投影电子束光刻中电子穿透掩膜的Monte Carlo模拟

利用基于Mott散射截面和介电函数模型的Monte Carlo方法模拟了电子穿透掩膜的能量损失分布，其计算结果与实验结果符合很好. 由此进一步计算了角度限制投影电子束光刻(SCALPEL)掩膜的穿透率和衬度，结果表明：散射体的厚度对衬度的影响较大，衬度随散射体厚度的增加而增强，而支撑体对衬度的影响较小；增大限制孔的孔径角时，透射率相应增大，但衬度会降低；衬度随入射电子的能量增加而减小. 关键词： Monte Carlo模拟 电子束光刻 掩膜     

Monte Carlo方法模拟低能电子在Al中的散射

基于文献[1]的工作,电子在固体中的弹性散射用Mott微分截面计算;非弹性散射分为单电子激发和等离子激发并由Streitwolf、Gryzinski及Quinn的截面描述.模拟了低能电子在Al块样及薄膜中的散射过程,对不同能量低能电子作用下Al的背散射系统、能谱又透射系数作了计算,结果与实验符合较好.也对背散射电子、低能损背散射电子表面分布作了计算,结果表明低能损背散射电子具有较好的空间分辨率.     

Peculiarities of elastic scattering of intermediate-energy electrons related to their capture at quasi-stationary levels of an atom in a continuous spectrum

A theoretical model of electron scattering on an atom is constructed to study elastic atomic scattering of intermediate-energy electrons. The proposed model is based upon the combined Mensing potential with two spheres of atomic electrons, which admits analytical solutions of the radial Schröbinger equation. A procedure for matching the parameters of this scatterer to an approximate electrostatic potential of an atom in the form of a screened Coulomb potential has been determined. The screening radius of the latter potential has been calculated proceeding from the properties corresponding to the Thomas-Fermi method. A model of a scatterer determined according to the aforementioned procedure can be used to calculate the energy dependence of the cross section of elastic electron scattering on some atoms with s, p, and d shells representing elements neighboring zirconium. The main result is the establishment of factors responsible for the appearance of maxima on the energy dependences of the cross section of elastic electron scattering. These maxima are related to the resonant trapping of impinging electrons by quasi-stationary levels in a continuous spectrum.     

Reflection and transmission of ballistic electrons at a potential barrier

The reflection as well as transmission of ballistic electrons at a potential barrier is studied as a function of the angle of incidence. The samples are based on high mobility two dimensional electron gases in AlGaAs/GaAs -heterostructures using split gate point contacts for collimated emission as well as detection of ballistic electron beams. The variable electrostatic barrier is formed as a depletion space charge layer by biasing a 45° tilted gate strip. An external magnetic field is used to adjust the angle of incidence. The experimental results are compared to a model for the transmission and reflection coefficients at a potential boundary.     

A New Simulation of Track Structure of Low-Energy Electrons in Liquid Water:Considering the Condensed-Phase Effect on Electron Elastic Scattering

A new Monte Carlo simulation of the trade structure of low-energy electrons(10keV) in liquid water is presented.The feature of the simulation is taken into consideration of the condensed-phase effect of liquid water on electron elastic scattering with the use of the Champion model,while the dielectric response formalism incorporating the optical-data model developed by Emfietzoglou et al.is applied for calculating the electron inelastic scattering.The spatial distributions of energy deposition and inelastic scattering events of low-energy electrons with different primary energies in liquid water are calculated and compared with other theoretical evaluations.The present work shows that the condensed-phase effect of liquid water on electron elastic scattering may be of the influence on the fraction of absorbed energy and distribution of inelastic scattering events at lower primary energies,which also indicate potential effects on the DNA damage induced by low-energy electrons.     

Tunnel barrier and noncollinear magnetization effects on shot noise in ferromagnetic/semiconductor/ferromagnetic heterojunctions

Based on the scattering approach, we investigate transport properties of electrons in a one-dimensional waveguide that contains a ferromagnetic/semiconductor/ferromagnetic heterojunction and tunnel barriers in the presence of Rashba and Dresselhaus spin-orbit interactions. We simultaneously consider significant quantum size effects, quantum coherence, Rashba and Dresselhaus spin-orbit interactions and noncollinear magnetizations. It is found that the tunnel barrier plays a decisive role in the transmission coefficient and shot noise of the ballistic spin electron transport through the heterojunction. When the small tunnel barriers are considered, the transport properties of electrons are quite different from those without tunnel barriers.     

