David Liljequist

Monte Carlo simulation of 0.1–100 keV electron and positron transport in solids using optical data and partial wave methods

Abstract A new Monte Carlo code for the detailed simulation of the transport of low-energy electrons and positrons in solids is presented, including a critical discussion of concepts and approximations in the scattering model. Inelastic scattering is calculated using a Bethe surface model based on optical and photoelectric data for the solid, making possible a good accuracy at low energies, and a high resolution (∼1 eV) in simulated energy loss spectra. Exchange corrections for electrons and relativistic corrections for energies up to ∼100 keV are included. Elastic scattering is calculated by means of a differential cross section obtained by relativistic partial wave analysis for an exchange corrected muffin-tin Dirac-Hartree-Slater atomic potential. In the simulation, no adjustments of parameters to empirical scattering data are made. For comparison, measurements have been made of the characteristic low energy loss spectrum of 100 keV electrons through a thin silicon film. Simulated results for electrons and positrons are also compared with other available experimental data, in particular at low (a few keV) energies. In general, very good agreement is obtained.

TRANSPORT MEAN FREE PATH TABULATED FOR THE MULTIPLE ELASTIC SCATTERING OF ELECTRONS AND POSITRONS AT ENERGIES 20 MEV

The transport mean free path, or transport cross section, is tabulated for the elastic scattering of electrons and positrons in solid matter by means of a correction factor tc applied to the result of a simple screened Rutherford cross section. The correction factor table is based on differential cross‐section calculations using a combination of partial‐wave analysis (PWA), the Wentzel–Kramers–Brillouin approximation, and the Born approximation, and covers kinetic energies from 100 eV to 20 MeV. Results at low energies are compared with PWA calculations of higher accuracy. Nuclear size effects are discussed but not explicitly included. Applications are discussed.

Influence of interelectrode distance and force level on the spectral parameters of surface electromyographic recordings from the lumbar muscles

In order to study the influence of interelectrode distance and force level on the electromyographic (EMG) spectral parameters and on their reliability, bipolar surface EMG measurements were performed on the lumbar muscles of 15 subjects. Two test contractions (45 s) at 40% of maximal voluntary contraction (MVC) were performed, one with 2 cm interelectrode distance and the other with 4 cm, followed by two contractions at 80% MVC with the same change in interelectrode distance. Increasing the interelectrode distance from 2 to 4 cm caused a significant mean decrease (about 8%) in the initial median frequency. It is shown that this shift is of an order of magnitude that may be expected from the bipolar electrode filter factor, and we further conclude that the observed individual variations in the shift are likely to be connected to fluctuations in the shape of the power spectrum and to variations in conduction velocity. No significant change was found for the median frequency slope when changing the interelectrode distance. Increasing the force (from 40 to 80% MVC) also caused a significant mean decrease (about 10%) in the initial median frequency. The median frequency slope became significantly more negative by more than 200%. We conclude, however, that torque fluctuations during the fatigue contractions should have had only minor influence on the standard error of measurement of the initial median frequency and of the median frequency slope.

Elastic scattering cross section models used for Monte Carlo simulation of electron tracks in media of biological and medical interest

Abstract Purpose: Elastic scattering is important for the spatial distribution of electrons penetrating matter, and thus for the distribution of deposited energy and DNA damage. Scattering media of interest are in particular liquid and gaseous water and gaseous nitrogen. The former are used as surrogates for tissue and cell environments (since more than 70% of the cell consists of water), while cross section data for nitrogen have been scaled and used as input in Monte Carlo (MC) codes simulating scattering in biologically relevant media. A short review is given of electron elastic scattering cross section models used in a biological and medical context and their experimental and theoretical background. Conclusions: Adequate theories and models exist for calculating elastic electron scattering in gaseous nitrogen and gaseous water (i.e., by free molecules) down to electron energies well below 100 eV. However, elastic electron scattering in liquid water at such low energies is apparently uncertain and not well understood. Further studies in the case of liquid water are thus motivated due to its biological importance.

