Angle-resolved elastic peak electron spectroscopy: Role of surface excitations

We analyze the possibility of determining the surface excitation parameter (SEP) from the dependence of the elastic backscattering signal intensity on the emission angle. It has been found that the shape of this dependence is reasonably well described by the theoretical model implemented in a typical Monte Carlo simulation strategy. As shown recently, the mean percentage deviation between the experimental angular dependence and the theoretical dependence is equal to 8.82% at 200 eV, 6.28% at 500 eV and 4.69% at 1000 eV. In the theoretical model used, the surface energy losses were ignored. Close inspection of the deviations between theory and experiments indicates systematic trends that can be ascribed to the surface energy losses. We found here that taking into the account the surface energy losses further improves the agreement between theory and experiment. The total mean percentage deviation, equal to 6.65%, decreases to 5.59% if the mathematical form of the Chen formula for SEP is used, or to 5.16% if the Oswald expression is used. The material dependent coefficients in the expression of SEP derived from the emission angle dependence of the elastic peak intensity differ from these coefficients resulting from other methods. We conclude that the determination of SEP from shape of the angular dependence requires the experimental data of high quality, and the reliable theoretical model describing elastic electron backscattering.     

Surface excitation probabilities in surface electron spectroscopies

The phenomenon of surface excitation is competitive in nature for elastic and other inelastic scattering processes in surface electron spectroscopies; the knowledge of influence of surface excitations in electron energy loss spectra is then essential for quantitative surface analysis with these spectroscopies. The inelastic scattering of an electron moving in the vicinity of a surface is considered in a self-energy formalism to estimate the contribution of surface excitation in electron-solid interactions via the total surface excitation probability. The formulation uses the optical bulk dielectric function and provides the spatial and angular dependence of the differential and total inelastic cross-sections. The kinetic energy range of probing electrons considered is 100-5000 eV and the numerical evaluation of total surface excitation probabilities are performed for several metals, Au, Ag, Cu, Ni, Fe and Ti; empirical formulae for the surface excitation probability are given for each of these materials and compared with experimental results for the surface excitation parameter. The total surface excitation probability is higher in Ag as compared to other metals under consideration, for identical conditions of electron-solid interactions.     

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.     

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.     

Elastic and inelastic backscattering of slow electrons from silicon

The elastic and inelastic backscattering from Si(111) surfaces and evaporated amorphous silicon were measured as a function of the primary energyE _p (30eVE _p 200eV). A detailed evaluation of the amplitude of the volume plasmon lossA _vp was carried out in the loss spectra. In contrast to single crystals amorphous silicon produces a smooth curve as function of the energy, both for the elastic backscattered electron current and forA _vp (E).To interpret the measured curves for the amorphous Si calculations were made for the elastic scattering and for the excitation probability of the volume plasmon in a randium-jellium-model. In the case of elastic scattering a random distribution of atoms is assumed. In the case of inelastic scattering the free electron model is used. Double scattering processes are included. The comparison between theory and experiment shows satisfactory agreement for elastic scattering. The energy dependent excitation probability of the volume plasmon is excellently represented by this model.     

Backscattering correction for quantitative Auger analysis: I. Monte Carlo calculations of backscattering factors for standard materials

The electron backscattering effect which is important for the quantitative interpretation of “matrix effects” in AES is investigated by applying the Monte Carlo calculation technique. The present calculation model is based on the use of a precise elastic scattering cross-section obtained by the partial wave expansion method, as well as on the combined use of Gryzinski's excitation function and Bethe's stopping power for inelastic scattering. Systematic calculations of the backscattering factors were performed for over 25 materials including pure elements, compounds, and alloys, which have been widely used as standard materials for practical Auger analysis. The results should enable the accuracy of quantitative analysis by AES to be improved.     

Monte-Carlo calculations of keV electron and positron slowing down in solids

A Monte-Carlo simulation technique based on the screened Rutherford differential cross section for the elastic scattering and Gryzinski's semiempirical expression for the inelastic core and valence electron excitation is used to describe electrons and positrons slowing down in solids. The theoretical results are compared with the experimental backscattering, absorption and transmission results for aluminum, silicon, copper, and gold thin film and semi-infinite targets and good agreement is observed. The simulated stopping profiles are fitted with a simple analytic expression. The profiles are Laplace-transformed to give a useful data base for analyzing phenomena associated with slow positron re-emission from solids.     

