The reaction of O2 with Al(1 1 0): A medium energy ion scattering study of nano-scale oxidation

Article abstract of DOI:10.1016/j.susc.2004.01.019

We have used medium energy ion scattering to study oxygen transport and oxidation kinetics of Al(110) at elevated temperatures in dry oxygen. Oxidation results in the formation of a stable stoichiometric Al₂O₃ layer with fairly abrupt interfaces. The time dependence of the film growth follows inverse logarithmic law, in agreement with the Cabrera-Mott (field-assisted) oxidation mechanism. The dependence of the growth rate on pressure is parabolic. Microscopic details on oxidation mechanism are studied by re-oxidizing a thin oxide layer with isotopically labeled oxygen. The depth profiling of oxygen traces in the oxide shows that oxygen ions are mobile species transported via migration of oxide network defects. This migration across the film is the rate-limiting step controlling oxidation.

Full text of DOI:10.1016/j.susc.2004.01.019

Surface Science 552 (2004) 199–214
www.elsevier.com/locate/susc
The reaction of O2 with Al(1 1 0): a medium energy
ion scattering study of nano-scale oxidation
a,
a
b
D. Starodub *, T. Gustafsson , E. Garfunkel
a
Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ08854-8019, USA
b
Department of Chemistry, Rutgers University, Piscataway, NJ08854-8087, USA
Received 16 October 2003; accepted for publication 15 January 2004
Abstract
We have used medium energy ion scattering to study oxygen transport and oxidation kinetics of Al(1 1 0) at elevated
temperatures in dry oxygen. Oxidation results in the formation of a stable stoichiometric Al2O3 layer with fairly abrupt
interfaces. The time dependence of the film growth follows inverse logarithmic law, in agreement with the Cabrera–
Mott (field-assisted) oxidation mechanism. The dependence of the growth rate on pressure is parabolic. Microscopic
details on oxidation mechanism are studied by re-oxidizing a thin oxide layer with isotopically labeled oxygen. The
depth profiling of oxygen traces in the oxide shows that oxygen ions are mobile species transported via migration of
oxide network defects. This migration across the film is the rate-limiting step controlling oxidation.
ꢀ 2004 Elsevier B.V. All rights reserved.
Keywords: Medium energy ion scattering (MEIS); Oxidation; Aluminum
1. Introduction
crucial role of the electric field and the ionic nature
of material transport in this process are well
established experimentally, in particular, for alu-
minum oxide. Negative surface bias with respect to
the substrate is shown to enhance oxidation, while
positive bias reduces the oxidation rate [2]. The
growth rate can also be accelerated by electron
bombardment [3,4], establishing a larger electric
field due to the increased charge on the surface.
The effect of the electric field on the oxidation
kinetics is supported by faster growth in ozone
compared to in oxygen [5], which can be related to
the higher electrostatic potential across the film
because of the larger electron affinity of ozone.
Information about the electric field across the
oxide film produced by the deposition of high
electron affinity species (Au, O3, NO2, Cl2) or
It is generally accepted that the growth of ultra-
ꢀ
thin (<30 A) metal oxide films is described by the
Cabrera–Mott oxidation mechanism [1]. In this
model, electrons tunnel freely from a metal to an
adsorbed oxygen atom through a dielectric film
in order to equalize the electrochemical potential.
This creates an electric field across the film, which
in turn makes possible atomic transport to the
interface where the oxidation reaction occurs. The
* Corresponding author. Tel.: +1-732-445-3926; fax: +1-732-
445-4991.
E-mail address: starodub@physics.rutgers.edu (D. Staro-
dub).
0039-6028/$ - see front matter ꢀ 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.susc.2004.01.019

200
D. Starodub et al. / Surface Science 552 (2004) 199–214
electron bombardment has been derived from the
change in the energy position and shape of the
oxidic Al3þ 2p peak in the X-ray photoemission
spectra [6–8]. Although most previous workers
agree that field-enhanced diffusion is real, the de-
tails of the atomic transport across aluminum
oxide remain a subject of controversy. Most
studies on aluminum oxidation have been pri-
marily concerned with the growth kinetics, which
alone does not yield an unambiguous conclusion
about the oxidation mechanism. Further insight
can be obtained by tracing the evolution of marker
species [9] (inert atoms or metal/oxygen atoms)
during oxidation. Results are scarce in the oxide
thickness range of interest, since few experimental
techniques are capable of providing sufficient
depth resolution for films several nm thick. Fi-
nally, aluminum oxidation is slow due to the low
concentration and mobility of defects (which
facilitate material transport across the film) and
thus it is difficult to follow the precise mechanism.
In the original formulation of Cabrera and
Mott [1] the migrating species is a metal intersti-
tial, injected at the oxide–metal interface. Later,
the possibility of surface-injected oxygen transport
was proposed [10], as well as vacancy transport,
place exchange, etc. Generally it is assumed that
oxide morphology (phase and crystallinity) and
bond strength determine the transport mechanism
[11]. Oxides with strong bonds (such as SiO2),
which form random open networks with a high
degree of short range order, are more permeable to
larger anions, while in compact oxides with weak
bonds the transport is provided by the smaller
cations. Aluminum oxide occupies an intermediate
position in the bond strength hierarchy. Therefore
aluminum ions, oxygen ions, or some combination
of the two have been suggested as the mobile
species in Al2O3. The nature of migrating species
may also vary for different oxidation conditions,
which affect the defect structure of the oxide. For
example, Al anodization studies [12,13] demon-
strate a strong dependence of the metal to oxygen
transport ratio on electrolyte type and anodization
current. In the case of dry oxygen oxidation, the
oxygen vacancy concentration in the oxide net-
work can be varied by changing the growth con-
ditions [6]. The rate of oxidation was found to be
higher for an oxide enriched in oxygen vacancies,
i.e. with a low oxygen to aluminum stoichiometric
ratio. The mobile species in such an oxide was
likely oxygen atoms. However, the transport
mechanism may well be different for stoichiometric
aluminum oxide. Studies of the growth of crys-
talline oxide islands beneath an amorphous oxide
film [14] during oxidation above 620 K suggest
oxygen permeation through this film. On the other
hand, interface incorporated Al interstitials [2,15]
and surface incorporated Al vacancies [16] have
also been proposed as migrating species. Ionic
transport can be greatly modified by the presence
of extended defects, such as dislocations and grain
boundaries in crystalline oxides or channels in
amorphous oxides. In many cases water vapor was
used as oxidant [3,16,17]. Though such oxidation
is important from a practical point of view, inter-
pretation of the data becomes more complicated,
as hydroxyl groups, incorporated into the oxide,
modify its defect structure and therefore affect the
transport mechanism [18].
In this paper we address the microscopic details
of the initial oxidation by a combined study of the
kinetic and microscopic processes in the simplest
case to analyze, namely thermal oxidation of an
aluminum single crystal in molecular (dry) oxygen.
At moderate temperatures (<600 K), oxidation
ꢀ
results in the growth of a thin (<30 A) [19]
amorphous film. At higher temperatures and
thickness there is a tendency for the film to crys-
tallize [20] into c-Al2O3, potentially involving new
transport routes, such as crystalline grain bound-
aries. Thermodynamic calculations [21] show that
crystallization (of an amorphous oxide overlayer)
is less likely to occur on Al(1 1 0) relative to the
other low index surfaces.
2. Experimental
2.1. Experimental technique
We have used medium energy ion scattering
(MEIS) to provide a quantitative depth-resolved
compositional analysis of the film structure. The
strength of MEISis that it is a well established,
quantitative technique [22], with a depth resolu-

