Density functional theory study of substitutional oxygen in diamond
A few studies have been recently presented for the existence of oxygen in diamond, for example, the N3 EPR centres have been theoretically and experimentally assigned the model made up from complex of substitutional nitrogen and substitutional oxygen as nearest neighbours. We present ab initio cal...
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irk-123456789-1562022019-06-19T01:31:35Z Density functional theory study of substitutional oxygen in diamond Etmimi, K.M. Briddon, P.R. Abutruma, A.M. Sghayer, A. Farhat, S.S. A few studies have been recently presented for the existence of oxygen in diamond, for example, the N3 EPR centres have been theoretically and experimentally assigned the model made up from complex of substitutional nitrogen and substitutional oxygen as nearest neighbours. We present ab initio calculations of substitutional oxygen in diamond in terms of stability, electronic structures, geometry and hyperfine interaction and show that substitutional oxygen with C₂v , S = 1 is the ground state configuration. We find that oxygen produces either a donor or acceptor level depending on the position of the Fermi level. Останнiм часом представлено декiлька дослiджень стосовно наявностi кисню в алмазi, наприклад теоретично i експериментально призначена модель для N3 EPR створена з комплексу замiщувального азоту та замiщувального кисню як найближчих сусiдiв. У цiй статтi представлено ab initio обчислення замiщувального кисню в алмазi з огляду на стiйкiсть, електроннi структури, геометрiю та надтонку взаємодiю, а також показано, що замiщувальний кисень з C₂v , S = 1 є конфiгурацiєю основного стану. Встановлено, що кисень продукує або ж донорний, або акцепторний рiвень в залежностi вiд положення Фермi рiвня. 2016 Article Density functional theory study of substitutional oxygen in diamond / K.M. Etmimi, P.R. Briddon, A.M. Abutruma, A. Sghayer, S.S. Farhat // Condensed Matter Physics. — 2016. — Т. 19, № 3. — С. 33301: 1–7. — Бібліогр.: 32 назв. — англ. 1607-324X PACS: 31.15.E-, 81.05.ug, 31.30.Gs DOI:10.5488/CMP.19.3330 arXiv:1609.04697 http://dspace.nbuv.gov.ua/handle/123456789/156202 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| description |
A few studies have been recently presented for the existence of oxygen in diamond, for example, the N3 EPR
centres have been theoretically and experimentally assigned the model made up from complex of substitutional
nitrogen and substitutional oxygen as nearest neighbours. We present ab initio calculations of substitutional
oxygen in diamond in terms of stability, electronic structures, geometry and hyperfine interaction and show
that substitutional oxygen with C₂v , S = 1 is the ground state configuration. We find that oxygen produces
either a donor or acceptor level depending on the position of the Fermi level. |
| format |
Article |
| author |
Etmimi, K.M. Briddon, P.R. Abutruma, A.M. Sghayer, A. Farhat, S.S. |
| spellingShingle |
Etmimi, K.M. Briddon, P.R. Abutruma, A.M. Sghayer, A. Farhat, S.S. Density functional theory study of substitutional oxygen in diamond Condensed Matter Physics |
| author_facet |
Etmimi, K.M. Briddon, P.R. Abutruma, A.M. Sghayer, A. Farhat, S.S. |
| author_sort |
Etmimi, K.M. |
| title |
Density functional theory study of substitutional oxygen in diamond |
| title_short |
Density functional theory study of substitutional oxygen in diamond |
| title_full |
Density functional theory study of substitutional oxygen in diamond |
| title_fullStr |
Density functional theory study of substitutional oxygen in diamond |
| title_full_unstemmed |
Density functional theory study of substitutional oxygen in diamond |
| title_sort |
density functional theory study of substitutional oxygen in diamond |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/156202 |
| citation_txt |
