Electron Trajectory Simulation Research Articles

Simulation of Dynamic Charging Processes in Ferroelectrics Irradiated with SEM

The paper presents some results of the dynamic simulation of charging processes in ferroelectrics exposed to electron beam of scanning electron microscope. The proposed approach is based on the joint numerical solution of the continuity equation and Poisson equation taking into account the intrinsic radiation-induced diffusion process. The dynamic model is combined with Monte-Carlo simulation of electron trajectories in an irradiated specimen to estimate the initial charge distribution function. The evaluated charging characteristics corresponding to experimental data specified for ferroelectric TGS electron beam-irradiated crystal are also described.

Photoelectron transport in the surface region of solids: universal analytical formalism for quantitative applications of electron spectroscopies

An advanced analytical theory describing electron transport in the surface region of solids may have accuracy comparable to Monte Carlo simulations of electron trajectories, however such an approach requires knowledge of a parameter called the single scattering albedo. This parameter is material dependent and can be calculated from the elastic mean free path and transport mean free path for signal electrons. An attempt is made to derive a simple expression that accurately describes the energy dependence of single scattering albedo in a wide energy range from 50 eV to 30 keV for 78 elemental solids. For these solids and the considered energy range, the mean percentage deviations between the reference values and values calculated from the fitted function were found to be generally well below 1%; the largest value of this deviation was equal to 0.86% (europium). Calculation of the single scattering albedo with high accuracy requires only five fitted coefficients for a given element. Recommendations are also given for calculations of this parameter for compounds. Different predictive formulas expressed in terms of the single scattering albedo are briefly discussed.

Direct-write deposition and focused-electron-beam-induced purification of gold nanostructures.

Three-dimensional gold (Au) nanostructures offer promise in nanoplasmonics, biomedical applications, electrochemical sensing and as contacts for carbon-based electronics. Direct-write techniques such as focused-electron-beam-induced deposition (FEBID) can provide such precisely patterned nanostructures. Unfortunately, FEBID Au traditionally suffers from a high nonmetallic content and cannot meet the purity requirements for these applications. Here we report exceptionally pure pristine FEBID Au nanostructures comprising submicrometer-large monocrystalline Au sections. On the basis of high-resolution transmission electron microscopy results and Monte Carlo simulations of electron trajectories in the deposited nanostructures, we propose a curing mechanism that elucidates the observed phenomena. The in situ focused-electron-beam-induced curing mechanism was supported by postdeposition ex situ curing and, in combination with oxygen plasma cleaning, is utilized as a straightforward purification method for planar FEBID structures. This work paves the way for the application of FEBID Au nanostructures in a new generation of biosensors and plasmonic nanodevices.

Secondary electron flight times and tracks in the carbon foil time pick-up detector

Carbon foil time pick-up detectors used in the time-of-flight measurements of MeV energy ions have been studied in connection to time-of-flight-energy spectrometer used for heavy ion elastic recoil detection analysis. In experimental coincident TOF-E data characteristic halos are observed around light element isobars, and the origin of these halos were studied. The experimental data indicated that these halos originate from single electron events occurring before the electron multiplication in the microchannel plate. By means of electron trajectory simulations, this halo effect is explained to originate from single electron, emitted from the carbon foil, hitting the non-active area of the microchannel plate. This electron creates a secondary electron from the surface and which ends up to the microchannel plate pore, is multiplied and create now a detectable signal. Other general timing gate parameters such as wire-to-wire spacing of the grids, acceleration potential of the 1st grid and the mirror grid potential gradient were also studied in order to improve the detector performance.

Development and discharge characteristics of negative hydrogen ion source for the SKKUCY-9 cyclotron

A negative hydrogen ion source was designed and manufactured for the SKKUCY-9 cyclotron at Sungkyunkwan University. This ion source is a penning ionization gauge type source. We analyzed the electromagnetic field distribution for simulation of electron temperature, electron trajectory, and average electric field in the anode using CST Particle Studio. We applied the ion bombardment position by electric field simulation data and confirmed the thermal distribution of the cathode. The anode structure was developed using these simulation results. The penning discharge of plasma in the ion source occurred at 0.4T. This ion source operates with a hydrogen flow of 1–5cm3/min. The ignition voltage is approximately 1.7kV and the arc current varies from 0.1A to 2A. The structure of the ion source was constructed and the experimental results are in good agreement and can be useful information for the operation of a negative ion source.