Analysis of reflection electron energy loss spectra (REELS) for determination of the dielectric function of solids: Fe, Co, Ni

A simple procedure is developed to simultaneously eliminate multiple scattering contributions from two reflection electron energy-loss spectra (REELS) measured at different energies or for different experimental geometrical configurations. The procedure provides the differential inverse inelastic mean free path (DIIMFP) and the differential surface excitation probability (DSEP). The only required input parameters are the differential cross section for elastic scattering and a reasonable estimate for the inelastic mean free path (IMFP). No prior information on surface excitations is required for the deconvolution. The retrieved DIIMFP and DSEP can be used to determine the dielectric function of a solid by fitting the DSEP and DIIMFP to theory. Eventually, the optical data can be used to calculate the (differential and total) inelastic mean free path and the surface excitation probability. The procedure is applied to Fe, Co and Ni and the retrieved optical data as well as the inelastic mean free paths and surface excitation parameters derived from it are compared to values reported earlier in the literature. In all cases, reasonable agreement is found between the present data and the earlier results, supporting the validity of the procedure.     

Quantitative interpretation of the low-loss electron signal

Low-loss electron spectra from clean elemental standards of C, Si, Cr, Fe, Cu, Ag, and Au are presented and theoretically interpreted with the aid of two basic theories. One of these assumes a simple elastic scattering and Bethe loss regime in which the low-loss signal arises from primary electrons that have undergone a single large-angle scattering event and whose energy loss is described by the continuous slowing down approximation. However, better qualitative agreement with experiment is obtained when multiple elastic scattering is considered via the transport approximation for electron deflection. The simple low-loss electron detector used to obtain the data is also described.     

Surface Corrugation in Rotational and Diffractive Scattering of O2 from LiF (001)

A quantum dynamic calculation on a five-dimensional O₂/LiF (001) model system is performed using the multi-configuration time-dependent Hartree method. The obtained results show that the mechanism of rotational and diffractive excitation in details: Comparison with the rotational excited state, the initially non-rotational state is seen to favor the inelastic scattering in the rotational excitation process. The surface corrugation can damp the quantum interferences and produce a greater amount of rotational inelastic scattering at the expense of the elastic process in the rotational excitation process. The diffraction process and the average energy transferred into the rotational and diffractive mode are also discussed.     

Angular pattern of electron diffraction by reflection in the plasmon channel of energy losses

We have constructed a theory for the excitation of plasmons by a fast charged particle that undergoes diffraction in a single crystal and then is scattered elastically and incoherently through a large angle. The theory allows the 30-year-old experimental results that have seemed strange to be explained. An increase in the diffraction contrast in the channel of inelastic electron scattering related to the excitation of a bulk plasmon compared to the diffraction contrast of elastically and incoherently reflected electrons was observed in these experiments. Based on this theory, we show that the excitation of a surface plasmon affects only slightly the angular diffraction pattern, leaving it almost the same as that for elastically reflected electrons. These peculiarities of elastic and inelastic diffraction can be used to identify the type of energy plasma loss.     

Evaluation of the inelastic mean free path (IMFP) of electrons in polyaniline and polyacetylene samples obtained from elastic peak electron spectroscopy (EPES)

The inelastic mean free path (IMFP) of electrons was determined experimentally for selected polyaniline and polyacetylene samples with Ag and Ni references using elastic peak electron spectroscopy (EPES). The surface composition was determined by XPS and density by helium pycnometry. The high resolution hemispherical ESA-31 and ADES-400 spectrometers were used for measurements in the energy range E = 0.5–3.0 keV and E =0.4 − 1.6 keV, respectively. The integrated elastic peak intensity ratios for sample and reference were calculated using the Monte Carlo (MC) algorithm based on the electron elastic scattering cross-sections database NIST SRD64 version 3.1 and applying TPP-2M IMFPs for polymers. Surface excitation parameters (SEP) and material parameters ( _ach ) for polymers were determined, using the model of Chen, from comparison of measured and MC calculated elastic peak intensity ratios. These corrections proved to be efficient in decreasing the percentage deviations between the obtained IMFPs and the TPP-2M formula IMFPs. The elastic peak of hydrogen was observed in the EPES spectra of polymers. The experimental contribution of the hydrogen to the total elastic peak was 0.58%, while this value obtained from the MC simulations was 1.98%.      

