Reaction and transport interplay in Al MOCVD investigated through experiments and computational fluid dynamic analysis

Article abstract of DOI:10.1149/1.3493617

An improved reactive transport model of a metallorganic chemical vapor deposition process for the growth of aluminum films from dimethylethylamine alane is developed. The computational fluid dynamics model is built under PHOENICS software for the simulation of the coupled fluid flow, heat transfer, and chemistry. The growth mechanism of aluminum films is based on well-established, in the literature, reaction order and activation energy of gas-phase and surface reactions. The improvement of the model against a simplified model is established. The interplay of reaction and transport is elucidated. In particular, the important effects of the gas-phase reaction and of the showerhead system are revealed; accounting for gas-phase along with surface reactions for the flow details in the showerhead and for the three-dimensional geometry induced by the distribution of the holes in the showerhead yields substantial enhancement of the predictive capability of the model. The satisfactory agreement between model predictions and growth-rate measurements allows one to understand and improve the process. The model is further used to investigate the effect of key operating parameters on the characteristics of the aluminum films. Simulation results are suggestive of modifications in the operating parameters that could enhance the growth rate and its spatial uniformity.

Full text of DOI:10.1149/1.3493617

Journal of The Electrochemical Society, 157 ͑12͒ D633-D641 ͑2010͒
D633
0
013-4651/2010/157͑12͒/D633/9/$28.00 © The Electrochemical Society
Reaction and Transport Interplay in Al MOCVD Investigated
Through Experiments and Computational Fluid Dynamic
Analysis
a,z
b,c
b
Theodora C. Xenidou, Nathalie Prud’homme, Ca onstantin Vahlas,
a
Nicholas C. Markatos, and Andreas G. Boudouvis
a
School of Chemical Engineering, National Technical University of Athens, Athens 15780, Greece
Centre Interuniversitaire de Recherche et d’Ingénierie des Matériaux, Ecole Nationale Supérieure
b
d’Ingénieurs en Arts Chimiques et Technologiques, 31030 Toulouse Cedex 4, France
An improved reactive transport model of a metallorganic chemical vapor deposition process for the growth of aluminum films
from dimethylethylamine alane is developed. The computational fluid dynamics model is built under PHOENICS software for the
simulation of the coupled fluid flow, heat transfer, and chemistry. The growth mechanism of aluminum films is based on well-
established, in the literature, reaction order and activation energy of gas-phase and surface reactions. The improvement of the
model against a simplified model is established. The interplay of reaction and transport is elucidated. In particular, the important
effects of the gas-phase reaction and of the showerhead system are revealed; accounting for gas-phase along with surface reactions
for the flow details in the showerhead and for the three-dimensional geometry induced by the distribution of the holes in the
showerhead yields substantial enhancement of the predictive capability of the model. The satisfactory agreement between model
predictions and growth-rate measurements allows one to understand and improve the process. The model is further used to
investigate the effect of key operating parameters on the characteristics of the aluminum films. Simulation results are suggestive
of modifications in the operating parameters that could enhance the growth rate and its spatial uniformity.
©
2010 The Electrochemical Society. ͓DOI: 10.1149/1.3493617͔ All rights reserved.
Manuscript submitted March 31, 2010; revised manuscript received September 3, 2010. Published October 14, 2010. This was
paper 2478 presented at the Vienna, Austria, Meeting of the Society, October 4–9, 2009.
Aluminum ͑Al͒ is the major element in complex metallic alloys
CMAs͒, including quasicrystalline phases, such as the Al Cu Fe
the heated substrate, and on the use of the perforated plate of the
showerhead system. The complete set of the experimental data was
͑
6
2
25 13
1
icosahedral one. Such phases present strong technological potential
utilized to formulate a comprehensive reactive transport model for
2
22,23
due to their interesting properties and combination of properties.
Al-MOCVD based on PHOENICS CFD software.
The aim of
This is especially the case for CMA films, applied on complex-in-
shape substrates. Metallorganic chemical vapor deposition
this work is to reproduce the experimental measurements through
realistic CFD modeling and, more importantly, to contribute to the
understanding of Al from DMEAA under subatmospheric pressure
conditions.
͑
MOCVD͒ is a promising technique to meet this challenge and for
this reason the growth of Al films was selected as the first important
step toward the establishment of a robust, innovative MOCVD pro-
cess for the production of CMA films.
DMEAA has been experimentally investigated as a precursor for
1
1-19
aluminum films by several groups.
of DMEAA dissociation were suggested to explain the
observations.
Plausible reaction pathways
Although MOCVD is essentially a chemical surface process,
3
12,14,24
transport phenomena are very complex in MOCVD reactors and the
Kinetic parameters, such as reaction order and
accurate control of the growth of films brings together various as-
activation energy, were reported for chemical reactions in the gas
4
,5
16,17
pects of fluid flow, heat transfer, and chemical kinetics. Extended
experimentation is required to determine operating conditions for
process optimization. Alternatively, modeling of the MOCVD pro-
cess and simulation at appropriately selected conditions could make
phase and on the surface.
According to these experimental ob-
servations, the Al growth rate increased to a maximum around
1
7
150°C and then decreased at substrate temperature above 150°C.
The activation energy of the surface reaction was found to be
9.96 kcal/mol when the substrate temperature was lower than
150°C, which is believed to be in the surface-reaction-limited re-
gime. The gas-phase reaction mechanism in Al MOCVD from
DMEAA was investigated using in situ real-time FTIR
6
-9
the time-consuming experimental investigation more efficient.
