Elastic Mean Free Path Research Articles

Analysis of effect of bulk vacancy defect on secondary electron emission characteristics of Al<sub>2</sub>O<sub>3</sub>

Based on the combination of the first-principles and Monte Carlo method, the effect of vacancy defect on secondary electron characteristic of Al<sub>2</sub>O<sub>3</sub> is studied in this work. The density functional theory (DFT) calculation results show that the band structure changes when the vacancy defects exist. The existence of Al vacancy defects results in a decrease in band gap from 5.88 to 5.28 eV, and in Fermi level below the energy of the valence band maximum as well. Besides, the elastic mean free paths and inelastic mean free paths of electrons in different crystal structures are also obtained. The comparison shows that the inelastic mean free path of electrons in Al<sub>2</sub>O<sub>3</sub> with O vacancy defects is much larger than those of Al<sub>2</sub>O<sub>3</sub> without defects and Al<sub>2</sub>O<sub>3</sub> with Al vacancy defects. When the energy of electrons is smaller than 50 eV, the inelastic mean free path of electrons in Al<sub>2</sub>O<sub>3</sub> without defects is longer than that in Al<sub>2</sub>O<sub>3</sub> with Al vacancy defects. The elastic mean free path of electrons slightly increases when the vacancy defects exist, and the elastic mean free path of electrons in Al<sub>2</sub>O<sub>3</sub> with Al vacancy defects is the largest. In order to investigate the secondary electron emission characteristics under different vacancy defect ratios, an optimized Monte Carlo algorithm is proposed. When the ratio between O vacancy defect and Al vacancy defect increases, the simulation results show that the maximum value of secondary electron yield decreases with the ratio of vacancy defect increasing. The existence of O vacancy defects increases the probability of inelastic scattering of electrons, so electrons are difficult to emit from the surface. As a result, comparing with Al vacancy defect, the SEY of Al<sub>2</sub>O<sub>3</sub> decreases greatly under the same ratio of O vacancy defect.

Scattering of electrons and positrons from aluminum isonuclear series

The current study investigates the scattering of electrons and positrons from aluminum isonuclear series within the framework of the Dirac relativistic partial wave analysis. For the neutral aluminum atoms, the scattering phenomena are described by employing a short-range complex optical potential. For the ionic series, on the other hand, this potential is supplemented by the Coulomb potential. The calculations are reported for the differential cross-section, total cross-section, integrated elastic cross-section, inelastic cross-section, momentum transfer cross-section, viscosity cross-section, and total ionization cross-section over the energy range 1 eV ≤ E i ≤ 1 MeV. The Sherman function S and spin asymmetry parameters T and U are also predicted for the same scattering systems over the same energy range. In addition, for the first time, we report a systematic study of the critical minima in the differential cross sections as well as the associated maximum spin polarization points in the Sherman function. We also compute the inelastic, elastic, momentum transfer, viscosity and total mean free paths for the aforesaid scattering systems. The Coulomb glory effect, the amplification of elastic backscattering of electrons from positive ions, is examined throughout the ionic series of aluminum. A comparison of our results to the reported theoretical and experimental studies reveals a good consistency over the compared energy range. The present theoretical method is thus expected to be useful for the fast generation of accurate cross-sections needed in many areas of science, technologies, and industries.

Positron Interactions with Some Human Body Organs Using Monte Carlo Probability Method

In this study, mean free path and positron elastic-inelastic scattering are modeled for the elements hydrogen (H), carbon (C), nitrogen (N), oxygen (O), phosphorus (P), sulfur (S), chlorine (Cl), potassium (K) and iodine (I). Despite the enormous amounts of data required, the Monte Carlo (MC) method was applied, allowing for a very accurate simulation of positron interaction collisions in live cells. Here, the MC simulation of the interaction of positrons was reported with breast, liver, and thyroid at normal incidence angles, with energies ranging from 45 eV to 0.2 MeV. The model provides a straightforward analytic formula for the random sampling of positron scattering. ICRU44 was used to compile the elemental composition data. In this work, elastic cross sections (ECS) and inelastic cross-sections (ICS) for positron interaction in human tissues were studied. The elastic scattering is obtained from the Rutherford differential cross-section. Gryzinski's excitation function is used within the first-born approximation to determine the core and valence of ICS. The results are presented graphically. The ECS increases rapidly as the scattering energy approaches zero and becomes dependent on the atomic number of elements in organs. The ICS has reached a maximum value of around 100 eV. Increasing positron energy leads to an increase in the elastic and inelastic mean free paths. The simulations agree with many other studies dealing with the same parameters and conditions.

