Crystal Structures and Electronic Properties of Single-Layer, Few

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Crystal Structures and Electronic Properties of Single-Layer, Few-Layer and Multilayer GeH Xiaoguang Luo, and Eva Zurek J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b11770 • Publication Date (Web): 12 Dec 2015 Downloaded from http://pubs.acs.org on December 14, 2015

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Crystal Structures and Electronic Properties of single-Layer, Few-Layer and Multilayer GeH Xiaoguang Luo1,2, Eva Zurek1,* 1 Department of Chemistry, State University of New York at Buffalo, Buffalo, NY 14260, USA 2 Department of Electronics, Nankai University, Tianjin 300071, China Abstract: Single-layer germanane (GeH) structures have been explored using evolutionary algorithms combined with first-principles methods. The chair GeH is the most stable structure among all uncovered single-layer GeH structures, which is similar to that found in graphane. Multilayer and few-layer GeH structures with 2~6 layers in their unit cells are constructed from the chair GeH in various possible stacking sequences. Many isoenergetic multilayer GeH structures are found using the semi-empirical dispersion correction of DFT-D3. It’s shown that the experimentally synthesized bulk GeH [Bianco et al., ACS Nano, 2013, 7, 4414] assumes the tr6 structure, not the previously claimed 2H structure. Band structure calculations reveal that the location of the direct band gap of multilayer GeH structures oscillate between the Г and A point in their first Brillouin zone depending on whether the unit cell contains an odd or even number of layers. The band gaps of multilayer and few-layer chair GeH structures are calculated to lie between 1.47~1.66 eV using the hybrid HSE06 functional, and they are dependent on the stacking sequences and interlayer distances.

KEYWORDS: 2D materials, layered materials, germanane, hydrogenated germanene TOC graphic 1.0

few-layer GeH multilayer GeH

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The Journal of Physical Chemistry

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1. Introduction Since the discovery of two-dimensional (2D) graphene, 2D materials composed of a single-layer or a few-layer have attracted increasing attention because of their exceptional properties, with numerous potential applications within, for example, high-speed electronics, optoelectronics, sensing, etc.1 In addition to studying new group IV single-layer materials composed of carbon (C)2,3, silicon (Si)4, and germanium (Ge),5,6 researchers have also investigated their corresponding hydride analogues: graphane (CH),7-12 silicane (SiH),13-15 and germanane (GeH).16-22 Another impetus for studying metal-hydrogen compounds is that they may become superconducting under conditions of high pressure, although most investigations have so far focused on bulk SiH4,23,24 GeH4·2(H2),25,26 GeH4,27 etc. Computations have shown that the pressure variable can change the relative stability of three-dimensional stacking polytypes of CH.11 And pressures of up to 10 GPa have been applied to GeH.28 Recently, multilayer GeH with millimeter-scale size has been synthesized using topochemical deintercalation from the Zintl phase CaGe2 precursor and then single-layer GeH has been mechanically exfoliated from multilayer GeH.16 It has been confirmed that single-layer GeH assumes a honeycomb lattice similar to that of CH. However, two different crystals of multilayer GeH have been reported: a tr6 structure (R-3m, trigonal-rhombohedral structure with a six-fold stacking sequence)20 and a 2H structure (P63mc, hexagonal structure with a two-fold stacking sequence).16-18,28 Because these materials may not form perfect crystals and may have turbostratic or amorphous structures, it is difficult to confirm the interlayer stacking sequence experimentally. In addition, because the layers are held together via relatively weak van der Waals interactions, it may be that different stacking sequences result in structures with nearly degenerate energies. Herein, we present a computational procedure that can generate multilayer crystal structures with different stacking sequence from a single-layer and then select those three-dimensional phases that are likely 2


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to be important. In general, the experimentally synthesized van der Waals layered materials should be among the structures singled out for further analysis. We used an evolutionary algorithm to predict a set of particularly stable single-layered GeH structures. Next, multilayer and few-layer GeH structures with 2~6 layers in their unit cells were constructed from the most stable single-layer GeH by building the chemically reasonable stacking sequences that can be generated within these unit cell constraints. Density functional theory calculations supplemented with a semi-empirical correction to account for dispersion, DFT-D3, illustrate that many isoenergetic multilayer GeH structures may be formed. The simulated XRD patterns of multilayer GeH show that the experimentally synthesized bulk GeH assumes the tr6 structure, not the previously claimed 2H structure.16-18,28 Band structure calculations show that the location of the direct band gap oscillates between the Г and A points in the first Brillouin zone (BZ), and it depends on whether the number of layers in the unit cell is odd or even. The hybrid HSE06 functional predicts that GeH structures with 1~6 layers in their unit cells will have band gaps within the range of 1.47~1.66 eV, and that the band gap depends on the stacking sequence and interlayer distance. 2. Calculation methods The structure prediction searches have been performed using the evolutionary algorithm XtalOpt,29 which has been successfully used to predict the structures of hydrogen-rich binary crystals.30-32 The structural relaxation and electronic structure calculations were carried out using density functional theory as implemented in the Vienna ab initio simulation package.33 The generalized gradient approximation (GGA) exchange and correlation functional of Perdew, Burke, and Ernzerhof was employed, unless otherwise stated.34 The projector augmented wave (PAW) method was used and the 4s24p2 electrons for Ge and 1s electrons for H were treated explicitly. A 3



