Metavalent Bonding in Layered Phase‐Change Memory Materials (Adv. Sci. 15/2023)

Metavalent Bonding In article number 2300901, Wei Zhang, Matthias Wuttig, and co‐workers elucidate how metavalent bonding (MVB) develops across the so called van der Waals (vdW)‐like gaps in layered Sb2Te3 and Ge–Sb–Te alloys. By tailoring the degree of MVB across the gaps via uniaxial strain, a large variation of optical reflectivity can be obtained, enabling potential photonic applications.


Results and Discussion
Here, we clarify how MVB develops across structural gaps in the trigonal phase of Sb 2 Te 3 and GST alloys, and how MVB can be effectively tailored by stacking disorder and uniaxial strain for tunable dielectric and optical properties by carrying out in-depth atomic imaging and optical experiments in combination with ab initio simulations. We focus on Sb 2 Te 3 in the following as the structural gaps are most frequently encountered for a given film thickness in its trigonal phase. The data on trigonal GeSb 2 Te 4 and Ge 2 Sb 2 Te 5 are included in the Supporting Information. A Sb 2 Te 3 thin film with a thickness of 300 nm was deposited on a silicon substrate via magnetron sputtering and was then annealed at 300°C over 30 min to form the t-Sb 2 Te 3 phase. A capping layer was also deposited immediately afterward to prevent oxidation. As shown in Figure S1 (Supporting Information), the energy dispersive X-ray (EDX) experiments showed the composition of the sputter thin films to be Sb 2 Te 3 . Clear structural features of trigonal Sb 2 Te 3 were confirmed by the X-ray diffraction (XRD) measurements. Subsequently, a specimen of the thin film was prepared with a thickness of about 80 nm for microstructure characterizations using the focused ion beam (FIB) system. The structural and chemical details of the t-Sb 2 Te 3 thin film were acquired by the high-angle annular dark field (HAADF) imaging technique on a spherical aberration-corrected scanning transmission microscope (STEM) equipped with an energy-dispersive X-ray (EDX) mapping analysis system. In contrast with the highquality thin films produced by epitaxial growth, structural defects are frequently created in t-Sb 2 Te 3 samples grown by sputtering. Figure 1a shows a typical HAADF image of the sputtered t-Sb 2 Te 3 thin film. The bright dots in the HAADF image correspond to the positions of the atomic columns in the view direction [1120], and the intensity is approximately proportional to Z 2 , where Z represents the averaged atomic number of each column. [60] As indicated by the blue arrows, the stacking sequence is reversed along the [0001] direction. Interestingly, at the boundaries between the inverse blocks (red arrows), the image contrast is slightly stronger (i.e., the gap area looks lightly darker) than at the gaps between the regular stacking blocks. A detailed analysis of the gap width in the areas marked by the yellow boxes, is shown in Figure 1b. We define the size of the gap (d gap ) separating two QLs as the distance between the two relevant Te planes. The measurements of the image intensity profile collected along the vertical direction show that the width of the gap between the QLs with normal stacking is indeed smaller than that with inverse stacking (see also Figure S2, Supporting Information).