A Straightforward Method for Measuring the Elastic and Inelastic Mean Free Paths for Scattering of Fast Electrons in Technologically Important Thin-Film Oxides

A Straightforward Method for Measuring the Elastic and Inelastic Mean Free Paths for Scattering of Fast Electrons in Technologically Important Thin-Film Oxides

Elastic and inelastic mean free paths for scattering of fast electrons in thin-film oxides

Quantitative transmission electron microscopy (TEM) often requires accurate knowledge of sample thickness for determining defect density, structure factors, sample dimensions, electron beam and X-ray photons signal broadening. The most common thickness measurement is by Electron Energy Loss Spectroscopy which can be applied effectively to crystalline and amorphous materials. The drawback is that sample thickness is measured in units of Inelastic Mean Free Path (MFP) which depends on the material, the electron energy and the collection angle of the spectrometer.Furthermore, the Elastic MFP is an essential parameter for selecting optimal sample thickness to reduce dynamical scatterings, such as for short-range-order characterization of amorphous materials.Finally, the Inelastic to Elastic MFP ratio can predict the dominant mechanism for radiation damage due to the electron beam.We implement a fast and precise method for the extraction of inelastic and elastic MFP values in technologically important oxide thin films. The method relies on the crystalline Si substrate for calibration. The Inelastic MFP of Si was measured as a function of collection semi-angle (β) by combining Energy-Filtered TEM thickness maps followed by perpendicular cross-sectioning of the sample by Focused-Ion-Beam. For example, we measured a total Inelastic MFP (β∼157 mrad) in Si of 145 ± 10 nm for 200 keV electrons.The MFP of the thin oxide films is determined by their ratio at their interface with Si or SiO2. The validity of this method was verified by direct TEM observation of cross-to-cross sectioning of TEM samples. The high precision of this method was enabled mainly by implementing a wedge preparation technique, which provides large sampling areas with uniform thickness.We measured the Elastic and Inelastic Mean Free Paths for 200 keV and 80 keV electrons as a function of collection angle for: SiO2 (Thermal, CVD), low-κ SiOCH, Al2O3, TiO2, ZnO, Ta2O5 and HfO2.The measured MFP values were compared to calculations based on models of Wenzel, Malis and Iakoubovskii. These models deviate from measurements by up to 30%, especially for 80 keV electrons. Hence, we propose functional relations for the Elastic MFP and Inelastic MFP in oxides with respect to the mass density and effective atomic number, which reduce deviations by a factor of 2–3. In addition, the effects of sample cooling on the measurements and sample stability are examined.

Understanding the Exposure Process in the Extreme Ultra Violet Lithography.

Although being the optical lithography, the extreme ultraviolet (EUV) lithography with 13.5-nm wavelength is very different from the deep ultraviolet (DUV) lithography with 193-nm wavelength. Hence, the understanding of the complex detailed EUV mechanisms to cause a chemical reaction in chemically amplified resists (CARs) is required to develop EUV resists and exposure process. In this paper, for organic, metal-organic and metal-oxide resists, the electron-scattering model of exposure mechanisms needs to include the elastic and inelastic mean free paths. On top of that, Dill's parameters of DUV and EUV resisters from the photo-generated reaction are discussed to indicate the physical and chemical characteristics. For CAR and EUV resists, Dill B parameter is large than Dill A and B parameters.

