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Surface Science 576 (2005) L65–L70
www.elsevier.com/locate/susc
Surface Science Letters
Reaction mechanisms of oxygen at SiO2/Si(100) interface
Toru Akiyama a,b,*, Hiroyuki Kageshima a
a NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japanb Department of Physics Engineering, Mie University, 1515 Kamihama, Tsu, Mie 514-8507, Japan
Received 17 August 2004; accepted for publication 4 January 2005
Available online 11 January 2005
Abstract
First-principles total-energy calculations are performed to clarify the reaction mechanisms of O atoms and O2 mol-
ecules at SiO2/Si(100) interface. The calculated energies reveal that the incorporation of O2 molecules into the substrate
dominates the interfacial reaction of the oxidant. The low energy barrier for O2 incorporation (0.2 eV) corresponds to
the hybridization of oxygen-2p orbitals of O2 and the valence band states of the Si substrate, while that for O atom
incorporation corresponds to the O–O bond dissociation and the formation of Si–O–Si bonds. The cooperative reaction
of each O atom in the O2 molecule with each Si atom at the interface leads to the low energy barrier.
� 2005 Elsevier B.V. All rights reserved.
Keywords: Density functional calculations; Oxidation; Silicon; Silicon oxides; Semiconductor–insulator interfaces
Silicon oxidation has received much attention
in these decades as fundamental phenomena in
materials. In addition, it is of great interest andimportance as a key process in the fabrication of
Si-based devices [1]. Due to recent demands for
further miniaturization of devices, the precise
control of SiO2 film growth by Si oxidation is
required [2]. Although many studies on the
mechanisms of Si oxidation have been carried
0039-6028/$ - see front matter � 2005 Elsevier B.V. All rights reserv
doi:10.1016/j.susc.2005.01.001
* Corresponding author. Address: Department of Physics
Engineering, Mie University, 1515 Kamihama, Tsu, Mie 514-
8507, Japan. Tel.: +81 59 232 1211x3978; fax: +81 59 231 9726.
E-mail address: [email protected] (T. Akiyama).
out [3–16], its understanding on atomic scale still
remains controversial.
In ordinary dry oxidation (i.e., the oxidant isgas-phase O2), it is widely believed that Si oxida-
tion consists of a diffusion process of oxidant in
SiO2 and its reaction process at the SiO2/Si inter-
face: The diffusion and the interfacial reaction
dominate the growth of thick and thin oxides,
respectively [4]. For both processes a number of
experimental studies have been intensively carried
out [3–10], while theoretical investigations on theoxide formation have focused on diffusion mecha-
nisms in SiO2 [12] and oxygen absorption mecha-
nisms on Si clean surfaces which can be regarded
as an initial stage of oxidation [13,14]. The physics
ed.
(a)
(b) (c) (d)OPL
OPL
0.75
0.25
0.0
0.500.0
0.250.50
0.751.00
OSi
ODB
-0.25
ODB OSi
Si
O
Energy E
(dO, d
Si) (eV)
O (I)
(I)
(II)
Fig. 1. (a) Energy surface for O atom incorporation as a
function of dSi and dO, and geometries of (b) the initial state
OPL structure, (c) the transition state ODB structure, and (d) the
final OSi structure. The dSi and dO denote the distances from
the initial position of the incorporated O atom (O(I)) and of
the interfacial Si atom (Si(I)), to their final positions along the
vectors ~RO and ~RSi, respectively. Here, ~RO and ~RSi are
determined from the initial and final position of O(I) and Si(I),
respectively. The ODB structure corresponds to (dO,
dSi) = (0.25,0.49). For each grid-point of (dO, dSi), we obtain
E(dO, dSi) with the constraint that all the atoms except for O(I)
and Si(I) are fully relaxed. The dashed line on the energy surface
denotes the adiabatic path. The initial positions of Si(I) and O(I)
L66 T. Akiyama, H. Kageshima / Surface Science 576 (2005) L65–L70SU
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of the interfacial reaction such as reaction mecha-
nisms of oxygen at the interface is still uncertain.
In this letter, we perform total-energy electronic
structure calculations to clarify the reaction mech-
anisms of oxygen at the SiO2/Si(100) interface[17,18]. We here take account both of oxygen
atoms and molecules as reaction species. 1 From
calculated energies, we determine the form of oxy-
gen dominating the interfacial reaction, and inter-
pret the experimental data available.
