Communication www.advmat.de Changes of Structure and Bonding with Thickness in Chalcogenide Thin Films Ider Ronneberger, Zeila Zanolli, Matthias Wuttig,* and Riccardo Mazzarello* constantly being refined. On the computa- Extreme miniaturization is known to be detrimental for certain properties, tional side, high-throughput methods have such as ferroelectricity in perovskite oxide films below a critical thickness. come into play, offering the possibility Remarkably, few-layer crystalline films of monochalcogenides display robust of systematic screening to predict novel in-plane ferroelectricity with potential applications in nanoelectronics. These stable 2D materials.[3,4] Among the recently discovered families of 2D com- applications critically depend on the electronic properties and the nature of pounds, group IV chalcogenides (IV = Ge, bonding in the 2D limit. A fundamental open question is thus to what extent Sn; chalcogen = S, Se, Te) are attracting bulk properties persist in thin films. Here, this question is addressed by a significant interest due to their remark- first-principles study of the structural, electronic, and ferroelectric properties able electronic properties, which include of selected monochalcogenides (GeSe, GeTe, SnSe, and SnTe) as a function in-plane ferroelectric polarization tunable by strain engineering.[5–12] of film thickness up to 18 bilayers. While in selenides a few bilayers are suf- A fundamental question arising in the ficient to recover the bulk behavior, the Te-based compounds deviate strongly study of 2D and few-layer materials is how from the bulk, irrespective of the slab thickness. These results are explained bulk properties emerge upon increasing in terms of depolarizing fields in Te-based slabs and the different nature of the film thickness. Interestingly, a number the chemical bond in selenides and tellurides. It is shown that GeTe and of different scenarios appear feasible. van SnTe slabs inherit metavalent bonding of the bulk phase, despite structural der Waals bonded materials like graphite or multilayer graphene exhibit only a very and electronic properties being strongly modified in thin films. This under- small interlayer coupling and hence weak standing of the nature of bonding in few-layers structures offers a powerful film thickness dependence of their prop- tool to tune materials properties for applications in information technology. erties. A stronger coupling can only be produced if adjacent bilayers are twisted, giving rise to exciting phenomena such as The isolation of graphene from graphite in 2004 and the subse- superconductivity in twisted graphene sheets.[13] A weak thick- quent discovery of other stable 2D materials have opened up a ness dependence is expected whenever interlayer coupling new field of research. 2D materials offer plentiful opportunities is accomplished by weak van der Waals forces. On the other for applications in information technology,[1,2] besides being of hand, covalently bonded materials like Si show pronounced great interest for fundamental research. Progress in this field relaxations or reconstructions at the surface to compen- has been impressive in the past few years. Experimental tech- sate for the lack of bonding partners.[14] The resulting atomic niques to produce these materials based on mechanical and rearrangements are usually restricted to a few monolayers. chemical exfoliation, as well as chemical vapor deposition, are Chalcogenides such as transition metal dichalcogenides also Dr. I. Ronneberger, Prof. R. Mazzarello Dr. Z. Zanolli Institute for Theoretical Solid State Physics Catalan Institute of Nanoscience and Nanotechnology (ICN2) JARA-FIT and JARA-HPC CSIC RWTH Aachen University BIST and European Theoretical Spectroscopy Facility (ETSF) Aachen D-52074, Germany Barcelona 08193, Spain E-mail: mazzarello@physik.rwth-aachen.de Dr. Z. Zanolli[+] The ORCID identification number(s) for the author(s) of this article Institute for Theoretical Solid State Physics can be found under https://doi.org/10.1002/adma.202001033. RWTH Aachen University Aachen D-52074, Germany © 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co. Prof. M. Wuttig KGaA, Weinheim. This is an open access article under the terms of the I. Physikalisches Institut Creative Commons Attribution-NonCommercial-NoDerivs License, JARA-FIT and JARA-HPC which permits use and distribution in any medium, provided the original RWTH Aachen University work is properly cited, the use is non-commercial and no modifications Aachen 52074, Germany or adaptations are made. E-mail: wuttig@physik.rwth-aachen.de [+]Presentaddress: Debye Institute for Nanomaterials Science, Utrecht Prof. M. Wuttig University, The Netherlands JARA-Institute Green IT (PGI 10) Forschungszentrum Jülich GmbH DOI: 10.1002/adma.202001033 Jülich 52428, Germany Adv. Mater. 