In‐Plane Twinning Defects in Hexagonal GeSb2Te4

Ge–Sb–Te (GST) alloys are an important family of phase‐change materials employed in non‐volatile memories and neuromorphic devices. Conventional memory cells based on GST rely on the switching between an amorphous state and a metastable, disordered rocksalt‐like phase. Recently, however, it has been proposed that a special type of defect in layer‐structured GST—the so called “swapped bilayer” defect—is responsible for a novel phase‐change mechanism observed in GST‐based superlattices. Thus, disorder appears to play an important role in both types of switching mechanisms. Here, the observation of a new in‐plane twinning defect in hexagonal GeSb2Te4 by direct atomic‐scale imaging experiments is reported, which serves as the key ingredient to account for the abundance of inverted stacking faults in hexagonal GST and superlattices. Ab initio simulations reveal a low energy cost for these extended defects, and indicate that such defects can affect the electrical properties by inducing electron localization. This work provides additional insight into the nature and effects of structural disorder in GST phase‐change materials.


Introduction
Phase-change materials (PCMs) undergo fast, reversible transitions between a crystalline and an amorphous state characterized by different optical and electronic properties. [1][2][3] The resulting property contrast has been exploited in optical and nanophotonic devices [4] and standalone electronic memories [5][6][7] was identified as the major ingredient to stabilize the swapped bilayer defects. [52][53][54] These swapped bilayers are mobile upon thermal annealing [48] or focused electron beam irradiation, [47] and could serve as the forefronts to alter the stacking sequence of layered GST structures. [55] However, it remains elusive whether this local structural rearrangement can account for the nanosecond switching in iPCM devices.
Atomic-scale structural characterization experiments via transmission electron microscopy revealed the presence of various defects in hexagonal GST and related superlattices, in addition to swapped bilayer defects. For instance, although perfect hexagonal GeSb 2 Te 4 (h-GST) consists of periodically stacked seven-layer atomic blocks, five-, nine-, and 11-layer blocks were also found in post-annealed thin films, corresponding to the stoichiometry of Sb 2 Te 3 , Ge 2 Sb 2 Te 4 , and Ge 3 Sb 2 Te 6 , respectively. [52] In Te-richer GST thin film or grains, even triple-layer atomic blocks were observed and were shown to be strain-stabilized, octahedrally bonded GeTe 2 nanostructures. [56] Another major stacking fault consists of atomic blocks with the same stoichiometry but inverse stacking sequence of the atomic layers. In this work, we provide a thorough understanding of the genesis of these inverted blocks via the identification of an in-plane twinning structure by sub-angstrom transmission electron microscopy. We also thoroughly investigate the structural and electronic properties of models of h-GST containing such defects by ab initio simulations based on density functional theory (DFT).

Results and Discussion
We deposited GeSb 2 Te 4 thin films via magnetron sputtering and annealed the samples at 300 °C for half an hour. X-ray diffraction (XRD) measurements confirmed that the hexagonal phase formed in the thin films ( Figure S1, Supporting Information). The films were then used to prepare the specimen for transmission electron microscopy experiments. The technical details can be found in Experimental Section. As shown in Figure 1a, the unit cell of the perfect h-GST phase consists of three septuple-layer structure blocks, and the compositional order inside an ideal septuple-layer block is -Te-Sb-Te-Ge-Te-Sb-Te-, as indicated by the yellow, green, and red spheres. We use "a," "b," and "c" to denote the atomic layers with in-plane atomic positions (0, 0), (2/3, 1/3), and (1/3, 2/3) of the hexagonal cell, respectively (see the side view in Figure 1a and the top view in Figure S2, Supporting Information). The complete stacking sequence of the unit cell is -g-abcabca-g-bcabcab-g-cabcabc-, where g represents a pseudo van der Waals (vdW) gap [57] between the structural blocks. As displayed in Figure 1b, the inverse stacking corresponds to the sequence -g-acbacba-g-cbacbac-g-bacbacb-. These two models are equivalent when periodically repeated.
