Wirkungsquerschnitte für elastische und unelastische Elektronenstreuung an amorphen Kohlenstoff- und Germaniumschichten

Absolute intensities of electrons scattered by amorphous carbon and germanium foils were measured for various energies (20–60 keV) and foil thicknesses (200–800 Å). Electrons scattered elastically were separated from those scattered inelastically by means of a retarding field. Thus total cross sectionsσ _e for elastic scattering andσ _u for inelastic scattering were obtained. Agreement of observed and theoretical values is satisfactory, especially regarding the dependence on electron energy.     

Eine Gegenfeldanordnung zur Messung von Energie- und Winkelverteilungen gestreuter Elektronen

In a previous paper direct electron-intensity measurements in Debye-Scherrer diagrams of aluminium have been described. A retarding field apparatus was used for investigations into the influence of crystal size and electron energy (15 to 50 keV) on the elastic diffraction intensities. The validity range of the kinematical theory could be determined. By means of a retarding field the inelastically scattered electrons were separated from the elastically scattered electrons (energy loss below 2 eV). In this paper the retarding field apparatus by which scattering intensities can be measured with good accuracy (≈ 2%) is described in detail. It is compared with other arrangements for the measurements of angular and energy distributions of scattered electrons.     

Messung der Wirkungsquerschnitte für elastische Elektronenstreuung in polykristallinen Al-Schichten bei verschiedenen Temperaturen

Absolute intensities of electrons scattered elastically in a polycrystalline aluminium foil were measured by means of a retarding field apparatus at 51 kev and in the temperature range 150–800 °K. From the integrated intensities of the Debye-Scherrer rings (I _R), of the temperature diffuse scattering (I _TDS) and of the temperature independent diffuse scattering (I _DS) the total cross sections σ of the foil for the corresponding scattering processes have been determined. The measured values σ _R (T) for Laue-Bragg scattering show very good agreement with the calculation, based on the dynamical two beam approximation, and σ _TDS (T) for the temperature diffuse scattering agrees fairly well with the kinematical value for the Einstein model of the vibrating crystal. The temperature independent part of the elastic background intensity is mainly due to elastic scattering of electrons in the amorphous oxide layer of the aluminium foil. It turns out, that the sum of all cross sections for the elastic scattering processes mentioned increases slightly with temperature.     

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.     

Elastische und unelastische Streuung von Deuteronen an Sr,Zr, Nb,Pd und Ag bei 11,8 MeV

Continuing previous experiments on the elastic and inelastic scattering of 11·8MeV deuterons on medium weight nuclei, Sr, Zr, Nb, Pd, and Ag targets have been studied. In addition to elastically scattered deuterons, angular distributions of inelastically scattered deuterons have been obtained for one group in Sr, and three groups in Zr and Nb, respectively, between 20° and 165°. The correlation between the diffraction maxima is discussed in terms ofBlair's phase rule. As in our previous results, this rule works poorly in the comparison between elastic and inelastic angular distributions. However the strongly excited inelastic groups which are interpreted as collective vibrational states do follow this rule. In the case of Pd and Ag, energy spectra at several scattering angles have been measured. The integrated differential cross sections of the inelastically scattered deuterons atΘ=90° of all investigated elements are compared with those of previous measurements. They show the influence of closed shells but no systematic decrease or increase with increasing atomic weight.     

Temperaturabhängigkeit des Streuuntergrundes im Elektroneninterferenzdiagramm polykristalliner Silberschichten

The filtered and unfiltered intensities of electrons (30 to 50 kev) scattered in thin polycrystalline silver foils (300 to 1400 Å) were measured by means of a retarding field apparatus in the temperature range from 170 to 380 °K. Further the absorption coefficients due to the inelastic and the different elastic scattering processes were determined. It is shown, that the diffuse elastic scattering intensity increases with temperature for all values of thickness and electron energy. From the measured absorption coefficients the contributions of the different elastic scattering processes to the total background intensity are calculated. It turns out, that the main contribution is due to multiple scattering processes including both Bragg reflections and thermal diffuse scattering. Furthermore it is shown, that in contrary to the filtered diagram the background intensity of the unfiltered diagram increases with temperature only for larger scattering angles. In the small angle region a reversed temperature behaviour is observed. This effect is caused by that part of inelastically scattered electrons at low angles coming directly from the primary beam and from the low order diffraction rings.     