Weak localization and dimensional crossover in compositionally graded AlxGa1−xN

The interaction between the itinerant carriers, lattice dynamics, and defects is a problem of long-standing fundamental interest for developing quantum theory of transport. Here, we study this interaction in the compositionally and strain-graded AlGaN heterostructures grown on AlN substrates. The results provide direct evidence that a dimensional crossover (2D–3D) occurs with increasing temperature as the dephasing scattering events reduce the coherence length. These heterostructures show a robust polarization-induced 3D electron gas and a metallic-like behavior down to liquid helium temperature. Using magnetoresistance measurements, we analyze the evolution of the interaction between charge carriers, lattice dynamics, and defects as a function of temperature. A negative longitudinal magnetoresistance emerges at low temperatures, in line with the theory of weak localization. A weak localization fit to near zero-field magneto-conductance indicates a coherence length that is larger than the elastic mean free path and film thickness (lφ>t>lel), suggesting a 2D weak localization in a three-dimensional electron gas. Our observations allow for a clear and detailed picture of two distinct localization mechanisms that affect carrier transport at low temperature.

Low-energy electron inelastic mean free path and elastic mean free path of graphene

Based on a recent experimental data of elastic transmissivity and the elastic reflectivity measured on graphene, we have performed a theoretical study on electron inelastic mean free path (IMFP) and elastic mean free path (EMFP) by an improved approximation in a classical electron trajectory framework. A hump feature, which is considered to be owing to the out-of-plane mode of the π + σ plasmon, is clearly shown in our IMFP results of multilayer graphene while it is not seen in that of monolayer graphene. The obtained EMFPs are one order of magnitude greater than previously reported results. This work shows that the classical electron trajectory framework still works for revealing the physics picture of low-energy electron interaction with graphene, even for the transverse direction of monolayer graphene, which is the thinnest material.

Inversion in a four-terminal superconducting device on the quartet line. I. Two-dimensional metal and the quartet beam splitter

In connection with the recent Harvard group experiment on graphene-based four-terminal Josephson junctions containing a grounded loop, we consider voltage biasing at opposite voltages on the quartet line and establish lowest-order perturbation theory in the tunnel amplitudes between a two-dimensional (2D) metal and four superconducting leads in the dirty limit. We present in addition general nonperturbative and nonadiabatic results. The critical current on the quartet line ${I}_{c}(\mathrm{\ensuremath{\Phi}}/{\mathrm{\ensuremath{\Phi}}}_{0})$ depends on the reduced flux $\mathrm{\ensuremath{\Phi}}/{\mathrm{\ensuremath{\Phi}}}_{0}$ via interference between the three-terminal quartets (3TQs) and the nonstandard four-terminal split quartets (4TSQs). The 4TSQs result from synchronizing two Josephson junctions by exchange of two quasiparticles ``surfing'' on the 2D quantum wake, and this mechanism is already operational at equilibrium. Perturbation theory in the tunnel amplitudes shows that the 3TQs are $\ensuremath{\pi}$-shifted but the 4TSQs are 0-shifted if the contacts have linear dimension which is large compared to the elastic mean free path. We establish the gate voltage dependence of the quartet critical current oscillations ${I}_{c}(\mathrm{\ensuremath{\Phi}}/{\mathrm{\ensuremath{\Phi}}}_{0})$. It is argued that ``observation of ${I}_{c}(0)\ensuremath{\ne}{I}_{c}(1/2)$'' implies ``evidence for the four-terminal 4TSQ'' for finite bias voltage on the quartet line and arbitrary interface transparencies. This statement relies on physically motivated approximations leading to the Ambegaokar-Baratoff-type formula for the quartet critical current-flux relation. It is concluded that the recent experiment mentioned above finds evidence for the four-terminal 4TSQ.

Impact of particle size and multiple scattering on the propagation of waves in stealthy-hyperuniform media.

Propagation of waves in materials that exhibit stealthy-hyperuniform long-range correlations is investigated. By using a modal decomposition of the field that takes multiple scattering into account at all orders, we study the impact of the concentration of particles on the transparency of such materials at low frequency. An upper frequency limit for transparency is defined that include both the particle size and the degree of stealthiness. We show that the independent scattering approximation is not relevant to calculate elastic mean free paths when wavelength becomes comparable to the size of particles. We find that transparency is very robust with regard to the degree of heterogeneity of the host random medium and the polydispersity of particles. Finally, it is shown that resonances can be used as the frequency filter.

