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Molecular dynamics study of Si(100)-oxidation: SiO and Si emissions from Si/SiO2interfaces and their incorporation into SiO2Norihiko Takahashi, Takahiro Yamasaki, and Chioko Kaneta
Citation: Journal of Applied Physics 115, 224303 (2014); doi: 10.1063/1.4876911 View online: http://dx.doi.org/10.1063/1.4876911 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/115/22?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Effects of suboxide layers on the electronic properties of Si(100)/SiO2 interfaces: Atomistic multi-scale approach J. Appl. Phys. 113, 073705 (2013); 10.1063/1.4791706 Interfacial silicon oxide formation during oxygen annealing of Ta 2 O 5 thin films on Si: Oxygen isotope labeling J. Vac. Sci. Technol. A 18, 2522 (2000); 10.1116/1.1286717 Incorporation of N into Si/SiO 2 interfaces: Molecular orbital calculations to evaluate interface strain and heat ofreaction Appl. Phys. Lett. 75, 680 (1999); 10.1063/1.124480 Time dependence of the oxygen exchange O 2 SiO 2 at the SiO 2 – Si interface during dry thermal oxidation ofsilicon J. Appl. Phys. 86, 1153 (1999); 10.1063/1.370858 Monolayer incorporation of nitrogen at Si–SiO 2 interfaces: Interface characterization and electrical properties J. Vac. Sci. Technol. A 16, 356 (1998); 10.1116/1.581005
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Molecular dynamics study of Si(100)-oxidation: SiO and Si emissionsfrom Si/SiO2 interfaces and their incorporation into SiO2
Norihiko Takahashi, Takahiro Yamasaki,a) and Chioko KanetaFujitsu Laboratories Limited, 10-1 Morinosato-Wakamiya, Atsugi 243-0197, Japan
(Received 27 February 2014; accepted 4 May 2014; published online 10 June 2014)
Dynamics of Si(100)-oxidation processes at the Si/SiO2 interface and in the SiO2 region are
investigated focusing on SiO and Si emissions from the interface and the following incorporation
into the SiO2 and/or substrate. Classical molecular dynamics (MD) simulations with variable
charge interatomic potentials are performed to clarify these atomic processes. By incorporating
oxygen atoms, two-folded Si atoms are formed after structural relaxation at the interface and are
emitted as SiO molecules into SiO2. The energy barrier of the SiO emission is estimated to be
1.20 eV on the basis of the enthalpy change in an MD simulation. The emitted SiO molecule is
incorporated into the SiO2 network through a Si-O rebonding process with generating an oxygen
vacancy. The energy barrier of the SiO incorporation is estimated to be 0.79–0.81 eV. The
elementary process of oxygen vacancy diffusion leading to the complete SiO incorporation is also
simulated, and the energy barriers are found to be relatively small, 0.71–0.79 eV. The energy
changes of Si emissions into the substrate and SiO2 are estimated to be 2.97–7.81 eV, which are
larger than the energy barrier of the SiO emission. This result suggests that, at the ideally flat
Si/SiO2 interface, the SiO emission into the SiO2 region occurs prior to the Si emission, which is
consistent with previous theoretical and experimental studies. The above mentioned typical atomic
processes are successfully extracted from some (or one) of MD simulations among many trials in
which a statistical procedure is partly employed. Our results give a unified understanding of Si
oxidation processes from an atomistic point of view. VC 2014 AIP Publishing LLC.
[http://dx.doi.org/10.1063/1.4876911]
I. INTRODUCTION
Si oxidation is a very important process in the fabrication
of many Si devices, such as MOSFET (metal-oxide-semicon-
ductor field-effect transistor) and nanowire- and nanodot-
transistor devices, and is often referred to as a base of various
oxidations.1–6 As the oxidation proceeds, stress accumulates
at the interface because of the incorporation of oxygen atoms.
For further oxidation processes, this stress needs to be
released. One of the stress relaxation processes is Si emission
into the Si substrate or SiO2 region.7–11 SiO emission into the
SiO2 region is another probable process.10,12,13 In this process,
the emitted SiO molecules diffuse interstitially and become
incorporated in the SiO2 network,12 leading to the growth of
SiO2. Energetics of these Si and SiO emissions have been
investigated using static first-principles calculations.10
However, there have been no studies on the dynamics of SiO
and/or Si emissions using the first-principles methods because
of the great cost for performing the dynamical simulations.
On the other hand, although the classical molecular dynamics
(MD) simulations are adequate to investigate the dynamics,
there are difficulties to take into account the effect of charge
transfer which is important especially at the interface.
In this study, classical MD simulations with variable
charge interatomic potentials are applied to investigate a se-
ries of atomic processes in Si oxidation. We first focus on
the SiO emission at the Si(100)/SiO2 interface and the
following SiO incorporation into the SiO2 network. An ele-
mentary process of oxygen vacancy diffusion leading to the
complete SiO incorporation is also investigated. In addition to
this process, we discuss different types of processes leading to
defects14–17 in SiO2, such as E0 center and non-bridging oxy-
gen hole center. Next, we focus on the Si emission into the Si
substrate and SiO2 region. Finally, we discuss a unified view
to understand the Si oxidation by estimating the energy bar-
riers and/or energy changes in these processes.