Untersuchungen zur normalen und anomalen Absorption von Elektronen in Silizium- und Germanium-Einkristallen bei verschiedenen Temperaturen

Absolute filtered intensities of the electrons scattered elastically in thin platelike Si and Ge crystals have been measured. From the intensities of the primary and the Bragg reflected beams measured as a function of incident direction the coefficients for normal and anomalous absorption can be obtained with good accuracy, using the two beam approximation of the dynamical theory. Moreover, for Si the foil thickness and structure potentials can be deduced which are in agreement with the thickness determined optically and with calculated structure potentials resp. The results partly are influenced by multiple beam effects, which, however, are shown to be describable by Bethe's second approximation. All absorption coefficients, measured for different reflections and different crystal temperatures, show an increase with temperature, which is rather weak for Si and stronger for Ge. This shows that there is an influence of temperature diffuse scattering on normal and especially on anomalous absorption, which increases with atomic number. The results can be interpreted quantitatively, using simple models for the various contributions to the absorption coefficients (excitation of single electrons, plasmons and phonons).     

Spectroscopy of charged particles elastically scattered by plane-parallel solid layers

The energy spectra of electrons elastically scattered by plane-parallel solid layers are presented. The solid surface is analyzed by a method based on the identification of similar spectra and is called electron Rutherford scattering in analogy with the well-known ion spectroscopy method. The effect of multiple scattering processes on peak intensities in the energy spectra of elastically scattered particles is analyzed. The applicability range of the strong single scattering approximation for the interpretation of the energy spectra of elastically scattered electrons is established.     

Weak localization of inelastically reflected electrons under auger emission conditions

A new type of weak localization of electrons emerging during electron emission is considered. It is manifested in singularities of the angular spectra of particles reflected inelastically from a solid and causing Auger ionization of the atoms. The orientational dependences in this case appear as a result of interference of two types of processes. In one case, an electron from the primary beam penetrates the solid, undergoes inelastic scattering, ionizes an atom, and is then scattered elastically through a large angle, after which it leaves the solid. In the other case, elastic scattering of an electron precedes its inelastic scattering due to the Auger ionization of an atom. The azimuthal angular dependences of currents created by inelastically reflected electrons contain information on new processes of weak localization of particles.     

An extension of the mean free path approach to X-ray absorption spectroscopy

In the partial electron yield (PEY) acquisition mode commonly used in X-ray absorption spectroscopy (XAS) both elastically and inelastically scattered electrons are acquired, the latter contribution dominating the detector signal. Hence, the majority of the inelastic scattering events will not result in signal attenuation as happens in the case of X-ray photoelectron spectroscopy (XPS). To determine the respective changes in the effective mean free paths (MFP) we have performed XPS and near edge X-ray absorption fine structure (NEXAFS) spectroscopy measurements for a series of self-assembled monolayers of alkanethiols on gold substrates. The length of the alkyl chain and, therefore, the film thickness was varied. In agreement with expectations, the obtained MFPs for the Au 4f photoelectrons and C_KLL Auger electrons in the PEY acquisition mode (with the respective inelastic contributions) exceed the corresponding values for the Au 4f and C_KLL electrons of the same kinetic energies in the constant final state acquisition mode. Furthermore, the effective PEY-MFP for the C_KLL Auger electrons increased with decreasing retarding voltage of the PEY detector, which correlates with the enhanced contribution of the inelastically scattered electrons in the acquired signal. The results obtained are of importance for the analysis of XAS spectra of thin organic films and polymers.     

Bremsstrahlung spectrum of nonrelativistic electrons scattered in metallic target: Theory and experiment

This work is devoted to theoretical and experimental investigation of the bremsstrahlung (BrS) spectrum of electrons with an energy of 10–30 eV scattered in a copper plate. Modeling of the photon yield from a target has been carried out taking into account the polarization BrS channel, elastic and inelastic electron scattering by medium atoms, photon absorption in the target material, and coherent effects when electrons interact with a polycrystalline structure of metal. An FEI Quanta 200 scanning electron microscope with a supplement for X-ray microanalysis was used. Good agreement between experimental and theoretical results has been obtained.     

Inelastic scattering of slow electrons in solids

A theory of the inelastic scattering of slow electrons in solids due to excitation of interband transitions is developed. It is shown that both nondirect and direct transitions occur which can be described by a generalization of the formalism used in solid state optics. Experiments with 30–200 eV electrons scattered from Si (111) surfaces with well defined surface structures as determined by low energy electron diffraction confirm the theoretical predictions. They indicate that the inelastic scattering of slow electrons can be understood in terms of the three-dimensional band structure of solids and suggest the use of inelastic low energy electron scattering as a tool for band structure analysis.     

Study of mean absorptive potential using Lenz model: toward quantification of phase contrast from an electrostatic phase plate

An electrostatic phase plate can provide better phase contrast, a fact that plays a promising role for the high-resolution observation of specimens containing light elements. However, in order to quantify the "phase" contrast from images recorded using the phase plate, the "absorption" (or scattering) contrast arising from electrons scattered elastically and inelastically outside of the phase-plate ring must be analyzed. Angular distributions of the elastic and inelastic scattering are predicted using the Lenz model. The mean absorptive potential, [Formula: see text] serving as an index for the contribution of "absorption" contrast, is calculated from the reciprocal mean free path of elastic and inelastic scattering, and is verified experimentally. The mean absorptive potential of a particular phase plate with inner and outer radii of 0.25mum (theta(1)=0.09mrad) and 1mum (theta(2)=0.4mrad), respectively, is approximately 0.11eV for carbon and is equivalent to that of an objective aperture of semiangle 17mrad (cutoff frequency 6.7nm(-1)).     

