Metal Templates and Boron Sources Controlling Borophene

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Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

Metal Templates and Boron Sources Controlling Borophene Structures: An Ab Initio Study Naiwrit Karmodak and Eluvathingal D. Jemmis* Inorganic and Physical Chemistry Department, Indian Institute of Science, Bangalore-560012, Karnataka India S Supporting Information *

ABSTRACT: Interlayer binding of 2D borophene phases are determined as a function of hole density (HD) and metal surfaces Cu, Ag, and Au. The Cu surface prefers formation of monolayers whereas the Au surface shows multilayer stacking. Ag surface enables formation of monolayers with higher HD and bilayers for borophenes with lower HD. The growth pattern of bilayers on metal templates are investigated using ab-initio molecular dynamic simulations. Formation of icosahedral B12 clusters and extension to sheets are also studied on Cu surface. Icosahedral sheet formation by boron atom deposition is found to be a thermodynamically unfavorable process on this surface. Thus, structure of borophene phases could also be tuned by modulating the parameters such as boron source or the metal templates, in addition to the substrate temperature and boron atom deposition rate.

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INTRODUCTION

stability of borophene is increased by two ways: buckling to a nonplanar sheet, or forming hexagonal holes.6,20,23 The nonplanar distortion as in δ6 sheet, reduces antibonding nature of frontier bands, whereas hexagonal holes remove excess electrons. The removal of one boron atom from every three unit cell of B−B2, i.e. B3−B6 results in an isoelectronic variant of graphene and MgB2 with hole density (HD) 1/9, known as the α′-boron sheet (B2−B6, Figure 1).6,23 It must be mentioned that the developments toward borophene gained momentum from a series of studies on boron clusters of increasing size, prime among them being the study by Wang and co-workers, of the boron cluster B36 with a hexagonal vacancy at the center, christened as borophene by them.24,25 It gave the anticipation of hexagonal holes in two-dimensional boron sheets, with or without metals.26 Interlayer stacking modulates the electron density of the borophene layers. The stacking of individual layers in δ6*-AA (or P6/mmm, Figure 1) sheet increases the binding energy. This removes the excess electrons in δ6* sheet, leading to a similar electron count as graphene.4 In every unit cell, formation of one interlayer B−B bond (blue spheres) removes the extra one electron in each layer.4 The band structure shows a Dirac cone at Fermi region. The AB stacking of δ6 sheet also enhances its stability w.r.t. monolayers due to formation of localized interlayer B−B bonds.4,14 This is denoted as δ6-AB (or Pmmm, Figure 1) sheet. The electron deficient δ3 sheet (HD 1/ 3) form multicenter interlayer B−B bonds to attain electron

The 2D boron allotropes show diverse structural possibilities with potential for unusual physical and chemical properties.1−13 Depending on hexagonal hole density (HD), extent of buckling from planarity and interlayer stacking, several varieties of borophene phases are known.1−9,13−18 The isoelectronic relationship with graphene and MgB2 serves as a familiar starting point to understand these structural varieties.19−21 The electron deficiency of graphitic boron sheet (δ3 sheet, Figure 1) is removed in MgB2, where one Mg compensates two electrons for every two boron atoms.20,22,23 Replacement of Mg by boron atom (blue spheres) placed at the hexagonal center (B−B2 denoted as δ6*) make the system unstable due to excess one electron per unit cell, occupying antibonding bands.3,6,23 The

Received: December 20, 2017 Revised: January 10, 2018

Figure 1. Schematic diagram connecting the monolayer and interlayer stacked borophene phases with graphitic boron sheet. © XXXX American Chemical Society

