Electron Trajectory Simulation Research Articles

KEEPING AN ELECTRON BEAM IN POTENTIAL WELL MAGNETIC SOLENOIDAL FIELD

An intense cylindrical magnetic field is considered in which potential well is created with the help of additional magnets. It is shown that the motion of electrons can be associated with model of three-dimensional oscillations in potential well. The results of numerical simulation of electron trajectories in gradient magnetic field with point secondary emission cathode located in the middle of the system are presented. The formation of the beam with energy of 55 keV in the radial and longitudinal directions during its transportation in solenoidal field with large gradient is considered. The operating modes of the gun are obtained, in which the particle experiences stable three-dimensional vibrations. The influence of the initial conditions during emission on the occurrence of oscillations is studied. It is shown that for the given electron energy and the fixed magnetic field, the parameter that determines the stability of particle motion is the polar angle of entry relative to the axis of the cylindrical magnetic field.

Optimizing Josephson Junction Reproducibility in 30 kV E-Beam Lithography: An Analysis of Backscattered Electron Distribution.

This paper explores methods to enhance the reproducibility of Josephson junctions, which are crucial elements in superconducting quantum technologies, when employing the Dolan technique in 30 kV e-beam processes. The study explores the influence of dose distribution along the bridge area on reproducibility, addressing challenges related to fabrication sensitivity. Experimental methods include e-beam lithography, with electron trajectory simulations shedding light on the behavior of backscattered electrons. Wedescribe the fabrication of various Josephson junction geometries and analyze the correlation between the success rates of different lithography patterns and the simulated distribution of backscattered electrons. Our findings demonstrate a success rate of up to 96.3% for the double-resist 1-step low-energy e-beam lithography process. As a means of implementation strategy, we provide a geometric example that takes advantage of simulated stability regions to administer a controlled, uniform dose across the junction area, introducing novel features to overcome the difficulties associated with fabricating bridge-like structures.

ELECTRON BEAMS IN THE GRADIENT MAGNETIC FIELD: CONTROL FOR CONVERTING LONGITUDINAL MOTION INTO TRANSVERSAL

The motion of electrons in a cylindrical magnetic field with the gradient-type potential is considered. The motion of electrons in the cylindrical magnetic field with the gradient-type potential is considered. It is found that in the selected field, the initial motion of electrons along the longitudinal axis is converted into motion along the radius. It is determined that such the transformation is due to the action of a solenoidal magnetic field with large longitudinal gradient. The transformation of the longitudinal direction of motion into the transverse one turned out to be stable in the energy range of 20...55 keV of electrons and in the range of 5...50 mm of radial dimensions of the particle beam. The main dependences of the motion of the electron beam in the given solenoidal magnetic field are studied with the help of the software tool. The results of numerical simulation of electron trajectories in the gradient magnetic field with the circular secondary emission cathode located in the middle of the system are presented. To study the mechanism of stability with respect to magnetic field, two experimentally realized magnetic fields were used. Based on these two fields, arrays of additional 4 fields are numerically synthesized. For the set of 6 named fields, the operation of the gun, in which the particle undergoes the stable transformation of the direction of motion, is numerically studied. It is shown that for the given electron energy and the fixed magnetic field, the parameter that determines the rotation of the particles is the magnetic field gradient at the boundary of the entry region. It is found that the rotation effect takes place for the considered range of radial beam sizes, which leads to particle focusing. The possibility is shown to control the vertical coordinate of the focused beam on the basis of the field adjustment, thereby giving the interpretation of the pore dependence of the registration of electrons on the detector. The dependence of the formation of the final distribution of particles on the amplitude and gradient of the magnetic field along the axis of the system is studied. The results of numerical simulation on the motion of the electron beam are presented. Based on the model of electron flow motion, the characteristics of the resulting electron beam are considered. It is shown that the beam, having radial dimensions of 5...50 mm, is transformed and focused vertically on the area of 1 mm.

