm/K. A good accordance to the model of Mayadas and Shatzkes for resistivity as well as Tellier and Tosser for temperature coefficient of resistance could be found. The reflection coefficient for electrons at grain boundaries is extracted for both models.

The search for the most conductive metal for narrow interconnect lines

A major challenge for the continued downscaling of integrated circuits is the resistivity increase of Cu interconnect lines with decreasing dimensions. Alternative metals have the potential to mitigate this resistivity bottleneck by either (a) facilitating specular electron interface scattering and negligible grain boundary reflection or (b) a low bulk mean free path that renders resistivity scaling negligible. Recent research suggests that specular electron scattering at the interface between the interconnect metal and the liner layer requires a low density of states at the interface and in the liner (i.e., an insulating liner) and either a smooth epitaxial metal-liner interface or only weak van der Waals bonding as typical for 2D liner materials. The grain boundary contribution to the room-temperature resistivity becomes negligible if the grain size is large (&amp;gt;200 nm or ten times the linewidth for wide or narrow conductors, respectively) or if the electron reflection coefficient is small due to low-energy boundaries and electronic state matching of neighboring grains. First-principles calculations provide a list of metals (Rh, Pt, Ir, Nb, Ru, Ni, etc.) with a small product of the bulk resistivity times the bulk electron mean free path ρo × λ, which is an indicator for suppressed resistivity scaling. However, resistivity measurements on epitaxial layers indicate considerably larger experimental ρo × λ values for many metals, indicating the breakdown of the classical transport models at small (&amp;lt;10 nm) dimensions and suggesting that Ir is the most promising elemental metal for narrow high-conductivity interconnects, followed by Ru and Rh.

Dielectric function of polycrystalline gold films: Effects of grain boundary and temperature

The experimental data of the dielectric function of gold films are vital in metal optics since optical and optoelectronic properties depend sensitively on the dielectric function. Even though significant discrepancies of the dielectric function exist among the measurements in the past 60 years, the contribution of the grain boundary is less studied. In this work, we measured the dielectric function of three different gold films using two ellipsometers covering the spectral range from 200 nm to 25 μm. Based on the Drude model and the Mayadas-Shatzkes model of the electron-grain boundary scattering, we find that electronic reflection coefficient at the grain boundary is a vital factor to influence the dielectric function of the polycrystalline gold films. Furthermore, the temperature dependent dielectric function of gold is measured from 300 K to 800 K. Performing extended Drude analysis with a frequency dependent relaxation rate, we get a deviation of relaxation rate from the Fermi liquid theory at energies below 0.1 eV from 300 K to 800 K.

The Electron-Optical System of a Gyrotron with an Operating Frequency of 263 GHz for Spectroscopic Research

We describe specific features of modeling numerically the operation of magnetron-injection guns, which form high-quality helical electron beams in gyrotrons operated in the short-wave part of the millimeter-wave band (at a wavelength of 1 mm). As an example, we consider the gun of a gyrotron having an operating frequency of 263 GHz designed for spectroscopic research. It is shown that there are good reasons to perform calculations and optimization of the magnetroninjection un in two steps. At the first step, a simplest two-dimensional model can be used, which allows only for the influence of the field of the electrodes and the intrinsic space charge of the beam on the beam parameters. At the second, final stage one should allow for such factors as roughness of the emitting surface and thermal velocities of electrons. The electron distribution function in oscillatory velocities and the coefficient of electron reflection from the magnetic mirror should be calculated. It is demonstrated that the magnetron-injection gun, which is optimized by the method presented, is sufficiently universal and can be operated both at the first and second cyclotron-frequency harmonics. This opens up the possibility of developing gyrotrons for spectroscopy applications at frequencies of 263 and 526 GHz, respectively, which are required for biological and medical research.

Temperature dependent behavior of thermal conductivity of sub-5 nm Ir film: Defect-electron scattering quantified by residual thermal resistivity

