To investigate the effects of surface chemisorbed hydrogen atoms and hydrogen atoms in the subsurface region of diamond on surface conductivity, models of hydrogen atoms chemisorbed on diamond with (100) orientation and various concentrations of hydrogen atoms in the subsurface layer of the diamond were built. By using the first-principles method based on density functional theory, the equilibrium geometries and densities of states of the models were studied. The results showed that the surface chemisorbed hydrogen alone could not induce high surface conductivity. In addition, isolated hydrogen atoms in the subsurface layer of the diamond prefer to exist at the bond centre site of the C-C bond. However, such a structure would induce deep localized states, which could not improve the surface conductivity. When the hydrogen concentration increases, the C-H-C-H structure and C-3Hbc-C structure in the subsurface region are more stable than other configurations. The former is not beneficial to the increase of the surface conductivity. However, the latter would induce strong surface states near the Fermi level, which would give rise to high surface conductivity. Thus, a high concentration of subsurface hydrogen atoms in diamond would make significant contributions to surface conductivity.

Due to its unique physical and chemical properties, diamond film has significant potential to be applied in MEMS/NEMS.1 Previous studies showed that a diamond surface would become hydrogen-terminated after hydrogen plasma treatment. It is interesting that hydrogen-terminated diamond film exhibits a high surface conductivity, while the bulk remains insulating.2,3 Based on the particular performances, several sensors made of hydrogenated diamond films, such as field emission cathode devices, field effect transistors, and so on, have been developed in recent years.4,5

Concerning the surface conducting mechanism of the hydrogen-terminated diamond films, Kawarada and co-workers attribute it to the surface chemisorbed hydrogen atoms, which would induce surface states in the band gap of the diamond film.6 However, some studies cannot find the surface states in the band gap of the diamond films after being chemisorbed by hydrogen atoms.7,8 Actually, during hydrogen plasma treatment, hydrogen atoms would not only cover the surface, but also diffuse into the subsurface region of the diamond films. Subsurface hydrogen atoms may make significant contributions to the high surface conductivity, which is supported by some reports.9,10 Thus, up to now, the effects of the hydrogen atoms on the surface conductivity of diamond films are far from clear, and the conducting mechanism of hydrogen-terminated diamond film remains controversial.

In this work, models of hydrogen atoms chemisorbed on diamond with (100) orientation and various concentrations of hydrogen atoms in the subsurface layer of the diamond were built. By using the first-principles method based on density functional theory, the equilibrium geometries and electronic structures were obtained for the various models. The results showed that the surface chemisorbed hydrogen atoms alone have no effects on the surface conductivity of the diamond films. However, a high concentration of subsurface hydrogen atoms would induce surface states near to the Fermi level, which may contribute to high surface conductivity.

All the calculations in this work were carried out by using CASTEP codes based on density functional theory. The electron–ion interaction was described by ultrasoft pseudopotentials, and general gradient approximation (GGA) by Perdew-Wang (PW91) was employed for the exchange-correlation potentials. The optimization of the atomic coordinates continued until the total energy converged within 10−6 eV/atom. The iterative calculation of the Kohn-Sham eigenstates was terminated when the eigenvalues converged within 10−6 eV/atom. The errors of the equilibrium geometries calculated with the selected parameters were lower than 0.2% compared with the experimental values.

Models of the hydrogen chemisorbed diamond surface and hydrogen in the diamond subsurface region were built. For the former, monolayer hydrogen atoms adsorbed on a C(100) surface with 2 × 1 reconstruction were adopted for its most stable configuration, which is reported elsewhere.6–8 The diamond surfaces were modelled with a finite slab consisting of ten layers, each having eight C atoms. At the top and bottom of the slab, the C atom layers were covered with one layer of hydrogen atoms. To avoid repulsive interactions, a vacuum layer with a thickness of 15 Å was adopted. All the atoms were allowed to relax freely during calculations. For the latter, supercell models composed of 64 carbon atoms and several hydrogen atoms were adopted to calculate the equilibrium geometries and electronic structures of the subsurface hydrogen in diamond. For the slice model, the wave functions were expanded into plane waves up to a cutoff energy of 280 eV. Concerning the Brillouin-zone integrations, a 4 × 4 × 1 grid of Monkhorst-Pack k-point sampling was used. For the supercell model, the cutoff energy was 320 eV and Monkhorst-Pack k-point sampling was generated with a 4 × 4 × 4 grid.

