121901-2
S. Song and F. Placido
Appl. Phys. Lett. 99, 121901 (2011)
flow of 190 sccm and O2 partial pressure of 0.04 Pa, at room
temperature).
Spontaneous surface oxidation of AlN (stage 1 in Fig. 2)
is a complex process, where oxygen molecules must undergo
collision, absorption, diffusion, nucleation, and finally
growth to form a complete thin oxide film.16 The surface ox-
ide layer usually reaches a finite thickness of a few nano-
meters at room temperature and atmospheric pressure, being
limited by the diffusion of oxygen through the new oxide
layer to reach unoxidised nitride. In our previous work on ki-
netic models,17 equations describing the spontaneous surface
oxidation were developed from the following generalized
approach of chemical reaction kinetics:
For a first order reaction
FIG. 2. Reflectance versus time for AlN deposition and surface oxidation.
h
For a second order reaction
ꢀ
ꢁi
t
dðtÞ ¼ d1 1 ꢁ exp ꢁ
þ d0:
(2)
s
needed for the simulation and fitting of optical monitor data
(assuming refractive index homogeneity in the layers, and
Al2O3 formed from AlN at surface9).
ꢂ
ꢃ
1
dðtÞ ¼ d1 1 ꢁ
þ d0:
(3)
1 þ t=s
Here, the oxide layer is being formed from the already
deposited AlN, therefore, oxide thickness can be determined
from the original AlN thickness that is converted into oxide.
Thus, an AlN film of thickness dAlN will lead to an oxide
layer of thickness dAl2O3, with a thickness correction factor,
f ¼ dAl2O3/dAlN. As the number of metal atoms per unit area
must remain the same before and after oxidation, we have
The Cabrera-Mott model (CM model)18 is an important
model for surface oxidation that is claimed to be suitable for
the growth of native oxides (spontaneous oxidation).19 The
rate of oxide growth is determined by the migration of
charged ionic species through the oxide film which is formed
in this model by the drive of the so called Mott potential UM
across the oxide film. The oxide growth rate is proportional
to the ionic flux. As the oxide layer is very thin in this work,
a simplified equation from the CM model is used in this
paper
doxide
dAlN
NAlN ꢀ DAlN ꢀ Moxide
Noxide ꢀ Doxide ꢀ MAlN
f ¼
¼
;
(1)
where DAlN and Doxide are densities, dAlN and doxide are
thicknesses, MAlN and Moxide are molecule weights, and
ꢄ
ꢅ
X2
A
A
X
NAlN and Noxide are the number of Al atoms in one molecule
ꢂ exp
ꢁ
¼ u ꢂ ðt þ sÞ;
(4)
of the nitride and oxide layer, respectively. Here, NAlN is 1
and Noxide is 2. Finally, the thickness correction factor is
obtained as 0.99.
here s is an initial time taken to grow the initial oxide thick-
ness, X is the thickness of oxide layer at time, t, and
The typical noise range of unfiltered reflectance meas-
ured in this system is 0.044%, as shown in Fig. 2. Calculated
reflectance values are 20.972% for 40 nm AlN and 21.199%
for 1 nm Al2O3 on 39 nm AlN. Thus, the change of reflec-
tance is 0.27% for 1 nm oxide formed from a 40 nm AlN
film. Accordingly, the uncertainty in the oxide thickness
from our raw data corresponds to 6 0.08 nm (¼0.5 ꢀ 1 nm
ꢀ 0.044%/0.27%).
DC0
ZeaUM
kT
u ¼ V0
and A ¼
;
(5)
2a
where V0 is the oxide volume per migrating ion, D is a diffu-
sion coefficient, 2a is the ion jump distance, Ze is the ion
charge, UM is Mott potential, and C0 is the concentration of
mobile ions.
Using the information above, we calculate the AlN layer
thickness and oxide layer thicknesses as a function of time.
The layer stack used for fitting the growing AlN layers was
AlN/SiO2(2 nm)/Si. For the oxidation stage, Al2O3/AlN/
SiO2 (2 nm)/Si was used. If the final deposited thickness of
the AlN film is dfinal and the remaining AlN thickness at a
given time is d, then the oxide thickness is constrained to be
f(dfinal-d), where f is the thickness correction factor. A pro-
gram for fitting the reflectance data was written in MATHCAD.
The initial thickness of AlN film deposited was calculated to
be 39.32 nm, and we estimate that 0.28 nm of Al oxide was
formed by spontaneous oxidation in stage 1, and the thick-
ness grew to 0.63 nm during the plasma-enhanced oxidation
in stage 2 (under 4.5 mTorr chamber pressure with Ar gas
In this paper, we introduce a combined model of the 2nd
order of chemical reaction kinetics and parabolic model,
which agrees with the experimental data very well. This is
ꢂ
ꢃ
1
dðtÞ ¼ d1 1 ꢁ
þ d0 þ d2 ꢂ t1=2
;
(6)
1 þ t=s
where d(t) is thickness at time t, s is time constant, d1 is the
final thickness of initial oxide layer, d2 is the parabolic
growth constant, and d0 is the initial thickness of the oxide
layer. Dimensions for t and s are s, for d0, d1, and d(t) are
nm, and for d2 is nm/s1/2
.
Equation (2), (3), and (4) are used for the analysis of
spontaneous surface oxidation of AlN (stage 1 in Fig. 2).
130.133.66.132 On: Wed, 03 Dec 2014 12:04:49
Song, Shigeng