Elastic and inelastic contributions to the auger electron appearance potential spectrum of titanium

The energy distribution of electrons contributing to the L-shell Auger electron appearance potential spectrum of a polycrystalline titanium surface has been measured. The Auger electron appearance potential spectrum is obtained by differentiating the total secondary electron yield of an electron bombarded sample as a function of incident electron energy. At the threshold for scattering from a core level the secondary yield increases. Most of the electrons contributing to this increase have energies below 30 eV, and result from secondary processes following Auger recombination of the core hole. The elastic yield decreases at the threshold, however, due to opening a new channel for inelastic scattering. A comparison of the elastic yield spectrum (DAPS), the total yield spectrum (AEAPS) and the soft X-ray yield spectrum (SXAPS), shows very similar line shapes, but differences in the relative strengths of the lines.     

Attenuation and escape depths of low-energy electron emission

Electron transport and emission is simulated by two Monte Carlo (MC) programs. The first version is based on elastic Mott cross sections and inelastic loss functions with full dispersion ΔE=ℏω(q), including electron impact and subsequent cascading processes. Surface effects like surface plasmons and the quantum mechanical surface transmittivity have been taken into account too. Especially for dielectric materials like SiO₂ and applied electric fields a second MC version is developed based on the electron scattering with acoustic and optical phonons, intra- and intervalley scattering and impact valence band ionization. A comparison of both versions results in a good agreement still in the energy region of several eV, but a predominance of the phonon-based second version is found for very low electron energies, e.g., for hot and ballistic electrons in dielectric materials.     

自旋极化电子与Xe原子的弹性碰撞

在电子与无自旋原子的弹性过程中,可认为电子是在一个向心的有效势V(r)中作相对论运动。由Slater定域近似下的相对论自洽场方法(SCF)求得该有效势。在求得有效势的基础上,采用相对论分波法,计算了极化电子与无自旋原子弹性碰撞的散射振幅,进而计算了微分截面和散射电子自旋极化参量。通过与有关的完全实验比较,明确了本文所采用理论方法的适用范围,即在E≥100eV的能量范围内,本文所用理论方法可较好地描述极化电子与无自旋原子的弹性碰撞过程。 关键词：     

Electron relaxation and transport in nanostructured and bulk silica

Processes of ballistic and hot electron relaxation in extended bulk as well as nanostructured silica have been analyzed by means of a phonon-based scattering model and respective Monte-Carlo computer simulation. Optical as well as acoustic phonons are taken into account. Trajectories of electrons and their energy attenuation in nanostructured silica are additionally affected by scattering processes at the grain boundaries between the nanoparticles, i.e. by surface phonon as well as potential scattering. Moreover, a flatter conduction band and a higher effective electron mass have been taken into account too. According to these calculations, electrons with an initial energy of several eV, but still below the valence band ionization threshold, were thermalized in 50–300 fs increasing with the silica grain size from 1 nm up to bulk material. The electron emission probabilities over the surface barrier into vacuum are extended up to depths of 60–100 nm, respectively, increasing with enhancement by an electric field.     

Ultrafast relaxation of electrons and selfconsistent electrical charging in insulators

Low energy electron scattering in insulators is described by a Monte Carlo program based on acoustic and optical phonon scattering as well as on impact ionization of valence band electrons, especially aimed to the scattering of ballistic and drifting electrons in wide gap dielectrics. There is a rapid relaxation of excited electrons within the conduction band of wide gap insulators like SiO₂ and Al₂O₃ over femtoseconds. The field-dependent transport and trapping parameters allow us to model the selfconsistent charge transport and charging-up of insulating samples during electron irradiation. The resulting spatial and time-dependent distributions of all currents j(x,t), charges ρ(x,t), the electric field F(x,t) and the potential V(x,t) are obtained and compared with experimental measurements.     

Resonance phenomena in low-energy electron scattering by planar crystalline nanostructures

Multiple scattering of low-energy electrons by a nanostructure consisting of planar crystalline films is analyzed. It is demonstrated that, at a particular ratio between the geometric and potential parameters of the system, there arise resonance states of scattered electrons in which the transmission coefficient of electrons increases drastically. Narrow transparency windows that correspond to almost complete transmission of the electron beam are formed at specific distances between the films in the resonance structure. A method for quantum-mechanical calculation of the parameters of the resonance structure is proposed.     

Mean free path of ballistic electrons in GaAs/AlGaAs superlattices

The mean free path of ballistic electrons in GaAs/AlGaAs superlattices was measured using the technique of hot electron spectroscopy in magnetic fields perpendicular to the growth direction. We utilize the fact that the total effective path of an injected hot electron is a function of the applied magnetic field. For a superlattice with 6.5 nm GaAs wells and 2.5 nm GaAlAs barriers we measure a mean free path of 80 nm. The experimental results of a ten-period SL sample are compared to a fully three-dimensional calculation of the transmission including interface roughness with island sizes of 10 nm. We demonstrate that the observed mfp is limited due to interface roughness scattering for temperatures up to 50 K.     