We made several HAADF scans in different areas of the sample and measured the size of the gaps, resulting in d gap = 2.92±0.03 Å for the gap of the QLs with normal stacking and d gap = 3.10±0.03 Å for the gap with inverse stacking. This increase in d gap by ≈6.2% already indicates that the nature of the chemical interaction at the gaps is not "pure" vdW, for which the gap size should be insensitive to the stacking order. The latter behavior has indeed been observed in vdW materials containing ample stacking faults. [61] We also measured the spacing between three normal QLs and QLs which include one inverse block, which gives a local c value of 30.39 ± 0.03 and 30.88 ± 0.03 Å, respectively. The averaged value over the whole thin film sample is c = 30.50 Å by XRD measurement ( Figure S1, Supporting Information), which is slightly larger than the literature data, 30.46 Å, measured for single-crystal bulk sample. [62] This difference could be attributed to the presence of inverse blocks in the thin film sample. As directly measured on the HAADF image in the view direction [1120], the angle of Sb-Te-Te layers is 167±2 o at the interfaces between normal QLs, while it becomes 105±2 o at the inverse boundaries between the inverse blocks, indicating a clear misalignment of bond chains across the gap. Figure 2a shows a zoom-in HAADF image of the inverse blocks. The atomic layers take three special sites, which are arranged in -A-B-Cstacking along the vertical direction, but change to -A-C-Bstacking in the inverse block. Due to the very close atomic number of Sb (51) and Te (52), the intensity for the Sb and Te atomic columns looks almost the same in the HAADF image. EDX mapping provides direct chemical element distribution on the atomic scale as shown by the color maps in Figure 2. From the element maps, it is clear that inside each QL, three Te layers and two Sb layers are alternately stacked along the [0001] direction, and the compositional order is unchanged in the neighboring blocks having inverse stacking sequence. Similar stacking disorder was also observed in layer-structured GeSb 2 Te 4 , Ge 2 Sb 2 Te 5 and GeTe/Sb 2 Te 3 superlattices. [63][64][65][66][67][68][69] The compositional order between normal and inverse atomic blocks remains the same, [66] and the enlarged interatomic spacing is consistently observed at the inverse stacking boundaries. [67] This stacking fault is a consequence of vacancy-ordering mediated structural transformation from the rocksalt phase, [40,70] which is absent in the high-quality epitaxial grown thin film of t-Sb 2 Te 3 ( Figure S3, Supporting Information).
Next, we carried out density functional theory (DFT) calculations to gain a deeper understanding of the stacking disorder and how these defects can affect the bonding characters and physical properties of layered PCMs. The vdW interaction was treated with Grimme's D3 method; [71] this and other technical details can be found in the Experimental Section. As shown in Figure 3a, the inplane arrangement of the A, B and C atomic layers takes the three special positions of a hexagonal cell, namely, (0, 0), (2/3, 1/3) and (1/3, 2/3), respectively. Upon structural relaxation, the pristine t-Sb 2 Te 3 unit cell shows lattice parameters a = 4.32 Å and c = 30.07 Å, short and long Sb-Te bonds equal to 3.02 and 3.18 Å, a much longer interatomic distance of 3.67 Å for the Te-Te contacts across the structural gap and a gap size of 2.69 Å. The Sb-Te-Te motif formed by a Sb-Te bond and a neighboring Te-Te contact has a bond angle of 167.13°, which is comparable to the bond angle between quasi-aligned atomic pairs inside the QL.
If we keep the lattice parameters fixed but include one inverse block and relax the atomic coordinates, we notice a drastic change in Sb-Te-Te bond angle to 98.19°and a small increase in the Te-Te contact d TT to 3.74 Å and in d gap to 2.79 Å at the boundary of the inverse block. If we allow the simulation cell to relax, the c edge increases by 0.57 Å, due mainly to the significantly longer Te-Te contact d TT = 3.83 Å (d gap = 2.91 Å) at the inverse boundary. The models with unrelaxed and relaxed simulation cell are denoted with inverse and inverse' in Figure 3a. Such increased width of the inverse boundary gap agrees well with the HAADF images shown in Figure 1. The total energy of the inverse and inverse' models are about 4.0 and 2.9 meV per atom higher than the pristine model. This reduction in total energy obtained by increasing the interatomic spacing explains why wider structural gaps are observed at the inverse stacking boundaries in the HAADF images. Projecting the Sb-Te-Te bond angle according to the [1120] view direction, the angle between the Sb-Te-Te layers is 168.63 o between normal QLs in the pristine model, but 103.38 o at the inverse stacking boundary in the inverse' model, consistent with the STEM values. All structural details of the trigonal models are summarized together with experimental data in Table 1. Additional calculations using other functional [72] and vdW corrections [73,74] were also considered. Overall, PBE+D3 calculations yield a better comparison with STEM experiments, and we stick to this combination for the following discussions.
In order to draw a comparison with standard vdW materials, we perform similar calculations for crystalline SnSe 2 and SiTe 2 in the 1T phase, where each atomic block is made of three atomic layers in an octahedral arrangement. In stark contrast with t-Sb 2 Te 3 , the changes in lattice parameter and total energy upon inclusion of inverse blocks ( Figure S4, Supporting Information) are exceedingly small in 1T-SnSe 2 and 1T-SiTe 2 (below 0.02 Å per unit block and 0.8 meV per atom). This difference further illustrates that Sb 2 Te 3 cannot be regarded as a vdW material. Trigonal GST alloys exhibit similar behavior as Sb 2 Te 3 with a clear increase in gap size at the inverse stacking boundaries ( Figure  S5, Supporting Information). Hence, the structural gaps in these layered phase-change tellurides should be referred as vdW-like gaps instead vdW gaps.