Figures 1(a) and 1(b) show the equilibrium geometries and total density of states corresponding to the monohydrogenated C(100) 2 × 1 reconstruction surface. They indicated that after hydrogenation, the surface lattice parameters change significantly compared with those of the clean C(100) surface and bulk diamond.8 The hydrogen atoms bond with the first layer of C atoms with a bond length of 1.10 Å. Surface C-C π bonding breaks after the coverage of the hydrogen atoms. Only C-C σ bonding with a bond length of 1.60 Å is in existence. The C-C bond lengths in the next several layers are also lengthened or shortened to varying degrees compared with that of bulk diamond (around 1.54 Å). In addition, the distances between the neighbouring layers relax sharply, as revealed in Fig. 1(a). The calculated geometries for the monohydrogenated C(100) surface in our work agree well with the previous results.7 

FIG. 1.

Equilibrium geometries (a) and density of states (b) corresponding to the monohydrogenated C (100) 2 × 1 reconstruction surface.

FIG. 1.

Equilibrium geometries (a) and density of states (b) corresponding to the monohydrogenated C (100) 2 × 1 reconstruction surface.

Close modal

Concerning the total density of states for the monohydrogenated C(100) surface, it is found in Fig. 1(b) that the band gap is wide with no empty states. Therefore, it is hard for electrons to jump from the valence band into the conduction band. The result can be attributed to its surface equilibrium geometry. After hydrogen atoms cover the dangling bonds of the clean diamond surface, the C-C π bonding breaks and only C-C σ bonding exists. Then, the surface states which are induced by C-C π bonding in the band gap of the clean C(100) surface disappear.11 Thus, the surface-adsorbed hydrogen atoms alone make no contribution to the high surface conductivity of the diamond. Our results show good consistency with the reports from other groups7,12 but contradict the experimental results in the literature.6 This is probably because the experiments reported in the literature6 were done under an air atmosphere, which may induce shallow acceptors to arise from the interactions between the C-H bond and surface radical adsorbates in air.13,14

With regard to the diffusion of hydrogen atoms into the subsurface region during plasma treatment, various possible existing sites of the hydrogen atoms in the diamond were proposed in the literature.15 Among these sites, the C-C bond centre site (C-Hbc-C) is demonstrated to be the most stable. Thus, to investigate the effect of low-concentration hydrogen in the subsurface region of the diamond on its surface conductivity, one isolated hydrogen atom at the bond centre of the C-C bond in a supercell model with 64 carbon atoms is adopted. Figures 2(a) and 2(b) show the equilibrium geometries and total density of states corresponding to the 64-carbon cubic cell with one hydrogen atom at the C-C bond centre site. Figure 2(a) shows that the C-C bond length is enlarged to 2.26 Å as the hydrogen atom settles at the centre site of the C-C bond. Next to the C-Hbc-C structure, the C-C bond length decreases to 1.48 Å, which is around 3.9% shorter than that of bulk diamond. The bond angles also change significantly. The angles of C-C-H and C-C-C become 99.23° and 117.45°, respectively, 20.9 and 2.1% smaller than those of bulk diamond. In the case of the total density of states shown in Fig. 2(b), a strong localized state appears near the Fermi level (at 0 eV). According to the electron density distribution analysis (shown in the inset in Fig. 2(b)), the states near the Fermi level originate from the strong bonding between the H 1s orbital and the neighbouring two C 2p orbital. For the C-H bond length of just 1.13 Å, strong interactions between the hydrogen atom and neighbouring carbon atoms are possible. Although the strong states appear in the middle of the band gap, they may not be beneficial to the improvement of the surface conductivity for its deep level.

FIG. 2.

Equilibrium geometries and density of states corresponding to the diamond with C-Hbc-C structure. (a) Equilibrium geometries. (b) Density of states.

FIG. 2.

Equilibrium geometries and density of states corresponding to the diamond with C-Hbc-C structure. (a) Equilibrium geometries. (b) Density of states.

Close modal

As a matter of fact, the concentration of the hydrogen atoms in the subsurface region of the diamond is very high. In addition, the hydrogen atoms in the subsurface region prefer to accumulate together.16 Therefore, studying one isolated hydrogen atom in the subsurface region is insufficient for investigating the effects of the subsurface hydrogen. Figures 3(a) and 3(b) show the equilibrium geometries and density of states corresponding to the diamond with C-Hbc-C-Hab structure. The C-Hbc-C-Hab structure is a configuration in which two hydrogen atoms are located at the bond-centred site and the antibonding site of the C-C bonding, respectively. According to the calculated total energies of the models, the total energy of the C-Hbc-C-Hab structure is 7.7 eV lower than that of the C-2Hbc-C structure, in which two hydrogen atoms are both located at the bond-centred sites of two neighbouring C-C bonds. This result is in line with the previous report.15 

FIG. 3.

Equilibrium geometries and density of states corresponding to the diamond with C-Hbc-C-Hab structure. (a) Equilibrium geometries. (b) Density of states.

FIG. 3.

