4D STEM – characterisation of materials and contrast enhancement in light matter

Abstract text (incl. figure legends and references)

The simultaneous availability of densely sampled real- and diffraction space data in momentum-resolved (MR) STEM increases the versatility of established imaging modes and enables the development of a multitude of new techniques. Prominent ones are first moment (FM) STEM imaging and ptychography, which will be outlined as to basic concepts, limitations and paradigm applications. Then, first results in the field of imaging weakly scattering organic specimens will be shown.

The flexibility provided by MR STEM as to the generation of FM, bright field (BF), dark field (DF) and annular BF (ABF) signals implies it being termed a universal imaging mode. However, it is found that many signals obey their own focus dependence already at moderate specimen thicknesses [1], as demonstrated in a 4D STEM focal series experiment in Fig. 1a, yielding the contrast dependencies in Fig. 1b. A simultaneous recording of, e.g., Z-contrast and FM STEM data at their optimum foci is thus usually not possible. Moreover, we discuss the second moment of the diffracted intensity as to its capability to recover the locations of the specimen surfaces in beam direction. Another important factor to be considered for the quantitative understanding of low-angle scattering is the redistribution of diffracted intensity due to (multiple) plasmon scattering [2], which we demonstrate by energy-filtered MR STEM as depicted in Fig. 1c. Here, the validity of a convolutional Lorentzian model is checked to account for multiple plasmon scattering.

By interpreting FM STEM using Ehrenfest"s theorem [3], electric field quantification in 2D materials is now possible at atomic scale as shown in Fig. 2. In addition, spontaneous, piezo- and ferroelectric specimens have thicknesses of several tens of nanometers, requiring a careful assessment of dynamical scattering. Whereas this leads to moderate systematic errors in unit cell averaged FM data in wurtzite GaN [4], field quantification in Pb- and Ba-based ferroelectrics is shown to be prone to substantial errors arising from dynamical scattering, mistilt and bonding, as demonstrated in a combined experimental and simulation study. In Fig. 3a, a PbZrTiO example is used to illustrate the presence of crystallographic tilt gradients across domain boundaries in 90° domains, leading to systematic errors easily misinterpreted as polarisation-induced electric fields. As a remedy, we present the gradient-based retrieval of the ferroelectric structure using mistilt-corrected, parametrised inverse multislice methods applied to the same 4D data set as depicted in Fig. 3b, from which ionic displacements can be measured accurately.

Whereas ptychographic phase retrieval is complicated in the presence of dynamical scattering, organic matter such as covalent organic frameworks (COFs) and proteins can be treated as (weak) phase objects. We present a study of the validity of this assumption by dose-dependent multislice simulations of viruses in amorphous ice, justifying the application of single-sideband and Wigner distribution deconvolution ptychography, and the quantitative interpretation of differential phase contrast (DPC) STEM [5], as exemplified for a COF in Fig. 4. These basic results will be used to envisage possible future directions to combine physical and life science microscopy.

[1] Ultramicroscopy 233, 113425 (2022)

[2] APL 121, 213502 (2022)

[3] Nat. Comm. 5, 5653 (2014)

[4] PRL 122, 106102 (2019)

[5] Nat. Methods 19, 01586 (2022)