2020, 32, 2001033 2001033 (1 of 10) © 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.advancedsciencenews.com www.advmat.de show van der Waals bonding between adjacent layers, hence zero. We characterize the out-of-plane relaxation by com- a weak film thickness dependence of their properties can be puting the difference in the z component of anion and cation expected. Van der Waals gaps have also been postulated for atoms in subsequent layers. Two distinct values denoted as sesquichalcogenides such as Sb2Te3, Bi2Te3, and Bi2Se3, but the zshort and zlong can be identified in the corresponding bulk small interlayer spacing across adjacent chalcogenide layers is phases. As for the in-plane structural features, we choose the indicative of significant interlayer coupling.[15] bond distance between neighboring anion and cation atoms In the case of group IV chalcogenides, most such com- in the selected atomic layer. Similarly, a short and a long in- pounds display a spontaneous in-plane ferroelectric polari- plane distance (dshort and dlong) is defined in the bulk phases. zation in the quasi 2D limit, whereas the bulk phases are The bulk values are indicated as dashed lines in the relevant either paraelectric (e.g., GeSe, SnSe) or ferroelectric but with plots. a polarization pointing in a different direction as compared to Figure 1 reveals striking differences between the GeSe and the 2D case (GeTe, SnTe). The change in the polarization as a SnSe slabs on one hand and the GeTe and SnTe slabs on the function of the number of layers is closely linked to the evolu- other hand. The structural features in the interior of the GeSe tion in the structure and the electronic properties of the film. In and SnSe models converge rapidly to the corresponding bulk this respect, the study of group IV chalcogenides is particularly values for increasing NBL. Only the outermost bilayers of the interesting because some of them (such as GeSe and SnSe) are slabs (for NBL > 1) display bond lengths that are distinct from held together by covalent bonds in their bulk state, whereas the bulk reference values, which is indicative of a surface others, including GeTe and SnTe, show a unconventional form effect. Such a thickness dependence is frequently observed for of bonding—called metavalent bonding (MVB).[15–18] MVB covalently bonded materials, where significant atomic rear- stems from a competition between electron delocalization as in rangements are present only in the vicinity of the surface. In metals, and electron localization characteristic for covalent and Figure 1, a splitting of both interlayer and in-plane distances ionic bonding,[16] and is characterized by a unique combination into three values (short, long, and “surface” bonds) can be iden- of properties[18] and unusual bond breaking.[19] In MVB adjacent tified. These atomic rearrangements partly stem from the fact atoms are held together by roughly one electron, namely half that orthorhombic GeSe and SnSe consist of atomic bilayers of the electron pair usually employed in covalent bonding.[17] It stacked along (001), which are separated by quasi van der Waals is plausible that materials that utilize MVB in the bulk phase gaps. These results are consistent with the relaxed structural should feature a change in bonding upon reducing the sample parameters for single bilayers discussed in refs. [22–24]. dimensions, since this favors electron localization. Concomi- By contrast, the structural behavior of the GeTe and SnTe sys- tant changes in atomic arrangement and physical properties are tems is characterized by pronounced changes as a function of expected to accompany the anticipated change in bonding. thickness that extend over all the layers. The interior region of Evidence for peculiar changes in atomic and electronic struc- the thicker slabs differs strongly from the corresponding bulk ture in thin chalcogenides has been reported.