II. CALCULATION METHOD
Here, we explain the variable charge method used in
this study. In an ideal Si/SiO2 system, a Si atom is bonded
with (i) four Si atoms in the Si region, (ii) four O atoms in
the SiO2 region, and (iii) two Si and two O atoms in the
interface region. Since the number of O atoms bonded to a Si
atom depends on the region, a net charge transfer induced by
the difference in the electronegativity between Si and O
atoms also depends on the region. Fixed charge MD methods
are inadequate for the systems in which Si atoms diffuse
from the Si region into the SiO2 region and vice versa. Even
if we can develop potential parameters with the charge trans-
fer effects, the application will be limited. On the other hand,
the charge equilibration (QEq) method developed by Rapp�eand Goddard,18 in which atomic charges are decided in every
MD step based on the configuration, is a natural way to study
the dynamics with atomic rebonding and/or diffusion proc-
esses in such hetero-interfacial systems.
a)Present address: National Institute for Materials Science, 1-2-1 Sengen,
Tsukuba 305-0047, Japan.
0021-8979/2014/115(22)/224303/11/$30.00 VC 2014 AIP Publishing LLC115, 224303-1
JOURNAL OF APPLIED PHYSICS 115, 224303 (2014)
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Kumagai et al.19 have developed variable charge intera-
tomic potentials in the framework of the QEq method for
Si/SiO2 systems. These potentials can describe covalent-ionic
mixed bond natures by adding the electrostatic and charge
transfer terms to Tersoff-type potentials.21 These potentials
used here are the same type as the COMB potential developed
by Shan et al.22 We use these potentials here. For the QEq
method, we have to evaluate the diatomic Coulomb integrals,
Jij, between all pairs of atoms in every MD step. Here, we
express them analytically using Slater-type 1s functions23 to
incorporate a shielding correction as follows:
Jij ¼1
Rij1� 1þ 11
8ðfiRijÞ þ
3
4ðfiRijÞ2 þ
1
6ðfiRijÞ3
� �e�2fiRij
� �(1)
for Si-Si and O-O, and
Jij ¼1
Rij1� 1
ðf2i � f2
j Þ2
1þ fiRij þ2f2
i
f2i � f2
j
!f4
j e�2fiRij
("
þ 1þ fjRij �2f2
j
f2i � f2
j
!f4
i e�2fjRij
)#(2)
for Si-O, where Rij is the interatomic distance between the i-th and j-th sites and fi is the Slater exponent of the i-th site.
We use fi¼ 1.2756 A�1 for Si atoms and 2.2422 A�1 for O
atoms, which we reoptimized to reproduce the charge distri-
bution in the Si/SiO2 system.19,20 The long range term of the
Coulomb integrals is solved by Ewald method. MD simula-
tions were performed using SCIGRESS MD-ME software.24
Lattice constants, densities, and bond lengths of crystal
Si and SiO2 were calculated using the potential parameters
and are shown in Tables I–III. The Si-O bond lengths in
SiO2 are slightly shorter than experimental values by about
3.5%, but other values in this work agree with the experi-
mental values to within 1.5%. Calculated atomic charges of
Si and O in the Si/SiO2 system (SiO2: a-quartz) are shown in
Fig. 1. The atomic charges of Si are almost zero in the Si
region (I), about þ0.7 in the Si/SiO2 interface (II), and about
þ1.4 in the SiO2 region (III), depending on the number of O
atoms bonded to the Si atom. The atomic charges of O in the
SiO2 region are about �0.7 (IV), and the absolute values are
half of the Si charges in the SiO2 region.
For energy barrier evaluations of elementary processes
of emission and incorporation of a SiO molecule and oxygen
vacancy diffusions, we use NTP ensemble MD simulations
and observe the enthalpy changes in the simulation trials. In
general, MD simulations under various conditions have to be
carried out to reveal the dynamics of the atomic processes.
This is because the motions of atoms vary based on the dis-
tribution of the initial atomic velocities even if the tempera-
ture is same, and the processes that occur in every simulation
are not completely the same. We successfully extracted the
typical events by carrying out 10–20 MD simulations for the
elementary processes of Si-O emission, Si-O incorporation,
and O vacancy diffusion, respectively. Each simulation was
done for 100 ps with various temperatures and initial atomic
velocities giving different Boltzmann distributions. Thus, the
total trial times for these phenomena are 1, 2, and 2 ns,
respectively. Supplemental static evaluations are also done,
and the results are compared with those from the MD
simulations.
III. RESULTS AND DISCUSSION
We examine the oxidation processes illustrated in
Fig. 2. In Sec. III A, we describe the dynamics of the SiO
FIG. 1. Si/SiO2 structure and charges of Si and O atoms obtained in our
calculations.
TABLE I. Lattice constants of Si and SiO2 (a-quartz) crystals.
Axes This work (A) exp. (A) D (%)
Si a 5.442 5.431a þ0.2
SiO2 a,b 4.898 4.916b �0.4
c 5.379 5.409b �0.6
aReference 25.bReference 26.
TABLE II. Densities of Si, crystal SiO2 (a-quartz), and amorphous SiO2.
This work (g/cm3) exp. (g/cm3) D (%)
Si 2.32 2.33a �0.4
SiO2 (crystal) 2.68 2.64b þ1.5
SiO2 (amorphous) 2.27 2.21c þ2.7
aReference 25.bReference 26.cReference 34.