The investigations of the h-GST thin film specimen by means of spherical aberration corrected (Cs-corrected) scanning transmission electron microscopy (STEM) showed a mixture of the two stacking sequences at the nanometer scale. Figure 1c,d shows two images of the h-GST film recorded using high angle annular dark field (HAADF) imaging technique along the [1120] direction. For the HAADF STEM image, the intensity peaks (bright spots) appear at the positions of the atomic columns and the image intensity is approximately proportional to the square of the averaged atomic number Z of each column along the view direction. The Ge-rich columns show lower image intensity than the Sb-rich and Te columns due to the relatively low Z value (Z = 32, 51, and 52 for Ge, Sb, and Te atom, respectively). In the images, the stacking sequences "abc" and "acb" are indicated by the blue and red arrows, respectively. Apparently, the size of the inverse blocks varies largely and these blocks are distributed randomly. From the image, the boundaries between the inverse blocks are flat and exhibit darker contrast (deep black lines) than the gaps between the regular stacking planes. We also found the boundaries where the blocks with inverse stacking sequence meet in-plane, as marked by orange boxes. The switching of the stacking sequence along the horizontal direction looks smooth, without any obvious cracks or strong lattice distortion. These The stacking sequence is -g-abcabca-g-bcabcab-g-cabcabc-. The Ge, Sb, and Te atoms are shown as red, yellow, and blue spheres. b) The atomic structure with inverted stacking. The stacking sequence is -g-acbacba-g-cbacbac-g-bacbacb-. c,d) Large scale HAADF images of GeSb 2 Te 4 with out-of-plane twin-like structures and in-plane twins. The blocks with normal and inverted stacking are indicated by the blue and red arrows, respectively. The in-plane twins are marked by the dashed orange boxes. A swapped bilayer defect is marked by the white box at the top right corner. The enlarged view of this defect is shown as inset at the bottom right corner.
in-plane twinning boundary structures can span over a single atomic block or a few blocks with swapped bilayers. A typical swapped bilayer defect is marked by the white box at the top right corner in Figure 1d. The zoom-in view of this defect is shown in the inset.
To rule out the effects of other defects, we focus on the in-plane twinning boundary structure that occurs within one atomic block. Figure 2a shows an enlargement of the in-plane twin boundary area in Figure 1d. At the core area inside the orange box, the shape and intensity of some image spots become less regular, due to the overlap of two stacking sequence structures and local distortions. As discussed later, the presence of extra image spots and atomic distortions can be attributed to the local shifts of atoms and the presence of compositional Ge/Sb disorder in the cation-like layers, which also affect the nearest bonding neighbors in the anion-like Te layers. Figure 2b,c shows a symmetrical boundary model that was proposed according to the local stacking sequence, representing the basic structural unit of the in-plane twin defects.
We carried out DFT calculations on defective h-GST models with orthorhombic supercells using the projector-augmented wave (PAW) pseudo-potentials, [58] the Perdew-Burke-Ernzerhof (PBE) functional, [59] and the Grimme's D3 correction for the van der Waals forces [60] with the VASP code. [61] More technical details can be found in Experimental Section. The defective model contained two standard septuple-layer (SL) GeSb 2 Te 4 blocks and one defective SL block (in total, 36 Ge, 72 Sb, and 144 Te atoms). Both the atomic positions and cell volume of the two models were fully relaxed. The structural details of the relaxed model are further illustrated in Figure 2b,c. The in-plane twin defect causes lattice expansion (4.29 Å × 44.84 Å × 40.81 Å) less than ≈1% along the y and z directions with respect to the pristine h-GST. The cell edges of pristine h-GST are a hex = b hex = 4.30 and c hex = 40.49 Å in the hexagonal unit cell that contains 21 atoms, and 4.30 Å × 44.63 Å × 40.49 Å in the orthorhombic supercell that contains 252 atoms. The energy cost of this defective block is ≈2.28 eV nm −1 , which is higher than the energy cost of bilayer defects in h-GST (≈1.67 eV nm −1 ). In terms of energy cost per atom, the defective model is ≈13.5 meV per atom higher than the pristine phase, also larger than that of bilayer defects in h-GST, ≈9.8 meV per atom. [52,54] This is due to the much higher defect density employed, that is, 1 in-plane twinning defect per ≈9.1 nm 2 versus 1 bilayer per ≈20 nm 2 . As discussed later, when the defect density of in-plane twinning is reduced by 50%, the energy cost is decreased to ≈1.18 eV nm −1 (≈6.9 meV per atom) with much reduced lattice expansion. In experiments, the planar density of in-plane twinning defects is also much lower than that of bilayer defects (1 bilayer per ≈75 nm 2 ). The statistical HAADF scans showed an estimated density value below 1 in-plane twinning defect per ≈150 nm 2 .