Equilibrium geometries and density of states corresponding to the diamond with C-Hbc-C-Hab structure. (a) Equilibrium geometries. (b) Density of states.

Close modal

Figure 3(a) shows that the C-C bond length of C-Hbc-C-Hab structure is similar to that corresponding to the C-Hbc-C structure mentioned above. However, due to the effects of the hydrogen atom at the antibonding site, the C-H bond length is not the same for the C-Hbc-C-Hab structure. The C-H bond lengths are 1.02, 1.34, and 1.34 Å, respectively. Meanwhile, the bond lengths of C-C bonding close to the C-Hbc-C-Hab structure and the bond angles also change dramatically. Different from that of the C-Hbc-C structure, the total density of states corresponding to the carbon supercell with C-Hbc-C-Hab structure exhibits a wide and clean band gap. It can be noted that the unoccupied state near the edge of the valence band may arise from interactions between the C 2p orbital and H 1s orbital, as revealed by electron density distributions shown in the inset of Fig. 3(b). For the short bond length of the C1-H1 bond, the bonding of the C1 2p orbital and the H1 1s orbital is much stronger than that of the C2 2p orbital and the H2 1s orbital. However, it seemed that the C2 and H1 atoms do not bond with each other obviously, because no evident overlap occurs between the C2 2p orbital and the H1 1s orbital. Thus, the H2 atom at the antibonding site really breaks the C-C bonding, and two C-H structures form in the subsurface layer. Considering the wide and clean band gap, it is hard for electrons to be transferred from the valence band to the conduction band. Therefore, the subsurface hydrogen with C-Hbc-C-Hab structure cannot induce high surface conductivity of the diamond.

Three possible configurations were investigated to evaluate the most stable structure when the number of the hydrogen atoms in the model increases to three. They are C-3Hbc-C structure, C-2Hbc-C-Hab structure, and C-Hbc-C-2Hab structure. In the C-3Hbc-C structure, three hydrogen atoms are all located at C-C bond-centre sites. In the C-2Hbc-C-Hab structure, two hydrogen atoms are located at C-C bond-centre sites and one hydrogen atom is located at the antibonding site. In the C-Hbc-C-2Hab structure, one hydrogen atom is located at the C-C bond-centre site and two hydrogen atoms are located at antibonding sites. According to the total energy of the three configurations, the C-3Hbc-C structure is the most stable with the lowest total energy, 9.8 and 10.2 eV lower than those of the C-2Hbc-C-Hab and C-Hbc-C-2Hab structures, respectively. Thus, the C-3Hbc-C structure is adopted to investigate the effects of a high concentration of hydrogen atoms on its surface conductivity.

Figures 4(a) and 4(b) are the equilibrium geometries and total density of states corresponding to the diamond with C-3Hbc-C structure. They show that when three hydrogen atoms are all located at C-C bond-centre sites, the C-C bonds bend inwards. This is caused by the interactions between the three hydrogen atoms. Then, the C-H bond lengths become 1.08 and 1.15 Å, respectively. The bond angles of H-C-H decrease to 82.64°, which is much smaller than the structure without hydrogen atoms. The other bond lengths and angles neighbouring the C-3Hbc-C structure also change significantly due to the existence of the hydrogen atom defects. The total density of states in Fig. 4(b) should be noted; it is interesting that two obvious peaks appear in the band gap near to the Fermi level. The peak below the Fermi level at around −0.8 eV is obviously an occupied state. It arises from the bonding states between the C 2p orbital and the H 1s orbital, as revealed by the electron density distribution in Fig 5(a). The second peak is located at around 0.3eV, a little above the Fermi level. It is an unoccupied state, which mainly originates from antibonding between the C 2p orbital and the H 1s orbital shown in Fig. 5(b). The strong states near the Fermi level shrink the band gap of the diamond and may act as shallow acceptors or donors, which would make remarkable contributions to the high surface conductivity of the hydrogenated diamond films.

FIG. 4.

Equilibrium geometries and density of states corresponding to the diamond with C-3Hbc-C structure. (a) Equilibrium geometries. (b) Density of states.

FIG. 4.

Equilibrium geometries and density of states corresponding to the diamond with C-3Hbc-C structure. (a) Equilibrium geometries. (b) Density of states.

Close modal
FIG. 5.

Electron density distributions corresponding to the states near the Fermi level of C-3Hbc-C structure. (a) Electron density distribution at -0.8 eV. (b) Electron density distribution at 0.3 eV.

FIG. 5.

Electron density distributions corresponding to the states near the Fermi level of C-3Hbc-C structure. (a) Electron density distribution at -0.8 eV. (b) Electron density distribution at 0.3 eV.