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DOI: 10.1021/acs.jpcc.7b12540 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C sufficiency as in C2/m sheet (Figure 1).4 The middle layer of this sheet is represented in blue and other two layers with green in Figure 1. This connectivity resembles the multicenter bonding pattern of polyhedral boranes and boron clusters. Thus, interlayer stacking varies drastically from HD 0 to 1/3. It is tempting to conclude that interlayer stacking pattern depends only on the HD of sheets. Bilayer possibilities of the sheets with intermediate HD are not studied extensively. The doping of metal atoms in planar boron clusters and borophenes enhances stability and tunes electronic structures.26 Thus, metal templates used during the synthesis of borophene phases could influence their structural preferences. In a theoretical study, monolayer planar sheets with higher HD are found to be favorable on Cu surface,11,12 while Ag and Au surfaces show higher preferences for icosahedral sheets.12 The recent synthesis of borophene phases on Au, Ag, and Cu surfaces, however gives a different notion. Both Mannix et al.1 and Feng et al.,2 reported the formation of single layer planar sheets on Ag (111) surface whereas a monolayer sheet, containing Ih-B12 units is obtained by Tai et al. on Cu foil.13 This monolayer is predicted to have similarity to 3D γ-B28 allotrope.27 Though spectroscopic evidence indicate presence of icosahedral units, the precise structure is debatable. The Au (111) surface also favors formation of planar borophene phases.28 The effect of growth temperature and deposition rate of boron atoms on the density and distribution of the hexagonal holes in monolayer borophenes are studied in detail.23 Here we use density functional theory to show how interlayer stacking and stability varies depending upon hole-density of sheets and metal templates. Ab-initio molecular dynamic simulations of possible growth pattern of different borophene phases on Cu, Ag and Au surfaces are studied, to understand the effect of boron source material on borophene structural variety.

metal surface, and Em is the optimized energy of the pure metal surface. The calculated lattice mismatch for the boron sheet and metal templates are in Table S2. The relative BE of monolayer and corresponding interlayer stacked sheets with varying HD are given in Table 1 w.r.t. α′ sheet in meV/atom. Table 1. Relative Binding Energies (BE) of Boron Sheets in meV/atom w.r.t. the α′ Sheeta sheet δ6* δ6*-AA4,36 δ6 δ6-AB4,36 α6 α6-AA36 α7 α7-AA36 α8 α8-AA α9 α9-AA α′ α′-AB8 β5 β5-AB β14 β14-AA36 β12 β12-AB χ3 χ3-AA δ4 δ4-AB δ3 δ3-AB

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COMPUTATIONAL DETAILS The computations are performed using Vienna ab initio simulation package (VASP).29−31 Generalized gradient approximation (GGA)32 with Perdew−Burke−Ernzerhof (PBE) functional is used to incorporate the electron exchange correlation and PAW pseudopotentials33 are used to treat the electron ion interactions. The energy cutoff for the plane wave basis set is 400 eV, and the equivalent set of k point grid with spacing of around 0.02 Å−1 is taken for all computations. The electronic energy convergence threshold is set to 10−6 eV in energy and 10−3 eV/Å for force. In order to avoid interactions between the adjacent periodic images, a vacuum space of around 20 Å is added along perpendicular direction of the sheets. The metal surfaces are modeled by taking four layers of the (111) surface, cleaved from a fcc lattice of metals with lattice constants of 3.614 Å for Cu, 4.085 Å for Ag, and 4.078 Å for Au. The bottom two layers of metal surface are fixed and the upper two layers are allowed to relax along with the boron sheet. The van der Waals interaction between boron sheet and metal surface has been incorporated by using vDW correction (DFT-D3 method).34 The binding energy values of the isolated monolayer and bilayer sheets are given in Table S1 (Supporting Information). The binding energy (BE) values for the isolated borophene sheets, E1, are calculated using the equation: E1 = 1/ n[Es − nEB]. Here, EB denotes single boron atom energy, Es is the optimized energy of the sheet, and n is the number of boron atoms. On the metal surfaces, BE is denoted as E2 = 1/n(Es‑m − [Em + nEB]). Es‑m is the optimized energy of the sheet with the

HD 0 0 1/16 (0.062) 1/16 (0.062) 1/12 (0.083) 1/10 (0.100) 1/9 (0.111) 2/15 (0.133) 5/36 (0.139) 1/6 (0.167) 1/5 (0.200) 1/4 (0.250) 1/3 (0.333)

BE (meV/atom)

