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Thermodynamics and Kinetics of InitialGas Phase Reactions in Chemical VaporDeposition of Titanium Nitride.Theoretical Study of TiCl 4 Ammonolysis STANISLAV YA.UMANSKII, 1,2 KONSTANTIN P.NOVOSELOV, 1 AIRATKH. MINUSHEV, 1 MAGDALENASIODMIAK, 3 GERNOT FRENKING, 3 ANATOLIA.KORKIN 4 1 AOZT Soft-Tec, Nakhimovskii prosp. 34, Moscow, 117218 Russia 2 N.N. Semenov Institute of Chemical Physics RAS, Kosigina 4, Moscow, 117977 Russia 3 Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Strasse,D-35032 Marburg, Germany 4 Advanced Systems Research Lab, SPS Motorola Inc., Mesa, Arizona 85202Received 9 January 2001; accepted 26 February 2001Dedicated to Professor Paul von R. Schleyer ABSTRACT: Thermodynamic equilibrium and kinetics of the gas-phasereaction between TiCl 4 and NH 3 have been studied computationally using resultsfrom recent quantum mechanical calculations of titanium tetrachlorideammonolysis. 1 These calculations were based upon the transition state theory forthe direct reactions and RRKM theory for the reactions proceeding viaintermediate complex. Rate constants for the barrierless reactions were expressedthrough the thermodynamic characteristics of the reagents and products usinga semiempirical variational method. The kinetic simulation of the gas-phase stepsof CVD was performed within a model of a well-stirred reactor at temperatures300–1200K and residence times between 0.1–2 s. At temperatures below 450 Kformation of donor–acceptor complexes between TiCl 4 and NH 3 is thedominating process. At higher temperatures sequential direct ammonolysis takesplace. At typical LPCVD conditions the only product of the first step of ammonolysis, TiCl 3 NH 2 , is formed in substantial amount. © 2001 John Wiley &Sons, Inc. J Comput Chem 22: 1366–1376,2001 Keywords: calculation of rate constants; RRKM theory; CVD processes;titanium nitride; TiCl 4 Correspondence to: M. Siodmiak; e-mail:
[email protected]/grant sponsors: Deutsche Forschungsgemeinschaft,Alexander von Humboldt Foundation (to A.K.), and Motorola,Inc. Journal of Computational Chemistry, Vol. 22, No. 13, 1366–1376 (2001)© 2001 John Wiley & Sons, Inc. GAS PHASE REACTIONS IN TITANIUM NITRIDE Introduction T itanium nitride has a unique combination of useful properties (high hardness and meltingpoint,goodelectricandthermalconductivity,chem-ical inertness, and excellent adherence to most met-als, semiconductors, and insulators) and numerousexisting and potential industrial applications. It has been even named “technologically the most impor-tant nitride.” 2 In microelectronics TiN has a broadarea of applications as a low-resistance contact anda diffusion barrier for metallization. 3 Several precursors such as TiCl 4 , 2, 4 Ti(NMe 2 ) 4 , 2, 5, 6 Ti(Net 2 ) 4 , 2, 5, 7 and Ti(NMeEt) 48 have been applied in titanium nitride chemicalvapor deposition (CVD). The reactions of TiCl 4 with N 2 and H 2 have been used first for TiNdeposition at high ( ∼ 900–1200 ◦ C) temperatures.The use of ammonia as a source of nitrogen lowersthe temperature to ∼ 500 ◦ C, 4 which opens thisprocess for a broader application in microelectronicindustry. Organometallic precursors, such asTi(NR 2 ) 4 , contain an excess of nitrogen. However,simple thermal decomposition of these precursorslead to high carbon contamination, while additionof ammonia improves the film composition andalso lowers the process temperature. Thus, thegas-phase ammonolysis of both inorganic andorganometallic precursors plays a key role intitanium CVD by leading to formation of reactiveintermediates, reduction of deposition temperature,and resulting in high-quality films.The reactions that occur during TiN CVD can betentativelydividedintothreegroups:adductforma-tion, ammonolysis, and Ti(IV) → Ti(III) reduction.These types of processes are well known in the gasphase and solution chemistry of TiCl 4 , while theirdetailed mechanistic description is far from beingwell understood. 