[5,12,20–24] However, features, even for slabs containing 18 bilayers. Such a behavior unambiguous evidence for changes in bonding has not been is neither known for covalently bonded materials nor for typ- obtained so far. In this work, we investigate the properties of ical metals. A closer look at GeTe and SnTe reveals a further thin-film models of GeTe, SnTe, GeSe, and SnSe—which are characteristic in the structural relaxation: upon growing film representatives of the two families of group IV chalcogenides— thickness the ratio between short and long nearest-neighbor as a function of slab thickness. At T = 0, bulk GeTe and SnTe distances reaches almost one in the out-of-plane direction in form a Peierls-distorted rocksalt structure with space group the interior of the film, thus increasingly deviating from the R3m,[25] a characteristic feature of many metavalently bonded bulk value. On the contrary, the in-plane ratio is increased in systems. On the contrary, GeSe and SnSe, which do not exhibit comparison to the bulk values. MVB, crystallize into an orthorhombic phase with space group The peculiar structural properties of the thin films of GeTe Pnma.[25] Here we restrict ourselves to quasi-2D models that are and SnTe can be explained by the large depolarizing fields obtained from the cubic (GeTe, SnTe) and orthorhombic (GeSe, present in the initial distorted bulk-like slabs. In contrast to SnSe) phase by cutting slabs perpendicular to the (001) direc- orthorhombic GeSe and SnSe, rhombohedral bulk GeTe and tion (see Figure 1). Using the same notation as in ref. [12], we SnTe cannot be considered as layered materials, but rather as denote these two quasi-2D phases with α and γ, respectively. Peierls-distorted systems along the 〈111〉 direction. Such Pei- The thickness of our models is varied by changing the erls distortion is a consequence of the competition between number of bilayers (NBL) from 1 up to 18. Here we define a electron delocalization and electron localization.[16] As a result, bilayer to consist of two layers (“sublayers”), each containing both GeTe and SnTe have a ferroelectric ground state in the atoms with similar z components (see Figure 1). This definition bulk phase with spontaneous polarization Ps pointing along is more convenient for our discussion. Nonetheless we note 〈111〉.[26,27] Thus, Ps has a finite component in the out-of-plane that some authors[6] instead use the term monolayer to denote direction. The depolarizing field associated with this compo- this building block. nent destabilizes the initial rhombohedral distortions of the Figure 1 summarizes the structural properties of slabs of slab models, leading to strong relaxations of the out-of-plane different thickness after relaxation. The data points for every distances. This relaxation would be suppressed if the depolar- slab are shown as a function of the layer indices. They are izing field would be compensated by an external field.[28,29] In colored as a function of NBL from red for the thinnest slab to fact, our freestanding slab models correspond to open-circuit blue for the thickest one. For convenience, the layer indices electric boundary conditions.[30] If the slabs were sandwiched are arranged in such a way that the slabs are centered around between two metallic electrodes, then the surface charges of Adv. Mater. 2020, 32, 2001033 2001033 (2 of 10) © 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.advancedsciencenews.com www.advmat.de Figure 1. Out-of-plane (top) and in-plane (bottom) structural features (i.e., interlayer distance z and nearest neighbor bond distances d) as a function of the layer index. The data points are color-coded according to the thickness of the films: from red (thinnest) to blue (thickest). The two (short and long) bulk values are shown in dashed lines. the slabs would be (partly) screened, so that the rhombohedral The increase in contrast between the short and long in- distortion of the bulk would be (partly) recovered. We checked plane distances originates from the suppression of the this effect for one of the slab models, namely that of GeTe with out-of-plane distortions and, thus, can be understood as an NBL = 7. The screening of the surface charges was achieved by indirect effect of the depolarizing field. This very effect sug- replacing the two surface Te atoms with “pseudo” Te atoms gests that the in-plane component of the polarization in the of fractional charges counterbalancing the initial depolarizing thin-film models of GeTe and SnTe could be enhanced as fields.[31] As a result, bulk-like distortions in the out-of-plane compared to the bulk phase. From a different perspective, direction were indeed obtained in the interior of the slab. this effect can be rationalized by the competition between The details of this simulation are reported in the Supporting electron localization and delocalization, which characterizes Information. MVB.