Preliminary results of the supplementary use of growth experiments
and computational fluid dynamics ͑CFD͒ simulations of Al MOCVD
process from dimethylethylamine alane ͑DMEAA͒ have already
10
16
been published by the authors. The selection of DMEAA as the
metal-organic precursor for Al, was based on the results of previous
spectroscopy. The gas-phase dissociation reaction of DMEAA into
dimethylamine ͑DMEA͒ and alane was found to be first order with
activation energy of 9.56 kcal/mol. Moreover, the gas-phase
DMEAA was unstable even at room temperature, resulting in disso-
ciation into DMEA and alane, and the dissociation rate accelerated
1
1-19
experimental studies on its decomposition
quent deposition of aluminum films.
and on the subse-
20,21
The published results con-
cerned the simulation of Al growth in the narrow temperature range
of 200–220°C and they provided an insight into the hydrodynamics
and the thermal patterns of the MOCVD reactor to be used in the
future production of the Al-based CMAs.
2
5
at higher values of gas temperature. Matsuhashi et al. revealed an
increase of the pressure in DMEAA container from
a
0.5 to 200 Torr in 500 h at ambient temperature. The alane is also
known to be very unstable in the gas phase and forms a dimer,
In the present work, the experimental investigation of Al growth
in an expanded temperature range enhances the improvement of a
2
6
trimer, and even a polymer. When the substrate temperature is
higher than 150°C, it is believed that alane can be readily polymer-
ized and it is not readily adsorbed on the surface to form aluminum
10
simple starting model, which is now ready to be used in the thor-
ough investigation of the MOCVD of Al-based multinary interme-
tallic films. Specifically, complementary measurements were ob-
tained in the temperature range of 160–260°C at 10 Torr and
concerned the dependence of the growth-rate profile on the process
temperature, on the distance between the gas delivery system and
1
2
films. The rapid dissociation of DMEAA in the gas phase brings
about the decrease of the growth rate when the substrate temperature
is above 150°C. A similar effect of temperature on the behavior of
1
8
DMEAA was also reported by Jang et al.; the temperature where
the maximum growth rate was obtained was 160°C, to be compared
1
7
with 150°C in the work by Yun et al. It was also reported that
when temperature is below 160°C, it is very difficult to distinguish
a mass-transport-limited regime from a surface-reaction-limited one.
c
Present address: University Paris Sud 11, LEMHE/ICMMO, Orsay Cedex, France
E-mail: thexen@central.ntua.gr
z
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D634
Journal of The Electrochemical Society, 157 ͑12͒ D633-D641 ͑2010͒
"
$-5&
394
283
203
144
97
8
6
4
2
Sw ei t rhi e ps l1a te
Sw ei t rhi eo su 2t plate
!
"#$%!$&'
Gas phase
competitive
phenomena
Surface
reaction
rate
limited
(
)*+%&+$
a
0,0015
0,0018
0,0021
0,0024
0,0027
,
(-.
!"$ !%&
/%&.
Figure 2. Arrhenius plot of the growth rate of Al films as a function of
substrate temperature, with and without the use of the shower plate.
Figure 1. ͑Color online͒ Schematic illustration of the experimental MOCVD
setup.
distributed though a showerhead system containing a 60 mm diam-
−
6
eter perforated plate. The base pressure of reactor is 10 Torr,
while the total pressure was fixed at 10 Torr.
All these experimental findings are taken into account in the
present reactive transport model, which is a more elaborate version
9
9% pure DMEAA ͑Epichem͒ was used as received in a stainless
10
steel bubbler. It was maintained at 9°C, corresponding to a saturated
vapor pressure of 0.7 Torr. The DMEAA bubbler was maintained at
this temperature during the entire period of its service in order to
of the one presented earlier. The effect of reactive transport in the
gas phase is added to the surface chemistry to account for the de-
crease of the Al growth rate at higher values of temperature. The
detailed description of the perforated plate of the showerhead sys-
tem, in a three-dimensional reactor discretization, further improves
the accuracy of the model predictions. The improved model is then
used to investigate the effect of key operating parameters on Al
growth rate and its spatial uniformity over the surface of the heated
substrate.
2
5
avoid degradation of the precursor. 99.9992% pure N ͑Air Prod-
2
ucts͒ was fed through two electropolished stainless steel gas lines
with VCR fittings. One line was used for bubbling through the Al
precursor and the other for the dilution of the input gas. The flow
rate of the dilution N was 305 sccm, while the bubbling N flow
2
2
rate was 25 sccm. Assuming saturation of the gas phase, these con-
ditions lead to an upper limit of the flow rate of DMEAA equal to
2
sccm.
Experimental
Table I summarizes the operating conditions and the results of
Growth experiments of Al films were performed in the experi-
mental setup schematically illustrated in Fig. 1. This MOCVD setup
is composed of a stagnant flow, cylindrical, vertical, stainless steel
reactor, the dimensions of which were reported previously. The
deposition chamber is made of double envelope, allowing the wall
temperature to be monitored through the circulation of thermally
regulated silicon oil. HF cleaned 5 ϫ 10 mm silicon coupons were
used as substrates. They were positioned horizontally at different
places on a 58 mm diameter susceptor and heated by a resistance
coil gyred just below the surface of the susceptor. The input gas is
the growth experiments. In the first four experiments ͑expl, l = 1,4͒
the perforated shower plate of the gas delivery system was used,
while in the last four experiments ͑expl, l = 5,8͒, the plate was
removed from the showerhead system. Growth rate was measured at
certain positions over the substrate, through the weight gain of each
sample. Figure 2 depicts the average growth rate of Al films on Si
substrates as a function of substrate temperature, in the range of
160–260°C. Only experiments corresponding to a 15 mm distance
between the perforated shower plate and the heated substrate are
included in the Arrhenius plot. As shown in Fig. 2, the growth rate
1
0
Table I. Experimental operating conditions and results for the growth of Al films.
