Insights from STEM and NBED studies into the local structure and growth mechanism of misfit layered compounds prepared using modulated reactants

Introduction

Misfit layered compounds, [(MSe)_1+d]_m[TSe₂]_n where M=Sn, Pb, Bi, RE, T=Ti, V, Nb, Ta, Cr and d is the difference in the relative density of the cations M and T per unit area of their adjacent planes, are a fascinating family of materials that contain interwoven layers of two constituents that have unrelated incommensurate structures [1, 2]. Initially, their non-integral stoichiometry puzzled researchers who did not realize their incommensurate structures from their complex diffraction patterns [3–6]. Following the observation of satellite reflections, Janner and Janssen were the first to recognize that the reflections due to the mutual modulation of the two subsystems composite crystal could be described with superspace symmetry [7]. Later extensions of this theory, based on the theory for incommensurately modulated crystals, were made by van Smaalen [8–11], Yamamoto [12], and Kato and Onoda [13, 14]. The periodic repetition of the interfaces enables atomic positions to be determined yielding local distortions of atom positions due to the finite thickness of the layers and the incommensurate structure [15]. More recently researchers continue to seek a better understanding of their stability relative to a mixture of binary compounds [16] and also to prepare new examples in this potentially broad class of materials [17, 18].

Recently a new technique that uses nanostructured amorphous precursors to direct the synthesis of specific metastable compounds has permitted the synthesis of many new metastable misfit layered compounds [(MSe)_1+d]_m[TSe₂]_n consisting of both new constituent structures [WSe₂, MoSe₂] as well as compounds with larger m and n values than can be prepared by traditional high temperature synthesis techniques [19–22]. Figure 1 contains a sequence of STEM images of a representative example of one of these new compounds, [(SnSe)_1.15]₁(VSe₂)₁ [23] at increasing levels of magnification. The STEM image in Figure 1C clearly shows the alternating layers consisting of two SnSe planes and a Se-V-Se trilayer. The images show that the layered structure self assembles with the constituent layers parallel with the local substrate surface. While prior TEM investigations showed that this synthesis approach can result in a variety of different volume defects [24], this particular sample appears structurally homogeneous. The STEM images reveal that different constituent layers have different local orientations resulting in a lack of long-range periodicity, consistent with prior literature [23].

Fig. 1:

Dark-field STEM images at different magnifications of a [(SnSe)_1.15]₁(VSe₂)₁ sample prepared using a modulated elemental precursor in cross-section.

In general, X-ray diffraction investigations reveal that the specular diffraction patterns of compounds grown using this low temperature growth approach contain only 00l diffraction maxima due to the alignment of the layers parallel to the substrate [19–22]. In plane X-ray diffraction patterns contain Bragg maxima that can be indexed as hk0 maxima of the independent constituent layers. In contrast to most of the misfit layered compounds formed via high temperature reactions, the in plane structures of structures grown using this new technique do not appear to distort to achieve one or more commensurate axes, even when samples of the same composition have been prepared in an ordered polymorph using traditional high temperature synthesis techniques [25]. For [(SnSe)_1.15]₁(VSe₂)₁ prior X-ray investigations yielded a c lattice parameter of 1.203(1) nm, a square in plane a-lattice parameter of 0.593(1) nm for the SnSe constituent and a hexagonal in plane a-lattice parameter of 0.341(1) nm for the VSe₂ constituent. X-ray and conventional electron diffraction along [hkl] where [hkl] (h, k≠0; l≠0) contain broad smears and no evidence of a superlattice c-axis lattice parameter, indicating coherence lengths of about (1–2) nm in these mixed-index directions [23].

