Quantitative STEM: A method for measuring temperature and thickness effects on thermal diffuse scattering using STEM/EELS, and for testing electron scattering models

Abstract

In the last two decades, advances in the dark field detectors and microscopes of scanning transmission electron microscopy (STEM) have inspired a resurgence of interest in quantitative STEM analysis. One promising avenue is the use of STEM as a nanothermometric probe. In this application, thermal diffuse scattering, captured by a CCD camera or an annular dark field detector, acts as an indirect measurement of the specimen temperature. One challenge with taking such a measurement is achieving adequate sensitivity to quantify a change in scattered electron signal on the order of 1% or less of the full electron beam. Another difficulty is decoupling the thermal effect on electron scattering from scattering changes due to differing specimen thicknesses and materials. To address these issues, we have developed a method using STEM, combined with electron energy loss spectroscopy (EELS), to produce a material-specific calibration curve. On silicon, across the range 89 K to 294 K, we measured a monotonically increasing HAADF signal ranging from 4.0% to 4.4% of the direct beam intensity at a thickness-to-mean-free-path ratio of 0.5. This yielded a calibration curve of temperature versus full-beam-normalized, thickness-normalized HAADF signal. The method enables thermal measurements on a specimen of varying local thickness at a spatial resolution of a few nanometers. We demonstrated the potential of the technique for testing electron scattering models by applying single-electron scattering theory to the data collected to extract a measurement of the mean atomic vibration amplitude in silicon at 294 K. The measured value, 0.00738 ± 0.00002 nm, agrees well with reported measurement using X-rays.