D. Starodub et al. / Surface Science 552 (2004) 199–214
201
tion in the near surface region significantly better
than 1 nm. The measurements have been per-
formed in a UHV analytical chamber with a base
pressure of 1 · 10À10 Torr, in conjunction with a
400 keV ion accelerator. Collection and energy/
angle separation of the scattered ions is performed
by a high-resolution toroidal electrostatic energy
analyzer [23] equipped with micro-channel plates
and a 2D position sensitive detector. The energy
resolution is 0.2% and the angular resolution is
about 0.4ꢁ. Auxiliary equipment includes a LEED
system to monitor the long range order of the
clean Al(1 1 0) surface.
detector placed in the [0 1 1] direction. For better
statistics, the scattering data have been summed
up in an angular range of 2ꢁ. In preliminary ex-
periments, we observed radiation damage, which
appears as increased background from the Al
substrate, for irradiation doses exceeding 3 · 1017
protons/cm2. Therefore, the beam position on the
sample was changed after 15% of this dose had
been accumulated.
2.2. Neutralization measurements
The area under a MEISpeak can be converted
into an areal density of the target element, pro-
vided the scattering cross-section and the charged
fraction of the scattered projectiles are known. We
We used a 98.0 keV incident proton beam. The
energy of a particle scattered at the surface is re-
lated to the incident energy by a kinematic factor.
This kinematic factor is a consequence of classical
energy and momentum conservation, and depends
on the scattering angle and target mass. That
makes MEISa mass-sensitive technique. As a
proton travels inside the sample, it loses energy to
electronic excitations [22,24]. This results in the
additional energy shift of the scattered projectile,
proportional to the path length in the solid. Thus,
a depth profile of the elements in the target can be
extracted from the energy distribution of the
scattered particles. To minimize the background
for the oxygen signal located at lower energies, the
scattering from the sub-surface (crystalline) alu-
minum substrate must be suppressed. This is
achieved by employing a specific channeling and
blocking scattering geometry, where the incident
proton beam and detector are aligned with major
crystallographic directions of the target. Then for
an ideal frozen lattice only the topmost atoms
of the crystalline substrate will contribute to the
scattered signal. In practice, due to thermal vi-
brations and shift of atoms from their ideal lattice
positions, a few sub-surface atomic layers are
partially visible to the detector. Due to the random
distribution of O and Al atoms in the amorphous
oxide overlayer, their visibility to incident ions is
not reduced in the channeling and blocking geo-
metry. Therefore, the increase of the O and Al
peak areas during oxidation can be directly related
to the oxide content. All measurements have been
done for a scattering angle of 120ꢁ, with the inci-
dent proton beam normal to the surface, and the
ꢁ
use cross sections obtained from the Moliere po-
tential, a screened Coulomb potential [25]. This
gives a good approximation for protons in the 100
keV range. The major source of error in the cal-
culation of the elemental areal densities is the
uncertainty in the knowledge of the charged frac-
tion of the backscattered protons. OÕConnor et al.
[26] have reported a decrease of the charged frac-
tion of 100 keV protons, scattered on Al(1 1 1),
from 92% to 86% as the oxygen coverage increased
from 0 to 0.5–0.7 monolayers. To determine the
charged fraction of the scattered protons, we em-
ployed a surface barrier detector (SBD) with fairly
poor energy resolution. By removing the charged
particles with an electric field, we detected the
neutral fraction of the scattered projectiles. We
found a proton charged fraction of 89% for the
clean Al(1 1 0) surface and 77% for oxide films with
ꢀ
thickness ranging from 8 to 20 A. The low SBD
resolution did not allow us to measure the energy
dependence of the charged fraction. To take this
into account we used the empirical energy depen-
dence of the charged fraction for oxidized Al [27].
This dependence fits well the measured value for
98 keV incident protons.
2.3. Sample preparation and oxidation procedure
A commercially manufactured Al crystal with
(1 1 0) orientation was electropolished in a solution
of perchloric acid and acetic anhydride. After
mounting the sample in the UHV chamber, it was

202
D. Starodub et al. / Surface Science 552 (2004) 199–214
cleaned by several cycles of sputtering with 1.0 keV
Neþ ions and sequential annealing, until a (1 · 1)
LEED pattern could be observed, and no carbon,
oxygen and heavy element contamination could be
detected by MEIS. The sample was heated from
behind by a tungsten filament. The temperature
was monitored by a chromel–alumel thermocou-
ple, attached to the rim of the sample.
573 K,
3×10-4 Torr
16O
18O
Al
Re-oxidation
time (min)
150
45
5
A difficulty in MEISwith the type of analyzer
we use is the influence of oxygen adsorption on the
efficiency of the channel plates [28]. The sample
was therefore oxidized in a separate chamber (base
pressure of 8 · 10À11 Torr) connected through an
interlock to the analysis chamber. To monitor the
location of oxygen incorporated and redistributed
during thermal treatment, a two-step isotopic
oxidation procedure was performed, using 16O and
then 18O-enriched (or vice versa) dry oxygen gas
(O2). We will refer to the first-grown oxide (with
16O) as the marker film, and the oxygen used in
the second step as the tracer. Research grade
(99.998%) 16O2 gas with the natural 16O abundance
(99.76%) was used. The 18O2 gas had an isotopic
enrichment of 99%. A mass-spectrometric analysis
of its composition, performed in the oxidation
chamber, revealed the presence of 0.1% of H216O
and 0.2% of C16O and C16O2 combined (which
may result from cracking in the mass spectrometer
or reactions on the chamber wall). To prevent
sample bombardment by electrons, all hot fila-
ments (except the sample heater) were turned off
during oxidation. The oxygen pressure was con-
trolled by a Pirani gauge calibrated against an ion
gauge in an oxygen environment.
0
80
82
84
86
88
Proton energy (keV)
Fig. 1. Evolution of the MEISspectra during re-oxidation of
Al(1 1 0) surface covered with thin Al216O3 film in 18O2 under
conditions indicated in the figure. The dotted line is the 18O
peak for a homogeneous Al218O3 film.
out in 18O2 at a pressure of 3 · 10À4 Torr and
temperatures of 573 and 673 K. Two oxidation
series have been performed, both starting with a
clean Al surface, and the oxide thickness was
measured after each oxidation step. The MEIS
spectra taken after the first step oxidation and
several re-oxidation steps at 573 K are presented in
Fig. 1. Upon saturation at RT the spectrum is
characterized by a surface Al peak and a 16O peak
from the oxide layer. Subsequent exposure to 18O2
results in appearance of an additional peak char-
acteristic of 18O with area proportional to amount
of incorporated oxygen. The kinetic data are
shown in Fig. 2. The dashed line shows an attempt
20
15
10
673 K
3. Results
The marker film was grown at room tempera-
ture (RT) and a pressure of 10À3 Torr. Under these
ꢀ
conditions, the film thickness saturates at ca. 8 A,
as measured by MEIS, after 10–15 min of oxida-
tion. This film is stable under 30 min vacuum an-
neal at 573 K. Two series of re-oxidation cycles,
aimed at examining the time and pressure depen-
dence of the oxide growth, were conducted. To
study the time dependence, the sample was first
exposed to 16O2, and re-oxidation was then carried
573 K
0
2000
4000
6000
8000
Time (s)
Fig. 2. Growth of Al2O3 oxide for two temperatures. Solid lines
are to guide the eye, dash line is a fit to the parabolic law.