TABLE III. Bond lengths of Si-Si in Si, Si-O in crystal SiO2 (a-quartz) and
amorphous SiO2. Si-O(s) and Si-O(l) denote short and long bonds in crystal
SiO2, respectively. An averaged value is shown for Si-O (amorphous) in this
work.
This work (A) exp. (A) D (%)
Si-Si 2.355 2.352a þ0.1
Si-O(s) 1.551 1.608b �3.5
Si-O(l) 1.554 1.611b �3.5
Si-O (amorphous) 1.593 1.620c �1.7
aReference 25.bReference 26.cReference 34.
224303-2 Takahashi, Yamasaki, and Kaneta J. Appl. Phys. 115, 224303 (2014)
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emission at the interface. We then describe the dynamics of
the SiO incorporation into the SiO2 network in Sec. III B and
the elementary processes of oxygen (oxygen vacancy) diffu-
sion accompanying the SiO incorporation in Sec. III C. In
Sec. III D, other possible emission processes of Si atoms
from the interface are investigated. Section III E gives a uni-
fied view for understanding the Si oxidation.
A. SiO emission at the Si/SiO2 interface
At a Si/SiO2 interface region, the stability of the SiO2
structure is different from that of bulk SiO2 due to the crystal
lattice of Si. A tridymite-type structure, which has been
observed experimentally,27 is one of the candidates of SiO2 at
the interface region. By the geometry-optimization of several
Si/SiO2 interface models using first-principles calculations,
the authors have found that the tridymite-type structure is the
most stable as a thin SiO2 layer on the Si(100) substrate.28,29
In the tridymite-type SiO2/Si interface model, extra O atoms
were introduced into Si dimers on the substrate surface befor
the optimization to eliminate dangling bonds due to the lattice
mismatch. In this study by classical MD simulations, the
above mentioned model structure is repeated twice in each
intefacial direction to make an unit cell of an initial structure
of the tridymite-type SiO2 layer on the Si(100) with a (4� 4)
surface. The unit cell, which contains 448 atoms, consists of
four SiO2 layers (corresponding to four completely oxidized
Si layers) and sixteen Si layers along the [100] direction. We
used the superlattice model. The volume of the unit cell and
internal coordinates of the atoms were reoptimized by the
classical molecular dynamics method. We have obtained a
unit cell of a¼ b¼ 1.546 and c¼ 3.332 nm.
Here, we assume that O atoms diffusing through SiO2
reach the interface and are introduced into feasible sites such
as Si-Si bond centers and/or bridging sites in the 1st Si layer.
Based on the results of previous investigations,11,15,30–33 we
introduced ten O atoms into the Si1L-Si2L bond centers and
Si1L-Si1L bridging sites (SiNL denotes a Si atom in the N-th
Si layer) at the Si(100)/SiO2 interface as shown in Fig. 3(a)
to prepare the initial configuration of the Si/SiO2 interface
structure being oxidized with accumulating the mechanical
stress. We then started an MD simulation at room tempera-
ture (25 �C) to relax the stress at the interface. The obtained
structure is shown in Fig. 3(b). Bridging O atoms (O1 and
O2) break the Si1L-Si2L bonds (Si31L-Si12L and Si41L-Si12L)
to change the four-fold coordinated Si2L (Si12L and Si22L)
into two-folded. These two-folded Si2L atoms become reac-
tive sites in the following oxidation steps.
Thus, we introduced two other O atoms (O3 and O4) in
the vicinity of these two-folded Si2L atoms (Fig. 4(a)) based
on the results of first-principles calculations.31 (A model of
isolated O atoms generated by dissociation of O2 molecule at
the interface is also shown in Fig. 4(b) for comparison.) We
then performed MD simulations for the configuration shown
in Fig. 4(a) under constant NTP ensembles with N¼ 460,
P¼ 1 atm, and various temperatures. To accelerate the reac-
tion process, the simulation was performed at a relatively
high temperature. Among the ten trials of the various tem-
perature conditions, SiO emission was observed in one trial
where the temperature was raised to 1400 �C from 25 �C in
the initial 2 ps. The snapshot at 20.3 ps is shown in Fig. 5. A
Si trimer was observed in the second and third Si layers
beneath the interface. It was formed after the formation of
the Si12L-O3 bond and the breaking of the Si12L-Si53L bond.
The formation of this Si trimer was found using
first-principles static energy calculations.31 After the Si
trimer formation, a SiO molecule (Si12L-O3) at the interface
moved toward the SiO2 region and was emitted into the SiO2
region, as shown in Fig. 6.
Figure 7 shows the change in enthalpy for this SiO emis-
sion process after the temperature was raised to 1400 �C. The
energy barrier of the Si12L-O3 molecule emission is 1.20 eV,
and after the emission, the system is stabilized by 1.35 eV at
37.3 ps in enthalpy from the initial configuration at 2 ps. This
SiO emission process has been predicted by both experimen-
tal12 and theoretical7,10,11,13 results. Our calculation success-
fully simulates the dynamics of this process.