For an SL block in pristine h-GST, both Ge and Sb atoms are in sixfold octahedral coordination. Regarding Te, the coordination number (CN) of the middle two Te atoms is six, but is reduced to three at the two edges. The center Ge atom forms six equivalent bonds with the neighboring Te atoms (≈3.00 Å), while the two outer Sb atoms both form three short bonds with edge Te atoms (≈3.01 Å) and three long bonds with middle Te atoms (≈3.18 Å). In the defective h-GST, the in-plane twinning defects result in local lattice distortions, homopolar bonds, as well as under-and over-coordinated Te atoms. The Sb-Sb and Te-Te homopolar bonds show bond lengths of ≈3.15 and ≈3.35 Å. The atoms forming these bonds are sixfold coordinated but have one non-octahedral bond. Regarding the middle Ge atom, it moves upward to form four short bonds with the upper four Te atoms (≈3.00 Å), and two long bonds with the two lower Te atoms (≈3.33 Å), resulting in six non-octahedral bonds with its Te neighbors. At the top edge, the under-coordinated Te atoms form two short Sb-Te bonds (≈2.89 Å), while at the bottom edge, the over-coordinated Te atoms form four long Sb-Te bonds (≈3.18 Å). None of these Sb-Te bonds are octahedral bonds. Due to the periodic boundary conditions, our defective model contains an inverse in-plane twin located at the left boundary in Figure 2c.
As shown in Figure 3, we computed the total density of states (TDOS) for the pristine and the in-plane twin model and the local density of states (LDOS) for defective atoms in the in-plane twin model. The pristine model has larger TDOS near the conduction band minimum (CBM). However, there is a very small region (indicated by the red arrow) where the in-plane twin model has a larger TDOS. This region corresponds to the peak in the LDOS of the Sb atom forming the homopolar bond. There is also a shoulder at slightly higher energies corresponding to a small peak in the LDOS of undercoordinated Te atoms (CN = 2). Furthermore, Te atoms with wrong coordination number (CN = 2/4) have larger LDOS near the valence band maximum (indicated by the blue arrow) as compared with standard threefold coordinated Te atoms (CN = 3). In particular, the LDOS of Te (CN = 2) has a large peak at about −0.5 eV. Note that the Te atoms with CN = 2/4 are regarded as defects in h-GST; despite that, in pure Te crystal, each Te atom has only two neighbors. [62][63][64][65] In h-GST and other related PCMs, a special bonding mechanism is dominant, known as metavalent bonding (MVB). [66][67][68][69][70] This bonding mechanism is a peculiar type of p-bonding characterized by pronounced electron delocalization. In the parent compound GeTe, the average number of p electrons per site is three; in h-GST, MVB still requests three p electrons per site on average, counting the vacant sites in the pseudo vdW gaps. These special sites in the pseudo gaps play an important role when a vacancy disordering process is triggered in h-GST via strong knock-on effects induced by extensive electron or ion beam irradiation. [71][72][73] Hence, the threefold Te atoms at the edge of the atomic septuple blocks are regarded as normal motifs, while under-or over-coordinated Te atoms are regarded as defects. Since the Te (CN = 4) atom forms four Sb-Te bonds, it shows a DOS peak at low energy, while the p electrons of the Te (CN = 2) atom creating an energetically less favorable trap state at about −0.5 eV (Figure 3).