The diffraction data combined with the gradual increase in long-range order along the c axis on annealing lead to an initial hypothesis that the intergrowth formed from random nucleation and subsequent lateral growth of individual constituent layers [19]. However, this hypothesis, which is based on independent nucleation and growth of each layer, does not provide a satisfactory explanation of why the 00l plane of the rock salt layer is always crystallographically parallel to the selenium planes of the diselenide. In contrast to epitaxial deposition methods, in which the material structure is built up ‘atom by atom’, the orientations of the constituent structures using this new synthesis approach are determined by the self-assembly process, which involves the nucleation and growth of the constituents during post-deposition annealing of the modulated precursor. Potential scenarios include: (i) the components (MSe or TSe₂) nucleate independently at essentially the same time; (ii) the components nucleate independently, but with one of the components nucleating before the other; and (iii) one of the components nucleates first, creating nucleation sites at the interface where the second constituent nucleates. Subsequent nucleation of the adjacent layers off of the initially formed layer in scenario (iii) could lead to preferred orientation of layers, but in a random stacking sequence.

In an attempt to unravel the formation mechanism of these semi-ordered structures using this low temperature growth approach, Atkins et al. recently reported a study exploring the formation of binary transition metal dichalcogenides from modulated elemental reactants [26]. They found that systems that only formed a 1T polymorph thermodynamically formed only a crystalline 1T polymorph when an elementally modulated precursor self assembles. This suggests that nucleation and orientation of Se-T-Se trilayers is determined by the orientation of previously nucleated layers. For systems that form polymorphs with a more complicated sequence of Se-T-Se layers, such as 2H or 3R, X-ray diffraction studies revealed broad smears along hkl where hkl (h, k≠0; l≠0) and no evidence of an expanded c-axis lattice parameter, indicate coherence lengths of about (1–2) nm in these mixed-index directions. Compared to a completely random stacking sequence, however, too many zone axes were observed in the STEM images, leading to the speculation that there was a random stacking sequence of a, b and c layers rather than the repeating a-b sequence expected for a 2 H polytype or a completely rotationally disordered sequence of Se-T-Se trilayers.

This prompted the STEM investigation of [(SnSe)_1.15]₁(VSe₂)₁ samples in both cross section and plan view presented herein, which probes the grain structure within the a-b planes and the stacking sequence of the layers. Using scanning nano-beam electron diffraction we found local regions with a single 12-fold symmetric diffraction pattern, regions with two superimposed 12-fold patterns, and regions with many superimposed 12-fold patterns, which provide evidence that specific relative orientations are favored. We also found regions with more complicated nano-beam electron diffraction patterns reflecting defects resulting from the non-equilibrium growth technique used to prepare the samples. The diffraction data suggests that growth occurs by the sequential nucleation of layers, with the adjacent crystalline interfaces providing nucleation sites that selectively orient the structure of the adjacent layers. This template effect provides an explanation for the unusual disordered structure of these materials, where individual constituent layers are crystalline but with extensive disorder between layers. Developing a more detailed understanding of the formation mechanism of intergrowths prepared using this new synthesis approach will facilitate extending this synthetic approach to new compositions as well as potentially new constituent structures.

Experimental

The samples used in this study were prepared using physical vapor deposition via a custom built high-vacuum deposition system [27], evacuated to a base pressure of 1×10^–7 mbar. Selenium (99.999% purity, Alfa Aesar^®) was evaporated using a custom-built effusion cell. Tin (99.98% purity, Alfa Aesar^®) and vanadium (99.7% purity, Alfa Aesar^®) were deposited using Thermionics™ 3 kW electron beam guns. The films were deposited on (100) oriented silicon substrates positioned approximately 25 cm above the sources on a motorized carousel. Pneumatic powered shutters, located between each source and substrate, controlled the time each element deposited for each layer in the repeating sequence. A custom LabVIEW program controlled the position of substrates, the opening and closing of shutters, and the order of deposited layers. A quartz microbalance crystal monitoring system controlled deposition rates. Se, Sn, and V were each deposited at approximately 0.4 Å/s.

The deposition of (SnSe)_1.15VSe₂ samples was done via a layer-by-layer process, repeatedly depositing a four element sequence of Se-Sn-Se-V. The film total thickness was determined by the number of (SnSe)_1.15VSe₂ repeating units deposited and we targeted total film thicknesses near 50 nm. Calibration of the deposition parameters is necessary to determine the amount of each element required for a Se-Sn-Se-V unit to self-assemble into a single (SnSe)_1.15VSe₂ unit cell after annealing [19, 20]. Composition of the films was analyzed by electron probe microanalysis (EPMA) using a thin film technique described by Phung [28]. Precursors were annealed under a nitrogen atmosphere (<1 ppm O₂) to self assemble the targeted compound. Optimal annealing conditions for (SnSe)_1.15VSe₂ were found to be 400°C for 20 min.

