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An ‘‘optical‐data’’ model for describing the dielectric response function of a medium was introduced earlier to predict energy‐loss rate and inelastic mean free path for low‐energy (

These lectures cover special topics about the interaction of swift electrons with condensed matter. The focus is on inelastic processes via the linear response function of the medium and sum rules that it satisfies. The spin dependence of low-energy electron interactions and exchange scattering in an electron gas, and the low-energy end of electron-hole cascades in metals are discussed. Aspects of the localization of initially unlocalized, coherent excitations are entered into briefly.

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The optical properties of thin films of poly(butene‐1‐sulfone), PBS, an electron beam resist, are presented for the range of photon energies from 2.5 to 39.0 eV. The density of these films is found to be (1.39 ± 0.02) g cm−3. A sum‐rule calculation is used to demonstrate the overall consistency of the data obtained. The optical data are used to calculate inelastic electron mean‐free paths in PBS as a function of incident electron energy from 100 to 10 000 eV.

Theoretical models and calculations are combined with experimental optical data to determine a model energy-loss function for SiO2. Sum-rule checks and comparisons with experimental information are made to insure overall consistency of the model. The model energy-loss function is employed to calculate electron inelastic mean free paths and stopping powers for electrons with energies ? 10 keV in SiO2.

Energy-loss straggling of ions with v\ensuremath{\ll}${v}_{F}$ in an electron gas has been evaluated from phase shifts determined from nonlinear, density-functional calculations. These results differ markedly from those obtained from linear theory and show oscillations in straggling with increasing nuclear charge which can be correlated with the scattering properties of electrons at the Fermi level.

A theoretical description of the inelastic interactions of electrons with solid polystyrene is presented. The response of the valence electrons to energy and momentum transfers is determined by a model insulator theory; carbon K-shell ionization cross sections are derived from atomic, generalized oscillator strengths. Contributions to the inverse mean free path and stopping power due to these two excitation processes are derived and tabulated for incident electrons with energies from 10 eV to 10 keV. Electron ranges in the continuous-slowing-down approximation are calculated and tabulated for electrons with energies from 15 eV to 10 keV.

The continuous-slowing-down-approximation range and range straggling for electrons with energies ? 10 keV in Al, Au, Ag, and Cu are calculated. The mean energy loss per unit pathlength, or the stopping power, is described by a statistical electron gas model. A correction to the stopping power due to the Z31 effect is included. Comparisons of the calculated CSDA ranges with experimental data are made.

The cross section for X-ray excitation of surface plasmons on a spherical void in an electron gas is derived using a hydrodynamical approximation. The result is compared to the cross sections for elastic scattering from the void, and other inelastic processes such as scattering from bulk plasmons, in order to provide information on the feasibility of detecting such surface plasmon excitations experimentally. Possible applications to the study of the mechanisms of void nucleation and growth are discussed.

Our apparatus has been modified to permit measurements of absolute photoemission as well as reflectance of liquids in the vacuum UV. Photon fluxes are determined by filling the tandem ion chambers with argon. An electrometer is connected to the sample cup, which must be properly biased, to read electron currents leaving the cup. After argon ion drift into the cup is taken into account, the yields of photoelectrons per incident photon and per absorbed photon are obtained. These yield curves for liquid formamide (HCONH2) are similar to each other over the energy range studied (16–25 eV). They are nearly constant between 16 and 18 eV at 13.5% and decline toward higher energies. The surface and volume plasmon energies for formamide are near 19 and approximately 27 eV, respectively. We suggest that photoelectron excitation of surface plasmons may enhance the photoemission yield, while excitation of volume plasmons may reduce it. Values of electron mean free path derived from the yields and a simple three‐step ...

Inelastic mean free paths and energy losses in aluminum metal are calculated for electrons with energies from a few eV to 10 4 eV above the Fermi level. We have represented the contribution from excitations of the valence electrons by using an electron gas model. The effect of damping in the electron gas on the mean free path and energy loss is included within the context of the Mermin-Kliewer-Fuchs model of the electron gas dielectric function. The influence of core polarizability and local field corrections are discussed briefly. The contributions to the mean free path and energy loss of electrons from ionization of inner shells have been evaluated from atomic models. Comparisons are made with experimental data taken over a wide range of energies.