Effect of Interplay between Parallel and Perpendicular Magnetic and Electric Fields on Partial Discharges

This paper reports on the influence of a magnetic field on the dynamics of partial discharges (PDs) in two distinct configurations with respect to the mutual orientation of electric fields. The broad application areas include electrical insulation systems of both high-voltage grids and industrial network devices as well as emerging segments such as electric vehicles or more electric aircraft. Traditionally, PD measurements are only carried out in an electric field. In all current-carrying power equipment, magnetic fields are also superimposed onto electric ones, thus influencing partial discharge behavior. It has been observed that the interplay between electric and magnetic fields influences the dynamics of PDs; parallel and perpendicular mutual orientations were specifically investigated. The measurement technique allowed us to quantitively detect the effect of magnetic fields on PDs in a corona point–plane arrangement. The novel element presented in this article is a detection of PD intensity modulated by a magnetic field, with both perpendicular and parallel orientations with respect to electric one, and a quantitative visualization in the form of the time-sequence diagrams. The simulation of electron trajectories in the presence of electric and magnetic fields revealed the elongation of the pathways and differentiation of the charged particle propagation times. The perpendicularly oriented magnetic field led to a twisting effect, whereas the parallel alignment reflected the propagation along a helical trajectory. A slightly stronger PD intensity amplification effect was observed in the case of a parallel alignment of electric versus magnetic fields as compared with the perpendicular orientation. The presented results may contribute to PD measurement methodology in both electric and magnetic fields as well as a better understanding of the underlying physical mechanisms. The observed effect of the modulation of the magnetically based PD dynamics may be relevant for the insulation systems of power equipment.

Development of a photoelectron spectrometer for hard x-ray photon diagnostics.

The development and characterization of an angle-resolved photoelectron spectrometer, based on the electron time-of-flight concept, for hard x-ray photon diagnostics at the European Free-Electron Laser, are described. The instrument is meant to provide users and operators with pulse-resolved, non-invasive spectral distribution diagnostics, which in the hard x-ray regime is a challenge due to the poor cross-section and high kinetic energy of photoelectrons for the available target gases. We report on the performances of this instrument as obtained using hard x-rays at the PETRA III synchrotron at DESY in multibunch mode. Results are compared with electron trajectory simulations. We demonstrate a resolving power of 10eV at incident photon energies up to at least 20keV.

Mechano-Chemical Properties of Electron Beam Irradiated Polyetheretherketone.

In this study, the mechano-chemical properties of aromatic polymer polyetheretherketone (PEEK) samples, irradiated by high energy electrons at 200 and 400 kGy doses, were investigated by Nanoindentation, Brillouin light scattering spectroscopy and Fourier-transform infrared spectroscopy (FTIR). Irradiating electrons penetrated down to a 5 mm depth inside the polymer, as shown numerically by the monte CArlo SImulation of electroN trajectory in sOlids (CASINO) method. The irradiation of PEEK samples at 200 kGy caused the enhancement of surface roughness by almost threefold. However, an increase in the irradiation dose to 400 kGy led to a decrease in the surface roughness of the sample. Most likely, this was due to the processes of erosion and melting of the sample surface induced by high dosage irradiation. It was found that electron irradiation led to a decrease of the elastic constant C11, as well as a slight decrease in the sample’s hardness, while the Young’s elastic modulus decrease was more noticeable. An intrinsic bulk property of PEEK is less radiation resistance than at its surface. The proportionality constant of Young’s modulus to indentation hardness for the pristine and irradiated samples were 0.039 and 0.038, respectively. In addition, a quasi-linear relationship between hardness and Young’s modulus was observed. The degradation of the polymer’s mechanical properties was attributed to electron irradiation-induced processes involving scission of macromolecular chains.

Simulating electron-excited energy dispersive X-ray spectra with the NIST DTSA-II open-source software platform.

