EELS log-ratio technique for specimen-thickness measurement in the TEM

We discuss measurement of the local thickness t of a transmission microscope specimen from the log-ratio formula t = lambda ln (It/I0) where It and I0 are the total and zero-loss areas under the electron-energy loss spectrum. We have measured the total inelastic mean free path lambda in 11 materials of varying atomic number Z and have parameterized the results in the form lambda = 106F (E0/Em)/ln (2 beta E0/Em) where F = (1 + E0/1,022)/(1 + E0/511)2, the incident energy E0 is in keV, the spectrum collection semiangle beta is in mrad, and Em = 7.6Z0.36. This formulation should allow absolute thickness to be determined to an accuracy of +/- 20% in most inorganic specimens.