Micrometre-scale strain mapping of transistor arrays extracted from undersampled atomic-resolution images

Strain maps extracted from atomic resolution images have the ultimate spatial resolution, but have a field of view limited by the sampling necessary to resolve atomic lattices. This has typically confined strain maps to dimensions less than ∼100 nanometers. To extend the field of view beyond this limit, we apply a modified geometric phase analysis to undersampled images of atomic lattices (i.e. with a pixel size too large to resolve atomic lattices). To reduce the effects of environmental and instrumental instabilities, the images were obtained by aligning series of rapid annular dark field scanning transmission electron microscopy acquisitions. We demonstrate that for undersampled images, a geometric phase analysis can still be performed on aliased frequencies and, as long as the appropriate scaling matrix is applied, provide accurate atomic displacement measurements at large scale. Experimental challenges related to the increased effects of scanning errors as the magnification is lowered are examined. Although such errors are found to significantly reduce geometric phase signals, it was still possible to produce strain maps for arrays of up to sixteen 20nm-technology transistors, corresponding to a field of view exceeding one micrometer.