On the validity of trajectory methods for calculating the transport of very low energy (

It is easily demonstrated that a trajectory picture of low energy electron transport in condensed matter is not compatible with the Heisenberg uncertainty principle. The uncertainty in the position of a low energy electron is large and may in fact be larger than an entire simulated trajectory. This might be interpreted to mean that trajectory methods are not applicable. However, this conclusion is not correct. In the present paper, the evidence for the validity of low energy electron trajectory simulation is discussed, as well as the wave aspects and quantum nature of low energy electron transport in liquids and amorphous solids.It is pointed out that the validity of a trajectory approach to low energy electron transport in a liquid or amorphous solid partly is due to its ability to reproduce the average results of coherent elastic multiple wave scattering in a randomlike medium, and moreover that this ability may be further enhanced by the presence of inelastic scattering. The resulting validity of the trajectory method may be referred to as circumstancial validity, which is of a nature different from the explicit validity of trajectory methods which are compatible with the uncertainty principle.A previous systematic analysis of the limits of circumstancial validity is revisited and discussed for the basic case of multiple elastic scattering of a particle in a random medium of point scatterers. The detailed limits of circumstancial validity are graphically demonstrated in terms of particle wavelength, average distance between scatterers and elastic mean free path. Their immediate applicability to neutron transport is noted. The approximate nature of the point scatterer model as regards electron transport is adressed. In order to obtain an extrapolation of the result of the point scatterer model, it is observed that an increasing error of the trajectory method appears together with an increased amplitude of the multiple wave scattering taking place within the medium. On the basis of this observation, an extrapolation is proposed which provides a rough estimate of the relative error of the trajectory method when applied to multiple elastic scattering of low energy electrons in real liquids or amorphous solids.

Quantum-path control and isolated-attosecond-pulse generation using H2+molecules with moving nuclei in few-cycle laser pulses

We theoretically investigate the high-order harmonic generation (HHG) and isolated-attosecond-pulse generation from a full one-dimensional (1D) model of H${}_{2}$${}^{+}$ molecule in 3-fs, 800-nm laser pulses by using numerical solutions of the non-Born-Oppenheimer time-dependent Schr\"odinger equation (TDSE). The numerical results with moving nuclei and the static nuclei are demonstrated. The harmonic spectrum from the 22nd to the cutoff becomes smooth and fewer modulations and an isolated-attosecond pulse with duration 129 as is generated when we consider the nuclear motion. We investigate the emission time of harmonics in terms of the time-frequency analysis, which shows that, with moving nuclei, the long trajectory is suppressed, and the short trajectories is enhanced. We apply the nuclear and electronic probability density and the simulation of classical electron trajectory to illustrate the physical mechanism of HHG.

Angular distribution of elastic electron backscattering from surfaces: determination of the electron inelastic mean free path

The development of analytical techniques based on measurements of electron elastic-backscattering probabilities stimulated an interest in the theoretical description of such phenomena. The most accurate and reliable theoretical models involve Monte Carlo (MC) simulations of electron trajectories in solids; however, this approach generally requires considerable computer effort. It has been shown that the performance of a modified analytical theory originally proposed by Oswald et al (1993 J. Electron Spectrosc. Relat. Phenom. 61 251), designated with the acronym OKGM, compares reasonably well with MC calculations. The MC data are usually underestimated by the OKGM model, and the mean percentage deviation, averaged over nine elements and five energies up to 5 keV, is equal to 8.8% for typical experimental configurations. However, the agreement between ratios of backscattering probabilities from MC simulations and the OKGM model agree much better due to the fact that underestimation of backscattering probability by the OMGM theory is partially cancelled. The percentage deviation between ratios from these theoretical models decreases to 3.14%. The OKGM model should then be useful for determining inelastic mean free paths (IMFPs) from measured elastic-peak intensities. The accuracy of the obtained IMFPs is comparable with IMFPs from MC simulations.

Monte Carlo Simulation of Electron Trajectory in Solid for Electron Beam Lithography

We have developed a GUI(Graphical User Interface)-based Monte Carlo simulation tool for electron beam lithography. Simulation was executed by changing initial energy, thickness of resist, and target material. We focused on penetration range, backscattering coefficient and spatial distribution of lost energy. Comparison with other theory indicates that our simulation is reliable in the 10-50keV range of the energy of the electron. It seems that backscattering coefficient is strongly affected by the kind of atoms in the target, not initial energy.

