Surface Science 601 (2007) 2339–2343
www.elsevier.com/locate/susc
Diffusion of oxygen atom in the topmost layer of the Si(1 0 0)
surface: Structures and oxidation kinetics
A. Hemeryck
a
a,*
, N. Richard b, A. Estève a, M. Djafari Rouhani
a
Laboratoire d’Analyse et d’Architecture des Systèmes, CNRS, 7, av. Colonel Roche, 31077 Toulouse, France
b
CEA-DIF, BP12, 91680 Bruyères Le Châtel, France
Received 12 January 2007; accepted for publication 22 March 2007
Available online 2 April 2007
Abstract
The incorporations and migrations of the atomic oxygen in the topmost layer Si(1 0 0)-p(2 · 2) silicon surface, are investigated theoretically using density functional theory. We show that the diffusion is dependent on the starting and the final surrounding environment
and does not simply consist in hops from one silicon–silicon bond to another. The activation energies range from 0.11 eV to 2.59 eV.
2007 Elsevier B.V. All rights reserved.
Keywords: Density functional calculations; Surface diffusion; Oxidation; Semiconducting surfaces
1. Introduction
Because of the obvious constant scaling down of the silicon-based devices in microelectronic [1] and because the
Deal–Grove Model breaks down for the ultrathin oxides
[2,3], the understanding of reaction mechanisms occurring
at the earlier stages of the silicon oxidation at the atomic
scale becomes important.
Considering elementary reaction processes on the
Si(1 0 0) surface, the oxidation also relies on the dissociation of the molecular oxygen, the adsorption, the penetration and the diffusion of the atomic oxygen in the topmost
layer, creating and breaking bonds between the oxygen and
silicon atoms near the surface and at the interface. These
diverse mechanisms have to be characterized not only in
terms of atomic structures and the corresponding stability
of resulting oxygen and silicon atoms, but also in terms
of oxidation kinetics, by defining their activation energies
in the oxidation reactions.
*
Corresponding author. Tel.: +33 1 69 26 40 58; fax: +33 1 69 26 70 53.
E-mail address: [email protected] (A. Hemeryck).
0039-6028/$ - see front matter 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.susc.2007.03.038
The oxidation kinetics have been tackled in many studies, for example, about the oxidant species diffusion in silica
using peroxy-like structures [4–7], or at the interface [8],
with Monte Carlo techniques or molecular dynamics
underlying threefold coordinated structures [9,10], all using
a silicon dioxide already formed on the silicon substrate.
With theoretical calculations, Kato et al. [11] carried out
investigations about the diffusion of atomic oxygen from
dimer bond to the backbond through an ‘‘on-top’’ configuration, Lee et al. [12] studied the chain migrations of
O2 ! O9. However, studies completely dedicated to the
kinetics of initial reactions of surface layer or subsurface
layer have never been performed to our knowledge. These
kinetics are important to determine the oxide growth at the
first stages of the silicon oxidation when the interface begins to form.
In this paper, our challenge draw up the mechanisms
linked to the capacity of an oxygen atom to incorporate,
and then to diffuse in the topmost surface layer. Actually,
the diffusions of oxygen atom from Si–Si bonds to Si–Si
bonds [12] are not sufficient, but it is primary to study each
diffusion considering the starting structure.
According to Ramamoorthy and Pantelides [13], the
complexity of the oxygen diffusion problem comes from
2340
A. Hemeryck et al. / Surface Science 601 (2007) 2339–2343
the breaking and reformation of bonds. Firstly, the different ways for the oxygen atom to incorporate in the surface
layer of the silicon substrate once the oxygen molecule dissociated, is studied. Then, the diffusion of these atoms in
the topmost layers is presented. The critical parameter in
a kinetic study is the activation energy, which is given for
each diffusion as well as the restructuring and the formation of bonds for the pathway structures. All the activation
energies calculated are associated to an occurrence time in
order to give a highlight on the most probable diffusions.
This time is determined at 900 C, a conventional thermal
growth temperature, considering a typical attempt frequency of m = 1014 s1 [14].
2. Calculation details
The calculations are performed using the density functional theory (DFT) with the plane wave-pseudopotentials
program package VASP [15]. The density is described with
the generalized gradient approximation (GGA) [16]. The
energy cutoff is fixed at 475 eV. The ions are described by
ultrasoft pseudopotentials [17]. All the atomic relaxations
are performed using the conjugate gradient method. We
take into account spin-polarization to properly describe
the possible spin conversion during diffusion. The Brillouin
zone is sampled at the C point. This only point is sufficient
to describe accurately the geometries of semiconductors.