The real and imaginary parts of the complex refractive index, n(..omega..) = n(..omega..)+ik(..omega..), of arc-evaporated carbon films have been obtained over the range of photon energies h..omega.. from 0.5 to 62.0 eV. Values of k(..omega..) obtained from transmission measurements in this energy range were combined with values of k(..omega..) from the literature in the infrared and soft-x-ray regions. A Kramers-Kronig analysis then yielded the values of n(..omega..). The density of the arc-evaporated carbon films was found to be 1.90 +- 0.05 g cm/sup -3/ by the ''sink-float'' method, and their thicknesses were determined optically. A sum-rule calculation yielded the effective numbers of valence and core electrons to be 4.2 and 1.8, respectively. The experimental values determined for n(..omega..) have been used to estimate values of the inelastic mean free path ..lambda..(E) for electrons of energy E from 200 to 3000 eV in amorphous carbon. Good agreement is found between ..lambda..(E) and experimentally determined values of electron attenuation length L(E) from the literature.

An electron slowing-down flux spectrum has been measured for ..beta.. particles, delta rays, and secondaries generated by the ..beta.. decay of neutron-activated /sup 164/Dy uniformly distributed in Al/sub 2/O/sub 3/. The energy range covered in these measurements extends from 1.5 to 32 keV. Fairly good agreement with predictions of the Spencer-Fano theory is found for energies above 10 keV. The overall shape of the spectrum is similar to that found earlier for metals and semiconductors. A companion theoretical calculation has been carried out based on cross sections for ionization of electrons from the inner shells of Al and O derived from generalized oscillator strengths, and on cross sections for valence-band electrons derived from a model-insulator theory. The effect of Auger cascade electrons is also included in the numerical solution of the electron slowing-down cascade equation. The theoretical spectra are smaller than the experimental results by as much as a factor of 4 in the energy range from 50 to 2000 eV.

The optical properties of Kapton type H polyimide film, obtained from reflectance measurements, are presented for photon energies from 0.5 to 70 eV. Equations for the energy‐loss function, with parameters fixed by the optical data, are employed to calculate mean free paths and stopping powers for low‐energy electrons (100 eV to 10 keV) in Kapton. The values obtained show good agreement with those predicted by recently proposed analytical formulae for electron mean free paths and stopping powers in solid organic insulators.

A statistical model is described and employed to calculate inverse mean free paths and stopping powers for electrons of energies from a few eV to 10 keV above the Fermi level in Al, Si, Ni, Cu, Ag, and Au. Brief tables of mean free paths and stopping powers for these solids are presented. In some cases graphical displays of inverse mean free paths and stopping powers are also included. The calculations based on this model are discussed and compared with previous work.

Many-body theory is used to calculate the inverse mean free path for plasmon excitation by an electron in a free-electron gas with damping of the plasmon states included. The theory is applied to the special case of Al for which experimental data on damping of the plasmons are available. Numerical calculations indicate an appreciable probability for exciting plasmons by incident electrons with energies below the threshold energy predicted by “no-damping” theories. Die Vielteilchentheorie wird benutzt, um die inverse mittlere freie Weglange fur Plasmo- nenanregung durch ein Elektron in einem freien Elektronengas bei Einschlus der Dampfung der Plasmonenzustande zu berechnen. Die Theorie wird auf den speziellen Fall von Al angewendet, fur das experimentelle Werte der Dampfung der Plasmonen vorliegen. Numerische Rechnungen zeigen eine betrachtliche Wahrscheinlichkeit fur die Anregung von Plasmonen durch einfallende Elektronen mit Energien unterhalb der Schwellenenergie, die durch die Theorie ohne Berucksichbigung der Dampfung vorhergesagt wird.

A swift ion moving through an electron gas is described in terms of the coherent states of the interacting system. This formulation is shown to lead simply to well known results for the wake potential generated in the medium by the passage of the ion and for the stopping power of a medium due to plasmon excitation.

A statistical model for the calculation of inelastic mean free paths and energy losses of electrons in solids is described. Results for the application of the model to the six solid media Al, Au, Ag, Cu, Ni, and Si are presented. Agreement between calculated mean free paths and experimental attenuation lengths indicates that the statistical model provides a useful method in the little-studied electron energy range from a few tens of electron volts to 10 keV.