Growth
temperature,
Ts
Wall
temperature,
Tw
Inlet
temperature,
Tin
Plate–
substrate
distance,
Dp–s ͑mm͒
Deposition
duration,
td
Average
growth rate,
GR
Sample
name
Case
͑°C͒
͑°C͒
͑°C͒
͑min͒
͑Å/min͒
I: with
shower
plate
exp1
exp2
exp3
exp4
exp5
exp6
exp7
exp8
160
200
220
260
220
240
260
260
25
25
25
25
25
75
25
50
65
65
65
65
67
75
25
75
15
15
15
15
15
20
15
21
120
120
120
120
120
30
161.6
237.8
227.2
79.0
544.6
335.3
453.5
418.5
II: without
shower
plate
120
50
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Journal of The Electrochemical Society, 157 ͑12͒ D633-D641 ͑2010͒
of Al films increases as the substrate temperature increases up to
D635
ٌ · ͑␳u͒ = 0
͓1͔
2
00°C when the shower plate is used. On the contrary, the Al
Momentum balance:
growth rate decreases with further increase of substrate temperature
above 200°C. This trend is observed for both cases examined, i.e.,
with and without the use of the shower plate, and is consistent with
previous experimental findings cited in the introduction. It is worth
mentioning that the objective of the reported experimental part was
to provide data on the growth rate of Al films under different depo-
sition conditions rather than to propose another value of the activa-
tion energy of the growth process.
T
ٌ
· ͑␳uu͒ = − ٌ P + ␳g + ٌ ·
ͫ
␮͑ ٌ u + ͑ ٌ u͒ ͒
2
3
−
␮͑ ٌ · u͒I
ͬ
͓2͔
Energy balance:
N
N
K
⌬
Hi
g
k
The Reactive Transport Model
cp ٌ · ͑␳uT͒ = ٌ · ͑␭ ٌ T͒ −
ji ·
−
H ␥ R
͚
͚͚
i
ik
Mi
i=1
i=1 k=1
The starting point for the present work is a simplified CFD
10
model constructed by Xenidou et al. to simulate the hydrodynamic
and thermal flow of the MOCVD reactor, including an overall sur-
face reaction to account for the growth of Al films from DMEAA.
The present reactive transport model includes two important refine-
ments that account more reliably for the reactor configuration and
for the growth chemistry; the first refinement concerns the transport
model while the second one is an addition to the reactive model. For
reasons of completeness, the main features of the reactive transport
model are presented below followed by the detailed description of
the model improvements.
͓3͔
Species balance:
eff
eff
ٌ
· ͑␳u␻ ͒ = − ٌ − ␳Di ٌ ␻ − ␳␻ D ٌ ͑ln M͒
i
ͩ
i
i
i
N
C
j
j
eff
i
T
+
+
M␻ D
− D ٌ ͑ln T͒
i
i
͚
ͪ
M D
ij
j=1,jꢀi
j
The reactive transport model for the MOCVD process relates the
physicochemical phenomena occurring in the reactor to the proper-
ties of the Al films. The core of the model is formed by the transport
model describing the gas flow and transport of energy and species in
the reactor. The basic components of the reactive model are ͑i͒ a
gas-phase chemistry part, including the reaction path and rate con-
stant for the homogeneous reaction, which influences the species
concentration distribution near the growth surface, and ͑ii͒ a surface
chemistry part which describes how reactions between gas-phase
species and adsorbed species on the surface lead to the film growth.
The coupling of transport phenomena and chemistry under the
framework of computational fluid dynamics is the master approach
followed in the simulation of chemical vapor deposition ͑CVD͒ pro-
cesses. Following the first publications on CVD reactor modeling in
K
g
k
Mi ␥ R
͓4͔
͚
ik
k=1
The transport equations are subject to the following boundary
conditions for velocity field, temperature profile, and species con-
centration distribution: ͑i͒ at the inlet, the velocity distribution is
considered uniform, the gas feed is assumed to be at constant tem-
perature, and the species mass fractions are set to the experimental
values; ͑ii͒ the operating pressure is specified at the outlet, where
zero normal derivatives are assumed for all other variables ␾ ͑␾
=
T,u ,u ,u ,␻ ͒; ͑iii͒ the no-slip condition for gas velocity is ap-
x z y i
plied at any solid surface; ͑iv͒ the temperature is fixed at the outer
walls of the reactor; and ͑v͒ the temperature is fixed inside the
susceptor at a position of 3–4 mm from the substrate surface; it is
the position where the thermocouple is located. A conjugate heat
transfer model is used to calculate the temperature inside the sus-
ceptor and on the substrate surface.
27-29
the late 70s and early 80’s,
the computational analyses of CVD
processes have been based on CFD models that combine either mul-
30-33
tidimensional flow with rather simple chemistry
or simple zero
or one-dimensional flow with detailed gas-phase and surface chemi-
3
4-37
The properties of the individual gas species and the binary dif-
cal reactions.
Since the late 90’s, however, the combination of
4
5
fusion coefficients are estimated using the kinetic gas theory. De-
tailed description of mixing rules used for the calculation of the
properties of the multicomponent gas mixture in terms of pressure,
temperature, and composition is given in earlier work. The
Lennard-Jones parameters of the individual chemical species are
taken from Choi et al.
