Journal of Crystal Growth 195 (1998) 733—739
A reaction-transport model for AlGaN MOVPE growth
Theodoros G. Mihopoulos, Vijay Gupta, Klavs F. Jensen*
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Abstract
We present a systematic study of the complex chemistry and transport phenomena underlying metalorganic vapor
phase epitaxy (MOVPE) of AlGaN; in particular, the mechanism underlying growth rate reduction at high temperatures
and pressures. Thermodynamics and kinetics of formation of Lewis acid—base adducts of the organometallic precursors
[TMGa—NH and TMAl—NH ] and the subsequent elimination of methane are investigated using hybrid density
functional theory and transition state theory. The adduct pathway leads to the formation of stable dimer and trimer ring
species containing Ga, Al, and N which strongly influence growth behavior in the reactor. Results from these studies,
combined with reported data for gas-phase decomposition of TMGa and TMAl, are used in macroscopic, finite element
reactor modeling studies to develop a reaction-transport model for AlGaN MOVPE growth. The model predicts growth
rates in excellent agreement with experimental data for growth of AlGaN in different reactor configurations, including
horizontal and ‘close-spaced-injector’ reactors. Formation of dimers and trimers is identified as the major pathway for
decreased growth efficiency with increasing pressure. A pathway involving nucleation and growth of oligomers from
dimers and trimers, and ultimately particle formation, is consistent with decreased growth efficiency for increasing
temperature. 1998 Elsevier Science B.V. All rights reserved.
PACS: 81.15.G; 81.05.Ea; 82.30.!b; 02.70.Dh
Keywords: Kinetic mechanism; Finite element; Aluminum nitride
1. Introduction
Metalorganic vapor phase epitaxy (MOVPE) of
AlGaN involves complex gas-phase and surface
reactions combined with flow, heat transfer, and
mass transfer processes. The results of these phys-
* Corresponding author. Fax: #1 617 258 8224; e-mail:
kfjensen@mit.edu.
ical and chemical rate processes determine the
quality of the deposited layers in terms of film
thickness, composition uniformity as well as impurity incorporation. The nature and relative importance of these processes are not well understood for
growth of group III nitride thin films. In the case of
AlGaN, the growth rate reduction at high temperatures and pressures as well as the variation in
severity of this effect with different reactor configurations are not well understood. Progress has
0022-0248/98/$ — see front matter 1998 Elsevier Science B.V. All rights reserved.
PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 0 6 4 9 - 6
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T.G. Mihopoulos et al. / Journal of Crystal Growth 195 (1998) 733–739
been made in simulation of fluid flow as well as heat
and mass transfer in MOVPE processes [1], but
predictions of growth rates and alloy compositions
for group III-nitride systems remain limited by the
availability of thermodynamic and kinetic data.
MOVPE of the III-nitrides is further complicated by the interaction of the group III and group
V precursors leading to adduct formation. Prereactions of group III precursors [e.g. trimethylaluminum (TMAl) and trimethylgallium (TMGa)]
with ammonia to form adducts have been reported
to lead to deposition in inlets, wall deposits and
particle formation [2]. These reactions have also
been hypothesized as being responsible for the
strong dependence of material properties on reactor configuration, and may determine whether device quality material can be grown in a particular
reactor configuration. Moreover, difficulties experienced in the incorporation of significant concentrations of Al cannot be explained through
thermodynamic models used for other III—V compound semiconductor systems. Development of an
understanding of chemistry and reaction mechanisms underlying MOCVD of AlGaN is critical,
therefore, to the fabrication of nitride-based devices.
The framework for nitride growth simulations is
similar to that for models of typical III—V semiconductor growth (e.g., GaAs and related alloys), but
the nitride growth modeling has added complexities. Since the deposition temperature is significantly higher in the nitride growth systems,
radiation, natural convection and thermal diffusion
effects are particularly pronounced and have to be
captured for accurate predictions. Moreover, the
precursors can no longer be considered dilute in an
inert carrier gas. A mixture of NH and H /N at
comparable flow-rates is used, with the precursors
highly reactive towards NH and NH itself de
composing at the growth surface. Implementation
of multi-component diffusion in species transport
equations is therefore essential to obtaining accurate growth rate predictions.
Table 1
Lennard—Jones parameters for the gaseous species used in the
kinetic model
Species
p (A)
e/k (K)
TMAl
MMAl
TMAl—NH
DMAl—NH
(DMAl—NH )
(DMAl—NH )
CH
H
NH
5.04
3.49
5.26
4.60
5.65
6.63
3.69
2.83
2.92
458.9
295.2
536.2
524.6
949.7
247.8
146.9
59.7
481.0
ential equations representing the conservation of
momentum, energy, total mass and individual species using the finite element method (FEM) [1]. The
FEM transport model solves for flow and heat
transfer (including conduction in the walls, convection, and, radiation) for realistic reactor configurations. The conservation of total mass and
individual species equations are then solved on the
same mesh to obtain the concentration profiles.