Values of k and p are given for predicting inelastic mean free paths for electrons with energies from 200 eV to 10 keV from the simple formula λ = kEp, based on theoretical calculations for ten elemental and compound solids. These results indicate that in the energy range 400 eV ⩽ E ⩽ 2000 eV, the value of p lies in the range 0.65–0.80. For Si and SiO2, presentation of the available experimental data and theoretical results illustrate the differences which exist in the values of electron mean free paths.

Theoretical calculations of the stopping power of the electron gas for slow ions, v${v}_{F}$, are reviewed. New results are presented for stopping power and effective charge based on nonlinear density-functional calculations. Extensive comparisons with available experimental data show that these new theoretical results are clearly superior to earlier calculations based on linear theory.

When damping is included in an electron gas, an increase in the straggling parameter of low energy ions is predicted. The magnitude of this effect is estimated. The calculations provide a step forward towards a better understanding of experimental data on low energy straggling, which appears to be consistently higher than existing calculations based on the (undamped) free electron gas model. More experiments for low velocities would be desirable in order to check the theoretical predictions. Bei Einschlus von Einfachanregungsdampfung in einem Elektronengas wird vorausgesagt, das der „Stragglingparameter” von Ionen mit kleiner Energie vergrosert wird. Die Grose dieses Effekts wird fur eine reprasentative Situation abgeschatzt. Die Berechnungen liefern einen Schritt, urn die experimentellen Daten des niederenergetischen Stragglings besser zu verstehen. Es scheint, das sie grober sind als die auf der Grundlage eines ungedampften freien Elektronengases berechneten. Um die theoretischen Vorhersagen zu bestatigen, waren mehrere Experimente bei kleineren Geschwindigkeiten wunschenswert.

A model is described for the calculation of differential inverse mean free paths (DIMFPs) for the inelastic interactions of electrons with solids. The energy loss function Im{-1/ e ( q , ω )} is represented as a sum of Drude-type functions. The adjustable parameters in the energy loss function are fixed by a fit to the energy loss function in the optical limit ( q → 0) obtained from data on the optical constants of glassy carbon. The extension of the optical energy loss function to arbitrary values of q in this model leads to an analytical expression for the DIMFP. Energy loss spectra for low energy electrons (less than 2000 eV) transmitted through carbon foils of various thicknesses are determined by solving the transport equation using a convolution method and the DIMFPs determined as described above. Comparisons of these calculated spectra with those measured by Jacobi show that the model provides a good description of both the broad straggling distribution and the fine structure due to plasmon excitation.

An insulator model, with parameters fixed by fits to optical data, is used to determine the energy‐loss function describing the response of valence electrons in poly(butene‐1‐sulfone). Generalized oscillator strengths describe the response of the inner shell electrons. This theoretical information is employed to calculate inelastic mean free paths and stopping powers in poly(butene‐1‐sulfone) for electrons with energies ≤10 keV.

A theoretical description of the inelastic interactions of low-energy electrons (E?10 keV) with solid organic insulators is presented. The response of the valence electrons to energy and momentum transfers is inferred from a model for the energy-loss function with parameters fixed by optical data. With this model energy-loss function, inverse mean free path and stopping power due to interactions with the valence electrons are calculated for several organic solids. Contributions to the inverse mean free path and stopping power due to K-shell ionization in carbon, nitrogen, and oxygen are obtained from theoretical atomic generalized oscillator strengths. Simple, analytical formulae are deduced which allow predictions of mean free paths and stopping powers for electrons in the energy range 100 eV?E?10 keV to be made for a large group of organic solids.

The prospects for obtaining better theoretical calculations of experimentally interesting electron interaction effects, over a wide range of electron energies, are now considerably improved through the development of models for valence electron excitation in simple insulators and through the availability of theoretical atomic generalized oscillator strengths for inner shell electron excitation in several low-Z atomic systems. We describe briefly the way in which this information may be used to calculate mean free paths, stopping powers, and electron slowing-down spectra in Al metal and the insulator Al2O3.

