Towards a Universal Algorithm for Calculating the Backscattering Factor in AES:
Part 1. Current Status
A. Jablonski (Institute of Physical Chemistry, Polish Academy of Sciences)
It has been recently shown that the backscattering factor (BF) in AES should be defined generally as an integral over depth of the product of the excitation depth distribution function (EXDDF) and the emission depth distribution function (EMDDF) [1]. Under certain simplifying assumptions, the general BF definition becomes the same as the expressions typically used for BF calculations [1]. Obviously, the determination of the BF requires knowledge of the reliable methods for calculating the EMDDF and the EXDDF.
Much information is presently available on calculations of the EMDDF. To describe the elastic electron collisions, we need the differential elastic scattering cross-sections (DCS) or the transport cross sections. There are complete databases containing these parameters. Furthermore, the DCSs can be calculated from the published computer programs (e.g. the ELSEPA software). In addition, several universal expressions for the EXDDF were published; the expression of Tilinin et al. [2] seems to be the most accurate. It is implemented in the NIST Database 82.
In contrast, we still face some problems in calculating the EXDDF for electron energies relevant for AES. Although information on the elastic scattering events is well established now, the description of the inelastic scattering events is, in many cases, insufficient or inaccurate. While the inelastic-scattering probabilities can be determined from the relevant differential inverse inelastic mean free paths (DIIMFPs), the needed data are available only for a limited number of elemental solids and compounds. In principle, the universal inelastic cross-section of Tougaard can be used in simulations; however it does not describe correctly the energy losses exceeding 50 - 100 eV and deviates considerably from the inelastic scattering cross-section for some elements (e.g., for Si). It has been indicated that the simulation of the individual energy losses can be circumvented by the use of the electron stopping power (SP) to describe the rate of decrease in energy of the primary electrons in the sample due to inelastic-scattering events. This approach is usually called the so-called continuous slowing-down approximation (CSDA). The CSDA is also attractive because relatively extensive data on the SP are available in the literature. It has been estimated that the CSDA approach works well for the primary electron energies exceeding 1000 eV [3].
Another parameter needed in calculations of the EXDDF is the ionization cross-section for a given subshell. It is presently recommended to use the semi-empirical expression of Casnati et al.
It should also be mentioned that the algorithms providing of the EXDDF can be used in calculations of the lateral distribution of the backscattered electrons. This information is very important in determination of the lateral resolution of scanning Auger electron microscopy (SAM).
[1] A. Jablonski, Surface Sci. 499 (2002) 219.
[2] I. S. Tilinin, A. Jablonski, J. Zemek, and S. Hucek, J. Electron Spectrosc.Relat.Phenom. 87, 127 (1997) 127.
[3] A. Jablonski, C. J. Powell and S. Tanuma, Surf. Interface Anal. 37 (2005) 861.
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