Electron energy relaxation in disordered superconducting NbN films

We report on the inelastic-scattering rate of electrons on phonons and relaxation of electron energy studied by means of magnetoconductance, and photoresponse, respectively, in a series of strongly disordered superconducting NbN films. The studied films with thicknesses in the range from 3 to 33 nm are characterized by different Ioffe-Regel parameters but an almost constant product q_Tl(q_T is the wave vector of thermal phonons and l is the elastic mean free path of electrons). In the temperature range 14-30 K, the electron-phonon scattering rates obey temperature dependencies close to the power law 1/\tau_{e-ph} \sim T^n with the exponents n = 3.2-3.8. We found that in this temperature range \tau_{e-ph} and n of studied films vary weakly with the thickness and square resistance. At 10 K electron-phonon scattering times are in the range 11.9-17.5 ps. The data extracted from magnetoconductance measurements were used to describe the experimental photoresponse with the two-temperature model. For thick films, the photoresponse is reasonably well described without fitting parameters, however, for thinner films, the fit requires a smaller heat capacity of phonons. We attribute this finding to the reduced density of phonon states in thin films at low temperatures. We also show that the estimated Debye temperature in the studied NbN films is noticeably smaller than in bulk material.

Alternative Approach for the Determination of Mean Free Paths of Electron Scattering in Liquid Water Based on Experimental Data.

Mean free paths of low-energy electrons in liquid water are of importance for modeling many physicochemical processes, but neither theoretical predictions nor experimental results have converged for these parameters. We therefore introduce an approach to determine elastic and inelastic mean free paths (EMFP, IMFP) based on experimental data. We show that ab initio calculations of electron scattering with water clusters converge with cluster size, thus providing access to condensed-phase scattering. The results are used in Monte Carlo simulations to extract EMFP and IMFP from recent liquid-microjet experiments that determined the effective attenuation length (EAL) and the photoelectron angular distribution (PAD) following oxygen 1s-ionization of liquid water. For electron kinetic energies from 10 to 300 eV, we find that the IMFP is noticeably larger than the EAL. The EMFP is longer than that of gas-phase water and the IMFP is longer compared to latest theoretical estimations, but both EMFP and IMFP are much shorter than suggested by experimental measurements of integral cross sections for amorphous ice.

Velocity map imaging of inelastic and elastic low energy electron scattering in organic nanoparticles.

Electron transport is of fundamental importance and has application in a variety of fields. Different scattering mechanisms affect electron transport in the condensed phase; hence, it is important to comprehensively understand these mechanisms and their scattering cross sections to predict electron transport properties. Whereas electron transport is well understood for high kinetic energy (KE) electrons, there is a discrepancy in the experimental and theoretical values for the Inelastic Mean Free Path (IMFP) in the low KE regime. In this work, velocity map imaging soft X-ray photoelectron spectroscopy is applied to unsupported organic nanoparticles (squalene) to extract experimental values of inelastic and elastic mean free paths (EMFPs). The obtained data are used to calculate corresponding scattering cross sections. The data demonstrate a decrease in the IMFP and increase in the EMFP with increasing electron KE between 10 and 50 eV.

Electron beam broadening in electron-transparent samples at low electron energies.