BD

312 −29 96 −109 82 −115 90 −127 59 −146 32 −79 0 −24 1 −64 59 −13 54 5 43 9 313 70 900 75

− 2/6 − 2/8 − 16/60 − 8/30 − 24/88 − 8/36 − No bond − multicenter − 18/62 − 2/10 − no bond − multicenter − multicenter

a Here E1 = 1/n[Es − nEB] denotes BE for free standing boron sheets. EB denotes the single boron atom energy; Es is the optimized energies of the sheet. n is the number of boron atoms. BD denotes bond density, defined as number of atoms involved in 2c B−B bond formation/total number of atoms per unit cell.

The ab-initio molecular dynamic simulations of the boron sheets on metal surfaces are performed for 20 ps with canonical (NVT) ensemble using the algorithm of Nose35 at finite temperatures of 1000K with a time step of 1.0 fs. The initial structures for extended sheets are build up from the corresponding optimized structures. The finite fragment of δ6-AB sheet simulated on Cu (111) surface consists of fortyfour boron atoms. For all the simulations, bottom two layers of the metal surface is kept constant. The convergence thresholds and the k-point grid are the same as those used for optimizing the respective structures, as mentioned earlier.

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RESULTS AND DISCUSSION The monolayers show different stacking possibilities denoted as AA, AB, AB1, and so on. Most stable patterns are shown in Figure 2, whereas Figure S1−S3 (Supporting Information) represents the slightly less stable stacking patterns for each of the monolayers. We use a nomenclature for the sheets similar to the one introduced by Wu et al.8 Though sheets with both highest and lowest HD (0 and 1/3 respectively) favor interlayer bond formation, the intermediate ones have variable preferB

DOI: 10.1021/acs.jpcc.7b12540 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

energy levels and tune the electronic properties. Formation of interlayer B−B bonds induces deformation within individual layers. The distortion of in-plane σ-framework in planar sheets reduces stability on interlayer stacking. The buckled monolayers favor interlayer bond formation to greater extent compared to planar sheets. This is seen for δ6 and δ6* sheets. Though both have zero HD, the buckled arrangement of boron atoms in the δ6 sheet favors interlayer stacking to a greater extent compared to the planar δ6* sheet. Therefore, stability of the δ6-AB sheet is relatively greater compared to that of the δ6*-AA sheet. The differing stabilities of borophene phases on metal surfaces are accounted by calculating BE for some of these monolayer and preferred bilayer sheets on Cu (111), Ag (111), and Au (111) surfaces as shown in Table 2. Since, δ6*-AA sheet Table 2. Relative Binding Energies (BE) of Boron Sheets in meV/atom on Metal Surfaces w.r.t. α′-Boron Sheeta

Figure 2. Optimized structure of bilayer boron sheets. The interlayer 2-center B−B bonds are shown in blue. The two boron layers are distinguished by different colors. The unit cell is shown in black dotted lines.

ΔE2 (meV/atom) sheet δ6*-AA δ6 δ6-AB α8 α8-AA α′ β5 β5-AA β5-AB β12 β12-AA β12-AB χ3

ences. BE for bilayers increases as HD increases from 0 and becomes maximum for α8-AA sheet with HD 1/12. The relative stability decreases upon further increase in HD. In the previous study by Gao et al., α6-AA and α7-AA bilayer sheets with HD 1/ 16 are reported to have the maximum stability.36 We found that these sheets are less stable than α8-AA sheet by 37 and 19 meV/atom, respectively. The interlayer B−B bonds remove electron density from skeletal bands of the sheet. Thus, interlayer stacking in the sheets with higher HD are less favorable. The nonplanar distortion in the corresponding monolayers of δ6-AB, α7-AA and α8-AA result in mixing of σ and π bands. Projected density of states (PDOS) plot for these sheets are shown in Figure 3a−c. The blue region denotes distribution of

HD 0 1/12 (0.0) 1/9 (0.111) 2/15 (0.133)

1/6 (0.167)

1/5 (0.2)

