Sub-nm Resolution, Sub-pm Precision Structure Mapping Robust to Thickness and Tilt Variations by Cepstral Analysis of Scanning Nanodiffraction 4D-STEM

Scanning nano-beam electron diffraction (NBED), obtained from 4D-STEM datasets enabled by fast, high dynamic range, and low noise pixelated detectors[1], offers a quick, precise, and high-resolution technique for structural characterization. Typical maps can be recorded in about a minute with sufficient signal to reach sub-pm precision. For sufficiently thin samples, such as 2D materials, kinematic descriptions of the diffraction patterns are sufficient for the direct determination of the full 3D structure including strain and tilt [2]. However, the nonlinear nature of dynamic diffraction complicates the analysis of samples thicker than a few nanometers. The scanning speed and spatial resolution achievable in 4D-STEM makes it difficult to implement precession schemes to reduce dynamical contrast. Here we present cepstral analysis [3] as a method to decouple the underlying lattice structure from its dynamical envelope, providing a robust, quantitative technique for the crystallography of arbitrary samples.