Instability and Spontaneous Reconstruction of Few-Monolayer Thick

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Instability and spontaneous reconstruction of few-monolayer thick GaN graphitic structures Alex V Kolobov, Paul Fons, Junji Tominaga, Berangere Hyot, and Bernard André Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b01225 • Publication Date (Web): 07 Jul 2016 Downloaded from http://pubs.acs.org on July 12, 2016

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Instability and spontaneous reconstruction of few-monolayer thick GaN graphitic structures A.V. Kolobov,∗,† P. Fons,† J. Tominaga,† B. Hyot,‡ and B. Andr´e‡ †Nanoelectronics Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba 305-8562, Japan ‡Universit´e Grenoble Alpes, CEA, LETI, MINATEC campus, F38054 Grenoble, France. E-mail: [email protected]

Abstract 2D semiconductors are a very hot topic in solid state science and technology. In addition to van der Waals solids that can be easily formed into 2D layers, it was argued that single layers of nominally 3D tetrahedrally bonded semiconductors, such as GaN or ZnO, also become flat in the monolayer limit; the planar structure was also proposed for few-layers of such materials. In this work, using first-principles calculations, we demonstrate that, contrary to the existing consensus, the graphitic structure of fewlayer GaN is unstable and spontaneously reconstructs into a structure that remains hexagonal in plane but with covalent interlayer bonds that form alternating octagonal and square (8|4 Haeckelite) rings with pronounced in-plane anisotropy. Of special interest is the transformation of the band gap from indirect in planar GaN towards direct in the Haeckelite phase, making Haeckelite few-layer GaN an appealing material for flexible nano-optoelectronics

III-V compound semiconductors, such as GaAs, AlAs, InAs, InP, GaN and their ternary and quaternary alloys, combine elements in columns III and V of the Periodic Table. They 1

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possess direct gaps with the resulting ability to efficiently emit and detect light, which makes them ideal for uses in lasers, light-emitting diodes and detectors for optical communications, instrumentation and sensing. In 2000, the Nobel prize for physics was awarded “for developing III-V semiconductor heterostructures used in high-speed- and optoelectronics”. 1 Transistors based on III-V materials are at the heart of many high-speed and high-frequency electronic systems and III-V CMOS technology is a mainstream part of semiconductor research. 2 For reviews of other optoelectronic applications of III-V semiconductors see, e.g. 3,4 . In most existing applications, III-V semiconductors are used in their 3D, or bulk, form with the characteristic dimensions of several nanometers, i.e. ca. 10 or more lattice constants. At the same time, following the success of graphene, the search for other two-dimensional (2D) materials has acquired momentum and transition-metal dichalcogenides (TMDC) with the generic formula of MX2 (M = Mo, W; X = S, Se, Te) have emerged as very promising materials. These materials possess a layered structure, where ca. 6 ˚ A-thick X-M-X triple layers (usualy referred to as monolayers), consisting of a metal plane sandwiched between two chalcogen planes, are held together by weak van der Waals (vdW) forces. Similar to graphene, mono- and few layer TMDC structures can be easily prepared. While bulk TMDCs are indirect gap materials, monolayer TMDCs possess a direct gap 5,6 and extraordinary large exciton and trion binding energies, 7–9 which makes them efficient competitors for conventional III-V optoelectronics. The ultimately thin layers of TMDC make these materials extremely energy efficient and suitable for transparent and flexible optoelectronics. 10 The progress achieved with layered semiconductors has generated increased interest in atomically thin layers of conventional III-V semiconductors as a new class of 2D materials. These materials are fundamentally different from the easily cleaved vdW solids. Because these materials in their bulk form are so-called tetrahedrally bonded semiconductors, with all atoms being sp3 hybridized, the surfaces contain a large number of dangling bonds making them unstable. In addition, in binary crystals, due to the different electronegativity of the constituent species, the two opposing surfaces associated with “cleavage” into hexagonal

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using the generalized gradient approximation (GGA), where additionally the effect of vdW interlayer interaction was accounted for using the DFT-D2 method. The inclusion of the vdW correction generally resulted in a shorter interlayer separation but did not change the structure in general. In both cases it was concluded that “both bi- and tri-layers prefer a planar configuration rather than a buckled bulk-like configuration”. 18 It was further proposed that application of epitaxial strain could increase the stability range of planar structures, e.g. the maximum number of GaN layers up to which the graphitic structure is stable increased from 10 in unstrained conditions to 16 for 5% tensile strain. 19 The stability of ultra-thin diamond layers was studied in, 20 also using the GGA approximation. It was found that a monolayer diamond layer became flat as graphene. The same trend was observed up to 5 atomic layers, where flat graphene layers were formed. Structures thicker than 12 atomic planes retained the diamond structure. For intermediate thicknesses, the internal layers were diamond-like sp3 -hybridized, while the outer layers were graphenelike. 20 It is also interesting to note that when the separation between two graphene layers stacked directly on top of each other was decreased to 1.56 ˚ A, strong covalent bonds were formed between the layers. 21 It should be noted here that bulk GaN with the wurtzite structure is a direct-gap semiconductor with a wide gap, which determines its huge potential for optoelectronics (the Nobel prize for physics was awarded in 2014 for successful use of “the difficult-to-handle semiconductor GaN to create efficient blue light-emitting diodes” 22 ). At the same time, graphitic GaN was predicted to be an indirect-gap material, 17,18 which significantly limits its application potential. We note here that while the formation of stable planar few-layer structures for naturally layered materials such as graphite or h-BN can be easily understood; for III-V materials the situation is more complex. While the formation of the flat outermost layers does serve to minimize surface dipoles, thus decreasing the energy of the system, the absence of covalent bonds between the layers is certainly energetically unfavourable, suggesting that the planar

