Dissociative Chemisorption of Trimethylgallium, Trimethylindium, and

ARTICLE pubs.acs.org/JPCC

Dissociative Chemisorption of Trimethylgallium, Trimethylindium, and Ammonia on Gallium and Indium Nitride Substrates. A Computational Study Beatriz H. Cardelino*,† and Carlos A. Cardelino‡ † ‡

Chemistry Department, Spelman College, Atlanta, Georgia 30314-4399, United States School of Earth & Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia 30332-0340, United States

bS Supporting Information ABSTRACT: The methyl or hydrogen dissociations of trimethylgallium [Ga(CH3)3], trimethylindium [In(CH3)3], and ammonia (NH3), adsorbed onto model substrates for gallium nitride (GaN) and indium nitride (InN), were studied using the hybrid program ONIOM. The model substrates consisted of 44 GaN units and 35 InN units, with no capping hydrogen atoms, and were simulated using a quantum mechanical semiempirical approach (PM6). The adsorbates were represented using density functional theory (DFT) and basis sets containing polarization functions [B3LYP/6-311G(d,p)/3-21G(d,p)]. Adsorption rate constants, as well as methyl and hydrogen unimolecular homolytic dissociation rate constants, were computed using a semiclassical procedure, for pressures between 1 and 100 atm and for temperatures ranging from 300 to 1400 K. Time-dependent dissociative chemisorption processes of Ga(CH3)3, In(CH3)3, and NH3 adsorbing onto GaN and InN were modeled by solving sets of coupled differential equations using stiff methods.

’ INTRODUCTION In 2002, it was discovered that the bandgap of the semiconductor indium nitride was not 2 eV as previously thought but, instead, a much lower 0.7 eV.1 Gallium nitride (GaN) emits invisible ultraviolet light because of its 3.4 eV bandgap, but when some of the gallium is exchanged for indium, forming clusters of indium nitride (InN), violet, blue, and green colors are produced. The wavelength emitted can be controlled by increasing the GaN/InN ratio, from near-ultraviolet to red, and also by the thickness of the InGaN layers.2 The advantages of InGaN alloys are that they have large heat capacity, resistance to ionizing radiation, a direct bandgap, and high carrier mobility,3 making them suitable for solar cells in satellites and other spacecraft. However, the growth of the InGaN alloys and heterostructures is a challenge due to the lower disassociation temperature of InN compared to that of GaN and by the large difference between the lattice constants of the binary InN and GaN4 (with c parameter in wurtzite crystals of 5.693 and 5.185 Å, respectively). To improve the phase stability of the InGaN layers, research efforts have been directed to investigate the use of high-pressure chemical vapor deposition (HPCVD). By utilizing high pressures of nitrogen gas, the InGaN growth surface can be stabilized, and the thermal decomposition process above the growth surface can be effectively suppressed.5 The influence of the growth temperature on the phase stability and composition of single-phase InGaN epilayers has been recently studied by HPCVD with an In/Ga ratio of 0.6, at a reactor pressure of 15 bar, at various growth temperatures.6 The results showed that a growth temperature of 925 °C (1198 K) led to the best single-phase InGaN layers with the smoothest surface and smallest grain areas. r 2011 American Chemical Society

The study being now reported is an extension of the investigation recently published on the adsorption of the trimethylindium source material [In(CH3)3] onto an InN substrate and its subsequent methyl dissociation as a function of temperature and high pressure.7 The present study includes the interaction of two different substrates, InN and GaN, with three different source materials, trimethylgallium [Ga(CH3)3], In(CH3)3, and ammonia (NH3), and two types of dissociative chemisorption processes: (a) methyl dissociation of adsorbed organometallic source materials and (b) release of atomic hydrogen or nitrogen from adsorbed nitrogen species resulting from NH3 reactions in the gas phase. In the previous investigation,7 the model substrates consisted of four In atoms coordinated to ten N atoms, with the outside surfaces capped with H atoms, except for some locations on the surface that represented the N-surface of the wurtzite InN substrate. In the present study, two types of model substrates were designed to represent pure GaN and pure InN, containing 44 Ga/44 N atoms and 35 In/35 N atoms, respectively, with no capping H atoms, and thus having substantially much larger surface area and depth, consisting of only group III and N atoms and having an equal number of group III and N atoms.

’ METHODS The computational software used for the calculation of optimized structures and electronic energies was Gaussian 09W,8 Received: December 29, 2010 Revised: March 24, 2011 Published: April 19, 2011 9090

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The Journal of Physical Chemistry C with the following options: (a) PM6,9 a semiempirical quantum mechanical approach using STO-3G basis sets,10 for calculations on free substrates; (b) density functional theory (DFT)11 with B3LYP functionals,12 using 3-21G(d,p) basis sets for In atoms and 6-311G(d,p) basis sets13 for all other atoms, for calculations on free adsorbates; and (c) a two-level ONIOM approach14 for calculations on substrate
adsorbate adducts, using PM6 and B3LYP/6-311G(d,p)/3-21G(d,p) as the low- and highlevel approximations, respectively. In addition, the calculations of reaction rate constants were performed based on transition-state theory, using the RRKM15 and Troe16 approaches, modified for the homolytic dissociation of large molecules17 and adapted for the solid state.7 Supporting Information Topic SI-1 summarizes the calculations performed to obtain Gibbs free energies. Finally, modeling of time-dependent processes was performed using MATLAB. 18 The above techniques were applied to the following stages of the investigation: (a) modeling the substrates, (b) adsorption and dissociation energies of adsorbed species, (c) temperatureand pressure-dependent reaction-rate constants for the dissociative chemisorption reactions, and (d) time-dependent simulations of the dissociative chemisorption processes. The RRKM method has been applied in the past, for example, in studies related to the lattice influence on gas
solid desorption.19 In the RRKM formulation, the basic assumption is that the reactive trajectory, originating in the reactants, must cross the dividing surface between reactants and products only once and then proceeds to products. Alternately, the VTST20 approach identifies a saddle point and a reaction path connecting it with the reactants and the products, and the position of the dividing surface is varied to yield the smallest rate constant. However, for reactions without an activation barrier, as is the case of unimolecular dissociation and recombination reactions, the RRKM method is often employed. (a). Modeling the Substrates. The semiempirical quantum mechanical program PM69 allows for calculations of relatively large molecules. In the present study, the substrates were comprised of as many as 88 atoms and the adsorbates up to 13 atoms. Thus, substrate models, with wurtzite crystal structure, large surface area, and depth at the adsorption site, were designed using PM6. The model substrates contained either Ga or In atoms and an equal number of N atoms. Only valence electrons are considered in semiempirical calculations, and the atomic orbitals for N, Ga, and In are represented with STO-3G basis sets10 containing 18 basis functions and 57 primitive functions (18b/57p). Three model substrates were designed: (a) a GaN substrate, with both a Ga-surface and an N-surface in the opposite face; (b) an InN substrate, with an extended N-surface; and (c) an InN substrate, with an extended In-surface. The GaN substrate model contained 44 Ga
N units and was designated NG88 when the N-surface was used for adsorption reactions and GN88 when the Ga-surface was used instead. The two InN substrate models contained 35 In
N units and were designated as NI70 and IN70, representing an extended N-surface and an extended In-surface, respectively. The difference between the GaN and InN dimensions was due to limitations on the available computer resources, which forced reducing the size of the model InN along the c crystal parameter, half a unit cell below the surface. Organometallic species were adsorbed onto the N-surfaces of the substrates, and the nitrogen species derived from the NH3 source were adsorbed onto the group III surfaces.

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Figure 1. Model substrates for GaN and InN. The group-III atoms are shown in lilac and the nitrogen atoms in blue. (a) GaN seen from the Ga surface (represented as GN88); (b) GaN seen from the N surface (or NG88); (c) side view of the GaN model substrate; (d) InN seen from the N surface (or NI70); (e) InN seen from the indium surface (or IN70); (f) side view of the N-surface of InN (NI70). The In-surface of InN (IN70) is similar to (f) but with the In and N atoms swapped. The adsorption sites are shown with circles on the top views and with arrows on the side views. Top view (a) displays the crystallographic a and b crystal parameters of the wurtzite unit cell; side view (c) displays the crystallographic a and c crystal parameters of the wurtzite unit cell.

In summary, the substrates had the following general characteristics: (a) they were wide and deep where adsorption occurred; (b) they contained the same number of group-III atoms as N atoms; (c) they consisted exclusively of group-III and N atoms, with no capping H atoms; (d) they had no unpaired electrons, such that the multiplicity of the adsorbate
substrate adduct was determined exclusively by the multiplicity of the adsorbate; (e) they maintained a wurtzite structure, showing only small distortions after the energy-optimization procedure, which occurred mainly in regions distant from the adsorption site; (f) their calculated heat capacities resembled that of pure wurtzite GaN or InN; and (g) the substrates were modeled using a quantum-mechanical approach, even though it was based on a low-level (semiempirical) approximation. Figure 1 shows the top and side views of the energy-optimized structures for the three model substrates. As can be seen in Figure 1(c), the GaN model substrate had the same width throughout the depth of the substrate. On the other hand, the number of atoms in the InN model was reduced, with the width diminishing down the substrate along the c crystal parameter of the wurtzite structure. Thus, to represent InN, two different structures were designed, one with a large N-surface and one with a large In-surface. The substrates were validated by comparing the model groupIII
nitrogen distances and the calculated heat capacities with experimental values, following an approach previously reported.7 The experimental distance in wurtzite InN is 2.135 Å, calculated as 3/8 of its crystallographic cell parameter c of 5.693 Å,21 and in wurtzite Ga
N is 1.944 Å, based on a c value of 5.185 Å.22 The experimental values for heat capacity were reported for the 298
1773 K range for GaN,23 the 320
1270 K range for GaN,24 and the 314
978 K range for InN.25 9091

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and 417 cm
1 for GaN, in wavenumber units. The Debye vibrational contribution to heat capacity (CPD) is given by
 3 Z νD T x4 e x hν CPD ¼ ncell 9N A kB ð2Þ dx x  TD kB T ðex
1Þ2 0

Figure 2. Experimental and calculated heat capacities for GaN and InN. The experimental values23 for GaN, labeled “Exp.GaN-1”, are shown in solid black; the experimental values24 for GaN, labeled “Exp.GaN-2”, are shown in solid dark gray; and the experimental values25 for InN, labeled “Exp.InN”, are shown in solid light gray. The model substrates GN88 and NG88 have the same structures, named differently to represent GaN when either the Ga-surface or the N-surface is used for adsorption, respectively. NI70 and IN70 represent the two indium nitride models, with a large N-surface or In-surface, respectively.

