Local thickness measurement through scattering contrast and electron energy-loss spectroscopy.

Scattering contrast measurements were performed on thin films of amorphous carbon and polycrystalline Au, as well as single-crystal MgO nanocubes. Based on the exponential absorption law, mass-thickness can be obtained within 10% accuracy by measuring the incident and transmitted intensities in the same image. For mass-thickness measurement of a thin amorphous specimen, a small collection semiangle improves the measurement sensitivity, whereas for the measurement of polycrystalline or single-crystal specimens, a large collection semiangle should be used to reduce diffraction-contrast effects. EELS thickness measurements on MgO nanocubes suggest that the Kramers-Kronig sum-rule method (with correction for plural and surface scattering) gives 10% accuracy at medium collection semiangles but overestimates the thickness at small collection semiangles, due to underestimation of the surface-mode scattering. The log-ratio method, with a formula for inelastic mean free path proposed by Malis et al. (1988), provides 10% accuracy at small collection semiangle, while that proposed by Iakoubovskii et al. (2008a) is preferable for medium and large collection semiangles. As a result of this work, we provide recommendations of preferred methods and conditions for local-thickness measurement in the TEM.