NIST DTSA-II is a free, open access, and fully-documented comprehensive software platform for electron-excited X-ray microanalysis with energy dispersive spectrometry (EDS), including tools for quantification, measurement optimization, and spectrum simulation. EDS simulation utilizes a Monte Carlo electron trajectory simulation that includes characteristic and continuum X-ray generation, self-absorption, EDS window absorption, and energy-to-charge conversion leading to peak broadening. Spectra are simulated on an absolute basis considering electron dose and spectrometer parameters. Simulated and measured spectra agree within ± 25% relative for K-shell and L-shell characteristic X-ray peaks from 1 to 11 keV, while the predicted M-shell intensity was found to exceed the measured value by a factor of 1.4-2.2 from 1 to 3 keV. The X-ray continuum (bremsstrahlung) intensity agreed within ± 10% over the photon energy range from 1 to 10 keV for elements from boron to bismuth. Simulated spectra can be used to develop analytical strategy, such as assessing detection of trace constituents.

Enhancement of the ion flux to the substrate through high-voltage biasing in an electron cyclotron resonance plasma and its application to high-speed deposition of conductive carbon film

A method for enhancing ion flux to the substrate via high-voltage pulse biasing is investigated in an electron cyclotron resonance plasma. When high-voltage pulse biases above 500 V are applied to the stage, an increase in the stage current is observed, especially in the case of diverging magnetic field configurations in front of the bias stage. The growth and decay time constants of the plasma density and emission intensity are evaluated using a time-resolved Langmuir probe and emission spectroscopy while the pulse is on, and the enhancement of the ionization rate during the bias application is estimated using the zero-dimensional global model. The estimated density enhancement from the model is in good agreement with the measured one. From the numerical simulation of secondary electron trajectory, it is concluded that the electron confinement from the magnetic field is the key factor in plasma density enhancement during stage biasing. Using the high-density plasma produced by the bias voltage, conductive carbon is deposited at a high deposition rate of ∼4 nm s−1.

Analytical formalism for calculations of parameters needed for quantitative analysis by X-ray photoelectron spectroscopy

Analytical formalism for calculations of parameters needed for quantitative analysis by X-ray photoelectron spectroscopy

LONGITUDINAL TRAP OF ELECTRON BEAM IN POTENTIAL PIT MAGNETIC SOLENOIDAL FIELD

A two-mode cylindrical magnetic field is considered, the potential of which has a minimum. The object of this work is the study of the parameters of an electron beam when it moves in a solenoid field with the longitudinal trap formed by the magnetic field, and the construction of the computational model of the motion of an electron beam. The problem is posed of the stability of the motion of electrons in such solenoid magnetic field. The possibility of obtaining oscillatory modes of particle motion has been studied. It was found that for oscillations of particles with an energy of tens of kiloelectronvolts in the potential well in a well, the field with the amplitude of tens of thousands of Oersteds is required. For the solenoid magnetic field of the solenoid, the formation of electron beam with an energy of 55 keV in the longitudinal and radial directions during its transportation is studied. A section of a magnetron gun was used as the physical object. One possible direction is to combine the two matched magnetic systems of the gun to create the potential magnetic field well. It is shown that, for the chosen conditions, the motion of electrons can be associated with the model of three-dimensional oscillations. In this work, on the basis of the Hamiltonian formalism of the motion of electrons in a magnetic field and an algorithm for numerically finding solutions to the differential equations of dynamics, a software tool is constructed that allows one to obtain arrays of values of particle trajectories in the volume. The use of the software made it possible to simulate the main dependences of the motion of the electron beam in a given two-mode solenoid magnetic field. The results of numerical simulation of electron trajectories in the gradient magnetic field with the point secondary emission cathode located in the middle of the system are presented. The formation of the beam with energy of 55 keV in the radial and longitudinal directions during its transportation in a solenoid magnetic field with a large gradient is considered. For significant time intervals, the possibility of three-dimensional oscillations is shown and the operating modes of the magnetic system are obtained, in which the particle undergoes stable three-dimensional oscillations. The influence of the initial conditions during emission on the occurrence of the reciprocating oscillatory effect has been studied. It is shown that for a given electron energy and fixed magnetic field, the parameter that determines the reflection of a particle, is the polar angle of entry relative to the axis of the cylindrical magnetic field. The dependence of the formation of the final distribution of particles on the amplitude and gradient of the magnetic field along the axis of the system is investigated. The results of numerical simulation on the motion of the electron flow are presented. The characteristics of the resulting electron beam are considered on the basis of a model of electron flow motion. The obtained simulation results show that it is possible to establish the phenomenon of oscillatory-return longitudinal motion under experimental conditions.
 Keywords: electron beam, magnetron gun, three-dimensional oscillations, electron dynamics, gradient magnetic field, mathematical modeling.