In the energy-optimized GaN model substrate, the average neighboring Ga
N distance was (1.96 ( 0.08) Å, about 1% larger than the experimental value, with the range representing the standard deviation. For the InN substrates, the N-surface (NI70) and the In-surface (IN70) models had averages of (2.18 ( 0.06) Å and (2.17 ( 0.06) Å, both about 2% larger than the experimental value. In GN88, the longest neighboring Ga
N distance was 2.13 Å and the shortest 1.84 Å, 9% larger and 5% smaller than the experimental Ga
N distance, respectively. The longest distance appeared on the second row of Figure 1(c), whereas the shortest one was on an edge between the first and second row. The longest distances for neighboring In
N atoms were 2.36 Å and 2.38 Å for NI70 and IN70, respectively, 11 and 12% larger than the experimental values. These distances appeared in the bottom row of NI70, Figure 1 (f), and between the second and third rows for IN70. The shortest distances for neighboring In
N atoms were 2.10 and 2.11 Å in NI70 and IN70, respectively, or 1.5 and 1% smaller than the experimental value, both occurring in the bottom section. Therefore, in all cases, the major deformations in the substrates occurred away from the adsorption site. Figure 2 displays the experimental heat capacities (Cp) for GaN and InN and the calculated values for the model substrates. The GaN experimental heat capacity values shown were given for the 298
1773 K23 and the 320
1270 K24 ranges. The InN values, given for the 314
978 K range,25 were extrapolated to 1200 K by fitting the reported values between 700 and 978 K to a second-order polynomial. The heat capacity of the models was calculated using statistical thermodynamics, under the following conditions: (a) no translational nor rotational contributions; (b) the vibrational contributions were calculated using the Debye approximation for solid state, subject to a cutoff frequency determined by the Debye cutoff temperature; and (c) Cp was solved by numerical integration. The Debye’s cutoff vibrational frequency (νD) is defined by kB νD ¼ T D h

where ncell is the number of interspersed atomic cells (two for InN and GaN); NA is Avogadro’s number; ν are the calculated harmonic vibrational frequencies; and T is the absolute temperature. Figure 2 shows the experimental values for heat capacities with solid lines and the calculated values with dashed lines. The unique calculation for GaN is shown in blue, and the calculations for the two InN model substrates (NI70 and IN70) are shown in red. The temperature range of interest in high-pressure chemical vapor deposition is between 600 and 1200 K. In that range, the calculated heat capacities for GN88 are 1% smaller to 7% larger than the values reported by Barin et al.23 and 5% smaller to 14% larger than Leitner et al. values.24 The calculated heat capacities for NI70 were, within the same temperature range, smaller than the reported values by Zie- borak-Tomaszkiewicz et al.25 by 10
8%, whereas for IN70, the calculated values were larger than the experimental values by 5
8%. (b). Adsorption and Dissociation Reactions. Seven types of reactions involving group-III and ammonia derivatives were considered: (a) methyl dissociation of gaseous group-III species (eq 3), (b) adsorption of group-III species onto gallium nitride (NG88) or indium nitride (NI70) model substrates (eq 4, where S represents the model substrate), (c) methyl dissociation of the adsorbed group-III species (eq 5); (d) atomic hydrogen dissociation from nitrogen species in the gas phase (eq 6); (e) adsorption of the nitrogen species onto gallium nitride (GN88) or indium nitride (IN70) model substrates (eq 7); (f) atomic hydrogen dissociation from nitrogen species adsorbed onto GN88 or IN70 (eq 8) or atomic nitrogen dissociation in the case of adsorbed N2; and (g) one heterogeneous bimolecular reaction based on a proposed mechanism for ammonia decomposition under dynamic conditions in a quartz reactor28 (eq 9). GIII ðCH3 Þx ðgÞ S GIII ðCH3 Þx
1 ðgÞ þ CH3 ðgÞ

ð3Þ S þ GIII ðCH3 Þx ðgÞ S S
GIII ðCH3 Þx

where TD is the Debye temperature of the solid (660 K for InN and 600 K for GaN27); h is Planck’s constant; and kB is Boltzmann’s constant. Thus, νD is equal to 459 cm
1 for InN

0exe3

S
GIII ðCH3 Þx S S
GIII ðCH3 Þx
1 þ CH3 ðgÞ

ð4Þ

1exe3 ð5Þ

Nx Hw ðgÞ S Nx Hw
1 þ H

1exe2

1ewe4 ð6Þ

S þ Nx Hw ðgÞ S S
Nx Hw

1exe2

S
Nx Hw S S
Ny Hz þ H or N 1ewe4

ð1Þ 26

1exe3

0 e w e 4 ð7Þ

1 e x, y e 2

0eze3

S
NH2 þ NH2 ðgÞ S S
N2 H4

ð8Þ ð9Þ

No reactions between the gaseous group-III and NH3 species have been considered. In the HPCVD experiments performed by the laboratory associated with the present study,6 it has been 9092

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common practice to incorporate the group-III materials and NH3 separated by a plug of nitrogen gas, sufficiently long to preclude reaction between the source materials in the gas phase. Calculations of Free Gaseous Species. Density functional theory (DFT)11 was used to perform calculations on the gaseous molecules: In(CH3)3, Ga(CH3)3, NH3, and the following derivatives: In(CH3)2, InCH3, In, Ga(CH3)2, GaCH3, Ga, NH2, NH, N, N2H4, NHNH2, NNH2, NHNH, NNH, H2, N2, CH4, and C2H6. The selected hybrid density functionals were those of B3LYP,12 as implemented in the Gaussian 09W quantum mechanical program.8 The basis sets used for all-electron calculations, provided by the computer program and invoked using the “gen 6D” command, were 3-21G with polarization functions for In and 6-311G with polarization functions for Ga, N, C, and H. These basis sets consisted of 39 basis functions and 93 primitive functions for In (or 39b/93p); 47b/90p for Ga; 19b/32p for C and N; and 6b/8p for H. Modeling the Substrate
Adsorbate Adducts. Calculations on the substrate
adsorbate systems were performed using ONIOM,14 a hybrid approach implemented in the Gaussian 09W program.8 For the present work, a two-level type of computation was selected, dividing the molecular adducts into two portions: an “active” part and its “environment”. ONIOM performs high-level and low-level calculations on the active part of the system, and a low-level calculation on the complete system, or “real” system. The energy difference between the two lowlevel calculations corresponds to the energy contribution from the environment, which is added to the high-level energy value, resulting in an “extrapolated” energy value for the system. Equation 10 shows how the energy terms are organized in ONIOM calculations, where “model high energy” represents the calculation on the active part with the high-level approach, “real low energy” the calculation of the complete system with the low-level approach, and “model low energy” the calculation of the active part with the low-level approach. model high energy þ ðreal low energy
model low energyÞ ¼ extrapolated energy ð10Þ In the present study, the adsorbate was considered to be the active site, for which the level of approximation selected was DFT11/B3LYP12 with large basis sets [6-311G(d,p) for H, C, N, and Ga; 3-21G(d,p) for In].13 The complete substrate
adsorbate adduct or “real” system was treated using the selected semiempirical approach (PM69) for valence-only calculations which uses STO-3G basis sets.10 It should be noted that B3LYP/ 6-311G(d,p)/3-21G(d,p) was the approach used for calculations on the free gaseous molecules, while PM6/STO-3G was the one used on the free model substrates. Subdividing the complex into two portions corresponding to the adsorbate, as the active site, and the substrate, as the environment, allowed for monitoring the effect that complexation had on either portion, separately. Since the two portions were handled with a similar type of approach (i.e., quantum mechanical calculations), they influenced each other in a similar way. This would not have been the case if the substrate would have been handled using, instead, molecular mechanics. (c). Reaction-Rate Constants. Dissociation Reactions. The forward dissociation reactions were considered to be homolytic and unimolecular and were calculated using the semiclassical approach previously described.7,17 The forward reaction rate