Close modal

Although it is difficult to induce surface high conductivity by isolated hydrogen defects in diamond, the interactions between the accumulated hydrogen atoms or between the hydrogen atoms and other defects would increase the possibility of surface conductivity. In our work, when the hydrogen was isolated in the diamond, it could only induce a deep localized level, which had little benefit for high surface conductivity. Two hydrogen atoms in the subsurface also could not increase the surface conductivity of the diamond. However, when the number of hydrogen atoms increased to three, the strong bonding between the C atoms and H atoms could induce surface states, which enhanced the surface conductivity significantly.

As mentioned above, strong interactions exist between the surface C and H atoms and subsurface C and H atoms, simultaneously. However, the combined effect from the surface and subsurface hydrogen atoms can be ignored because of two factors. One is that the intensive overlaps of electron clouds between the C-H bonding on the surface and that in the subsurface layer inevitably lead to weak interactions between surface C-H structures and various subsurface C-H structures. The other is that the distances between the surface C-H bonding and subsurface C-H bonding are too large to induce a strong combined effect.

  1. When hydrogen atoms are adsorbed on the clean diamond surface, the C-C π bonding breaks and then only C-C σ bonding exists. The surface states induced by C-C π bonding in the band gap of the clean C(100) 2 × 1 reconstruction surface disappear. The surface-adsorbed hydrogen atoms make no contribution to the high surface conductivity of the diamond.

  2. A low concentration of hydrogen atoms in the subsurface region would induce localized deep levels or even keep the wide and clean band gap of the diamond. However, it could not induce high surface conductivity.

  3. High concentrations of hydrogen atoms in the subsurface region would induce unoccupied surface states and occupied surface states, which make remarkable contributions to high surface conductivity.

This work was supported by the National Nature Science Foundation of China under Grant No. 51075004 and the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions.

1.
M.D.
Drory
and
J.W.
Hutchinson
,
Science
263
,
1753
(
1994
).
2.
M.I.
Landstrass
and
K.V.
Ravi
,
Appl. Phys. Lett.
55
,
1391
(
1989
).
3.
F.B.
Liu
,
J.D.
Wang
,
B.
Liu
,
X.M.
Li
, and
D.R.
Chen
,
Diamond Relat. Mater
16
,
454
(
2007
).
4.
B.
Rezek
,
D.
Shin
,
H.
Watanabe
, and
C.E.
Nebel
,
Sensors and Actuators B: Chemical
122
,
596
(
2007
).
5.
C.
Schreyvogel
,
M.
Wolfer
,
H.
Kato
,
M.
Schreck
, and
C. E.
Nebel
,
Sci. Rep.
4
,
3634
(
2014
).
6.
H.
Kawarada
,
H.
Sasaki
, and
A.
Sato
,
Phys. Rev. B.
52
,
11351
(
1995
).
7.
J.
Furthmüller
,
J.
Hafner
, and
G.
Kresse
,
Phys. Rev. B.
53
,
7334
(
1996
).
8.
F. B.
Liu
,
J. D.
Wang
,
D. R.
Chen
,
M.
Zhao
, and
G. P.
He
,
Acta Phys. Sin.
59
,
6556
(
2010
).
9.
K.
Hayashi
,
S.
Yamanaka
, and
H.
Watanabe
,
J. Appl. Phys.
81
,
744
(
1997
).
10.
A.
Hoffman
and
R.
Akhvlediani
,
Diam. Relat. Mater.
14
,
646
(
2005
).
11.
J. D.
Wang
,
F. B.
Liu
,
H. S.
Chen
, and
D. R.
Chen
,
Mater. Phys. Chem.
115
,
590
(
2009
).
12.
K.
Bobrov
,
A.
Mayne
,
G.
Comtet
,
G.
Dujardin
,
L.
Hellner
, and
A.
Hoffman
,
Phys. Rev. B.
68
,
195416-1
(
2003
).
13.
F.
Maier
,
M.
Riedel
,
B.
Mantel
,
J.
Ristein
, and
L.
Ley
,
Phys. Rev. Lett.
85
,
3472
(
2000
).
14.
C. E.
Nebel
,
B.
Rezek
,
D.
Shin
, and
H.
Watanabe
,
J. Appl. Phys.
99
,
033711-1
(
2006
).
15.
J. P.
Goss
,
R.
Jones
,
M. I.
Heggie
,
C. P.
Ewels
,
P. R.
Briddon
, and
S.
Öberg
,
Phys. Rev. B.
65
,
115207-1
(
2002
).
16.
J.
Chevallier
,
D.
Ballutaud
,
B.
Theys
,
F.
Jomard
,
A.
Deneuville
,
E.
Gheeraert
, and
F.
Pruvost
,
Phys. Status Solidi. A
174
,
73
(
1999
).