Xu et al. Nanoscale Research Letters 2012, 7:460
http://www.nanoscalereslett.com/content/7/1/460

NANO EXPRESS

Open Access

Spontaneous formation of graphene-like stripes
on high-index diamond C(331) surface
Maojie Xu1, Yaozhong Zhang1, Jing Zhang1, Jiyun Lu1, Bingjian Qian1, Dejiong Lu1, Yafei Zhang1*, Liang Wang2,
Xiaoshuang Chen2 and Hidemi Shigekawa3

Abstract
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 thereconstructed 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.
Keywords: Surface reconstruction, Density functional theory, Graphene, Diamond
PACS: 68.35.bg, 68.47.Fg, 68.35.Md

Background
Diamond holds a variety of extraordinary physical andchemical 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 withboron, 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 versatiletechnique for the growth of diamond. A large body ofexperiments and theories are dedicated to understanding
the growth process [8]. Graphitic-like surface reconstructions on stepped C(111) surfaces are predicated byfirst-principles calculations [9]. Surface graphitization of
diamond nanoparticles is investigated from an experimental viewpoint [10]. A unique character of diamond
growth is the existence of sp2-hybridized bonds in the* Correspondence: yfzhang@sjtu.edu.cn
1
Key Laboratory for Thin Film and Microfabrication of the Ministry of
Education, Research Institute of Micro/Nano Science and Technology,
Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China
Full list of author information is available at the end of the article

graphitic-like layer of diamond surfaces, in contrast toother 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 [11]. 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 thestudy of high-index diamond surfaces. The graphite-likesp2 bonding is expected to give rise to the significant difference between high-index diamond and Si surfaces.
Graphene, a two-dimensional atomic crystal withgraphite-like sp2 bonding, has attracted considerable
interests due to its novel physical and chemical properties and its potential applications in nanoelectronics andoptoelectronics [14]. Large-scale graphenes are grown
on metal substrates [15]. Here, we explore the formationof 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 thesecond layer, leading to local sp3 to sp2 rehybridizationand the formation of graphene-like stripes on the surface. The driving force for the graphitic-like© 2012 Xu et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons
Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction
in any medium, provided the original work is properly cited.

Xu et al. Nanoscale Research Letters 2012, 7:460
http://www.nanoscalereslett.com/content/7/1/460

reconstruction is the presence of high-density dangling
bonds on the surface, which gives rise to the rebondingof 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 ofelectronic states (LDOS) analysis reveals the occurrenceof 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 DMol3 codes [18]. We use the PerdewBurke-Ernzerhof generalized gradient approximation[19]. 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 [20] 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 perunit 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 Figure 1a andthe dashed box in Figure 1b 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
Figure 2 indicate the supercell used for the calculations.
Results and discussion
Figure 1 shows the atomic structure of the graphene-like
stripes formed on the reconstructed diamond C(331)surface calculated after the structural relaxation of thebulk-terminated surface. We allow this surface to relax
using a steepest descent algorithm. The top-layer C
atoms exhibit the sp2 bonding configuration in thegraphene-like structure, as shown in Figure 1b. Upon
structural relaxation, the terrace C atoms (see 4 and 10
C atoms in Figure 3) delaminate from the subsurface
diamond and form the graphene-like stripes along the½0
11 direction. The energetically favorable hexagonalrings are found to emerge in the graphitic layer on thereconstructed surface. The driving force for thegraphitic-like reconstruction on the surface is the

Page 2 of 5(a)[2 1 1 ][111 ](b)[0 1 1]Figure 1 Calculated atomic structure of diamond C(331) surface
with graphene-like stripes. (a) The dashed lines indicate thesupercell viewed from the ½011 direction. The large circles denote
the C atoms, and the small circles denote the H atoms. (b) The
dashed box indicates the supercell viewed from the [331] direction,and the bottom is viewed from the ½011 direction. The large circles
denote the C atoms of the graphitic layer, and the smaller circles
indicate the sp3-bonded C atoms in the outmost surface. The other
C and H atoms are represented by the smallest circles.

Xu et al. Nanoscale Research Letters 2012, 7:460
http://www.nanoscalereslett.com/content/7/1/460

Figure 2 Calculated atomic structure of H-passivated C(331)(1 × 1) surfaces. The dashed lines indicate the supercell viewed
from the ½011 direction. The large circles denote the C atoms, andthe small circles indicate the H atoms.

