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-

figurations with one Si self-interstitial (ISi) in the unit cell are 4.84, 4.71

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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224303-11 Takahashi, Yamasaki, and Kaneta J. Appl. Phys. 115, 224303 (2014)

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