[16] Adv. Mater. 2020, 32, 2001033 2001033 (3 of 10) © 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.advancedsciencenews.com www.advmat.de To substantiate these claims, we turn to the discussion of the electronic and ferroelectric properties as a function of slab thickness. We have computed the spontaneous in-plane polari- zation Ps of all the slab models using the Berry phase approach, within the framework of the modern theory of polarization.[32,33] Further computational details are given in the Supporting Information. The evaluation of Ps requires a finite bandgap. In Figure 2, the bandgaps of all the slab models are reported. Large values are found for very thin slabs, which decrease with increasing NBL. The lack of smoothness of the curves stems from the fact that transitions between direct and indirect gaps occur (Figures S2 and S3, Supporting Information). For thick films, the bandgaps of the four compounds satisfy: Egap (SnTe) < Egap (GeTe) < Egap (SnSe) < Egap (GeSe). These trends are in line with the relationship between the bulk bandgaps, although it must be stressed that the bandgaps of the slab models of GeTe and SnTe do not converge to the bulk values owing to the relaxation Figure 2. Bandgaps of the slabs as a function of thickness. GeTe and SnTe induced by the depolarizing fields. display more significant (absolute and relative) variations in the gap size The absolute values of the spontaneous polarization P as with increasing film thickness than GeSe and SnSe. function of NBL are shown in Figure 3. In this figure, we also Figure 3. Spontaneous polarization P as a function of NBL. The film thickness t = t0 ⋅ NBL (t0 being the bulk thickness of one bilayer) is shown on the upper horizontal axis. Both 2D (top) and 3D (bottom) values of P are shown. The thin red and blue lines in the figures on the left indicate the in-plane component (along the 〈110〉 direction) of the bulk polarization of GeTe and SnTe, respectively. The stars refer to computational data provided in previous work, namely Chang et al.,[5] Fei et al.,[6] and Wan et al.[11] Adv. Mater. 2020, 32, 2001033 2001033 (4 of 10) © 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.advancedsciencenews.com www.advmat.de compare our results with previous work.[5,6,11] Concerning SnTe, slabs of GeSe/SnSe, for which the charge values become com- some discrepancies with ref. [5]—where the VASP package parable to the ones of GeTe/SnTe). was used—are observed. Deviations with respect to previous The computed values of the dynamical charges in the out-of- * VASP calculations are obtained for bulk SnTe too (Table S3, plane direction Z zz are shown in the Supporting Information. Supporting Information): these can be ascribed to the smaller These quantities are about one order of magnitude smaller than cell angles obtained upon relaxation using VASP, resulting in the corresponding bulk and in-plane slab values, for each material larger Te displacements and, thus, higher polarizations. As considered. This can be understood by taking into account that regards GeTe, GeSe, and SnSe, there are some quantitative in the slab configurations the dynamical charges are computed deviations with refs. [6,11] (due most probably to the use of under the condition of zero out-of-plane macroscopic displace- different codes and pseudopotentials) but the trends are ade- ment field (Dz = 0). The latter corresponds to the definition of quately reproduced. For all the models, we have verified that Callen charge.[35] The Born effective charge is given by the product the polarization is computed on the same Berry-phase branch of the out-of-plane dielectric constant and the Callen charge:[35] (see Supporting Information for further details). Very different behavior between GeTe/SnTe and GeSe/SnSe systems can be * Z zz ( Born ) = ε zz∞ Z zz* ( Callen ) (2) seen. The models of GeSe and SnSe display finite ferroelectric polarization only for odd numbers of bilayers. This is related to As discussed below, the out-of-plane dielectric constant the mirror symmetry of two consecutive bilayers, due to which of quasi 2D materials cannot be determined correctly from their polar displacements counterbalance each other.