Towards a Universal Algorithm for Calculating the Backscattering Factor in AES:
Part 2. Further Developments
A. Jablonski (Institute of Physical Chemistry, Polish Academy of Sciences)
There is a need to extend the backscattering factor (BF) calculations to the higher primary energies (up to 25 keV) that are available on modern AES instruments, and to the wider range of incidence angles of the primary beam that are often utilized. Furthermore, the relevant theoretical model should be applicable to any solid. A new algorithm satisfying the above requirements is under construction now. Several new features are implemented into this algorithm.
To enable the calculations of the BF, there is an obvious need for a universal source of the stopping power (SP) values, valid in a wide energy range, from below 1 keV to 25 keV or more. An attempt has been made recently to propose a predictive expressions for the SP [1,2]. The relevant analysis was based on the SP values calculated from optical data for numerous elemental solids in a wide energy range. A new analytical expression has been proposed for the electron stopping power (SP) valid for electron energies between 200 eV and 30 keV. This expression is a simple function of atomic number, Z, and electron energy, E. Accuracy of this predictive SP formula has been estimated to be about 10%. Although this expression was derived on the basis of the calculated SPs for elemental solids,. it has been found that this equation can be generalized to compounds [2].
An extensive comparison of the predicted SPs with the SPs calculated from the optical data and with the experimental SPs is presented. Although, we observe generally a good agreement in an energy range from 200 eV to 30 keV, there are several elements for which more pronounced deviations are observed, e.g. Ni (mean percentage deviation equal to 26.2%), Cu (26.8%), Bi (29.1%). No explanation for such behavior can be offered now.
A new Monte Carlo strategy is proposed which makes possible fast and accurate calculations of the ionization efficiency in a layer located at a certain depth in a solid. Consequently, we obtain a convenient tool for calculating the excitation depth distribution function (EXDDF), and finally the BF. This approach is attractive because it can be applied to any material with an empirical formula for the stopping power, available data for differential elastic-scattering cross sections, and a semi-empirical formula for inner-shell ionization cross sections. The BFs for the Si KL23L23, Cu L3M45M45, Ag M5N45N45, and Au M5N67N67 Auger transitions in the corresponding elemental solids are reported. These BFs were calculated for normal incidence of the primary beam, primary energies from near threshold for ionization of the relevant core levels to 20 keV, and Auger-electron emission angles of 10o, 60o, and 80o. A satisfactory agreement between these BFs and values obtained from a more accurate algorithm, in which individual inelastic-scattering events were simulated, has been found. Percentage deviations between BFs from the two algorithms were < 2 % for Au, < 5 % for Ag, < 7 % for Cu, and < 10 % for Si for primary energies likely to be used in practical AES. These deviations arise mainly from the use of stopping powers from the empirical formula rather than more reliable SP values calculated from experimental optical data.
[1] A. Jablonski, S. Tanuma and C. J. Powell, Surf. Interface Anal. 38 (2006) 76.
[2] A. Jablonski, S. Tanuma and C. J. Powell, J. Surface Anal., in press.
戻る