The interaction of a relativistic electron with a system of plasmons is considered. First-order perturbation theory is used to calculate the rate of excitation of plasmons by the incident electron; the excitation rate leads to a mean free path. It is shown that relativistic corrections to the mean free path are generally quite negligible and thus the mean free path calculated using a nonrelativistic incident electron, when expressed in the “proper fashion”, is also correct relativistically. Es wird die Wechselwirkung eines relativistischen Elektrons mit einem Plasmonensystem betrachtet. Storungsrechnung erster Ordnung wird benutzt, um die Anregungsrate der Plasmonen durch die einfallenden Elektronen zu berechnen; die Anregungsrate fuhrt zu einer mittleren freien Weglange. Es wird gezeigt, das relativistische Korrekturen zur mittleren freien Weglange im allgemeinen vollig vernachlassigt werden konnen und die unter Annahme eines nichtrelativistischen einfallenden Elektrons berechnete mittlere freie Weglange auch relativistisch korrekt ist, wenn sie in der „richtigen Weise” ausgedruckt wird.

In this paper a simple derivation is given of the distribution of photons emitted when an energetic charged particle passes through a thin layer of dielectric material. This derivation emphasizes the individual microscopic events which occur during such a process. The distribution function is shown to agree with that obtainable from the transition radiation theory of Frank and Ginzburg and from the plasmon decay theory of Ferrell for the case of a thin foil. The special case of a double foil bounded by vacuum is considered in detail, and a general formula is found for the photon distribution function. An approximation analogous to that of Born's in quantum mechanics is developed to treat the case of a general composite foil whose thickness is small compared with λ but which may be large compared with vλ/c, where λ is the wavelength of the light emitted and v is the speed of the charged particle.

We consider in a classical formulation the interaction of a particle of charge ${Z}_{1}e$ incident at a given impact parameter with an electron bound isotropically and harmonically to the origin with a frequency $\ensuremath{\omega}$. Using a perturbation expansion that assumes that the displacement of the bound electron is small compared to the impact parameter, and integrating over the impact parameter from some minimum value to infinity, we are led to an expression for the stopping power. The leading term in this expansion is proportional to ${({Z}_{1}{e}^{2})}^{2}$ and is the usual result for this type of model, while the second term gives us the ${({Z}_{1}{e}^{2})}^{3}$ correction. The ${Z}_{1}^{3}$ correction for the Lenz-Jensen statistical model for the atom is presented. The predictions of this theory are in excellent agreement with available experimental data.

The interaction of a fast charged particle moving in a free-electron gas is described in the random phase approximation (RPA). The mean free path for the second order process of double-plasmon excitation in the free-electron gas is calculated. We find that the inverse mean free path for the double-plasmon excitation process is related to the inverse mean free path for single plasmon excitation by λ = 0.0103 rλ−1p. Thus, for electron densities corresponding to those in a real metal (1 < rs < 6) double-plasmon excitation may be important in the interpretation of certain experimental results as, for example, characteristic energy loss measurements. Die Wechselwirkung schneller, geladener Teilchen, die sich in einem Gas freier Elektronen bewegen, wird mit der „random phase”-Naherung (RPA) beschrieben. Es wird die mittlere freie Weglange fur den Prozes zweiter Ordnung der Plasmonen-Zweifachanregung in dem Gas freier Elektronen berechnet. Es wird gefunden, das die inverse mittlere freie Weglange fur den Doppelanregungsprozes der Plasmonen mit dem der Einfachanregung der Plasmonen durch λ = 0.0103 rλ−1p verknupft ist. Fur Elektronendichten, die denen in realen Metallen (1 < rs < 6) entsprechen, kann somit Doppelanregung von Plasmonen bei der Interpretation gewisser experimenteller Ergebnisse, wie zum Beispiel Messungen charakteristischer Energieverluste, bedeutend werden.

The spontaneous ``Cerenkov‐like'' emission of phonons is calculated for a charged particle moving in an arbitrary direction with a supersonic velocity through a solid. The coupling of the particle to the lattice is through the electric fields of piezoelectric origin; first‐order perturbation theory is used to calculate the rate of energy loss by the particle to the phonon field. A special case is considered for particle motion along the axis of hexagonal symmetry for a class 26 crystal (such as CdS) using a quasi‐isotropic model to describe the tensor properties of the solid. Comparison of the induced emission and absorption of phonons with the spontaneous emission indicates that the ``Cerenkov‐like'' emission is negligible under most conditions.

The stopping power of an electron gas for slow ons was calculated based on nonlinear, density-functional methods. These new theoretical results show substatnial increases in stopping powers for protons compared to calculations based on linear theory and provide a good qualitative description of the Z1-oscillations found in experimental data.