Cu

Ag

Au

− 50 69 − − 0 −29 63 91 −78 112 92 −58

69 13 −42 5 −70 0 −28 −12 −40 −49 39 19 −49

44 21 −30 17 −48 0 6 8 15 16 50 28 15

Here E2 = 1/n(Es‑m − [Em + nEB]) represents the BE of boron sheets on metal surfaces. Es‑m is the optimized energies of the sheet with the metal surface. Em is the optimized energy of the pure metal surface, and EB denotes the single boron atom energy; n is the number of boron atoms. a

has higher lattice mismatch with Cu surface, its BE is calculated only on Ag and Au surfaces. The BE trend for monolayers on metal surfaces depend upon their HD, as seen earlier.12 The sheets with higher HD are preferred on both Cu and Ag surface. Au surface shows similar stability ordering as isolated sheets. The α′ (HD = 1/9) sheet is preferred to the most, followed by β5 sheet (HD = 2/15) on Au (111) surface. However, relative stability difference for other sheets w.r.t. the α′ sheet is less (Table 2). Among the three metal surfaces, Cu (111) has highest surface energy, as reported recently by Tran et al., and hence, its interaction with boron sheets would be highest.37 Thus, sheets with higher HD would become more stable on this surface, due to greater metal−sheet interactions. Au (111) and Ag (111) surface energies are lower and almost similar to each other. However, the work function of Ag (111) surface is much lower compared to both Cu and Au surface.12,38 This compensates for the lower surface energy of Ag surface and relative stability trend for boron monolayers resemble the Cu (111) surface. On the Au (111) surface, the sheet to metal interaction is less, leading to a stability ordering similar to that of the isolated sheets. In general, frontier metal d- and s-bands interact with σ and π bands of planar boron sheets. However, in case of buckled

Figure 3. PDOS plot for bilayer sheets (a) δ6-AB, (b) α7-AA, and (c) α8-AA. The blue region denotes distribution of s + px + py bands and the red region the pz bands.

s, px and py bands and red for pz bands. In α8-AA sheet (Figure 3c), HD and interlayer B−B bond formation modulates the energy levels such that Fermi-level separates the valence and conduction bands. A direct band gap is opened up of 0.45 eV near to the Gamma as shown in the Band diagram for α8-AA sheet in Figure S4 (Supporting Information). The δ6-AB (a) and α7-AA (b) show a metallic behavior, such that s + px + py and pz bands overlap each other near the Fermi region. Thus, interlayer stacking of borophene sheets could rearrange the C

DOI: 10.1021/acs.jpcc.7b12540 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Figure 4. PDOS plot of the boron sheets without and with metal surfaces. (a) β12 sheet with 15 boron atoms (b) β12 sheet on Cu surface. (c) β12 sheet with 20 boron atoms. (d) β12 sheet on Ag surface. (e) α′-sheet. (f) α′-sheet on Au surface. Metal d-bands are denoted as green curves and the boron sheet bands by red and blue curves.

Figure 5. (a) Initial structure of finite fragment of δ6-AB sheet on Cu surface. (b and c) Conformation after 1.5 and 8.5 ps, respectively. (d) Initial conformation of Ih-B12 cluster on Cu surface. (e) Conformation of the Ih-B12 cluster after 1.5 ps. (f) Ih-B12 sheet, where one B12 unit is connected to six other B12 units in the surroundings, resembling the 3D-α boron allotrope.

sheets such as α′-sheet on Au surface, σ and π band mix among each other. The PDOS plot of β12 sheet on Cu and Ag surface and α′-sheet on Au surface in Figure 4, shows mixing between metal d bands and boron states. The interaction between metal s-bands and boron sheet is not plotted here. In presence of metal surface, boron sheet bands are distributed throughout the energy range compared to the PDOS plot without the surface. In β12 sheet, vacant or partially filled σ and π levels present near to Fermi region interact with filled metal bands. After interaction with the surface, some of the vacant σ levels (blue

curve in Figure 4, parts a and c) near the Fermi region are stabilized and move below the Fermi region (Figure 4, parts b and d). This leads to an attractive interaction. In sheets with lower HD, interaction is repulsive, since overlap would be between filled frontier boron states and filled metal bands. Thus, difference in relative BE between the most preferred (Higher HD) to less preferred ones (Lower HD) are greater for Ag and Cu surface. In contrast, noblest Au surface have lower interaction with boron sheets having both higher and lower HD. Even though buckling enhances overlap for α′-sheet, the D