Scanning transmission electron microscopy (STEM) at low primary electron energies has received increasing attention in recent years because knock-on damage can be avoided and high contrast for weakly scattering materials is obtained. However, the broadening of the electron beam in the sample is pronounced at low electron energies, which degrades resolution and limits the maximum specimen thickness. In this work, we have studied electron beam broadening in materials with atomic numbers Z between 10 and 32 (MgO, Si, SrTiO3 , Ge) and thicknesses up to 900 nm. Beam broadening is directly measured using a multisegmented STEM detector installed in a scanning electron microscope at electron energies between 15 and 30 keV. For experimental reasons, the electron beam diameter is defined to contain only 68% of the total intensity instead of the commonly used 90% of the total beam intensity. The measured beam diameters can be well described with calculated ones based on a recently published model by Gauvin and Rudinsky. Using the concept of anomalous diffusion the Hurst exponent H is introduced that varies between 0.5 and 1 for different scattering regimes depending on t/Λel with the specimen thickness t and the elastic mean free path length Λel . The calculations also depend on the fraction of the beam intensity that defines the electron beam diameter. A Hurst exponent H of 1 is characteristic for the ballistic scattering regime with t/Λel → 0 and can be excluded for the experimental conditions of our study with 6 ≦ t/Λel ≦ 30. We deduced H = 0.75 from measured beam diameters which is larger than H = 0.5 that is expected under diffusion conditions. The deviation towards larger H values can be rationalised by our definition of electron diameter that contains only 68% of the total beam intensity and requires therefore larger sample thicknesses before the diffusion regime is reached. Our results clearly deviate from previous analytical approaches to describe beam broadening (Goldstein etal., Reed, Williams etal., Kohl and Reimer). Measured beam diameters are compared with simulated ones, which are obtained by solving the electron transport equation. This approach is advantageous compared to the commonly used Monte Carlo simulations because it is an exact solution of the electron transport equation and requires less computer time. Simulated beam diameter agree well with the experimental data and yield H = 0.80. LAY DESCRIPTION: In scanning transmission electron microscopy (STEM), a focused electron beam is scanned over an electron-transparent sample and an image is formed by detecting the intensity of the transmitted electrons by a STEM detector. STEM resolution is ultimately limited by the electron beam diameter and can be better than 0.1nm for the best microscopes. However, the electron-beam diameter increases with increasing specimen thickness because electrons are scattered by the interaction of the specimen material and electrons. Electron scattering leads to a change of the electron propagation direction and reduces focusing of the electron beam. The associated electron-beam broadening degrades the lateral resolution of STEM and generally limits the maximum specimen thickness that can be imaged with good resolution. STEM is up to now mainly performed at high electron energies of 80 keV and above. Lower electron energies are beneficial for the study of weakly scattering and radiation-sensitive materials but electron beam broadening becomes more pronounced with decreasing electron energies. Knowledge of beam broadening is therefore particularly important for the interpretation of STEM images that are taken with low-energy electrons. In this work we have studied electron-beam broadening in different materials with thicknesses up to 900nm at low electron energies between 15 and 30keV. Beam broadening is directly measured with a newly developed technique. We compare measured beam diameters with different models on beam broadening from literature and find that only a recently published model is well suited to describe the experimental results under our experimental conditions. In addition, beam broadening is simulated by modelling electron propagation in the specimen. The simulation results agree well with the measured beam diameters.

Electronic transport through defective semiconducting carbon nanotubes

We investigate the electronic transport properties of semiconducting (m, n) carbon nanotubes (CNTs) on the mesoscopic length scale with arbitrarily distributed realistic defects. The study is done by performing quantum transport calculations based on recursive Green’s function techniques and an underlying density-functional-based tight-binding model for the description of the electronic structure. Zigzag CNTs as well as chiral CNTs of different diameter are considered. Different defects are exemplarily represented by monovacancies and divacancies. We show the energy-dependent transmission and the temperature-dependent conductance as a function of the number of defects. In the limit of many defetcs, the transport is described by strong localization. Corresponding localization lengths are calculated (energy dependent and temperature dependent) and systematically compared for a large number of CNTs. It is shown, that a distinction by (m − n)mod 3 has to be drawn in order to classify CNTs with different bandgaps. Besides this, the localization length for a given defect probability per unit cell depends linearly on the CNT diameter, but not on the CNT chirality. Finally, elastic mean free paths in the diffusive regime are computed for the limit of few defects, yielding qualitatively same statements.

Electrons and positrons elastic collisions with pyrimidine and tetrahydrofuran

The present study shows results of theoretical calculations for positrons and electrons elastic scattering from pyrimidine and tetrahydrofuran over a broad energy range. The work has been motivated by the fact that very few experimental data exist for most of the nucleobases in particular for positrons. Concerning the theoretical tool, we have made improvements on the method using the independent atom-screened additivity rule by calculating differential elastic cross sections and its integrals in a straightforward manner. Moreover, elastic scattering of electrons and positrons by atoms of the biomolecule was evaluated by means of relativistic (Dirac) partial wave analysis. Results concerning the total elastic cross sections (ECS) for electrons and positrons are shown and discussed in comparison to existing experimental and theoretical data. As central result, our electron ECS from pyrimidine and tetrahydrofuran are in good agreement with existing experimental data in the range 10 eV to 1 keV. Another important improvement concerns our data for positron; as it will be shown in the present study, our positron ECS can be considered as a correction of existing data in the literature using the independent atom screened additivity rule. Parameterization of our electron and positron total ECS, elastic mean free paths, first elastic transport cross sections and first elastic transport mean free paths are provided for pyrimidine and tetrahydrofuran in the energy range 10 eV to 100 keV.