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[21]. For the C(331) surface, the delamination of the terrace C atoms can lead to the formation of graphite-likesp2 bonds, thereby reducing the energetically unfavorable dangling bonds.
The representative C-C bond lengths for thegraphitic-like reconstructed C(331) surface are shownin Figure 3. 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 andPage 3 of 5

1.46 Å. These values are quite close to the bondlength 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 sp3-hybridized in character, although they havestretched 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 thegraphitic-like reconstruction of the C(331) surface.
The energetic stability of the C(331) surface is studied
by comparing its absolute surface energy (ASE) withthose 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 physicallyequivalent. After full structural relaxation, the samen × m surface reconstruction is observed to occur onboth sides of the slab. Therefore, it allows calculating
directly the ASE. For the slab with N atoms at theatomic configuration fRi g , the surface energy per 1 × 1nm
surface cell, Esurf, can be calculated from the total energy Etot ðN; fRi gÞ of the slab subtracted by N times thebulk diamond energy μ per atom. The surface energy isexpressed as
nm
Esurf
¼

1
fEtot ðN; fRi gÞ  Nμg:
2nm

ð1Þ

Since two equivalent surfaces are involved in the calculations for a slab, a prefactor,12, is added in Equation 1.

Figure 3 Representative structural parameters of C(331) surface with the graphene-like stripes viewed from the [0 1̄1] direction.
Interatomic distances are given in Ångström. The large circles denote the C atoms, and the small circles denote the H atoms.

Xu et al. Nanoscale Research Letters 2012, 7:460
http://www.nanoscalereslett.com/content/7/1/460

Page 4 of 5nmTable 1 Absolute surface energies Enmforsurf and γ
various orientations and reconstructions

Orientation

Reconstruction

Esurf (eV/1 × 1 cell)

γ (J/m2)

2×1

0.993

2.91

(1.369)(4.06)−1.903

−5.57

(111)

H-covered

(110)

(331)

(−2.760)(−8.19)1 × 1 relaxed

1.824

3.27

(3.264)(5.93)

H-covered−4.971−8.91(−5.496)(−9.99)1 × 1 graphitic

2.040

2.31

H-covered−5.808−6.58

The values in parentheses from [21] are listed for comparison.

For the n × m surface reconstruction, the nm gives thenumber of the 1 × 1 surface cell. The surface energy perunit area is as follows:

γ nm ¼

nm
Esurf
;
A

500

(a)

ð2Þ

s
p
Sum

400

DOS (arb. units)

300
200
100
0

-20 -15500 (b)
400

-10

-5

0

5

10

300
200
100
0

-20

-15

-10

-5

0

5

Energy (eV)Figure 4 LDOS and PDOS of (a) H-passivated and (b) graphiticlike reconstructed C(331) surfaces. The zero energy corresponds
to the FL. The peak near the FL in the LDOS curve of (b) is
associated with the localized electronic states at the surface andsubsurface regions, which may have a significant impact on thesurface conductivity.

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
1
H¼ fEtot ðN; NH ; fRi gÞ  Nμ  NH μH g;
Esurf
2

ð3Þ

where Etot ðN; NH ; fRi gÞ 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 definednmin [21]. Table 1 collected the surface energies Esurf,nmH, and Esurf for various orientations and reconstrucγ
tions. The computed energies for low-index C(111) andC(110) surfaces agree well with the previous investigation [21]. The graphitic-like reconstructed C(331) surface is found to have lower γ nm than low-index C(111)and C(110) surfaces, indicating that the C(331) surface is
one of the stable crystalline diamond surfaces.
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. Figure 2 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.
Figure 4a 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. Figure 4b shows the LDOS of
the reconstructed C(331) surface with the graphene-like
stripes. The zero energy corresponds to the FL, whichlifts 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 predominantwith the p character for the graphitic-like reconstructedC(331) surface.

Conclusions
We carry out first-principles DFT calculations to study the
spontaneous formation of graphene-like stripes on thereconstructed 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 thelocalized electronic states at the surface and subsurface
regions. These states may have a significant impact on thesurface conductivity. The graphene-like stripes directly

Xu et al. Nanoscale Research Letters 2012, 7:460
http://www.nanoscalereslett.com/content/7/1/460

formed on a semiconductor surface may be used fornanoelectronic and optoelectronic devices.
Abbreviations
ASE: absolute surface energy; DFT: density functional theory; FL: Fermi level;
LDOS: local density of electronic states; PDOS: partial electronic density ofstates.