We further estimated a static energy barrier of the
Si12L-O3 emission to compare with the value estimated from
the enthalpy change. Relative values of the static energies at
nine configurations in the Si-O emission process are plotted
on the graph in Fig. 7. The initial configuration, which is
before the Si-O emission, is at 0 ps, and the final one, after
the emission, is at 37.3 ps. We generated seven replicas dis-
tributed equidistantly between the two configurations. Each
replica is geometry-optimized under the condition of fixed
cell volume and a temperature of 0 K with the constraint that
the center of mass of the SiO is fixed in the z-direction,
which is perpendicular to the interface. The upper horizontal
axis in Fig. 7 is the z-coordinate of the center of mass of the
SiO relative to that of the initial configuration. The obtained
static energy barrier of the Si12L-O3 emission is 3.08 eV,
which is larger than the dynamic estimation (1.20 eV). In the
static energy calculation, the energy barrier is estimated
along a specific path between the initial and final configura-
tions under the condition of constant volume and 0 K. This
always gives a higher energy barrier than for the minimum
energy path, and in most cases, than that estimated by dy-
namical simulations, in which a wider search space is taken
into account.
FIG. 2. Atomistic model of the silicon oxidation processes with emission
and incorporation of SiO and oxygen vacancy diffusion. Si emission is also
depicted.
224303-3 Takahashi, Yamasaki, and Kaneta J. Appl. Phys. 115, 224303 (2014)
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After the emission of the Si12L-O3 molecule in the MD
simulation, as shown in Fig. 6, another SiO bond (Si22L-O4)
is formed at the interface. This bond is similar to the Si12L-O3
bond formed before its emission into the SiO2 region. We con-
tinued the MD simulation to t¼ 100 ps expecting the second
Si-O emission to occur, but the Si22L-O4 was not emitted.
Hence, we also estimated the energy barrier of the Si22L-O4
emission by calculating the static energies in a method similar
to the Si12L-O3 emission. The obtained energy barrier is
2.81 eV, which is comparable to that of the first Si12L-O3
emission estimated by the static calculations.
B. SiO incorporation into the amorphous SiO2
network
SiO molecules emitted from the Si/SiO2 interface may
diffuse through the SiO2 region. If the SiO molecules are
incorporated into the SiO2 network during the diffusion, the
SiO2 layer would grow thick12 being oxidized by penetrating
O atoms from the SiO2 surface. Thus, we investigated the
mechanism of the SiO molecule incorporation into the amor-
phous SiO2 network. The amorphous-like SiO2 structure was
prepared using a melt and quench method. A crystal SiO2
(a-quartz) model, which has 432 atoms in the unit cell, was
melted by raising the temperature to 2727 �C, and quenched
to a room temperature of 25 �C at the rate of 10 �C/ps. The
structural properties of the obtained amorphous SiO2 model
are listed in Tables II and III. The density of our amorphous
SiO2 model is larger than the experimental value. This is
mainly because of the shorter averaged Si-O bond length.
We put one SiO molecule in the unit cell of the obtained
amorphous SiO2 model, where no atoms of the SiO2 network
bond with the SiO. Twenty MD simulation trials were per-
formed under constant NTP conditions with various tempera-
tures and initial atomic velocities. SiO incorporation
occurred in one (T¼ 1400 �C, P¼ 1 atm) of the trials.
The incorporation process through the simulation trial is
decomposed into three steps (Figs. 8(a)–8(c)). In the first step,
a Si-O bond (Si1-O1) of the SiO2 network elongates from
1.62 A (at t¼ 0 ps) to 1.77 A (at t¼ 2 ps) due to thermal vibra-
tion (Fig. 8(a)). In the second step, the SiO molecule moves to
the position between the elongated Si-O bond, bonding with
the Si1 and O1 atoms (Fig. 8(b)). The Si3 atom of the SiO
molecule is two-fold coordinated in this configuration. In the
third step, another Si-O bond (Si2-O2) is broken, and the O2
atom is rebonded with the Si3 atom (Fig. 8(c)). The SiO mole-
cule has almost been incorporated into the SiO2 network by
this step, though the Si2 and Si3 atoms are three-folded, and
there is an oxygen vacancy site between them. Oxygen atom
diffusion to the vacancy site will complete the network con-
nection around the incorporated SiO molecule (Fig. 8(d)). In
our simulation trials, such processes did not occur because of
FIG. 3. (a) An initial structure of
Si/SiO2 with introduced ten O atoms.
Eight O atoms are at bond centers
between the first and second layer Si
atoms and two O atoms are at bridging
sites in the first Si layer. The open and
closed circles denote Si and O atoms,
respectively. NL (N¼ 1, 2, …) denotes
an N-th Si layer around the interface.
(011), (100), and (0�11) cross sections
are shown. (b) A snapshot at 5 ps,
when two Si2L atoms (Si12L and Si22L)
became two-folded.
224303-4 Takahashi, Yamasaki, and Kaneta J. Appl. Phys. 115, 224303 (2014)
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the limitation of the simulation time. The elementary process
of oxygen (oxygen vacancy) diffusion from Figs. 8(c) to 8(d)
will be examined with another set of simulations in Sec. III C.
Figure 9 shows the change in enthalpy for SiO incorpo-
ration into the SiO2 network. Energy barriers around t¼ 2
and 11 ps are due to the bond breaking of Si1-O1 and
Si2-O2, respectively, and their heights are almost the same
(0.79 eV and 0.81 eV). The configuration shown in Fig. 8(c)
is more stable than the initial one by 2.42 eV.