9 At lower temperatures titanium tetrachlorideandammonia formdonor–acceptorcomplexes.Tak-ing into account steric repulsion between ligands,1:1 and 1:2 complexes between TiCl 4 and NH 3 should be the most expectedadducts. 10, 11 However,a product with an overall TiCl 4 :5NH 3 mass bal-ancewasobservedinthegas-phasemixtureofTiCl 4 and NH 3 at a temperature below 220 ◦ C. 12 We spec-ulate that this product is composed of a mixtureof NH 4 Cl with an ammonia adduct of the par-tially ammonolyzed TiCl 4 . In the temperaturerange between 220 ◦ and 430 ◦ C TiCl 4 :5NH 3 decomposesto ClTiN, which at higher temperatures reacts withammonia forming TiN x powder. 12 In liquid ammonia up to threechlorine atoms aresubstituted by NH 2 groups, while in methylamineonly two TiCl bonds are ammonolyzed. Trimethy-laminereducesTi(IV)toTi(III),andformsacomplexwith resulting titanium trichloride—TiCl 3 :2NMe 3 . 13 There is a limited number of theoretical stud-ies relevant to titanium nitride CVD available inthe literature. In our recent article, 1 which is de-scribed in detail below, we studied the mechanismof TiCl 4 ammonolysis and formation of donor–acceptor complexes by sequential substitution of Cl atoms through NH 2 groups. The energies of TiCl 4 :NH 3 complex formation and the energy of thefirst step of ammonolysis, which are also availablefrom refs. 14 and 15, are summarized below: Reaction Energiesin kcal/mol CCSD(T) 1 MP4 14 B3LYP 14 G2 15 TiCl 4 + NH 3 → 23.6 12.1 17.0 14.9TiCl 4 :NH 3 TiCl 4 + NH 3 → 10.8 20.5 2.9 12.2TiCl 3 (NH 2 ) + HCl The energyvaluesforboth reactions aresensitiveto the choice of computational method and the ba-sis set. The G2 theory is considered to be one of themost accurate sources of theoretical thermochemi-cal values. The values of the first step of the TiCl 4 ammonolysis obtained in refs. 1 and 15 are in fairlygood agreement, while a much larger divergence between the complex formation energies is found,which is probably due to the smaller basis set usedin our calculations. 1 Thus, in our thermodynamicequilibrium analysis (see below) we also used thecomplex formation energy from ref. 15 to evaluatethe effect of the balance of the species in a CVD re-actor.In this article we present the results of a thermo-dynamic and kinetic analysis of TiCl 4 ammonolysisand formation of donor–acceptor complexes usingcalculatedreactants,intermediates,transitionstates,and products of subsequent ammonolysis steps. Inour kinetic study we have applied transition statetheoryandasimplifiedversionoftheRRKMtheory,whicharedescribedbelow.Accordingtoourresults,the firststep oftheammonolysis isthe predominantreaction, which occurs in the low-pressure CVD re-actor. JOURNAL OF COMPUTATIONAL CHEMISTRY 1367 UMANSKII ET AL. Mechanism of TiCl 4 Ammonolysis andDonor–Acceptor Complex Formation The sequence of elementary reactions including1:1 and 1:2 complex formations and ammonolysisstudied in ref. 1, which provides the data for a ther-modynamic and kinetics analysis presented in thisarticle, can be presentedby the following scheme:TiCl 4 − x (NH 2 ) x + NH 3 ↔ TiCl 3 − x (NH 2 ) x + 1 + HCl; (1a)TiCl 4 − x (NH 2 ) x :NH 3 (1b) x = 0–3,Ti(NH 2 ) 4 + NH 3 ↔ Ti(NH 2 ) 4 :NH 3 (1c)TiCl 4 − x (NH 2 ) x :NH 3 + NH 3 ↔ TiCl 3 − x (NH 2 ) x + 1 :NH 3 + HCl; (2a)TiCl 4 − x (NH 2 ) x :2NH 3 (2b) x = 0–3,Ti(NH 2 ) 4 :NH 3 + NH 3 ↔ Ti(NH 2 ) 4 :2NH 3 (2c) Computational Details The molecular geometries of reactants, prod-ucts, and transition states in eqs. (1) and (2) have been optimized using three different theoreticalmethods: HF, MP2, 16 and B3LYP 17 as implementedin the Gaussian98 program package. 