Electron transmission measurements of electron mean free path in supported thin films from 1–5 keV

Measurements are made of the transmission of medium energy electrons through in vacuo deposited films in order to determine the inelastic electron mean free path as a function of energy. Films of Al, Ge and Au are deposited in small increments on 20–30 Å carbon substrates supported by “holey” carbon films. The no-loss electron current is measured for each thickness as a continuous function of incident energy in the range of 1–5 keV. Although this preliminary experiment does not result in a precise separation of elastic and inelastic scattering effects, the attenuation lengths estimated are in reasonable agreement with measured and calculated in-elastic mean free paths. Elastic scattering cross sections appear to be smaller than estimated by simple theory.     

Magneto-optical studies of ballistic electron transport in single barrier heterostructures

We report an investigation of ballistic electron transport in GaAs/AlGaAs p-i-n single barrier structures with magnetic fields of up to 14T applied parallel to the tunneling direction (B//z). The energy distribution and relaxation processes of the non-equilibrium electron population injected into the p-doped collector from the Landau levels of the emitter accumulation layer are studied by means of electroluminescence (EL) spectroscopy. The observation of emitter Landau level structure in the ballistic electron EL spectra shows that the 2D to 3D tunneling process is elastic. In addition to the ballistic electron EL, cross-barrier recombination between the electron and hole accumulation layers is observed. This allows a precise determination of the initial energy distribution of the injected electrons.     

Elastic and total cross-sections for electron scattering by acetylene in the intermediate energy range

We present a joint theoretical-experimental study on electron scattering by C₂H₂ in the intermediate energy range. We report calculated elastic differential, integral, and momentum-transfer as well as total (elastic + inelastic) and absorption cross-sections at impact energies ranging from 10 to 500 eV. Also, experimental absolute elastic cross-sections are reported in the (50-500)-eV energy range. A complex optical potential is used to represent the electron-molecule interaction dynamics. The iterative Schwinger variational method, combined with the distorted-wave approximation, is used to solve the scattering equations. Experimentally, the angular distributions of the scattered electrons are converted to absolute cross-sections using the relative flow technique. The comparison of our calculated with our measured results, as well as with other experimental and theoretical data available in the literature, is encouraging.Received: 26 August 2004, Published online: 5 October 2004PACS: 34.80.Bm Elastic scattering of electrons by atoms and molecules     

Relativistic scattering calculations: On the study of surface magnetism by polarized and unpolarized electrons

A relativistic theory of elastic electron scattering, in which spin-orbit coupling and magnetic exchange interaction are both taken into account, has been applied to crystal atoms of the ferromagnets Ni, Fe and Gd. The spin-orbit- and exchange-induced scattering asymmetries obtained for polarized electrons are in good agreement with results from spin-orbit- only and exchange-only calculations. The residual deviations decrease with increasing energy. Interference effects give rise to sizeable values (up to about 4%) of a left-right scattering asymmetry for unpolarized electrons. This implies the possibility of studying surface ferromagnetism by unpolarized electron scattering.     

计算中低能量电子与水分子弹性散射微分截面

运用耦合通道光学势方法计算了在中低能量下的电子与水分子碰撞弹性散射微分截面,其中靶的极化效应被包含在一个从头算的等价局域势中.随后将计算结果与实验值和其它理论计算结果进行了比较.结果显示这种计算方法对于电子与极化分子体系碰撞是非常适用的.     

Effects of the atomic structure and interference oscillations in the electron photorecombination spectrum in a strong laser field

Electron photorecombination in the presence of a strong low-frequency laser field has been analyzed using an exactly solvable quantum model. It has been shown that interference patterns in the electron photorecombination spectrum are more sensitive to the details of the atomic potential than those in the case of other non-linear processes. For electron photorecombination on Xe⁺ ions, the manifestation of the Ramsauer effect in the cross section for the elastic scattering of slow electrons on Xe⁺ ions has been predicted in the electron photorecombination spectrum modified by the laser field.     

Multiplication of high-energy electrons in irradiated materials studied using the Boltzmann kinetic equation

Processes involved in the formation of electron collision cascades created by nonrelativistic high-energy electrons, which can develop in materials exposed to electron and gamma radiation fluxes, have been considered. The problem is solved using the Boltzmann kinetic equation for high-energy electrons moving in a medium. A model scattering indicatrix is constructed for this equation with an arbitrary potential of interaction between colliding particles. Using this scattering indicatrix, the distribution of the particle energies is obtained. Based on this energy distribution (with an arbitrary interparticle interaction potential), a cascade function is found that describes the multiplication of knock-out electrons (electron cascade) generated when a high-energy electron with a certain energy is scattered on the electron subsystem of the irradiated material. The cascade function has been calculated for the Coulomb potential of the interaction between a high-energy electron and atomic-shell electrons.