A quantum chemical study on gas phase decomposition pathways of triethylgallane ( TEG , Ga ( C 2 H 5 ) 3 ) and tert-butylphosphine ( TBP , PH 2 ( tC 4 H 9 ) ) under MOVPE conditions †

The gas phase decomposition reactions of precursor molecules relevant for metal–organic vapour phase epitaxy (MOVPE) of semiconductor thin films are investigated by computational methods on the densityfunctional level as well as on the ab initio (MP2, CCSD(T)) level. A comprehensive reaction catalogue of uniand bimolecular reactions is presented for triethylgallium (TEG) as well as for tert-butylphosphine (TBP) containing thermodynamic data together with transition state energies. From these energies it can be concluded that TEG is decomposed in the gas phase under MOVPE conditions (T = 400–675 1C, p = 0.05 atm) to GaH3 via a series of b-hydride elimination reactions. For elevated temperatures, further decomposition to GaH is thermodynamically accessible. In the case of TBP, the original precursor molecule will be most abundant since all reaction channels exhibit either large barriers or unfavorable thermodynamics. Dispersion-corrected density functional calculations (PBE-D3) provide an accurate description of the reactions investigated in comparison to high level CCSD(T) calculations serving as benchmark values.


Introduction
Semiconductor materials composed of group 13 and group 15 elements (aka.III/V materials) grown on silicon surfaces have potential applications as highly efficient solar cells and lasers. 1 ''Silicon photonics'' aims at the combination of optical data processes with Si-based microelectronics technology, but is hampered by the indirect band gap of silicon and thus optically active overlayers have to be formed. 2These materials are often deposited onto silicon substrates by a vapor phase epitaxy procedure from metal-organic precursor molecules (MOVPE).In order to tune the materials towards direct optical gaps, metastable quaternary group III/V materials were developed which exhibit lattice constants close to the Si bulk value. 3owever, these materials can be grown quasi-epitaxially on Si(001) applying a 40-50 nm buffer layer of GaP. 4,5The quality of the III/V material's optoelectronic properties is highly dependent on the structural quality of the GaP nucleation layer which goes hand in hand with the cleanliness of the Si substrate surface, choice and purity of the precursors and the specific suitability of the applied growth conditions. 6Crystal defects can be propagated by mechanical strain caused by the heterolayers' lattice mismatch to silicon or different thermal expansion coefficients.On the other hand, non-ideal reactor conditions lead to incomplete precursor decomposition and undesirable doping defects, e.g.carbon incorporation. 7It is the declared goal of material scientists to minimize these defects during growth of promising III/V materials.0][11][12] It is, for instance, difficult to obtain reactionspecific barriers from experiment (e.g.mass spectrometry) as the appearance of detected species can only be related to the overall temperature and reaction (growth) rate. 8,12,16ne frequently applied precursor in the growth of III/V materials is trimethylgallane (Ga(CH 3 ) 3 , TMG), which has a lower decomposition rate than triethylgallane (Ga(C 2 H 5 ) 3 , TEG) and pyrolyzes only at high temperatures (above 480 1C) 16 in the gas phase.Surface-assisted decomposition mechanisms, on the other hand, exhibit significantly lower barriers (o130 1C). 14owever, there is an increased tendency for carbon incorporation, because reactive and therefore uncontrollable radical species are formed from TMG, e.g.dimethylgallane and methyl radicals, which remain strongly bound to the Si surface. 12,14By introducing ligands larger than methyl, decomposition temperatures (thermal barriers) were found to decrease: tri-tertbutylgallane, e.g., undergoes clean decomposition via b-hydride elimination already at 260 1C (low barrier of 160 kJ mol À1 ) 15 without carbon incorporation. 16It has been found that this problem can be circumvented by using TEG as an epitaxy precursor, which delivers GaN layers with high intensity photoluminescence and higher electron mobility than those grown with TMG. 17 Some pathways for TEG were investigated previously but no barriers were reported. 13,15Low-barrier b-hydride elimination seems to play a major role in successful growth procedures and precursors with larger ligands were addressed by experimental and theoretical studies. 15,16,18s a common source for group 15 elements tert-butylarsine (AsH 2 (t-C 4 H 9 ) TBA) and tert-butylphosphine (PH 2 (t-C 4 H 9 ), TBP) 19a are used as MOVPE precursors.Some decomposition pathways for TBP were computed in an early computational study on the HF level, 19b supporting the suggestion of breaking of the phosphorous-carbon bond in the initial step.19c A concise examination of decomposition pathways of TBP including barriers is not yet available.TEG and TBP fulfill general requirements for MOVPE precursor molecules such as lowered toxicity, suitable lab handling characteristics and, as investigated in this study, well-defined chemical stability.9 We want to briefly outline the experimental setup to set the stage for the computational investigations.20 The original precursors are flushed into the reaction chamber in a hydrogen gas stream at 0.05 atm total pressure.TEG and TBP are kept separated in the gas phase by alternating the precursor flushes with pure hydrogen flushes, which rinse the reaction chamber.This procedure is referred to as flow-rate modulated epitaxy (FME) and was found to produce GaP layers of very high quality.20 Hence, stable donor-acceptor complexes or oligomers of group 13 and 15 species, which have been extensively revised by Timoshkin and others, [21][22][23][24][25] will presumably not be of major importance for the decomposition.The partial pressures of Ga and P precursors are very low so that the formation of elemental Ga or P clusters 26,27 can be neglected.
The aim of this study is now to investigate a comprehensive reaction catalogue for the important MOVPE precursors TEG and TBP in the hydrogen gas atmosphere 28 via accurate computations on the DFT and ab initio level providing thermodynamic energies and barriers.To this end, 61 elementary reactions and reaction barriers for a rationally chosen subset of those were calculated on the MP2 and PBE-D3 levels of approximation and checked against benchmark calculations on the CCSD(T) level.The presented decomposition catalogue covers four mechanism classes (homolytical bond cleavage, b-hydrogen decomposition, H 2 and alkane elimination reactions) for unimolecular reactions and three classes (radical recombination, H 2 and alkane elimination reactions) for bimolecular reactions with several reactants.Primarily, this study aims at revealing the resulting decomposition products from the gas phase.Secondly, it presents the chemical mechanisms of the most prominent decomposition classes, showing thermodynamic and kinetic trends for those reactions under experimental conditions.Thirdly, the accurate benchmark data allow an error estimation for production type DFT calculations.This will help both experimental and theoretical scientists to understand the specific decomposition behavior and tune reactor conditions towards clean and complete decomposition.
For the presented results some assumptions had to be formulated which include the limitation of reactions with a maximum of two reaction partners (e.g.precursors + H 2 ), no agglomeration of multiple precursors of the same (due to low partial pressures) and of different types (due to separated input of Ga and P sources, respectively).Furthermore, reactor wall effects and the reactor layout are neglected in this study; however, processes related to the substrate surface will be investigated in future studies.