D. Starodub et al. / Surface Science 552 (2004) 199–214
203
to fit the time dependence of the oxide layer
673 K,
15 min
thickness at 573 K to a parabolic rate law (X2 / t),
corresponding to the slowest step in the oxidation
process being diffusion governed by the gradient of
the electrochemical potential. Since the experi-
mental curve exhibits a tendency to saturation, this
fit is clearly not satisfactory, and therefore we will
explore oxidation kinetics described by logarith-
mic-type rate laws as explained below. Unfortu-
nately, it was not possible to measure the kinetics
of oxidation at 673 K for longer times because of
the development of significant roughness of the
oxide layer. Detailed information about the iso-
topic distribution in the oxide layer follows from
shape and position of the O peaks. As an example,
a comparison in Fig. 1 of the 18O peak upon 150
min re-oxidation in 18O2 with that for 18O forming
a uniform surface oxide film after exposure of a
clean Al(1 1 0) surface to 18O2 (dotted line) clearly
reveals a very different shape at similar total area
(concentration). A broader energy distribution, a
slight shift towards lower energy and a less steep
slope of the front edge for the former peak indicate
that upon re-oxidation isotopic intermixing, which
is non-uniform in depth, occurs. To measure the
pressure dependence of the oxidation, 18O2 gas was
used to form a marker film, and re-oxidation (in
16O2) then took place for 15 min at different
pressures. This oxidation sequence is preferable to
measure a possible loss of oxygen from oxide,
since it cannot be masked by incorporation of 18O-
containing impurities during second-stage oxida-
tion in 16O2. Fig. 3 shows MEISenergy spectra
recorded upon re-oxidation at 673 K. A pressure
dependence of the oxidation rate is clearly ob-
served from the change of the 16O area with pres-
sure. The 18O peak broadens dramatically during
re-oxidation, which can be attributed to a place
exchange reaction with newly incorporated oxy-
gen. The reduction of the 18O area indicates oxy-
gen loss into the gaseous phase. At the same time,
the maximum of the 18O peak shifts only insig-
nificantly towards lower energy, implying that the
maximum in the 18O depth distribution remains at
the surface. This behavior is reflected in the shape
of the 16O peak. For higher oxidation pressures, a
distinct surface 16O intensity reduction, as com-
pared to that expected for a uniform film, is indi-
16O (tracer)
18O (marker)
16O depletion
Re-oxidation
pressure
(Torr)
3 × 10-3
1 × 10-3
3 × 10-4
1 × 10-4
79
80
81
82
83
Proton energy (keV)
Fig. 3. Oxygen MEISspectra upon re-oxidation of thin
Al218O3 film in 16O2 at various pressures.
cated in Fig. 3. As a result, the maximum of the
16O peak for high pressures shows a significant
shift to lower energies, and is located in central
part of the peak. This corresponds to the perme-
ation of oxygen ions through a relatively stable
surface marker film and preferential oxide build up
at the oxide–metal interface. The observed isotopic
distributions can be explained only by assuming
that the oxygen ions are the mobile species
responsible (at least in part) for material transport
during oxidation.
4. Theory of oxidation kinetics in ultra-thin films
The oxide thickness range of interest (from 5 to
ꢀ
30 A) is well below the typical width of a space-
charged layer. Therefore, space charge can be
ignored, and the electric field across the oxide
(established only by the surface charges on the
gas–oxide and oxide–metal interfaces) can be
considered as uniform. Furthermore, electronic
and ionic currents accompanying growth can be
considered independently. The mechanism of
electron/hole tunneling through the oxide layer is
ꢀ
very efficient for films thinner than 30 A, estab-
lishing an electronic current equilibrium. Under
these assumptions, the potential drop across the
film Du equals the difference between the metal

204
D. Starodub et al. / Surface Science 552 (2004) 199–214
work function and the affinity level of chemisorbed
oxygen (which is the sum of the oxygen affinity
and the oxygen atom binding energy). The electric
field set up by this potential provides a driving
force for slow ion incorporation and/or transport.
Note that this transport occurs in a non-equilib-
rium system, and therefore cannot be described by
the gradient of the electrochemical potential. Two
types of oxidation kinetics can occur in this case
depending on the mechanism of ionic transport
(which in turn is determined by the oxide mor-
phology). The general expression for a potential
barrier to be overcome for a field-assisted jump of
an ion between two adjacent sites can be written as
[11]
species, and X is the oxide volume per incorpo-
rated oxygen (aluminum) ion.
The validity of Eq. (2a) can be tested by plot-
ting 1=X as a function of lnðt=X2Þ. A straight line
with a slope defined by Du should be obtained.
The values of N and W0 can be extracted from an
Arrhenius plot of u.
An alternative microscopic mechanism for ion
movement is via extended defects in the oxide
layer, such as structural channels or, for poly-
crystalline films, grain boundaries. As the film
grows, these easy pathways for ion migration
gradually become blocked by the formation of
oxide within them [29]. Also, their characteristic
length can become small with respect to the layer
thickness, slowing the rate of ion motion. Thus,
though the activation energy is again larger for
thicker films, its change is directly proportional to
the oxide thickness, provided X2 > qaDu=k or
in case of a thickness independent electric field:
DW ¼ kX. Then the exact solution of the growth
equation is direct logarithmic kinetics with a linear
dependence of X on lnðtÞ:
W ¼ W0 À qaE þ kX;
ð1Þ
where q is the ionic charge, 2a is the jump length, k
is a structural term, and X is the oxide thickness.
The intrinsic barrier for an ion jump is W0. The
second term describes the lowering of W by an
electric field E across the oxide, and the third term
takes into account the blocking of extended defects
as the film thickens.
T
k
Provided the potential difference across the film
Du is constant, the increase of the film thickness X
reduces the electric field E ¼ Du=X in the oxide. If
the ion movement takes place by generation of
point defects, such as vacancies or interstitials, the
third term in Eq. (1) can be neglected, and the
change in the activation energy DW ¼ W À W0 for
ion movement is inversely proportional to X:
DW ¼ ÀqaDu=X. The approximate solution of the
resulting growth equation gives an inverse loga-
rithmic dependence of the thickness on time t [1]:
X ¼ ln½1 þ nðTÞ Á tŠ;
ð3Þ
where nðT Þ is defined by the system parameters.
A direct logarithmic law also results if oxidation
is rate-limited by electron tunneling [18].
5. Discussion
5.1. Film characterization: stoichiometry and inter-
face structure
ꢀ
ꢁ
x1
X
t
X2
¼ À ln
À lnðx1uÞ;
ð2aÞ
From an ion scattering point of view all the Al
nuclei in a random oxide network contribute
equally to the scattering signal. Due to channeling/
blocking only the top atomic layer and fractions of
a few sub-surface layers of the crystalline Al sub-
strate are visible to the detector. As the oxide
grows, the oxygen atoms form bonds with alumi-
num atoms and displace them from their lattice
sites. The displaced Al atoms can now become
visible to the ion beam and be detected. Therefore,
the Al signal will increase upon oxidation. If a
stoichiometric amorphous Al2O3 oxide is formed,
where x1 and u are constants determined by
physical parameters of the system:
ꢂ
ꢃ
W0
T
u ¼ NXm exp
À
;
ð2bÞ
ð2cÞ
ꢄ
ꢄ
ꢄ
ꢄ
ꢄ
ꢄ
ꢄ
ꢄ
qaDu
T
x1 ¼
:
Herein m is a lattice vibration frequency of the
order of 1012
s
À1, T is the oxidation temperature,
N is the areal density of the potentially mobile