We also evaluate the impact of the inverse block on the dielectric properties of trigonal Sb 2 Te 3 and GST. Figure 3b shows the imaginary part ( 2 ) of the dielectric function for pristine, inverse and inverse' t-Sb 2 Te 3 (the real part 1 is shown in Figure S6, Supporting Information). A reduction in the 2 values is clearly observed below 1.6 eV if the bond alignment across the vdWlike gaps is broken (inverse structure). 2 further decreases when the Te-Te interatomic distance is increased (inverse' structure). The decrease is accompanied by a gradual blue-shift of the peak value. The difference in 2 between pristine and inverse' t-Sb 2 Te 3 amounts to a ≈14% reduction in the peak value: this is significant but is much smaller than the peak-value difference between trigonal and amorphous Sb 2 Te 3 , ≈63% (see Ref. [75] and the following discussion), because in the inverse' models the Sb-Te bonds are still highly aligned and closely coupled inside each atomic block, including the inverse one.
In the amorphous model, high angular disorder is present, breaking the alignment of p orbitals at short interatomic distance. Here, we considered two additional hypothetical structures to break the bond alignment inside the atomic blocks. Specifically, we computed the structural and optical properties of Sb 2 Te 3 taking the other two frequently observed phases of pnictogen sesquichalcogenides, namely, the orthorhombic Sb 2 Se 3 structure and the monoclinic As 2 Se 3 structure. The relative atomic coordinates were kept unchanged, while the cell volume was relaxed to reduce the internal stresses. The hypothetical structures obtained are shown in Figure 3a (right panel) and are denoted as o-and m-Sb 2 Te 3 . If we set a large cutoff of 3.4 Å for Sb-Te bonds, we observe aligned Te-Sb-Te-Sb-Te chains in o-Sb 2 Te 3 , however, there is no alignment through the weak atomic contacts across the zigzag gaps. As shown in Figure 3c, its dielectric function is strongly weakened with a large reduction in the peak value of ≈53% with respect to t-Sb 2 Te 3 . In m-Sb 2 Te 3 , the bond alignment for Sb-Te bonds is completely absent, resulting in very low values of 2 , which is even weaker than the one of the amorphous phase. [75] To gain a better understanding of the difference in dielectric functions of these models, we performed electronic structure and chemical bonding analyses. As shown in Figure 4a, the overall DOS shape of the pristine and defective t-Sb 2 Te 3 models is similar, except for some small numerical differences around the energy gap. The profile of 2 is composed of the joint density of states (JDOS) and the transition dipole moments (TDMs), accounting for the density of possible inter-band excitations and the transition probability for each excitation, respectively. [76] The JDOS profiles almost overlap for the pristine and inverse model, yet the inverse' model shows lower JDOS values below 1.6 eV. Regarding the TDMs, the pristine model shows consistently higher values than the inverse and inverse' models between 0.5 and 1.6 eV. Therefore, the transition probabilities for the relevant excitations are reduced if the weak-bond alignment across the vdWlike gaps is broken (inverse t-Sb 2 Te 3 ), thus decreasing 2 . This is in line with the fact that, generally, a reduction in the overlap of the wave functions involved in the optical transitions leads to a decrease of the corresponding transition probabilities. [76] Much larger differences in DOS, JDOS and TDM profiles are observed between pristine t-Sb 2 Te 3 and the two hypothetical structures (Figure 3b), leading to a wider contrast window in 2 . We also calculated the ET and ES values (see Experimental Section) to characterize the bonding differences between the Sb 2 Te 3 models discussed above (see Figure 4c). We also considered other sesqui-chalcogenides (i.e., V 2 VI 3 , V = As, Sb or Bi; VI = S, Se or Te) in their ground state for comparison. [46] The detailed atomic structures and lattice parameters of the latter compounds are included in Figure S7 (Supporting Information). We used the normalized ET value, i.e., the electron transfer divided by the formal oxidation state of the respective atom, and the ES value of the shortest bond in each model. Consistent with literature, three alloys, namely, Sb 2 Te 3 , Bi 2 Te 3 and Bi 2 Se 3 in the trigonal structure, are located in the MVB region (marked in green), while other sesqui-chalcogenides appear in the covalent bonding (CVB) region (marked in pink). The alloys located in the CVB region show distinct properties with respect to the MVB alloys, and the bond rupture of the former proceeds mostly via single-ion evaporation instead of multiple-ions in APT experiments. [44,46] If a hypothetical trigonal phase is considered for Sb 2 Se 3 , it may also display MVB features with a stronger dielectric function than the orthorhombic phase (see Figure S8, Supporting Information). Nevertheless, it is more difficult for lighter pnictogen sesquichalcogenides to form the trigonal phase, because these alloys show a stronger sp 3 mixing that competes with the p orbital dominant MVB mechanism. This change in bonding tendency stems from the smaller energy separation between the valence shell s and p orbitals in lighter elements.
