We employ first-principles density functional theory calculations to study the surface reconstruction, energetic stability, and electronic structure of diamond C(331) surface. Spontaneous formation of graphene-like stripes on the reconstructed surface is found to occur as the surface terrace C atoms transform from sp3 to sp2 hybridization upon structural relaxation. The comparison of the calculated absolute surface energies of C(331), C(111), and C(110) surfaces demonstrates the energetic stability of the graphitic-like C(331) surface. Local density of electronic states analysis reveals the occurrence of localized electronic states near the Fermi level, which may have a significant impact on the surface conductivity.
Diamond holds a variety of extraordinary physical and chemical properties, facilitating its possible applications in novel functional devices[1–7]. As a semiconductor with a wide bandgap of 5.47 eV, it is a promising candidate for short-wavelength optoelectronic devices such as ultraviolet light-emitting diodes. The extreme mechanical hardness of diamond endows it with potential applications in nanomechanical devices. When doped with boron, it was found to display superconductivity around liquid helium temperature. To utilize the qualities of diamond, it is imperative to grow high-quality materials. Chemical vapor deposition is an efficient and versatile technique for the growth of diamond. A large body of experiments and theories are dedicated to understanding the growth process. Graphitic-like surface reconstructions on stepped C(111) surfaces are predicated by first-principles calculations. Surface graphitization of diamond nanoparticles is investigated from an experimental viewpoint. A unique character of diamond growth is the existence of sp2-hybridized bonds in the graphitic-like layer of diamond surfaces, in contrast to other group IV element semiconductors (Si and Ge), which do not exhibit energetically favorable sp2 bonding configurations. This may account for different surface reconstructions on Si and diamond surfaces. Besides low-index surfaces, high-index Si surfaces are extensively investigated to unveil their atomic and electronic structures[12, 13], whereas less attention has been paid to the study of high-index diamond surfaces. The graphite-like sp2 bonding is expected to give rise to the significant difference between high-index diamond and Si surfaces.
Graphene, a two-dimensional atomic crystal with graphite-like sp2 bonding, has attracted considerable interests due to its novel physical and chemical properties and its potential applications in nanoelectronics and optoelectronics. Large-scale graphenes are grown on metal substrates. Here, we explore the formation of graphene-like stripes on a reconstructed high-index diamond C(331) surface using first-principles density functional theory (DFT) calculations. During the structural relaxation of the bulk-terminated surface, the terrace C atoms in the first layer delaminate from the second layer, leading to local sp3 to sp2 rehybridization and the formation of graphene-like stripes on the surface. The driving force for the graphitic-like reconstruction is the presence of high-density dangling bonds on the surface, which gives rise to the rebonding of top-layer atoms. The comparison of the calculated absolute surface energies of C(331), C(111), and C(110) demonstrates the relative stability of the C(331) surface with the graphitic-like reconstruction. Local density of electronic states (LDOS) analysis reveals the occurrence of localized electronic states near the Fermi level (FL), which may play an essential role in determining the surface conductivity[16, 17].
The calculations are conducted in the framework of the DFT method by DMol3 codes. We use the Perdew-Burke-Ernzerhof generalized gradient approximation. A double numeric basis set including d-polarization function, all electron treatment, and an 8 × 2 × 1 Monkhorst-Pack k- point mesh for the Brillouin zone sampling are employed to carry out geometry optimization and electronic band structure calculations. Spin-unpolarized self-consistent field calculations are performed with a convergence criterion of 2.0 × 10−5 hartree (1 hartree = 27.2114 eV) for total energies. The maximum force tolerance is 0.004 hartree Å−1, and the maximum displacement tolerance is 0.005 Å.
The periodically repeated slabs separated by approximately 10 Å of vacuum are used to represent the surface structures. Each slab of C(331) surface is composed of 11 atomic layers with 40 C atoms and 6 H atoms per unit cell. The H atoms are used to passivate the surface C atoms at the bottom of the slabs to make the calculation more efficient. The dashed lines in Figure1a and the dashed box in Figure1b indicate the supercell used for the calculation. Each slab of H-passivated C(331) surface is composed of 12 atomic layers with 40 C atoms and 12 H atoms per unit cell. The dashed lines in Figure2 indicate the supercell used for the calculations.