DOI: 10.1021/acs.jpcc.7b12540 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C filled metal bands interact with filled levels of the sheet (parts e and f), leading to a repulsive interaction. The situation is similar for the β5 and δ6 sheet, as the frontier σ and π bands remains filled. As a result, though stability ordering is preserved, the relative stability difference between sheets with higher and lower HD on Au surface is reduced compared to that for the freestanding situation. With this information, let us analyze the stability of bilayer sheets on metal templates. On metal surfaces, greater the interaction between first layer of borophene and metal surface, lower will be interlayer interaction of boron sheets. Thus, greater reactivity of Cu surface reduces stability of all bilayers compared to monolayers (Table 2). The ΔE2 for β12 bilayers are reduced the most, as the monolayer β12 sheet has the highest stability. Similar is the situation on the Ag surface. The BE is reduced for stable monolayer after formation of bilayers. The slightly less stable monolayers such as δ6, α8 and β5 sheet favor formation of bilayers. Au surface reduces the stability of β12-AA bilayer only. Relative BE for β5 bilayers and β12-AB are almost similar to the corresponding monolayers. Whereas for δ6 and α8 sheet, stability is increased upon stacking. Therefore, Au surface favors interlayer stacking for both monolayers with higher and lower HD. The δ6*-AA sheet has lower stability on both Ag and Au surface. Here, metal to sheet interaction would be repulsive, since interlayer stacking already satisfy electron count of the sheet. Filled levels of the sheet interact with filled metal bands. The PDOS plot, S5 (Supporting Information) depicts the metal to sheet interaction for δ6*-AA sheet. Thus, BE values on metal templates given in Table 2 suggest that the Cu surface would lead to formation of monolayer sheets only. Formation of the bilayers is less favorable. On Ag surface, interlayer stacking is possible for less stable monolayers. The stable ones lead to decrease in BE upon interlayer stacking. Hence, in experiments after completion of monolayer formation, limited regions are found to form bilayers with structures slightly different from the monolayers.1,2 On the other hand, Au surface would be the most suitable for interlayer stacking of boron sheets. The lower interaction with metal surface would favor formation of bilayer sheets. The possible growth mechanism are studied on metal surfaces by simulating a finite fragment of δ6-AB sheet on Cu surface at 1000K temperature with a time step of 1 fs. The fragment disintegrates to form a single planar structure with hexagonal holes after 8.5 ps. (Parts a−c in Figure 5 show the structural changes for the fragment during simulation). The Ag surface also shows a similar incidence when the finite fragment of δ6-AB sheet is simulated at same temperature (Figure S6, Supporting Information). This shows that after complete formation of single layer, formation of second layer should initiate. Thus, interaction of monolayer with metal surface is important for formation of further layers. Dynamic simulations of corresponding monolayer and δ6-AB sheet are performed at 1000K on Au surface to determine their thermodynamic stabilities. The Figures S7 and S8 (Supporting Information) shows the top and side views of the sheets on Au surface at initial and after 20 ps time scale. During simulations, in-plane bond distances change slightly in both cases. However, the interlayer distances in the δ6-AB sheet do not show much of an increment. The metal templates indeed control the structural preferences of borophene phases; however, the boron source material plays a significant role. The recent synthesis of icosahedral sheet on Cu foil proves this further. In this experiment by Tai et