X-ray reflection (XRR) and X-ray diffraction (XRD) data were obtained on a Bruker D8 Discover diffractometer, using Cu Kα radiation. θ-2θ locked coupled scan geometry was used to acquire scans of the precursors and annealed samples between 0 and 10°2θ (X-ray reflectivity) and between 10 and 65°2θ (X-ray diffraction). The FullProf program package [29] was used to refine the position of atomic planes of atoms along the c-axis using (00l) reflections.

STEM investigations of plan-view and cross-section specimens of the (SnSe)_1.15VSe₂ samples were carried out at a TEM/STEM JEOL 2200FS operated at 200 kV, equipped with an in-column energy filter, an energy-dispersive X-ray detector and a high-angle annular dark-field detector. In addition to the structure studies by means of conventional TEM (CTEM) and scanning TEM (STEM) electron energy filtered electron diffraction patterns were recorded under the condition of nano-beam electron diffraction (NBED). The spot size used for energy filtered NBED was between 10 nm and 20 nm. Plan-view specimens were prepared by a special rupture technique purpose-developed for disordered misfit compounds, which have been referred to previously as ferecrystals. Cross-section specimens were prepared by conventional polishing and subsequent dimpling followed by ion milling.

Results and discussion

The synthesis of the [(SnSe)_1.15]₁(VSe₂)₁ sample used in this study followed the previously published procedure [23]. The specular X-ray diffraction pattern contained only 00l reflections and the c-lattice parameter, 1.20127(4) nm, is slightly smaller than the lattice parameter range reported for different samples in a previous publication, 1.2027(7)–1.2032(7) nm [23]. The results of the refinement are listed in Table 1, and the distances between the different atomic layers shown in Figure 2 are fairly close to the values reported by Atkins et al. The refined misfit parameter is 0.04 smaller than the published value of 0.15 as calculated from an hk0 X-ray pattern [23]. However, the value is consistent with the Sn/V atomic composition ratio of 1.12(1) measured by EPMA.

Fig. 2:

Average structure obtained from Rietveld refinement of a [(SnSe)_1.15]₁(VSe₂)₁ specular X-ray diffraction scan.

To probe the variation on the sample in plan view, Figure 3 contains a representative dark-field STEM image and chemical EDX maps and a STEM image all from the same area. Our EPMA data showed that the composition was uniform between the different micron areas that were investigated. The EDX maps extend these results, showing that the sample is chemically homogenous within the 0.7 nm spot size used. The bright and dark areas in the STEM dark-field image are therefore caused not by chemical differences, but by differently orientated grains scattering the electron beam with different efficiency. The bright areas are domains orientated where the beam is perpendicular to the c axis of the ferecrystal, for example, area “A” in Figure 4B. Tilted grains, areas “B” and “C” in Figure 4B, cause the dark areas.

Fig. 3:

Dark-field STEM image of a plan-view sample. (A) DF-STEM overview, (B) EDX maps for Sn, V and Se, respectively, (C) sketch illustrating the occurrence of bright and dark areas in the dark-field STEM image.

Fig. 4:

Plan-view CTEM micrograph. Some of the individual grains evident in this image are outlined with dotted yellow lines. The Moiré fringes due to the interference of grains with different orientations are also evident, and some of these regions have been highlighted with blue and red tinting. Some of the Moiré fringes resulting from grains with different relative tilting on both sides of the interface (see sketch on right) are tinted blue. Moiré fringes resulting from different extents of rotational disorder are tinted red.