[6] More- standard supercell calculations. Following ref. [36], the super- over, the absolute value of P decreases to zero as ≈1/NBL. cell value can be estimated using an effective-medium theory in In contrast to this, finite values of polarization P are obtained terms of the vacuum thickness and the bulk dielectric constant for all the slabs of GeTe and SnTe. As a matter of fact, this quan- as tity becomes nearly constant for large NBL. The reason for this behavior is that the structural motifs of consecutive bilayers are 1 1 − f (3) ≈ f + ∞ distorted in the same direction and the associated Berry phases ε zz ∞ ε zz ,bulk do not counterbalance each other but, instead, add up. Further- more, P shows a maximum at NBL = 5 for GeTe and NBL = 4 for where f denotes the amount of vacuum in the supercell. The SnTe. The maximal values of ≈ 65 and ≈ 23 µC cm–2 reached Born effective charges in the out-of-plane direction obtained in by GeTe and SnTe slabs, respectively, are not only higher this way are of the same order of magnitude as the in-plane * than the corresponding bulk components along 〈110〉 (≈53.1 ones (Supporting Information). The Z zz in the middle of the and ≈18.8 µC cm–2), but even slightly higher than the total slab increase with the slab thickness, but are still smaller than bulk polarizations of 60 and 21 µC cm–2. This is striking obser- the bulk values. vation, which is indicative for MVB as discussed in more detail Going further, we use the DFPT values of the Born effec- below. tive charges to validate the computed spontaneous polarization The Born effective charge tensor Zs,*αβ , defined as using the approximate formula Ω ∂Pα e Zs,*αβ ( Born ) = (1) P~ ∑ Zs,*αβ ∆us,β (4) Ω β e ∂us,β E =0 provides important information on the bonding properties of where Δus,β are the displacements of atom s from its cen- solids, as well as the strength of the electron–phonon coupling. trosymmetric configuration in direction β. We find that this In fact, large values of Zs,*αβ have been shown to be fingerprints approach provides an accurate estimate of the polarization for of MVB, in conjunction with other peculiar properties, such as the thinnest model of SnTe. However, for GeTe, the approxi- large dielectric constants and large effective coordination num- mate formula is not accurate, due to the large magnitude of the bers.[18] Instead of using the Berry-phase polarizations to esti- atomic displacements. mate the Zs,*αβ values, we compute the latter quantities in an We complete the overview of the electronic properties by independent way by employing density functional perturbation computing the optical dielectric tensor ε∞ for the same ten thin- theory (DFPT).[34] In Figure 4 the in-plane components Z xx * nest models. At the surface, the electronic and optical proper- * and Z yy of the Born effective charge tensor for both cations (top) ties of materials are strongly affected by the abrupt variation and anions (bottom) are shown as a function of the layer index of the electronic density perpendicular to the surface and the for the ten thinnest slab models (NBL = 1,…,10). As in Figure 1, resulting fluctuations of the electric field at the atomic scale the data points are color-coded according to the thickness NBL. (local fields). As a consequence, periodic-boundary-condition * The qualitative behavior of Z xx and Z yy* with increasing supercell calculations fail to describe the out-of-plane optical NBL is similar to the trend displayed by the in-plane distances. response functions.[36] Here we only discuss the in-plane The Born effective charges of the GeTe and SnTe slabs in the components ε xx ∞ and ε yy∞ of the dielectric tensor. In periodic- interior region do not converge to the bulk values but, instead, boundary-condition calculations, their values depend on the show smaller absolute values. As regards GeSe and SnSe, the thickness of the simulation cell, which consists of the slab and values of all but the outermost layers almost coincide with the a vacuum region.[37] To compare the different 2D models we use bulk ones. Born effective charges are consistently larger in the formula of ref. [38], in which the dielectric tensor is nor- GeTe/SnTe as compared to GeSe/SnSe (except for the thinnest malized by a geometrical thickness given by the bulk interlayer Adv. Mater. 