Since ammonia and hydrogen or nitrogen are used
at comparable flow-rates, mixture rules were used
to compute the transport parameters and multicomponent diffusion was accounted for in the species conservation. The thermodiffusion component
which drives high molecular species away from hot
regions, towards cold regions, has also been included because of the high temperature and high
molecular weight adduct and related oligomer species involved. The diffusion coefficients were estimated from the Chapman—Enskog formulas [3]
based on Lennard—Jones parameters for the gasphase species. The Lennard—Jones parameters for
the gaseous species used in this model have been
either taken from the literature or estimated using
group contribution methods [4], and are summarized in Table 1.
3. Kinetic model
2. Reactor model
The reaction-transport model is based on numerical solution of the nonlinear, coupled partial differ-
A kinetic mechanism for AlGaN deposition,
consisting of both gas-phase and surface reactions, has been developed. The AlN portions of the
T.G. Mihopoulos et al. / Journal of Crystal Growth 195 (1998) 733–739
735
Fig. 1. Schematic of the AlN deposition and reaction pathways.
Table 2
Kinetic mechanism for the growth of AlN
Reaction
Gas phase reactions
G1 TMAl
G2 TMAl#NH
G3 TMAl : NH
G4 TMAl : NH #NH
G5 2DMAl—NH
G6 DMAl—NH #(DMAl—NH )
G7 DMAl—NH #(DMAl—NH )
L
G8 (DMAl—NH ) #(DMAl—NH )
L
G9 (DMAl—NH )
G10 (DMAl—NH )
Surface reactions
S1 TMAl#s
S2 TMAl : NH #s
S3 MMAl#s
S4 DMAl—NH #s
S5 (DMAl—NH ) #s
S6 Al*
S7 AlN*
k
E
66.5
0.0
22.0
27.0
13.0
0.0
0.0
0.0
0.0
40.0
40.0
0.0
0.0
0.0
0.0
0.0
20.0
20.0
P
P
Q
P
P
P
P
P
P
P
P
MMAl#2CH
TMAl : NH
DMAl—NH #CH
DMAl—NH #CH #NH
(DMAl—NH )
(DMAl—NH )
(DMAl—NH )
L>
(DMAl—NH )
L>
AlN (particle)
AlN (particle)
3.5;10
3.0;10
5.0;10
2.0;10
2.0;10
4.0;10
1.0;10
1.0;10
1.0;10
1.0;10
1.0;10
P
P
P
P
P
P
P
Al*#3CH
Al*#3CH #NH
Al*#CH
AlN*#2CH
2 AlN*#4CH
AlN(s)#s
AlN(s)#s
coll (p"0.1)
coll (p"0.1)
coll (p"1.0)
coll (p"1.0)
coll (p"1.0)
6.0;10
6.0;10
Note: Activation energies are in kcal/mol and pre-exponentials are in (cm/mol)L\ s\ (for gas-phase reactions) where n is the order of
the reaction and in (cm/mol) s\ for surface reactions.
p denotes the sticking coefficient for the collisional type surface reaction.
Acronyms used above are: MMAl"AlCH , TMAl"Al(CH ) , TMAl : NH "Al(CH ) : NH , DMAl—NH "(CH ) Al—NH .
mechanism are presented here. The previously developed mechanism for GaN [5] was used for Ga
species and adducts. The mechanism for AlN consists of ten gas-phase reactions and seven surface
reactions (see Fig. 1 and Table 2). Quantum chemistry computations using the density functional theory (DFT) methods such as the Becke 3-parameter
density functional theory using the Lee—Yang Parr
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T.G. Mihopoulos et al. / Journal of Crystal Growth 195 (1998) 733–739
correlation functional (B3LYP) were performed to
investigate the structure and reactivity of the Lewis
acid—base adducts formed by TMAl with NH . The
Gaussian94 package [6] was used for all quantum
chemistry calculations.
Gas-phase decomposition reactions for ammonia have been studied in the combustion community [7] and simulations with reported kinetic
parameters show no significant gas-phase decomposition on typical MOVPE conditions [5].
There is, however, very little information available
on ammonia decomposition kinetics at the AlGaN
surface. Because of the high temperatures and NH
flow-rates employed in nitride MOVPE growth, an
excess of active N species, readily available for
growth, is assumed at the surface.
TMAl is known to exist in an equilibrium between the monomer form AlMe and the dimer
form Al Me , with the heat of dissociation of the
one mole of dimer into two moles of monomer
being 20.3 kcal/mol [8,9]. At bubbler conditions,
the equilibrium is dominated by the dimer form.