高能电子弹性和非弹性散射的动力学理论——多片层法

本文综述了弹性多片层理论在反射电子显微镜中的应用。根据实验事实,提出了弹性理论的局限性。进而从量子力学推导出描述高能电子非弹性散射的新多片层理论,并把它应用到计算电子与等离激元和固体声子相互作用的非弹性过程中。该理论可以用来模拟非弹性电子所成的高分辨原子场。     

氢原子谱线测定EACVD中电子平均温度

采用蒙特卡罗方法,对以CH₄/H₂混合气体为原料气体的EACVD中氢原子的发射过程进行了模拟。在模拟中考虑了电子与H₂的弹性碰撞及振动激发、分解、电子激发、相应于H_α, H_β, H_γ谱线的激发、电离及分解电离等非弹性碰撞过程;与CH₄的碰撞考虑了弹性动量传输及振动激发、分解、电子激发、电离及分解电离等非弹性碰撞过程。研究了不同CH₄浓度下基片表面上电子平均温度与氢原子谱线相对强度的关系,给出了一种对EACVD中电子平均温度进行实时监测的方法。对于有效控制工艺条件,生长出高质量的金刚石薄膜具有重要意义。     

Monte Carlo calculations of keV electron and positron slowing down in solids. II

An improved Monte-Carlo simulation technique has been used to investigate positron and electron slowing down in solid matter. Elastic scattering is based on exact cross sections of effective crystalline potentials and inelastic processes are described by Gryzinski's semiempirical expression for each core and valence electron excitation. Calculations with normal and oblique angles of incidence have been made for positrons and electrons impinging on semi-infinite aluminium, copper, tungsten, and gold. Interesting differences have been found between positron and electron penetration and backscattering features.     

Phonon-induced backscattering in helical edge states

A single pair of helical edge states as realized at the boundary of a quantum spin Hall insulator is known to be robust against elastic single particle backscattering as long as time reversal symmetry is preserved. However, there is no symmetry preventing inelastic backscattering as brought about by phonons in the presence of Rashba spin orbit coupling. In this Letter, we show that the quantized conductivity of a single channel of helical Dirac electrons is protected even against this inelastic mechanism to leading order. We further demonstrate that this result remains valid when Coulomb interaction is included in the framework of a helical Tomonaga Luttinger liquid.     

Untersuchung der Prozesse in der aktiven Zone der Hohlkatodenbogenentladung I. Die Energieverteilungsfunktion der Elektronen,die Anregungs- und Ionisationsgeschwindigkeit

In this paper the processes of excitation and ionization inside the cathode of a hollow cathode are discharge will be studied. The electron energy distribution function is calculated from the kinetic equation. For this we take into account the following processes: elastic and inelastic collisions of electrons with atoms, Coulomb interaction between emitted fast electrons and electrons of the plasma.     

Interference effect in combined elastic and inelastic scattering of an energetic electron reflected from a disordered medium with generation of a surface plasmon

Quantum interference in combined elastic and inelastic scattering of an energetic electron with excitation of a surface plasmon leads to a change in the shape of the corresponding peak in the electron-energyloss spectrum. The plasmon generation is suppressed near the frequency \({{\omega _p } \mathord{\left/ {\vphantom {{\omega _p } {\sqrt 2 }}} \right. \kern-\nulldelimiterspace} {\sqrt 2 }}\). The suppression increases with increasing surface-plasmon wave length, because the interference of the energetic-electron scattering processes differing in the sequential order of elastic and inelastic scattering becomes progressively more destructive. The decrease in the height of the surface-plasmon peak in the electron-energy-loss spectrum leads to a non-dissipative broadening in this peak. Quantum interference also causes a specific feature to occur in the azimuthangle dependence of the spectral intensity as the electron energy loss increases in the immediate vicinity of the surface-plasmon peak.     

氢原子谱线与高质量金刚石薄膜

采用蒙特卡罗方法,对以CH₄/H₂混合气体为源气体的电子助进热丝化学气相沉积(EACVD)中的氢原子发射过程进行了模拟。在模拟中考虑了电子与H₂的弹性碰撞及振动激发、分解、电子激发(包括H_α, H_β, H_γ谱线的激发)、电离及分解电离等非弹性碰撞过程;与CH₄的碰撞考虑了弹性动量传输及振动激发、分解、电子激发、分解激发(包括H_α, H_β, H_γ谱线的激发)、电离及分解电离等非弹性碰撞过程。研究了不同实验条件下产生的H, CH₃的数目与氢原子谱线相对强度的关系,给出了一种利用氢原子谱线来获得最佳成膜实验条件的方法。对于有效控制工艺条件,生长出高质量的金刚石薄膜具有重要意义。     

Large-angle scattering of heavy ions: (II). General structure of inelastic cross section

Closed-form expressions are derived for the differential cross section of inelastic heavy-ion scattering at large angles. The inelastic transition amplitude given by the distorted-waves theory for excitation of low-lying collective states is evaluated by an extension of analytic methods developed in the preceding paper for elastic large-angle scattering. The very close relation between the inelastic and elastic cross sections is displayed. In particular it is shown that the angular distributions have a universal form, and that the backward-angle inelastic excitation function has, aside from a slowly varying overall energy dependence, an oscillatory gross structure of diffractive origin which is nearly identical to that of the elastic excitation function, irrespective of the physical mechanism involved.