The reaction pathways and activation energies are calculated with the nudged elastic band method (NEB) [18].
The Si(1 0 0)-p(2 · 2) used in this paper, is modelled as a
periodic cell of a slab Si48H16 consisting in six layers of
eight silicon atoms, with the two lowest layers kept fixed
in their crystalline positions to simulate the bulk, whereas
the other layers are allowed to fully relax. A channel and
a buckled dimer row on the surface are present on the surface due to the p(2 · 2) reconstruction [19]. A vacuum inter-slab zone of 10 Å is placed along the z-axis to create
a surface effect, and the dangling bonds of the silicon atoms
underneath the slab are passivated with 16 hydrogen
atoms.
3. Results and discussion
3.1. Oxygen atom incorporations
Previous calculations [20,21] have revealed that once the
oxygen molecule is dissociated, the oxygen atoms are stabilized first on the silicon surface in ‘‘on-top’’ configurations
due to the presence of the dangling bond on each surface
silicon atom. The energetic diagram in Fig. 1 confirms that
the oxygen atom prefers to incorporate in the topmost
layer in a Si–Si bond centre since the backbond (BB) and
the dimer bond are energetically more favourable [22,23]
leading to a two-steps oxidation process: adsorption and
then incorporation of oxygen atom. Starting from the
‘‘on-top’’ configuration, we estimate three possible incor-
Fig. 1. Energetic diagram of the one oxygen atom structures, the white
circles correspond to silicon atoms and the black ones to the oxygen
atoms. Figure A corresponds to a down backbond position, B to a 2nd
layer Si–Si bond position, C to a dimer bond position, D to a Si–O–Si
bridge in the channel, E to an ‘‘on-top’’ position, F to a siloxane bridge.
porations of the oxygen atom. The corresponding pathways are described in Fig. 2.
3.1.1. Oxygen atom incorporation in the dimer bond:
pathway #1
When the oxygen atom is in on-top position, the dimer
bond is broken and the SiO bond is 1.54 Å long. During
the incorporation of the oxygen atom, the length of the
SiO bond increases whereas the length of the dimer bond
decreases until the dimer bond is reformed. The oxygen
atom in the on-top position can be easily incorporated in
the dimer bond with a small activation barrier of magnitude of 0.11 eV (hti = 2.97 · 1014 s), as shown in Fig. 2,
#1.
The final structure obtained is more stable by 1 eV than
the on-top configuration. In this structure, the Si–O–Si angle is close to 85 and the Si–O bonds are both of 1.70 Å
long. The reformed dimer bond has a distance of 2.32 Å
and the buckling in the dimer is locally reduced.
3.1.2. Oxygen atom incorporation in the backbond:
pathway #2
In on-top configuration, the Si@O bond measures
1.54 Å and the Si–Si backbond is of 2.38 Å long. During
the diffusion process, the Si@O length stretches until
1.62 Å and then, the oxygen atom incorporates in the Si–
Si backbond still formed. So, the incorporation in the
backbond, has a higher activation energy of 0.38 eV
(hti = 4.28 · 1013 s) compared to the incorporation in
the dimer bond (Fig. 2, #2) for an equal energy gain of
around 1 eV. This result is consistent with the previous values obtained by Kato [11].
Finally, the BB breaks and the final structure has a Si–
O–Si angle of 125, Si–O bonds of 1.62 Å and 1.69 Å, and a
Si–Si distance of around 3 Å. We can notice that the oxygen atom is more linked to the surface silicon atom.
3.1.3. Oxygen atom diffusion in the siloxane bridge:
pathway #3
We define as ‘‘siloxane bridge’’, referred ‘‘surface-bridging oxygen’’ and noted ‘‘sBO’’ in Ref. [23], a bridge created
by an oxygen atom incorporated between two dangling
bonds of silicon atoms of two adjacent dimers: a Si–O–Si
bridge is then formed between two dimers perpendicularly
to the dimer row (schematised in Fig. 1-F).