The deposition rate was described by the formula adopted by
multidimensional fluid dynamics with multireaction chemistry has
become feasible due to the increasing availability of computational
5,38,39
power and efficiency.
More detailed overview of the develop-
4
6
ment of CVD simulation models in the past decades can be found in
Ref. 5. In recent years, successful attempts have been made in em-
4
7
4
0,41
ploying CFD models to optimize CVD process conditions
and
42
hydrodynamic design of CVD reactors with respect to growth-rate
uniformity. The present reactive transport model is based on the
state-of-the-art approach that combines three-dimensional fluid dy-
namics with homogeneous and heterogeneous reactions, enabling a
realistic description of the transport phenomena and of the growth
process inside the MOCVD reactor. Such an approach ensures that
the present model can be used as a reliable tool in the optimization
of the reactor design; the framework for this work has been recently
developed combining the simplified model of the MOCVD process
4
8,49
many researchers
diffusion of reactive species through the boundary layer,
that combines surface reaction and gas-phase
N
1
1
␴i
=
+
͓5͔
Rd RS
͚
D
Ri
i=1
2
The calculated deposition rate Rd ͑mol/m s͒ was converted to
the experimentally measured growth rate, GR ͑Å/min͒ as
43
with evolutionary algorithms.
Ms
11
The transport phenomena in the gas mixture are described by the
conservation equations of mass, momentum, and energy, coupled to
the conservation equations for the individual chemical species, un-
der the following reasonable assumptions: the gas multicomponent
mixture is treated as a continuum; laminar gas flow conditions exist;
steady-state conditions prevail; the equation of state obeys the ideal
GR = 6 ϫ 10 R
͓6͔
d
␳s
The variation of the growth rate is calculated through the maxi-
mum, minimum, and average growth rate, i.e., by
GRmax − GRmin
10
gas law. The reader is referred to earlier work for detailed discus-
sion of the simplifying assumptions. The complete set of the non-
⌬G =
͓7͔
GR
44
linear partial differential equations is as follows:
Mass balance:
The transport equations for mass, momentum, energy, and
5
0
chemical species described above have the general form
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D636
Journal of The Electrochemical Society, 157 ͑12͒ D633-D641 ͑2010͒
0
␾
ٌ
· ͑␳u␾͒ = ٌ · ͑⌫ ٌ ␾͒ + S + SЈ␾
͓8͔
␾
␾
0
␾
In Eq. 8, the S = S + SЈ␾ is the generalized source term, linear-
␾
␾
ized in variable ␾. To numerically solve these equations, PHOEN-
22
ICS CFD software was used, which is based on the finite volume
5
0
method. The momentum and continuity equations were coupled
through the SIMPLEST ͑Semi-Implicit Method for Pressure-Linked
Equations ShorTened͒ scheme and the upwind differencing scheme
was used for the convective terms. The discretized transport equa-
tions were solved in a segregated way, i.e., the coupling between the
velocity components, the pressure correction, the temperature, and
each of the species mass fractions is accounted for through iteration.
To ensure convergence, linear relaxation was used for pressure cor-
rection and temperature and false time step relaxation was applied to
all other variables.
Improvement 1.— While the axial symmetry of the vertical
MOCVD reactor supports the two-dimensional ͑2D͒ approximation
of the reactor, the nonuniform distribution of the holes over the
shower plate requires a three-dimensional ͑3D͒ simulation. In the
10
starting simplified model, the MOCVD reactor was spatially dis-
cretized in 2D curvilinear coordinates based on the assumption of
axial symmetry of the vertical reactor. The latter assumption was
supported by the approximate treatment used to simulate the flow
through the perforated plate. According to that approximation, the
shower plate was not included in the solution domain and the cor-
responding control volumes were treated as solid. To overcome the
discontinuity of the flow in the solution domain, the pressure loss
due to friction was specified using the Darcy–Weisbach equation for
5
1
laminar flow,
L
d2
⌬
P = 32␮uz
͓9͔
In the present improved model, the reactor is discretized in 3D
curvilinear coordinates to account for the detailed configuration of
the perforated shower plate as shown in Fig. 3. The shower plate
consists of 1450 holes of 0.76 mm diameter. The thickness of the
plate is 1 mm. In this case, the approximate boundary condition
described above was removed and the computational domain was
extended inside the plate for the gas flow through the plate to be
adequately resolved; this required a finer computational grid inside
the holes of the plate.
Figure 3. ͑Color online͒ Schematic illustration of the showerhead gas deliv-
ery system.
composes almost immediately without contributing to the film
1
2,26
growth.
Thus, the first reaction is responsible for the degradation
of DMEAA in the gas phase, resulting in the decrease of the growth
rate at higher substrate temperatures. Moreover, the gas-phase reac-
tion was considered to occur only in the forward direction, because
Improvement 2.— In the preliminary analysis of the MOCVD
reactor, in the temperature range of 200–220°C, a fast reaction was
assumed to occur on the substrate surface in one step according to
the reverse reaction can occur very slowly under
a H2
1
6
environment. Note that the activation energy was obtained from
the cited references; the pre-exponential factor of the gas-phase re-
action was extracted from the Arrhenius plot of the Al–N dissocia-
tion reaction-rate constant ͑see Fig. 6 in Ref. 16͒. The pre-
exponential factor of the surface reaction was fitted to the
experimental data.
͓
͑CH ͒ C H ͔NAlH ͑g͒ → Al͑s͒ + ͓͑CH ͒ C H ͔N͑g͒ + 3/2H ͑g͒
3
2
2
5
3
3 2
2
5
2
͓
10͔
The rate constant was chosen to be large enough for the growth
rate to be independent of its value. This assumption is valid in the
transport-limited regime where the surface reaction is very fast and
the growth rate approaches the diffusive flux of the species to the
substrate surface. The rate of consumption of reactants and the rate
of production of products were based on the stoichiometry of the
overall surface reaction ͑Eq. 10͒.