We estimated the static energy barriers of the SiO incor-
poration through the three steps (Figs. 8(a)–8(c)) again. First,
we picked up four representative configurations at 0.0, 2.0
(Fig. 8(a)), 10.0 (Fig. 8(b)), and 12.0 ps (Fig. 8(c)). These
configurations were geometry-optimized by fixing the center
of mass of the SiO molecule after adjusting the volume to
that of 0 ps. Those optimized configurations were set as the
end points for replicas. We generated two, six, and one repli-
ca(s), respectively, in the periods of 0–2, 2–10, and 10–12 ps
and optimized their geometries by fixing the center of mass
position of the SiO under the condition of T¼ 0 K. Relative
values of the static energies of these replicas are plotted on
the graph in Fig. 9. The upper horizontal axis value in Fig. 9
FIG. 4. (a) The initial configuration
produced from the structure shown in
Fig. 3(b). Two additional O atoms (O3
and O4) are also shown. They are
introduced in the vicinity of two-
folded Si12L and Si22L, respectively.
(b) A model of isolated O atoms at the
interface is shown for comparison.
FIG. 5. Snapshot of Si/SiO2 at 20.3 ps.FIG. 6. Snapshot of Si/SiO2 at 37.3 ps. A SiO molecule (Si12L-O3) moved
toward the SiO2 region at around 23–25 ps.
224303-5 Takahashi, Yamasaki, and Kaneta J. Appl. Phys. 115, 224303 (2014)
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is a summation of distances between two neighboring repli-
cas, which is defined as
di ¼Xi�1
j¼0
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXN
p¼1
jrðjÞp � rðjþ1Þp j2
vuut ; (3)
where rp(j) is the position vector of p-th atom in j-th replica.
The calculated energy barriers are 1.58 and 0.87 eV, which
are larger than 0.79 and 0.81 eV obtained by the MD simula-
tion. The reason for the energy barrier difference between
the MD simulation and the static energy calculation is the
same as the SiO emission case explained in the previous
section.
C. Elementary process of oxygen vacancy diffusion inamorphous SiO2 network
In order to investigate the oxygen (oxygen vacancy) dif-
fusion process to complete the stoichiometric SiO2 network
after the SiO incorporation shown in Fig. 8(c), we prepared a
model structure, which has one oxygen vacancy in the stoi-
chiometric amorphous SiO2 unit cell explained in the previ-
ous section. We performed twenty MD simulations under
constant NTP conditions with various temperatures and ini-
tial atomic velocities. In one trial under the condition of
T¼ 1400 �C and P¼ 1 atm, we observed an elementary pro-
cess of the oxygen vacancy diffusion accompanying recon-
nection of the network, which is shown schematically in Fig.
10. The initial configuration (Fig. 10(a)) has an oxygen va-
cancy between Si2 and Si3. In the first step, the two folded
O4 atom between Si2 and Si4 moves to a three-fold coordi-
nated site (Fig. 10(b)) where the O4 is bonded to Si3 and Si4
with a weak bond to Si2. In the second step, the O4 atom
FIG. 7. Change in enthalpy for the SiO emission at the Si/SiO2 interface
(thick solid line). Energy values by static calculations are also plotted (open
circles). The upper horizontal axis is the z-coordinate value of the center of
mass of the SiO relative to that of the initial configuration. A dotted line is
between corresponding points of MD and static calculations.
FIG. 8. SiO molecule incorporation into the SiO2 network. (a) 2 ps, (b) 10
ps, (c) 12 ps, and (d) a predicted step to complete the SiO2 network around
the incorporated SiO molecule after oxygen vacancy diffusion. An open
square denotes the oxygen vacancy site.
FIG. 9. Change in enthalpy for the SiO incorporation into the SiO2 network
(closed plots). Energy values by static calculations are also plotted (open
circles). The upper horizontal axis is summation of distances between two
neighboring replicas for static calculations. Dotted lines are between corre-
sponding points of MD and static calculations.
FIG. 10. Elementary processes of oxygen vacancy diffusion in the SiO2 net-
work. (a) 0 ps, (b) 7.8 ps, (c) 10.0 ps, (d) 18.6 ps, and (e) 23.0 ps. An open
square denotes the oxygen vacancy site.
224303-6 Takahashi, Yamasaki, and Kaneta J. Appl. Phys. 115, 224303 (2014)
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moves to the upper right in Fig. 10(c), and the Si2-O4 bond
is broken. Both Si2 and O4 are two-fold coordinated in this
configuration. In the third step, O4 moves to almost the cen-
ter of the triangle formed with Si2, Si3, and Si4 to become
three-fold coordinated again (Fig. 10(d)). This configuration
is similar to that of Fig. 10(b). In the final step, O4 moves
downward, and the Si4-O4 bond is broken (Fig. 10(e)). The
oxygen vacancy transferred to the site between Si2 and Si4.
Thus, after the vibration around the center of the triangle
formed with Si2, Si3, and Si4, the O4 atom diffuses into the
neighboring oxygen vacancy site by way of the three-fold
coordinated state (O� Si3).
Figure 11 shows the change of the enthalpy during this
elementary process of oxygen vacancy diffusion. There are
two energy barriers of 0.79 eV (t¼ 7.8 ps) and 0.71 eV
(t¼ 18.6 ps). They correspond to the unstable configurations
of Figs. 10(b) and 10(d), in which the O4 is three-folded.