Results and discussion
Figure1 shows the atomic structure of the graphene-like stripes formed on the reconstructed diamond C(331) surface calculated after the structural relaxation of the bulk-terminated surface. We allow this surface to relax using a steepest descent algorithm. The top-layer C atoms exhibit the sp2 bonding configuration in the graphene-like structure, as shown in Figure1b. Upon structural relaxation, the terrace C atoms (see 4 and 10 C atoms in Figure3) delaminate from the subsurface diamond and form the graphene-like stripes along the direction. The energetically favorable hexagonal rings are found to emerge in the graphitic layer on the reconstructed surface. The driving force for the graphitic-like reconstruction on the surface is the presence of high-density dangling bonds which have unpaired electrons. This situation is similar to the reconstruction of the C(111) surface, where the top-layer C atoms are rearranged to make the dangling bonds become the nearest neighbors and form the π bonding. For the C(331) surface, the delamination of the terrace C atoms can lead to the formation of graphite-like sp2 bonds, thereby reducing the energetically unfavorable dangling bonds.
The representative C-C bond lengths for the graphitic-like reconstructed C(331) surface are shown in Figure3. The distance between the delaminated C atom and the subsurface C atom increases to approximately 2.51 Å, much larger than the bond length of diamond (1.54 Å). The bond lengths for the C atoms in the graphitic structure decrease to 1.44 and 1.46 Å. These values are quite close to the bond length of graphite (1.42 Å), whereas much smaller than that of diamond. The C atoms with the unsatu-rated dangling bonds at the subsurface positions remain sp3-hybridized in character, although they have stretched by almost 34%. The C-C bonds are stretched to 1.62 and 1.57 Å for the outmost C atoms attached to the second-layer C atoms. The severe subsurface rebonding increases the elastic strain, which is energetically unfavorable. The competition between the favorable sp2 bonding in the graphitic layer and the unfavorable strain energy leads to the graphitic-like reconstruction of the C(331) surface.
The energetic stability of the C(331) surface is studied by comparing its absolute surface energy (ASE) with those of low-index diamond C(111) and C(110) surfaces[21–23]. In the centrosymmetric slab used for computing the ASE, the top and bottom surfaces are physically equivalent. After full structural relaxation, the same n × m surface reconstruction is observed to occur on both sides of the slab. Therefore, it allows calculating directly the ASE. For the slab with N atoms at the atomic configuration, the surface energy per 1 × 1 surface cell,, can be calculated from the total energy of the slab subtracted by N times the bulk diamond energy μ per atom. The surface energy is expressed as
Since two equivalent surfaces are involved in the calculations for a slab, a prefactor,, is added in Equation 1. For the n × m surface reconstruction, the nm gives the number of the 1 × 1 surface cell. The surface energy per unit area is as follows:
where A is the area of a 1 × 1 surface cell for a given surface orientation n. For the H-covered C(331) surface, the surface energy per 1 × 1 surface cell is given by
where is the total energy of the slab, NH is the number of H atoms, and μH is the chemical potential of the H atom in the reservoir that is defined in. Table1 collected the surface energies,, and for various orientations and reconstructions. The computed energies for low-index C(111) and C(110) surfaces agree well with the previous investigation. The graphitic-like reconstructed C(331) surface is found to have lower than low-index C(111) and C(110) surfaces, indicating that the C(331) surface is one of the stable crystalline diamond surfaces.
Absolute surface energiesandfor various orientations and reconstructions
Esurf (eV/1 × 1 cell)
2 × 1
1 × 1 relaxed
1 × 1 graphitic
The values in parentheses from are listed for comparison.