D. Starodub et al. / Surface Science 552 (2004) 199–214
205
the incorporation of three oxygen atoms into the
Thickness (Å)
oxide network should be accompanied by an in-
crease of the Al yield by two atoms. The slope of a
plot of the areal density of visible Al atoms as a
function of O coverage (areal density) gives the
number of displaced Al atoms per O atom in the
oxide. From this, the stoichiometry of the oxide
can be determined (Fig. 4(a)). A straight line with
a slope of 2/3 (solid line), corresponding to the
stoichiometric oxide, is within the error of the
least-square linear fit (dashed line). This implies
growth of stoichiometric Al2O3 for film thick-
0
2
4
6
8
10 12 14
1.0
0.8
0.6
0.4
Slope = 2/3
(a)
0.5
0.4
0.3
0.2
0.1
ꢀ
nesses ranging from 8 to 15 A. Extrapolation of
this line to zero oxide thickness (O coverage) gives
an intercept for the Al yield of 0.349 AÀ2. The
ꢀ
experimentally measured Al signal for a cleÀa2n
ꢀ
Al(1 1 0) surface in this geometry is 0.313 A
.
À2
ꢀ
(b)
There is therefore some 0.036 A to be accounted
for. Assuming an Al density of 2.7 g/cm3, the ex-
cess in the measured Al yield corresponds to an
0.0
0.5
0.2
0.4
0.6
0.8
1.0
O areal density (Å-2)
ꢀ
effective 0.6 A thick layer of displaced Al, which is
ꢀ
less than one interlayer distance (1.432 A) for
0.4
0.3
0.2
0.1
Al(1 1 0). That amount can be due to lateral stress
in the substrate layers and/or changes in the top-
most Al(1 1 0) layer from relaxation introduced by
the oxide.
The above considerations permit a partial
determination of the interface composition and
structure, but they are not sensitive to larger scale
(involving lateral distances of more than several
atomic spacings) interface roughness. For in-
stance, a simple peak area intensity analysis does
not allow us to distinguish between oxide growth
by means of a uniform increase of the film thick-
ness and in-depth island growth with subsequent
lateral expansion underneath a thin continuous
surface oxide film. The latter growth mode has
been reported [14] for Al oxidation at tempera-
tures above 620 K. This type of information can be
obtained by taking into account the evolution of
the Al and O peak widths (not simply the area)
with oxide growth. The interface morphology is
reflected in the peak shape, which can be charac-
terized numerically at one level by the root mean
square width [28]. In the case of a Gaussian dis-
tribution, the rms width is just twice the standard
deviation r. Interface/surface roughening (or is-
land formation) would result in a rise of the low-
(c)
0.4
0.0
0.1
0.2
0.3
0.5
O peak width (keV)
Fig. 4. (a) Visible Al yield as a function of O coverage. The best
linear fit (slope ¼ 0.69 0.03) is shown by the dashed line. The
solid line is the linear fit with a fixed slope of 2/3 corresponding
to a stoichiometric Al2O3. The diamond shows the measured Al
yield for the clean Al surface. (b) O peak width as a function of
O coverage, and the least-square linear fit through origin; (c) Al
peak width as a function of O peak width; the slope of the
fitting straight line is 1. For all plots, filled symbols stand for
films grown at fixed pressures, open at fixed time.
energy tail and an increase of the rms peak width.
Fig. 4(b) shows the dependence of the O peak
width wO on O coverage. Because oxidation has
been performed in two sequential steps using
different O isotopes, the O peak width is calculated
as the sum of the 16O and 18O peak widths
weighted by their fraction in the overall O yield. A

206
D. Starodub et al. / Surface Science 552 (2004) 199–214
correction was also applied to account for the
instrumental resolution and the average peak
broadening due to straggling, using the relation-
Thus, Al(1 1 0) oxidation at 573 K results in the
growth of a uniform stoichiometric Al2O3 film
with both microscopic and macroscopic interface
features not deviating by more than one atomic
layer of Al from ideal (homogeneous flat layer)
growth.
The situation changes for oxidation at 673 K.
For a pressure exceeding 10À3 Torr, the measured
spectra could not be fit to a model with a flat
oxide–metal interface. In this case the O and Al
peaks exhibited slightly longer (as compared to
simulations) low-energy tails, attributed to the
onset of roughness. This result was confirmed by
angular-resolved X-ray photoemission measure-
ments. Upon oxidation under the above condi-
tions, the angular dependencies of the ratio of the
oxidic Al3þ component intensity to that of metallic
Al0 component (not shown) could only be fit to a
simulation assuming interface island formation.
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
ship wO ¼ WO2 À ð2 Á rÞ , where WO is the O peak
width calculated from the spectra and r ¼ 0:18
keV. The data points lie on a straight line within
the error bars. The limiting case of lateral island
growth would result in a constant O peak width.
In-depth growth of islands would lead to a faster
penetration of oxygen atoms into the substrate (as
compared to the thickening of a homogeneous flat
film) at the same oxygen uptake rate. Therefore
this situation would yield a faster increase of O
peak width with coverage. The observed linear
dependence can be associated with homogeneous
in-depth growth without interface/surface rough-
ening (the surface remains flat with, in effect, layer-
by-layer oxidation of the substrate). The zero
intercept implies a flat oxide-metal interface. Fig.
4(c) presents a plot of the Al peak width wAl as a
5.2. Growth kinetics
function of the O peak width. The former is de-
2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
fined as wAl
¼
WA2l À ð2 Á rÞ À WA2lð0Þ À ð2 Á rÞ
As discussed in Section 4, the growth kinetics of
an ultra-thin oxide layer can typically follow either
a direct or an inverse logarithmic rate law.
Experimentally, it is usually difficult to distinguish
between direct and inverse logarithmic growth,
because they result in very similar time depen-
dencies for the oxide thickness, and the latter one
is only an approximate solution to the growth
equation. Besides, an accurate measurement of the
oxide thickness by commonly used techniques re-
quires well-defined values of some macroscopic
thin film properties, namely optical parameters for
ellipsometry or electron mean free path and sen-
sitivity factors for photoelectron spectroscopy.
Sometimes, analysis of the physical parameter
values of a system assuming different rate laws can
help in choosing between the different possible
models [17,30]. For ion scattering, the scattering
cross-sections are known with high precision. This
allows an accurate measurement of the areal oxy-
gen density from the O peak area, which can be
converted into oxide thickness assuming the bulk
density of Al2O3 (3.7 g/cm3). Fig. 5(a) and (b)
shows two presentations of the 573 K data from
Fig. 2, aimed at determining the kinetic law that
describes them better. A quantitative measure of
in order to exclude the instrumental resolution and
the contribution from the Al substrate. Here WAl is
the Al peak width from the measured spectrum,
and WAlð0Þ is the Al peak width for zero oxygen
coverage, experimentally measured to be 0.48 keV.
A straight line as shown in Fig. 4(c) fits the
resulting dependence of the Al peak width vs. the
width of the O peak. The fact that the slope is
equal to 1 implies that both O and oxidized Al
expand into the substrate at the same rate. As
expected for a uniform flat film, extrapolation to a
zero oxygen peak width gives to a good approxi-
mation a zero intercept.
In order to check for roughness, we sometimes
collected additional spectra at a scattering angle of
60ꢁ, with the incident beam impinging along the
ꢂ
[1 0 1] orientation, and with the detector aligned
along the [0 1 1] direction. This tilted incident beam
makes the data for this configuration more sensi-
tive to surface and/or interface roughness. We
have been able to fit the energy spectra (see Section
5.3) for both scattering geometries using the same
model of the elemental distributions with an
abrupt oxide–metal interface. This indicates
insignificant surface/interface roughness.