The final configuration of Fig. 10(e) is slightly more stable
than the initial configuration of Fig. 10(a) by 0.13 eV.
The energy barriers in the elementary process of diffusion
in Fig. 10 have also been estimated by calculating the static
energies through the divided four periods. The recipe to evalu-
ate the energy barriers is the same as those explained in previ-
ous sections. The picked up representative configurations are
shown in Fig. 10 and are at 0.0, 7.8, 10.0, 18.6, and 23.0 ps in
Fig. 11. The position of O4 is fixed in each geometry-
optimization process. The number of generated replicas in
each of the periods is three. Relative values of the static ener-
gies of these replicas are plotted on the graph in Fig. 11. The
calculated energy barriers are 1.19 eV and 0.94 eV, which are
larger by about 0.40 eV and 0.23 eV, respectively, than those
obtained by the MD simulation. Uematsu et al.7,8 estimated
an energy barrier of 1.64 eV for oxygen diffusion in the SiO2
network using the diffusion equations based on the Si emis-
sion model. Their energy barrier is an effective global value,
while our values of 0.79 eV and 0.71 eV correspond to a local
hopping to neighboring sites by way of an O� Si3 state.
Longer time simulations in various network configurations
will give the effective global barrier.
In addition to this elementary process of oxygen va-
cancy diffusion, we found, in another trial among the twenty
MD simulations, the generation of a pair of a Si dangling
bond and an O dangling bond (Non-Bridging Oxygen, NBO
shown in Fig. 12) due to the vibrational elongation of the Si-
O bond from 1.67 A (at t¼ 0 ps) to 1.90 A (at t¼ 4.8 ps). The
O atom of this elongated Si-O bond is the second nearest
neighbor of the introduced oxygen vacancy. The Si dangling
bond transferred from downward to upward on the identical
Si atom, while the O dangling bond (NBO) does not move
(Fig. 12). The energy barrier of this motion is 2.52 eV, which
is larger than those in the case of oxygen vacancy described
above. The pair of Si and O dangling bonds is equivalent to
the pair of three-folded Si and one-folded O atoms. Such
three-folded Si and one-folded O atoms move independently,
and they could become an E0 center35,36 and Non-Bridging
Oxygen Hole Center (NBOHC)37–39 by hole trapping, which
lead to degradation of devices.
D. Si emission into the substrate and the SiO2 region
We discuss here what occurs after the Si atoms are emit-
ted from the Si/SiO2 interfacial region. The emitted Si atoms
may diffuse into the substrate as Si self-interstitials and may
form the oxidation-induced-stacking-faults.40–44 They may
also be emitted to the SiO2 region, and diffuse to the surface
or are involved in the SiO2 network. If one of the Si atoms
encounters an oxygen atom that is traveling in the SiO2 net-
work, a SiO molecule will be formed and it will also diffuse
or be incorporated into the SiO2 network.
We first calculated the energy changes in processes
when the two-folded Si atom at the interface (Si22L shown in
Fig. 3(b)) is emitted and moves to a self-interstitial site in
the substrate. It is noted here that two O atoms (O3 and O4
in Fig. 4(a)) introduced in the simulation of the SiO emission
were not introduced in the following Si emission processes:
Almost all the interfacial stress originates from ten O atoms
introduced into the Si1L-Si2L bond centers and Si1L-Si1L
bridging sites. The root-mean-square displacement of Si1L-4L
atoms before and after the incorporation of the O3 and O4
was estimated to be 0.083 A, which is so small that the stress
from the O3 and O4 is negligible.45 Thus, the interfacial
FIG. 11. Change in enthalpy during the elementary process of oxygen va-
cancy diffusion in the SiO2 network (closed plots). Energy values by static
calculations are also plotted (open circles). The upper horizontal axis is a
summation of the distances between two neighboring replicas for static cal-
culations. Dotted lines are between corresponding points of MD and static
calculations.
FIG. 12. A pair of a Si dangling bond and an O dangling bond (non-bridging
oxygen) due to the elongation of the Si-O bond. The Si dangling bond trans-
ferred from downward to upward in the same Si atom by a transition
between two puckered structures. An open square denotes the introduced ox-
ygen vacancy.
224303-7 Takahashi, Yamasaki, and Kaneta J. Appl. Phys. 115, 224303 (2014)
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stress before the Si emission is almost equal to that before
the SiO emission. We consider the three types of interstitial
sites shown in Fig. 13, i.e., (a) S1 (Split-h110i), (b) H1
(Hexagonal site), and (c) T1 (Tetrahedral site). Energy
changes after the geometry optimizations are 2.97, 3.06, and
3.65 eV for S1, H1, and T1, respectively (Table IV). In all
cases, a Si trimer (1st Si trimer shown in Fig. 13(a)) is
formed at the interface, eliminating one of the two dangling
bonds generated after the removal of the two-folded Si atom.
Another two-folded Si atom remains at the interface (Si12L
shown in Fig. 3(b)). We then removed this atom and put it in
one of the other self-interstitial sites. Assuming that the type
of the second self-interstitial is the same as the first one, it is
put as far as possible from the first one in the same x-y plane
within the restriction of the 4 � 4 periodicity. The energy
changes of S2, H2, and T2 (Fig. 13) after geometry optimiza-
tions are 2.72, 2.50, and 2.98 eV, respectively (Table IV).