Computational details
Geometry optimizations without symmetry constraints were carried out using the Gaussian09 optimizer (standard convergence criteria) 30 combined with Turbomole (version 6.3.1) 31,32nergies and gradients (SCF convergence criterion 10 À8 a.u., grid m4).Optimizations were carried out within the density functional approximation applying the GGA functional PBE 33 (widely used in materials science studies) 29 and on an ab initio level using the MP2 method.For the PBE calculations, dispersion effects were considered for the calculation of electronic reaction energies and molecular structure optimizations by applying the DFT-D3 method with an improved damping function (further called PBE-D3). 34,35ne aim of this study is to establish a methodological standard for future studies on the gas phase and surface chemistry in these systems.Therefore, the geometries and energies derived at the MP2 level were used as the gas phase benchmark data for the PBE-D3 calculations of these molecular properties.Complementing the MP2 energies, CCSD(T) [36][37][38][39] energies of elementary reactions were derived based on MP2 geometries (on PBE-D3 geometries for transition states) to verify the accuracy of MP2 and PBE-D3.Minimum and transition state structures (the latter characterized by one imaginary mode) were confirmed by calculating the Hessian matrices on PBE-D3 (analytically 40 ) and MP2 (numerically 41 ).The reactants and products connected by a transition state were identified via an intrinsic reaction coordinate (IRC) calculation.Thermodynamic corrections were subsequently derived by statistical thermodynamics in the double harmonic approximation under the assumption of no hindered rotations. 12,42The results regarding atomic species were complemented with entropic corrections applying the Sackur-Tetrode equation assuming an ideal gas and Maxwell-Boltzmann statistics. 43The RI approximation was used for all PBE, MP2 and CCSD(T) calculations. 44,45All methods were used together with a triple-z set of Gaussian basis functions (def2-TZVPP). 46The levels of approximation are denoted PBE-D3/TZ, MP2/TZ and CCSD(T)/TZ in the following.Radical species are denoted by the symbol '' '' and found to exhibit doublet spin states with the exception of P (quartet ground state).All other species involved in this study exhibit a singlet ground state with the exception of P(t-C 4 H 9 ) and PH (triplet ground state).Maximum deviation of the ideal values for the hS 2 i operator is o0.03 for the radical species, indicating a single-reference character suitable for the unrestricted Kohn-Sham/Hartree-Fock methods applied.The electronic states have been consistently confirmed by the presented PBE-D3, MP2 and CCSD(T) calculations in line with previous results on GaCH 3 , PH and PH 3 . 47,48The accuracy of the methods applied was measured by comparing the energies to high level CCSD(T)/TZ data and will be presented in the Results section.To our knowledge, experimental thermodynamic data are unfortunately not available for the reactions investigated here.In the ESI, † the structures derived are compared to the available experimental data. 49-52