First, we investigate the reaction mechanisms of
O atoms. From an extensive search for stable
geometries, we find that a peroxy linkage configu-ration in the form of an Si–O–O–Si bond is the
most stable atomic configuration in the SiO2 re-
gion. The energies with this configuration are
1.44–2.48 eV lower than those of the other config-
urations. 2 The exploration of the transition state
structures reveals that O atoms diffuse by jumping
the positions of the peroxy linkage with an energy
barrier of �1.0 eV. This jumping process consistsof switching [12] and twisting of the Si–O–O–Si
bond, indicating that O atoms near the interface
diffuse by the exchange of moving atoms with host
O atoms.
Fig. 1(a) shows the energy surface for O atom
incorporation, starting from the initial OPL struc-
ture with the peroxy linkage [Fig. 1(b)]. The energy
variation for O atom incorporation is a complexhypersurface in a multidimensional space [19,20].
In order to determine the reaction pathway in a
multidimensional space, we obtain the optimized
energies E(dO,dSi) by performing calculations in
which all the atoms except for the incorporated
O atom (O(I)) and the interfacial Si atom (Si(I))
are fully relaxed. Here, dO and dSi are the position
1 We here consider the oxidation by gas-phase O2 (dry
oxidation). Since the dissociation energy of gas-phase O2 (the
experimental value is 5.11 eV) is large enough, it is highly likely
that O2 molecules are dominantly incorporated into the oxide.
However, the possibility that O2 molecules dissociate near the
interface and each of them reacts with the Si substrate cannot
be completely eliminated.2 The energy of O atom without bonds with host atoms is
higher than that of the most stable structure with peroxy
linkage configuration by 2.48 eV. This assures that the initial
state structure for the interfacial reaction of O atoms is the
structure with peroxy linkage.
are also shown by dashed circles in (c) and (d). The O atom
bonded with O(I) in the OPL structure is labeled as O(II). The
host Si and O atoms are represented by white and gray circles,
respectively. Small white circles represent terminating H atoms.
of the incorporated O atom and that of the inter-facial Si atom, respectively. In the energetically
lowest adiabatic path shown by the dashed line
in Fig. 1(a), Si(I) first moves towards the SiO2 re-
gion. Through the transition state ODB structure
[Fig. 1(c)], O(I) intervenes in the nearby interfacial
Si–Si bond, resulting in the formation of a new Si–
Reaction coordinate (A.)0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
2.0
0.0
-2.0
-10.0
-8.0
-6.0
-4.0
Ene
rgy
(eV
)
(a)
(b)
(c) (d)
(e)
(f)
Fig. 2. Energy variation for incorporation of the O2 molecule.
Each plot is obtained from the geometry optimization where all
atoms except for O atoms of the O2 are fully relaxed: The O
atoms of the O2 are relaxed so that the center of O2 is fixed at
the artificially controlled position along the reaction coordinate
[14,19]. The reaction coordinate is defined as the vector
determined from the initial and final positions of the center of
the O2, where the final structure is determined by the extensive
search for stable structures of the O2 in the substrate. The zero
of the energy is set to the energy of the O2 molecule in the SiO2
region. Geometries represented by open symbols are shown in
Fig. 3.
T. Akiyama, H. Kageshima / Surface Science 576 (2005) L65–L70 L67
SURFA
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O–Si bond: The ODB structure becomes the final
OSi structure [Fig. 1(d)] by this O atom insertion.
From the energies of the adiabatic path, we find
that the energy barrier of the O atom incorpora-
tion is 0.9 eV.Analyses of wave functions clarify that the en-
ergy barrier corresponds to the dissociation of
the O–O bond and the formation of the Si–O–Si
bonds. The r-bonding orbital (with the 2pr char-
acter) between O(I) and another O atom [O(II) in
Fig. 1(b)] in the OPL structure is broken, and the
corresponding orbitals hybridize with the valence
band states of the Si substrate in the ODB struc-ture. They finally result in the r-bonding states
(hybridization of O-2p orbitals and Si-sp3 states)
of SiO2 which constitute the covalent character
of Si–O–Si bonds. Simultaneously, the 2sr and
2sr* orbitals between O(I) and O(II) become two
distinct 2s-like states in the ODB structure, showing
that the dissociation of the O–O bond occurs at
the ODB structure.Next, we investigate the mechanisms of O2
incorporation into the substrate taking into ac-
count the spin degree of freedom. In the SiO2 re-
gion, the O2 molecule in a spin-triplet state is
stable at the opening space of SiO2 with the O–O
bond almost parallel to the c axis. The length of
the O–O bond is 1.29 A and the incorporation en-
ergy of gas-phase O2 is 2.15 eV, comparable tothose of the O2 in bulk SiO2 [12]. Therefore, it is
expected that the microscopic mechanisms of the
diffusion of the O2 molecule from the bulk region
to this structure are similar to that of O2 in bulk
SiO2.
