Two-dimensional gaussian fitting for precise measurement of lattice constant deviation from a selected-area diffraction map

Abstract

Unlike X-ray diffraction or Raman techniques, which suffer from low spatial resolution, transmission electron microscopy can be used to obtain strain maps of nanoscaled materials and devices. Convergent-beam electron diffraction (CBED) and nanobeam electron diffraction (NBED) techniques detect the deviation of a lattice constant (i.e. an indicator of strain) within 0.01%; however, their use is restricted to beam-insensitive samples. Selected-area electron diffraction (SAED) does not have such limitations but has low spatial resolution and precision. The use of a spherical aberration corrector and a nanosized selected-area aperture improves the spatial resolution, but the precision is still low. In this study, a two-dimensional stage-scanning system is used to acquire arrays of diffraction patterns at different positions of the sample under fixed beam conditions. Data processing with iterative nonlinear least-squares fitting enabled the spot displacement for each point of the scan area to be measured with precision comparable to that of the CBED or NBED technique. The precise strain determination, in combination with the simplicity of the measurement process, makes the nanosized SAED technique competitive with other methods for strain mapping at nanoscale dimensions.