Results
A catalogue of 61 elementary decomposition reactions was assembled and electronic reaction energies of these reactions were calculated using PBE-D3/TZ, MP2/TZ and CCSD(T)/TZ.Thermodynamic corrections were added for low pressure atmospheres (0.05 atm) and temperatures of 400 1C, 500 1C and 675 1C according to the experimental growth conditions.In the following sections, we present the data for the reaction energies of (i) decomposition of TEG, (ii) decomposition of TBP and (iii) selected transition state energies for TEG and TBP.In the first two sections, uni-and bimolecular reactions are considered separately.Higher order reactions were not considered here due to the low pressure environment.Furthermore, four different possible classes of decomposition reactions were considered for unimolecular reactions: or (c) molecular hydrogen (H 2 ) as reaction partners.

Thermodynamics of decomposition reactions of TEG
The reaction energies for unimolecular decomposition reactions of TEG are presented in Table 1.The reaction energies for bimolecular decomposition reactions of TEG are presented in Table 2. Here, all reactions listed are energetically accessible.Entropy effects are much smaller since the number of reactants does not change from educts to products (except BG2, BG5).For some radical species the MP2/TZ results deviate considerably from the CCSD(T)/TZ benchmark values (e.g.BG3, BG4, BG7) -the differences are mostly less on the PBE/TZ level.This is in line with the known difficulty of the MP2 method to describe radical species accurately.The energetic ordering of decomposition reactions with the following partners (from the least to the most favorable) is alkane elimination  radicals (BG1, BG4, BG7, BG8) { radical recombinations (with or without elimination products; BG2, BG3, BG5, BG6, BG10, BG13).Reactions AG11-AG14 (b-hydride elimination reactions), AG19 and AG20 (H elimination reactions), AG15 and AG17 (alkane elimination reactions) and BG15-BG18 (alkane elimination reactions with H ) were chosen for subsequent investigation of reaction barriers under the condition of low H concentration.

Thermodynamics of decomposition reactions of TBP
The reaction energies for unimolecular decomposition reactions of TBP are presented in Table 3.Most of the reactions are energetically and thermodynamically unfavorable.Only b-hydrogen elimination reactions (AP6 and AP7) are exothermic, although the entropy effects are very large for all unimolecular reactions.For the P-containing species a good agreement was found between the computational methods applied except for AP9 and AP12 which can be attributed to the difficulty of DFT dealing with atomic species.The reaction energies for bimolecular decomposition reactions of TBP are presented in Table 4.
All elimination reactions are energetically (except BP8) and thermodynamically accessible.As for the bimolecular reactions with Ga species, entropic effects are small (except BP8, which results in three species).Reactions AP6 (b-hydrogen elimination) and BP8 (alkene + H 2 elimination with H 2 ) were chosen for the subsequent transition state analysis.No transition state could be found for reaction BP7.To summarize the part of the study focusing on the reaction energies: unimolecular decomposition reactions exhibit much larger changes in DG upon considering increasing temperatures compared to bimolecular reactions.As expected, all reactions leading from radical species to saturated products are exergonic (see also ref. 10) while larger radical species tend to be more stabilized than small ones.All b-hydrogen elimination reactions (alkene elimination reactions) are exergonic (Ga and P species) and so are many uniand bimolecular alkane and H 2 elimination reactions from Ga species.All unimolecular H 2 and alkane eliminations from P species are endergonic.This catalogue's bimolecular decomposition reactions are, generally, exergonic.Gas phase reactivity cannot be understood from the thermodynamic data alone.However, they give a strong hint on which reaction classes are relevant for the investigation of reaction kinetics in terms of transition state theory.This will be described for the reactions indicated in the previous paragraphs in the next section.