18 Analyticalharmonic frequencies have been computed at theHF level of theory for all stationary structuresand at the B3LYP and MP2 levels for selectedmolecules. HF vibrational frequencies are scaled by 0.89. 19 Single-point coupled-cluster CCSD(T) 20 calculations have been performed using B3LYP-optimized geometries. The relative energies com-puted at the CCSD(T)//B3LYP level include zero-point energy (ZPE) corrections. All calculationswere carried out using a quasi-relativistic effectivecore potential (ECP) for titanium with a valence ba-sis set (441/2111/21), which was derived in ref. 21from the [55/5/3] valence basis set. 22 An ECP witha valence basis set (4/5)/[2s3p] 23 extended by a d-type polarization function 24 was used for chlorine.It has been demonstrated for a representative set of transition metal complexes 25 that ECPs generatedfor ab initio methods can be applied in DFT-basedcalculations as well. Standard 6-31G ∗ basis set 26 were used for nitrogen and hydrogen atoms.The resulting energy diagrams at the CCSD(T)level for the four subsequent ammonolysis stepsincluding formation of 1:1 and 1:2 complexes be-tween the reactants, and the products are shownon Figure 1a–d (see ref. 1 for details). Figure 1a alsoincludes the data from ref. 15, which are given inparentheses. The reaction energies and activation barriers are similar within ∼ 2 kcal/mol in refs. 1and 15 while Cross and Schlegel 15 presented lowerenergies ofdonor–acceptorcomplexes with one andtwo ammonia coordinated to TiCl 4 .SubstitutionoftheClatomsbyNH 2 groupsisen-dothermic, and the heat of reaction increases withthe number of amino groups in the molecule (seeTable I). Because substitution of Cl by NH 2 reducesthe binding energyin thecomplexeswith ammonia,ammonolysis ofthe complexesis moreendothermicthan similar reactions of four-coordinated mole-cules (see ref. 1 for details).Except for the first step of ammonolysis, substi-tution of Cl by NH 2 proceeds via transition statesthat have energies below the reaction products (seeFig. 1a–d). This holds for reactions that proceedvia 1:1 complexes, and it results in the formationof four coordinated molecules (TS1) and for thosethat proceed via 1:2 complexes leading to 1:1 com-plexes (TS2). Weak hydrogen-bonded intermediatecomplexes, located on the reaction paths betweentransition states TS1 and TS2 and the separatedproducts have not been considered in our quantumchemical calculations. 1 They were also neglected inthe present study of the thermodynamics andkinet-ics of TiCl 4 ammonolysis. Rate Constants of Elementary Reactions The general form of the reaction energy profile( U rp ( q r ), q r is the reaction coordinate), which is con-sistent with the results of recent quantum chemicalstudies, 1, 15 is shown in Figure 2. According to theresults (see Fig. 1a–d), the energy of the productscan be lower (Fig. 2a) or higher (Fig. 2b) than thetransition state for substitution of Cl atom by theNH 2 group. The hydrogen-bonded complexes lying between the products of ammonolysis [see eqs. (1)and (2)] and HCl have not been considered becausesuchweakintermediateadductsdonotsignificantlyinfluence the rate of bimolecular reaction. 