Monte Carlo study of electron-beam penetration and backscattering in multi-walled carbon nanotube materials: The effect of different scattering models

A systematic study of electron-beam penetration and backscattering in multi-walled carbon nanotube (MWCNT) materials for beam energies of ∼0.3 to 30 keV is presented based on event-by-event Monte Carlo simulation of electron trajectories using state-of-the-art scattering cross sections. The importance of different analytic approximations for computing the elastic and inelastic electron-scattering cross sections for MWCNTs is emphasized. We offer a simple parameterization for the total and differential elastic-scattering Mott cross section, using appropriate modifications to the Browning formula and the Thomas-Fermi screening parameter. A discrete-energy-loss approach to inelastic scattering based on dielectric theory is adopted using different descriptions of the differential cross section. The sensitivity of electron penetration and backscattering parameters to the underlying scattering models is examined. Our simulations confirm the recent experimental backscattering data on MWCNT forests and, in particular, the steep increase of the backscattering yield at sub-keV energies as well as the sidewalls escape effect at high-beam energies.

A graphene-based large area surface-conduction electron emission display

The fabrication and functionality of a 21cm graphene-based transverse electron emission display panel is presented. A screen-printed triode edge electron emission geometry has been developed based on chemical vapor deposited (CVD) graphene supported on vertically aligned carbon nanotubes (CNT) necessary to minimize electrostatic shielding induced by the proximal bulk substrate. Integrated ZnO tetrapod electron scatterers have been shown to increase the emission efficiency by more than 90%. Simulated electron trajectories validate the observed emission characteristics with driving voltages less than 60V. Fabricated display panels have shown real-time video capabilities that are hysteresis free (<0.2%), have extremely stable lifetimes (<3% variation over 10h continuous operation) in addition to rapid temporal responses (<1ms).

Attosecond streaking in a nano-plasmonic field

A theoretical study of the application of attosecond streaking spectroscopy to time-resolved studies of the plasmonic fields surrounding isolated, resonantly excited spherical nanoparticles is presented. A classification of the different regimes in attosecond streaking is proposed and identified in our results that are derived from Mie calculations of plasmon fields, coupled to classical electron trajectory simulations. It is shown that in an attosecond streaking experiment, the electrons are almost exclusively sensitive to the component of the field parallel to the direction in which they are detected. This allows one to probe the different components of the field individually by resolving the angle of emission of the electrons. Finally, simulations based on fields calculated by finite-difference time-domain (FDTD) are compared with the results obtained using Mie fields. The two are found to be in good agreement with each other, supporting the notion that FDTD methods can be used to reliably investigate non-spherical structures.

Study on Image Drift Induced by Charging during Observation by Scanning Electron Microscope

The mechanism of image drift in the observation of a boundary between a metal and an insulator by scanning electron microscope (SEM) is clarified by electron-trajectory simulation and experiment. In the region involving a straight boundary between a large-area metal layer and an insulating substrate, the largest image drift is expected to be observed owing to an asymmetric charging on the sample surface. The simulation result shows that a metal–insulator boundary in the SEM image shifts toward the metal part over several seconds, which is induced by a positively charged area outside of the irradiation region in the insulator part. This simulation result is confirmed to qualitatively coincide with the experimental one. In addition, we demonstrate that the direction and magnitude of the image drift can be controlled by changing the charging voltage of the insulating substrate by applying a bias voltage to the anode facing the sample surface.

Study on Image Drift Induced by Charging during Observation by Scanning Electron Microscope

The mechanism of image drift in the observation of a boundary between a metal and an insulator by scanning electron microscope (SEM) is clarified by electron-trajectory simulation and experiment. In the region involving a straight boundary between a large-area metal layer and an insulating substrate, the largest image drift is expected to be observed owing to an asymmetric charging on the sample surface. The simulation result shows that a metal–insulator boundary in the SEM image shifts toward the metal part over several seconds, which is induced by a positively charged area outside of the irradiation region in the insulator part. This simulation result is confirmed to qualitatively coincide with the experimental one. In addition, we demonstrate that the direction and magnitude of the image drift can be controlled by changing the charging voltage of the insulating substrate by applying a bias voltage to the anode facing the sample surface.

Inverse bremsstrahlung heating rate in atomic clusters irradiated by femtosecond laser pulses

In the interaction of atomic clusters with femtosecond laser pulses, nanoplasmas with high density and high temperature are created. The heating is mainly determined by inverse bremsstrahlung (IB) due to electron-ion collisions. In many approaches for the calculation of the IB heating rate such as the Born approximation, large-angle scattering events are underestimated. However, rescattering events of an electron on the same atomic ion play an important role because they increase the amount of energy exchanged between the electrons and the laser field. In noble gas plasmas, the electron-ion interaction is often considered to take place between point-like particles. For typical noble gas clusters studied in experiments, one is advised to take into account not only the screening by the surrounding plasma medium but also the inner structure of the ions what can be accomplished by the use of appropriate model potentials. In the present paper, the IB heating rate is calculated from the classical simulation of individual electron trajectories. Results are presented for xenon clusters and argon clusters with different degree of ionization. Especially for higher energies, the consideration of the ionic structure increases the heating rate compared with the scattering on point-like particles. The Born approximation, however, overestimates this effect.