Transition states of TEG and TBP decomposition reactions
Several elementary decomposition reactions were identified from the catalogue presented in Tables 1-4, where the thermodynamic data indicate their importance for the gas phase decomposition chemistry of the MOVPE growth of GaP.For those reactions, transition states linking reactants and products of the reactions in Tables 1-4 were investigated.Subsequently, the possible decomposition pathways were formulated which determine the possible decomposition products.Furthermore, those pathways contain the structural data which provide rationalization of the underlying reaction mechanisms.
The selection criteria for the reactions considered in this section are the following: (i) elementary steps are exergonic, (ii) they do not depend on any other species than the carrier gas H 2 (which is present in sufficient concentration), and (iii) the reactant species will realistically be available either as original precursors or via exclusively exergonic preceding reactions.The transition states (TS) were optimized with PBE-D3/TZ.The electronic activation energies of the selected reactions and the frequencies of the transition state modes are given in Table 5.The energies vary from 67.3 (BG18) to 312.3 kJ mol À1 (AG15), exemplifying the strong differences between barriers for different mechanisms.It becomes clear that the barriers for TEG and derived species are much lower compared to the two barriers investigated for decomposition reactions of TBP (except AG15).It is also striking that entropy has a much smaller influence on the barrier height compared to the reaction energies (Tables 1-4), except for the bimolecular reactions involving H 2 (BG15-BG18, BP8), where the barriers are drastically increased by the inclusion of entropic effects.This can be understood in terms of the entropy-lowering association of two species to one transition structure in the bimolecular case.The vibrational modes of the TS structures connecting educts and products can also be taken to distinguish the different mechanism classes: transition states containing H 2 exhibit much higher mode energies (41100 cm À1 ) compared to alkane elimination reactions (377-717 cm À1 ).Before discussing the implications of the reaction catalogue introduced, an evaluation of the accuracy for the methods chosen will be presented.

Accuracy of PBE-D3/TZ and MP2/TZ vs. CCSD(T)/TZ
In order to validate the accuracy of the broadly applicable PBE-D3/ TZ and MP2/TZ methods, statistical data regarding the deviations from the highly accurate CCSD(T)/TZ computations are given in Table 6.All presented deviation criteria of PBE-D3/TZ energies are of the same order as the respective deviations of MP2/TZ energies with respect to CCSD(T)/TZ//MP2/TZ.This validation of PBE-D3 is important as for calculations of larger systems the application of DFT-based methods will be preferred over the costly post-HF methods, especially for investigation of surface-assisted reactions where the MP2 method is currently only feasible for small systems.Energies of reactions where radical species are involved have a larger deviation and represent the respective maximum absolute deviations of this catalogue's reactions.This is known for species with an unpaired electron and mainly due to the inaccurate exchange contribution to the energy in GGA exchangecorrelation functionals. 54However, focusing on decomposition reaction energies, the description of even large radicals by PBE-D3/TZ seems to be of sufficient accuracy relative to CCSD(T)/TZ.
The relative and absolute deviations of the examined energy barriers are larger, as it is known for GGA functionals to underestimate reaction barriers. 55Remarkably, RMS, RAD and MAE of PBE-D3/TZ are smaller compared to MP2/TZ with respect to CCSD(T)/TZ.This overestimation of activation energies is a known shortcoming of MP2.Similar trends of reaction energy deviations for DFT relative to CCSD(T)/TZ were also found in other studies on Ga precursor decomposition. 12In conclusion, the accuracy of the methods is sufficient for the purpose of identifying relevant decomposition products and analyzing the respective mechanisms.
In the following, uni-and bimolecular decomposition schemes including mainly exergonic reactions are presented for TEG and TBP.From those schemes several pathways were assembled involving the reaction energies together with the reaction barriers presented above.