The H adsorption on the graphitic-like reconstructed C(331) surface is found to give rise to the reversion of sp2 hybridization back to sp3 hybridization. Figure2 shows the calculated atomic structure of the H-covered C(331) (1 × 1) surface. The top-layer C atoms display sp3 bonding configuration. Thus, the H atoms can give rise to the dereconstruction of the graphitic-like C(331) surface.
Figure4a shows the LDOS of the H-passivated diamond (331) surface. The zero energy corresponds to the FL which is at the position of the top valence band. An energy bandgap of 4.2 eV is obtained from the calculated electronic band structure. Figure4b shows the LDOS of the reconstructed C(331) surface with the graphene-like stripes. The zero energy corresponds to the FL, which lifts up to a position in the bulk bandgap. The peak near the FL in the LDOS curve is attributed to the localized electronic states at the graphitic surface and subsurface regions, which may give rise to the semimetallic or metallic conduction along the surface. Further partial electronic density of states (PDOS) analysis reveals that the localized electronic states near the FL is predominant with the p character for the graphitic-like reconstructed C(331) surface.
We carry out first-principles DFT calculations to study the spontaneous formation of graphene-like stripes on the reconstructed diamond C(331) surface. The sp2-hybridized bonding in the graphitic layer on the surface plays a central role in reducing the energetically unfavorable dangling bonds on the bulk-terminated surface, thereby lowering the surface free energy. A sharp peak is found to occur near the FL in the LDOS curve, which arises from the localized electronic states at the surface and subsurface regions. These states may have a significant impact on the surface conductivity. The graphene-like stripes directly formed on a semiconductor surface may be used for nanoelectronic and optoelectronic devices.
Dr. MJX obtained his Ph.D. from University of Tsukuba, Japan, and is currently working with Prof. YFZ as postdoctoral research fellow in Shanghai Jiao Tong University, China. Mr. YZZ, Ms. JZ, Mr. BJQ, Mr. JYL, and Mr. DJL are currently postgraduate students in Shanghai Jiao Tong University. Dr. YFZ obtained his Ph.D. from Lanzhou University, China, and is currently working as a professor in Shanghai Jiao Tong University. Dr. LW obtained his Ph.D. from Shanghai Institute of Technical Physics, Chinese Academy of Sciences, China, and is working with Prof. YFZ as postdoctoral research fellow. Dr. XSC obtained his Ph.D. from Nanjing University, China, and is currently working as a professor in Shanghai Institute of Technical Physics, Chinese Academy of Sciences, China. Dr. HS obtained his Ph.D. from Tokyo University, Japan, and is currently working as a professor in University of Tsukuba, Japan.
absolute surface energy
density functional theory
local density of electronic states
partial electronic density of states.
This work is supported by the National High-Tech R&D Program (863 Program) of China under contract no. 2011AA050504, the National Natural Science Foundation of China (grant no. 61006002), the U-M/SJTU Collaborative Research Program and the Analytical and Testing Center of SJTU.
Key Laboratory for Thin Film and Microfabrication of the Ministry of Education, Research Institute of Micro/Nano Science and Technology, Shanghai Jiao Tong University
National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences
Institute of Applied Physics, University of Tsukuba
Field JE: The Properties of Natural and Synthetic Diamond. New York: Academic; 1992.