Results and Discussion
Comparison with the simplified model.— At first, the improve-
ment of the present reactive transport model was evaluated in com-
1
0
parison to the reference simplified one. Figure 4 compares the
predictions of the two models with the experimental measurements
In the present work, to calculate the growth rate of Al films in the
temperature range of 160–260°C, a reactive model was formulated.
It considers both homogeneous and heterogeneous chemical reac-
in terms of the Al growth-rate profile at growth temperature ͑T ͒ of
s
16,17
tions obtained from the literature.
Although plausible reaction
200°C and plate–substrate distance ͑Dp–s͒ of 15 mm. The continu-
ous curve is the prediction of the improved model, while the dotted
line corresponds to the simplified model. It can be seen that although
the simplified model follows the evolution of the experimental
growth rate in the radial direction, it fails to capture the rapid in-
crease of the growth rate toward the edge of the substrate, i.e., at
25 mm. On the other hand, the improved model performs much
better at the edge of the substrate. Taking into account the experi-
mental error of the growth rate ͑Ϯ8 Å/min at 200°C͒, the predic-
tions of the improved model are very satisfactory.
mechanisms, including adsorption of DMEAA, surface reactions,
1
4
and desorption of hydrogen and DMEA were reported, the activa-
tion energy is available only for the overall reaction. Thus, the
chemical reactions considered in the improved reactive model of the
Al growth process are listed in Table II. The first reaction occurs in
the gas phase, resulting in the DMEAA dissociation into DMEA and
alane, while the second one occurs on the surface, resulting in the
growth of Al films on the heated substrates. It was assumed that
once DMEAA is dissociated in the gas phase, gas-phase alane de-
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Journal of The Electrochemical Society, 157 ͑12͒ D633-D641 ͑2010͒
D637
Ref.
Table II. Chemical reactions and rate constants for reaction k „m = 1,2…, km = Am exp„−E ÕRT….
m
Activation
energy
Pre-
exponential
factor
͑kcal mol−1͒
a
Reactions
Classification
7
1
2
͓͑CH ͒ C H ͔NAlH ͑g͒ → ͓͑CH ͒ C H ͔N͑g͒ + AlH ͑g͒
Volumetric
Surface
9.56
9.96
2.4 ϫ 10
16
18
3
2
2
5
3
3
2
2
5
3
0
͓͑CH ͒ C H ͔NAlH ͑g͒ → Al͑s͒ + ͓͑CH ͒ C H ͔N͑g͒ + 3/2H ͑g͒
4.0 ϫ 10
3
2
2
5
3
3
2
2
5
2
a
−
1
−
1
T
h
e
p
r
e
-
e
x
p
o
n
e
n
t
i
a
l
f
a
c
t
o
r
i
n
t
h
e
g
a
s
-
p
h
a
s
e
r
e
a
c
t
i
o
n
i
s
g
i
v
e
n
i
n
u
n
i
t
s
o
f
s
a
n
d
t
h
a
t
o
f
t
h
e
s
u
r
f
a
c
e
r
e
a
c
t
i
o
n
i
n
m
s
.
Validation of the model.— The improved model is validated
predicted growth rates at 160°C are very high compared to the ex-
perimentally measured ones. This significant divergence can be ex-
plained by the incubation time of Al growth on silicon substrates.
According to our experimental observations, the incubation time,
during which no appreciable deposition had been observed at
160°C, was approximately 2 min at the center of the susceptor and
almost 15 min at its edge; i.e., at 25 mm from the center. The incu-
bation time was not taken into account in the calculation of the
growth rate; that is, the incubation time was not subtracted from the
total duration of each experiment. Similar incubation times of Al
against experimental measurements obtained in the MOCVD setup.
Remember that the first set of experiments was carried out with the
use of the perforated plate while in the second set the plate was
removed from the showerhead system. Figure 5 shows the compari-
son of the model predictions with the experimental growth rates
when the perforated plate is used ͑case I͒. As shown in Fig. 5a, the
300
250
200
1
4,18
experiment
growth from DMEAA have also been observed on Si and SiO2.
In agreement with literature results, the incubation time decreases
with increasing deposition temperature in the investigated range of
temperature.
The agreement between experimental and predicted growth-rate
profiles is satisfactory at higher values of temperature ͑200–260°C͒,
as depicted in Fig. 5b-5d. Note that growth rate decreases with in-
simplified model
improved model
creasing T , and this trend is also predicted by the improved model.
s
We emphasize that this is the important effect of the second modi-
fication of the model, i.e., the addition of the gas-phase reaction
which is responsible for the rapid degradation of the Al precursor in
the gas phase.
Figure 6 presents the predicted Al growth rates with experimen-
tally measured ones for case II, i.e., without the shower plate. Note
that the model is modified to describe the plate-free showerhead
system. According to the experimental measurements, when the
shower plate is removed from the gas delivery system, growth rates
0
5
10
15
20
25
Distance in the radial direction (mm)
Figure 4. Al growth rate along the radial direction at T = 200°C and
s
Dp–s = 15 mm. Experimental measurements vs model predictions.