Density functional theory study of substitutional oxygen in diamond / K.M. Etmimi, P.R. Briddon, A.M. Abutruma, A. Sghayer, S.S. Farhat // Condensed Matter Physics. — 2016. — Т. 19, № 3. — С. 33301: 1–7. — Бібліогр.: 32 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT etmimikm densityfunctionaltheorystudyofsubstitutionaloxygenindiamond AT briddonpr densityfunctionaltheorystudyofsubstitutionaloxygenindiamond AT abutrumaam densityfunctionaltheorystudyofsubstitutionaloxygenindiamond AT sghayera densityfunctionaltheorystudyofsubstitutionaloxygenindiamond AT farhatss densityfunctionaltheorystudyofsubstitutionaloxygenindiamond |
| first_indexed |
2025-07-14T08:35:14Z |
| last_indexed |
2025-07-14T08:35:14Z |
| _version_ |
1837610686375526400 |
| fulltext |
Condensed Matter Physics, 2016, Vol. 19, No 3, 33301: 1–7
DOI: 10.5488/CMP.19.33301
http://www.icmp.lviv.ua/journal
Density functional theory study of substitutional
oxygen in diamond
K.M. Etmimi1, P.R. Briddon2, A.M. Abutruma3, A. Sghayer1, S.S. Farhat1
1 Physics Department, Faculty of Science, University of Tripoli, Tripoli, Libya
2 School of Electrical, Electronic and Computer Engineering Newcastle University,
Newcastle upon Tyne, England, NE1 7RU, UK
3 High Institute for Comprehensive Professions (Al-Shmokh Institution), Tripoli, Libya
Received July 20, 2015, in final form December 22, 2015
A few studies have been recently presented for the existence of oxygen in diamond, for example, the N3 EPR
centres have been theoretically and experimentally assigned the model made up from complex of substitutional
nitrogen and substitutional oxygen as nearest neighbours. We present ab initio calculations of substitutional
oxygen in diamond in terms of stability, electronic structures, geometry and hyperfine interaction and show
that substitutional oxygen with C2v , S = 1 is the ground state configuration. We find that oxygen produces
either a donor or acceptor level depending on the position of the Fermi level.
Key words: density functional theory, diamond, oxygen, hyperfine interaction
PACS: 31.15.E-, 81.05.ug, 31.30.Gs
1. Introduction
High electron and hole mobilities at room temperature and unrivalled thermal conductivity at room
temperature, mean that diamond could be thematerial of choice for high-power and high-frequency elec-
tronics. Many defects in a diamond such as nitrogen [1–3] and boron [4] are the main chemical elements
now well identified. Nitrogen as a simple substitutional defect forms a deep level at 1.7 eV [5] below the
conduction band edge and the boron gives a shallower level at 0.37 eV above the edge of the valence
band [6]. For this reason, a variety of other chemical defects in a diamond are now being investigated.
Oxygen is expected to be one of important impurities in a diamond due to its relatively close size of
carbon atom and abundance, and its has been suggested to lead to n-type conductivity in a diamond [7].
Experimentally, oxygen was found in mineral inclusions in a diamond [8] and combustion analysis of
converting diamond to graphite indicated high levels of oxygen in natural diamond [9]. Moreover, a
small number of optical centres may be related to oxygen [10, 11].
Electron-paramagnetic-resonance (EPR) spectroscopy is a powerful probe used to identify enormous
centres in diamond with nucleus spin of none zero. A small percentage (0.04%) of natural oxygen is 17O
[12] which is consistent with little evidence of the involvement of oxygen in electron paramagnetic res-
onance centres in diamond [13]. However, enrichment of diamond in the 17O isotope can occur during
diamond growth [12] or 17O ion implantation [7, 12] where the former undergoes insufficient control of
the gas environment during diamond growth [12], and the latter is induced by lattice damage where the
oxygen may be trapped for instant vacancy. EPR centre called KUL12 was detected to be an S = 1/2 centre
interacting with one I = 5/2 nucleus with A∥ = −362 MHz and A⊥ = −315 MHz. Unfortunately, there is
no other direct measurement of this centre.