By studying the temperature-dependent behavior (300 K down to 43 K) of electron thermal conductivity (κ) in a 3.2 nm-thin Ir film, we quantify the extremely confined defect-electron scatterings and isolate the intrinsic phonon-electron scattering that is shared by the bulk Ir. At low temperatures below 50 K, κ of the film has almost two orders of magnitude reduction from that of bulk Ir. The film has ∂κ/∂T &amp;gt; 0, while the bulk Ir has ∂κ/∂T &amp;lt; 0. We introduce a unified thermal resistivity (Θ = T/κ) to interpret these completely different κ ∼ T relations. It is found that the film and the bulk Ir share a very similar Θ ∼ T trend, while they have a different residual part (Θ0) at 0 K limit: Θ0 ∼ 0 for the bulk Ir, and Θ0 = 5.5 m·K2/W for the film. The Ir film and the bulk Ir have very close ∂Θ/∂T (75–290 K): 6.33 × 10−3 m K/W for the film and 7.62 × 10−3 m K/W for the bulk Ir. This strongly confirms the similar phonon-electron scattering in them. Therefore, the residual thermal resistivity provides an unprecedented way to quantitatively evaluating defect-electron scattering (Θ0) in heat conduction. Moreover, the interfacial thermal conductance across the grain boundaries is found larger than that of Al/Cu interface, and its value is proportional to temperature, largely due to the electron's specific heat. A unified interfacial thermal conductance is also defined and firmly proves this relation. Additionally, the electron reflection coefficient is found to be large (88%) and almost temperature independent.

Features of the scattering of protons and relativistic electrons intersecting a thin planar target at a small angle to its surface

The processes of scattering of protons and relativistic electrons incident on a planar target at a small angle to its surface have been simulated by the Monte Carlo method. The spatial and energy distributions of the beams of particles both passed through the target and reflected from it have been calculated. The dependence of the characteristics of beams on the initial energy and direction of injection of particles, as well as on the material and thickness of the target, has been considered. The transmission, reflection, and absorption coefficients for electrons in the target have been calculated. The initial energy in the calculations is varied in the range of 7–100 MeV and the angle between the trajectory of particles and the surface of the target is in the range of 1°–45°. The thickness of the target varies from 0.2 to 3 mm. Aluminum, iron, and copper targets have been considered. It has been shown that the intersection of targets at small angles not only increases the transverse dimensions of a beam, but also changes the direction of its motion. The results of the reported calculations of the scattering of relativistic electrons intersecting a foil at small angles to its surface are in qualitative agreement with experimental data.

Effect of size quantization of the reflection coefficient of an electron beam incident on a thin heteroepitaxial film

The effect of size quantization of the reflection coefficient of electrons incident on a thin single-crystal film located on a substrate has been theoretically predicted. Two methods for observing this effect experimentally are proposed. In the first method, the variation in the intensity of the beam of specularly reflected electrons can be measured by varying the small glancing angle α of the electron beam with a particle energy on the order of 10 keV. In the second method, intensity oscillations of the diffracted beam as a function of the variation in the reflection angle β are measured in the case of a small fixed glancing angle α (on the order of 1°–3°). Thus, the second variant corresponds to studying the intensity distribution along streaks (reflexes) in the case of electron diffraction on a smooth surface. In the second case, the appearance of elastically scattered electrons along the streaks between diffraction reflexes is predicted. Their number (the beam intensity) varies periodically as a function of the angle β.

Improvement of the helical electron beam quality and the gyrotron efficiency by controlling the electric field distribution near a magnetron injection gun

A technique for controlling the electric field distribution near the cathode of a magnetron injection gun is developed. The feasibility of improving the quality of a helical electron beam by optimizing the electric field distribution in a pulsed 4-mm-wave gyrotron is studied theoretically and experimentally. Field distributions are obtained that minimize the electron velocity spread in the beam, coefficient of electron reflection from a magnetic mirror, and intensity of parasitic low-frequency oscillations. It is demonstrated that the gyrotron efficiency can be increased through a rise in the beam quality at the optimized electric field distribution.

General R-matrix approach for integrating the multiband [formula omitted] equation in layered semiconductor structures

A Fortran 90 code is provided for calculating the electron reflection and transmission coefficients in semiconductor heterostructures within the 14-band k ⋅ p approximation. The code may easily be adapted for use with any k ⋅ p model, including magnetic field and/or strain effects, for example. Numerical instability, which is problematic in type-II systems due to the simultaneous presence of propagating and evanescent states, is reduced by developing a novel log-derivative R-matrix approach based on the Jost solution to the k ⋅ p equation. Program summary Program title: multiband-kp Catalogue identifier: AEKG_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEKG_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 7088 No. of bytes in distributed program, including test data, etc.: 90 237 Distribution format: tar.gz Programming language: Fortran 90 Computer: HP 128-node cluster (8 Intel 3.0 GHz Xeon processors per node) Operating system: RedHat Enterprise Linux 5.1 RAM: 11 MB Classification: 7.3, 7.9 External routines: LAPACK [1], ODE [2] Nature of problem: Calculating the electron transmission (or reflection) coefficient for single, double or multiple semiconductor quantum wells. Solution method: Makes use of a log-derivative reflection matrix approach which is based on obtaining the Jost solution to the multiband envelope function k ⋅ p equation. Restrictions: Accuracy depends on the limitations of the k ⋅ p model. In this implementation a “bare” 14-band model is used. Unusual features: By default Intelʼs math-kernel-library (MKL) [3] runs in serial mode. MKL also has built in parallel matrix algorithms which can be invoked without explicit parallelization in the source code. In this case all of the 8 CPUs in one node are used by the LAPACK subroutines. Running time: The given sample output, for the transmission coefficient at 750 different energies, required 376.51 CPU seconds (less than 7 minutes on a single CPU).