400
44 00
(
a)
ex
peri
m
ent
(
b)
ee xpe rr iment
m
o
d
e
l
mm odel
33 00
33 00
22 00
22 00
11 00
0
11 00
0
5
1
0
1
5
20
25
0
5
1
0
1
5
2
0
25
Figure 5. Al growth rate along the radial
direction, at ͑a͒ Ts = 160°C, ͑b͒ Ts
D
is
ta
nce
i
n
t
h
e
r
adia
l
d
i
r
e
ct
i
on
(
DD istanc ee in the ra dd ial dire cc tion (mm)
=
=
200°C, ͑c͒ T = 220°C, and ͑d͒ Ts
260°C. Experimental measurements vs
s
4
0
0
model predictions, for the case with the
perforated plate, case I. The plate–
substrate distance is Dp–s = 15 mm.
44 00
(
c)
(( d)
e
x
p
e
r
i
m
ent
ee xperiment
m
o
d
e
l
mm odel
30
0
33 00
200
22 00
100
11 00
0
00
0
5
10
15
20
25
0
5
10
15
20
255
DD istanc ee in the ra dd ial dire cc tion (mm)
DD istanc ee in the ra dd ial dire cc tion (mm)
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D638
Journal of The Electrochemical Society, 157 ͑12͒ D633-D641 ͑2010͒
1200
11 200
(( b)
ex
peri
m
ent
e
(( a)
1000
11 000
m
odel
m
800
88 00
600
66 00
400
44 00
200
22 00
0
00
Figure 6. Al growth rate along the radial
direction, at ͑a͒ Ts = 220°C, Dp–s
= 15 mm, ͑b͒ T = 240°C, D = 20 mm,
0
5
1
0
15
20
25
0
5
10
15
20
22 5
s
ta
nce
i
n
t
e
r
adia
l
ct
i
on
(m
s
p–s
͑
c͒ T = 260°C, D = 15 mm, and ͑d͒
s p–s
Ts = 260°C, Dp–s = 21 mm. Experimental
measurements vs model predictions, for
the case without the perforated plate, case
II.
1
2
11 200
(
c)
e
(
d
)
ee xx periment
1000
0
11 000
m
mm odel
800
88 00
600
66 00
400
44 00
200
22 00
0
00
0
5
10
15
20
25
0
5
10
15
2
2
0
0
22 5
DD istanc ee in the ra dd ial dire cc tion (mm)
DD istanc ee in the ra dd ial dire cc tion (mm)
become higher at the center of the substrate while they decrease in
plate. The negative values of the axial velocity around 15 mm indi-
cate the presence of a large recirculation zone that extends outside
the showerhead system when the plate is removed, as shown in Fig.
8. The origin of this relatively large zone may be attributed to the
local pressure drop due to the velocity increase and the change of
the flow direction at the showerhead.
The relative effect of gas-phase and surface reaction in the tem-
perature range of 160–260°C can be deduced from the DMEAA
consumption, presented in Fig. 9. Note that the points represent the
model predictions at the experimental operating conditions tabulated
in Table I. The straight lines are linear trend lines of the discrete
points. The primary ͑left͒ axis is used for the consumption of
DMEAA through the gas-phase reaction, while the secondary ͑right͒
axis is used for the surface reaction. As expected, the consumption
of DMEAA in the gas-phase increases with temperature. Specifi-
cally, the DMEAA degradation is almost 82.5% at 160°C, while it
exceeds the value of 97.5% at 260°C when the shower plate is used.
When the perforated plate is removed from the showerhead system,
the DMEAA degradation follows a similar trend but the correspond-
the radial direction. This change in the growth-rate radial profile was
observed for the temperature range investigated ͑220–260°C͒ and is
also confirmed by the model. To identify the origin of this change in
the radial profile of the growth rate, the distribution of the DMEAA
over the substrate was further investigated. As expected, the distri-
bution of the DMEAA mass fraction follows a similar trend with
that of the growth rate for both cases examined, i.e., with and with-
out the shower plate. The significant increase of the DMEAA mass
fraction at the center of the substrate, when the plate is removed
from the showerhead system, is due to the dominant convection
related to the high velocity of the gas mixture. This is shown in Fig.
7
, which depicts the distribution of the axial component of the ve-
locity along the radial direction of the reactor, with and without the
6
ww ith pp late
ww itho uu t plate
4
2
0
-- 2
0
5
10
15
20
22 5
D
Figure 7. Axial component of the velocity along the radial direction of the
reactor, at 5 mm distance above the substrate. T = 220°C and Dp–s
Figure 8. ͑Color online͒ Velocity vectors in the MOCVD reactor at Ts
= 220°C with ͑left͒ and without ͑right͒ the perforated shower plate.
s
=
15 mm.
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Journal of The Electrochemical Society, 157 ͑12͒ D633-D641 ͑2010͒
D639
1
00
20
increases significantly. The decrease of the growth rate is more rapid
above 220°C, a consequence of the significant DMEEA degradation
in the gas phase. The increased variation of the growth rate with
temperature is also shown in Fig. 10b, where the normalized growth
rate profiles at different values of temperature are compared. It can
be seen from Fig. 10b that the growth rate variation is greater at a
distance of about 16 mm from the center of the substrate and at the
edge of the substrate, i.e., at 25 mm. Moreover, there seems to be a
particular distance ͑around 22.5 mm͒ where the variation of the
growth rate starts increasing in the opposite direction.
It appears that any temperature below the reference value per-
forms much better, as accompanied by a greater growth rate with an
improved spatial uniformity. However, recall that the experimental
growth rate at 160°C is lower compared to 220°C due to the in-
creased incubation time, as discussed previously. Therefore, a value
in the range 200–220°C could be considered as an optimal value of
substrate temperature.
with plate
without plate
9
5
0
5
0
15
10
5
9
8
8
0
1
20
160
200
240
280
320
o
Effect of reactor pressure.— Parameter continuation on P was
performed and growth rate profiles were calculated for values of
pressure in the range of 5–30 Torr, by steps of 5 Torr. The reference
value of reactor pressure is 10 Torr. As shown in Fig. 11a, the in-
crease of pressure above the reference value causes a decrease of the
growth rate, which approximates the value of 1.6 Å/min at 30 Torr.