The N3 and OK1 centres have been suggested to contain oxygen; the former in a nearest neighbour
nitrogen-oxygen pair, and the latter in a second nearest neighbour nitrogen-oxygen pair. Previously, we
analysed N3 and OK1 in a broader study [14] and we concluded that the most suitable candidate struc-
ture for N3 is Ns–Os . For OK1, none of the proposed models yield hyperfine tensors in agreement with
© K.M. Etmimi, P.R. Briddon, A.M. Abutruma, A. Sghayer, S.S. Farhat, 2016 33301-1
http://dx.doi.org/10.5488/CMP.19.33301
http://www.icmp.lviv.ua/journal
K.M. Etmimi et al.
experiment. Three of the EPR centres found in synthetic diamonds grown in carbonate medium in recent
experimental study [15], using the high pressure apparatus BARS [16, 17] showed that OX1, OX2 and OX3
centres are oxygen atoms occupying substitutional, interstitial and next to vacancy sites, respectively.
The previous theoretical work using ab initio calculations [18] shows that substitutional oxygen ex-
hibits carbon vacancy character which gives rise to an occupied a-level into the middle of the band gap
and unoccupied t -level just below the conduction band. A theoretical work has predicted that oxygen
introduces a mid-gap donor level in the band gap of a diamond, which is above the fundamental level of
vacancy being 2 eV above the top of valence band. So, in a material containing both types of centres, one
would expect a charge transfer to occur, which gives rise to EPR active defect.
In this work, extensive calculations on different models containing oxygen atoms were carried out,
and the total energies and other properties of defects were determined using ab initio calculations.
2. Method
The structures were modelled using density-functional calculations with the exchange-correlation in
a generalised gradient approximation [19] by the AIMPRO code [20, 21]. The Brillouin-zone is sampled
using the Monkhorst-Pack scheme [22] with a uniform mesh of 2× 2× 2 special k-points. For several
sample structures, we calculated the total energies using a 4×4×4 mesh, which indicated that the relative
total energies are converged to better than 10 meV.
The valence states were represented by a set of atom-centred s- and p- with the addition of a set of
d -like Gaussian functions [23] to allow for polarization, and the Kohn-Sham states were expanded with
the help of a contracted basis with a total of 22 functions on each carbon and oxygen atom. For the
charge density evaluation, the plane waves with a cut-off of 300 Ha were used, yielding structures op-
timized until the total energy changes by less than 10−5 Ha. The lattice constant and the bulk modulus
were within 1% and 2%, respectively, of experimentally determined values. The lattice constant was op-
timized, keeping the symmetry of the supercell fixed, giving a value of 3.5719 Å, close to the experimental
value of 3.5667 Å [24]. The calculated direct and indirect band gaps agree with the published plane-wave
values [25] (5.68 and 4.18 eV).
In general 216-atom, simple-cubic supercells of side length 3a0 are used. Core-electrons are elimi-
nated by using pseudo-potentials [26], the 1s electrons of C and O are in the core, and the 3p electrons are
treated as the valence ones, so that hyperfine interactions are obtained by reconstructing the all-electron
wave functions in the core region [27, 28]. The atomic calculations for the reconstruction in the hyperfine
calculations were performed using a systematic polynomial basis [29]. Electrical levels were calculated
using the marker method by comparing acceptor and donor with B and N, respectively.
3. Results and dissections
Different charged forms O0
s , O
+
s and O−
s of substitutional oxygen in diamond are examined. In all
cases, the C2v configuration is found to be favoured.
In the neutral charge state, we find several metastable structures for substitutional O0
s in a diamond.
Interestingly, the spin orientation was crucial in terms of determining the stability. The lowest in energy
exhibits a C2v S = 1, as schematically shown in figure 1 (a). The oxygen atom undergoes a distortion
along 〈001〉, the oxygen moves strongly off centre to form two C–O bonds leaving behind two C dangling
orbitals. This suggests that it may undergo a symmetry lowering distortion, probably of a chemical re-
bonding. Three structures [figures 1 (b), (c) and (d)] were found to be energetically indistinguishable and
higher in energy than the ground state configuration by just 0.2 eV. The oxygen atom in figure 1 (c) is in
a fourfold coordinated arrangement with C–O bonds of lengths 1.73 Å.