Escape probability of low energy electrons and positrons emitted in random directions beneath a plane solid surface

Abstract Simulations of escape probability and angular distribution have been made with the low energy Monte Carlo code LEEPS for electrons and positrons with initial energies E=0.5–20 keV, scattered in Be, Al, Cu and Au. The simulated escape probability T(x) for an electron or positron starting in random direction from a depth x beneath the plane surface of a semi-infinite homogeneous solid (atomic number Z) is well described by T(x)=A exp (−x/R) exp (−(x/1.9R) 2 ) . By least-square fit to simulated data, the parameters A and R are expressed as functions of Z and E. The formula gives about one or a few percent lower values than the simulated T(x) for start depths x smaller than the initial elastic mean free path; this is related to the larger simulated probability of glancing angle escape for such small start depths. The scaling properties of T(x) are discussed, and comparison is made with previous calculations and with measurements. The parameter R is for electrons related to the Bethe range r by R/r≈0.587(1+α)−0.47, where α=r/λtr and λtr is the transport mean free path at the initial electron energy. For low and medium Z, α≈0.15Z at energies 2–20 keV.

Simple method for the simulation of multiple elastic scattering of electrons

A screened Rutherford cross section is modified by means of a correction factor to obtain the proper transport cross section computed by partial‐wave analysis. The correction factor is tabulated for electron energies in the range 0–100 keV and for elements in the range from Z=4 to 82. The modified screened Rutherford cross section is shown to be useful as an approximation for the simulation of plural and multiple scattering. Its performance and limitations are exemplified for electrons scattered in Al and Au.

Evidence for fast diffusion of57Fe implanted in cu from depthselective conversion-electron Mössbauer spectroscopy (DCEMS)

The DCEMS technique has been applied to observe drastic changes with time of the ion-implanted57Fe concentration profilein a Cu foil. Spectral changes observed at selected electron energies may be related to changes as a function of depth in the57Fe local surroundings.

Scattering of 7.3 keV conversion electrons from a 57Co source covered gradually by gold absorbers of various thicknesses

The conversion electrons emitted with initial energy of 7.3 keV from the K-shell of 57 Fe atoms were measured with an electrostatic spectrometer set to the instrumental resolution of 7 eV. The source – 57 Co on an Al backing – was covered in successive steps by six evaporated Au layers and changes of the line shapes were recorded. The thicknesses of the Au absorbers determined by neutron activation analysis varied from 2.7 to 21 nm, i.e. upto about three times the inelastic mean free path of the 7.3 keV electrons. The individual elastic and inelastic scattering events in the Al backing, Au absorbers and carbonaceous contamination overlayer were simulated by the Monte Carlo method. When the Au energy loss function derived by Yoshikawa et al. was applied in MC simulations, a reasonable agreement with measured line shapes was reached even for the thickest Au absorbers. � 2002 Elsevier Science B.V. All rights reserved.

CEMS and DCEMS investigations of Al-implanted iron

Abstractα-Fe surfaces were implanted with a nominal dose of 5×1017 Al ions/cm2 at 50 keV and a current density of about 3.7 μA/cm2. Samples of different shapes and thicknesses have been used in order to test the influence of heat flow from specimen to target holder during implantation. Integral and energy differential (“depth-selective”)57Fe conversion electron Mössbauer spectroscopy (CEMS and DCEMS) were employed. The spectra indicated a magnetic phase characterised by a broad hyperfine field distributionP(Bhf), a non-magnetic phase, and α-Fe. The relative intensity of the non-magnetic phase was enhanced if the thermal contact during implantation became worse. An energy dependence of DCEM spectra in the L-electron range was observed. Model calculations using L-electron weight functions and experimental concentration profiles obtained by secondary neutral mass spectroscopy (SNMS) yielded fair agreement between calculated and experimental phase signals. The results demonstrate that the non-magnetic Fe-Al alloy phase with high Al concentration is located closer to the surface than the magnetic alloy phase, which extends to much larger depth than expected.

Discussion of very low energy electron 57Fe Mössbauer spectroscopy

The weight function, i.e. the probability of detecting a Mossbauer event as a function of its depth below the sample surface, is estimated for 57Fe electron Mossbauer spectroscopy, taking into account detection of very low energy ( ∼ 10 eV) electrons. The effects of detector characteristics and detector arrangements are studied. Intensity and surface sensitivity are compared to conventional ICEMS and DCEMS theories.