D. Starodub et al. / Surface Science 552 (2004) 199–214
207
16
14
12
10
8
1.000
0.995
0.990
1.00
0.98
0.96
0.94
0.92
0.12
0.10
0.08
0
100
200
300
0
100
200
300
400
t0 (s)
t0 (s)
(b)
(a)
1
2
3
4
10
10
10
10
t/X2 (s/Å2)
t (s)
Fig. 5. Time dependence of Al2O3 thickness plotted as: (a) 1=X against lnðt=X2Þ, in order to test inverse logarithmic kinetics; (b) X
against lnðtÞ, to test direct logarithmic kinetics. Open and filled symbols correspond to two oxidation sequences. The insets show the
correlation coefficient R for these data as a function of the time shift t0, as described in the text. The straight line is the least-square
linear regression for inverse logarithmic kinetics with t0 ¼ 144 s, corresponding to the maximum value for R.
the quality of the fit is the linear correlation coef-
ficient R, which has a value of 1 when the data
points lie on a straight line, and 0 if their x and y
coordinates are not correlated. From a compari-
son of (a) and (b), the kinetic data can be better fit
by the inverse logarithmic growth law. One should
keep in mind, however, that an initial oxide
Assuming the validity of the inverse logarithmic
law, the physical parameters for the Al2O3/Al
system (N, W0 and Du) have been derived from the
least-square linear fits of Eqs. (2a)–(2c) to the data
3
ꢀ
from Fig. 2. The values of X ¼ 30:5 A and
ꢀ
2a ¼ 2:48 A are calculated from the alumina bulk
density of 3.7 g/cm3, and the charge for O ions is
presumed to be q ¼ À2e. The potential difference
across the film in the temperature range of 573–
673 K is found to be 0.8 0.2 V. This result agrees
well with the value of 0.73 V, reported for dry
oxidation of aluminum foil at 1 Torr [32]. The
corresponding value of the electric field in the
oxide is ꢀ7 MV/cm. This is within the limits for
the breakdown field of 3–13 MV/cm in thick an-
odic alumina film [33], which suggests good
dielectric properties of the grown oxide film. The
slope of the Arrhenius plot for u defines the barrier
W0 for ionic motion (or incorporation into oxide,
whatever is larger) in the absence of a field:
W0 ¼ 1:67 Æ 0:13 eV. This is in excellent agreement
with the value of 1.60 eV, determined in an earlier
study [32]. The concentration of the potentially
mobile species on the interface, where defect
injection occurs, is found from the intercept:
N ¼ 2 Â 10ð12Æ1Þ cmÀ2. Assuming an electrostatic
field E ¼ 7 Â 106 V/cm according to the evaluation
above, the charge density at the gas–oxide and
oxide–metal interfaces can be estimated from
GaussÕ theorem for the field across a flat capacitor:
N ¼ je0E=q, where j ¼ 9 is the alumina dielectric
ꢀ
thickness of 8 A is ascribed to time t ¼ 0. That
explains the departure from linearity of the two
points in Fig. 5(a) for smaller oxidation times,
which are comparable with the time t0 required to
ꢀ
grow 8 A of oxide starting with a clean surface.
This time is less than 300 s for RT oxidation at
1 · 10À3 Torr, and can be expected to be much
smaller at 573 K. For both data presentations, the
linearity can be improved by introducing a time
shift t ! t þ t0. Additionally, a similar shift t !
t þ s provides a better approximation to the solu-
tion of the Cabrera–Mott growth equation [31].
Insets to Fig. 5 show how the correlation coeffi-
cient changes with varying t0 for both types of
kinetics. For the inverse logarithmic dependence, R
reaches a maximum value of 0.99893 at t0 ¼ 144 s.
The least-square linear fit for this t0 is shown by
the solid line in Fig. 5(a). On the contrary, if the
data are plotted as X against lnðtÞ, a maximum in
the correlation coefficient (R ¼ 0:99797) is ob-
tained at an unreasonably large time shift of about
600 s (see inset in Fig. 3(b)). Thus, the oxidation
kinetics is better described by the Cabrera–Mott
theory.

208
D. Starodub et al. / Surface Science 552 (2004) 199–214
constant. The result of 1.7 · 1013 cmÀ2 falls in the
concentration range obtained from kinetic data.
This concentration is at least two orders of mag-
nitude larger than that reported by others [19,32].
The obvious disagreement is reflected in the much
faster oxidation rate observed in this work, as
compared to other results [15,32]. To reconcile the
controversy, we speculate that then enhancement
in the oxidation rate may result from its depen-
dence on crystallographic orientation. This might
be expected if incorporation of migrating species
(e.g. injection of oxygen vacancies into oxide) oc-
curs at the oxide–metal interface. While previous
kinetic studies have been concerned with oxidation
of Al(1 1 1) or polycrystalline Al surface, in this
work the open and defect-rich Al(1 1 0) face has
been used. This could account for a larger number
of species available for migration in this case. A
detailed study of oxidation kinetics on Al(1 1 1)
and Al(1 0 0) faces is required to confirm this
assumption. These closely packed faces with a
more perfect structure can be expected to generate
a smaller number of Al species available for the
formation of new oxide bonds, decreasing the rate
of formation of interface oxygen vacancies. The
effects of modification of the oxide structure by
water contamination can also not be excluded.
Another piece of evidence favoring inverse
logarithmic kinetics comes from the analysis of the
evolution of the oxygen peaks with increasing
oxygen exposure, summarized in Fig. 6. At 473 K
the re-oxidant (tracer) peak slowly broadens as
oxidation proceeds, but at all exposures it remains
narrower than the marker peak. The width of the
marker peak is also affected by oxidation. It in-
creases at about the same rate as that of the tracer.
At the higher oxidation temperature (573 K), the
widths of the oxygen peaks become approximately
equal, and increase with the same rate as the oxide
grows. Finally, as seen from Fig. 6(c), for oxida-
tion at 673 K the rate of the broadening is larger
for the tracer signal, and it becomes wider than the
marker signal. The width of the marker peak
eventually becomes almost constant at the highest
exposures. Marker film broadening during oxida-
tion reflects the increase in the width of the marker
depth distribution. In other words, the oxygen
species from the marker oxide are affected by the
marker
0.5
0.4
0.3
tracer
(a)
(b)
(c)
473 K
0.6
0.5
0.4
573 K
tracer
1.0
0.9
0.8
0.7
0.6
0.5
0.4
marker
673 K
0
1
2
3
Exposure (106 L)
Fig. 6. Variation of the oxygen peak widths with exposure for
oxidation at (a) 473 K; (b) 573 K; (c) 673 K. Filled squares
correspond to the marker (first step oxidant), and open circles
to the tracer (re-oxidant). Data are obtained at both fixed
pressure of 3 · 10À4 Torr and fixed oxidation time of 15 min.
Solid lines are logarithmic fits to guide the eye.
re-oxidant, pushing them away from the surface.
Oxygen transport along extended defects (charac-
teristic of direct logarithmic kinetics) or by jumps
from an interstitial site to another (adjacent)
interstitial site would keep the marker oxide, and
hence the relevant oxygen peak width, unchanged.
On the other hand, in the place exchange (inter-
stitialcy) mechanism an interstitial ion injected at
the interface knocks out a network atom, forcing it
to become an interstitial and subsequently to re-
place the next network atom, and so on. This
mechanism, as well as oxygen migration by va-
cancy movement would result in a broadening of
the marker distribution. Therefore, we associate
the observed marker peak broadening with oxygen
transport by means of point defects jumps, char-
acteristic for inverse logarithmic kinetics. Thus,
both the kinetic data and the oxygen redistribution
in the film upon re-oxidation confirm the Cabrera–

