By Maurizio Dapor
The interplay of electron beams with strong objectives has been studied because the early a part of the final century. current curiosity is spurred on via the elemental function performed via the electron-solid interplay in - between different components - scanning electron microscopy, electron-probe microanalysis and Auger electron spectroscopy. This booklet goals to enquire chosen features of the interplay of electrons with topic (backscattering coefficient for bulk pursuits, absorption, backscattering and transmission for supported and unsupported skinny movies, implantation profiles, secondary electron emission and so on); to review the probabilistic legislation of interplay of the person electrons with the atoms (elastic and inelastic go sections); to introduce the Monte Carlo technique and its use for computing the macroscopic features of the interplay techniques. each one bankruptcy compares thought, simulations and experimental data.
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Additional info for Electron-Beam Interactions with Solids: Application of the Monte Carlo Method to Electron Scattering Problems
83) it is possible to see that µν = K 2 − 2EV + V 2 . e. 85) the following equation holds: d2 k(k + 1) − + K 2 − Ul± (r) Gl± = 0 . 86) For large values of r, Gl± is essentially sinusoidal. Indeed, when r is large enough, V (r) is negligible, Ul± is almost constant and the solution of the equation is therefore a linear combination of the regular and irregular spherical Bessel functions multiplied by Kr (see Appendix C). Taking account of the fact that Gl± = (r/µ1/2 ) G± l , we can therefore conclude that G± l jl (Kr) cos ηl± − nl (Kr) sin ηl± .
18) This equation, deduced here with the classical theory, is substantially correct. 166 (Bethe equation) . 166: for lower energies the predicted stopping power becomes negative. Therefore, the low-energy stopping power requires a diﬀerent approach, and its evaluation is based on the optical data of the material of interest. 2 Dielectric Function and Stopping Power The response of a medium to an energy transfer h ¯ ω and momentum transfer q is described by the complex dielectric function ε(q, ¯hω), which is related to the optical data.
Since the total number of particles has to be conserved, then ηA + ηB + ηT = 1 for any given thickness. Note that if the ﬁlm is deposited on a substrate, the fractions mentioned above are diﬀerent from those corresponding to unsupported thin ﬁlms. 2 Electrons in thin ﬁlms 57 diﬀerence is due to the backscattering from the substrate. In order to distinguish supported and unsupported thin ﬁlms, we shall use the symbols ζA , ζB and ζT for the absorbed, backscattered and transmitted fractions, respectively, for supported thin ﬁlms.