Decomposition scheme for TEG
In the light of the results given in Tables 1 and 2, the plethora of possible reactions is reduced to the following set: unimolecular b-hydride elimination reactions or homolytical bond cleavage reactions of Ga-C, C-C or C-H can be formulated for TEG.Furthermore, recombinative elimination reactions of alkanes or hydrogen are energetically accessible for some decomposition products.In the bimolecular case, alkane and H 2 elimination reactions are possible with reactants like H 2 or radicals (H , C 2 H 5 ).This leads to the decomposition pathways of first (Fig. 1, top) and second (Fig. 1, bottom) order reactions.However, all homolytical cleavage reactions of saturated species are endoenergetic and endergonic and are not considered further in this study.Specifically, the bond energies for TEG were calculated to be 404.6 kJ mol À1 for the terminal C b -H bond, 376.2 kJ mol À1 for the C a -C b bond and 292.3 kJ mol À1 for the Ga-C bond (AG2, AG3, AG1 for PBE-D3/TZ in Table 1).As a consequence, the remaining pathways build a decomposition scheme for TEG.The major pathways are discussed in the following subsections in detail.
Pathway 1, ''b-hydride eliminations''.The possibility of reaction via b-hydride elimination is a significant advantage to TEG compared to, for instance, TMG which has been studied extensively for CVD applications. 12Since a carbon atom in the b-position to gallium is absent in TMG, only endergonic homolytical cleavage reaction can occur, hence a decomposition reaction is less likely. 15The suggested decomposition pathway 1 for TEG has four elementary steps and leads to   1) confirms this assumption.Entropy covers this effect and leads to the observed different trend in DG # .The fourth step within this pathway exhibits the highest barrier.The H 2 elimination from GaH 3 is slightly exergonic and has a barrier of DG # 400 = 200.5 kJ mol À1 .The subsequent homolytical cleavage to Ga and H is highly endergonic in the gas phase (DG 400 = 192.0kJ mol À1 , see Table 1).Hence, via this pathway GaH 3 will likely be the main product with the possibility of GaH at elevated temperatures.From the graphical representation, it appears that the differences in the reaction profile with an increase in temperature might be due to entropy effects on the transition states.But a closer analysis of the numbers in Tables 1 and 5 reveals that the temperature effects of the intermediates are much stronger compared to the transition states.
Pathway 2, ''n-butane elimination''.A recombinative elimination of n-butane from TEG leads to monoethylgallium (Ga(C 2 H 5 )) in a single step (Fig. 3), but the barrier for this reaction is very large (DG # 400 = 326.2kJ mol À1 ) and unlikely to be surmounted even at elevated temperatures.If monoethylgallium can be formed by any (e.g.surface-assisted) process, a b-hydride elimination reaction may result in gallium monohydride (GaH) in a low barrier step (DG # 400 = 82.6 kJ mol À1 ).GaH is an interesting intermediate as it can be formed from many different sources (see Fig. 1).
Pathway 3, ''monoethylgallane decomposition processes''.Next to the low-barrier b-hydride elimination described in pathway 1, monoethylgallane can directly decompose to GaH (Fig. 4, reaction to the right) by the elimination of ethane (DG # 400 = 199.8kJ mol À1 ).Furthermore, H 2 elimination to Ga(C 2 H 5 ) (Fig. 4, reaction to the left) can occur with a higher barrier of DG # 400 = 215.6 kJ mol À1 .Since both processes are thermodynamically and kinetically less favorable than the b-hydride elimination (Fig. 2), they are not highly relevant gas phase reactions.
Pathway 4, ''2nd order pathway, ethane elimination''.The bimolecular decomposition reactions with a radical reactant or H 2 are exergonic.A highly interlinked decomposition network can be formulated (Fig. 1, bottom) leading to both radical and non-radical products.Formally, atomic Ga can be reached via an alkane elimination pathway with hydrogen radicals H as reactants (e.g.DG 400 (BG1) = À156.6kJ mol À1 , Table 2).Assuming low concentrations of these radicals in the gas phase for thermodynamic reasons (H 2 dissociation: DG 400 = 326.4kJ mol À1 ) no barrier was calculated for such elimination steps.Reactions with molecular hydrogen (H 2 ), which is used as a carrier gas and available in high concentrations, are more likely.The pathway shown in Fig. 5 contains three steps of H 2 addition reactions to saturated Ga species, which decompose under simultaneous ethane elimination in subsequent steps to Ga(C 2 H 5 ) 2 H, Ga(C 2 H 5 )H 2 and GaH 3 , respectively.Note that electronic barriers are lower throughout compared to the corresponding unimolecular b-hydride elimination barriers of these species (Table 5), although an additional H-H bond is broken.However, upon applying thermodynamic corrections to the transition state energies of this bimolecular decomposition class the barriers are drastically increased.The very high initial barrier for the H 2 -assisted reaction (BG1, DG # 400 = 208.5 kJ mol À1 ) indicates that the decomposition reactions via second-order reactions are less important.
Comparing uni-and bimolecular alkyl elimination from gallane species (Fig. 2 and 5), yet another trend can be  1 and 2. Endergonic steps (at 400 1C) are crossed out or do not appear at all.Decomposition mechanisms are classified as radical cleavage reactions (magenta), alkane (orange), H 2 (yellow) and b-hydride (green) elimination reactions.Bimolecular elimination of alkanes or H 2 is considered with the H (red) or C 2 H 5 (turquoise) radicals or H 2 (blue) as reaction partners.
observed: while the thermodynamics of unimolecular b-hydride elimination reactions strongly depend on temperature (Fig. 2), this is not the case for the bimolecular C 2 H 6 elimination of the same species (Fig. 5).On the other hand, the barriers are significantly increasing with an increase in temperature for the bimolecular classes, whereas the unimolecular barriers are not affected by temperature (see also Table 5).