After the removal of the second interfacial Si atom, another
Si trimer (2nd Si trimer shown in Fig. 13(a)) is formed at the
interface, eliminating all of the dangling bonds at the inter-
face in the 4 � 4 periodicity, while a dangling bond remains
after the removal of the first one. Therefore, the energy
change of S2 (H2, T2) is reduced compared to that of S1
(H1, T1). We also estimated the formation energies of S, H,
FIG. 13. Si self-interstitials in the
Si/SiO2 system. (a) Split-h110i (S), (b)
hexagonal (H), and (c) tetrahedral (T)
configurations. For S, H, and T config-
urations, Si self-interstitials formed by
1st Si (denoted by open triangles) and
2nd Si (denoted by filled triangles) are
shown. For S configurations, the Si
atoms originated from lattice sites are
shown by arrows. Differences between
X1 and X2 (X¼S, H, T) configura-
tions are explained in the text. 1st and
2nd Si trimers are formed in S, H, and
T configurations.
TABLE IV. Formation energies (eV) of Si self-interstitials formed by the
1st Si (S1, H1, and T1) and the 2nd Si (S2, H2, and T2) in the Si/SiO2 sys-
tem. Energy values for the Si self-interstitials in the bulk Si structure are
also shown. In the bulk Si, the energy difference between S and H configura-
tions is small, and the T configuration is less stable than the S and H configu-
rations, which are qualitatively consistent with the previous studies by the
first-principles calculations.a,b
Si/SiO2 Bulk Si
1st 2nd
Split-h110i (S) 2.97 2.72 4.84 3.31a 2.94b
Hexagonal (H) 3.06 2.50 4.71 3.31a 2.92b
Tetrahedral (T) 3.65 2.98 5.47 3.43a 3.25b
aReference 46.bReference 47. FIG. 14. Possible sites, A, B, and C, for Si interstitials in SiO2.
224303-8 Takahashi, Yamasaki, and Kaneta J. Appl. Phys. 115, 224303 (2014)
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and T in a perfect Si crystal. The obtained values are larger
than those in Si/SiO2 by 5.35–5.57 eV.48 This indicates that
the two-folded Si atom at the interface is emitted more pref-
erentially than a four-folded Si atom in the bulk Si.
We next estimated the energy changes in cases when the
two-folded interfacial Si atom (Si22L shown in Fig. 3(b)) is
emitted to the SiO2 region and moves to three possible sites,
A, B, and C, shown in Fig. 14. Through structural relaxations,
each of the Si atoms in the A and B sites has moved to make
a bond with one of the surrounding O atoms, while the Si
atom in the C site stays in almost the same position as the ini-
tial one and makes no bonds. The calculated energy changes
are 3.69, 5.18, and 7.81 eV for A, B, and C, which are larger
than those of Si self-interstitials in the substrate (2.97, 3.06,
and 3.65 eV for S1, H1, and T1). These results suggest that
the Si emission occurs more preferentially into the substrate
than into the SiO2 region at the ideal Si/SiO2 interface.
E. A unified view of Si oxidation
Both SiO and Si emission processes can occur at the
interface during the Si oxidation. Two-folded Si atoms are
easily generated to release the accumulated strain at the
interface. Such Si atoms can be emitted as SiO molecules or
as atomic Si. The emitted SiO molecules can diffuse into the
SiO2 region (case 1). The emitted Si atoms can go either into
the substrate (case 2) or into SiO2 (case 3). For case 1, we
examined the whole process until the emitted SiO molecule
is completely incorporated into the SiO2 network. The whole
process can be divided into three steps: (i) the emission of
the SiO molecule, (ii) incorporation of the SiO molecule into
the SiO2 network with a deficiency of an O atom (O va-
cancy) near the incorporated molecule, and (iii) disappear-
ance of the O vacancy by diffusion. We estimated the barrier
energies of those three steps in Secs. III A–III C. For cases 2
and 3, we estimated in Sec. III D the energy changes of the
FIG. 15. Energy change of the oxidation processes with the SiO emission. Energy values are shown for the configurations corresponding to (a) the ideal
Si/SiO2 with no dangling bonds (E0) and six O2 molecules before the incorporation into the interface, (b) Fig. 4(b) (E(Si/10O/SiO2þ 2O)) i.e., the Si/SiO2 with
incorporated 10 oxygen atoms shown in Fig. 3(b) (E(Si/10O/SiO2)) with two isolated oxygen atoms at the interface, (c) Fig. 4(a) (E(Si/12O/SiO2)), (d) Fig. 6,
where a SiO molecule is emitted into the SiO2 region (E(Si/SiO2þSiO)), (e) Fig. 8(c), where the emitted SiO molecule is incorporated into the SiO2 network
with a neighboring oxygen vacancy (E(þVO)), and (f) the emitted SiO molecule completely incorporated into the SiO2 network without no oxygen vacancy
in SiO2 (E(Si/SiO2þSiO2)). Energy values are relative to that for the configuration (b). In (b)0, the energy value corresponding to Fig. 3(b) (E(Si/10O/SiO2))
with an O2 molecule in vacuum is shown for comparison.
