Dark-field electron holography as a recording of crystal diffraction in real space: a comparative study with high-resolution X-ray diffraction for strain analysis of MOSFETs

Abstract

Diffraction-based techniques, with either electrons or photons, are commonly used in materials science to measure elastic strain in crystalline specimens. In this paper, the focus is on two advanced techniques capable of accessing strain information at the nanoscale: high-resolution X-ray diffraction (HRXRD) and the transmission electron microscopy technique of dark-field electron holography (DFEH). Both experimentally record an image formed by a diffracted beam: a map of the intensity in the vicinity of a Bragg reflection spot in the former, and an interference pattern in the latter. The theory that governs these experiments will be described in a unified framework. The role of the geometric phase, which encodes the displacement field of a set of atomic planes in the resulting diffracted beam, is emphasized. A detailed comparison of experimental results acquired at a synchrotron and with a state-of-the-art transmission electron microscope is presented for the same test structure: an array of dummy metal–oxide–semiconductor field-effect transistors (MOSFETs) from the 22 nm technology node. Both techniques give access to accurate strain information. Experiment, theory and modelling allow the illustration of the similarities and inherent differences between the HRXRD and DFEH techniques.