Spontaneous formation of graphene-like stripes on high-index diamond C(331) surface
© Xu et al.; licensee Springer. 2012
Received: 3 July 2012
Accepted: 30 July 2012
Published: 16 August 2012
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.
KeywordsSurface reconstruction Density functional theory Graphene Diamond 68.35.bg 68.47.Fg 68.35.Md
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.
Results and discussion
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.
Absolute surface energies and for various orientations and reconstructions
Esurf (eV/1 × 1 cell)
2 × 1
1 × 1 relaxed
1 × 1 graphitic
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.
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.
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