However, on dilution with the carrier gas the partial pressure of the Al-containing species decreases
significantly and, according to the Le Chatelier
principle, the equilibrium shifts towards the
monomer. Diluting 20 sccm H transporting
+0.15 sccm Al Me with 4 SLM carrier gas im plies that more than 85% of the Al-containing
species will be in the monomer form. Furthermore,
the adduct formation between TMAl and NH
(which is in excess) occurs instantaneously upon
mixing, (reaction G2), further depleting the TMAl
and shifting the equilibrium towards the monomer
state. G1 represents the unimolecular decomposition of TMAl. The rate parameter for the decomposition of TMAl has been obtained by taking the
reported Al—C bond strength [10] equal to the
activation energy and by assuming that the preexponential factor will be similar to the ones obtained from TMGa decomposition studies [11].
TMAl decomposition has been proposed to occur
through the loss of CH radicals, and the loss of the
first CH radical has been taken to be the rate
limiting step.
The precursor materials TMGa, TMAl and
NH are known to undergo parasitic pre-reactions
to form TMG : NH and TMAl : NH adducts.
TMAl : NH has also been isolated on argon ma
trices from a merged jet of TMAl and ammonia
[12]. The TMAl : NH adduct is a white crystalline
solid which on heating at 70°C eliminates CH to
give DMAl—NH [13]. Irradiation of matrix
isolated TMAl : NH
yields methane and
DMAl—NH [14]. The alkyl-aluminum amide,
DMAl—NH , has been shown to exist as a trimer,
both in the solid phase as well as the gas-phase
[13]. The formation of these intermediate species
such as TMAl : NH followed by thermal elimina
tion of CH play a significant role in AlN deposi
tion. AlN has been successfully deposited from
single source precursors, TMAl : NH [15] and
[DMAl—NH ] [16], giving further support to the
importance of these species.
G2 is the adduct formation reaction between
TMAl and NH . The forward reaction rate para
meters have been estimated from collision theory
and the reverse rate parameters have been obtained
from quantum chemistry calculations. G3 and G4
represent the CH elimination reactions for the
adduct. The CH elimination reaction from the
Lewis acid—base adduct has been studied experimentally [17]. The *H
in solution was meaP"L
sured as !19.6 kcal/mol. Quantum chemistry
calculations (at the B3LYP/6-31G(d,p) level) gave
*H
in the gas-phase as !4.2 kcal/mol. The
P"L
difference in the heat of reaction could be due to
effects of solution, phase change, and inaccuracies
in the quantum chemistry calculations. Using
quantum chemistry techniques, the activation energy for this intra-molecular reaction pathway was
determined to be 27 kcal/mol. Coordination with
a second NH molecule further lowers the activa
tion energy for the loss of CH to 13 kcal/mol. This
is consistent with the lower *H
value obtained
P"L
from quantum chemistry. The same experimental
study also found the CH elimination reaction to
be catalyzed by excess TMAl and DMAl—NH .
Furthermore, the DMAl—NH catalyzed pathway
was shown to be suppressed in the presence of
excess NH [17]. Under typical nitride growth con
ditions, the NH /TMAl ratio is &5000 and TMAl
is not present in excess. Thus, both, the TMAl and
DMAl—NH catalyzed pathways should not be im
portant for MOCVD growth and are ignored in
this mechanism.
T.G. Mihopoulos et al. / Journal of Crystal Growth 195 (1998) 733–739
The monomeric species, DMAl—NH can form
dimers (G5), which can further undergo polymerization reaction to form trimers (G6) and higher
n-mers (G7 and G8). Both monomer and dimers are
postulated to contribute to growth. Although the
trimer has been employed as a precursor to deposit
AlN, such growth runs were successful only using
low pressure MOCVD (&10\ Torr), and resulted
in polycrystalline films [16]. The vapor pressure of
these species is very low, thereby making growth
from these species unlikely at typical growth conditions. Hence, it has been postulated that the trimers
and higher n-mers either deposit on the walls or are
swept out of the reactor and do not contribute to
growth. The polymerization/agglomeration reaction leads to a sharp fall-off in the growth rate with
increasing pressure. All n-mers above the trimer
have been lumped as a single component in this
model. This allows us to represent the polymerization reaction in a few simple steps in the absence
of more detailed kinetic information.
The strong bond in the adduct-derived dimer
and trimer ring species in AlN leads to the possibility of gas-phase nucleation and particle formation in
the reactor (G9 and G10). It is postulated that at
high temperatures, the dimers have sufficient energy to lose the methyl groups to form AlN particles. These particles are carried away from the
deposition zone by thermophoresis and they therefore do not contribute to the growth. The result is
a further depletion of growth species from the reactor. This behavior is consistent with the observed
drop in growth-rate with increasing temperature in
reactors with ample opportunities for mixing and
gas-phase reactions.