constants (kdissoc) for eqs 3, 5, 6, and 8 were calculated based on a method designed for the gas phase17 and modified to make it appropriate for reactions that include solids.7 The reverse rate constants (kassoc) were calculated using pseudo thermodynamic equilibrium constants obtained from reaction Gibbs energies. The semiclassical approach was based on quantum mechanics and transition-state theory, with the critical configuration determined from (a) linear interpolations for the geometry of the intermediate structures, (b) Morse potentials for the intermediate electronic energies (Er, eq 11), and (c) Hase’s relationship for the vibrational frequencies that become annihilated (νr, eq 12). The Morse potential (Er) as a function of bond distance (r) was given by: !!2
0:5 2μ Er ¼ Ed 1
exp
πν0 ðr
r 0 Þ ð11Þ Ed where Ed stands for the energy difference between the dissociating products and the unperturbed molecule determined from quantum mechanics; ν0 is the vibrational frequency of the dissociating bond determined from normal vibrational analyses; μ is the reduced mass between the dissociating portions; and r0 is the initial distance between the dissociating atoms. The vibrational frequencies that become annihilated (νr) were obtained from the following equation, as a function of bond separation (r) !
0:5 2μ ðr
r 0 Þ ð12Þ νr ¼ νi Rv exp
πν0 Ed where vi stands for the vibrational frequency of the unperturbed molecule that becomes annihilated, and Rv is a term to dampen the rapid decrease of the vi values along the reaction coordinate. In the case of gaseous dissociations, Rv was taken to be equal to one, but in the case of substrate reactions, Rv was chosen so that the Gibbs energy of the separating molecule would equal the sum of the Gibbs energies of the products at the end of the reaction path. These values of Rv less than one increased artificially the Gibbs energy of the critical configuration. Consequently, adjustments were made to the values of the rate constants for substrate reactions obtained from comparisons between rate constants of gaseous reactions with and without Rv. As was noted before, ONIOM calculations provided DFT energy values for the adsorbate portion of the adduct or “model high” values and “extrapolated” energy values for the adduct. In the case of dissociation reactions of adsorbed species (eqs 5 and 8 in the forward direction), the electronic energies used for the rate constant calculations were the “model high” values for the undissociated species, the “model high” values for the major group, and the DFT values for the gaseous leaving group. Adsorption Reactions. The rate of adsorption for eqs 4 and 7 was represented by eq 13, assuming a Hertz
Knudsen flux (F), where the partial pressure of species i (Pi) was equal to its molar concentration ([i]) times RT. Rate of Adsorption ¼ Sc  F ¼ Sc
¼ Sc

RT 2πM i

1 ð2πM i RTÞ1=2

Pi

1=2 ½i

ð13Þ

In the previous equation, Sc is the sticking coefficient, Mi the molar mass of species i, R the gas constant, and T the absolute 9093

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Figure 3. Sketch of the Gibbs free energy for the adsorption
desorption reaction path of GaCH3 onto GaN, at 1 atm and 300 K. GA,desor = Gibbs activation free energy for desorption. GA,adsor = Gibbs activation free energy for adsorption. ΔGrxn = Gibbs energy for the reaction; going from left to right, ΔGrxn = ΔGdesor; going from right to left, ΔGrxn = ΔGadsor.

temperature. The sticking coefficient Sc was assumed to be
 GA , adsor Sc ¼ f ðθÞ exp
ð14Þ RT where f(θ), a function of surface coverage, was taken to be equal to 1, and GA,adsor was the activation Gibbs free energy for the adsorption process. The rate constant for the adsorption process was expressed as

 GA, adsor RT 1=2 exp
kads ¼ f ðθÞ ð15Þ 2πM i RT In this study, GA,adsor was estimated as the energy difference between the Gibbs free energy of the critical configuration and the Gibbs free energies of the free model substrate plus the gaseous adsorbate. Figure 3 shows the relationship between the activation Gibbs free energy for desorption and adsorption (GA,adsor and GA,desor, respectively) and the Gibbs free energy for the reaction (ΔGrxn). The rate constants for the desorption reactions (kdesor) (eqs 4 and 7, in the reverse direction) were calculated using the pseudo thermodynamic equilibrium constant for adsorption (Kadsor) or desorption (Kdesor), as follows     ΔGadsor 1 ΔGdesor K adsor ¼ exp
¼ exp ¼ ð16Þ K desor RT RT kdesor ¼

kadsor ¼ kadsor  K desor K adsor

ð17Þ

For the adsorption/desorption reactions, the electronic energies used in the calculation of reaction rates were the “extrapolated” energy from the ONIOM calculation (see eq 10) for the undissociated molecule, the semiempirical (PM6) energy for the substrate, and the DFT energy for the free gaseous species. Bimolecular Reaction. Dirtu et al.28 proposed and found experimental evidence for the formation of N2H4 as an intermediate in the thermal decomposition of ammonia under dynamic conditions in a quartz reactor. The proposed mechanism involved the formation of N2H4, from a heterogeneous reaction involving two molecules of NH2. In the present investigation, adsorbed NH2 was assumed to react with gaseous NH2 (eq 9), and the value of the bimolecular rate constant was extracted from the study mentioned above.

Figure 4. Energy-optimized structures of the adducts of: (a) In(CH3)3 with the GaN model substrate (NG88) and (b) N2H4 with the InN model substrate (IN70).

(d). Time-Dependent Simulations. Several time-dependent models were constructed comprising sets of chemical reactions described by ordinary differential equations. The systems of differential equations were solved using built-in stiff solvers within the MATLAB18 computer program. In addition to eqs 3
9, the sets included some of the chemical reactions shown below as termination reactions (eqs 18
20). Other possible compounds based on carbon and/or nitrogen species were ignored.

CH3 þ CH3 f C2 H6

ð18Þ

H þ H f H2

ð19Þ

N þ N f N2

ð20Þ

All reactions were characterized by forward and reverse rate constants. Special cases of eqs 5 and 8 represent direct formation of group-III and nitrogen layers during epitaxial growth under pulsed chemical vapor deposition. Since pulsing was assumed, reactions of adsorbed group-III species with gaseous nitrogen species, and reactions of adsorbed nitrogen species with gaseous group-III species, were not considered. The numerical stability of the calculations was checked using mass balance equations on the group-III, carbon, nitrogen, and hydrogen atoms.

’ RESULTS AND DISCUSSION The results are discussed following the four stages of the project: (a) optimized structures of the substrate
adsorbate adducts of GaN or InN with group-III or NH3 derivatives; (b) 0 K energies for adsorption and dissociation reactions; (c) temperature- and pressure-dependent reaction rate constants for adsorption and dissociation reactions; and (d) time-dependent simulations. (a). Optimized Structures of the Adsorbate
Substrate Adducts. Forty adduct structures were energy optimized. As a

general rule, lower multiplicities resulted in lower energies for organometallic and N2Hx species, whereas higher multiplicities gave lower energies for NHx species. An example is shown in Figure 4 with the energy-optimized structures of the adduct of In(CH3)3 with the GaN model substrate (NG88) and N2H4 with the InN model substrate (IN70). To evaluate the deformation 9094

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Figure 5. Substrate
adsorbate distances for Ga(CH3)x, In(CH3)x, and NxHy species onto GaN (NG88 and GN88) and InN (NI70 and IN70) model substrates. The horizontal lines show the experimental substrate metal
nitrogen bond average distances. The first atom of the adsorbate names refers to the atom that adsorbed onto the substrates.

that the adsorbate and the substrate undergo with adsorption, two comparisons can be made: (a) the bond distances of the adsorbate atom with its substituents before and after adsorption and (b) the bond distances between the substrate atom where adsorption occurs and its coordinate atoms. Supporting Information, Table SI-1, contains the relevant bond distances obtained. Figure 5 shows the adsorbate
substrate distance for the 40 adducts studied. The horizontal dashed lines show the average experimental Ga
N distance (lower) and In
N distance (higher) in wurtzite crystals. All average adsorbate
substrate distances were within 20% of the crystal values (1.944 Å for GaN and 2.135 Å for InN), except for Ga(CH3)3 and In(CH3)3 on GaN, which were weak van der Waals complexes. The bond distances between the adsorbing atom of the adsorbate and its substituents were within 6% of the values in the free gaseous species. On the other hand, the bond distances between the atom in the substrates where adsorption occurred and its coordinated atoms were within 11% the value in the crystal. Adsorption onto GaN affected the N
N distance by less than 5% and onto InN by less than 12% with respect to the gaseous species. (b). Adsorption and Dissociation Energies. The adsorption energies were estimated using “extrapolated” energies of the ONIOM calculation of the adducts, the DFT energies for the adsorbates in the gas phase, and the PM6 energies of the free model substrates. The dissociation energies were estimated based on the “model high” energies of the ONIOM calculations of the adducts and the DFT energies for the gaseous leaving groups. The calculated adsorption and dissociation energies obtained are listed in Supporting Information, Table SI-2. The data on adsorption energies indicate that: (a) at 0 K, adsorption onto the substrates was an exergonic process for all species; (b) adsorption onto InN was 1 to 7 times more exergonic than onto GaN, except for Ga(CH3)3, GaCH3, In(CH3)3, and N2 which were between 26 and 41 times larger; and (c) adsorption energies were dominated by the drop in energy of the substrate, which easily overcame the small increase in adsorbate energies. It was found that the effect that adsorption had on the substrate was related to the electronic configuration of the adsorbate’s attacking atom. Figure 6 displays the drop in energy on the substrate, classified in terms of the configuration of the attacking atom. The classification took into account that organometallic and N2Hx species preferred lower multiplicities, and NHx species preferred higher multiplicities. The attacking atoms

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Figure 6. 0 K change in substrate energy due to adsorption, for Ga(CH3)x, In(CH3)x, and NxHy species onto GaN model substrates (NG88 and GN88) and InN model substrates (NI70 and IN70), in terms of the electron configuration of the attacking atom. The attacking atom was classified as containing: 0 = no free electrons; lp = a lone electron pair; lp and db = a lone electron pair and a double bond; lp and tb = a lone electron pair and a triple bond; 1-u = one unpaired electron; 1-u and lp = one unpaired electron and one lone electron pair; 1-u, lp, and db = one unpaired electron, a lone electron pair, and a double bond; 2-u = two unpaired electrons; 3-u = three unpaired electrons. The error bars show the range of values.

