Spontaneous formation of graphenelike stripes on highindex diamond C(331) surface
 Maojie Xu^{1},
 Yaozhong Zhang^{1},
 Jing Zhang^{1},
 Jiyun Lu^{1},
 Bingjian Qian^{1},
 Dejiong Lu^{1},
 Yafei Zhang^{1}Email author,
 Liang Wang^{2},
 Xiaoshuang Chen^{2} and
 Hidemi Shigekawa^{3}
DOI: 10.1186/1556276X7460
© Xu et al.; licensee Springer. 2012
Received: 3 July 2012
Accepted: 30 July 2012
Published: 16 August 2012
Abstract
We employ firstprinciples density functional theory calculations to study the surface reconstruction, energetic stability, and electronic structure of diamond C(331) surface. Spontaneous formation of graphenelike stripes on the reconstructed surface is found to occur as the surface terrace C atoms transform from sp^{3} to sp^{2} 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 graphiticlike 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.
Keywords
Surface reconstruction Density functional theory Graphene Diamond 68.35.bg 68.47.Fg 68.35.MdBackground
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 shortwavelength optoelectronic devices such as ultraviolet lightemitting 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 highquality 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[8]. Graphiticlike surface reconstructions on stepped C(111) surfaces are predicated by firstprinciples calculations[9]. Surface graphitization of diamond nanoparticles is investigated from an experimental viewpoint[10]. A unique character of diamond growth is the existence of sp^{2}hybridized bonds in the graphiticlike layer of diamond surfaces, in contrast to other group IV element semiconductors (Si and Ge), which do not exhibit energetically favorable sp^{2} bonding configurations. This may account for different surface reconstructions on Si and diamond surfaces[11]. Besides lowindex surfaces, highindex Si surfaces are extensively investigated to unveil their atomic and electronic structures[12, 13], whereas less attention has been paid to the study of highindex diamond surfaces. The graphitelike sp^{2} bonding is expected to give rise to the significant difference between highindex diamond and Si surfaces.
Graphene, a twodimensional atomic crystal with graphitelike sp^{2} bonding, has attracted considerable interests due to its novel physical and chemical properties and its potential applications in nanoelectronics and optoelectronics[14]. Largescale graphenes are grown on metal substrates[15]. Here, we explore the formation of graphenelike stripes on a reconstructed highindex diamond C(331) surface using firstprinciples density functional theory (DFT) calculations. During the structural relaxation of the bulkterminated surface, the terrace C atoms in the first layer delaminate from the second layer, leading to local sp^{3} to sp^{2} rehybridization and the formation of graphenelike stripes on the surface. The driving force for the graphiticlike reconstruction is the presence of highdensity dangling bonds on the surface, which gives rise to the rebonding of toplayer 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 graphiticlike 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].
Methods
The calculations are conducted in the framework of the DFT method by DMol^{3} codes[18]. We use the PerdewBurkeErnzerhof generalized gradient approximation[19]. A double numeric basis set including dpolarization function, all electron treatment, and an 8 × 2 × 1 MonkhorstPack k point mesh for the Brillouin zone sampling[20] are employed to carry out geometry optimization and electronic band structure calculations. Spinunpolarized selfconsistent 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.
Results and discussion
The representative CC bond lengths for the graphiticlike 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 unsaturated dangling bonds at the subsurface positions remain sp^{3}hybridized in character, although they have stretched by almost 34%. The CC bonds are stretched to 1.62 and 1.57 Å for the outmost C atoms attached to the secondlayer C atoms. The severe subsurface rebonding increases the elastic strain, which is energetically unfavorable. The competition between the favorable sp^{2} bonding in the graphitic layer and the unfavorable strain energy leads to the graphiticlike reconstruction of the C(331) surface.
Absolute surface energies ${\mathbf{E}}_{\mathbf{\text{surf}}}^{\mathbf{n}\times \mathbf{m}}$ and ${\mathbf{\gamma}}^{\mathbf{n}\times \mathbf{m}}$ for various orientations and reconstructions
Orientation  Reconstruction  E_{surf} (eV/1 × 1 cell)  γ(J/m^{2}) 

(111)  2 × 1  0.993  2.91 
(1.369)  (4.06)  
Hcovered  −1.903  −5.57  
(−2.760)  (−8.19)  
(110)  1 × 1 relaxed  1.824  3.27 
(3.264)  (5.93)  
Hcovered  −4.971  −8.91  
(−5.496)  (−9.99)  
(331)  1 × 1 graphitic  2.040  2.31 
Hcovered  −5.808  −6.58 
The H adsorption on the graphiticlike reconstructed C(331) surface is found to give rise to the reversion of sp^{2} hybridization back to sp^{3} hybridization. Figure2 shows the calculated atomic structure of the Hcovered C(331) (1 × 1) surface. The toplayer C atoms display sp^{3} bonding configuration. Thus, the H atoms can give rise to the dereconstruction of the graphiticlike C(331) surface.
Conclusions
We carry out firstprinciples DFT calculations to study the spontaneous formation of graphenelike stripes on the reconstructed diamond C(331) surface. The sp^{2}hybridized bonding in the graphitic layer on the surface plays a central role in reducing the energetically unfavorable dangling bonds on the bulkterminated 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 graphenelike stripes directly formed on a semiconductor surface may be used for nanoelectronic and optoelectronic devices.
Authors’ information
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.
Abbreviations
 ASE:

absolute surface energy
 DFT:

density functional theory
 FL:

Fermi level
 LDOS:

local density of electronic states
 PDOS:

partial electronic density of states.
Declarations
Acknowledgments
This work is supported by the National HighTech R&D Program (863 Program) of China under contract no. 2011AA050504, the National Natural Science Foundation of China (grant no. 61006002), the UM/SJTU Collaborative Research Program and the Analytical and Testing Center of SJTU.
Authors’ Affiliations
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