A trigonally symmetric state was also examined and was found to be metastable. The C3v S = 0 struc-
ture in the figure 1 (b) exhibits a slight displacement along 〈111〉, where one of the four neighbouring
C atoms move from 1.73 Å to 1.72 Å compared to the on-site structure in figure 1 (c). The energy differ-
ences [between figure 1 (b) and (c)] are just of a few meV. Symmetrically equivalent to the ground state
configuration [figure 1 (a)], the spin averaged structure with two equivalent carbon neighbours to O is
33301-2
DFT study of substitutional oxygen in diamond
(a)
1.451.45
2.022.02
O
C1 C2
C3
C4
(b)
1.72
1.74
1.74
1.74
(c)
1.73
1.73 1.73
1.73
(d)
1.641.64
1.82 1.82
(e)
2.08
1.63
1.63 1.63
Figure 1. (Color online) Schematic structures of the substitutional oxygen in both the S = 0 and S = 1
configurations. Grey and red spheres represent C and O. (a) C2v , S = 1, (b) C3v , S = 0, (c) Td , S = 0, (d)
C2v , S = 0, (e) C3v , S = 1. Bond lengths in Å.
moved closer to the impurity, lowering the symmetry to C2v , however, it is 0.21 eV higher in energy than
the most stable one.
The structure in the figure 1 (e) exhibits C3v S = 1 where the oxygen is significantly displaced off-
site along 〈111〉 producing an elongated C–O bond to 2.08 Å which significantly increased the energy to
0.57 eV compared to the most stable configuration.
Generally, the substitutional O atom bonds relatively weakly to the carbon dangling bonds in the
vacancy, the reason for this probably being the oxygen atom having a relatively small atom compared to
carbon and it can be understood as having vacancy-like characteristics, which has proved successful in
explaining the electronic structure of the defects in a diamond [30].
In the positive charge state, three different symmetry configurations are obtained. The differences
are within a few meV as listed in table 1. The lowest structure has C2v symmetry lower than two other
33301-3
K.M. Etmimi et al.
Table 1. Relative energies for different structureswith different symmetries of Os . The zero of energy for
neutral, positive and negative charged state is set to the O0
s S = 1 C2v , O
+1
s S = 1/2 C2v and O−1
s S = 1/2
C2v , respectively.
Symmetry Charge state Spin configuration Relative energy
C3v neutral S = 0 0.20 eV
Td neutral S = 0 0.20 eV
C2v neutral S = 0 0.21 eV
C3v neutral S = 1 0.57 eV
C3v positive S = 1/2 0.04 eV
Td positive S = 1/2 0.05 eV
C3v negative S = 1/2 0.57 eV
Td negative S = 1/2 1.13 eV
structures by just 0.04 eV for C3v and 0.05 eV for Td configuration, respectively, where all structures
with spin S = 1/2. The energy difference is so tiny that one cannot be certain which possesses the lowest
energy. Similarly to O+
s , the C2v S = 1/2 configuration is found to be favoured in the negatively charged
state. Moreover, there are two other metastable configurations which are high in energy as listed in
table 1.
Electronically, we present the previously calculated energy structure of on-site configuration quoted
by Gali et al. [18] that possesses the ground state configuration [figure 2 (c)]. Its band gap consists of one
(a)
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
Γ R M Γ X Γ M R Γ
E
ne
rg
y
(e
V
)
k
a∗
1
a1
b1
(b)
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
ΓRMΓX
E
ne
rg
y
(e
V
)
k
(c)
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
ΓRMΓX
E
ne
rg
y
(e
V
)
k
a∗
1
t∗
2
Figure 2. (Color online) Band structure for S = 1 and S = 0 configurations of substitutional oxygen in
diamond. Filled and empty circles show filled and empty bands, respectively. The energy scale is defined
by the valence band top at zero energy. (a) C2v S = 1, (b) C3v S = 0, (c) Td S = 0.
33301-4
DFT study of substitutional oxygen in diamond
fully non-degenerate one-electron states a1 near the middle of the band gap and one triplet degenerate t2
state close to the conduction band, with a total occupation of two electrons, where a1 and t2 levels are
introduced in the band gap due to C vacancy [31]. Apparently, the a1 and t2 levels hybridizedwith oxygen
valence states s and p atomic orbitals, which gives rise to four levels a1, t2, a∗
1
and t∗
2
, two states will be
in the band gap, the anti-bonding a∗
1
level will be occupied by two electrons and triplet degeneracy t∗
2
will be unoccupied.