Study by AES, EELS Spectroscopy of electron Irradiation on InP and InPO4/InP in comparison with Monte Carlo simulation

We give the great interest to characterise the InP and InPO4/InP submitted to electron beam irradiation owing to the Auger Electron Spectroscopy (AES) associated to both methods Electron Energy Loss Spectroscopy (EELS). The incident electron produces breaking of (In-P) chemical bonds. The electron beam even acts to stimulate oxidation of InP surface involving on the top layers. Other, the oxide InPO4 developed on InP does appear very sensitive to the irradiation due to electron beam shown by the monitoring of EELS spectra recorded versus the irradiated times of the surface. There appears a new oxide thought to be In2O3. We give the simulation methods Casino (Carlo simulation of electron trajectory in solids) for determination with accuracy the loss energy of backscattered electrons and compared with reports results have been obtained with EELS Spectroscopy. These techniques of spectroscopy alone do not be able to verify the affected depth during interaction process. So, using this simulation method, we determine the interaction of electrons in the matter.

Electric-field-direction dependent spatial distribution of electron emission along electrically biased carbon nanotubes

The spatial distribution of lateral electron emission from individual electrically biased carbon nanotubes (CNTs) along the tube axis is resolved for the first time by combining multiprobe simultaneous emission current collection and electron trajectory simulations. The spatial distribution is found to be asymmetric along the tube axis and depends on the direction of the electric field in CNTs. The average emission density of the half tube with a higher electric potential is higher than that of the other half with a lower electric potential. The electric-field-direction dependent asymmetric spatial distribution of the electron emission is absent in all pre-existing well-established mechanisms but is well explained in terms of the recently proposed phonon-assisted electron emission (PAEE). This, together with a quantitative description of experimentally measured emission currents, provides solid evidence for the validity of the PAEE mechanism. PAEE from CNTs is predicted to take place near room temperature; thus, it opens up a new and promising route for fabricating cold electron emitters with a high emission density and a low working voltage.

Measurement of surface potential of insulating film on a conductive substrate in a scanning electron microscope specimen chamber

An electrostatic force microscope system in a scanning electron microscope specimen chamber was developed to measure the surface potential of an insulator film on a conductive substrate irradiated by an electron beam. As the accelerating voltage varies with the constant beam current, the surface charges positively if the voltage is lower than 1 kV or higher than 3 kV but negatively if the voltage is between 1.1 and 2.7 kV. This positive-negative-positive potential alternation is explained by the relationship between the electron range and the film thickness, and verified by the Monte Carlo simulation of electron trajectories. By selecting the acceleration voltage as 30 kV to show less potential variation with time, the spatial potential distribution at the specimen surface is obtained, and a negative dip is observed around 50 μm from the edge of the irradiated area. The authors find that the depth of the dip increases with an increase in the electron dose, and the negative potential distribution spreads over 300 μm is obtained, which is almost 10 times larger than the primary electron range in the specimen. The characteristic variation in the distribution agrees with a hypothetically derived charge distribution obtained in a different experiment.

Experimental verification of the shape of the excitation depth distribution function for AES

In the common formalism of AES, it is assumed that the in-depth distribution of ionizations is uniform. There are experimental indications that this assumption may not be true for certain primary electron energies and solids. The term “excitation depth distribution function” (EXDDF) has been introduced to describe the distribution of ionizations at energies used in AES. This function is conceptually equivalent to the Phi-rho-z function of electron microprobe analysis (EPMA). There are, however, experimental difficulties to determine this function in particular for energies below ∼ 10 keV. In the present paper, we investigate the possibility of determining the shape of the EXDDF from the background of inelastically scattered electrons on the low energy side of the Auger electron features in the electron energy spectra. The experimentally determined EXDDFs are compared with the EXDDFs determined from Monte Carlo simulations of electron trajectories in solids. It is found that this technique is useful for the experimental determination of the EXDDF function.

Photoelectron Thermometry as a Novel Method to Measure Thermodynamic Temperature

Photoelectron spectroscopy as a practical method for measuring thermodynamic temperature is investigated. The present analysis is based on the sensitivity of the Fermi–Dirac distribution function to temperature variation, and the effect of energy resolution of the photoelectron measurements on the resulting temperature determination. A newly designed electron energy analyzer implementing an einzel lens system is presented. From simulations of electron trajectories, the energy resolution of the analyzer was estimated to be 2 meV which is sufficient to achieve an accuracy better than 1 K for the temperature range from 25 K to 300 K.