27, 28 Thesimplified reaction profiles shown by dashed lineson the product side have been used in our semiem-pirical calculations of the reaction rates.Reactions with the energy profiles shown inFigure 2a and b proceed via a long-lived interme- 1368 VOL. 22, NO. 13 GAS PHASE REACTIONS IN TITANIUM NITRIDE FIGURE 1. Energy diagram for TiCl 4 ammonolysis and formation of donor–acceptor complexes with ammoniaat CCSD(T) level: (a) first step—TiCl 4 (data from ref. 15 are given in parenthesis); (b) second step—TiCl 3 NH 2 ;(c) third step—TiCl 2 (NH 2 ) 2 ; (d) fourth step—TiCl(NH 2 ) 3 . TABLE I. Zero Kelvin Heats of Reaction ( H 0 ) of the Subsequent Steps of Ammonolysis of TiCl 4 − x (NH 2 ) x Molecules andTheir 1:1 and 1:2 Complexes with Ammonia (in kcal/mol). Reaction y HF B3LYP MP2 CCSD(T)TiCl 4 :yNH 3 + NH 3 → 0 9.2 10.5 12.1 10.8TiCl 3 NH 2 :yNH 3 + HCl 1 12.3 13.2 14.2 13.22 10.5 11.7 12.5 11.4TiCl 3 NH 2 :yNH 3 + NH 3 → 0 13.4 13.2 14.9 13.5TiCl 2 (NH 2 ) 2 :yNH 3 + HCl 1 16.6 17.0 18.7 17.22 20.2 18.8 21.4 19.7TiCl 2 (NH 2 ) 2 :yNH 3 + NH 3 → 0 20.0 19.2 21.2 19.7TiCl(NH 2 ) 3 :yNH 3 + HCl 1 21.9 22.0 24.6 23.12 28.0 29.5 28.5 30.7TiCl(NH 2 ) 3 :yNH 3 + NH 3 → 0 25.6 25.2 27.8 26.0Ti(NH 2 ) 4 :yNH 3 + HCl 1 30.4 28.3 31.1 28.82 38.9 35.3 44.3 38.3 JOURNAL OF COMPUTATIONAL CHEMISTRY 1369 UMANSKII ET AL. FIGURE 2. Schematic representation of the reactionpath profiles of the ammonolysis reaction: (a) the barrierenergy is higher than the energy of products; (b) thebarrier energy is lower than the energy of products. diate (excited) complex, C ∗ , which can be stabilizedto C, or it decomposes either to the reactants, X + YortotheproductsZ + W.Atfixedtotalenergy E sucha reaction canbe described by the following schemeof microscopic processes:X + Y k dr ( E ) ⇄ k f ( E ) C ∗ k dr ( E ) → Z + W,C ∗ + M k st ( E ) → C + M.(3)The energy-dependentrate constants correspondto the following elementary reactions: k f ( E )—formation of excited reaction complex, C ∗ ; k dr ( E )and k dp ( E )—decomposition of C ∗ into reactants andproducts, respectively; and k st ( E )—stabilization of the reaction complex, C ∗ , collisions with the bathgas molecules, M.The macroscopic temperature-dependant rateconstants shown on the scheme below are de-termined by the above-mentioned microscopicprocesses:X + Y k + rp k + rc Z + W k − rp k − cp C k − rc k + cp (4)To decompose into the products intermediatecomplex, C ∗ must possess a substantial internal en-ergy above the ground state of reagents E (C ∗ ) > E 0 (Fig. 2a) or H 0 (Fig. 2b) ∼ 10–18 kcal/mol (seeFig. 1a–d and refs. 1 and 15). An estimation hasshown that for such energies it holds: k dr ( E ) ≫ k dp ( E ) (5)In the pressure range of 1–1000 Torr and with anenergy of C ∗ above E 0 ( H 0 ) we also have: k dr ( E ) ≫ [M] k st ( E ). (6)Equations (5) and (6) result from the rather low binding energyoftheintermediatecomplexCandarapidincreaseof k dr with energy: k dr ∼ ( E − H c ) s − 1 ,where s is the number of vibrational degreesof free-dom of the intermediate complex, C, and H c is itsenthalpy of formation (see Fig. 2).If inequalities 5 and 6 are satisfied, the bimole-cular reaction and complex formation can be con-sidered independently. Then, forward and reversereactionsbetweenthestabilizedcomplex,C,andthereaction products, Z + W, can be neglected ( k + cp and k − cp ∼= 0)in the macroscopickinetic scheme in eq. (4).The rate constant k + rp ( T ) of the forward bimole-cular reaction can be evaluated using the standardtransition state theory expression: k + rp ( T ) = N A k B T 2 π ¯ h exp − F =+ − F X − F Y k B T cm 3 s × mol,(7)where N A is the Avogadro number, F X , F Y , and F =+ are the Helmholtz free energies of the reactants Xand Y and transition complex C =+ , respectively,in the standard reference state corresponding to 1molecule in 1 cm 3 .The rateconstant k + rc ( T )can beexpressedthroughthe decomposition rate constant k − rc ( T ) using theprinciple of the detailed balance: k + rc ( T ) = N A exp − F C − F X − F Y k B T k − rc ( T ) cm 3 s × mol,(8)where F C is the Helmholtz free energy of the com-plex, C. 1370 VOL. 22, NO. 13