From pristine to inverse and to inverse' t-Sb 2 Te 3 , a gradual change in ET and ES values toward the boundary between MVB and CVB is observed, indicating gradually weakened MVB. Regarding o-and m-Sb 2 Te 3 , their ET and ES values are clearly located in the CVB region. We conclude that the breaking of the alignment of both the weakly coupled Te-Te contacts and the strongly coupled Sb-Te bonds undermines MVB, leading to smaller TDMs and a reduction in the dielectric function peak. Our dielectric function and bonding calculations also confirm the presence of non-negligible orbital overlap in addition to the vdW forces across the gap regions in pristine t-Sb 2 Te 3 , supporting previous experimental observations. [46,59] More specifically, in this region, there is no electron transfer between the weakly coupled Te atoms, but there exists a non-negligible amount of shared electrons, denoted as ES gap . Indeed, in pristine t-Sb 2 Te 3 , ES gap equals 0.37 e, which is larger than previous calculations [46] because of the shorter Te-Te interatomic distance, 3.67 Å, obtained by our DFT calculations upon inclusion of vdW corrections. This finite charge mediates the development of MVB across the structural gaps, and its value varies with the Te-Te interatomic distance, largely influencing the dielectric properties. Indeed, in the inverse and inverse' models, ES gap is reduced to 0.33 and 0.29 e, and the Te-Te contact length is increased to 3.74 and 3.83 Å, respectively.
Finally, uniaxial strain was applied to the c axis to tailor ES gap further, as sketched in Figure 5a. For the sake of convenience, we only considered the pristine and inverse models, which have the same set of lattice parameters, for the strain calculations. We kept the a-and b-edge fixed, while increasing and decreasing the c-edge from −2.0 to +2.0 Å, corresponding to a change of less than ±7% lattice strain. As shown in Figure 5b, the ES gap value increases upon compressive strain and decreases upon tensile strain for both the pristine and inverse t-Sb 2 Te 3 models. The difference in ES gap between the pristine and inverse models gets larger at −2.0 Å because of the stronger overlap (the Te-Te interatomic distance reaches 3.37 Å) and better alignment of p orbitals www.advancedsciencenews.com www.advancedscience.com  (the Sb-Te-Te bond angle reaches 171°) in the pristine model (see more structural details in Table 2). The ES gap value is largely reduced to around 0.17 e for both models under tensile strain at +2.0 Å, and the Te-Te interatomic distance is increased to above 4.1 Å. The strain effects also induce changes in the ET and ES values for the atoms inside the atomic blocks. As shown in Figure 5c, compressive strain makes the bonding more MVB-like, while tensile strain drives the system toward the CVB region. The change in bonding character and in overlap between the p orbitals has direct impact on the dielectric properties, since it strongly affects the optical transitions. As shown in Figure 5d,e, a systematic reduction in 2 from −2.0 to +2.0 Å is observed in both pristine and inverse t-Sb 2 Te 3 below 1.9 eV, accompanied by a blue-shift of the peak value. The tailoring of 2 upon straining is clearly more effective in the pristine model due to the bond alignment across the vdW-like gaps. The same trend holds for 1 ( Figure S6, Supporting Information) and ∞ (Figure 5f). The compressive strain results in a large increase in ∞ from 66 at equilibrium to 132 when the c-edge is reduced by 2.0 Å in pristine t-Sb 2 Te 3 , due to the enhanced MVB and increased ES gap . Note that the total energy also rises, because the edge Te atoms are all negatively charged, inducing stronger electrostatic repulsion when getting closer. Nevertheless, the increase in total energy in the pristine model, 24 meV per atom (−2.0 Å), is lower than that in the inverse model, 40 meV per atom (−2.0 Å), indicating the former bonding scenario to be more comfortable. When the c-edge is stretched at +2.0 Å, there is hardly any difference in ∞ , 1 and 2 between the pristine and inverse model, because MVB is broken across the gaps due to the large interatomic distance over 4.1 Å. In this limit, only the aligned Sb-Te bonds inside each QL contribute to the dielectric function.
