低能电子在水中的弹性散射

基于平均散射截面概念,结合Mott截面,计算E≤10 keV范围低能电子在水中弹性散射的微分散射截面、总散射截面及弹性散射角概率分布,与应用Rutherford模型的计算结果及实验结果符合较好.在此基础上,给出一个低能电子在水中弹性散射的模拟方法,既严格可靠,又能够方便地应用于低能电子在水中径迹结构的模拟.     

Focusing of electrons reflected from a crystal with loss of energy

A study is made of the features arising in the spatial distributions of reflected electrons as a result of a focusing effect. Experiments are conducted on single-crystal Mo (100) with primary electron energies of 0.5–2 keV and detection of electrons which lose fixed amounts of energy up to 300 eV. An analysis of the data establishes the dependence of the electron focusing efficiency on the amount of energy loss. It is shown that when electrons are reflected with single losses through plasmon excitation, the magnitude of the effect is determined mainly by the average number of scattering atoms encountered by an electron along its path to the surface. When the energy losses are high, defocusing owing to multiple elastic and inelastic scattering of the electrons is found to predominate. Zh. Tekh. Fiz. 68, 128–133 (June 1998)     

低能电子致DNA链断裂的纳剂量蒙特卡罗模拟

为了对DNA损伤进行纳剂量蒙特卡罗模拟,先根据D.Emfietzoglou给出的介电响应理论和Born修正模型计算了低能电子与液态水的非弹性反应截面,在Geant4-DNA的基础上建立了纳剂量蒙特卡罗程序的物理模块,同时参照国际纳剂量蒙特卡罗程序使用的模型参数建立了纳剂量蒙特卡罗程序的前化学模块、化学模块、DNA几何模块及DNA损伤模块。利用本程序,采用H. Nikjoo给出的对电子均匀照射DNA情形的模拟方法,还模拟计算了不同能量电子均匀照射DNA所导致的DNA链断裂产额,并与已公布的实验数据进行比对,二者符合良好。     

Direct Monte Carlo simulation of scattering processes of kV electrons in aluminum; comparison of theoretical N(E) spectra with experiment

A Monte Carlo simulation of the scattering processes of kV electrons penetrating into aluminum was performed. The simulation is based on the use of different types of differential cross-sections for individual elastic and inelastic scattering: (i) Elastic scattering; the differential cross-sections derived by partial wave expansion method. (ii) Inelastic scattering; Gryzinski's excitation function for inner-shell electron excitation, Streitwolfs excitation function for conduction electron excitation, and Quinn's mean free path for plasmon excitation. For verification the energy loss spectra obtained from the Monte Carlo calculations were then compared with experiment done with commercial type Auger microprobes, JAMP-3, for angle of incidence 45° and JAMP-10 for normal incidence at primary electron energies of 1.5 and 3.0 keV, respectively. The results show satisfactory agreement between theory and experiment.     

Analytical and numerical approaches to calculating the escape function for the emission of medium-energy electrons from uniform specimens

A program for the simulation of electron transport by the Monte Carlo method has been developed. This program implies the model of single scattering and dielectric approach (to calculate the characteristics of an inelastic interaction). The escape functions for aluminum, germanium, and gold in the 0.012–20 keV energy range were calculated. The characteristic lengths determining the electron dynamics (the elastic and inelastic mean free paths, isotropization length, and integral path) were calculated using the differential cross sections for both elastic and inelastic interactions for these elements. The analysis of the relations between the characteristic lengths made it possible to determine the applicability range of the analytical expressions for the emission functions obtained in [1]. The comparison of the results obtained analytically and numerically confirmed the conclusion of [1] about the form of the analytical approximation of the emission function for electrons of various energies and showed the validity of the obtained analytical expressions for the escape lengths of electrons.     

High-resolution study of quasi-elastic electron scattering from a two-layer system

In large-angle elastic scattering events of keV electrons a significant amount of momentum is transferred from the electron to a nucleus in the target. As a consequence kinetic energy is transferred from the energetic electron to the nucleus, and hence these processes can be referred to as ‘quasi-elastic’. How much energy is transferred depends on the mass of the nucleus. In this paper, we present measurements from a two-layer system (a germanium layer and a carbon layer), and at high energies the quasi-elastic peaks of Ge and C are clearly resolved. It is demonstrated that the sample geometry has a huge effect on the observed relative intensities. It is shown that the intensities are influenced by the elastic scattering cross-section of the atoms in the film, film composition and selective attenuation, due to varying amount of inelastic scattering for layers of the film. However truly quantitative agreement is not obtained.     