D. Starodub et al. / Surface Science 552 (2004) 199–214
209
Mott mechanism with inverse logarithmic growth
kinetics.
oxide growth rate integrated over 15 min. A rea-
sonable fit by a straight line with a slope of 0.5
(solid) supports a parabolic pressure dependence
of the growth rate, in agreement with previous
work [15,34]. The best linear fits are shown by the
dashed lines. The slope, averaged over all data, is
0.47 0.03, in agreement with parabolic pressure
dependence.
Additional information about the microscopic
growth mechanism can be extracted, at least in
principle, from the oxide growth rate as a function
of oxygen pressure. This dependence is expected to
be different when defect injection occurs at the
gas–oxide (oxygen interstitials or metal vacancies)
and oxide–metal (oxygen vacancies or metal in-
terstitials) interfaces. In the both cases, the gas
pressure determines the concentration of oxygen
ions on the oxide surface (which are assumed to be
in equilibrium with the gas phase in this P–T –t
range) and thus the magnitude of the electric field
across the film, lowering the activation barrier for
the injection and transport of the migrating spe-
cies. A dependence of the surface electrostatic
potential on pressure is evident from the mea-
surements of contact potential [34]. If injection
takes place at the gas–oxide interface, an addi-
tional contribution to the pressure dependence of
the growth rate arises because in this case the
pressure controls not just the barrier for defect
incorporation into oxide, but also the number of
species available for this incorporation. Unfortu-
nately, the change in the oxidation kinetics
emerging from this contribution is too small to
allow an experimental distinction between these
two cases. Fig. 7 shows the oxygen uptake in the
oxide versus pressure during re-oxidation (for 15
5.3. Profiling of 16O/18O tracers in the oxide film
The analysis above of the integrated peak
characteristics provides kinetic and structural
information. A consideration of the evolution of
the peak widths also reveals some features of the
microscopic processes involved in the material
transport across the film during oxidation. This
section will deal with a more accurate analysis of
the evolution of the peak shape, achieved by sim-
ulation of the MEISspectra by modeling the
elemental depth distributions. Some important
qualitative observations can be made by visual
examination of the peak shape. Fig. 8 compares
the energy spectra for the aluminum oxide film
before (a) and after (b) re-oxidation at 3 · 10À4
Torr for 120 min. The latter film consists of 57% of
16O and 43% of 18O. The leading edge positions for
both oxygen peaks coincide with the backscattered
proton energy calculated for the nuclei located at
the surface. Also, the two oxygen peaks have the
same width. These two facts imply that the oxygen
isotopes are intermixed throughout the film.
However, the peak shapes are clearly different,
indicating a variation of the oxygen isotopic ratio
across the film. A difference spectrum of the two
spectra in Fig. 8(a) and (b) is shown in Fig. 8(c).
The presence of both negative and positive con-
tributions in the 16O peak reflects the displacement
of the marker 16O from the surface deeper into the
film, caused by 18O incorporation during re-oxi-
dation. The areas of the negative and positive
parts are equal. Thus, no oxygen loss from the film
occurs during oxidation at 573 K. Quantitative
information can be obtained by numerical decon-
volution of the peaks. First we outline the depth
distribution model for the simulation. We then
discuss the time evolution of the depth profiles
during re-oxidation.
16
ꢀ
min in O2) of an 8 A thick Al2O3 layer. The
change in the O areal density corresponds to the
15 min
re-oxidation
1
673 K
573 K
10
1
0.1
473 K
Slope = 0.47 0.03
10-4
10-3
Pressure (Torr)
Fig. 7. The pressure dependence of the oxide thickness incre-
ment during re-oxidation. The straight solid lines have a slope
of 1/2. The dashed lines are the least-square linear fits with an
average slope of 0.47 0.03.

210
D. Starodub et al. / Surface Science 552 (2004) 199–214
18O
(re-oxidant)
0.08
16O
18O
Al
d
0.04
c
(a)
16O
c0
(a)
0.00
before overall O
0.08
120 min
(marker)
0.04
after
(b)
(b)
0.00
0.08
Al
oxide interface substrate
0.04
0.00
+
(c)
-
5
0
10
15
20
25
30
(c)
Depth (Å)
Fig. 9. The depth distributions for (a) 18O, (b) 16O, and (c) Al,
used to simulate the energy spectra in Fig. 8. The values of c0, d
and dc define the oxygen profile shape according to Eq. (4). The
dashed line in panel (b) corresponds to the total concentration
of the two O isotopes, the rectangle (solid line) is the 16O profile
before re-oxidation, and the shadowed area indicates the net
amount of 16O that has moved during re-oxidation.
80
81
82
83
86
87
88
Energy (keV)
Fig. 8. Energy spectra for protons scattered from: (a) Al(1 1 0)
oxidized in 16O2 at RT during 30 min, pressure 1 · 10À3 Torr;
(b) the same specimen re-oxidized in 18O2 at 573 K during 120
min, pressure 3 · 10À4 Torr. Vertical dashed lines indicate the
calculated positions for backscattering from surface atoms of
16O, 18O and Al. The solid line is the best fit to the experimental
data shown by the open symbols, simulated using depth profiles
for Al, 18O and 16O from the Fig. 9. The difference spectrum in
the oxygen region for the spectra in (a) and (b) is shown in
panel (c). The negative peak at the surface position for the 16O
isotope implies displacement of the marker oxygen from the
surface deeper into oxide.
overall oxygen concentration inside the film, and
an abrupt oxide boundary with the substrate, as
shown by the dashed line in Fig. 9(b). This con-
centration corresponds to the density of bulk
alumina and has a value of 0.0655 AÀ3. The overall
ꢀ
O areal density, calculated from the peak areas,
determines the boundary position (and oxide
thickness). The tracer (re-oxidant) depth profile
across the film, ntðzÞ, where z is the coordinate
perpendicular to the surface, can be conveniently
described by the expression
5.3.1. Model for the oxygen distribution in the oxide
film
As we have shown in the Section 5.1, the oxide
film has a stoichiometric composition and a rela-
tively sharp (with respect to the thickness) inter-
face. Therefore, in the model we assume a constant
ꢀ
ꢁ
z
d
k
ntðzÞ ¼ c0 þ ðÀ1Þ Á dc Á erfk
;
k ¼ 1; 2;
ð4Þ

D. Starodub et al. / Surface Science 552 (2004) 199–214
211
which covers a broad range of concentration
profile shapes (erf denotes the error function). The
meaning of the variables c0, dc and d is clear from
Fig. 9(a), which depicts the re-oxidant distribution
modeled by Eq. (4) with k ¼ 2. The value of c0
defines the surface concentration of the re-oxidant,
dc is the gradient between the surface and interface
concentrations, and d is the width of the transition
region. For k ¼ 1 and c0 ¼ dc we obtain a solution
to the diffusion equation with a constant surface
concentration for the diffusing species. The marker
(first oxidant) distributions after the first and the
second oxidation stages are shown in Fig. 9(b) by
solid lines. It is defined as nmðzÞ ¼ 0:0655 À ntðzÞ.
One can clearly see a significant movement of
the marker species, forced by the new oxide
growth.
oxidation. Therefore, we adopted the profile ob-
tained for the visible atoms in the clean Al(1 1 0)
substrate in all simulations.
Provided the elemental depth profiles are
known, the backscattering energy spectra can be
calculated following the standard procedure [40].
The electronic stopping power in the oxide, which
determines the proton energy loss in the target,
was found from the semi-empirical energy depen-
dencies for elemental stopping powers [41] using
BraggÕs rule. The stopping power in the substrate
was adjusted to take into account the higher
electronic density along the proton trajectories in
the vicinity of the atomic strings, by using this
density as the only fitting parameter for the clean
Al(1 0 0) surface peak simulation. To include the
statistical broadening of the proton energy distri-
bution due to the random electronic scattering in
the target (straggling) we used a Gaussian energy
distribution (convoluted with the instrumental
resolution). The standard deviation in the limit of
high-energy ions interacting with free electrons
was given by Bohr [42]. However, this approxi-
mation does not provide a satisfactory estimate of
straggling for protons in the 100 keV energy range.
Therefore we have applied more realistic values,
obtained for the elemental targets in the frame-
work of the Lindhard and Scharff formalism [43]
based on the local electronic density approxima-
tion. BraggÕs rule was used for straggling evalua-
tion in alumina. The quality of the fit was defined
by the rms deviation v of the calculated spectra
from the experimental ones. The three free
parameters in Eq. (4) are constrained by the im-
posed restriction that the area under the tracer
profile should be equal to the areal density calcu-
lated from the peak area. Thus, only c0 and d in
Eq. (4) have been varied independently. Their
optimization has been performed by plotting
contour plots of v as a function of these parame-
ters. The best fits to the spectra in Fig. 8(a) and (b)
are shown by the solid line. The fit for the marker
oxide before re-oxidation (Fig. 8(a)) is based on
the marker oxygen profile shown as a solid line
rectangle in Fig. 9(b). The shadowed area shows
the net 16O movement forced by the new oxygen
incorporation. It is associated with the negative
part of the 16O peak in the Fig. 8(c).
Finally, the Al profile is sketched in Fig. 9(c).
The aluminum atomic density within the oxide has
À3
ꢀ
been given its stoichiometric value of 0.0437 A
.
The excess interface Al (see Section 5.1) has been
formally accounted for by introducing an addi-
ꢀ
tional 1 A-thick layer of Al with a density of
0.0602 AÀ3. The Al substrate is modeled by a step-
ꢀ
like structure, each step corresponding to one
atomic layer of the substrate. The step width
ꢀ
(1.432 A) is equal to the interlayer separation for
the Al(1 1 0) surface. The step height corresponds
to the fraction of that layer visible to the detector
in the scattering geometry used for the measure-
ments. It is obtained by a complete-crystal Monte–
Carlo simulation [35] for the clean Al(1 1 0)
surface. Optimization of the crystal structure/
dynamics parameters by fitting the angular scat-
tered yield gave the values for relaxation in the first
and second interlayer distances of )8.5% and
+5.4%, respectively, in a good agreement with
previous studies [36–38], and 1-d rms vibrational
amplitudes enhanced by 90% in the first and 50%
in the second layer compared to the bulk value
ꢀ
(0.105 A [39]). Using these values we obtain a
À2
ꢀ
predicted yield of 0.302 A
in the blocking
direction, in good agreement with experiment for
the clean surface. Though the presence of an oxide
layer can be expected to modify the relaxation and
vibration amplitudes of the interface substrate
atoms, we did not observe a significant change in
the shape of the angular scattering yield upon