To probe the lateral structure of the [(SnSe)_1.15]₁(VSe₂)₁ sample, CTEM was performed on plan-view samples. Figure 4A contains a representative image, which contains both distinct grains (some of which are outlined with dotted lines) and areas containing Moiré fringes (some of which are highlighted with red or blue tinting). The range of grain sizes observed is consistent with the average grain sizes determined from the linewidths of the in plane diffraction patterns reported previously for [(SnSe)_1.15]₁(VSe₂)₁ samples [23] and with the lateral size of the domains within a single constituent layer observed in the cross-section STEM image (Figure 1). The Moiré fringes in the middle of Figure 4A, shaded in red and blue, are evidence for a superimposition of grains at interface regions. Figure 4B illustrates how Moiré fringes occur when grains with different tilting angles overlap each other. Regions with this type of Moiré fringing are highlighted in blue. Moiré fringes also occur when grains with different rotational orientations overlap and regions with this type of fringing are highlighted in red. The CTEM images require that any proposed growth mechanism result in a collection of grains with a variety of orientations within the sample and are generally consistent with the structural picture obtained from previous XRD structural studies [23].

To probe the extent of local order both within and between different grains, NBED diffraction patterns were collected in a large number of positions. Occasionally, diffraction patterns were obtained that contained evidence of a supercell along the c axis, as shown in Figure 5. Integration of the intensity along the different family of planes (Figure 6) enabled an average separation of the reflections of 0.271(2) nm^–1 to be calculated from Gaussian fits. This yields a c-lattice parameter of 3.69(3) nm for the supercell in this region of the sample, which is approximately three times the lattice parameter determined from XRD, implying that an ordered domain is formed with a stacking of three, or a multiple of three [(SnSe)_1.15]₁(VSe₂)₁ structural units. This unexpected discovery of local regions with ordering between the layers suggests that it might be possible to prepare samples with an ordered supercell over larger domains using this new synthesis approach. One potential approach to explore would be to vary the post deposition processing conditions. Rapid thermal annealing experiments and/or annealing in controlled overpressures of chalcogen might enable the volume fraction of the ordered regions to be significantly increased. This experimental control and the ability to quantify the ordering would be very valuable, as it might be expected that thermal and electrical transport properties could vary both with the domain size of the local order and the identity of the local order within a domain.

Fig. 5:

An energy-filtered NBED pattern obtained from the [(SnSe)_1.15]₁(VSe₂)₁ sample that contained a series of resolvable supercell reflections along the c axis. Different hkl families of reflections for the SnSe and VSe₂ constituents are shown in red and blue, respectively.

Fig. 6:

A line profile of intensity along the 0–2l family of reflections in Figure 5. The positions of the reflections were used to calculate the c-lattice parameter of the supercell as described in the text.

To probe the extent of orientational ordering both between and within different grains, plan-view specimens were examined using energy-filtered NBED. The energy filtering was necessary to depress the background caused by inelastically scattered electrons. A representative selection of diffraction patterns obtained from a large number and variety of locations is shown in Figure 7. While some of the patterns contained a large number of reflections in the expected [hk0] diffraction cones approaching that anticipated for a random orientation of grains, others had evidence for 12-fold symmetry including a pattern that had only a 12-fold pattern, indicating that the arrangement of the layers is not rotationally random from layer to layer. This provides strong evidence that following an initial nucleation event in a specific layer in the precursor, adjacent layers nucleate off of the first crystalline layer and subsequent layers nucleate off of the growing domain. Since the hk0 reflections do not contain any information on the stacking order, the layers could be stacked in a random order, but with specific rotational relationships between them. This is consistent with the report by Atkins on the growth of transition metal diselenide films from layered precursors and agrees with the extrapolation of their findings [25]. The 12-fold symmetry also implies that within the beam size of the NBED experiment, there must be crystalline domains where there is a coincidence of the 3-fold symmetry axis of the dichalcogenide layer and the 4-fold axis of the square structure of the SnSe layer. Locally this could occur through displacements of atoms in the constituent structures while still maintaining the average unit cell sizes and symmetries determined for each constituent from the X-ray diffraction studies if the lateral extent of coordinated displacements is small.

Fig. 7:

Selected energy-filtered NBED patterns obtained from a plan-view specimen.