Monochromatic photons between 775 and 500 A were incident almost normally (15°) on the surface of liquid hexamethyl phosphoric triamide (HMPT). Incident and reflected beam strengths were measured with a double ion chamber filled with argon and the current leaving the cup of liquid was determined. After subtracting a portion of the current due to Ar+ drift into the cup, we obtained the photocurrent and, hence, the absolute photoemission yield. The yield falls from 9% at 16 eV to 5% at 25 eV. Such a falloff with increasing photon energy is expected from theory. The values are about double those calculated from theory using a three‐step model for the photoemission and using the Born approximation to calculate electron mean free paths. Conversely, if the experimental yields are used in the three‐step model, the electron mean free paths calculated from the data range from about 935 A at 16 eV to about 80 A at 24 eV and are about two to three times the theoretically predicted values.

A simple quantum mechanical description of two interacting metal half-spaces is presented. Plasmon dispersion and single-particle excitation are included in a phenomenological fashion via a “plasmon-pole model”. The van der Waal's energy calculated for the system is in good agreement with the results obtained by other workers using the random-phase approximation.

A simple expression is derived for estimating the contribution of surface losses to the stopping power of foils with plane parallel surfaces for normally incident nonrelativistic charged particles. Estimates are presented for electrons incident on foils of carbon and aluminum. The simple expression is modified in an approximate way to apply to the polycrystalline samples used in the work of Ichinokawa et al. and an estimate of the surface-loss contribution to the stopping power of polycrystalline graphite for electrons is given.

The binding energies of electrons trapped in the oscillatory wake of electron-density fluctuations trailing a fast ion in a solid are shown to decrease with increasing damping in an electron gas.

The influence of damping in an electron gas on ion-cluster energy loss is determined using the Mermin form of the dielectric response function. In a stopping medium corresponding to carbon, the vicinage function is modified significantly compared with the zero-damping limit for a dicluster with its axis parallel to its velocity. This change results in variations in dicluster stopping power of \ensuremath{\sim}20% as a function of internuclear separation compared with the small-damping values. For the dicluster axis oriented at random or perpendicular to the velocity, only small changes in dicluster stopping power occur beyond those accounted for by increases in mean excitation energy with increasing damping.

The interaction of electrons with the solids Al and Al2O3 is described based on the electron gas model for the conduction band electrons in Al, a model insulator theory for the valence electrons in Al2O3, and inner shell ionization derived from atomic, generalized oscillator strengths. Contributions to the inverse mean free path and stopping power from the various interaction processes are tabulated for electron energies from 0.5 eV to 10 keV for Al and from 10 eV to 10 keV for Al2O3. Electron range in the continuous-slowing-down approximation and straggling are tabulated for electron energies from 10 eV to 10 keV for both materials.

This report summarizes experimental and theoretical studies designed to yield information on the interaction of ionizing radiations with various communications materials. The optical properties of Kapton have been measured over the energy range from 0.5 eV to 76 eV. Theoretical models combined with experimental optical data have been used to calculate mean excitation energies, mean free paths, and stopping powers for low-energy electrons (100 eV to 10 keV) in various solid organic insulators. The contribution to both the mean free path and stopping power due to K-shell ionizations in carbon, nitrogen, and oxygen where then obtained from theoretical atomic generalized oscillator strengths and added to the valence electron contributions. A model involving the diffusion of excitons has been proposed to explain data, reported in the literature, showing that a thin metallic surface layer may partially protect organic crystals against radiation damage. The stopping powers of several metals for electrons have been calculated from an electron gas statistical model and used to calculate the continuous slowing-down-approximation range and range straggling for electrons with energies or = 10 keV. Microdosimetric calculations have been made of the structure of heavy-ion tracks in silicon. Results show that these tracks are very small in lateral extent compared with the dimensions of critical volumes in currently used microelectronic components.

The stopping power of a target, composed of atoms with atomic number Z2, for a projectile of charge Z1e and velocity v1, depends in first Born approximation on the projectile charge as (Z1e)2. Recently [1], we extended this theory to include the (Z1e)3 dependence in a classical treatment which is equivalent to a second Born approximation. The Z1 3 contribution was calculated for the statistical model of the target atom in the Lenz-Jensen approximation.

The mean excitation energy of polystyrene has been evaluated from the dielectric function for this organic solid. The result, $I=68.7$ eV, is in good agreement with a value in the literature obtained using the more conventional technique of extracting this parameter from stopping-power data.