Decomposition scheme for TBP
Building upon the data presented in Tables 3 and 4, a decomposition scheme for TBP (Fig. 6) can be set up similar to TEG (Fig. 1).The reaction energies lead to the conclusion that TBP can decompose via homolytical bond cleavage and the elimination of hydrogen gas, alkane or alkene compounds, respectively.
As it turns out, most unimolecular reactions (Fig. 6, left) can be neglected, since they are strongly endergonic (Table 3).Considering reactions with H 2 , a hydrogen or an alkyl radical (e.g.H , t-C 4 H 9 ), a bimolecular decomposition scheme of exclusively exergonic reactions can be formulated which involves radical and non-radical intermediate species.Within this scheme (Fig. 6, right), no P species smaller than the radical PH 2 can be reached from TBP.If dehydrogenated P(t-C 4 H 9 ) is present, PH and atomic P can be reached on exergonic paths.The major pathways are discussed in the following.Pathway 5 ''b-hydrogen elimination''.Fan et al. propose an ''intramolecular b-hydrogen elimination'' mechanism for TBP, confirmed by temperature-dependent FT-IR measurements performed during MOVPE in a H 2 atmosphere similar to the conditions in our study. 56This exergonic alkene elimination (i-C 4 H 8 , isobutene) is the only unimolecular decomposition mechanism considered here as all other classes are highly   This journal is © the Owner Societies 2014 endergonic.It can be formulated for TBP as well as for the triplet species P(t-C 4 H 9 ) (AP6 and AP7).It involves the transfer of a hydrogen atom from a b-carbon atom of the butyl group to the phosphorous center.As the formal acceptor orbital of the P atom is occupied, the reaction cannot directly be compared to the b-hydride mechanism discussed for the Ga species (which exhibits an empty p-orbital). 57A transition state with a rather large P-C distance was found (left path in Fig. 7).A detailed analysis of this reaction class is beyond the scope of this study and will be presented elsewhere. 58The barrier for this reaction (AP6, DG # 400 = 217.4kJ mol À1 ) is significantly higher than typical barriers of the calculated b-hydride elimination of Ga species (AG11-AG14, DG # 400 = 82.6-149.9kJ mol À1 ).Furthermore, the trend of Gibbs energy barriers for the reaction with an increase in temperature is reversed with respect to the Ga b-hydride eliminations indicating differences in the mechanism.The equivalent decomposition from the triplet P(t-C 4 H 9 ) will not be discussed in detail here since its formation from TBP by eliminating H 2 is endergonic (AP10, DG 400 = 123.2kJ mol À1 ).
Pathway 6, ''second order pathway, alkane elimination''.The bimolecular decomposition network of TBP is less interlinked compared to the bimolecular network of Ga species, since only a small number of decomposition products can be formulated.Reactions of TBP with a radical may lead to P(t-C 4 H 9 )H or PH 2  , from which recombination with further radical partners (e.g.H ) may lead to the original precursor or phosphine (PH 3 ).
The most important bimolecular decomposition pathway for TBP is the exergonic concerted elimination of isobutene and H 2 .
A transition state can be found for this single-step reaction and is very high in energy (BP8, DE # = 264.6 kJ mol À1 ).As expected for a bimolecular reaction, the unfavorable entropy factor increases this barrier even further to DG # 400 = 337.3kJ mol À1 rendering it highly improbable that this barrier could be overcome at the given temperature (see the right path in Fig. 7).Several bimolecular reactions can be formulated for P(t-C 4 H 9 ), but applying the assumption given above (low reactant concentration due to missing decomposition pathways of TBP to this intermediate) no reaction barrier was calculated for these.Considering the thermodynamic schemes of both uni-and bimolecular decomposition pathways from TBP, only phosphine (PH 3 ) is likely to be formed in significant concentrations aside the original precursor in the gas phase.Notably, it is known from the experiment that the fraction of the original precursor finally arriving on the surface is very large for P species 4,56 in line with the large barriers presented here.