A. Hemeryck et al. / Surface Science 601 (2007) 2339–2343
2341
Fig. 2. Minimum-energy pathways #1, #2, #3 for the incorporation in dimer bond #1, in the backbond #2, and in the siloxane bridge #3, respectively, the
oxygen atoms are in black and the silicon atoms are in grey.
The sBO has a Si–O–Si angle of around 105 and then
distorts the two dimers: the dimer silicon atoms move out
of their crystalline positions, and the final Si–O bonds are
of around 1.75 Å. We have to specify that the siloxane
bridge structure is less stable than the on-top configuration
by 0.29 eV, as shown in Fig. 2, #3.
The incorporation of the oxygen atom in the sBO configuration is characterized by a large activation barrier of
0.88 eV (hti = 6 · 1011 s) and has a low probability to
occur in the case of the migration of a single atom. However, this diffusion has to be taken into account, because
it is the only way for an oxygen atom to diffuse along the
dimer row, without the full incorporation of the oxygen
atom. Moreover, Yamasaki et al. [23] show that the sBO
position is energetically favourable configuration when
the number of oxygen atoms is superior at 3, and promotes
the full coverage of the first layer. We will show in a further
paper, that the activation barrier we found is reduced with
the presence of other oxygen atoms.
These calculations underline that the thermodynamically favourable first incorporation occurs in the Si–Si centre bonds in the dimer bond as well as in the backbond
because their activation energies are both small compared
to the 2 eV obtained during the dissociative chemisorption
[20,21]. These two first incorporations are consistent with
the silanone structure [24,25] which appears to be an primordial state during the silicon oxidation. Once incorporated, the oxygen atom is able to diffuse from Si–Si bond
to another adjacent Si–Si bond.
3.2. BB to BB diffusion: pathway #4
The corresponding pathway is shown in Fig. 3. In our
case, this diffusion occurs through an intermediate state
like a two-steps reaction process. The intermediate state
used is the sBO configuration as described above. The
starting configuration is the backbond. This pathway is
constructed with the help of two diffusions pathways calculations, the first from the BB centre to the sBO position,
and the second from the sBO configuration to the BB centre of the second dimer. The BB centres and the sBO positions are fully relaxed.
Fig. 3. Minimum-energy pathway #4 for the BB to BB diffusion through
the siloxane bridge, obtained with two minimum-energy pathway calculations. The two BB points (global minima – points A and E) and the
siloxane bridge position (local minimum – point C) are fully relaxed,
whereas the other points of the curve are stressed. The oxygen atoms are in
black and the silicon atoms are in grey.
The energy barrier for this extraction is large (1.86 eV
(hti = 9.6 · 107 s)). At this low level of coverage, the high
activation barrier obtained to extract the oxygen atom
from the BB gives a low probability to the reaction to
occur. The stressed ‘‘peak point’’ of the diffusion (point B
and D in Fig. 3) is close to the sBO configuration shown
in Fig. 2, #3 but the Si–O–Si angle is larger (125.6 measured in the peak point structure compared to 104.7 in
the sBO structure). The siloxane bridge is more stable of
0.57 eV compared to the peak point, this value is the activation energy to get the BB from the siloxane bridge (hti =
3 · 1012 s).
The reaction intermediate, i.e. the siloxane bridge, is
clearly a metastable state, as it exists two more stable states
of around 1.5 eV in the surroundings of the oxygen atom.
Typically, this diffusion shows that the oxygen atom migration needs to break and to recreate Si–O and Si–Si bonds.
This two-steps reaction process provides strong evidence
that the diffusion process is an adiabatic reaction because
of the symmetry in the reaction minimum-energy pathway.
3.3. Channel crossing
From the BB position, the oxygen atom can diffuse
through the channel. We investigate two ways for the
oxygen atom to go across the channel schematised in
2342
A. Hemeryck et al. / Surface Science 601 (2007) 2339–2343
Fig. 4. Channel side view and schematisation of the pathways for the
channel crossings: #5 via a Si–O–Si bridge and #6, the white circles
correspond to silicon atoms and the black and dash circles to the oxygen
atoms.
Fig. 4: through a Si–O–Si bridge (pathway #5) or through
hops from Si–Si bond to Si–Si bond (pathway #6).
