Understanding the Shape of GeTe Nanocrystals from First Principles

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Understanding the Shape of GeTe Nanocrystals from First Principles Philipp M. Konze,† Volker L. Deringer,† and Richard Dronskowski*,†,‡ †

Institute of Inorganic Chemistry and ‡Jülich−Aachen Research Alliance (JARA-HPC), RWTH Aachen University, Landoltweg 1, 52056 Aachen, Germany S Supporting Information *

ABSTRACT: Nanocrystals with rationally tailored morphologies and properties are a thriving research field. The phase-change material (PCM) germanium telluride (GeTe) has recently been synthesized in a plethora of nanocrystalline forms and morphologies, but a mechanistic understanding of these experimental findings has been largely missing so far. Here, we present comprehensive dispersion-corrected density functional theory (DFT-D) simulations of the low-index crystal facets of GeTe and how they interact with relevant ligand molecules. These results enable a systematic understanding of experimental findings regarding GeTe nanocrystals and clarify the origin of the broad range of particle shapes observed. This study also affords semiquantitative signposts assisting future synthetic studies of nanocrystalline PCMs.

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INTRODUCTION Germanium telluride (GeTe) is a fascinating functional material despite its formal simplicity: it counts among the simplest ferroelectrics,1−4 is used as a phase-change material (PCM) for data-storage devices,5,6 and forms the parent compound for a much larger family of PCMs.7−9 Driven by such diverse applications, novel synthetic techniques have been developed which gave rise to numerous micro- and nanocrystalline structures of GeTe.10−14 Various groups reported very different morphologies, ranging from perfectly octahedral GeTe crystals to likewise perfect cubes (Figure 1a−b), and more complex shapes have been observed as well.15 Nonetheless, the precise mechanisms which determine this diverse nanomorphology are far from completely understood. Throughout materials chemistry, the targeted synthesis of nanocrystals is a very active field of study.16−20 Among the most important examples are lead chalcogenides, which find diverse applications in nanocrystalline form21−25 and as “building blocks” for nanocrystal superlattices.26−28 Exploring nanocrystal properties by first-principles modeling has become an important task29 that we have recently reviewed for the case of IV−VI semiconductors,30 and it is anticipated in particular that synergistic approaches of both experiment and theory may be developed in the future. Indeed, proofs-of-concept exist for chemically related compounds: for example, the particle morphology of the topological crystalline insulator SnTe has been predicted from first-principles density functional theory (DFT),31,32 and these modeling results harmonize well with the outcome of vapor−liquid−solid (VLS) growth experiments.32−35 This reasoning can seamlessly be extended from free nanocrystals to ligands on particle surfaces, as shown for PbSe in a seminal study.36 Comparable, predictive models have © XXXX American Chemical Society

been established for other classes of nanoscale materials such as CdS nanorods37 or TiO2.38 In this work, we provide a comprehensive set of firstprinciples computations that quantify the stability of all relevant GeTe crystal surfaces, with and without ligands attached. We have previously introduced an ab initio model for the particular case of GeTe(111)39,40 but must now far expand this earlier work: indeed, the (001) and (011) surfaces pose a new challenge due to the underlying crystal symmetry, as we will discuss in detail below. Together, our simulations allow us to derive general stability rules for the nanomorphology of GeTe, to rationalize the outcome of previous syntheses, and to provide predictive guidelines for future experimental work.