FIG. 16. Energy changes of the oxida-
tion processes with the Si emissions
into the substrate and SiO2. Energy
values are shown for the configurations
corresponding to (a) the ideal Si/SiO2
with no dangling bonds (E0) and five
O2 molecules before incorporation into
the interface, (b) the Si/SiO2 with
incorporated 10 oxygen atoms (five ox-
ygen molecules), shown in Fig. 3(b)
(E(Si/10O/SiO2)), (g) the left part of
Fig. 13, where the Si self-interstitials
(S1, H1, and T1) are formed (E(S1),
E(H1), and E(T1)), (h) the right part of
Fig. 13, where two Si self-interstitials
(S2, H2, and T2) are formed (E(S2),
E(H2), and E(T2)), and (i) Fig. 14,
where a two-folded Si atom is emitted
to the SiO2 region (E(A), E(B), and
E(C)). Energy values are relative to
that for the configuration (b).
224303-9 Takahashi, Yamasaki, and Kaneta J. Appl. Phys. 115, 224303 (2014)
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Si emitted into the substrate and into SiO2. Assuming that
the emitted SiO (case 1) is completely incorporated into the
SiO2 network, we can estimate the energy change from the
initial to final configurations. The energy gain is 19.48 eV
per oxygen molecule, which is almost comparable to the co-
hesive energy for the reaction of Si(crystal)þO2(molecule)
! SiO2(crystal) (21.48 eV).49,50 The energy discrepancy
between them (2.00 eV) originates from the remaining strain
at the Si/SiO2 interface where the Si trimer is formed and/or
the difference between interfacial and bulk SiO2 structures.
An energy change of the SiO emission (case 1) is shown
in Fig. 15, and those of the Si emissions into the substrate
(case 2) and into SiO2 (case 3) are shown in Fig. 16. The
energy barrier of the SiO emission is 1.20 eV, as described in
Sec. III A, while that of the Si emission is speculated to be
larger than 2.97 eV because the formation energies of the Si
self-interstitials are 2.97–3.65 eV (S1, H1, and T1) and the
energy changes of the Si emission into the SiO2 region are
3.69–7.81 eV (A, B, and C) as described in Sec. III D. This
result suggests that the SiO molecule, rather than the atomic
Si, can be the dominant form of the emitted Si atom at the
abrupt Si/SiO2 interface, which is consistent with previous
first-principles calculations.10 Yamabe et al.51,52 have exper-
imentally shown that the roughness growth of the SiO2 sur-
face is caused by reoxidation of the SiO molecule emitted
from the Si/SiO2 interface: When SiO2 is thin, the emitted
SiO molecule diffusing through SiO2 reaches the surface and
is reoxidized there, which results in an increase in the surface
roughness. As SiO2 becomes thicker, the roughness growth
is saturated because the emitted SiO molecules are incorpo-
rated into the SiO2 network and reoxidized there before
reaching the surface. Atomistic mechanisms of these phe-
nomena can be explained consistently by our results.
IV. CONCLUSIONS
We investigated the dynamics and mechanisms of Si ox-
idation processes through SiO and Si emissions from Si/SiO2
interfaces and the following incorporations into SiO2.
Focusing on two-folded Si atoms formed at the interface due
to the incorporation of oxygen atoms, the emission processes
of these atoms were investigated using MD and static energy
calculations. The energy barrier of the SiO emission is esti-
mated to be 1.20 eV. We also investigated the mechanism of
the SiO incorporation into the SiO2 network and the follow-
ing oxygen vacancy diffusion by simulating the elementary
process. The obtained energy barriers of these processes are
0.79–0.81 eV and 0.71–0.79 eV. During the investigation of
the elementary process of oxygen vacancy diffusion, we
found the possibility of the embryos of NBO and NBOHC
being thermally generated. We estimated the energy changes
of Si emissions into the substrate and SiO2 region. The
obtained values are 2.97–7.81 eV, which are larger than the
energy barrier of the SiO emission. These results suggest
that the SiO emission into the SiO2 region occurs prior to the
Si emission at the ideally flat Si/SiO2 interface, which is con-
sistent with previous theoretical and experimental stud-
ies.10,51,52 We successfully extracted these atomic processes
and revealed their dynamics by carrying out MD simulations
in which statistical procedure was partly employed with
varying initial atomic velocities by giving different
Boltzmann distributions. Our results give an atomistic pic-
ture of the behavior of the Si species emitted from the
Si/SiO2 interface during Si oxidation, leading to a unified
understanding of Si oxidation processes.
ACKNOWLEDGMENTS
We thank Dr. Tomohisa Kumagai for his helpful com-
ments on the variable charge potential method.
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and tetrahedral (T) configurations in a bulk Si using the cubic unit cell that
contains 1,000 Si atoms. Formation energies obtained for S, H, and T con-
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and 5.47 eV, respectively (Table IV) and that of a Si vacancy (VSi) is
3.70 eV. The sums of ISi and VSi are 8.54, 8.41, and 9.17 eV for the S, H,
and T.49In the oxidation processes with the SiO emission (Fig. 15), the total
energy gain between (a) initial and (f) final configurations is 102.32 � (�6.41)
¼ 108.73 eV. The energy gain between the ideal Si/SiO2 with five O2 mol-
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the energy gain for the Si oxidation by the two oxygen atoms introduced
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other is bound with interface Si.) On the other hand, the cohesive energy
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224303-11 Takahashi, Yamasaki, and Kaneta J. Appl. Phys. 115, 224303 (2014)
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