3.3.1. The channel crossing through an intermediate:
pathway #5
This pathway, formed with the help of the association of
two diffusion pathways calculations, consists in a stabilized
oxygen atom bonded to two channel silicon atoms (a and b
in Fig. 4). In this intermediate configuration which is a local minimum of the pathway (point C in Fig. 5, #5), the
two silicon atoms (a and b) are four-bonded. This structure
is fully relaxed. In fact, one of the BB in the bulk under the
dimer row is broken, because these two silicon atoms are
shifted from their crystalline positions of 0.7 Å along the
z-axis. The Si–O–Si angle for this channel intermediate is
of 106.7 and the Si–O bonds are around 1.7 Å. Yamasaki
et al. referred this oxygen atom position as a bBO, meaning
bulk-bridging oxygen [23]. This particular position is obtained when a Pb0 centre is created during the oxidation
of deeper layers.
As explained in the previous part for the BB to BB diffusion, the BB starting configuration (point A in Fig. 5, #5)
is the most stable state and it is very difficult to move out
the oxygen atom from the BB. The extraction shown in
Fig. 5, #5, needs thus to overcome an large energy barrier
of 1.87 eV (hti = 1.1 · 106 s) to reach the bBO position.
The bBO position is a metastable state less stable than
the BB structure by 0.56 eV. The large activation energy
and the less favourable bBO position obtained reveal that
this diffusion at low coverage can not be reach.
We can notice that during this diffusion, the oxygen
atom gets to an on-top position in the channel called ‘‘peak
point’’ of the diffusion minimum-energy pathway with a
Si–O length of 1.53 Å similar to the on-top position on
the surface. The second step in this diffusion is the pathway
from the intermediate (point C in Fig. 5, #5) to the BB
(point E in Fig. 5, #5) at the opposite side of the channel.
This process requires an activation barrier of 1.36 eV
(hti = 6.89 · 109 s) through the stressed peak point D.
This two steps pathway is symmetric underlying that the
diffusion process is adiabatic, as the second step is the
back-reaction of the first step.
3.3.2. The channel crossing through hops #6
The second pathway to cross the channel occurs via several hops from Si–Si bond to Si–Si bond by extracting an
oxygen atom from the BB to insert it in the second layer
Si–Si bond (as described #6 in Figs. 4 and 5).
The oxygen atom is initially in the BB position and diffuses towards the second layer BB. We can notice here that
the second layer BB configuration is less favourable than
the first layer BB with an energetic difference of 0.18 eV.
In the second layer the Si–O–Si angle is larger than in the
BB, with 143 and 116, respectively, and the Si–O bonds
are typically around 1.63–1.65 Å. During the migration,
the Si–O bond near the surface is stretched and then
breaks, leading once again to a on-top configuration in
the channel: this point corresponds to the ‘‘peak point’’
of the diffusion pathway.
To reach the second layer, the oxygen atom had to overcome a huge activation barrier of 2.59 eV (hti = 1.31 ·
103 s), which is consistent with Watanabe et al. (2.4 eV)
[26]. This high-energy barrier suggests that this kind of diffusion is not probable at low coverage. But, Watanabe also
found an experimental value of 0.3 eV during the layer-bylayer oxidation. This large energetic difference can be explained by the fact that experimentally, the first layer is
fully oxidized, whereas in our calculations the surface has
only one diffusing oxygen atom, or by the stress effects at
the interface lowering the activation barrier for the second
layer. Moreover, it has been shown that the diffusion is
made easier with the presence of other oxygen atoms, as
shown in the case of chain diffusions [12].
The diffusions to cross the channel or to get lower layer
are difficult at low coverage. When the number of oxygen
Fig. 5. Minimum-energy pathways #5 and #6 for the channel crossing through a Si–O–Si bridge #5 and using hops from Si–Si to Si–Si bonds #6. The
pathway #5 obtained is due to the addition of two calculations. The two BB points (global minima – points A and E) and the channel intermediate state
(local minimum– point C) are fully relaxed, whereas the other points of the curve are stressed. The oxygen atoms are in black and the silicon atoms are in
grey.
A. Hemeryck et al. / Surface Science 601 (2007) 2339–2343
atoms incorporated in the surface increases, the most probable diffusion is the pathway #5, as suggested by Yamasaki
et al. [23]. Our calculations confirm that the oxidation proceeds first in a lateral manner and then by layer-by-layer
way, and that a high coverage close to the full coverage
of the first layer is necessary to oxidize the deeper layer.