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METHODS AND MODELING Electronic Structure Computations. Structural parameters and energies were derived from DFT computations in the generalized gradient approximation after Perdew, Burke, and Ernzerhof (PBE).41 Previous simulations at the PBE level have agreed well with experimental findings for clean GeTe(111) surface reconstructions,39,42 surface oxidation,40,43 and SnTe nanomorphology.31−35 In the present study, we furthermore introduce organic ligands and study their interactions with the surfaces; this calls for the use of dispersion corrections44 on top of the pure PBE functional. Throughout this work, we hence apply the “D3” scheme45 which has shown excellent performance both for organic and inorganic systems (a recent review is in ref 46). Received: July 18, 2016 Revised: August 24, 2016

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DOI: 10.1021/acs.chemmater.6b02940 Chem. Mater. XXXX, XXX, XXX−XXX

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Chemistry of Materials

bulk In the following, we denote μGe = Ebulk GeTe − ETe as the Gebulk poor limiting case, and μGe = EGe as the Ge-rich limit. To evaluate ligand−surface systems, we calculate the binding energy Eb as36

E b = E ligand + slab − (E ligand + E slab)

such that negative binding energies indicate stabilizing surface− ligand interactions. We finally arrive at a surface energy for such systems using the coverage Θhkl which enables us to compare slab models of different size.36 Because the search for an ideal ligand concentration is only feasible for a number of carefully selected ligands, we survey a small range of low surface coverages, for which we assume that the binding energy is independent of coverage54

γ = γclean + E bΘhkl With such a set of surface energies for different crystal facets and ligands, we are able to predict crystal shapes using Wulff’s classical theorem.55 It is based on the idea of surface energy minimization, and can be written as w=

γ dhkl = hkl γ001 d001

where dhkl is the shortest distance from the (hkl) surface to the center of the crystal. Idealized morphologies, with their respective surface energy ratio, are illustrated in the Supporting Information (Figure S1).

Figure 1. GeTe microcrystals may be synthesized in different shapes, showing either (a) octahedral14 or (b) cube-like11 morphologies. Their origin can be explained by symbolic Wulff constructions for (idealized) rocksalt-type GeTe: octahedra are dominated by favorable {111} facets, whereas cubes are enclosed by low-energy {001} facets. Quantitative predictions require DFT-computed energies which will be presented in the present paper. Panel a reprinted with permission from ref 14. Copyright 2008 American Chemical Society. Panel b reprinted with permission from ref 11. Copyright 2010 American Chemical Society.

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RESULTS AND DISCUSSION Modeling the Clean Surfaces. Bulk α-GeTe follows the motif of the rocksalt type but lacks inversion symmetry;56−58 this makes the construction of surface slabs more difficult than “simply” cleaving them from the bulk. Hence, previous work proposed a structural model based on a central layer of idealized rocksalt-type β-GeTe, covered on either side by a sufficient number of α-GeTe bilayer motifs to achieve this symmetry element for the slab models nonetheless.39 This way, a stable dense GeTe(111)-(1 × 1) surface with Te termination, labeled (111)Te, has been predicted to be thermodynamically most viable. This prediction was recently verified by careful experiments.42 On the basis of the small deviation of α-GeTe from the ideal rocksalt type (concomitant with a computed energy difference of a mere 4 kJ mol−1 per formula unit), we here propose a surface model that is initially carved from ideal rocksalt-type β-GeTe, but then allowed to relax within symmetry constraints. Figure 2 shows these slab models before and after structural optimization. The initial, ideal octahedral environments for both Ge and Te quickly distort during DFTD relaxation, leading to a pronounced splitting into shorter and longer Ge−Te-bonds. Within the constraints imposed by the surface model, this slab supercell thus mirrors the bond-length alternation found in α-GeTe, and the Ge−Te distances at the surface are indeed very close to those in the rhombohedrally distorted bulk structure (where we compute 2.85 and 3.29 Å for the short and longer bond, respectively, at the same level of theory). We now start to explore surface energies and first draw a comprehensive phase diagram for the clean surfaces (Figure 3a). Compared to the (111) surface, both GeTe(001) and GeTe(011) are here predicted to be principally competitive: for both models we arrive at surface energies of 30−40 meV Å−2, which lies within the region of the previously assumed lowest