Our calculation shows that C2v S = 1 in the neutral charge state is the most stable structure, where the
t2-level is split into three levels, b1a1b2 as shown schematically in figure 2 (a), where b2 lies in the con-
duction band. The b1 and a1 levels are odd and even combinations of the neighbouring carbon dangling
bonds which are farther apart than the other two to oxygen, respectively.
Other previous density functional calculations [18] found that Os has Td symmetry and is the most
stable configuration in neutral, negative and positive charge states. However, it is unclear whether the
S = 1 was considered. We find that the spin states for the neutral and positively charged states follow
the Hund rule, so the positive and neutral defects have S = 1/2 and S = 1, respectively. Compared to the
band gap of the well-known substitutional nitrogen (it has C3v ), Os with C3v S = 0 symmetry has more
levels. In addition to a1 level associated with the radical on the unique carbon, there is one empty doublet
degeneracy e0 and a singlet empty a0 from anti-bonding between O and there are three identical carbon
atoms neighbouring the oxygen as shown in figure 2 (b). The oxygen atom is more shared with the three
close neighbours.
Os is theoretically electrically active, with donor, double donor and acceptor levels being estimated
to be at Ec − 2.8 eV, Ev + 0.04 eV and Ec − 1.9 eV, respectively. These levels are in disagreement with
the previous density functional calculation [18] of values Ev + 1.97 eV, Ev + 1.39 eV and Ev + 2.89 eV,
respectively. Oxygen can exhibit an amphoteric behaviour depending on the location of Fermi level. Since
the acceptor level of oxygen lies below a donor level such as Ns and the donor level of oxygen lies above
the acceptor level such as V [32], one would expect the charge transfer to occur in thematerial containing
both types of centres. Previously, in [14] we showed that Nitrogen-Oxygen complexes render both an
acceptor and donor; we find the (−/0) and (0/+) levels at Ev +3.7 eV and Ev +1.5 eV.
Hyperfine tensors for themost stable configurations within different charge states of oxygen and four
Table 2. Calculated hyperfine tensors (MHz) of oxygen and the four nearest neighbour 13C in substitu-
tional O. θ and φ are given relative to the directions 〈001〉 and 〈100〉, respectively.
Species A1 A2 A3
C2v , S = 1
17O −198 (90,315) −181 (00,00) −165 (90,45)
C1 −1 (147,225) −1 (90,135) 4 (123,45)
C2 −1 (147,45) −1 (90,135) 4 (57,45)
C3 205 (126,315) 86 (90,45) 86 (144,135)
C4 205 (54,315) 86 (90,45) 86 (144,315)
C2v , charge=+1, S = 1/2
17O −568 (00,129) −552 (90,45) −538 (90,315)
C1 41 (125,45) 18 (102,144) 18 (142,250)
C2 41 (55,45) 18 (102,126) 18 (142,20)
C3 197 (125,315) 86 (90,45) 86 (145,135)
C4 197 (55,315) 86 (90,45) 86 (145,315)
C2v , charge=−1, S = 1/2
17O −19 (90,135) 31 (00,00) 40 (90,45)
C1 −7 (82,225) −4 (172,224) −4 (90,315)
C2 −7 (98,225) −4 (172,46) −4 (90,315)
C3 238 (126,315) 105 (90,45) 105 (144,135)
C4 238 (54,315) 105 (90,45) 105 (144,315)
33301-5
K.M. Etmimi et al.