Fig. 2 shows the energy variation for the O2
incorporation into the Si substrate, starting from
the stable structure of O2 in the SiO2 region [Fig.3(a)]. Through the transition state structure [Fig.
3(b)], the O2 moves to the substrate with the
rotation of the O–O bond. This results in the for-
mation of the metastable structure with a peroxy-
linkage-like Si–O–O–Si configuration [Fig. 3(c)].
In the metastable structure, each of the interfacial
Si atoms simultaneously forms an Si–O bond with
each of the O2 molecule: Si(I) and Si(II) are bondedwith O(I) and O(II), respectively. The calculated en-
ergy barrier of 0.2 eV for O2 incorporation corre-
sponds to the transition between the initial and
the metastable structures. The cooperative reac-
tion of each O atom with each of the interfacial
Si atoms results in the appearance of the Si–O–
O–Si configuration.
From the metastable structure, O(II) intervenes
in the nearby interfacial Si–Si bond. Through an-other transition structure (not shown here) whose
energy is only 0.05 eV higher than that of the
metastable structure, a new Si–O–Si bond is
formed [Fig. 3(d)]. The dissociation of the O2 mol-
ecule occurs between this structure and the geom-
etry shown in Fig. 3(e). After the dissociation, O(I)
intervenes in the nearby interfacial Si–Si bond, and
another Si–O–Si bond is formed. This O insertionresults in the formation of the final structure [Fig.
3(f)], which is similar to the structure with two O
atoms incorporated [15].
The distribution of valence electrons in the tran-
sition state structure [Fig. 4(a)] clarifies that the
atomic process corresponding to the energy barrier
is the bond formation between O(I) and Si(I). From
analyses of wave functions, we find that thehybridization between the O-2p orbitals and the
(d)
(a) (b)
(c)
(e) (f)
Si(I)O(I)
O(II)
Si(II)
O(I)
Si(I)
Fig. 3. Geometries of O2 molecule near the interface. O atoms
of O2 are labeled as O(I) and O(II), and Si atoms forming weak
Si–O bonds are indicated by Si(I) and Si(II). The host Si and O
atoms are represented by white and gray circles, respectively.
1.0E-2 5.0E-4
-2.0E-3Si
O
Si
O O
O
O
O
(II)
(I)
2.0E-3
(a) (b) (c)
Fig. 4. Contour plots of: (a) valence electron density; (b) the
squared wave function of one of the O-2pr-like hybridized
states on a plane including Si(I) and O(I), in the transition state
structure shown in Fig. 3(b); (c) the difference between the
squared wave function of the O-2pr-like hybridized state in the
transition state structure and that of the 2pr orbital for gas-
phase O2, on a plane including O(I) and O(II), are also shown.
The difference is obtained by subtracting the wave function of
the 2pr orbital from the wave function of the hybridized state.
The values shown in figures are the contour spacing in units of
e/(a.u.)3.
3 These experimental results imply that molecular-type
oxygen diffuses toward the interface during oxidation.
L68 T. Akiyama, H. Kageshima / Surface Science 576 (2005) L65–L70SU
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valence band states of Si substrate constitutes this
bond. Fig. 4(b) shows the distribution of the wave
function corresponding to one of the hybridized
states. This state possesses a 2pr-like character.
However, the wave function has amplitudes
around Si(I). The simple difference between this
state and the 2pr orbitals of O2 [Fig. 4(c)] clearlyshows that the wave function is delocalized around
the O–O bond. Therefore, this state also possesses
the Si–O covalent character, indicating that the
transition state structure corresponds to the inter-
section between the energy surface of the O2 mol-
ecule in the SiO2 region and that of the Si–O–O–Si
configuration at the interface.
The reaction mechanisms of the O2 molecule re-vealed for the first time in the present calculations
are quite different from those of the O atom. It in-
volves the formation of the Si–O–O–Si configura-
tion, in addition to the dissociation of the O–O
bond and the formation of S–O–Si bonds. The en-
ergy barrier of O2 incorporation is determined by
the formation of the Si–O–O–Si configuration.