For all simulations, plane-wave basis sets with a cutoff energy of 500 eV and the projector augmented-wave method47 were employed as implemented in the Vienna Ab Initio Simulation Package (VASP).48−50 Structural optimizations were performed until residual forces fell below 10−3 (10−2) eV Å−1 for clean (ligand-covered) slabs, respectively. Dense k-point meshes51 were chosen for each slab model.52 Surface Energies. The route to compute surface energies for clean and ligand-covered surfaces has been described earlier,36,39,53 but we will summarize the essential concepts here. The surface energy γclean for a clean (that is, relaxed but otherwise pristine) slab is53 1 slab γclean = [E − NGe μGe − NTe μTe ] 2A Thereby, the slab model contains NGe and NTe atoms, respectively, exposes a surface area of A on either side, and attains a DFT energy of Eslab. Assuming thermodynamic equilibrium, the above expression can be rewritten to depend on only one of the constituent chemical potentials μ39 1 slab bulk γclean = [E − EGeTe − (NGe − NTe)μGe ] 2A where Ebulk GeTe denotes the computed total energy of bulk αGeTe, and the chemical potential of germanium can take values in the range of bulk bulk bulk EGeTe − E Te < μGe < EGe

B


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pressure.32 Both the (001) and (011) surface models bear similar amounts of Ge and Te atoms (Figure 2), and thus, they show up as horizontal lines in the surface phase diagram; by contrast, the (111) surface energies depend on the environment39 and thus, so does the ratio of different γhkl. Consequently, the predicted nanomorphology of GeTe varies strongly with environment: from a predominantly octahedral geometry for the Ge-poor region (Figure 3b), whereas all three low-index facets become competitive in the Ge-rich case (Figure 3c). In most practical laboratory scenarios, we would expect a Ge-poor environment because GeTe itself is nonstoichiometric, with cation vacancies leading to a Ge deficiency of up to 10% depending on how the sample is prepared.61 Surface−Ligand Interactions. With a full set of clean GeTe surface models at hand, we may now turn to ligand− surface interactions. We thus begin to investigate scenarios most pertinent to wet-chemical syntheses. To compute binding energies for ligands on surfaces, we used several starting structures as partly discussed in previous work.40 For (001) and (111), six and four starting geometries were evaluated, respectively. The geometry of the surface layer at (011) is similar to the (001) one, and it leads to principally competitive62 surface energies, independent of the chemical potential landscape. Nevertheless GeTe(011) is unknown to experimentalists, so from this point on, the (011) surface will be neglected, focusing instead on GeTe(001) and GeTe(111). An overview of starting geometries for all surface models is given in the SI (Figure S2). Figure 4 shows three representative surface−ligand adducts so predicted. Both 1,4-dioxane and ethanol do not bind

Figure 2. Structural models for GeTe(001) and GeTe(011) based on rocksalt-type β-GeTe. Relaxation readily leads to distorted octahedra reminiscent of those in α-GeTe (insets), with visible segregation into shorter and longer bonds. The asterisks shown indicate the inversion centers of our structural models, ensuring two identical surfaces terminating the slab.

Figure 3. With the surface phase diagram (a) at hand, a Wulff construction predicts the equilibrium crystal shape in different chemical environments. The Ge-poor (b) and Ge-rich (c) cases differ strongly, going from a truncated octahedron to a crystal with significant contributions of all three low index surfaces.

Figure 4. Selected surface−ligand structures explored here. Though some molecules are only bonded to the surface by longer-range dispersive interactions (dashed lines; panels a and b), others form covalent bonds to the surface (c). Computed binding energies as well as surface−ligand distances are given to support these variations. Note that propionate prefers attachment to (111)Ge, and only the respective most preferable one is shown in each panel.

surface energy of (111)Te. Our computations agree well with previous studies39,59 where applicable.60 To emphasize how the different surface energies depend on μGe, we now derive morphologies for the two delimiting cases (Figure 3b−c). Using the chemical potential as an axis, we can describe differences between the chemical availability of certain elements, and for tellurides this approach has been shown to correlate with experimental conditions such as the Te partial

strongly on either (111) surface, and so these ligands do not strongly influence the computed surface energies. Furthermore, there is little preference for particular sites or ligand orientations: the difference between the respective most and least favorable binding energies on (111)Te is ΔEb = −0.04 eV both for 1,4-dioxane and for ethanol; the ligands are rather C