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geometry may not be the most stable phase for few-layer structures and calling for further studies of this issue. Experimentally, little is known about the structure of atomically thin III-V layers, which is a direct consequence of their bulk structure: the 3D nature of covalent bonds does not allow to exfoliate a bulk crystal, similar to graphene or TMDCs and layers grown on substrates are necessarily affected by the presence (and the structure) of the latter. There are limited reports on the growth of nanosheets of tetrahedrally bonded semiconductors. For ZnO, the formation of planar layers was observed experimentally for growth on Ag(111), with the transition to the bulk wurtzite structure in the 3–4 ML coverage range. 23 It is not clear if the smaller critical thickness observed experimentally (compared to a theoretical prediction of 10 layers 15 ) was caused by the interaction with the substrate. It is also not clear to what extent the presence (and the structure) of the substrate affects the structure of few-layer III-V semiconductors. Recent progress in GaN epitaxial growth on graphene, 24–32 a perfectly flat material that does not possess any dangling bonds thus minimizing the chemical interaction between the substrate and the overlayer, opens some interesting opportunities in this direction. Wherever reported, however, the thickness of GaN exceeded the critical thickness and the structure of the grown GaN was wurtzite. 25,27–30 An interesting approach to fabricate few-layer nanosheets of GaN was proposed in. 33 The authors obtained few-layer GaN by heating in ammonia at ca. 650 ◦ C few-layer flakes of GaS and/or GaSe. Since the starting materials possess mica-like morphology, nanosheets could be easily fabricated by micromechanical cleavage. 6-10 layer GaN was produced using this method, whose structure was wurtzite. As recently noted in, 34 “monolayer and few layer materials made of GaN and other III-V semiconductors are now a challenge for the experimentalist”. In this work, we revisit the issue of structural stability of GaN in the few-layer limit using rigorous first-principles density functional simulations, based on both geometry optimization and phonon simulations, and demonstrate that the current consensus is incorrect and the

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flat, i.e. the surface dipoles are minimized as required for structure stabilization. Thirdly, whilst in the wurtzite phase all interlayer bonds are polarized in the same direction, in the 8|4 phase, the neighboring Ga-N interlayer bonds have inverted polarisation directions and the overall polarization arising from the interlayer bonds is zero. The flatness of the outermost atomic layers and the net zero polarization resulting from the interlayer bonds ensure minimization of the surface dipoles and stabilize the structure. The formation of the 8|4 zeolitic motifs for a structure that is expected to be hexagonal is not totally unexpected. Such motifs have been reported to form at grain boundaries of graphene and other 2D materials 35 and continuous lattices formed from 8|4 motifs were also found to be stable. 34,36,37 Such motifs are ideally suitable for compositions where only heteropolar bonds are expected. Furthermore, zeolitic structures were found to be energetically competitive with wutzite nanostructures for ZnO, 38 another material that forms a planar graphitic phase in the monolayer limit. 15,23 Hence, the formation of the 8|4 phase may be a general feature of few-layer materials that tend to minimize the energy associated with with polar surfaces by acquiring the graphitic phase in the monolayer limit. It may be also interesting to note that the electronic properties significantly differ between the hexagonal and 8|4 phases of the same material. 36 Sometimes, the 8|4 bonding pattern is referred to as Haeckelite. 37,39 The term was originally proposed for monolayers of carbon-based structures and later also used for other 2D materials. In what follows, we shall also use this term. We note that the term Haeckelite was recently used for description of hypothetical GaN monolayers with the 8|4 bonding motif and the corresponding nanotubes 34 What is fundamentally different between the cited work 34 and the present study, is that in 34 the hypothetical 8|4 atomic bonding was in plane and it was argued that such a phase should be structurally (meta)stable, if realized, while the energy of this phase was somewhat larger than that of the graphitic phase. In the present work, we demonstrate that this phase actually is energetically the most favourable for a certain range of thicknesses but the 8|4

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bonding pattern is not located in plane but in the direction of the growth, i.e. perpendicular to individual GaN layers. We note, that qualitatively the results do not depend on the inclusion of vdW correction in DFT simulations. We performed such simulations both with and without vdW correction (Grimme’s DFT-2D correction was used as implemented in CASTEP) and obtained the same results in terms of the structure (with slightly different bond lengths). This result, is similar to the previous work 18 , 19 where the effect of vdW interaction on few-layer (graphitic) GaN was also rather small. To make sure that the obtained result is not an artifact of the functional used, we additionally re-calculated the energies of the Haeckelite phase described above and a hypothetical graphitic phase obtained as a transient phase in our structural relaxation using the solid-state functional PBEsol: the order of phase stability remained unchanged Following the structure optimization, we further performed phonon calculations in order to check the stability of the obtained phases. First, we checked the stability of the few-layer graphitic phase. These results are exemplified by the phonon dispersion curves of the 3 ML slab (Fig. 4, left). The presence of imaginary frequencies (visualized as negative frequencies in Fig. 4) at finite-k unambiguously demonstrates that the graphitic phase is unstable; the location of the imaginary modes suggests that the true stable phase has a double unit cell size.. On the other hand, the similar dispersion curves calculated for the Haeckelite structure (Fig. 4, right) do not have any imaginary modes, clearly demonstrating that the Haeckelite phase is stable. We argue that the stability of the obtained Haeckelite phase in the few-layer limit is determined by the combination of the following factors. The formation of (additional) interlayer bonds makes this structure energetically more favorable than the planar graphitic structure. At the same time, the outermost atomic planes in the Haeckelite phase remain nearly flat, thus minimizing the surface dipoles associated with the presence of oppositely charged cations and anions. Finally, the net zero moment associated with interlayer bonds

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Instability and Spontaneous Reconstruction of Few-Monolayer Thick

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