were classified as containing: (a) no free electrons, as was the case of Ga(CH3)3 and In(CH3)3 where adsorption occurred due to donation from the lone pair of the N atom of the substrate; (b) a lone electron pair, as was the case of GaCH3, InCH3, NH3, and N2H4; (c) a lone electron pair together with a double bond, such as NNH2 and NHNH; (d) a lone electron pair together with a triple bond, the case of N2; (e) only one unpaired electron, such as Ga(CH3)2, In(CH3)2, and NH2NH; (f) one unpaired electron and one lone electron pair, the case of Ga, In, NH2, and NHNH2; (g) one unpaired electron, a lone electron pair, and a double bond, such as NNH and NHN; (h) two unpaired electrons (NH); and (i) three unpaired electrons (N). The main results shown in Figure 6 are that adsorption affected the InN model substrates more than the GaN model substrates and that adsorbates with open shells resulted in mean substrate energy changes 19 and 5 times larger for the GaN and InN model substrates, respectively. The data regarding the methyl dissociation energies at 0 K for the organometallic species, and the atomic hydrogen or nitrogen dissociation energies for the nitrogen species, in the gas phase and adsorbed onto GaN or InN model substrates show that: (a) all dissociations were endergonic, with two exceptions that showed negative dissociation energies within the margin of error of the calculations (NNH and NHN on InN); (b) within 17%, the dissociation energies for all species were very similar for both substrates; (c) all dissociation energies were within 24% of the gas dissociations, except for NNH and NHN; and (d) out of a total of 40 dissociation energies, seven adsorbed onto GaN and nine adsorbed onto InN resulted in lower dissociation energies than in the gas phase. (c). Temperature- and Pressure-Dependent Rate Constants. The reactions studied can be classified as: (i) methyl or hydrogen dissociation of gaseous species; (ii) adsorption/ desorption; and (iii) methyl or hydrogen dissociation of adsorbed species. The calculated rate constants for adsorption (kadsor) and desorption (kdesor) and for methyl or hydrogen dissociation (kdissoc) and their reverse process (kassoc) were fitted into the 9095

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The Journal of Physical Chemistry C

ARTICLE

Table 1. Arrhenius-Type Parameters for Methyl and Hydrogen Dissociation Reactions in the Gas Phase, To Fit the Following Expression: k = APmTn exp{
((Ea)/(RT))} where P = Atmospheric Pressure, T = Absolute Temperature, and R = Gas Constant Dissociation

Ga(CH3)3

Association
1

m

n

A (s
1 M
1)

Δk/ka

94.9

1.20


8.93

8.13  10þ46

0.60

Ea/R (K)

m

n

A (s )

Δk/k

Ea/R (K)

35651

0.21


8.41

2.29  10þ46

0.61

a

þ112

Ga(CH3)2

20456

0.91


32.29

3.40  10

0.42

5334.6

1.91


32.69

8.56  10þ109

0.41

Ga(CH3) In(CH3)3

29705 36406

0.99 0.36


5.77
17.23

1.08  10þ30 3.22  10þ73

0.21 0.95


257.1 4538.2

1.98 1.36


5.92
17.71

1.29  10þ25 1.01  10þ74

0.21 0.94

In(CH3)2

22118

0.87


30.10

1.66  10þ107

0.37

7824.5

1.86


30.36

4.83  10þ104

0.37

In(CH3)

27968

0.99


5.82

9.12  10

0.21


262.1

1.98


5.95

1.27  10þ25

0.21

NH3

50086

0.99


2.22

2.73  10þ20

0.22


1888.1

1.98


3.70

3.10  10þ18

0.24

NH2

44349

1.00


0.78

2.97  10þ13

0.22


1440.4

1.99


2.27

2.74  10þ12

0.23

NH

39161

1.00

0.81

1.51  10
15

0.23


1625.7

1.99


0.59

5.12  10
16

0.23

N2H4

40556

0.69


6.91

2.10  10þ38

0.41

3007.8

1.68


8.26

1.10  10þ36

0.42

NHNH2-g NHNH2-u

28796 34300

0.91 0.66


5.84
5.69

1.15  10þ32 2.28  10þ32

0.28 0.43

913.8
1045.1

1.90 1.66


6.51
6.47

8.45  10þ28 3.52  10þ29

0.28 0.43

NHNH

25377

0.99


2.83

9.08  10þ20

0.22


1662.8

1.98


4.31

6.64  10þ18

0.23

NNH2

18841

1.00


3.06

1.47  10þ21

0.19


736.5

1.99


4.44

5.10  10þ18

0.19

NNH


914

1.00


1.20

1.45  10þ11

0.21


314.3

1.99


2.29

9.08  10þ09

0.22

109990

1.00

0.69

3.40  10
15

0.23


1620.9

1.99


0.61

1.86  10
17

0.23

C2H6

42237

0.71


12.87

2.06  10þ58

0.48


1069.7

1.70


13.58

1.46  10þ51

0.48

CH4

52433

0.90


4.37

2.44  10þ29

0.28

577.5

1.89


6.20

5.68  10þ27

0.30

H2

50557

1.00

0.87

1.00  10
15

0.23


1623.4

1.99


0.59

1.20  10
16

0.23

N2

þ29

Δk/k = relative standard error for estimates of the reaction rate constant (k), based on the multiple linear regression performed to obtain the Arrheniustype parameters.

a

following Arrhenius-type equation   EA k ¼ APm T n exp
RT

ð21Þ

where R is the gas constant; P is the atmospheric pressure; and T is the absolute temperature. The remaining parameters, the collision factor A, the Arrhenius activation energy EA, and the exponential indices m and n are determined from a multilinear regression. Methyl or Hydrogen Dissociation of Gaseous Species. Table 1 contains the Arrhenius-type parameters obtained for the dissociation and association reactions in the gas phase, to fit eq 21. Comparison between the predicted rate constant for gaseous species and experimental values is provided under Supporting Information, Topic SI-2. Comparison of the structures of the group-III adducts undergoing methyl dissociation shows that the average metal
C equilibrium distance was 2.14 Å with a 14% spread, whereas for the nitrogen-containing adducts undergoing H dissociation, the average N
H equilibrium distance was 1.04 Å with an 8% spread. On the other hand, the average metal
C critical configuration distance of the group-III adducts was 4.49 Å with a 45% spread, whereas for N
H the average critical configuration distance was 3.20 Å with a 97% spread. Table SI-3 of the Supporting Information contains the distances of the critical configurations and forward and reverse Gibbs activation energies for all gaseous dissociations. Adsorption/Desorption Rate Constants. Table 2 contains the Arrhenius-type parameters for the adsorption and desorption reactions to fit eq 21. The values of parameter Rv (eq 12) used for the reactions are listed in Supporting Information, Table SI-4. In

addition, the description of the algorithm used to compute the adjustment of the estimated rate constants to account for the use of Rv values less than one appears as Supporting Information, Topic SI-3. A comparison of the adsorption rate constants for the species onto GaN and InN is shown in Figure 7. All estimated rate constants for a given compound adsorbing onto the two substrates were very similar except for Ga(CH3)3, GaCH3, In(CH3)3, and N2. The rate constants for adsorption of In(CH3)3 onto InN were much larger than onto GaN, whereas the opposite was true for Ga(CH3)3, GaCH3, and N2. The average adsorption distance for the metal species was 2.33 Å, with values ranging from 1.78 to 4.11 Å. On the other hand, the average adsorption distance for the nitrogen species was 2.15 Å, with a smaller range between 1.88 and 2.35 Å. At 10 atm and 1000 K, ΔGdesorp was exergonic for the following species: Ga(CH3)3, Ga(CH3), In(CH3)3, In(CH3), NH3, N2H4, both N2H2 isomers, and N2 adsorbed onto the GaN model substrate, while ΔGdesorp was exergonic only for Ga(CH3)3, In(CH3)3, and for one isomer of N2H2 adsorbed onto InN model substrates. These data are summarized in Table SI-4 in the Supporting Information. Dissociation Rate Constants of Adsorbed Species. Table 3 contains the Arrhenius-type parameters for the methyl/hydrogen/nitrogen dissociation and association reactions of adsorbed species, to fit eq 21. The values of parameter Rv (eq 12) used for the reactions are listed in the Supporting Information, Table SI-5. Figure 8 displays the calculated rate constants at 10 atm and 1000 K for methyl or hydrogen dissociation (or nitrogen in the case of N2) in the gas phase and with the species adsorbed onto GaN and InN. The figure shows that, in most cases, the values of the rate constants increased with adsorption. GaCH3, N2H4, and 9096

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ARTICLE

Table 2. Arrhenius-Type Parameters for Adsorption/Desorption Reactions, To Fit the Following Expression: k = APmTn exp{
((Ea)/(RT))} where P = Atmospheric Pressure, T = Absolute Temperature, and R = Gas Constant adsorption

desorption
1


1

m

n

A (s
1)

Δk/ka


752


1.69


12.89

1.70  10þ73

0.58

104535


1.18


15.13

3.67  10þ69

0.63

0.57

867


1.69


16.74

9.39  10þ86

0.59

4.68  10þ37

0.64

134007


0.72


10.86

1.23  10þ52

0.64


9.32

1.37  10þ56

0.57


820


1.69


14.92

9.21  10þ77

0.58


0.24


8.32

1.56  10þ41

0.63

111317


1.24


16.11

1.32  10þ75

0.63


394


0.69


9.32

7.70  10þ52

0.57

5014


1.69


9.43

1.57  10þ61

0.58

In NH3


142
267

0.22 0.05


8.77
7.06

4.78  10þ40 2.81  10þ39

0.64 0.68

124935 7752


0.77
0.94


9.96
11.38

7.60  10þ51 6.81  10þ57

0.65 0.68

NH2


316


0.07


7.86

7.10  10þ34

0.62

75105


1.06


12.52

1.16  10þ56

0.63

þ35

0.76

112906


0.30


7.59

7.68  10þ46

0.77

Δk/k

a

species

Ea/R (K)

m

n

Ga(CH3)3


394


0.69


9.32

4.84  10þ55

0.57

Ga(CH3)2


311


0.18


8.16

4.20  10þ39

0.62

Ga(CH3)


394


0.69


9.32

9.98  10þ58

Ga


129

0.27


8.74

In(CH3)3


394


0.69

In(CH3)2


307

In(CH3)