To illustrate how such a pattern could result from a preferred orientation of layers, Figure 8 contains one potential stacking sequence that yields a 12-fold symmetric pattern. The pattern was creating a building unit consisting of a VSe₂ layer and a SnSe layer in which the SnSe unit cell was slightly distorted from the average unit cell determined from X-ray diffraction studies to create long range coherence of the structures in the a-b plane. The STEM image in Figure 1C contains evidence for a six layer repeating pattern from the zone axis that is visible. If we choose this zone axis arbitrarily to be in a “c” orientation, then the six layer repeat pattern is c-(a,b)-(a,b)-(a,b)-(a,b)-c, where (a,b) indicates that we do not have any information as to whether it is an “a” or “b” layer We built up a 6 unit repeating pattern containing the arbitrarily chosen c-b-a-a-b-c sequence as an example of a representative potential unit cell. Figure 8B shows the stacking sequence, 8A provides an image of the projection of the structure onto the a-b plane, and Figure 8C shows a cross sectional image where one sees a zone axis in the 1st and 3rd layer of the repeating unit. The resulting diffraction pattern simulated from this structure is shown in Figure 9 next to that obtained experimentally from the region that contained a single domain diffraction pattern. The qualitative agreement between the experimental and simulated pattern provides support that such a model for the stacking sequence is reasonable.

Fig. 8:

An example of a distorted SnSe lattice and a stacking of 3 SnSe-VSe₂ pairs that results in the observed 12-fold symmetry in the diffraction pattern. The resulting diffraction pattern is shown in Figure 9.

Fig. 9:

The simulated diffraction pattern from the stacking sequence shown in Figure 8 and the energy-filtered NBED pattern obtained from plane view sample of the [(SnSe)_1.15]₁(VSe₂)₁ sample.

This type of long-range order could result from the layers templating off one another during the growth process in specific orientations. To probe this effect, we calculated the dependence of the energy as a function of orientation of a fragment of a SnSe bilayer sandwiched between VSe₂ layers. Figure 10 shows that, while the exact energies vary depending on the size of the SnSe fragment, there is a periodic minimum in the energy of the interface every thirty degrees. Subtle differences must be responsible for the favoring of specific stacking sequences, and it is probable that different domains might have different stacking sequences and different domain sizes. Finding such ordered regions suggests that during growth, layers crystallize off of existing crystallized layers, and this template effect on nucleation is the likely cause of the orientational relationship between layers. The influence of different stacking sequences on physical properties is not known.

Fig. 10:

Calculated energies for SnSe fragments sandwiched between VSe₂ layers as a function of rotational angle between the two subsystems. The five systems differ in the radius of the SnSe fragment (which determines the number of Sn and Se ions in the fragment) and the size of the simulation cell determined by the VSe₂ sublattice (6×6, 10×10, and 12×12 VSe₂ units, respectively). The calculations employ density functional theory combined with a parameterized van der Waals interaction as outlined in reference [30]. For both subsystems the lattices are kept as perfect periodic systems (or a fragment thereof) with all structural parameters taken from the experimental results given in by Atkins [30].

Conclusions

The difference in the strength of the interaction between the sample and the different probes used, X-rays and electrons, reveals information about the structures on different length scales. The XRD results provide no evidence of a supercell, but suggest that the sample consists of SnSe bilayer and VSe₂ trilayers that are randomly rotated with respect to one another. The cross-section dark-field STEM images provide evidence for long-range order in small domains, although the extent of this information is limited by the small number of layers that are in a zone axis orientation. Some of the energy-filtered NBED patterns obtained in cross section of the [(SnSe)_1.15]₁(VSe₂)₁ sample, however, contained a series of spots along hkl families of reflections suggesting a supercell along the c axis which must be a multiple of 3 times the c-axis unit cell determined using x-rays. Some of the NBED patterns obtained contained evidence for 12-fold symmetry, including one pattern that appeared to be a single crystalline domain. This pattern was modeled by stacking layers with a thirty degree rotation between layers. The presence of these highly ordered local regions strongly suggests that the structure forms via a template nucleation of one layer off of the next. Presumably the component that nucleates first creates a nucleation site at it’s surface for nucleation of the other component. This suggests that a variety of processing conditions should be tried to increase the extent of long range order. While the nano-beam diffraction [hk0] patterns provide strong evidence that the layers template off of one another during growth, it does not contain information on the stacking sequence.