On the other hand, note the significant increase of the growth rate by
a factor of 7 when pressure is decreased to the lowest value of
Deposition temperature ( C)
Figure 9. DMEAA consumption ͑%͒ in the gas-phase and in the surface
reaction. The straight lines are linear trend lines of the discrete points.
ing values are smaller. For example, at 220°C the DMEAA con-
sumption is almost 90.6% ͑without plate͒ to be compared with
4.1% ͑with plate͒. The enhancement of the gas-phase consumption
5
Torr. Growth rate uniformity is improved at the lower pressure
9
investigated, as also depicted in Fig. 11b. The intersection point of
the curves is almost 1 mm away from the edge of the substrate. It is
concluded that any value of the operating pressure lower than the
reference one is expected to improve the properties of the Al films.
of DMEAA, when the perforated plate is used, may be attributed to
the trapping of the gas mixture components inside the large recircu-
lation zone created in the showerhead system. These large percent-
ages of DMEAA degradation in the gas phase are responsible for the
decrease of DMEAA consumption through the surface reaction
when temperature increases and subsequently for the decrease of the
growth rate above 160°C. Note that the conversion of DMEAA into
Al remains lower than 5% even for the lower temperature investi-
gated ͑i.e., 160°C͒. The slight increase of the surface-reaction yield
Effect of dilution gas flow rate.— Parameter continuation on Fd
was performed and growth rate profiles are calculated for values of
flow rate from 105 to 505 sccm in steps of 100 sccm. As shown in
Fig. 12a, the reference value of F is 305 sccm. The results show
d
that any increase of the flow rate of dilution nitrogen causes an
increase of the growth rate. It appears that the dominant convection
related to higher flow rates, and thus higher velocities, yields higher
DMEAA concentrations and therefore higher growth rates. This
trend in the growth rate is followed by a decrease of growth rate
variation, as depicted in Fig. 12b. The increased values of the
growth rate, mainly in the center of the substrate, are responsible for
the improvement of the growth rate uniformity at the higher values
of the flow rate.
with increasing T is attributed to the corresponding decrease of
gas-phase degradation of DMEAA.
s
In the following, the improved reactive transport model is used
for a systematic parametric analysis of the MOCVD reactor for Al
growth. All simulations were performed by first selecting a set of
reference conditions and then by varying the value of each one of
the operating parameters. The reference conditions selected in the
present study correspond to the experimental sample exp3 ͑see Table
I͒. The predictions of the model along with the experimental mea-
surements at reference conditions are shown in Fig. 5c.
Conclusions
Effect of substrate temperature.— Parameter continuation on Ts
was performed and growth rate profiles were calculated for values of
temperature from 160 to 300°C in steps of 20°C. Note that the rela-
tive growth rate is equal to unity at reference conditions ͑Ts
This paper presents an improved computational fluid dynamics
model that enables the elucidation of the reaction and transport in-
terplay in the growth process of Al films from DMEAA. The reac-
tive transport model was successfully constructed under the frame-
work of PHOENICS CFD software to simultaneously solve the
conservation equations of mass, momentum, and energy under
steady-state conditions. A simplified model previously developed to
describe the Al-MOCVD under low-pressure conditions was used as
=
220°C͒ and that growth rate variation was defined through Eq. 7.
The growth rate is equal to 227.2 Å/min at reference conditions.
The results in Fig. 10a indicate that any increase of the substrate
temperature causes a decrease of the growth rate while its variation
2,
0
100
11 ,4
1
,
8
R
e
l
a
t
i
v
e
G
r
o
wt
h
R
a
t
e
90
(( b)
((( a)
c
n
s
s
v
t
ion
)
T =3
ss
o
1,
111 ,2
1,
4
77 0
1
,
2
66 0
o
Figure 10. ͑a͒ Relative growth rate and
growth rate variation as a function of sub-
strate temperature. ͑b͒ Normalized growth
rate profile at different values of substrate
TTT =1 6666 00 C
sss
1,
0
50
11 ,0
ooo
0,
8
40
TT = 111 66 000 CC
sss
0,
6
33 0
000 ,8
0,
4
20
temperature, T ͑in steps of 20°C͒.
s
0,
2
10
oo
TTT =3 0000 00 C
sss
0,
0
0
00 ,6
140
160
180
200
2
20
240
260
280
300
320
0
5
10
15
20
25
30
ooo
S
u
b
s
tr
a
t
e
t
em
p
e
r
a
t
u
r
e
(
C
)
DD is tt an cc eee in tt hhhh e rr aa dd ial ddd ire ccc tio nnn ( mmm m ))
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D640
Journal of The Electrochemical Society, 157 ͑12͒ D633-D641 ͑2010͒
8
88 0
111 ,4
RRR elat iiii ve G rrr owt hhh Rat ee
(( a)
7
70
(
b
)
PP = 3 00 T ooo r rr
TT h iiii c kkkk n ee s ss v aa ri aa t ii ooo n ( %% ))
6
66 0
111 ,2
5
55 0
P
=
5
T
o
r
r
Figure 11. ͑a͒ Relative growth rate and
growth rate variation as a function of re-
actor pressure. ͑b͒ Normalized growth rate
profile at different values of reactor pres-
sure, P ͑in steps of 5 Torr͒.