A (s

M )

Ea/R (K)

Gallium Nitride Substrate

NH


328

0.69


6.58

1.93  10

N


125

0.31


8.71

5.86  10þ36

0.64

114144


0.68


10.59

1.34  10þ50

0.65

N2H4


394


0.69


9.32

1.85  10þ48

0.57

7456


1.69


10.26

5.38  10þ58

0.58

NHNH2


313


0.16


8.08

1.65  10þ35

0.61

104365


1.15


14.02

7.11  10þ61

0.61

NH2NH


313


0.15


8.08

9.17  10þ33

0.61

103509


1.15


14.03

7.20  10þ60

0.61

NHNH NNH2


394
311


0.69
0.15


9.32
8.08

5.23  10þ48 6.19  10þ41

0.57 0.64

8168 11910


1.69
1.14


14.83
12.85

2.73  10þ72 7.88  10þ63

0.60 0.65

NHN


315


0.30


8.45

2.32  10þ38

0.60

96144


1.29


14.82

5.09  10þ69

0.62

þ33

0.61

109753


1.14


14.55

3.42  10þ61

0.62

0.85

6928


0.13


7.40

2.09  10þ50

0.85

NNH


312


0.15


8.08

3.18  10

NN


382

0.86


6.16

1.69  10þ40

Ga(CH3)3


394


0.69


9.32

5.93  10þ49 þ37

Indium Nitride Substrate 0.57

11548


1.69


14.50

3.97  10þ75

0.59

Ga(CH3)2


318


0.21


8.20

6.81  10

0.61

327392


1.19


19.73

1.86  10þ80

0.61

Ga(CH3)


313


0.15


8.08

1.07  10þ42

0.65

49287


1.14


14.42

1.15  10þ67

0.65

Ga In(CH3)3


161
394

0.14
0.69


8.83
9.32

4.38  10þ37 5.81  10þ74

0.62 0.57

342248 12624


0.84
1.69


18.73
11.42

8.95  10þ71 2.48  10þ91

0.63 0.58

In(CH3)2


317


0.23


8.26

7.04  10þ39

0.62

318157


1.22


16.68

1.50  10þ74

0.62

þ52

In(CH3)


394


0.69


9.32

3.78  10

0.57

48047


1.69


15.73

4.13  10þ76

0.59

In


142

0.23


8.77

2.66  10þ39

0.64

347821


0.76


15.86

2.04  10þ66

0.64

NH3


262

0.03


7.11

4.53  10þ38

0.67

15408


0.96


11.23

2.60  10þ56

0.67

NH2


315


0.09


7.92

4.31  10þ33

0.61

272063


1.08


11.67

3.02  10þ52

0.61

NH


371

0.83


6.22

3.00  10þ30

0.80

206769


0.16


4.49

5.17  10þ33

0.80

N N2H4


101
354

0.43 0.16


8.62
7.23

1.10  10þ32 1.38  10þ41

0.66 0.69

254174 17005


0.56
0.83


11.83
8.13

3.31  10þ46 2.32  10þ52

0.66 0.70

NHNH2


311


0.18


8.14

4.86  10þ37

0.61

243844


1.17


12.06

8.15  10þ58

0.62

þ31

0.60

285615


1.16


19.95

1.06  10þ73

0.60

NH2NH


310


0.17


8.13

7.63  10

NHNH


394


0.69


9.32

1.80  10þ50

0.57

10290


1.69


15.59

6.47  10þ75

0.60

NNH2


312


0.16


8.09

1.36  10þ41

0.64

15630


1.15


12.70

1.68  10þ62

0.64

NHN


316


0.19


8.16

5.43  10þ38

0.62

215957


1.18


11.55

7.23  10þ58

0.63

NNH


313


0.17


8.11

3.09  10þ30

0.60

263914


1.16


11.75

1.19  10þ51

0.61

NN


269

0.13


7.83

4.70  10þ29

0.64

141268


0.86


9.59

2.65  10þ42

0.64

Δk/k = relative standard error for estimated reaction rate constants (k), based on the multiple linear regressions performed to correct for the Rv parameter in eq 12 and to obtain the Arrhenius-type parameters. a

NHNH on both substrates were the exception, as well as In(CH3)3 and NHNH2-u on GaN. The figure also shows that, for the methyl dissociation of organometallic species, the rate constant for the third methyl group was the smallest and for the second methyl group was the largest. In addition, the dissociation rate constant for the third H atom of NH3 increased substantially

with adsorption, the same as for the N dissociation of adsorbed N 2. The average initial metal
C distance for the group-III species adsorbed onto GaN and InN model substrates was 2.11 Å, with values ranging from 1.94 to 2.32 Å. On the other hand, the average initial N
H distance was 1.19 Å, with a range between 9097

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The Journal of Physical Chemistry C

Figure 7. Comparison of adsorption rate constants for the species onto GaN and InN model substrates (NG88 and NI70 for the metal species, GN88 and IN70 for the N species), at 10 atm and 1000 K.

1.02 and 2.05 Å. At 10 atm and 1000 K, ΔGdissoc was endergonic for all species except for the methyl dissociation of Ga(CH3)2 adsorbed onto GaN and of In(CH3)2 adsorbed onto InN. The hydrogen dissociation of NHN and NNH adsorbed onto both substrates was also exergonic under those conditions. The ΔGdissoc values obtained are shown in the Supporting Information, Table SI-5. (d). Time-Dependent Simulations. Sets of chemical equations were selected to model processes related to the dissociative chemisorption of Ga(CH3)3, In(CH3)3, and NH3 adsorbed onto GaN and InN. All reactions involved forward and reverse directions, except for one bimolecular heterogeneous reaction to produced N2H4 (eq 9). The rate constant for eq 9 was borrowed from an experimental study of the thermal decomposition of ammonia under dynamic conditions in a quartz reactor.28 The simulations were carried out under four pressure and temperature conditions: (a) 10 atm, 1200 K (labeled 10/ 1200); (b) 10 atm, 1400 K (or 10/1400); (c) 20 atm, 1200 K (or 20/1200); and (d) 20 atm, 1400 K (or 20/1400). The processes studied by time-dependent simulations were: (a) Methyl dissociation of Ga(CH3)3 or In(CH3)3 in the gas phase (eqs 3 and 18), for a total of four chemical reactions and six unknown species concentrations [Ga(CH3)3, Ga(CH3)2, GaCH3, Ga; or, In(CH3)3, In(CH3)2, InCH3, In; plus CH3 and C2H6]. (b) Methyl dissociation of Ga(CH3)3 or In(CH3)3, adsorbed onto GaN or InN (eqs 5 and 18), for a total of four chemical reactions, four adsorbed species, and two gaseous species [S
Ga(CH3)3, S
Ga(CH3)2, S
GaCH3, S
Ga; or, S
In(CH3)3, S
In(CH3)2, S
InCH3, S
In; plus CH3 and C2H6]. (c) Hydrogen dissociation from NH3 and its derivatives in the gas phase, but also including a bimolecular heterogeneous reaction of adsorbed NH2 (onto GaN or InN) with gaseous NH2 to produce N2H4 (eqs 6, 7 for NH2 and N2H4, and 9, 19, and 20), for a total of 14 chemical reactions, 12 gaseous species, and 2 adsorbed species (NH3, NH2, NH, N, N2H4, NHNH2, NHNH, NNH2, NHN, N2, H, H2, S
NH2, S
N2H4). (d) Hydrogen dissociation from NH3 and NH3 derivatives adsorbed onto GaN or InN, including a bimolecular heterogeneous reaction of adsorbed NH2 with gaseous NH2 to produce N2H4 (eqs 6, 7 for NH2, and 9, 19, and 20) for a total of 18 chemical reactions, 4 gaseous species, and 12 adsorbed species (S
NH3, S
NH2, S
NH,

ARTICLE

S
N, S
N2H4, S
NHNH2, S
NH2NH, S
NHNH, S
NNH2, S
NHN, S
NNH, S
N2, NH2, N, N2, H, H2). (e) A box model for the organometallic source including, simultaneously, reactions for: (i) methyl dissociation of source materials in the gas phase, (ii) adsorption/desorption of the species onto the model substrates (either GaN or InN), and (iii) methyl dissociation of the adsorbed species (eqs 3
5 and 18), for a total of 21 chemical reactions and 18 species [Ga(CH3)3, Ga(CH3)2, GaCH3, Ga, In(CH3)3, In(CH3)2, InCH3, In, S
Ga(CH3)3, S
Ga(CH3)2, S
GaCH3, S
Ga, S
In(CH3)3, S
In(CH3)2, S
InCH3, S
In, plus CH3 and C2H6]. The source material consisted of an equimolar mixture of Ga(CH3)3 and In(CH3)3. (f) A box model for the ammonia source including, simultaneously, reactions for: (i) hydrogen dissociation of source materials in the gas phase, (ii) adsorption/desorption of the species onto the model substrates (either GaN or InN), (iii) one bimolecular heterogeneous reaction of adsorbed NH2 with gaseous NH2 to produce N2H4, and (iv) hydrogen dissociation of the adsorbed species (eqs 6
9, 19, and 20) for a total of 38 chemical reactions and 24 species [NH3, NH2, NH, N, N2H4, NHNH2, NHNH, NNH2, NHN, S
NH3, S
NH2, S
NH, S
N, S
N2H4, S
NHNH2, S
NH2NH, S
NHNH, S
NNH2, S
NHN, S
NNH, S
N2, N2, H, H2]. The time-dependent calculations were continued until no more changes on the major concentrations were detected. As an example, Figure 9 shows the products of dissociation of gaseous Ga(CH3)3, under the four conditions considered. It is easily seen that GaCH3 is the major product of dissociation, under all conditions, and that temperature has an effect on how much Ga(CH3)2 remains and very little effect on the amount of atomic Ga. It should be noted that steady state conditions for the box models [(e) and (f)] occurred much faster than for models (a) through (d). Methyl Dissociation from the Organometallic Materials. The simulations for the methyl dissociation of the organometallic source materials, in the gas phase and adsorbed onto either GaN or InN model substrates, under the four temperature
pressure conditions considered, gave the following results: (a) Percent dissociation. The percent dissociation for both source materials in the gas phase was less than 0.03%. When Ga(CH3)3 was adsorbed onto GaN, it increased to 4
10% whereas for In(CH3)3 adsorbed onto the same substrate, it only increased to 0.04
0.06%. On the other hand, adsorption of Ga(CH3)3 onto InN increased dissociation to 80
99%, and adsorption of In(CH3)3 onto InN increased dissociation to 99.9%. (b) Major dissociation species. The major dissociations species were GaCH3 and InCH3 in all simulations except for the dissociation of Ga(CH3)3 adsorbed onto InN at 1400 K, for both pressures considered, for which the main dissociation product was Ga(CH3)2, followed by GaCH3. (c) Adsorption effect. Dissociation of the species adsorbed onto InN was more efficient than adsorbed onto GaN; in the case of Ga(CH3)3 that was so by factors ranging between 10 and 20 times, whereas for In(CH3)3 the factors were between 2000 and 3000 times. A comparison of the dissociation of the source material adsorbed onto 9098