Next, we focus on the localization of the electronic states, which could have an impact on the transport properties. We considered larger models and employed the CP2K code [74] to optimize the geometry and compute the electronic properties. We took the relaxed defective orthorhombic supercell presented in Figure 2c and expanded the model along the x direction by three times, which allowed to assess the impact of compositional Ge/Sb disorder. The cell edges of the supercell model are 12.87 Å × 44.84 Å × 40.81 Å (containing 756 atoms). In the disordered models, 50% Ge and 50% Sb atoms occupy the center cation-like layer, whereas 25% Ge and 75% Sb occupy the two outer cation-like layers. The models with and without compositional disorder were relaxed further, prior to the electronic structure calculations. To determine the degree of localization of the Kohn-Sham states α, we employed the inverse participation ratio (IPR). This quantity is defined as: where Ψ α,i are the expansion coefficients of α with respect to some localized basis set and i runs over all the basis functions. In CP2K, Gaussian-type orbitals are employed as basis set. In the thermodynamic limit, the IPR is equal to zero for extended states, whereas it is finite for localized states and provides an estimate for the inverse of the number of atoms on which the state is localized. We anticipate that, in our models, there are a few electronic states that are localized in two directions, but delocalized along the third, perpendicular direction. These states are thus 1D; nevertheless, we refer to them as "localized" in the following to distinguish them from states that are extended in two or three directions. The IPR values are always non-zero for finite systems; nevertheless, our models are large enough to clearly distinguish between "localized" (i.e., 1D) and "extended" states. The IPR values of the latter are of the order of 0.001. As shown in Figure 4a,b, strongly localized states can be found below the Fermi level. There are two quasi-degenerate such states with ultrahigh IPR at energies of −0.341 eV (Figure 4a) in the clean model, corresponding to the two undercoordinated Te atoms (CN = 2). One of the two localized states is plotted in Figure 4c, showing that its charge density is localized around both two-fold coordinated Te atoms. The presence of compositional Ge/Sb breaks the degeneracy (Figure 4b) and the two states are now localized on different undercoordinated Te atoms, as shown in Figure 4d. We stress again that these states are, in fact, 1D, since they are strongly localized along the y-and z-axis but are extended along the x-axis, as shown in the top view of the structures in Figure 4c,d. Thus, they differ from exponentially localized states in disordered systems, such as the ones observed at the tail of valence band in rocksalt GST due to vacancy clusters. [25] Apparently, compositional Ge/Sb disorder in the cation-like layers does not alter the extended nature of the state along the x-axis. Regarding the conduction band, there are a few states with large IPR values of ≈0.01 in the energy range of 0.3-0.4 eV. An example of such states is plotted in Figure 4e. The state is localized around the Sb-Sb homopolar bond, in agreement with our previous DOS analysis. The presence of compositional Ge/Sb disorder affects these states significantly, turning the wave functions into a more complex shape. As shown in Figure 4f, the charge density is localized not only around the homopolar Sb−Sb bonds but also along Sb−Te chains. [29] We also doubled the size of the orthorhombic model along the y-axis by adding regions with perfect stacking (resulting in large models that contain 1512 atoms), which reduces the defect density by 50%. The localization features remain the same ( Figure S3, Supporting Information). Hence, we can conclude that in-plane twins lead to the formation of 1D electronic states along the x direction that are strongly localized along the perpendicular directions.
At last, we also built models with misaligned twinning defects to account for the extra image spots observed in Figure 2a. Starting with the orthorhombic model shown in Figure 4c, we broke the alignment of the in-plane twinning defects in the three slices along the x direction, separating them consecutively by one lattice unit, 7.47 Å (= 1/6×44.84 Å) along the y direction, as shown in Figure 5a. Note that, owing to the periodic boundary condition in the x direction, the model we built has extremely large density of "kinks" (i.e., shifts) between adjacent in-plane twinning defects. This model turns out to be rather energetically unfavorable with a large energy penalty of ≈122 meV per atom as compared to the model with aligned twinning defects (shown in Figure 4). Moreover, after atomic relaxation, the atoms in the kink region move away from the initial atomic sites (Figure 5a), which is inconsistent with the HAADF image in Figure 2a. The large energy penalty and serious atomic distortions indicate that the actual in-plane twinning defect structures should be highly aligned with only a small number of kinks, as sketched in Figure 5b. To describe such structures, one should thus consider huge models, which constitute a challenge for ab initio methods. However, the marginal presence of kinks is not expected to have strong influence on the overall electronic structure as yielded by our models with aligned twinning defects.

Conclusion
We reported a thorough atomic scale characterization of the in-plane twinning defects with inverted stacking sequence inside a single atomic block. The DFT calculations indicate the relatively low energy cost of ideal defects without kinks. Local distortion, homopolar bonds, and under-and over-coordinated Te atoms were observed in these models. Regarding the electronic structure, the homopolar bonds and wrong coordinated Te atoms inside the twinning defect lead to the formation of 1D electronic states near the valence band maximum and the conduction band minimum. These states are extended along the direction parallel to the defect but strongly localized along the other two directions. The presence of kinks (which are needed to explain the extra spots in the HAADF images) is expected not to affect significantly the electronic structure, as long as their concentration is low. We note that extended defects, such as bilayer and stacking faults, can be manipulated through heat treatment, [36] synthesis methods, and chemical composition. [75] This property could in principle be exploited for tuning the density of these inplane twinning defects, thus tailoring the electrical transport properties of layer-structured phase-change chalcogenides.