Small-angle elastic scattering of 2.5 MeV neutrons

Differential cross sections and asymmetries of 2.50 MeV polarized neutrons elastically scattered by In, Ho, Hg, Bi and U have been determined for scattering angles from 2.1° to 9.1°. The measurements were carried out by the use of a neutron positional spectrometer. The results, when compared with the predictions of the electromagnetic interaction, indicate some deviation of 〈σ(θ)P(θ)〉 from the expected values. The observed cross sections are systematically greater than those evaluated within the framework of the optical model.     

Bremsstrahlung,Cerenkovstrahlung und Übergangsstrahlung in einer dünnen Schicht

We present a formula for the coherent emission of Bremsstrahlung, Cerenkov radiation and transition radiation of a single electron traversing a thin foil at an oblique angle of incidence and changing its velocity (direction or amount) inside the foil. As an example we consider the bombardment of silicon foils with 50 keV electrons. The statistical scattering of the electrons inside the foil is taken into account by means of a measured scattering pattern.     

High energy electron diffraction at Si(001) surfaces

Elastic scattering of 10 keV electrons at Si(001) surfaces at grazing incidence was investigated. The intensity of the specularly reflected elastically scattered electrons as a function of the angle of incidence I_el(γ) was measured for different azimuthal angles and was compared with calculations using the dynamical diffraction theory. It turned out that the contribution of the elastically scattered electrons to the total intensity of the reflections strongly decreases with decreasing angle of incidence. Exciting the reflection (008) the elastic contribution is around 30%, decreasing to about 12% in the case of the reflection (004). In the calculations multiple beam effects, absorption, a smooth variation of the potential at the surface and a reduction of the topmost interlayer spacing were taken into account. There is satisfactory agreement between the structures of experimental and calculated intensity curves, I_el(γ) indicating a slight compression of the surface lattice to be probable. Quantitative agreement, however, for absolute intensities was not obtained.     

Simultaneous energy analysis in a large angular range: A novel neutron spectrometer,its resolution and applications

A new type of crystal spectrometer for elastic and inelastic neutron scattering has been set up by modifying an existing flat-cone diffractormeter at the BER II-reactor in Berlin (West). The main difference to conventional triple axis spectrometers is the analyser part. It consists of large crystal plates which reflect the neutrons out of the horizontal plane into a curved multicounter. This allows simultaneous measurements in a large and continuous range of scattering angles for a constant energy transfer. The resolution function has been calculated and compared with experimental results. There is the possibility to focus acoustical phonons. We present applications together with experimental results such as quasielastic diffuse scattering in orientationally disordered crystals and inelastic scattering due to acoustical phonons. In combination with the flat-cone technique all elastic and inelastic scattering events of a single crystal can be collected in a systematic and efficient way.in collaboration with the Hahn-Meitner Institut, Berlin (West)     

The scattering of fast neutrons from W184

Neutrons with energies of 0.3 to 1.5 MeV are scattered from W¹⁸⁴. Pulsed-beam fast time-of-flight techniques including a magnetic bunching system are utilized to resolve the elastically scattered neutrons from those inelastically scattered. The differential elastic cross section is measured at 50 keV intervals with an ≈20 keV incident neutron energy spread. The differential cross sections for inelastic scattering resulting in the excitation of residual nuclear levels at 111±5, 365±10, 690±40, 900±25, 1000±30, and 1120±30 keV are determined. In all instances the inelastically scattered neutrons are emitted, within experimental error, isotropically. The experimental results are compared with those obtained in previous work and with the predictions of theory.     

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.     

Elastische und unelastische Streuung von Elektronen an Gasen

The theoretical differential cross section for the elastic scattering and for the excitation of optical transitions in helium by electron impact has been refined in Born approximation by use of the two parameter Eckart eigenfunction for the ground state and for the excited states. The angular distributions of 25 kev electrons scattered elastically and inelastically by helium were measured in the angular range 2·3·10^?4≦?≦4·10^?2. The intensity distribution of the elastically scattered electrons is in accordance with the theoretical curve for?>7·10^?3 and is disturbed at smaller angles by the primary beam. Normalization of the experimental values to the theoretical elastic differential cross section leads to agreement between the experimental differential cross section for the excitation of the 2¹ P and 3¹ P state and the scattering formulae given in this paper. There are small systematic deviations (<20%) for the 2¹ P differential cross section in the angular range 3·10^?3<?<1·10^?2 only. The oscillator strength of these two transitions has been determined from the scattering measurements:f ₂₁=0·312±0·04 andf ₃₁=0·0898±0·006.