2020, 32, 2001033 2001033 (5 of 10) © 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.advancedsciencenews.com www.advmat.de * Figure 4. In-plane components of the Born effective charge tensor Z *xx and Z yy (with Z *xx < Z yy * ) for cations (top) and anions (bottom) as a function of the layer index. The data points are color-coded according to the thickness of the films: from red for the thinnest models to blue for the thickest * models. For SnTe, distortions are rather small and the models closely approach the cubic phase: for this reason, the Z *xx and Z yy data points almost overlap. The dashed lines correspond to the bulk values. distance (defined as the bulk lattice constant along z divided lie below the corresponding bulk values and slowly increase by 2). This approach properly describes transition metal dichal- with NBL. The moderate difference in ε∞ between GeTe/SnTe cogenides, where the 2D dielectric constant weakly depends on slabs and the bulk models suggests that they have a similar in- the thickness of the quasi 2D material. In monochalcogenides, plane bonding state. In contrast, thin films of GeSe and SnSe however, this dependence is more complex: Dewandre et al.[23] have much lower values of ε∞, which is indicative of covalent have shown that the effective dielectric thickness is not propor- bonding. Interestingly, the thinnest films of GeSe/SnSe show tional to the geometric thickness. significantly enhanced values of ε∞, although the bulk values The two components ε xx ∞ and ε yy∞ are plotted as a function of are recovered quickly. NBL in Figure 5. Again a similar trend is observed regarding the The unusual structural properties of the α models of GeTe convergence toward the bulk. The values for GeTe/SnTe slabs and SnTe call for a detailed study of their bonding mechanism. Adv. Mater. 2020, 32, 2001033 2001033 (6 of 10) © 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.advancedsciencenews.com www.advmat.de Figure 5. The in-plane components of the optical dielectric tensor ε∞ as a function of film thickness. Bulk values are shown as dashed lines. In their bulk state, GeTe and SnTe show a peculiar combina- maximally localized Wannier functions[42] (additional informa- tion of physical properties that have been attributed to MVB, tion is provided in the Computational Details section). namely: strong anharmonicities, moderate electronic con- The computed electron-transfer values hardly depend on the ductivity, large effective coordination numbers breaking the film thickness. The charge-transfer values for NBL ≥ 3 are 0.44, 8-N rule, large values of Born effective charges and dielectric 0.62, 0.82, and 0.80 for GeTe, SnTe, GeSe, and SnSe, respec- constants.[18] On the contrary, the properties of GeSe and SnSe tively, in quantitative agreement with the electron transfer in are compatible with ordinary covalent bonding.[18] As displayed the corresponding bulk phases (Supporting Information). We in Figures 4 and 5, there is a remarkable dependence of the now focus the analysis on the electron sharing data (Figure 6): latter properties on slab thickness for GeTe and SnTe, but not different values of this bond indicator are obtained for different for the Se-based compounds. This raises the question if and atomic layers and, for each layer, for in-plane or out-of-plane how the nature of the bonding changes with film thickness. bonds. In addition, Peierls-distorted systems possess short and It has recently been demonstrated that bonding in crystals long bonds. Here we consider only “short-bond” data because can be defined and characterized employing two fundamental the sum of the electrons in the short and long-bonds is con- indicators: the electron transfer and the number of electrons stant upon Peierls distortion. Similarly to the trends in the shared between pairs of neighboring atoms.[17] An electron structural properties, the electron sharing in the interior of thin sharing between neighboring atoms equal to 2 corresponds to films of the selenides quickly converges to the bulk values upon the Lewis picture of a perfect covalent bond. In contrast, MVB increasing thickness. In contrast, the GeTe rhombohedral bulk is characterized by electron-sharing values close to 1 and small value (upper dashed line in Figure 6) is not recovered in the amounts of electron transfer (significantly below 1.0). These slab models, not even in the thickest ones. More specifically, conditions reflect a substantial amount of electron delocaliza- the larger in-plane distortion in the thin-film models of GeTe tion, yet do not imply metallic properties. The electron transfer and SnTe leads to shorter bonds and more pronounced in- is determined from ab initio quantum-mechanical calculations plane electron sharing compared to the bulk values, whereas by integrating the net charge density of an atom over its basin the absence of out-of-plane distortion in the center of the slabs and subtracting the charge of the free reference atom.