4
4
0
PP = 5 TTTT orr
111
33 0
20
00 ,8
11 0
PPP = 3 00 T ooo r rr
0
0
00 ,6
0
5
10
15
20
25
30
35
0
5
10
15
20
25
33 0
R
e
ac
t
o
r
P
r
e
s
s
u
r
e
(T
o
r
r
)
DD is tt an cc eee in tt hhhh e rr aa dd ial ddd ire ccc tio nnn ( mmm m ))
4
60
11 ,6
RRR ela tt iv ee GG row tt hh Ra tt ee
(
a
)
(( b)
333 ,5
T
h
i
c
k
nes
s
va
ri
at
i
on
(%
)
50
11 ,4
333
40
11 ,2
2,
5
F
d
=
10
5
s
c
c
m
Figure 12. ͑a͒ Relative growth rate and
growth rate variation as a function of di-
lution gas flow rate. ͑b͒ Normalized
growth rate profile at different values of
dilution gas flow rate, Fd ͑in steps of
100 sccm͒.
2
3
0
11 ,0
111 ,5
20
00 ,8
111
10
0,
F == 5555 000 55 sss cc cccc mm
d
0
,
5
0
0
00 ,4
0
100
200
300
400
500
600
0
5
10
15
20
2
5
30
DD il uuu ti oo n g aa s ff lll ow rrr at ee (s cc cm ))
DD i sss t aa n cc eee in tt hhhh e rr aa dd ial ddd ire ccc tio nnn ( mmm m ))
a reference model to establish the improvement of the present
model. Two important refinements were found to improve the model
predictions, namely the detailed description of the perforated shower
plate, which influences the spatial distribution of the growth rate
over the substrate, and the addition of the gas-phase reaction, which
is responsible for the decrease of the growth rate at higher values of
temperature.
The improved model was validated against experimental mea-
surements that demonstrate the influence of the growth temperature,
of the distance between the showerhead system and the heated sub-
strate, and of the use of the perforated plate in the gas delivery
system. The good agreement between model predictions and experi-
mental data fully supports the gas and surface chemistry reported in
the literature. Moreover, simulation results revealed the important
effect of the gas-phase degradation of DMEAA in comparison to the
limited contribution of the surface reaction to the film growth on the
heated substrate.
Based on the improved model, simulation results indicated that
the growth rate and its spatial variation strongly depend on the
growth temperature, on the reactor pressure, and on the inlet flow
rate of the dilution gas. It is concluded that the improved reactive
transport model can be used as a tool to guide future experimental
work toward optimal parameter values for desired growth rates and
growth shapes of Al-based complex metallic alloys.
List of Symbols
A
g
u
pre-exponential factor of reaction rate
gravity acceleration, m s−
2
−
1
component of the velocity vector, m s
−1
u
velocity vector, m s
cp specific heat, J kg K−1
−1
d
diameter of the holes of the shower plate
2
−1
D
binary diffusion coefficient, m s
T
thermal diffusion coefficient, kg m s−1
−1
D
eff
effective diffusion coefficient, m2 s−1
D
Dp–s distance between the shower plate and the substrate, mm
exp experimental sample
activation energy, kcal mol−
1
E
Fd flow rate of dilution gas, sccm
enthalpy of formation, J mol−
unity tensor
1
H
I
j
k
l
L
M
diffusive mass flux, kg m− s−1
2
kinetic rate
with respect to experimental sample
thickness of the shower plate
gas mixture molecular weight, kg mol
−
1
Ms molecular weight of deposited ͑solid͒ material, kg mol−
1
N
P
R
number of gas species
pressure, Pa
gas constant, 8.34132 J mol K−1
−
1
Rd deposition rate, mol m−
2
−1
s
D
maximum diffusive mass flux at the surface, kg m s−1
−2
R
Rg gas phase reaction rate, mol m
−3
s
s
−2
R
surface reaction rate, mol m
s
S
S
generalized source term, various
constant part of the generalized source term, various
SЈ linear part of generalized source term, various
temperature, K
td duration of experiment, min
Acknowledgments
0
This work was supported by the General Secretariat for Research
and Technology of Greece and by the French Ministry of Foreign
Affairs through the Programme for “Greece–France cooperation in
Research and Technology” ͑contract 15207XG, 2006-08͒. The sup-
port of the Agence Nationale de la Recherche in France, through
contract NT05-3_41834, and of the European Commission through
the network of excellence NMP3-CT-2005-500140 is also acknowl-
edged.
T
Greek
␥
⌫
gas phase stoichiometric coefficient
generalized diffusion coefficient, kg m−
growth rate variation, %
1
⌬
G
⌬
P
␭
pressure loss
gas mixture thermal conductivity, W m− K−1
1
␮
␳
gas mixture viscosity, Pa s
gas mixture density, kg m−
Centre Interuniversitaire de Recherche et d’Ingénierie des Matériaux as-
sisted in meeting the publication costs of this article.
3
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Journal of The Electrochemical Society, 157 ͑12͒ D633-D641 ͑2010͒
D641
density of deposited ͑solid͒ material, kg m−3
␳
s
͑1998͒.
␴
␾
␻
surface stoichiometric coefficient
generalized variable ␾, various
gas species mass fraction
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2
2
3. N. C. Markatos, Rev. Inst. Fr. Pet., 48, 631 ͑1993͒.
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with respect to the mth surface reaction
m
max maximum value
min minimum value
k
s
w
x
y
2
2
2
2
3
3
3
3
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at the wall of the reactor
in the x-direction
in the y-direction
in the z-direction
z
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