Before closing, we provide an overview about the change in bonding character and optical response upon phase transition in Sb 2 Te 3 . Upon heating, the amorphous phase first crystallizes into the rocksalt-like phase with a change in bonding mechanism from CVB to MVB. As shown in Figure 6a, all the Sb-Te octahedral bonds are strongly coupled, but the alignment of p orbitals could be broken when encountering atomic vacancies, which occupy 1/3 of the Sb sublattice. The interatomic distance between two Te atoms separated by a vacancy is over 6.12 Å, and no shared electron exists over such long distance. Further thermal annealing drives a vacancy ordering process, inducing a structural transformation into the trigonal phase. The high amount of atomic vacancies segregates into 2D vacant layers, resulting in shorter Te-Te interatomic distances across the gap as compared to the previous case. The shared electrons between the weakly coupled Te atoms enable MVB between QLs, which can be further strengthened by adding uniaxial compressive strain. The four configurations, namely, the amorphous, rocksalt, trigonal and strained trigonal (−2.0 Å) Sb 2 Te 3 , indeed display well-separated 2 and optical reflectivity R (Figure 6b). Our optical measurements of Sb 2 Te 3 thin films annealed at different temperatures confirmed that trigonal phase indeed has a higher reflectivity than the rocksalt phase ( Figure S9, Supporting Information). Inverted stacking sequence and uniaxial strain have similar effects on other layered PCMs, including GeSb 2 Te 4 and Ge 2 Sb 2 Te 5 ( Figure S10, Supporting Information). Note that the calculated optical contrast between amorphous and rocksalt Sb 2 Te 3 is smaller than that of GeSb 2 Te 4 , [70] which can be attributed to the larger number of "broken bonds" in rocksalt Sb 2 Te 3 due to the larger concentration of vacancies in the cationlike sublattice, namely 1/3 versus 1/4 vacant sites in rocksalt Sb 2 Te 3 and GeSb 2 Te 4 , respectively. This observation is consistent with previous optical measurements, showing a reduction in ΔR upon crystallization for increasing concentration of vacancies in the crystalline state. [77]

Conclusion
In summary, we have carried out atomic imaging experiments and ab initio calculations to gain an in-depth understanding on the structural and bonding nature of the inverted stacking disorder in trigonal Sb 2 Te 3 . We have elucidated the importance of electron sharing between the edge Te atoms across the gaps for the existence of MVB along the vertical direction, and we have clarified how MVB is affected by the breaking of p orbital alignment across the gaps. The degree of MVB was further tailored by adding uniaxial strain perpendicular to the vdW-like gaps, thus enabling a systematic tuning of the optical properties in the trigonal phase and potentially widening the programming window between the amorphous and rocksalt phase for optical and photonic PCM applications that require multilevel programming capacities. Nevertheless, the tradeoff on programming speed, power consumption and manufacturing complexity (for the implementation of mechanical forces) need to be carefully assessed when utilizing the trigonal phase. It may also be feasible to exploit the large variation in dielectric function in MVB alloys induced by strain for optical applications, i.e., the elastic strain engineering approach coupled with microelectromechanical systems, [78][79][80] or the thin film bending approach using flexible substrates. [81] Our suggestion for such use is to grow high-quality thin films to minimize the presence of inverse blocks, allowing tuning of optical properties more effectively. The bonding mechanism and optical characters in layered chalcogenides could be further explored by evaluating the thickness-dependent properties in ultrathin films [82][83][84][85][86] or in the alternately grown heterostructure thin films, such as the TiTe 2 /Sb 2 Te 3 heterostructure. [87][88][89][90] At last, we note that presence of the inverse block defects should also affect the electronic and thermal conduction like other extended defects, such as swapped bilayers [91] and stacking faults with non-QL blocks, [92] which could be tailored for thermoelectric [93,94] and topological [92,95] applications of trigonal Sb 2 Te 3 and related chalcogenides.

