Atomic-resolution analytical scanning transmission electron microscopy of topological insulators with a layered tetradymite structure

The recent discovery of topological insulators has uncovered exciting new quantum materials with potential applications in the emergent fields of topological spintronics and topological quantum computation. At the heart of uncovering the new physical properties of these materials is the characterization of their atomic structures, composition, defects, and interfaces. The technique of atomic-resolution analytical scanning transmission electron microscopy has already provided many insights and holds great promise for future discoveries. This perspective discusses advances that have been achieved in the atomic-scale characterization of topological insulators with a layered tetradymite structure, and it proposes future directions to link atomic-scale features to exciting new physical phenomena. © 2020 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0014113., s


INTRODUCTION
Topological insulators (TIs) have emerged as fascinating quantum materials 1,2 that have led to renewed interest in the tetradymite family of Bi,Sb-chalcogenides [e.g., Bi 2 Se 3 , Bi 2 Te 3 , Sb 2 Te 3 , (Bi,Sb) 2 Te 3 , etc.]. 3,4 For example, bismuth chalcogenides offer efficient spin-to-charge conversion because they have large spin-orbit coupling and spin-momentum locking of surface states, 2,5 generate a spin-transfer torque, 6,7 undergo currentinduced spin polarization, 8 and exhibit ferromagnetic resonancedriven room-temperature spin pumping. 9 This workhorse system has also garnered interest due to its layered crystal structure: similar to graphene, transition metal dichalcogenides, and other twodimensional (2D) materials, tetradymites consist of layers that are covalently bonded in the a-b plane and separated by van der Waals bonding in the c-direction. However, unlike for other 2D materials, each tetradymite layer is a five-atom-thick quintuple layer (QL). The identification and characterization of the dominant defects in Bi,Sb-chalcogenides are critical for emerging technologies based on their exotic properties. Therefore, analytical scanning transmission electron microscopy (STEM) is an ideal technique for elucidating these defects. Unlike many characterization techniques that provide either bulk (e.g., x-ray diffraction) or hundreds-of-nanometer-to micrometer-scale information (e.g., xray photoelectron spectroscopy, Raman spectroscopy, and atomic force microscopy), STEM makes it possible to perform local analysis on the Angstrom scale.
Atomic-resolution imaging via annular dark-field STEM (ADF-STEM) and accompanying elemental mapping using energydispersive x-ray (EDX) spectroscopy and electron energy-loss spectroscopy (EELS) have been instrumental in identifying and characterizing a variety of defects in TIs. These defects span across dimensionalities, from point (0D) to line (1D), planar (2D), and volume (3D) defects. In STEM, when aberrations of the lenses are corrected, a focused electron beam (<1 Å) interacts with a thin (<100 nm) sample in transmission mode to create mostly elastically scattered electrons that are used to directly image atomic positions. [10][11][12] The scattered electrons are collected by an annular detector with intensities proportional to Z n , where Z is the atomic number of the element imaged, and the exponent n is in the range of EELS data for the O K-edge, measured on and off a defect site are also shown. 24 1.2-2.0. [13][14][15][16] The electron probe is then rastered across the sample to collect these images, simultaneously producing x rays characteristic of core electron states 17 and low-angle inelastically scattered electrons, which are used to create EDX and EELS signals, respectively ( Fig. 1). [18][19][20][21][22] As a result, analytical STEM is an unparalleled source of detail about the atomic structure and composition of defects in materials.