Koide Y, Liao MY, Alvarez J, Imura M, Sueishi K, Yoshifusa F: Schottky photodiode using submicron thick diamond epilayer for flame sensing. Nano-Micro Lett 2009, 1: 30.View Article
Isberg J, Hammersberg J, Johansson E, Wikstroem T, Twitchen DJ, Whitehead AJ, Coe SE, Scarsbrook GA: High carrier mobility in single-crystal plasma-deposited diamond. Science 2002, 297: 1670. 10.1126/science.1074374View Article
Purtov KV, Petunin AI, Burov AE, Puzyr AP, Bondar VS: Nanodiamonds as carriers for address delivery of biologically active substances. Nanoscale Res Lett 2010, 5: 631. 10.1007/s11671-010-9526-0View Article
Liu YL, Sun KW: Protein functionalized nanodiamond arrays. Nanoscale Res Lett 2010, 5: 1045. 10.1007/s11671-010-9600-7View Article
Jiang X, Zhao J, Zhuang C, Wen B, Jiang X: Mechanical and electronic properties of ultrathin nanodiamonds under uniaxial compressions. Diam Relat Mater 2010, 19: 21. 10.1016/j.diamond.2009.10.011View Article
Jiang X, Zhao J, Jiang X: Mechanical and electronic properties of diamond nanowires under tensile strain from first principles. Nanotechnology 2011, 22: 405705. 10.1088/0957-4484/22/40/405705View Article
Butler JE, Mankelevich YA, Cheesman A, Ma J, Ashfold MNR: Understanding the chemical vapor deposition of diamond: recent progress. J Phys Condens Matter 2009, 21: 364201. 10.1088/0953-8984/21/36/364201View Article
Kern G, Hafner J: Ab initio molecular-dynamics studies of the graphitization of flat and stepped diamond (111) surfaces. Phys Rev B 1998, 58: 13167. 10.1103/PhysRevB.58.13167View Article
Chen J, Deng SZ, Chen J, Yu ZX, Xu NS: Graphitization of nanodiamond powder annealed in argon ambient. Appl Phys Lett 1999, 74: 3651. 10.1063/1.123211View Article
Bechstedt F, Stekolnikov AA, Furthmüller J, Käckell P: Origin of the different reconstructions of diamond, Si, and Ge (111) surfaces. Phys Rev Lett 2001, 87: 16103.View Article
Chadi DJ: Theoretical study of the atomic structure of silicon (211), (311), and (331) surfaces. Phys Rev B 1984, 29: 785. 10.1103/PhysRevB.29.785View Article
Baski A, Erwin SC, Whitman LJ: The structure of silicon surfaces from (001) to (111). Surf Sci 1997, 392: 69. 10.1016/S0039-6028(97)00499-8View Article
Castro Neto AH, Guinea F, Peres NMR, Novoselov KS, Geim AK: The electronic properties of graphene. Rev Mod Phys 2009, 81: 109. 10.1103/RevModPhys.81.109View Article
Li XS, Cai WW, An JH, Kim S, Nah J, Yang DX, Piner R, Velamakanni A, Jung I, Tutuc E, Banerjee SK, Colombo L, Ruoff RS: Large-area synthesis of high-quality and uniform graphene films on copper foils. Science 2009, 324: 1312. 10.1126/science.1171245View Article
Balaban T, Klein DJ, Folden CA: Diamond-graphite hybrids. Chem Phys Lett 1994, 217: 266. 10.1016/0009-2614(93)E1379-UView Article
de Vita A, Galli G, Canning A, Car R: Graphitization of diamond (111) studied by first principles molecular dynamics. Appl Surf Sci 1996, 104: 297.View Article
Delley B: From molecules to solids with the DMol3 approach. J Chem Phys 2000, 113: 7756. 10.1063/1.1316015View Article
Perdew JP, Burke K, Ernzerhof M: Generalized gradient approximation made simple. Phys Rev Lett 1996, 77: 3865. 10.1103/PhysRevLett.77.3865View Article
Monkhorst HJ, Pack JD: Special points for Brillouin-zone integrations. Phys Rev B 1976, 13: 5188. 10.1103/PhysRevB.13.5188View Article
Stekolnikov A, Furthmüller J, Bechstedt F: Absolute surface energies of group-IV semiconductors: dependence on orientation and reconstruction. Phys Rev B 2002, 65: 115318.View Article
Marsili M, Pulci O, Bechstedt F, Del Sole R: Electronic structure of the C(111) surface: solution by self-consistent many-body calculations. Phys Rev B 2005, 72: 115415.View Article
Silva F, Achard J, Bonnin X, Michau A, Tallaire A, Brinza O, Gicquel A: 3D crystal growth model for understanding the role of plasma pre‐treatment on CVD diamond crystal shape. Phys Stat Sol (a) 2006, 203: 3049. 10.1002/pssa.200671101View Article
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