Experimental Section
Magnetron Sputtering: The Sb 2 Te 3 thin films were deposited using a stoichiometric Sb 2 Te 3 alloy target by radio frequency voltage source in the AJA Orion-8 sputtering system. The power is ≈50 W, and the deposition rate is ≈6.7 nm min −1 . The films with the thickness of ≈300 and ≈450 nm were prepared on a pure Si substrate and a Si substrate covered with Pt layer of ≈120 nm, respectively. The thin films were then annealed at 80°C and 300°C over 30 min under high vacuum of ≈10 −8 torr to form the rocksalt and trigonal phase, respectively.
Molecular Beam Epitaxy: The Sb 2 Te 3 thin film of ≈150 nm was deposited in the MBE Chamber at a base pressure of about 10 −11 mbar (10 −10 mbar during growth). The Si (111) substrate was passivated by Sb to obtain high-quality thin film, and the deposition rate was 0.2 nm min −1 . The sources were elemental Sb and Te effusion cells.
Structural Characterizations: The thickness and composition of the films were measured by a Hitachi SU8230 SEM equipped with a Bruker QUANTAX ESPRIT 2 XFlash7 Energy Dispersive X-ray spectrometer (EDX). The structure of the annealed thin films was determined by X-ray diffraction (XRD) measurements using a setup of Bruker D8 ADVANCE, the range of 2 was set between 10 to 60°. The cross-section TEM specimen was prepared by a dual beam focused ion beam (FIB) system (Helios NanoLab 600i, FEI) with a Ga ion beam at 30 kV and polished at 5 kV to remove potential damage on the surface of the lamellar. The atomic resolution STEM-HAADF imaging experiments and EDX mapping analyses were performed on a Hitachi HF5000 environmental aberration-corrected electron microscope equipped with a probe aberration corrector and an Oxford Instruments X-MaxN 100 TLE spectrometer, operated at 200 keV.
Optical Measurements: The optical measurements were performed with the thin film deposited on Pt substrate to prevent potential absorption from Si substrate. The reflection of the films was measured by the Ocean Optics-HDX01528 spectrograph equipped with the HL-2000-FHSA Tungsten halogen light source. The wavelength range was set from 390 to 760 nm.
Ab Initio Calculations: DFT calculations were carried out using the VASP code [96] with the projector augmented-wave (PAW) pseudopotentials, [97] the Perdew-Burke-Ernzerhof (PBE) functional [98] and Grimme's D3 dispersion correction. [71] Other functional [72] and vdW corrections [73,74] resulted in a similar trend in lattice expansion and reduction in dielectric function with the inclusion of inverse block defects, as presented in Table 1 and Figure S11 (Supporting Information). Trigonal Sb 2 Te 3 , GeSb 2 Te 4 and Ge 2 Sb 2 Te 5 were all modeled in their hexagonal unit cell or supercell. The amorphous Sb 2 Te 3 was generated using VASP following a standard melt-quench protocol, [99] and the rocksalt Sb 2 Te 3 was built in a 3×3×3 supercell, where the distribution of vacancies was generated using a random number generator. Both sets of models contained 180 atoms. The frequency-dependent dielectric matrix was calculated within the independent-particle approximation using VASP, which was shown to be adequate to account for the optical contrast between crystalline and amorphous PCMs. [100][101][102][103] The relaxed structures were calculated with the Quantum ESPRESSO code, [104] which provided ground-state wave-functions for the bonding analysis using the Critic2 code. [105] The Critic2 code calculates the domain overlap matrices (DOM) over Bader's basins, and the delocalization or localization indices (DIs/LIs) among or within such basins measure the quantity of electrons being localized in the atomic basin or shared between the two atoms.
Statistical Analysis: The statistical analysis for STEM measurements is provided in the main text and the Supporting Information, wherever applicable.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.