212
D. Starodub et al. / Surface Science 552 (2004) 199–214
5.3.2. Time dependence of the oxygen depth profiles
The rate limiting process for oxidation can be
either interface defect incorporation or diffusion
across the oxide. In the former case, the defect
injection is followed by its rapid transport across
oxide, resulting in a relatively sharp boundary
between 18O and 16O distributions. If the migration
across oxide is slow, the re-oxidant distribution
will slowly broaden with time, increasing the tracer
concentration at the oxide–metal interface.
The time evolution of the oxygen incorporation
is presented in Fig. 10(a), which shows a set of the
re-oxidant (18O) profiles for two oxidation tem-
peratures and several oxidation times. They are
described by Eq. (4) with k ¼ 2 and best-fit values
for parameters c0 and d. As re-oxidation begins,
the tracer surface concentration quickly ap-
proaches the saturation level, which is maintained
later at an approximately constant temperature-
independent value. The re-oxidant preferentially
incorporates in the interface region, rather than at
the surface. Fig. 10(b) shows how the surface and
interface 18O concentrations change with oxidation
time. While the surface concentration becomes
only slightly larger, steady growth of the interface
18O incorporation with time occurs. At 673 K, the
interfacial tracer concentration eventually levels
off slightly below the overall oxygen concentration
in the oxide. After that, the 18O distribution evo-
lution is mostly restricted to propagation deeper
into the substrate. The observed slow broadening
of the tracer distribution is consistent with the
migration across the oxide being a kinetically rate-
limiting process. This assumption was verified by a
simple estimate of oxidation energetics. Overall
(effective) activation energy W for oxidation
(which is dependent on oxide thickness) was de-
rived from the kinetic analysis in Section 5.2. This
energy is determined by the larger of the activation
barriers for oxygen defect incorporation Wi at one
of the interfaces and for jumps between two sites
within oxide Wd . On the other hand, an analysis of
the tracer depth profiles can be employed to ex-
tract parameters explicitly defining the rate of the
oxygen motion across the oxide film after its
injection. The tracer peak shapes upon re-oxida-
tion at 473 and 573 K for a short time (up to 15
min) could be simulated modeling the re-oxidant
depth distribution by a complementary error
function with the diffusion length d as a single
fitting parameter (Eq. (4) with k ¼ 1 and c0 ¼ dc).
Assuming that the (classical) relationship d ¼
pffiffiffiffiffi
2 Dt holds, the apparent diffusion coefficient D
for the tracer atoms has been calculated at these
temperatures (and for the same pressure as that
used for kinetic studies). However, one should
exercise care applying this expression because the
diffusion equation is not valid for the strongly non-
equilibrium system under consideration. Thus, use
of D can be regarded rather as a simplified way
to characterize the rate of oxygen motion. An
Arrhenius plot of D provides an estimate of the
activation energy Wd for an oxygen jump inside the
film. In this way the energetics of defect incorpo-
0.07
3×10-4 Torr
0.06
573 K
0.05
60 min
673 K
20 min
0.04
0.03
0.02
0.01
150 min
interface
10 min
120 min
60 min
30 min
surface
(b)
(a)
0
5
10
15
20
25
50
100
150
Depth (Å)
Time (min)
Fig. 10. (a) 18O (re-oxidant) depth distributions upon oxidation at 3 · 10À4 Torr and temperature of 573 K (solid lines) and 673 K
(dotted lines) for various times; (b) time dependence of the surface (filled symbols) and interface (open symbols) 18O concentrations.
Squares and circles correspond to 573 and 673 K, respectively. Dashed lines in both panels show the overall O concentration in oxide
layer.

D. Starodub et al. / Surface Science 552 (2004) 199–214
213
c(16O) = 0.517 0.002 Å-2
c(18O) = 0.464 0.003 Å-2
ration and migration can be separated. If W is
larger than Wd , then overcoming the surface or
interface barrier is the rate-limiting step for oxi-
dation, and surface/interface processes define its
rate. If W is equal to Wd , the rate-limiting step is O
movement within oxide, as we assumed from the
above consideration of the time evolution of the
re-oxidant distribution in the film. Our estimate
for the diffusion activation barrier at an oxide
0.50
0.45
0.40
0.35
18O:
473 K
573 K
673 K
16O:
573 K
673 K
ꢀ
thickness of ꢀ10 A gives Wd ꢁ 1:3 Æ 0:3 eV, which
0
1
2
3
Exposure (106 L)
compares well with W ¼ 1:47 eV from kinetic
data. Therefore we conclude that oxygen move-
ment inside the oxide is the likely rate-limiting step
during oxidation.
Fig. 11. Amount of marker oxygen isotope in the oxide after
re-oxidation under different conditions. The marker oxides
formed by 16O and 18O isotopes are shown by open and filled
symbols, respectively. Dashed linÀe2s are drawn to guide the eye.
The difference of about 0.06 A in the initial 16O and 18O
ꢀ
5.3.3. Surface exchange reaction
concentrations corresponds to oxide initially formed by 16O-
containing impurities in 18O2. The horizontal dashed lines imply
that no oxygen loss takes place during oxidation at the tem-
peratures up to 573 K.
A surface exchange reaction is an incorporation
of oxygen from the gaseous phase into the oxide
by replacement of the surface network oxygen. If
this reaction is accompanied by release of the
network oxygen into the gaseous phase, it does not
contribute to the oxide growth. Therefore, care
needs to be exercised, if the oxidation kinetics is
evaluated from the 18O amount incorporated into
the 16O-formed film. In the case of Si oxidation,
the fraction of surface-incorporated 18O which
contributes to oxide growth is less than 1% for 100
nm films, and increases for thinner films [44]. The
rate of the surface exchange reaction can be linked
to the concentration of surface active centers for
defect incorporation or of potentially mobile spe-
cies [45]. Thus, it is possible to relate oxygen ex-
change to the oxidation mechanism. The exchange
reaction is expected to occur, if oxygen (rather
than the metal) is the dominant migrating species.
Oxygen loss from the 18O-formed oxide film dur-
ing further oxidation in 16O2 can be directly mea-
sured by monitoring 18O2 and 16O18O species in the
gas phase [45]. In our work, the change in the
marker signal in oxide was measured by MEIS.
The dependence of the marker concentration on
the oxygen exposure during re-oxidation at vari-
ous temperatures is shown in Fig. 11. Either 16O
(open symbols) or 18O (filled symbols) was used to
form the marker film. The re-oxidation exposure
was varied by changing the oxidation time or the
pressure. The data for 473 and 573 K are well fit
with horizontal lines, indicating an absence of
oxygen loss into the gas phase. The average mar-
À2
ker concentration is 0.517 A for the 16O marker
ꢀ
and 0.464 A for the 18O marker. The difference is
due to the fact that a fraction of the 18O2-grown
marker film is formed by 16O-containing impuri-
ties. From Fig. 11, an exchange reaction between
the oxide and the gaseous oxygen molecules is
detected at 673 K, since some of the initially
present oxygen is removed from the film. At the
highest exposure of 2.7 · 106 L at this temperature,
10% of 16O incorporated in the oxide during the
second oxidation step, was simply exchanged with
18O; in this case, 30% of the original 18O amount
left the film. The observation of the exchange
reaction only at elevated temperatures can be
attributed to a high activation barrier for this
reaction. Another important factor is the lowering
of the electric field across the oxide for thicker
films grown at higher temperatures. At 573 K, the
À2
ꢀ
ꢀ
oxide thickness did not exceed 15 A, and thus the
gradient of the electric field across the oxide is
large, resulting in the potential barrier for an in-
ward oxygen jump being much smaller than for an
outward jump. This prevents oxygen, already fixed
in the oxide, from moving into the gaseous phase.
When the oxide becomes thicker, the barrier for
the outward movement is reduced due to the lower

