Resolution attainable in analysis

To reiterate STEM is mainly practised because point-by-point analysis can be carried out. The information available is at least three-dimensional a two-dimensional image, which is a projection of the specimen, and for each picture element, one or more spectra either electron energy loss or X-ray emission, or any other spectrum such as optical cathodoluminescence. An important question is, given an incident probe of a certain size, do say, how large is the region from which the spectra originate  

The answer to this question is in three parts. The first part is related to the properties of the electron probe, such as the size of the probe and its broadening, as well as the impact parameter problem, i.e. the characteristic distance beyond which the influence of the electric field from the swift electrons is negligible. The second part is more a specimen problem, namely the spatial 

The impact parameter can be estimated simply from the following consideration the transverse electrostatic pulse contains frequencies of the order of v/b, where v is the velocity of the fast electron. Thus a core electron bound with an energy AE can only be promoted to empty states above the Fermi level in the conduction band if r b = hv/AE. This fundamental property of the radiation can also be seen by explicitly integrating the resultant electric field at an atomic site a distance b away (as given in eq. (3.12)), over the momentum space d q giving  

The functions Kq and Ki are modified Bessel functions which decay asymptotically as X (r) oc r e The expression (3.15) shows that the energy density of the evanescent wave decays exponentially with v/cob. For 100 kV incident electrons, this translates to an approximate relationship between the energy loss and the impact parameter, 

The parameter b is to be interpreted as the resolution obtainable in a perfect instrument, where the resolution is limited only by the uncertainty principle. For losses in the valence region, where AE might be 20 V, b is about 2 nm for the carbon K-loss at 185 V, b is about 0.2 nm. Only for losses around 200 V and above does b shrink to atomic dimensions. 

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