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(inert) Te-terminated counterpart is hardly affected (Eb = −0.1 eV). In addition, there is a surprisingly small change of surface energy for the (001) surface (Eb = −0.9 eV), when compared to the drop in surface energy for (111)Ge. For (001), one could expect a similar bonding situation as for (111)Ge: in both cases, there are Ge atoms terminating the surface. The (001) surface exposes Ge atoms coordinated by five Te neighbors, and so only one out of six bonds is broken compared to the bulk. At (111), by contrast, only three Ge−Te bonds remain for each surface atom. With only one Ge−Te bond broken at (001), we there see much smaller energy changes compared to (111). Until now, we have neglected the influence of ligand coverage, simply aiming to achieve similar coverage for all different (hkl) surfaces. Albeit far from a densest packing, for especially strongly bonded ligands (like halide ions; see next section) these coverages lead to negative surface energies: thus the crystal should dissolve into an infinity of surfaces, that is, disintegrate completely. Alternatively expressed, for negative surface energies, a divergent surface area is energetically favorable, which makes the bulk solid thermodynamically unstable. For surface−ligand systems, this is not necessarily true,63−65 as the competing bulk halides are energetically more favorable than a halide-covered GeTe-surface. One might even use this behavior as an advantage in stabilizing small structures as has been done for the homologous PbSe, where nanocrystal quantum dots thus were passivated without significantly altering their optoelectronic properties.66 Future work within the field of PCMs might be able to make use of such behavior in stabilizing fragile devices against uncontrolled surface oxidation and subsequent degradation. Ultimately, however, the Wulff construction is ill-defined for negative surface energies, and so it can no longer be used to predict crystal shapes. Charting Ligand Binding Preferences. Rather than comparing dozens of different surface phase diagrams for all ligands considered, we aim for a more comprehensive view in Figure 6; there, we have ordered the ligands according to computed binding strength and selectivity, arriving at a two-

insensitive as to where exactly they will bind. Only if the ligand interacts strongly, chemically, with the surface, which we here observe for the propionate anion (Figure 4c), only then do we observe high deviations between different starting configurations (ΔEb = −0.31 eV for propionate on (111)Ge). Binding energies and surface−ligand distances are readily available and reveal key differences between the interaction of a ligand toward different surfaces, as well as between different ligands toward a single facet. The binding energy of a charged molecule on the surface can exceed that of a less reactive species by an order of magnitude. For example, a water molecule will adsorb on the surface with a binding energy of −0.3 eV, whereas hydroxylation of the surface (that is, adsorption of OH−) results in Eb = −2.7 eV. However, to reveal the consequences of such binding energies, we need to use surface phase diagrams, as dif ferences between facets are what determines the final morphology. With a plethora of possible ligands and adsorption sites, it is all but hard to get lost in details. On purpose, we thus begin by discussing selected, representative ligands and will only later attempt a more complete picture. Figure 5 shows surface phase

Figure 5. Surface phase diagrams for water (a), propionic acid (b), and propionate (c) adsorbed on GeTe surfaces. Though water and propionic acid show little interaction with the surfaces, as well as low selectivity toward a particular facet, the propionate anion in panel (c) exemplifies the strong interaction between an anionic ligand and (111)Ge.

diagrams for three exemplary ligands: water, propionic acid, and propionate. As before, the first two exhibit small binding energies (−0.3 and −0.6 eV for water and propionic acid, respectively) and thus change the energetic landscape of the surfaces only slightly. Nonetheless, as per the definition of the Wulff construction, even a seemingly small change in surface energies can tip the scales and lead to a transition between cube and octahedron (SI). With this in mind, Figure 5c shows the surface phase diagram of an anionic ligand, propionate. Here, we see what a chemist might expect: a steep drop of the surface energy for the (highly reactive) (111)Ge surface (Eb = −2.0 eV) due to saturation of the “dangling” bond, whereas that of its