4. Conclusions
In this paper, we have presented a list of the possible
incorporations from the on-top configuration and migrations from Si–Si bond to Si–Si bond of the atomic oxygen
in the topmost layer Si(1 0 0)-p(2 · 2) silicon surface. Thus,
diffusion barriers are also extremely sensitive to the local
topology and range, in the topmost layer, from 0.11 eV for
the oxygen incorporation in the substrate to 1.87 eV
for the diffusion in the first layer in the channel (2.59 eV
for the incorporation in the second layer). But in all cases,
oxygen atom seems to diffuse preferentially in the dimer
and in the backbond Si–Si bonds, whereas the other diffusions such as the incorporation in the siloxane bridge are
promoted when the coverage is increased. The migration
pathway is also influenced not simply by the adiabatic minimum-energy pathway, but also by the dynamics of the diffusion hop and the local atomic configuration.
References
[1] G.E. Moore, Electronics 38 (1965).
[2] B.E. Deal, A.S. Grove, J. Appl. Phys. 36 (1965) 3770.
[3] E.P. Gusev, H.C. Lu, T. Gustafsson, E. Garfunkel, Phys. Rev. B 52
(1995) 1759.
[4] T. Bakos, S.N. Rashkeev, S.T. Pantelides, Phys. Rev. Lett. 88 (2002)
055508.
2343
[5] M.A. Szymanski, A.L. Schluger, A.M. Stoneham, Phys. Rev. B 63
(2001) 224207.
[6] J.R. Chelikowsky, D.J. Chadi, N. Binggeli, Phys. Rev. B 62 (2000)
R2251.
[7] A.M. Stoneham, M.A. Szymanski, A.L. Schluger, Phys. Rev. B 63
(2001) 241304.
[8] T. Akiyama, H. Kageshima, Appl. Surf. Sci. 216 (2003) 270.
[9] A. Pasquarello, M.S. Hybertsen, R. Car, Nature 396 (1998) 58.
[10] K.-O. Ng, D. Vanderbilt, Phys. Rev. B 59 (1999) 10132.
[11] K. Kato, T. Uda, K. Terakura, Phys. Rev. Lett. 80 (1998) 2000;
K. Kato, T. Uda, Phys. Rev. B 62 (2000) 15978.
[12] Y.J. Lee, J. von Boehm, M. Pesola, R.M. Nieminen, Phys. Rev. B 65
(2002) 085205.
[13] M. Ramamoorthy, S.T. Pantelides, Phys. Rev. Lett. 76 (1996) 267.
[14] H.Z. Massoud, J.D. Plummer, E.A. Irene, J. Electrochem. Soc. 132
(1985) 1745.
[15] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169;
G. Kresse, J. Joubert, Phys. Rev. B 59 (1999) 1758.
[16] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244.
[17] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892.
[18] G. Mills, H. Jònsson, G.K. Schenter, Surf. Sci. 324 (1995) 305;
H. Jònsson, G. Mills, K.W. Jacobsen, in: B.J. Berne, G. Ciccotti,
D.F. Coker (Eds.), Classical and Quantum Dynamics in Condensed
Phase Simulations, World Scientific, Singapore, 1998, p. 385.
[19] A. Ramstad, G. Brocks, P.J. Kelly, Phys. Rev. B 51 (1995) 14504.
[20] N. Richard, A. Estève, M. Djafari Rouhani, Comp. Mater. Sci. 33
(2005) 26.
[21] A. Hemeryck, N. Richard, A. Estève, M. Djafari Rouhani, J. NonCryst. Solids 353 (2007) 594.
[22] Y. Miyamoto, A. Oshiyama, Phys. Rev. B 41 (1990) 12680.
[23] T. Yamasaki, K. Kato, T. Uda, Phys. Rev. Lett. 91 (2003) 146102.
[24] A. Hemeryck, A. Mayne, N. Richard, A. Estève, Y.J. Chabal, M.
Djafari Rouhani, G. Dujardin, G. Comtet, J. Chem. Phys. 126 (2007)
114707.
[25] Y.J. Chabal, K. Raghavachari, X. Zhang, E. Garfunkel, Phys. Rev. B
66 (2002) 161315.
[26] H. Watanabe, K. Kato, T. Uda, K. Fujita, M. Ichikawa, T.
Kawamura, K. Terakura, Phys. Rev. Lett. 80 (1998) 345.