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The Journal of Physical Chemistry C

ARTICLE

Table 3. Arrhenius-Type Parameters for Methyl/Hydrogen Dissociation Reactions of Adsorbed Species, To Fit the Following Expression: k = APmTn exp{
((Ea)/(RT))} where P = Atmospheric Pressure, T = Absolute Temperature, and R = Gas Constant dissociation species

Ea/R (K)

Ga(CH3)3

38957

m

0.14

association
1

n

A (s )


9.56

2.62  10þ51 þ102

Δk/k

a

Ea/R (K)

Gallium Nitride Substrate 0.59 3163

m

n

A (s
1 M
1)

Δk/ka

1.13


11.99

7.68  10þ52

0.59

Ga(CH3)2 Ga(CH3)

22693 30085

0.65 0.65


29.26 2.67

2.07  10 3.57  10
03

0.63 0.30

7984 1406

1.64 1.64


28.50 7.47

2.80  10þ92 2.78  10
21

0.63 0.30

In(CH3)3

43782


0.04


28.59

2.11  10þ108

0.86

10677

0.95


30.71

1.12  10þ112

0.86

1.32  10

0.52

8722

1.57


16.01

1.09  10þ58

0.52

þ91

In(CH3)2

22650

0.58


25.00

In(CH3)

28482


0.12

2.75

4.19  10þ05

0.09

2067

0.87

1.22

8.38  10þ03

0.09

NH3

50244


0.34

3.82

1.80  10þ03

0.59


1444

0.65

1.58

1.73  10þ04

0.59

NH2

45493


0.07

1.97

3.91  10þ07

0.18

1326

0.92

4.04

1.67  10
03

0.18

NH

41768


0.18

2.13

3.11  10þ07

0.05

703

0.81


0.06

3.20  10þ08

0.06

N2H4-a N2H4-b

42006 43157

0.86 0.87


5.16
5.85

2.44  10þ31 3.42  10þ33

0.40 0.42

4204 4646

1.85 1.86


12.36
12.21

1.09  10þ48 9.67  10þ47

0.41 0.42

NHNH2-g

25541

0.22


2.57

1.00  10þ22

0.40


527

1.22


1.95

3.10  10þ13

0.40

þ27

NHNH2-u

34948

0.69


4.40

9.79  10

0.33


1487

1.68


3.14

1.55  10þ18

0.34

NH2NH-gb

24770

0.74


4.79

3.65  10þ29

0.39


589

1.73


5.03

1.78  10þ23

0.39

NHNH-a

27622


0.42

3.67

8.05  10þ02

0.52


1357

0.57

1.22

1.21  10þ05

0.53

NHNH-b

27889


0.41

3.65

8.10  10þ02

0.52


1456

0.58

1.32

7.03  10þ04

0.52

NNH2

19477


0.21

2.85

4.26  10þ08

0.43

864

0.78


0.24

1.25  10þ12

0.43

313 435

0.17 0.17

1.30 0.56

7.35  10þ08 7.30  10þ10

0.10 0.03

2170 1926

1.17 1.16

5.14 4.51

3.31  10
10 1.89  10
08

0.10 0.05

112295


0.12

1.29

9.59  10þ08

0.02

666

0.87


0.46

2.70  10þ09

0.03

NHN NNH NNc

Indium Nitride Substrate Ga(CH3)3

28803

0.06


10.48

þ52

0.63


2189

1.05


15.62

5.11  10þ57

0.64

9.97  10

0.56


1451

1.75


22.18

1.21  10þ76

0.56

1.64  10
03

0.30

1419

1.65


1.13

5.08  10þ00

0.30

2.49  10

þ98

Ga(CH3)2

16086

0.75


27.83

Ga(CH3)

28354

0.65

2.54

In(CH3)3

30213

0.05


26.62

6.53  10þ103

0.90


1012

1.05


31.62

1.13  10þ110

0.90

In(CH3)2

12862

0.60


23.15

9.16  10þ85

0.52

30

1.59


20.11

1.07  10þ69

0.52

In(CH3) NH3

27433 54685


0.12
0.22

1.18 3.62

2.73  10þ09 7.60  10þ04

0.09 0.60

1104 2608

0.87 0.77

0.34 2.54

1.07  10þ06 7.81  10þ02

0.09 0.60

NH2

46509


0.07

1.21

4.06  10þ09

0.19

2298

0.92

4.86

1.22  10
06

0.19

3.05  10

0.05

1993

0.84


5.09

7.57  10þ20

0.05

þ10

NH

42149


0.16

1.14

N2H4-a

45362

0.85


6.36

1.45  10þ34

0.39

1323

1.85


10.61

6.02  10þ41

0.39

N2H4-b

41714

0.87


6.38

2.62  10þ34

0.39

3001

1.86


18.29

1.51  10þ61

0.40

NHNH2-g

22547

0.29


2.73

7.75  10þ22

0.37

1704

1.28


5.87

3.07  10þ24

0.37

NHNH2-u

31351

0.72


4.53

2.26  10þ28

0.32

32

1.71


6.12

6.48  10þ25

0.33

NH2NH-gb NHNH-a

25911 33327

0.69
0.43


6.58 3.21

6.58  10þ34 1.93  10þ04

0.45 0.51


258 1233

1.68 0.56


2.05 4.56

1.87  10þ17 3.30  10
04

0.45 0.51

NHNH-b

36802


0.35

3.59

1.62  10þ04

0.51

1720

0.65

4.98

4.38  10
04

0.51

NNH2

23664


0.24

1.24

6.01  10þ13

0.42

2046

0.75

1.03

1.42  10þ10

0.42

NHN


16

0.21

1.24

5.10  10þ08

0.04

5891

1.21

1.59

4.89  10þ00

0.05

NNH


8

0.23

1.25

4.62  10þ08

0.02

2911

1.23

1.65

6.97  10þ00

0.03

111101


0.10

1.89

4.48  10þ07

0.04

1302

0.89


0.65

2.69  10þ06

0.04

NNc

Δk/k = relative standard error for estimated reaction rate constants (k), based on the multiple linear regressions performed to correct for the Rv parameter in eq 12 and to obtain the Arrhenius-type parameters. b Calculations of adsorbed NH2N did not converge. c This reaction corresponds to the dissociation of a nitrogen atom. a

GaN with the dissociation in the gas phase shows an increase of 102 to 104 times for Ga(CH3)3 and 5 to 65 times for In(CH3)3. A similar comparison for the InN substrate was 103 to 105 times more efficient for Ga(CH3)3 and 104 to 105 times for In(CH3)3.

(d) Temperature effect. Increasing temperature increased dissociation of Ga(CH3)3 between 10 and 70%, except in the gas phase at 20 atm, when it increased by a factor of 130. Increasing temperature increased dissociation of In(CH3)3 at 10 atm in the gas phase by 10% but decreased 9099

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The Journal of Physical Chemistry C

Figure 8. Comparison of calculated rate constants for the methyl/ hydrogen/nitrogen dissociation of gaseous and adsorbed species, at 10 atm/1000 K. The first atom of the species is the atom adsorbed onto the substrate. “a” corresponds to dissociation of the H atom attached to the adsorbed N atom; “b” corresponds to the H atom attached to the N atom which in turn is attached to the adsorbed N; “g” corresponds to the gem H atom; “u” corresponds to the unique H atom.

Figure 9. Time-dependent dissociation of gaseous Ga(CH3)3, under four conditions of pressure and temperature: (a) 10 atm, 1200 K; (b) 10 atm, 1400 K; (c) 20 atm, 1200 K; and (d) 20 atm, 1400 K. Ga(CH3)2 is shown in blue, GaCH3 in red, and atomic Ga in green.

its dissociation at 20 atm in the gas phase by a factor of 7 and adsorbed to GaN between 30 to 80%. There was no effect detected when In(CH3)3 was adsorbed onto InN. (e) Pressure effect. Increasing pressure decreased dissociation of gaseous Ga(CH3)3 by 40% at 1200 K but increased its dissociation by a factor of 60 at 1400 K. On the other hand, increasing pressure increased dissociation of gaseous In(CH3)3 2 to 13 times. When the species were adsorbed onto GaN, dissociation was reduced by 40%; when the species were adsorbed onto InN, dissociation of Ga(CH3)3 was reduced by 20% and of In(CH3)3 was unaffected. Figure SI-3 of the Supporting Information displays the final percent concentrations from the above simulations. Figure 10 displays the total percent dissociation resulting from the simulations, under the four conditions of temperature and pressure studied. H-Dissociation from Ammonia Derivatives. Simulations were performed for the dissociation of gaseous NH3 or NH3 adsorbed onto either the GaN or InN substrates, under the four conditions

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Figure 10. Total percent dissociation resulting from the simulations of methyl dissociation from Ga(CH3)3 and In(CH3)3, in the gas phase, and adsorbed onto model substrate GaN (NG88) and model substrate InN (NI70), at four conditions of pressure and temperature: 10 atm/1200 K; 10 atm/1400 K; 20 atm/1200 K; and 20 atm/1400 K.