Figure 6. Facet selectivity of surface−ligand interactions versus their computed binding energy. Using this plot, trends for surface−ligand interactions can be estimated even if their interactions are too strong to evaluate them using Wulff’s theorem. Halides are shown in yellow, whereas ligands containing oxygen are shown in blue. D


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they have revealed. To achieve octahedral morphology, one may introduce charged ligands such as carboxylic acids or halides. Whether such (111)-dominated particles show ferroelectric polarization or properties remains to be explored. On the other hand, cubic GeTe nanocrystals can be obtained in unreactive solvents because of a shift in the (001) surface energies. By and large, PCMs are today synthesized by physical means, that is, by sputter deposition. The rationally controlled, chemical synthesis of well-defined nanoparticles may open up a valuable, alternative route,20 one that is already well established in related group-IV chalcogenides such as PbSe. There, and here, predictive atomistic simulations should likely play an increasingly important role.

dimensional chart. The horizontal coordinate is the energy gained when a particular ligand bonds to the surface (the one most favorable configuration throughout all surfaces and starting configurations is always given, and more negative values mean stronger bonds). The second, vertical axis is spanned by the selectivity (which we define as the ratio of the respective largest (111) to (001) binding energy). In other words, the further up a ligand lies in this chart, the more it favors the (111) surface, and one with a selectivity of S111 = 1.0 will be attracted to both surfaces to a similar degree. Figure 6 immediately indicates that the ligands studied here fall into two distinct groups. The top right region contains ligands that bind strongly to the surface, and often prefer the highly reactive (111)Ge surface, whereas the bottom left region contains ligands with weaker interactions and a preference for (001). Morphology from First-Principles. We now establish the link to experimentally observed crystal shapes. Figure 7 iconizes

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.6b02940. Delimiting values for the Wulff construction based on (001) and (111) surfaces and the idealized nanomorphologies that evolve from them; initial ligand adsorption sites for all surfaces investigated. (PDF) (CIF) (CIF) (CIF) (CIF)

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AUTHOR INFORMATION

Corresponding Author Figure 7. Two experimentally observed morphologies of GeTe microcrystals, complemented by Wulff constructions for three idealized cases, as well as the corresponding results for selected ligands. The bar width corresponds to the effect of the chemical potential and is given for equal surface coverages of 2.7 nm−2. With these models at hand, a reproduction of distinct morphologies is possible and can be associated with experimentally observed geometries.

*E-mail: [email protected].

the transition from cubic to octahedral crystals which have both been observed in experiments (Figure 1). Below the idealized polyhedra, we show predictions based on the surface energies computed here for clean surfaces and two selected ligands. The width of these bars shows the range of different morphologies accessible, each based on the chemical potential of Ge, as in the surface phase diagrams. For clean surfaces theory predicts a predominantly octahedral crystal, which is in line with the observation of abundant (111) surfaces in vacuo.42,43 Chemical ligands, however, drastically change this picture, and even less reactive species such as 1,4-dioxane result in cube-shaped crystals.

Notes

Present Address

(V.L.D.) Engineering Laboratory, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, United Kingdom. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Dr. Adam Slabon for useful discussions and remarks on this manuscript. We acknowledge support by the Deutsche Forschungsgemeinschaft (funding within SFB 917 “Nanoswitches”) and the Jülich-Aachen Research Alliance (JARAHPC computer time).

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CONCLUSIONS We have introduced first-principles surface models for all relevant low-index surfaces of GeTe. By simulating both clean and ligand-covered surfaces of different chemical nature, and translating surface stabilities into equilibrium morphologies, we have witnessed almost the entire range between octahedral and cubic nanocrystals, thereby lending microscopic understanding to experimental results. Rather than individual numbers, the most important outcome of these simulations is the general, chemical trends E


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Understanding the Shape of GeTe Nanocrystals from First Principles

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