Figure 3. (Color online) Unpaired electron Kohn-Sham functions for positive substitutional oxygen with
C3v symmetry.
nearest neighbours are listed in table 2. There are no hyperfine values for substitutional oxygen in litera-
ture so far. O+
s with C3v structurally resembles P1 centre, although the present calculation shows that this
configuration is metastable within a few meV. C3v symmetry means that one of the four neighbouring
C atoms is farther away from the oxygen than the other three, the hyperfine tensor on these carbon atoms
is small (A∥ = 89 MHz, A⊥ = 42 MHz) compared to those in P1 centre, which means that the spin density
is not mostly localized on the carbon radical site. It is distributed on the anti-bond between O and four
neighbouring carbon atoms as shown in figure 3. In the negatively charged state with C2v symmetry, the
spin density is strongly localized in the vicinity of the carbon radical sites, leading to small, anisotropic
hyperfine tensors for the oxygen, whereas in neutral charged state, the relatively larger values for the
hyperfine O compared to the negatively charged state are due to the relatively big amount of spin density
on the O-site, and to some extent on the carbon radical atoms, from odd and even combinations of the
neighbouring carbon dangling bonds for the highest and second highest occupied levels, respectively. In
the positively charged state, the even combinations of neighbouring carbon dangling bonds make the
values of hyperfine tensor on O still larger.
4. Conclusions
We have used ab initio computational modelling mainly for the stability and electronic structure on
different forms of the substitutional oxygen in diamond. Energetically we find that S = 0 C2v is the most
stable structure where both S = 0 and S = 1 are considered.
The band gap of substitutional oxygen gives rise to two states, one a1 state located near the middle of
the band gap and the other t2 state located close to the conduction band edge. The t2 state is populated
when O becomes negatively charged or neutral S = 1 configuration.
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Дослiдження методом теорiї функцiоналу густини кисню
замiщення в алмазi
K.M. Етмiмi1, П.Р. Брiддон2, A.M. Абутрума3, A. Сайер1, С.С. Фархат1
1 Фiзичний вiддiл, факультет природничих наук, Унiверситет Трiполi, Трiполi, Лiвiя
2 Коледж електричної, електронної i комп’ютерної iнженерiї, Унiверситет Ньюкасла,
Ньюкасл-апон-Тайн, Великобританiя
3 Вищий iнститут комплексних професiй, Трiполi, Лiвiя
Останнiм часом представлено декiлька дослiджень стосовно наявностi кисню в алмазi, наприклад теоре-
тично i експериментально призначена модель для N3 EPR створена з комплексу замiщувального азоту
та замiщувального кисню як найближчих сусiдiв. У цiй статтi представлено ab initio обчислення замiщу-
вального кисню в алмазi з огляду на стiйкiсть, електроннi структури, геометрiю та надтонку взаємодiю, а
також показано, що замiщувальний кисень з C2v , S = 1 є конфiгурацiєю основного стану. Встановлено,
що кисень продукує або ж донорний, або акцепторний рiвень в залежностi вiд положення Фермi рiвня.
Ключовi слова: теорiя функцiоналу густини, алмаз, кисень, надтонка взаємодiя
33301-7
http://dx.doi.org/10.1038/263275a0
http://dx.doi.org/10.1038/263309a0
http://dx.doi.org/10.1063/1.108685
http://dx.doi.org/10.1063/1.107368
http://dx.doi.org/10.1103/PhysRevB.66.045406
http://dx.doi.org/10.1088/0953-8984/22/38/385502
http://dx.doi.org/10.1002/pssa.201300036
http://dx.doi.org/10.1021/cg100322p
http://dx.doi.org/10.1002/pssa.201431163
http://dx.doi.org/10.1088/0953-8984/13/50/319
http://dx.doi.org/10.1103/PhysRevLett.77.3865
http://dx.doi.org/10.1002/(SICI)1521-3951(200001)217:1%3C131::AID-PSSB131%3E3.0.CO;2-M
http://dx.doi.org/10.1016/j.cpc.2007.08.007
http://dx.doi.org/10.1103/PhysRevB.13.5188
http://dx.doi.org/10.1007/11690320_4
http://dx.doi.org/10.1103/PhysRevB.62.6851
http://dx.doi.org/10.1103/PhysRevB.58.3641
http://dx.doi.org/10.1103/PhysRevLett.95.205502
http://dx.doi.org/10.1103/PhysRevB.50.17953
http://dx.doi.org/10.1103/PhysRevE.76.026704
http://dx.doi.org/10.1016/0378-4363(83)90432-1
http://dx.doi.org/10.1098/rspa.1957.0138
http://dx.doi.org/10.1016/S0925-9635(01)00489-7
Introduction
Method
Results and dissections
Conclusions
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