The surface mechanism consists of chemisorption reactions for the reactive species from the gas
phase and the growth reactions. The rate of the
chemisorption reactions is given by the rate of the
collision of the gaseous species with the surface,
modified by a sticking coefficient. The sticking coefficient is taken to be 0.1 for TMAl and the adduct
and unity for all other species. Reaction S6 represents the growth resulting from the decomposition
of TMAl or the adduct, while S7 represents the
growth from the adduct-derived route. Reaction S6
assumes there is excess of active N species available
for growth at the surface. The rate parameters for
737
the two growth reactions have been taken to be the
same to minimize the number of fitting parameters.
Since there is very little information available on
the effect of H on AlN growth, this interaction has
not been considered in this mechanism.
Predictions based on this mechanism are consistent with growth rate data for a horizontal reactor
[2] as well as experimental data from a “closedspace-injector” reactor [18]. Figs. 2 and 3 show
experimental data and model predictions for AlN
growth over a wide temperature range (400—900°C)
at 85 Torr and wide pressure range (30—270 Torr) at
600°C, respectively. Excellent agreement is observed over the whole parameter space. Comparison between the model predictions and
experimental data from the “closed-space-injector”
reactor [18] is shown in Figs. 4 and 5, and is found
to be consistent.
While the growth rate of GaN varies linearly
with the inlet mole fraction of the TMGa, the
growth rate of AlN increases sub-linearly with the
inlet mole fraction of TMAl. Growth efficiency is
defined as the growth rate divided by the group III
molar flow-rate. While the absolute growth efficiency varies with the reactor configuration and depends on operating conditions, such as the carrier
gas flow-rate and pressure, the relative AlN/GaN
growth efficiency can serve as an indication of the
Fig. 2. Comparison of predicted (solid line) and experimentally
observed [2] (points) growth rates of AlN in the horizontal
reactor, as a function of temperature (P"85 Torr).
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T.G. Mihopoulos et al. / Journal of Crystal Growth 195 (1998) 733–739
Fig. 3. Comparison of predicted (solid line) and experimentally
observed [2] (points) growth, as a function of pressure
(¹"600°C).
Fig. 5. Growth rates of GaN and AlN in the close-spaced injection reactor as a function of the inlet molar flow rate of TMGa
and TMAl, respectively. (Operating conditions: 1060°C,
76 Torr.) Comparison of predicted (solid line) growth rates and
experimental data [18].
Table 3
Relative aluminum incorporation efficiency for AlGaN growth
Reactor configuration
Close-spaced injector
(76 Torr)
Horizontal (85 Torr)
Fig. 4. Solid versus gaseous aluminum fraction for AlGaN
growth in the close-spaced-injection reactor. Comparison of
predicted (solid line) composition and experimental data [18].
efficiency of the reactor to incorporate Al in the
nitride film. Table 3 shows the relative Al-incorporation efficiency for the two different reactor configurations. For the “close-spaced-reactor”, upon
increasing the substrate temperature from
800—1060°C, the relative Al-incorporation efficiency drops to almost half, from 0.91 to 0.40. For the
horizontal reactor, the relative Al-incorporation is
AIN/GaN growth efficiency
800°C
1060°C
0.91
0.40
0.70
0.00
lower compared to the “close-spaced-reactor” at
800°C, and drops to zero at higher temperatures.
These results underscore the importance of reactor
geometry and operating conditions in the growth of
AlN based materials. The “closed-space-reactor”,
which has a thin thermal boundary layer and short
residence time, is less affected by adduct reactions
and achieves higher Al incorporation than the horizontal reactor under similar conditions.
4. Conclusions
In summary, a chemical mechanism based on the
available knowledge of AlGaN deposition coupled
with computational chemistry results has been
T.G. Mihopoulos et al. / Journal of Crystal Growth 195 (1998) 733–739
developed. Formation of dimers and trimers has
been identified as the major pathway for decreased
growth efficiency with increasing pressure. A pathway involving nucleation and growth of oligomers
from dimers and trimers, and ultimately particle
formation, is consistent with decreased Al-incorporation efficiency with increasing temperature.
Model predictions are in good agreement with
experimental data from two different reactor configurations, an horizontal reactor and a “closespaced-injector” reactor. The results show the
combined influence of deposition chemistry and
transport phenomena on MOVPE of group III
nitrides, underscoring the need to understand the
many rate processes involved. The accurate predictions across different reactor configurations lend
confidence to further use of the kinetic model for
reactor design and process optimization.
Acknowledgements
This work was supported by DARPA under contract CMDA 972-96-3-0014.
739
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