PROGRESS TO DATE
Analytical STEM is an excellent technique for the study of crystalline defects and interfaces, where local information about a material is critical. Not surprisingly, it has yielded numerous insights into structural distortions in a variety of tetradymite TIs. Although STEM is capable of detecting and characterizing defects of all dimensions, the majority of the existing body of work on tetradymite TIs is focused on 2D defects and interfaces. Due to similar energies, the atoms in rhombohedral Bi,Sb-chalcogenide TIs (space group R3m) can stack in either ABC or ACB geometries. This commonly gives rise to twinning, which is equivalent to a 60 ○ rotation of the tetradymite crystal structure. When the stacking order changes from ABC to ACB within a single grain as it grows along the crystallographic c-axis, a basal (lamellar) twin forms. Such twins frequently have been observed in Bi 2 Se 3 25-28 and Bi 2 Te 3 29-32 [ Fig. 2(a)]. Density functional theory (DFT) calculations for Bi 2 Te 3 predict that this twin is favored to occur within the van der Waals gap between the QLs, rather than within the covalently bonded QL. 29 Moreover, a location-sensitive reduction of the bandgap is predicted for Bi 2 Se 3 thin films with basal twins. 28 Atomic-resolution ADF-STEM images have enabled the identification of these basal twin locations in thin films 28 and nanowires, 33 as well as the quantification of the van der Waals gap expansion due to basal twinning. 29 In addition, ADF-STEM imaging has enabled the discovery of other, less common stacking-related defects within these TI films. For instance, the substrate steps have been shown to create threading defects, 30 and the associated domain boundaries have been correlated with electrostatic fields that locally charge Dirac states. 33 Stacking faults can also lead to the insertion of regular arrays of extra atoms between M 2 X 3 QLs 34,35 [ Fig. 2(b)]. This can create disorder 34 or else produce different stoichiometries, such as Bi 1 Te 1 35 [ Fig. 2(c)]. Understanding such deviations in the atomic structure is particularly important because of how the structure alters the physical properties: Bi 1 Te 1 has been identified to be a dual topological insulator, in which a weak topological insulator phase and a topological crystalline insulator phase coexist. 35 In tetradymite TI films, when two adjacent grains possess dissimilar stacking orders, a rotational twin results [ Fig. 2(d)]. In the case of Bi 2 Te 3 , these rotational twins have been reported to act as "structural doping" because the changes in the interatomic distance at the grain boundary create occupied states within the bandgap. 36 This free-electron creation increases the density of states near the conduction band minimum and reduces the electron mobility, which has important implications for devices. Such rotational twins have been observed and characterized using STEM in both Bi 2 Se 3 25,26 and Bi 2 Te 3 30,32,36 films. Atomic-level insights into the interfaces in tetradymite materials are especially important because of the role of metallic surface states in TIs. 8,43,44 Of particular interest is the interface between tetradymite thin films and their growth substrates because it provides clues about how to engineer defect-free films. Because tetradymite films grow by van der Waals epitaxy, they do not require strict lattice matching with the substrate. As such, they have been grown on a variety of 3D substrates, such as (111)-oriented Si, 25,30,32,45,46 InP, 25,26,43,47,48 GaAs, 49 and SrTiO 3 , 8 and (001)oriented GaAs, 38 AlN, 50 and Al 2 O 3 . 27,51,52 When studied with STEM, some interfaces have been shown to be atomically sharp, 43,44,53,54 but in many cases, the interfacial region has been observed to be poorly crystalline [ Fig. 2(e)] or contain nanoscale grains, 25,28,47,55 or to have a chalcogen-rich layer 30,37,38,49,52,56 [Figs. 2(f) and 2(g)]. In contrast, tetradymites grown on 2D materials, such as graphene, 57,58 hexagonal boron nitride, 39 and others, 59,60 possess mostly atomically sharp interfaces. In the special case of an Sb 2 Te 3 /Bi 2 Te 3 interface, elemental intermixing has even been observed over a distance of several QLs. 61,62 STEM imaging and spectroscopy provide otherwise unattainable local information about 3D structures and their compositional variations within tetradymites. For example, it was discovered that the FexCu 1−x Se tetragonal inclusions are single-crystalline and epitaxially oriented in the hexagonal structure of Bi 2 Te 3 , despite large (∼20%) lattice mismatch. 63 STEM analysis has also shown that dopants and matrix elements sometimes segregate at grain  Fig. 2(i)]. Cu-rich precipitates in a lower-Cu-content doped Cu:Bi 2 Se 3 matrix present yet another unusual case, where excess Cu is accommodated by intercalation into the van der Waals gap, leading to disorder, stacking faults, strain, and bending of the QLs 41 [ Fig. 2(j)]. Dopant atoms have been identified in tetradymites to occupy multiple atomic positions in the host crystal, as well as to create disorder. Direct imaging with ADF-STEM and compositional analysis with EELS have revealed, for instance, that Cr is a substitutional dopant on the cation Bi,Sb sites in (Bi,Sb) 2 Te 3 , retaining the overall film stoichiometry without Cr segregation inside the film 64 [ Fig. 2(k)], although Cr segregation has been observed for Bi 2 Se 3 films. 42 In contrast, Mn dopants in Bi 2 Te 3 have been observed to substitute for either the Bi cation or, for high Mn doping levels, for the Te anion, as well as to intercalate into the van der Waals gap and at the substrate interface. 40 Other dopants, such as K and Cu, have been reported to intercalate into the van der Waals gap between QLs, creating dislocations and stacking faults. 41,65 The exact composition and the defects in the structure can have a significant impact on the physical properties of these TI materials. For example, in the case of Cu:Bi 2 Se 3 , various Cu-doped structures identified directly by atomic-resolution imaging have been shown to have different dielectric properties. 41 In the case of Bi 2 Se 3 thin films containing basal twins, it is predicted that the presence of twins will result in opening the electronic bandgap. 28,29 Additionally, strain arising from dislocations and low-angle grain boundaries, identified WHAT IS NEXT?
While many excellent results have been reported on the crystalline structure and defects in tetradymite TIs using atomicresolution STEM, most of them have only taken advantage of direct ADF imaging of the structures and, in some cases, complemented it with compositional mapping using EDX and EELS. However, there are additional capabilities in atomic-resolution analytical STEMs that can be utilized to better characterize and understand these tetradymite TIs. Notably, a wealth of information is present in the EELS data. 68 For example, by measuring the core-level electronic excitations, local variations in the electronic band structure of the material can be evaluated and understood. 69,70 These measurements could be particularly useful for the TI materials in which the band structure at the surfaces and interfaces is different from those in the bulk due to the nature of these materials. 28,39,[71][72][73][74][75][76] Using core-loss EELS data, it should be possible to measure the effects of interfaces and defects on the local electronic properties of TI films and to evaluate the stability of topological properties. Another only lightly explored capability of analytical STEM is the use of EELS for measuring low-energy (0 eV-50 eV) excitations accruing in the TI films. 66,77,78 Measuring plasmonic oscillations at the surfaces and interfaces of TIs will provide a great deal of knowledge about the localization and features of charge modulations in the metallic portions of these materials. 79,80 It will also make it possible to measure the dielectric properties of the material across the entire film, which is essential for the determination of the electrical and optical characteristics of the material. Using monochromated EELS, the local phonon modes can be measured in these films to determine the thermal transport across QLs, planar defects, and interfaces. 81,82 In particular, by probing the relationship between the local structure and exotic physical properties, many avenues exist for intriguing STEM-based discoveries in TIs. Recent advances in STEM instrumentation, in particular the development of ultrahigh-energyresolution monochromators and single-electron-counting detectors, should make it possible to perform these measurements with very high precision. So far, this field has only glimpsed the tip of the iceberg.

ACKNOWLEDGMENTS
This project was supported by SMART, one of the seven centers of nCORE, a Semiconductor Research Corporation program, sponsored by NIST.

DATA AVAILABILITY
Data sharing is not applicable to this article as no new data were created or analyzed in this perspective.