[39] The yields small corresponding electron-sharing values. electron sharing is obtained from the so called delocalization It is interesting that the two families of monochalcogenides indices.[40] Here we employ these two indicators to investigate behave so differently. It has recently been shown that GeTe and the bonding mechanisms in our quasi 2D models. For this pur- SnTe exhibit MVB, while GeSe and SnSe are characterized by pose, we use the package critic2,[41] in which the delocalization covalent bonding.[17] This classification is based on the signifi- indices are computed using an efficient technique based on cant difference in the values of electron sharing between the Adv. Mater. 2020, 32, 2001033 2001033 (7 of 10) © 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.advancedsciencenews.com www.advmat.de Figure 6. Amount of electrons shared between pairs of atoms in the thin-film models of GeTe, SnTe, GeSe, and SnSe. For each compound, the upper and lower plots correspond to in-plane and out-of-plane pairs of atoms, respectively. The dashed lines indicate the bulk values of this bond indicator. For GeTe, the two dashed lines correspond to the rhombohedral (higher value) and to the cubic (lower value) phase. For bulk GeSe and SnSe, the in- plane and out-of-plane electron-sharing values are different. two families. On the contrary, the charge transfer values are for a more pronounced electron delocalization, in line with relatively small in all of the four compounds. This trend can the more “metallic” structure. At the same time, a more sig- be seen even more clearly from the map of ref. [16], where the nificant Peierls distortion in the parallel direction (film plane) normalized electron transfer is considered, which is obtained is observed. This in-plane distortion is so pronounced that by dividing the absolute charge transfer by the formal oxida- the total polarization is larger for the thin film models. These tion state. The corresponding values for the four monochal- findings are very plausible for a system that displays MVB and cogenides discussed here are GeTe (0.17), GeSe (0.325), SnTe exemplify the impact of reduced dimensions on the competi- (0.313), and SnSe (0.41). This moderate charge transfer is not tion between electron localization and delocalization. compatible with ionic bonding. Such impact is even more dramatic in ultrathin buckled These two different classes of monochalcogenides also show films (1–4 BLs) of GeTe[20] obtained by cutting slabs perpen- pronounced differences in the thickness dependence of their dicular to the (111) direction of the bulk phase. These films structure, their electronic properties and their bonding. The form a layered structure consisting of alternating short and data displayed in Figure 6 underscore the different behavior long bonds. For such systems, the reduced dimensionality sup- of Se-based compounds, compared with Te-based systems: for presses electron delocalization and leads to both in-plane and GeSe and SnSe, 4 BLs can be considered as a minimal thickness out-of-plane covalent bonding.[20] Therefore, the nature of the for recovering the bulk in-plane and out-of-plane bond-indicator bonding in the 2D limit also depends on the orientation of the values in the central layers of the slabs. In fact, for such thick- slab. Interestingly, ultrathin slabs of SnTe (4–8 layers) grown nesses, the bulk limit is obtained for all but the outermost two along (001) on graphene can form a γ-phase similar to the GeSe layers of the slabs. In contrast, in GeTe and SnTe, even the phase,[12] which may display covalent bonding, in contrast to 10 BL stacks have not reached bulk values. The thinnest models the α-phase. Hence, the reduced dimensionality can increase (1–4 BLs) possess out-of-plane electron sharing values and struc- electron localization and even destabilize MVB. tural parameters compatible with covalent bonding. However, In perspective, we expect that metavalently bonded mate- for thicker models, about 0.9 electrons are shared between adja- rials generally exhibit unusual properties in the quasi 2D limit. cent atoms along the vertical direction in the slab center. This Depending on the film thickness and the crystallographic value is close to the one of the cubic phase. Hence, there is no direction relative to the bonding configuration, the nature of Peierls distortion in this direction, in agreement with the data the bonding can be tuned, enhancing the versatility of these on the film structure displayed in Figure 1. This is indicative materials for applications in nanoelectronics and information Adv. Mater. 