Page 5 of 5

8.

9.

10.
11.

Competing interests
The authors declare that they have no competing interests.
12.
Authors’ contributions
MJX did the calculations and wrote the manuscript. YFZ conceived andsuggested the calculations. YZZ, JZ, BJQ, JYL, DJL, LW, XSC, and HS discussed
about the calculations and revised the final manuscript. All authors read andapproved the final manuscript.

13.
14.
15.

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 iscurrently working as a professor in University of Tsukuba, Japan.

16.
17.
18.
19.
20.
21.

Acknowledgments
This work is supported by the National High-Tech R&D Program (863Program) of China under contract no. 2011AA050504, the National Natural
Science Foundation of China (grant no. 61006002), the U-M/SJTUCollaborative Research Program and the Analytical and Testing Center of
SJTU.
Author details
1
Key Laboratory for Thin Film and Microfabrication of the Ministry of
Education, Research Institute of Micro/Nano Science and Technology,
Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China.
2
National Laboratory for Infrared Physics, Shanghai Institute of TechnicalPhysics, Chinese Academy of Sciences, Shanghai 200083, People's Republicof China. 3Institute of Applied Physics, University of Tsukuba, Tsukuba
305-8573, Japan.

22.

23.

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.
Kern G, Hafner J: Ab initio molecular-dynamics studies of thegraphitization of flat and stepped diamond (111) surfaces. Phys Rev B
1998, 58:13167.
Chen J, Deng SZ, Chen J, Yu ZX, Xu NS: Graphitization of nanodiamondpowder annealed in argon ambient. Appl Phys Lett 1999, 74:3651.
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.
Chadi DJ: Theoretical study of the atomic structure of silicon (211), (311),
and (331) surfaces. Phys Rev B 1984, 29:785.
Baski A, Erwin SC, Whitman LJ: The structure of silicon surfaces from (001)to (111). Surf Sci 1997, 392:69.
Castro Neto AH, Guinea F, Peres NMR, Novoselov KS, Geim AK: The
electronic properties of graphene. Rev Mod Phys 2009, 81:109.
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 highquality and uniform graphene films on copper foils. Science 2009,
324:1312.
Balaban T, Klein DJ, Folden CA: Diamond-graphite hybrids. Chem Phys Lett
1994, 217:266.
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.
Delley B: From molecules to solids with the DMol3 approach. J Chem Phys
2000, 113:7756.
Perdew JP, Burke K, Ernzerhof M: Generalized gradient approximation
made simple. Phys Rev Lett 1996, 77:3865.
Monkhorst HJ, Pack JD: Special points for Brillouin-zone integrations. Phys
Rev B 1976, 13:5188.
Stekolnikov A, Furthmüller J, Bechstedt F: Absolute surface energies ofgroup-IV semiconductors: dependence on orientation andreconstruction. Phys Rev B 2002, 65:115318.
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.
Silva F, Achard J, Bonnin X, Michau A, Tallaire A, Brinza O, Gicquel A: 3D
crystal growth model for understanding the role of plasma pretreatment on CVD diamond crystal shape. Phys Stat Sol (a) 2006,
203:3049.

doi:10.1186/1556-276X-7-460
Cite this article as: Xu et al.: Spontaneous formation of graphene-like
stripes on high-index diamond C(331) surface. Nanoscale Research Letters
2012 7:460.

Received: 3 July 2012 Accepted: 30 July 2012
Published: 16 August 2012
References
1. Field JE: The Properties of Natural and Synthetic Diamond. New York:
Academic; 1992.
2. 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.
3. Isberg J, Hammersberg J, Johansson E, Wikstroem T, Twitchen DJ,
Whitehead AJ, Coe SE, Scarsbrook GA: High carrier mobility in singlecrystal plasma-deposited diamond. Science 2002, 297:1670.
4. 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.
5. Liu YL, Sun KW: Protein functionalized nanodiamond arrays. Nanoscale Res
Lett 2010, 5:1045.
6. 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.
7. Jiang X, Zhao J, Jiang X: Mechanical and electronic properties of diamond
nanowires under tensile strain from first principles. Nanotechnology 2011,
22:405705.

Submit your manuscript to ajournal and beneﬁt from:
7 Convenient online submission
7 Rigorous peer review
7 Immediate publication on acceptance
7 Open access: articles freely available online
7 High visibility within the ﬁeld
7 Retaining the copyright to your article

Submit your next manuscript at 7 springeropen.com