High-resolution planar electron beam induced current in bulk diodes using high-energy electrons

Understanding the impact of high-energy electron radiation on device characteristics remains critical for the expanding use of semiconductor electronics in space-borne applications and other radiation harsh environments. Here, we report on in situ measurements of high-energy electron radiation effects on the hole diffusion length in low threading dislocation density homoepitaxial bulk n-GaN Schottky diodes using electron beam induced current (EBIC) in high-voltage scanning electron microscopy mode. Despite the large interaction volume in this system, quantitative EBIC imaging is possible due to the sustained collimation of the incident electron beam. This approach enables direct measurement of electron radiation effects without having to thin the specimen. Using a combination of experimental EBIC measurements and Monte Carlo simulations of electron trajectories, we determine a hole diffusion length of 264 ± 11 nm for n-GaN. Irradiation with 200 kV electron beam with an accumulated dose of 24 × 1016 electrons cm−2 led to an approximate 35% decrease in the minority carrier diffusion length.

Detection and suppression of the trapped-electrons-transportation-type flashover in a linear accelerator

The polarization energy relaxation around trapped electrons type of flashover happened in the Superconducting Demo Linac of the China Initiative Accelerator Driven Subcritical System project, which greatly limited the acceleration capability of the accelerator. This problem seriously affects the stability of accelerator operation and becoming the most urgent issue to be solved. From the reticulated and radial traces through the inner and outer conductors on the electrical aging windows of the RF couplers, the surface discharge or flashover was inferred from the pick-up couplers. The simulation of field-emission electron trajectory in the superconducting cavity and the online monitoring of the flashover signal showed that the discharge occurred by the bombardment and accumulation of field-emission electrons from the cavity. Therefore, the antenna of the pick-up coupler was redesigned and applied to the Linac. The new design removed the abnormal signal caused by discharges during more than one year operation of the cavity, thereby improving the acceleration capability and stability performance of the accelerator.

Rock adhering to cemented carbide surfaces – The role of image acquisition

In rock drilling, cemented carbide rock drill buttons are rotating and impacting the rock to crush it, and water or air is used to flush away the debris. The wear of the buttons is influenced by many factors, of which the type of rock being drilled is a major one, e.g. drilling sandstone is more severe than granite. A notable mechanism in the contact between rock and button is the transfer of rock material to the button surface, both replacing the binder in the cemented carbide and covering the surface. Whether this transfer is improving or impairing the wear resistance of the buttons can be debated. At first glance it seems granite is more prone to cover the button surface than sandstone. However, the image acquisition technique and magnification have a great influence on the measured rock coverage, and it is found to be similar between the rock types when investigated in closer detail. The connection between rock transfer and wear resistance must be more complex, if any exists. This investigation highlights the importance of understanding the acquisition technique, particularly regarding the depth sensitivity in relation to what is analysed. The depth sensitivity can be problematic if thin layers are missed. It can also give valuable information regarding the thickness of adhered layers, if different analysis techniques and settings are combined. New and improved instruments for scanning electron microscopy have made it possible to use lower acceleration voltages with high resolution and thus made the technique possible to use in a more surface sensitive mode. Varying the acceleration voltage probes the sample at different depths, thereby revealing the thickness profile of the adhered layer. Together with simulation of electron trajectories, the thickness of the adhered layer can be mapped with a method not exclusive to the samples in this work.