Comparative analysis of characteristic electron energy loss spectra and inelastic scattering cross-section spectra of Fe

The inelastic electron scattering cross section spectra of Fe have been calculated based on experimental spectra of characteristic reflection electron energy loss as dependences of the product of the inelastic mean free path by the differential inelastic electron scattering cross section on the electron energy loss. It has been shown that the inelastic electron scattering cross-section spectra have certain advantages over the electron energy loss spectra in the analysis of the interaction of electrons with substance. The peaks of energy loss in the spectra of characteristic electron energy loss and inelastic electron scattering cross sections have been determined from the integral and differential spectra. It has been shown that the energy of the bulk plasmon is practically independent of the energy of primary electrons in the characteristic electron energy loss spectra and monotonically increases with increasing energy of primary electrons in the inelastic electron scattering cross-section spectra. The variation in the maximum energy of the inelastic electron scattering cross-section spectra is caused by the redistribution of intensities over the peaks of losses due to various excitations. The inelastic electron scattering cross-section spectra have been analyzed using the decomposition of the spectra into peaks of the energy loss. This method has been used for the quantitative estimation of the contributions from different energy loss processes to the inelastic electron scattering cross-section spectra of Fe and for the determination of the nature of the energy loss peaks.     

蒙特卡洛方法计算材料表面激发参数

电子非弹性散射平均自由程（IMFP）是用表面电子能谱进行表面化学定量分析时极为重要的一个参数,它可以用测量的弹性峰电子能谱分析以及蒙特卡洛模拟来确定.为了更加精确地确定电子非弹性散射平均自由程,必须对弹性峰电子能谱中的表面激发效应进行修正,通常使用介电响应理论方法计算得到的表面激发参数.然而,通过理论计算得到的表面激发参数不能包含电子在材料内部输运过程中弹性散射的影响,进而影响所测的电子非弹性散射平均自由程的准确度.在这个工作中,我们采用蒙特卡洛方法来确定包含弹性散射效应时的表面激发参数.所得到的表面激发参数在不同能量、角度情况下,尤其是在弹性散射效应显著的60°以上的大角度入射、出射情况下,都与实验测量值符合得非常好.基于这些新确定的表面激发参数,可以在弹性峰电子能谱测量中获得更为准确的电子非弹性散射平均自由程数据.     

Experimental confirmation of the EPES sampling depth paradox for overlayer/substrate systems

Elastic-peak electron spectroscopy (EPES) has been one of the main tools for obtaining the inelastic mean free path of electrons in solids. Recently it has become clear that, if this type of experiment is done using an energetic electron beam (20-40 keV) and large scattering angles, then the recoil energies of the elastic scattering event for different elements can be resolved. This recoil energy is mass dependent and this fact makes it possible to separate the elastic-peak contributions due to electrons scattered from light and heavy elements. Here we use this energy separation to determine experimentally the sampling depth for an overlayer/substrate system. The sampling depth for a (high-Z) Au overlayer on a (low-Z) C substrate is found to be about two orders of magnitude smaller than for a C overlayer on a Au substrate, whereas the inelastic mean free path of electrons in both materials differ much less. This effect is shown to be a consequence the strong Z dependence of the elastic scattering cross section. The dependence of the spectra on the electron kinetic energy and sample rotation is also dramatically different for both sample geometries.     

The effect of multiple electron-electron scattering on the energy distribution of electrons in a correlated pair

A unit event of electron-electron scattering in LiF layers is studied by correlation spectroscopy of scattered electrons. The energy distribution of electrons in a correlated pair when a 15-to 55-eV free electron is scattered by a valence electron of LiF is studied. It is shown that single electron-electron scattering prevails and the distribution is uniform when the energy of the primary electron is below 25 eV. As the energy of the primary electron increases, the formation of correlated pairs of electrons with equal energies becomes the most probable. With the energy of the primary electron above 40 eV, the pairs with substantially different electron energies dominate. Such evolution of the energy distribution of the electrons in the pair stems from the fact that first one and then the other electron of the pair successively takes part in electron-electron scattering. A phenomenological model for the single scattering and double scattering of primary electrons in LiF films is considered. Results obtained indicate that the strengths of single scattering and double scattering channels become comparable at electron energies above 25 eV.     