al., the sheet is obtained by deposition of boron oxide vapors on the Cu surface.13 The instability of icosahedral sheets from boron atom deposition on Cu surface are determined using abinitio dynamic simulations. A single Ih-B12 cluster deposited on this surface is simulated at 1000 K temperatures with a timestep of 1 fs. The cluster disintegrates after 1 ps and ultimately becomes a planar structure as shown in Figure 5, parts d and e. A similar incidence is observed while simulating a unit of three Ih-B12 clusters connected to each other by B−B bonds on the Cu surface (Figure S9, Supporting Information). The cluster disintegrates after 3 ps from the initial time scale. However, the extended Ih-B12 sheet (Figure 5f) is found to be thermodynamically stable on the Cu (111) surface when simulated at same temperature (Figure S10, Supporting Information). Thus, cluster formation and further extension to the sheet is unlikely by boron atom deposition on this surface. However, the extended sheet could form by other means. The growth mechanism of boron nanostructures from boron oxide vapors involves several complex steps, as discussed by Sun et al.39 This certainly vary from the situation when boron atoms are deposited by radiating a solid boron source with laser.1,2 Therefore, structure of borophene phases obtained on Cu surface differ extensively w.r.t. the planar phases obtained on Ag surface.

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CONCLUSIONS The interlayer binding ability of bilayer borophene phases is analyzed by changing the HD from 0 to 1/3. The extent of interlayer B−B bond formation depends upon the geometry of sheets. However, possibility to form interlayer bonds decreases as HD increases. On metal surfaces, bilayer stability depends on the metal to first-layer interaction. Formation of the second layer of borophene using the atom deposition technique would start only after completion of the first monolayer phase and largely depends on interaction between the first layer and the metal surface. The greater the interaction, the lower will be the possibility to form a second layer. Hence, the Au surface is only favorable for bilayer formation due to its lower binding ability with the boron sheet, whereas on the Cu surface, the greater binding ability of the first layer reduces the possibility of second layer formation. The Ag surface has limited possibilities. The organization of boron atoms to Ih-B12 clusters and further to icosahedral sheets is found to be unfavorable on the Cu surface by boron atom deposition. Alternate boron sources are needed to enable the synthesis of icosahedral sheets on Cu. Indeed, the structural preferences of borophenes are controlled by boron sources and metal templates in addition to other factors such as growth temperature and deposition rate of boron atoms.

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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.jpcc.7b12540. Table S1 and S2 giving the lattice mismatch and BE of the boron sheets, respectively, Figures S1−S3 showing the bilayer stacking possibilities, Figure S4 showing the band diagram for α8-AA sheet, Figure S5, showing the PDOS plot of δ6* sheet with and without metal templates, Figures S6−S9 showing molecular dynamic simulations for the finite fragment and extended δ6-AB sheet on Ag and Au surfaces at different time periods, E

DOI: 10.1021/acs.jpcc.7b12540 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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and Figure S10, showing the dynamic simulation of the Ih-B12 sheet on the Cu surface. (PDF)

AUTHOR INFORMATION

Corresponding Author

*(E.D.J.) E-mail: [email protected]. ORCID

Eluvathingal D. Jemmis: 0000-0001-8235-3413 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Supercomputer Education and Research Centre, IISc, for computational facilities, the Council of Scientific and Industrial Research for a Senior Research Fellowship to N.K., and the Department of Science and Technology for a JC Bose fellowship to E.D.J.

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DOI: 10.1021/acs.jpcc.7b12540 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C (37) Tran, R.; Xu, Z.; Radhakrishnan, B.; Winston, D.; Sun, W.; Persson, K. A.; Ong, S. P. Surface Energies of Elemental Crystals. Sci. Data 2016, 3, 160080. (38) Skriver, H. L.; Rosengaard, N. M. Surface energy and work function of elemental metals. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 46, 7157−7168. (39) Sun, X.; Liu, X.; Yin, J.; Yu, J.; Li, Y.; Hang, Y.; Zhou, X.; Yu, M.; Li, J.; Tai, G.; Guo, W. Two-Dimensional Boron Crystals: Structural Stability, Tunable Properties, Fabrications and Applications. Adv. Funct. Mater. 2017, 27, 1603300.

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DOI: 10.1021/acs.jpcc.7b12540 J. Phys. Chem. C XXXX, XXX, XXX−XXX