Electron Scattering and Electrical Conductance in Polycrystalline Metallic Films and Wires: Impact of Grain Boundary Scattering Related to Melting Point

For electrical conductance in polycrystalline metallic films and wires, the reflection coefficient of electrons at grain boundaries is explored and found to be proportional to the square root of the melting points of metals. As validated by available experimental results, this exploration enables classical models to take an essential role in theoretically predicting the electrical conductance of low-dimensional metals. One thus sees that the mechanism dominating the suppression of electrical conductance is transformed from the surface scattering into the grain boundary scattering as the ratio of film thickness (or wire diameter) to grain size rises. Furthermore, the impact of grain boundary scattering becomes less important for metals with lower melting points.

Effects of anisotropy and spin-asymmetry of ferromagnetic materials in ferromagnetic/Cr2O3/ferromagnetic trilayers

Strong effects of ferromagnetic (FM) materials on the exchange coupling are observed at different temperatures in FM1(3 nm)/Cr2O3(6 nm)/FM2(10 nm) trilayers with FM≡Co, Fe, or Ni80Fe20. Changes of the anisotropy of FM and spin-asymmetry of the reflection coefficients for spin-up and spin-down electrons of FM contacted the antiferromagnetic layer influence the strength of interfacial and interlayer coupling of the trilayers. Thus, the reduction of the interfacial coupling and the enhancement of the interlayer coupling with increasing temperature result in quite different magnetic behavior of different trilayers.

Drude Relaxation Rate in Grained Gold Nanoantennas

The effect of grain boundaries on the electron relaxation rate is significant even for large area noble metal films and more so for plasmonic nanostructures. Optical spectroscopy and X-ray diffraction show a substantial improvement in plasmon resonance quality for square-particle nanoantennas after annealing due to an enlarged grain size from 22 to 40 nm and improved grain boundaries described by the electron reflection coefficient. The electron relaxation rate due to the grains is shown to decrease by a factor of 3.2.

Townsend's Secondary Ionization Coefficient of MgO Film in Ar and Electron Reflection at the Surface

Previously, a Monte Carlo simulation (MCS) was carried out to determine the Townsend's secondary ionization coefficient γ of a MgO film using the experimental values of starting voltage between the electrodes covered by the MgO film. The electrodes were mounted at the center of a chamber as a modeled plasma display panel (PDP) cell filled with Ar. The purpose of the study was to examine the effect of the energy in a nonequilibrium state of electrons on the Townsend's secondary ionization coefficient. It was confirmed that the energy nonequilibrium effect appeared and the effect strongly depended on the initial energy distribution of electrons emitted from the cathode. The values of γ considered in the nonequilibrium of electron energy were approximately 20% larger than those considered in energy equilibrium under the operating conditions of the PDP. In this study, we investigated the effect of electron reflection on both electrode surfaces on the secondary ionization coefficient and the electron transmission coefficient. The electric power injection into the gap space based on the electron transmission coefficient and the dynamic characteristics of electron flux at the anode are explained using the electron reflection coefficient obtained in our previous experiments.

Intersubband electron interaction in 1D–2D junctions

We have shown that the electron transport through junctions of one-dimensional and two-dimensional systems, as well as through quantum point contacts, is considerably affected by the interaction of electrons of different subbands. The interaction mechanism is caused by Friedel oscillations, which are produced by electrons of the closed subbands even in smooth junctions. Because of the interaction with these oscillations, electrons of the open subbands experience a backscattering. The electron reflection coefficient, which describes the backscattering, has a sharp peak at the energy equal to the Fermi energy and may be as high as about 0.1. This result allows one to explain a number of available experimental facts.