Figure 11. Total percent dissociation of NH3, from the quasi-gas-phase models with two species adsorbed onto model substrates GaN (GN88) or InN (IN70) and from the simulations with NH3 adsorbed onto model substrates GaN (GN88) and InN (IN70), at four conditions of pressure and temperature: 10 atm/1200 K; 10 atm/1400 K; 20 atm/1200 K; and 20 atm/1400 K.

of temperature and pressure mentioned above. The simulations starting with gaseous NH3 were quasi-gas-phase simulations since adsorption/desorption of two of the species (NH2 and N2H4) was included. Also included was the heterogeneous bimolecular reaction (eq 9) between adsorbed NH2 and gaseous NH2 needed to produce the intermediate N2H4. Figure 11 displays the percent dissociation products of NH3 of the simulations. Figures SI-4 and SI-5 of the Supporting Information depict the final concentrations obtained for the quasi-gas-phase simulations and the simulations starting with adsorbed NH3. The following points may be made: (a) Percent dissociation. The percent dissociations for the quasi-gas-phase models were very small, with a range of 0.06
0.11% at 1200 K and 0.2
9% at 1400 K, being somewhat more effective when the two species adsorbed onto GaN instead of InN. When the simulations started with NH3 adsorbed onto InN, the percent dissociations were below 0.01%, whereas when NH3 was adsorbed onto GaN, the percent dissociations were between 7 and 10% at 1400 K. (b) Major dissociation species. N2H4 was the major species in the gas phase for all quasi-gas-phase simulations. The principal adsorbed product for the quasi-gas-phase 9100

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The Journal of Physical Chemistry C simulations was mainly adsorbed N2H4 for GaN and adsorbed NH2 for InN (with one exception for GaN at 20 atm/1400 K, for which it was adsorbed NH2). When the simulations started with NH3 absorbed onto GaN, the main dissociation product was adsorbed N2H4. On the other hand, when the simulation started with NH3 adsorbed onto InN, the main dissociation product was adsorbed NH2NH, except at 20 atm/1400 K when it was adsorbed N2H4. (c) Adsorption effect. Comparison of the dissociation between the simulations starting with NH3 adsorbed onto GaN or gaseous NH3 showed a 55-fold increase at 10 atm/1400 K for the former. The reverse was true for NH3 adsorbed onto InN, where the dissociation for gaseous NH3 at 20 atm/1200 K was 20 times that of adsorbed NH3 and 360 times at 20 atm/1400 K. Not much difference was detected between the quasi-gasphase model on GaN and on InN. The differences in dissociation between the adsorbed NH3 on GaN and on InN ranged between 10 and 1100 times. (d) Temperature effect. Increasing temperature increased dissociation for the quasi-gas-phase models, between 3 and 84 times for GaN and 3 and 28 times for InN, with the higher values corresponding to the higher pressures. An increase in temperature on the simulation starting with NH3 adsorbed onto GaN resulted in an increase of 170 times. On the other hand, when the simulation started with NH3 adsorbed onto InN, the increase in dissociation was 31 times at 10 atm and 2 times at 20 atm. (e) Pressure effect. Dissociation increased with pressure for the quasi-gas-phase models, from 2 times at 10 atm to 48 times at 20 atm for GaN and 13 times at 20 atm for InN. Increasing pressure decreased dissociation for adsorbed NH3, as follows: 1.5 times for GaN and 1.5 times at 10 atm to 28 times at 20 atm for InN. Box Model Simulations. Box model simulations included, simultaneously, the following three types of reactions: (a) dissociation/association reactions in the gas phase, (b) adsorption/desorption reactions onto the model substrate, and (c) dissociation/association reactions of adsorbed species. Simulations were carried out using two different souce materials: (a) Ga(CH3)3 and In(CH3)3, simultaneously, with equimolar initial concentrations, and (b) NH3. The simulations were performed with the species adsorbing onto either GaN or InN model substrates. As stated before, four pressure and temperature conditions were selected: 10 atm/1200 K, 10 atm/1400 K, 20 atm/1200 K, and 20 atm/1400 K. A. Box Model Simulation for the Organometallic Source (a) Percent dissociation. Calculations ran to a nanosecond for GaN and to 10
22 s for InN. The percent dissociation for Ga(CH3)3 was on the order of 10
4% for GaN and 10
3% for InN. The percent dissociations for In(CH3)3 were on the order of 10
2 for GaN and 10
3% for InN. Thus, Ga(CH3)3 dissociated better onto InN, and In(CH3)3 dissociated better onto GaN. Overall, dissociation was most effective for In(CH3)3 on GaN. (b) Major dissociation species. In general, the main dissociation species were gaseous and adsorbed Ga(CH3)2 and In(CH3)2, with one exception: among the gaseous species for the dissociations onto GaN, gaseous InCH3 was the

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Figure 12. Percent dissociation products of organometallic gaseous and adsorbed species on GaN or InN model substrates, from box model simulations, at four pressure
temperature conditions: 10 atm/1200 K, 10 atm/1400 K, 20 atm/1200 K, and 20 atm/1400 K.

main product. Overall, gaseous InCH3 was the main species in the GaN simulations and gaseous Ga(CH3)2 in the InN simulations. (c) Adsorption effect. The concentration of adsorbed species was about 300 to 1400 times larger than the concentration of gases for the GaN simulations, whereas for the InN simulations, they were 20 to 1300 times smaller. In the case of GaN simulations, the higher factors occurred for 10 atm/1400 K and 20 atm/1200 K; in the case of InN simulations, the higher factors occurred at 1400 K. The variation of adsorption effects can be explained by the effect that temperature and pressure have on the concentrations of gaseous and adsorbed species on GaN or InN. (d) Temperature effect. In general, increasing temperature increased dissociation by factors ranging between 7 and 130 times, with the minimum for GaN simulations at 10 atm and the maximum for InN simulations at 10 atm. Dissociation products increased by a factor of 11 times at 20 atm, for both substrates. The resulting increase in dissociation products was due to an increase in adsorbed dissociation products for the GaN simulations and an increase in gaseous dissociation products for the InN simulations. (e) Pressure effect. In general, increasing pressure decreased dissociation by factors ranging between 2 and 9 times, with the maximum for InN simulations at 1400 K. The only exception was at 1200 K for InN, where an increase in pressure resulted in an increase in dissociation by 30%. The effect on GaN simulations was due to a decrease of the adsorbed dissociated species, whereas the effect on InN simulations was due to an increase (at 1200 K) or a decrease (at 1400 K) of the gaseous products. Figure 12 displays the percent dissociation products of organometallic gaseous and adsorbed species on GaN or InN model substrates, from the box model simulations at the four pressure
temperature conditions considered. Figure SI-6 of the Supporting Information shows the final percent concentrations from these box model simulations. B. Box Model Simulations for the Ammonia Source (a) Percent dissociation. The values ranged from 10
7
10
6 for the 1200 K dissociations to 10
5
10
4 for the 1400 K dissociations. Gaseous percent dissociations were higher for GaN than for InN, factors ranging from 14 to 50 times, for all cases except for 10 atm/1200 K with a decrease by a 9101

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The Journal of Physical Chemistry C

Figure 13. Percent dissociation products of NH3 from box model simulations on GaN and InN model substrates, at four pressure
temperature conditions: 10 atm/1200 K, 10 atm/1400 K, 20 atm/ 1200 K, and 20 atm/1400 K.

factor of 4. Percent dissociation for adsorbed species was higher for InN than for GaN (factors of less than 6), except for 20 atm/1200 K (smaller by a factor of 3). Overall, percent dissociation was very similar for GaN and InN at 10 atm/1200 K and 20 atm/1400 K, and it was 3 times higher for GaN at 20 atm/1200 K and 6 times higher for InN at 10 atm/1400 K. (b) Major dissociation species. The main gaseous dissociation product was N2H4 for both substrates, with the exception of N2H2 (as NHNH) at 10 atm/1200 K for InN. The main adsorbed species was NH2 for GaN but for InN was NNH2 at 10 atm/1200 K, NH2NH at 10 atm/1400 K, NH2 at 20 atm/1200 K, and N2 at 20 atm/1400 K. Overall, the main dissociation products were the adsorbed species. (c) Adsorption effect. Adsorbed species over gaseous species on GaN were more prevalent at 1200 K (40 times at 10 atm and 16 times at 20 atm). Adsorbed species over gaseous species were always more prevalent on InN, by factors ranging between 11 and 148 times. In general, InN and GaN had about the same amount of adsorbed species at 10 atm/1200 K, and InN had about 70 times more than GaN at 10 atm/1400 K, 3 times less at 20 atm/1200 K, and 58 times more at 20 atm/1400 K. (d) Temperature effect. Increasing temperature increased the percent of dissociation products in all instances, more so for gaseous species on GaN and for adsorbed species on InN. Overall, the increase of dissociation products with temperature was 13 times at 10 atm for GaN, 56 times at 20 atm for GaN, 67 times at 10 atm for InN, and 199 times at 20 atm for InN. (e) Pressure effect. Increasing pressure slightly increased the dissociation products of the GaN simulations, at both temperatures considered, and the gaseous dissociation products of the InN simulation at 1400 K. Overall, the effect of pressure was very small, with an increase by a factor of 5 for the GaN simulation at 1400 K and a decrease by a factor of 3 for the InN simulation at 1200 K. Figure 13 displays the percent dissociation of NH3 from box model simulations on GaN and InN model substrates, at the four pressure
temperature conditions considered. Figure SI-7 of the Supporting Information shows the final concentrations from these box model simulations.