Discussion
The results presented in the previous sections will be discussed in the light of the assumptions presented earlier.In the first Results section, thermodynamic data were presented for many elementary reactions starting from the precursors TEG (Ga(C 2 H 5 ) 3 ) and TBP (PH 2 (t-C 4 H 9 )).Of course, it cannot be excluded that a reaction might be missing in the catalogue but considering the large amount of data and the various mechanism classes we are confident to have included the important reactions.Initially, all fragments were further investigated even when no direct route to this fragment was found.This enables a complete picture of the Ga and P species and a comprehensive evaluation of the methodology.The reaction channels described here encompass uni-and bimolecular reactions.As pointed out in the Introduction, unimolecular reactions are assumed to occur more likely than higher order reactions in a low-pressure atmosphere.Calculations of homolytical bond cleavage reactions (e.g.symmetric dissociation of  Additionally, some classes of bimolecular reactions have to be considered.These are reactions with the carrier gas H 2 which are thermodynamically accessible. 53But also the radicals H , C 2 H 5 , t-C 4 H 9 , etc. might be available in small concentrations as they can be produced in the course of a MOVPE procedure.Especially interesting is the formation of atomic hydrogen which can potentially be thermally desorbed from the substrate at 480-580 1C 16 as well as hydrogen (or carbon hydrates) via recombinative desorption. 59As this work focused on pure gas phase reactions, the investigation of the latter reactions only becomes important when the surface is explicitly considered in the next phase of this study.Heterolytic dissociation reactions leading to ionic species are not considered as those will not occur in the gas phase and are of minor importance when focusing on relevant decomposition products.For example, an alternative (''barrierless'') mechanism for reaction AP6 involving an unstable, ionized intermediate step was proposed for the As-precursor TBA, 15 but the mechanism is probably surface-mediated.It becomes clear that the conclusions about viability of a reaction mechanism cannot be drawn from the thermodynamic data alone.Reaction barriers were calculated only for those exergonic reactions that were likely to occur based on the above assumptions.AP6, for instance, is strongly exergonic but exhibits a large barrier which will result in a very low reaction rate at all but the highest temperatures.Generally, transition state theory is valid here as large molecules and high temperatures are considered. 48he distribution of particles and temperature in the chamber are fluctuating irregularly.The Si-wafer is locally heated, so the highest temperature region is at and directly above the surface.The carrier gas flow induces a flux that transports the heated gas away from the wafer towards the gas outlet.As a consequence, the temperatures applied in this study (experimental surface temperatures of 400, 500 and 675 1C) represent upper bounds for the temperature in the gas phase.This has consequences in interpreting the calculated energies: since the change in Gibbs energy becomes more negative (or less positive) with an increase in temperature for all elementary reactions, a higher temperature means a more exergonic reaction.Thus, the presented thermodynamic values represent a lower bound for the discussed MOVPE precursors.In the real system, the reaction enthalpies will be less favorable due to colder local temperatures further away from the surface.The situation is different for the reaction barriers: as the barrier of a reaction generally increases with an increase in temperature (except AG20 and AP6), the calculated data are upper bounds for the barriers.In the real system, lower temperatures will result in smaller barriers.However, as the temperature dependence of Gibbs energy barriers is not strong, this effect will not be decisive.More important will be the higher kinetic energy of the molecules to overcome these (slightly raised) barriers at higher temperature.
Decomposition reactions on the surface have entirely different mechanisms and may lead to different inert and reactive intermediates.Catalytic effects of the surface might change the relevant barriers drastically, hence studies in this field have to be taken into account. 16,60Thus we will continue our work in this field by applying periodic calculations to the GaP-Si system within the methodology validated here.

Conclusions
In this study, we present a comprehensive reaction catalogue for the gas phase decomposition reactions of triethylgallane (Ga(C 2 H 5 ) 3 , TEG) and tert-butylphosphine (PH 2 (t-C 4 H 9 ), TBP) with thermodynamic and reaction barrier data based on DFT and ab initio (MP2, CCSD(T)) energies.From these data, conclusions can be drawn for the gas phase species relevant for the MOVPE growth of III/V-semiconductor GaP on silicon substrates.For TEG, we find a series of b-hydride elimination reactions as the most probable pathway leading to GaH 3 or even GaH at elevated temperatures (675 1C).Radical cleavage and other reactions as often proposed earlier are found to exhibit unfavorable thermodynamic characteristics.For TBP, a group 15 analogue of the b-hydride elimination reaction is found to be the energetically most accessible reaction.For all uni-and bimolecular TBP decomposition reactions, the computed barriers are very high leading to the conclusion of mainly the original precursor arriving at the surface.Methodologically, we could show that dispersion-corrected DFT computations at the PBE-D3 level perform well in comparison to MP2 and CCSD(T) benchmark data and can be used for further studies of these systems.
(a) homolytical bond cleavage, (b) b-hydrogen elimination, (c) alkane elimination and (d) H 2 elimination.Three classes were considered for bimolecular decomposition reactions: alkane elimination with (a) a hydrogen radical (H ), (b) alkyl (ethyl, tert-butyl) radicals (C 2 H 5 , t-C 4 H 9 ) Four mechanism classes are listed with elementary reactions of the original precursors and their decomposition products.All reactions shown are endoenergetic (DE 4 0), while b-hydride and alkane elimination reactions are exergonic (DG o 0) for elevated temperatures.This is due to entropic effects resulting in large differences between DE and DG values.Higher temperatures therefore favor these decomposition reactions.The general ordering (from the least to the most favorable reactions considering DE) of the investigated decomposition mechanisms is homolytical cleavage reactions { b-hydride elimination reactions o H 2 elimination reactions o alkane elimination reactions.