МОДЕЛЮВАННЯ КОЛИВАЛЬНИХ І ПОВОРОТНИХ ТРАЄКТОРІЙ ЕЛЕКТРОНІВ В ГРАДІЄНТНОМУ МАГНІТНОМУ ПОЛІ МАГНЕТРОННОЇ ГАРМАТИ

Розглянуто рух електронів в циліндричному магнітному полі зі змінною напруженістю вздовж осі поля. Використано математичні та чисельні моделі перетворення експеримегтальних даних аналітичними функціями. З метою отримання прецизійних характеристик вивчено формування пучка з енергією 55 кеВ в повздовжньому і радіальному напрямках при його транспортуванні в магнітному полі соленоїда. Показано, що руху електронів можна зіставити оптичну модель проходження світлових променів в середовищі з градієнтним коефіцієнтом, що залежить від радіуса. Побудовано програмний засіб, використання якого дало можливість промоделювати основні залежності руху електронного пучка в заданому соленоїдальному магнітному полі. Представлено результати чисельного моделювання траєкторій електронів в градієнтному магнітному полі магнетронній гармати з вторінноемісійним катодом. Розглянуто формування пучка з енергією 55 кеВ в радіальному і поздовжньому напрямках при його транспортуванні в соленоїдальному магнітному полі з великим градієнтом. Отримано режими роботи гармати, при яких частка відчуває ефект "пляшкового горлечка" і завершує свій рух поверненням в прикатодну область. Таким чином, отримані біфуркаційні режими динаміки часток при їх русі вздовж осі транспортування як вперед на мішень, так і назад в прикатодну область. Вивчено вплив початкових умов при емісії на виникнення зворотного ефекту. Показано, що при заданій енергії електрона і фіксованому магнітному полі параметром, що визначає відображення частки, є полярний кут вльоту щодо осі циліндричного магнітного поля. Досліджено залежність формування підсумкового розподілу від амплітуди і градієнта магнітного поля вздовж осі системи. Наводяться результати чисельного моделювання по руху трубчастого електронного потоку. Вивчено можливість управління поздовжньої координати точки повернення електрона. На основі моделі руху електронного потоку розглянуті характеристики результуючого електронного пучка.

Measurement of fogging electrons present in scanning electron microscope specimen chamber

The purpose of this study is (1) to quantify the influence of fogging electrons (FGEs), and (2) to find the conditions for reducing the amount in the vacuum specimen chamber of the electron beam instruments. FGEs are generated on the surface of both the specimen and objective lens electrode and flies within the working distance. When a 100 mm sized copper electrode is used as a specimen and a bias voltage of −200 to +200 V is applied to the specimen, the electron current flowing through the specimen or grounded objective lens electrode is measured with a pico-ammeter. The characteristics of FGEs can be interpreted by electron trajectory simulation. The FGE current at the specimen is minimal when the objective electrode is made of carbon, compared to when the electrode is made of aluminum, copper or stainless steel (SUS304).

Theoretical calculations of the mean escape depth of secondary electron emission from compound semiconductor materials

We have performed a systematic Monte Carlo simulation of primary and secondary electron trajectories to predicate the mean escape depth of secondary electron emission for six compound semiconductors, i.e., TiN, VN, GaAs, InAs, InSb, and PbS. Mott's cross section is used for the description of electron elastic scattering in the simulation model, and the full-Penn's dielectric function approach is adopted for the modeling of electron inelastic scattering, where the energy loss function obtained with the optical data is contributed from phonon excitation, interband transition of the loosely bound valance electrons, and inner-shell electron excitations. We have calculated the excitation depth distribution function, emission depth distribution function, and their combining effect in probability depth distribution function at different primary energies for the excited and emitted secondary electrons in these materials. The calculation leads to the primary energy dependence of mean escape depth whose values are found in the range of 0.4–1.4 nm for these materials.