’ CONCLUSIONS Realistic models of gallium nitride (GaN) and indium nitride (InN) substrates were designed using the ONIOM14 hybrid approach, as implemented in the Gaussian 09W8 quantum

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mechanical program. The following two quantum-mechanical levels of approximation were selected for the ONIOM calculations: density functional theory11 [B3LYP12/6-311G(d,p)/ 3-21G(d,p)13] and semiempirical (PM69/STO-3G10). The model substrates contained 44 units of GaN and 35 units of InN, to achieve a large surface area and depth at the site where adsorption occurred. The validity of the model substrates was confirmed by comparing (a) closest group-III
nitrogen bond distances with experimental values in the vicinity of the adsorption site and (b) predicted heat capacities with experimental values. The predicted heat capacities were obtained using the Debye approximation for solid state and the Debye cutoff vibrational frequency. Adsorption and desorption rate constants were estimated for trimethylgallium [Ga(CH3)3], trimethylindium [In(CH3)3], and ammonia (NH3) and their dissociation products, onto the two model substrates (for GaN and InN). The predicted rate constants were based on transition state theory applied to homolytic unimolecular reactions using the RRKM15
Troe16 approach, adapted to large molecules using a semiclassical approach,17 adjusted to solid state based on Debye’s approximations,7 and assuming a Hertz
Knudsen flux. The rate constants were fitted into Arrhenius-type equations, and the values of the parameters were reported, together with standard errors for the estimated rate constants. Methyl dissociation rate constants for Ga(CH3)3 and In(CH3)3 adsorbed onto the two model substrates (GaN and InN) were calculated, as well as hydrogen dissociation rate constants for NH3 adsorbed onto the two model substrates. The calculated rate constants were based on transition state theory for homolytic unimolecular reactions using the RRKM15
Troe16 approach, adapted to large molecules using a semiclassical approach,17 and adjusted to solid state based on Debye’s approximations.7 The rate constants were fitted into Arrheniustype equations, and the values of the parameters were reported, together with standard errors for the estimated rate constants. Time-dependent models for the dissociation of Ga(CH3)3, In(CH3)3, and NH3, in the gas phase and adsorbed onto GaN and InN, were designed using coupled differential equations of concentrations as a function of time. These systems of equations were solved by stiff methods, using MATLAB.18 The dissociation of organometallic species and ammonia was considered separately since the source materials are introduced into highpressure chemical-vapor-deposition reactors separated by a plug of inert carrier gas. The models were run under four conditions of temperature and pressure: 10 atm/1200 K; 10 atm/1400 K; 20 atm/1200 K; and 20 atm/1400 K. Three types of timedependent models were designed: (a) dissociation of the organometallic source material, either in the gas phase or adsorbed onto GaN or InN; (b) dissociation of the ammonia source material, either in the gas phase (but allowing for NH2 and N2H4 to absorb onto GaN or InN) or adsorbed onto GaN or InN; (c) box models which represented adsorption and dissociation reactions for ammonia or for both organometallic species, simultaneously. With respect to the dissociation of organometallics in the gas phase, the simulations with one single organometallic material showed percents of dissociation products of less than 0.03, under the four conditions considered. Adsorption onto InN substantially increased dissociation of both Ga(CH3)3 and In(CH3)3. The main dissociation species for these simulations were the monomethyl compounds (GaCH3 and InCH3). Changes in 9102

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The Journal of Physical Chemistry C temperature and pressure had some effect on the gaseous dissociation products of Ga(CH3)3. When both organometallic source materials were present simultaneously and materials were allowed to adsorb and desorb (i.e., in the box models), percent dissociation was below 0.1; In(CH3)3 dissociated more than Ga(CH3)3; Ga(CH3)3 dissociated better when the substrate was InN; and In(CH3)3 dissociated better when the substrate was GaN. The simulations of gaseous and adsorbed NH3 without adsorption/desorption reactions showed percent dissociations of less than 10, with better dissociation when the substrate was GaN. Gaseous or adsorbed N2H4 (or NH2NH) and NH2 were the major dissociation species. Increasing temperature affected more dissociation of NH3 when the substrate was GaN. Increasing pressure promoted dissociation when the source was gaseous NH3 but had the opposite effect for adsorbed NH3. When a box model approach was used, in which adsorption and dissociation were considered simultaneously, the percent dissociation decreased. However, increasing temperature favored dissociation when the substrate was InN, whereas increasing pressure favored dissociation when the substrate was GaN. Other species, such as NHNH and NNH2, became major dissociation species, depending on the conditions of pressure and temperature. The InN substrate had more concentration of products of dissociation than the GaN substrate at higher temperatures. Increasing temperature particularly increased the percent of gaseous dissociation products in the GaN simulation. The increase in pressure had a very small effect.

’ ASSOCIATED CONTENT

bS

Supporting Information. Topic SI-1, entitled “Calculation of Gibbs free energy”, describes the calculations performed to obtain Gibbs free energy for gaseous species, as well as for the clusters. Table SI-1, entitled “Bond distances in adducts of groupIII and ammonia derivatives with GaN and InN model substrates”, contains: (a) closest bond distance between adsorbate and model substrate, (b) bond distances between adsorbing atom of the adsorbate and its substituents, and (c) bond distance between substrate atom where adsorption occurs and its coordinate atoms. Table SI-2, includes “0 K energies of adsorption and methyl, hydrogen or nitrogen dissociation, in units of kJ mol
1”. Topic SI-2, contains “Comparison between predicted and experimental rate constants for methyl dissociation of gaseous Ga(CH3)3 and In(CH3)3, and hydrogen dissociation of gaseous NH3”. Table SI-3, entitled “Parameters of the dissociation reactions in the gas phase at 10 atm and 1000 K”, displays the equilibrium bond distance, the separation between separating atoms at the critical configuration, the value of the optimized dampening parameter Rv, the Gibbs activation energy for dissociation (Eact,dissoc), the Gibbs activation energy for association (Eact,assoc), and the Gibbs energy change for the reaction (ΔGdissoc), obtained at 10 atm and 1000 K. Table SI-4, entitled “Parameters of the adsorption/desorption reactions onto GaN and InN, at 10 atm and 1000 K”, displays separation at critical configuration, Gibbs activation energy for desorption (Gact,desorp), Gibbs activation energy for adsorption (Gact,adsorp), Gibbs energy change for the desorption reaction (ΔGdesorp), and value of the optimized dampening parameter Rv (see eq 12), obtained at 10 atm and 1000 K. Table SI-5, entitled “Parameters of the methyl/hydrogen dissociation of species adsorbed onto gallium and indium nitride, at 10 atm and 1000 K”, displays

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separation at critical configuration, Gibbs activation energy for desorption (Gact,desorp), Gibbs activation energy for adsorption (Gact,adsorp), Gibbs energy change for the desorption reaction (ΔGdesorp), and value of the optimized dampening parameter Rv (see eq 12), obtained at 10 atm and 1000 K. Topic SI-3, shows “Adjustment of the estimated rate constants to correct for values of Rv (eq 12 of the manuscript) less than one”. Seven plots are available with results from the time-dependent simulations: (a) Figure SI-3 entitled “Percent concentrations from simulations of methyl dissociation from Ga(CH3)3 and In(CH3)3, in the gas phase, and adsorbed onto GaN and InN”. (b) Figure SI-4 entitled “Percent concentrations from simulations of hydrogen dissociation from gaseous NH3, with two adsorbed species (NH2 and N2H4) onto GaN and InN”. (c) Figure SI-5 entitled “Percent concentrations from simulations of hydrogen dissociation from adsorbed NH3 onto GaN and InN”. (d) Figure SI-6 entitled “Percent concentrations from box model simulations for the dissociative chemisorption reactions of an equimolar mixture of Ga(CH3)3 and In(CH3)3”. (e) Figure SI-7 entitled “Percent concentrations from box model simulations for the dissociative chemisorption reactions of NH3”. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The investigation described in this paper was supported by NSF award DMR-0705219 and Subcontract A11224 from Rensselaer Polytechnic Institute/NSF award DMR-0117792. ’ REFERENCES (1) Wu, J.; Walukiewicz, W.; Shan, W.; Yu, K. M.; Ager, J. W., III; Haller, E. E.; Lu, H.; Schaff, W. J. Effects of the narrow band gap on the properties of InN. Phys. Rev. B 2002, 66, 201403. (2) Kachkanov, V.; O’Donnell, K. P.; Pereira, S.; Martin, R. W. Intentional and Unintentional Localization in InGaN. Philos. Mag. 2007, 87 (13), 1999–2017. (3) Wu, J.; Walukiewicz, W.; Yu, K. M.; Shan, W.; Ager, J. W., III; Haller, E. E.; Lu, H.; Schaff, W. J.; Metzger, W. K.; Kurtz, S. Superior radiation resistance of In1-xGaxN alloys: Full-solar-spectrum photovoltaic material system. J. Appl. Phys. 2003, 94 (10), 6477–6482. (4) Yam, F. K. Z.; Hassan, Z. InGaN: An overview of the growth kinetics, physical properties and emission mechanisms. Superlattices Microstruct. 2008, 43, 1–23. (5) Dietz, N. Indium-nitride growth by HPCVD: Real-time and ex-situ characterization. In III-Nitrides Semiconductor Materials; Feng, Z. C., Ed.; Imperial College Press: London, 2006; ISBN 1-86094-636-4, Chapter 6, pp 203
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