Simulation of positron and electron elastic mean free path and diffusion angle on DNA nucleobases from 10 eV to 100 keV

Positron and electron interaction collisions in living cells are efficiently simulated by Monte Carlo (MC) codes where huge data tables are needed. Present study provides detailed results of charged particles elastic interactions needed in MC on DNA nucleobases (adenine, thymine, cytosine and guanine, deoxyribose, and phosphoric acid). Indeed, electron and positron elastic cross sections, elastic mean free paths, and elastic angular distributions P(θ) are calculated from 10 eV to 100 keV using a corrected form of the independent atom method taking into account the geometry of the biomolecule. Our calculated results are compared with theoretical data available in the literature in absence of experimental data, in particular for positron. Moreover, our numerical results are presented in analytic format modeled to be used for fast sampling in the MC simulation of elastic collisions; particularly, we provide a useful analytic expression for sampling the elastic diffusion angle. For positron collisions on adenine, the relative error between numerical and analytic elastic diffusion angles is not exceeding 2% in the energy full range 10 eV to 100 keV.

Electron-beam broadening in amorphous carbon films in low-energy scanning transmission electron microscopy

Resolution in scanning transmission electron microscopy (STEM) is ultimately limited by the diameter of the electron beam. The electron beam diameter is not only determined by the properties of the condenser lens system but also by electron scattering in the specimen which leads to electron-beam broadening and degradation of the resolution with increasing specimen thickness. In this work we introduce a new method to measure electron-beam broadening which is based on STEM imaging with a multi-segmented STEM detector. We focus on STEM at low electron energies between 10 and 30 keV and use an amorphous carbon film with known thickness as test object. The experimental results are compared with calculated beam diameters using different analytical models and Monte-Carlo simulations. We find excellent agreement of the experimental data with the recently published model by Gauvin and Rudinsky [1] for small t/λel (thickness to elastic mean free path) values which are considered in our study.

Numerical analysis of electronic conductivity in graphene with resonant adsorbates: comparison of monolayer and Bernal bilayer

We describe the electronic conductivity, as a function of the Fermi energy, in the Bernal bilayer graphene (BLG) in presence of a random distribution of vacancies that simulate resonant adsorbates. We compare it to monolayer (MLG) with the same defect concentrations. These transport properties are related to the values of fundamental length scales such as the elastic mean free path $L_{e}$, the localization length $\xi$ and the inelastic mean free path $L_{i}$. Usually the later, which reflect the effect of inelastic scattering by phonons, strongly depends on temperature $T$. In BLG an additional characteristic distance $l_1$ exists which is the typical traveling distance between two interlayer hopping events. We find that when the concentration of defects is smaller than 1\%--2\%, one has $l_1 \le L_e \ll \xi$ and the BLG has transport properties that differ from those of the MLG independently of $L_{i}(T)$. Whereas for larger concentration of defects $L_{e} < l_1 \ll \xi $, and depending on $L_{i}(T)$, the transport in the BLG can be equivalent (or not) to that of two decoupled MLG. We compare two tight-binding model Hamiltonians with and without hopping beyond the nearest neighbors.

Elastic and inelastic mean free paths of 200 keV electrons in metallic glasses

The elastic and inelastic mean free paths of three metallic glass alloys, Ni60Nb40, Pd82Si18 and Ni80P20, have been measured from focused ion beam prepared thin samples with measured thickness gradients. The elastic/inelastic mean free paths of the three alloys are 35±0.5/97±3, 26±0.5/148±3 and 40±0.5/129±2.5nm, respectively. Elastic mean free paths predicted from atomic scattering cross sections consistently underestimate the experimental data. A model based on the Wentzel atomic model was developed and the fit to available data is in much better agreement with experiments, with a maximum deviation of ~4nm. The parametrized model is thus capable of predicting the elastic mean free path for other amorphous materials. Existing models for the inelastic mean free path are not in good agreement with the experimental data.