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     

Observation of interband transitions in polarized electron energy loss spectra of Gd(0001)

We have detected the 4f ⁷(5d6s)³→4f ⁸(5d6s)² interband transition in an angular-resolved, inelastic scattering experiment with spin-polarized, low-energy electrons from ferromagnetic Gd(0001). The spectrum of the inelastic scattering asymmetry clearly reveals the dominant spin-dependent energy loss mechanism involved. Furthermore its comparison with elastic scattering data allows a characterization of the combined role of diffraction and energy loss processes in inelastic electron scattering.     

Backscattered electron spectra from graphite

The backscattered electron spectra from graphite sample were studied both experimentally and theoretically at impact energies between 500 and 5000 eV. The angle of the incident electron beam was 50° and the detection angle was 0° with respect to the surface normal, respectively. Monte Carlo (MC) simulations were performed based on the Classical Transport Theory (CTT) model to mimic the experimental spectra. In our simulations, both elastic and inelastic scattering of primary electrons and secondary electron emission from graphite are taken into account. There is found satisfactory agreement between measured and calculated electron spectra.     

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.     

The influence of abrupt electric field variations on the distribution function of hot electrons

Some analytical models of quiescent hot electron distributions are extended to the transient conditions, in order to describe the response of hot electrons to step changes in the magnitude of the electric field. These models apply to semiconductors having one or several equivalent energy minima in the conduction band, and isotropic lattice scattering due to low-energy acoustic phonons (elastic in-valley scattering) and to high energy single-level acoustic phonons (inelastic inter-valley scattering) or dispersionless optical phonons (inelastic in-valley scattering). Step changes in the field magnitude are considered with respect to the time and space (one-dimensional) variables, separately. In both cases, the spherically-symmetrical term ƒ_O of the electron distribution function may be expressed using a Laguerre polynomial expansion in the energy variable. For a positive step change in field magnitude, transient electron drift velocities in excess of the steady-state “scattering-limited” values are found in both silicon and germanium.     

Separation of angular and energy relaxations of nonequilibrium electrons in a solid

We demonstrate that the collision integral of the kinetic equation for the interaction of hot electrons with phonons can be split into substantially different parts that correspond to elastic and inelastic collisions. In particular, this applies to electrons with energies of about 1 eV that propagate in semiconductors. The difference in the characteristic energy and momentum relaxation times makes it possible to separate the angular and energy relaxation processes. If the differential cross section of elastic scattering depends, not on the scattering angle, but on the directions of incident and scattered electrons (which is observed, e.g., for the interaction of an electron with piezoelectric lattice vibrations in A^IIIB^V compounds), the Laplacian in the equation that describes the spatial and energy distributions of electrons can be replaced by an elliptical operator; i.e., the electron diffusion turns out to be anisotropic.     

Effect of elastic scattering on the kinetics of mesic atom formation

The differential, total and transport elastic cross sections are calculated with an adiabatic effective (µ^––H) potential and with regard to inelastic transitions. The elastic cross section is greater than the inelastic one by an order of value in the atomic-capture energy region. The excess increases with particle mass. The effect of the elastic scattering on the energy distribution of Coulomb capture is considered within the approximation of continuous elastic energy losses. An appreciable increase of the capture probability due to elastic scattering is obtained in the low-energy region.     

Radial dose distribution from carbon ion incident on liquid water

We report calculations of the radial dose deposited along carbon-ion tracks in liquid water using different techniques depending on the energy range of secondary electrons. The models are developed in relation with the experimental data on electron penetration lengths. For electrons with energies higher than 45 eV, we use the Katz model. However, the main focus is on the low-energy electrons, which are largely responsible for DNA damage within 10 nm from the tracks. For these electrons, the dose calculation is based on their random walk behaviour. The results of this combined approach are compared to experimental measurements. Contributions to the deposited energy by electrons of different ranges of energy are discussed.     

Spin dependent mean-free path of low-energy electrons in ferromagnetic materials

Spin resolved attenuation measurements of electrons transmitted through overlayers of Fe and Co show that the electron inelastic mean free path (IMFP) in these materials is spin-dependent at low energies. The spin-up IMFP is larger than the spin-down IMFP. The values from different studies are in reasonable agreement. The data suggest that the origin of the spin dependence is mainly due to inelastic processes. Effects from spin dependent elastic scattering have not been identified directly in these experiments. The spin filter effect based on preferential attenuation of spin-down electrons can be used as a basis of spin polarization detectors.