A theoretical model for the energy dependence of electron channelling patterns in scanning electron microscopy

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Abstract
Equations given by Hirsch and Humphreys (1970) and by Spenceret al(1972) for describing the contrast in electron-channelling patterns (ECP) are generalized by taking into account the energy losses which the fast electrons experience in the specimen. In this way a theory is established which considersdiffraction, backscatteringandenergy losses.This theory is used and calculations are made of the dependence of the contrast in ECP on the energy of the backscattered electrons. Unlike earlier theories for ECP the present work gives the correct behaviour of the backscattering coefficient for large foil thicknesses. It is shown that the visibility can be strongly enhanced by using an energy-analysing detector, in agreement with experimental results. The signal-to-noise ratio is evaluated to find the energy window which gives optimum contrast. For Si, Cu and Au these windows are approximatelyE0>E>E0− 700eV,E0>E>E0− 250 eV andE0>E>E0− 400 eV respectively. Calculations of the mean escape depth as a function of energy show that the electrons are emitted from a thin surface layer for small energy losses. The resolution can therefore be significantly improved in the backscattered mode by using an energy-analysing detector.