Fig. 1
Fig. 1 Unimolecular (top) and bimolecular (bottom) decomposition reaction schemes for TEG considering information from Tables1 and 2. Endergonic steps (at 400 1C) are crossed out or do not appear at all.Decomposition mechanisms are classified as radical cleavage reactions (magenta), alkane (orange), H 2 (yellow) and b-hydride (green) elimination reactions.Bimolecular elimination of alkanes or H 2 is considered with the H (red) or C 2 H 5 (turquoise) radicals or H 2 (blue) as reaction partners.

Fig. 2
Fig. 2 Three-step b-hydride elimination from TEG to gallane (GaH 3 ), followed by a H 2 elimination step to GaH.Changes in Gibbs energy (DG) and barriers relative to the respective reactants (in kJ mol À1 ) at experimental temperatures.Distances are given in Å.

Fig. 3
Fig. 3 Two-step decomposition of TEG to GaH via Ga(C 2 H 5 ).Changes in Gibbs energy (DG) and barriers relative to the respective reactants (in kJ mol À1 ) at experimental temperatures.Distances are given in Å.

Fig. 5
Fig. 5 Bimolecular C 2 H 6 elimination reactions of Ga(C 2 H 5 ) n H (3Àn) (n = 3, 2, 1) with a reaction partner H 2 .Changes in Gibbs energy (DG) and barriers relative to the respective reactants (in kJ mol À1 ) at experimental temperatures.Distances are given in Å.

Fig. 6
Fig. 6 Unimolecular (left) and bimolecular (right) decomposition reaction schemes for TBP considering information from Tables3 and 4. Endergonic steps (at 400 1C) are crossed out or do not appear at all.Decomposition mechanisms are classified as radical cleavage reactions (magenta), alkane (orange), H 2 (yellow) and b-hydrogen (green) elimination reactions.Bimolecular elimination of alkanes and/or H 2 is considered with the H (red) or t-C 4 H 9 (turquoise) radicals or H 2 (blue) as reaction partners.

Fig. 7
Fig. 7 Decomposition of TBP via b-hydrogen elimination of isobutene (reaction to the left) and bimolecular concerted elimination of isobutene and H 2 (reaction to the right) leading to phosphine, respectively.Changes in Gibbs energy (DG) and barriers (in kJ mol À1 ) at experimental temperatures.Distances are given in Å.

Table 2
Bimolecular decomposition reactions of TEG and related products.Changes in electronic (DE) and Gibbs energy (DG) for temperatures of 400 1C (a), 1C (b) and 675 1C (c) are given in kJ mol À1 .Mechanisms are grouped as alkane or H 2 elimination reactions with H (BG1-BG11), C 2 H 5

Table 3
Unimolecular decomposition reactions of TBP and related products. This c) DE AP1 P(t-C 4 H 9 )H 2 -P(t-C 4 H 9 )H + H journal is © the Owner Societies 2014

Table 4
Bimolecular decomposition reactions of TBP and related products.Changes in electronic (DE) and Gibbs energy (DG) for temperatures of 400 1C (a), 500 1C (b) and 675 1C (c) are given in kJ mol À1 .Mechanisms are grouped as alkane/alkene and/or H 2 elimination reactions with H (BP1-BP5),

Table 5
Transition state

Table 6
Statistical deviation of PBE-D3/TZ and MP2/TZ reaction energies (DE) w.r.t.CCSD(T)/TZ energies and barriers (DE # ) w.r.t.CCSD(T)/TZ and MP2/TZ energies.Method1//method2 indicates an energy calculation by method1 on the structure optimized with method2 a Root mean square error in kJ mol À1 .bMaximum absolute error in kJ mol À1 .cRelative average deviation in %. d Relative maximum deviation in %.This journal is © the Owner Societies 2014