2020, 32, 2001033 2001033 (8 of 10) © 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.advancedsciencenews.com www.advmat.de technology. For instance, few-layer Pb-based compounds (PbS, and 0.05 kbar, respectively. Scalar relativistic ultrasoft and norm- PbSe, PbTe), which are metavalently bonded in the bulk, could conserving pseudopotentials were employed and the generalized show analogous bonding properties as GeTe and SnTe. The gradient approximation by Perdew, Burke, and Ernzerhof (PBE)[48] behavior of thin films of Sb could also resemble the one of these of the exchange-correlation functional was used. Semiempirical tellurides, due to the similar bonding configuration in the bulk: van der Waals corrections[49] were included for the GeTe, GeSe, this point could be relevant to the understanding of monatomic and SnSe systems but not for SnTe, since these corrections do phase-change memories based on nanoconfined Sb.[43–45] On not properly describe the rhombohedral distortion. It is verified the contrary, covalently bonded materials such as selenides are that the structural trends shown in Figure 1 do not depend on the generally less sensitive to the dimensionality reduction. Few- details of the functional by performing geometry relaxation for layer monochalcogenides are thus an excellent playground to selected slab models of SnTe using two widely employed van der investigate bonding in 2D materials, and the interplay between Waals functionals (see Supporting Information). Further com- dimensionality and electronic localization. putational details on the Berry phase and bond-indicator calcula- In conclusion, we have shown that, for quasi-2D γ models of tions are provided in the Supporting Information. GeSe and SnSe, bulk properties—including bond lengths, die- lectric constants, and bonding indicators—are recovered in the interior of slab models containing just a few bilayers. On the Supporting Information other hand, the structure of thin films of GeTe and SnTe shows pronounced deviations from the bulk phases, even for thick- Supporting Information is available from the Wiley Online Library or nesses exceeding 18 bilayers. We have explained this behavior from the author. in terms of strong depolarizing fields in GeTe and SnTe films and the different nature of the chemical bond in selenides and tellurides. As a result, the two groups of materials also exhibit Acknowledgements different ferroelectric properties. Thin films of GeSe and SnSe I.R. and Z.Z. contributed equally to this work. The authors acknowledge arrange themselves in such a way that consecutive, quasi van useful discussions with M. Stengel, M. Pohlmann, M. Kaminski and der Waals-coupled bilayers are mirror symmetric. Hence, the T. Sohier. M.W. and R.M. also acknowledge the computational resources polar displacements counterbalance each other.[5] In contrast, granted by JARA-HPC from RWTH Aachen University under projects GeTe and SnTe adopt a structure where consecutive bilayers JARA0150, JARA0183 and JARA0198, as well as funding by the Deutsche are distorted in the same direction and polarizations add up. Forschungsgemeinschaft (DFG) within the collaborative research center SFB 917 “Nanoswitches”. Z.Z. acknowledges financial support However, the strong depolarizing fields due to the out-of-plane by the Ramon y Cajal program RYC-2016-19344 (MINECO/AEI/FSE, component of the polarization relax the slabs away from the UE), the CERCA programme of the Generalitat de Catalunya (Grant bulk structure. As far as bonding properties are concerned, we 2017SGR1506), the Severo Ochoa programme (MINECO, SEV-2017- have shown that the GeSe and SnSe γ-phase models exhibit 0706), and by the DFG Grant No. ZA 780/3-1. covalent bonding similarly to the bulk phase, whereas the α-phase models of SnTe and GeTe do not approach the bulk behavior upon increasing thickness. Instead, they show full out-of-plane electron delocalization, which results in increased Conflict of Interest in-plane Peierls distortion. This peculiar behavior is a finger- The authors declare no conflict of interest. print of MVB in these materials. We thus expect similar effects when thin films of the metavalently bonded PbSe and PbTe are considered. 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