The Study of Microchannel Plate Gain Using SIMION

Microchannel plates (MCP) are widely used for particle detection. The gain of chevron MCPs is related to geometrical parameters, but no study has been done through SIMION simulation. The purpose of this study is to model a chevron MCP and its secondary emission process using SIMION and determine the relationship between microchannel plate gain, voltage, channel bias angle, and diameter. Two geometry files simulated MCP electric field and shape, and a Lua program simulated secondary emission. Simulation results showed that MCP gain is proportional to voltage, angles between 5 and 15 degrees maximize gain, and gain is inversely proportional to the diameter. This study accurately simulates a chevron MCP and yields the relationship between gain, voltage, channel bias angle, and diameter. Further studies are needed to simulate electron trajectories for improved precision.

Calibration of energy slits and simulation of electron trajectories in the alpha magnet’s 3D field

At the PBP-CMU Electron Linac Laboratory, high-brightness electron beams are produced from the radio-frequency (RF) linear accelerator (linac) system that consists of a thermionic RF electron gun, an alpha magnet, a traveling-wave linac structure, quadrupole magnets and steering coils. Several diagnostic devices are installed in the accelerator system to characterize electron beam properties. In this work, we study on measurement of electron beam energy downstream the RF gun using the alpha magnet equipped with energy slits in the vacuum chamber and a current transformer. Calibration of the energy slits’ posit ions for various stepper motor encoder numbers was conducted before installing the slits in the magnet’s vacuum chamber. The calibration result was imported into the energy calculation software that links to the stepper motor encoder and the energy value will then be automatically calculated. Moreover, dynamic simulations using a software ASTRA were performed to investigate electron’s trajectories in the alpha magnet’s field with different initial electron positions and angles. The results from this study will be used to estimate the result and accuracy of energy measurement using the alpha magnet. It was found that, for different initial horizontal and vertical positions at the alpha magnet entrance, the energy of electron will be measured to be lower than its actual energy by around 0.5% and the measured energy will decrease when the initial position is moving away from the middle point. In case of horizontal particle’s angle, the error of energy measurement increases up to 1% at the angle of 3° before the beam hitting the alpha magnet chamber. For the vertical particle’s angle, the electron that has the initial angle less than or larger than 1.5° will hit the vacuum chamber.

Reducing virtual source size by using facetless electron source for high brightness

Brightness of an electron source is key for the high spatial resolution of electron microscopy and analysis. A small source size is essential for high brightness, and it has been achieved by using small crystal facets; however, the emission current is reduced when the facet area is decreased. To achieve a small source size while maintaining a large emission current, we conceived of the novel idea of a facetless electron source with a curved emission surface. Computational simulations of electron trajectories revealed that the virtual source, which is the spot at which back-projected trajectories are focused, of a facetless source was smaller than that of the conventional source with a facet and that the brightness of the facetless source was approximately four times larger. To achieve electron emission from a curved surface, we fabricated a facetless source by coating amorphous carbon on a metallic electron source. Electron emission from the coated surface showed a homogeneous pattern, which is clear evidence for emission from the curved surface of the facetless source.

Electron-Induced Effects at Diagnostics and Modification of Ferroelectrics: Mathematical Modelling, Simulation and Optimal Control

The paper is devoted to developing the theoretical basis of the mathematical modelling and computer simulation intended to analyze and control the electron beam-stimulated effects in ferroelectric materials. In order to simulate the electron beam-induced charging dynamics of ferroelectrics the modification of drift-reaction-diffusion model was proposed. The calculation was based on the numerical solution of the continuity equation and Poisson equation. The parameters of the electron irradiation doze and source function were estimated by 3D Monte-Carlo simulation of electron trajectories in the solid specimen. The computation was associated with typical ferroelectrics (LiNbO3, LiTaO3) irradiated by intermediate-energy electron bunches specified for SEM. The contribution roles of drift component as well as diffusion component during dynamic charging process were discussed. The simulation results enable us to predict charge distribution, dynamic of the potential distribution, electric field and electron beam-induced component of polarization at the given experimental parameters. These findings can be used to control polarization switching in ferroelectrics electron beam-irradiated by the SEM techniques.