On the other hand, the energy barrier for the Oatom is dominated by the dissociation of r-bondsof the peroxy linkage and the formation of an Si–
O–Si bond. It should also be noted that the
appearance of Si–O–O–Si is the consequence of
cooperative reaction of each O atom of the O2 with
each of the interfacial Si atoms. The difference be-
tween the energy barrier of the O atom and that of
the O2 molecule is due to the difference of themicroscopic process that determines the energy
barrier.
The calculated energies at the interface and the
barriers for incorporation clearly show that O2
molecules are the dominant reaction species during
Si thermal oxidation, consistent with experimental
data obtained from secondary ion mass spectrom-
etry and medium energy ion scattering 3 [8,9]. Theenergy of the initial structure shown in Fig. 3(a) is
lower than that of the OPL structure with an en-
ergy gain of 1.0 eV per O2 molecule. Assuming
that the concentration of oxygen in the oxide re-
gion is described by the Boltzmann distribution,
this energy difference leads to the solubility of O2
molecules being at least 105 times that of O atoms
T. Akiyama, H. Kageshima / Surface Science 576 (2005) L65–L70 L69
SURFA
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at 1000 �C: The O2 molecules diffusing in the oxide
react directly with the substrate without dissocia-
tion. In addition, the energy barrier for O2
(0.2 eV) is lower than that for O atoms (0.9 eV).
Thus, the energy barrier for O atom incorporationby way of the dissociation of O2 molecule in the
SiO2 region of the interface (at least 1.9 eV) is lar-
ger than that for direct O2 incorporation. This as-
sures that O2 molecules are the dominant reaction
species even if the dynamics of reaction species is
taken into account. Furthermore, the effect of trip-
let–singlet conversion for O2 molecules unchanges
the reaction species. We also estimate the probabil-ity of triplet–singlet conversion exchange P from
the energy slopes shown in Fig. 2 based on the
Landau–Zener theory [21]. Around 800–1200 �C,the probability P is found to be �0.003. The trip-
let–singlet conversion narrows the channel of O2
incorporation [14], and results in the reduction of
the interfacial reaction rate. However, the oxide
growth rate by O2 incorporation approximatelyexpressed by the product of the solubility of O2
in SiO2 and the interfacial reaction rate [4] is still
higher than that of O atoms.
Finally, we comment on the experimentally re-
ported activation energies. The calculated energy
barrier for the O2 molecule (0.2 eV) seems to agree
well with the activation energy of 0.3 eV for ultra-
thin oxide obtained from scanning reflection elec-tron microscopy combined with Auger electron
spectroscopy [6]. However, it is lower than the
activation energies for ultrathin oxide obtained
from reflection difference spectroscopy (1.2 eV)
[7] and for oxide layers with a thickness of 10–
100 nm (1.76–2.00 eV) [4,5]. This implies that the
interfacial reaction process involves other mecha-
nisms or effects in addition to the oxygen insertioninto the Si–Si bonds at abrupt, flat, and relaxed
interfaces clarified in the present study. The effects
of interfacial roughness, accumulation of interfa-
cial strain and its release mechanisms, or effects
of polymorphism of amorphous SiO2 could be cru-
cial to the interfacial reaction. It is therefore of
importance to elucidate these mechanisms or ef-
fects in order to completely reveal the mechanismsof Si thermal oxidation, but this is beyond the
scope of the present work. One of the essential
mechanisms of the interfacial reaction, which does
not correspond to the previously consented sever-
ance of the interfacial Si–Si bonds but to the for-
mation of weak Si–O bonds, is revealed in the
present study.
In summary, we have presented first-principlescalculations that clarify the reaction mechanisms
of oxygen at the SiO2/Si interface. We have found
that O2 molecules around the interface are domi-
nantly incorporated into the Si substrate. We have
also found that the corporative reaction with the
interfacial Si atoms enables O2 molecules dissoci-
ate with low energy barrier. The hybridization of
the O-2p orbitals of the oxidant and the valenceband states of the Si substrate is the principal fac-
tor of the reaction.
Note added. Very recently, a dynamical study
for reaction of O2 molecules at SiO2/Si interface
was carried out by the first-principles molecular
dynamics [22].
Acknowledgement
We would like to thank Dr. M. Otani, Dr. M.
Uematsu, Prof. K. Shiraishi, and Prof. Y. Takah-
ashi for their discussions and comments. Calcula-
tion codes used in this work are based on Tokyo
Ab-initio Program Package (TAPP) which has
been developed by us. Computations were partlydone at RCCS (National Institutes of Natural Sci-
ences) and at ISSP (University of Tokyo).
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