214
D. Starodub et al. / Surface Science 552 (2004) 199–214
[9] A. Atkinson, Rev. Mod. Phys. 57 (1985) 437.
[10] F.P. Fehlner, N.F. Mott, Oxid. Met. 2 (1970) 59.
[11] K.R. Lawless, Rep. Prog. Phys. 37 (1974) 231.
[12] J.A. Davies, B. Domeij, J.P.S. Pringle, F. Brown, J.
Electrochem. Soc. 112 (1965) 675.
field, and a non-negligible probability of escaping
into the gas phase exists.
6. Conclusions
[13] F. Brown, W.D. Mackintosh, J. Electrochem. Soc. 120
(1973) 1096.
In summary, we have presented an MEISstudy
of the thermal oxidation of Al(1 1 0) in the regime of
continuous Al2O3 film formation. At temperatures
up to 573 K we observe growth of the planar stoi-
chiometric oxide film. A roughness onset was de-
tected at 673 K. Kinetic data are consistent with the
Cabrera–Mott oxidation mechanism. Sequential
16O2, then 18O2, oxidation shows preferential
incorporation of re-oxidant near the oxide–metal
interface at prolonged oxidation times, accompa-
nied by a redistribution of the network oxygen in
the original oxide. We regard that as evidence of the
oxygen species being the major contributor to the
material transport across the oxide film. Our
interpretation of the isotopic substitution results
suggests rapid interface formation of oxygen de-
fects and their subsequent slow migration across the
oxide overlayer. The latter is a rate-limiting process
controlling oxidation reaction. Some oxygen loss
into the gaseous phase was observed only at the
highest oxidation temperature used. Our results
demonstrated that MEISis able to reveal oxygen
depth distribution details on a sub-nm scale.
[14] R.K. Hart, J.K. Maurin, Surf. Sci. 20 (1970) 285.
[15] B.E. Hayden, W. Wyrobisch, W. Oppermann, S. Hachicha,
P. Hofmann, A.M. Bradshaw, Surf. Sci. 109 (1981) 207.
[16] T. Do, N.S. McIntyre, Surf. Sci. 440 (1999) 438.
[17] T. Do, S.J. Splinter, C. Chen, N.S. McIntyre, Surf. Sci. 387
(1997) 192.
[18] F.P. Fehlner, Low Temperature Oxidation: The Role of
Vitreous Oxides, John Wiley & Sons, New York, 1986.
[19] J. Grimblot, J.M. Eldridge, J. Electrochem. Soc. 129 (1982)
2369.
ꢃ
[20] A. Jimenez-Gonzalez, D. Schmeisser, Surf. Sci. 250 (1991)
ꢃ
59.
[21] L.P.H. Jeurgens, W.G. Sloof, F.D. Tichelaar, E.J. Mitte-
meijer, Phys. Rev. B 62 (1999) 4707.
[22] J.F. van der Veen, Surf. Sci. Rep. 5 (1985) 199.
[23] R.M. Tromp, M. Copel, M.C. Reuter, M.H. von Hoegen,
J. Speidell, R. Koudijs, Rev. Sci. Instrum. 62 (1991) 2679.
[24] D. Semrad, P. Bauer, Nucl. Instr. Meth. Phys. Res. B 12
(1985) 24.
ꢁ
[25] G. Moliere, Z. Naturforsch. 2a (1947) 133.
[26] D.J. OÕConnor, E.R. Wouters, A.W.D. van der Gon, J.F.
van der Veen, P.M. Zagwijn, J.W.M. Frenken, Surf. Sci.
296 (1993) 131.
[27] J.A. Phillips, Phys. Rev. 97 (1955) 404.
[28] H.C. Lu, E.P. Gusev, E. Garfunkel, T. Gustafsson, Surf.
Sci. 351 (1996) 111.
[29] C.J. DellÕOca, L. Young, Appl. Phys. Lett. 13 (1968)
228.
[30] F.P. Fehlner, J. Electrochem. Soc. 131 (1984) 1645.
[31] R. Ghez, J. Chem. Phys. 58 (1973) 1838.
Acknowledgements
€
[32] M.J. Dignam, W.R. Fawcett, H. Bohni, J. Electrochem.
Soc. 113 (1966) 656.
This work was supported by the SRC and by
NSF grant no. DMR 0218406.
[33] N. Klein, M. Albert, J. Appl. Phys. 53 (1982) 5840.
[34] C.T. Kirk, E.E. Huber, Surf. Sci. 9 (1968) 217.
[35] J.W.M. Frenken, R.M. Tromp, J.F. van der Veen, Nucl.
Instr. Meth. Phys. Res. B 17 (1986) 334.
References
[36] J.R. Noonan, H.L. Davis, Phys. Rev. B 29 (1984) 4349.
[37] J.N. Andersen, H.B. Nielsen, L. Petersen, D.L. Adams, J.
Phys. C: Solid State Phys. 17 (1984) 173.
[1] N. Cabrera, N.F. Mott, Rep. Prog. Phys. 12 (1948 – 1949)
163.
[38] B.W. Busch, T. Gustafsson, Surf. Sci. 415 (1998) L1074.
[39] D.S. Gemmell, Rev. Mod. Phys. 46 (1974) 129.
[40] E.P. Gusev, H.C. Lu, T. Gustafsson, E. Garfunkel, Phys.
Rev. B 52 (1995) 1759.
[2] G.L. Hunt, I.M. Ritchie, Oxid. Met. 2 (1970) 361.
[3] H.D. Ebinger, J.T. Yates, Phys. Rev. B 57 (1998) 1976.
[4] V. Zhukov, I. Popova, J.T. Yates, Phys. Rev. B 65 (2002)
195409.
[41] H.H. Andersen, J.F. Ziegler, The stopping and ranges of
ions in matter, vol. 3, Pergamon, New York, 1977.
[42] N. Bohr, Mat. Fys. Medd. Dan. Vid. Selsk. 18 (1948) 8.
[43] J. Lindhard, M. Scharff, Mat. Fys. Medd. Dan. Vid. Selsk.
27 (1953) 15.
[5] I. Popova, V. Zhukov, J.T. Yates, Surf. Sci. 518 (2002) 39.
[6] C. Ocal, S. Ferrer, N. Garcia, Surf. Sci. 163 (1985) 335.
[7] I. Popova, V. Zhukov, J.T. Yates, Phys. Rev. Lett. 89
(2002) 276101.
[8] I. Popova, V. Zhukov, J.T. Yates, Langmuir 16 (2000)
10309.
[44] I. Trimaille, S. Rigo, Appl. Surf. Sci. 39 (1989) 65.
ꢀ
[45] T. Akermark, Oxid. Met. 50 (1998) 167.