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plane-wave cutoff energy of 500 eV and Monkorst-Pack k-points meshes with reciprocal space resolution of 2π × 0.02 1/Å were used. The convergence criteria were set to 1 × 10-6 eV and 0.01 eV/ Å for energy and force, respectively. A vacuum space of 15 Å was used to model the single-layer and few-layer structures. The semi-empirical van der Waals correction of DFT-D3-BJ was used for geometry optimizations.35 Band gaps were typically obtained with the PBE functional, and in select cases the screened hybrid HSE06 functional was employed. The bilayer crystal structures were constructed as follows. First, we choose one of the fixed single-layered structures. The second layer can be added by translational and/or rotational operations on the duplicated single-layer using a suitable interlayer distance. The translational and rotational steps can be adjusted to a desired value with arbitrary small precision. It can be guaranteed that all possible bilayer structures can be obtained in this way if the single-layer structure is known. Finally, we removed duplicate, continuously variable, and low symmetry structures using XtalComp and Spglib.36,37 After obtaining bilayer structures, we can add the third, fourth, fifth, and sixth layer and then repeat the corresponding operations. In order to reduce the number of GeH structures with four, five, and six layers in their unit cells, another restriction prohibiting duplicated layers was added to code. For example, those structures with AABCDE stacking sequences of six layer GeH structures were removed because of AA duplications. 3. Single-layer structures Previous theoretical investigations on CH structures have reported several 2D structures.7-12 It has been shown that the chair CH isomer is the most stable and other CH structures are metastable to the chair configuration (see Figure 1a). Since Ge and C are both group 14 elements, it can be expected that GeH structures should be similar to CH structures. Our calculations confirm this expectation. Figure 1 shows eight different single-layer GeH conformations. Following the naming 4


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convention in the investigation of CH structures in Refs. 7-12, the first six GeH structures (Figure 1a-f) are named as chair, stirrup, boat-1, boat-2, twist-boat, and tricycle GeH. The Ge atoms in these six structures are four coordinate and a top view shows that they belong to six-atom rings. We classify these six GeH structure as type I. The GeH structure shown in Figure 1g is named “chair-extension” because it can be built by replacing H atoms by Ge atoms in the chair GeH and then saturating the surface Ge atoms by H atoms. In order to maintain the ratio of 1:1 composition, each surface Ge atom must be saturated with two hydrogen atoms. This structure belongs to type II, which consists of quasi 2D GeH isomers that can be derived from type I structures via replacing hydrogen atoms by germanium and saturating germanium’s dangling bonds by the right number of atoms to achieve the desired stoichiometry. Table 1 suggests that type II structures should also be metastable to chair GeH. Therefore, we only show one of these metastable type II GeH structures. We refer to the GeH structure shown in Figure 1h as “rings4” GeH because it is comprised of buckled four-atom square rings of Ge atoms. The Ge atoms of “rings4” are five coordinate, bonding with the nearest four Ge atoms and one H atom. We classified rings4 GeH structure as type III. The symmetries and relative energies of the calculated GeH structures are shown in Table 1. The chair GeH is the most stable phase among all investigated conformations, in-line with previous results for CH.7-12 The Ge-H bond length is between 1.56~1.57 Å in all of the considered GeH conformations. The small bond length deviation is a result of H-H repulsion. As shown in Figure 1a, the directions of Ge-H bonds in the chair layer are perpendicular to the surface, which means they are in an ideal environment and no H-H repulsion should exist. In the other GeH structures, the Ge-H bonds no longer lie perpendicular to the plane of germanium atoms and H-H repulsion is one of the reasons for the different GeH bond lengths. The calculated Ge-Ge bond length of 2.46~2.48 Å for type I and II are between that of 2.51 Å in cubic germanium (Fd-3m, diamond structure) and 5



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that of 2.44 Å for a sp2 bonded buckled germanene single-layer. The Ge-Ge bond length in rings4 of 2.64 Å is much longer than in the other GeH structures, which is because it has a totally different structure type and coordination numbers.

Table 1. The symmetry, binding energy Eb, formation energy Ef, and band gap using GGA-PBE of predicted single-layer GeH structures. binding energy formation energy band gap (eV/fu) (eV/fu) (eV) type I chair P-3m1 (164) -2.893 -0.126 0.97 stirrup Pmna (53) -2.882 -0.115 1.70 boat-1 Pmmn (59) -2.879 -0.112 1.48 boat-2 Pbcm (57) -2.873 -0.106 2.57 twist-boat Pcca (54) -2.875 -0.108 1.69 tricycle Pbcm (57) -2.886 -0.120 1.55 type II chair-extension Pmma (51) -2.863 -0.096 1.22 type III rings4 P4/nmm (129) -2.759 0.008 – name

symmetry

For the chair GeH its buckling distance ∆z (see Figure 1a) of 0.74 Å is a little larger than that of a buckled germanene single-layer of 0.69 Å in our calculations. The H atoms pull the bonding Ge atoms out of the plane, which makes the buckling distance ∆z of chair GeH larger than that of germanene. Moreover, the lattice constant a = 4.09 Å of the chair GeH is larger than that of germanene, a = 4.06 Å, which is in accordance with the longer Ge-Ge bond length of chair GeH in comparison with that of germanene. The structural features of single-layer chair GeH are similar to those reported in the investigation of CH8-10 and SiH.14,15 Table 1 shows that chair GeH is the most stable single-layer GeH structure. The energy difference between the GeH structures we considered is less than 30 meV/atom, which is on the order of room temperature energy (kT). The stability of GeH structures follows the order: type III

Crystal Structures and Electronic Properties of Single-Layer, Few

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