Ab initio structures and energetics of selected hydrogenated silicon clusters containing six to ten silicon atoms

Transcription

1 9 July 1999 Ž. Chemial Physis Letters A initio strutures and energetis of seleted hydrogenated silion lusters ontaining six to ten silion atoms Mark T. Swihart a,), Steven L. Girshik a Department of Chemial Engineering, UniÕersity at Buffalo SUNY, Buffalo, NY , USA Department of Mehanial Engineering, UniÕersity of Minnesota, 111 Churh Street SE, Minneapolis, MN 55455, USA Reeived 13 Novemer 1998; in final form 26 January 1999 Astrat The strutures and energies of eight fully saturated polyyli polysilanes ŽSi6H 8, Si6H 10, Si7H 8, Si7H 10, Si8H 12, Si H, Si H, and Si H were investigated using a initio moleular orital alulations. Strutures and virational frequenies were omputed at the HFr3-21GŽ. d level. A omplete asis set extrapolation method Ž CBS-4. was used to alulate the energies of the strutures. Heats of formation were evaluated ased on homodesmoti reations involving disilane, trisilane, and isotetrasilane. The alulations predit a negative free energy of reation for luster formation from silane Ž with H as a y-produt. 2 for onditions typially used in hemial vapor deposition of silion from silane. q 1999 Elsevier Siene B.V. All rights reserved. 1. Introdution Homogeneous nuleation of partiles during hemial vapor deposition Ž CVD. of thin films is an important prolem in miroeletronis manufaturing, where partile ontamination is a sustantial soure of yield loss. Nuleation of hydrogenated silion partiles during thermal CVD of silion from silane is a prototypial ase. As part of a larger study of the thermohemistry and hemial kinetis of partile nuleation during silane thermal deomposiwx 1, we have used a initio methods to alulate tion the strutures and energetis of several hydrogenated silion lusters ontaining six to ten silion atoms. The partiular lusters investigated are those that, in a preliminary kineti and thermodynami model wx 1, ) Corresponding author. Fax: q ; swihart@eng.uffalo.edu were predited to play the most important role in partile nuleation from silane. Aurate determination of the enthalpy and entropy of these lusters is neessary if we are to model and understand the partile nuleation proess in whih they partiipate. For a nuleation proess involving ondensation of a supersaturated vapor, we would expet the overall free energy hange in going from monomers to a luster to inrease with luster size, reah a maximum, and then derease with luster size for all larger lusters. When that is the ase, the luster size where the free energy hange reahes its maximum an e identified as a ritial luster size, and all lusters larger than that size are expeted to grow irreversily into partiles. For a hemial nuleation proess like the one that leads to silion hydride partile formation, it is not lear that the overall free energy hange should have suh a simple dependene on luster size. The free energy hange may r99r$ - see front matter q 1999 Elsevier Siene B.V. All rights reserved. Ž. PII: S X

2 528 M.T. Swihart, S.L. GirshikrChemial Physis Letters go through multiple loal maxima that an individually at as ottleneks in the luster growth proess. In addition, the free energy hange in this system depends oth on the size of the luster Žnumer of Si atoms. and its degree of hydrogenation Žnumer of H atoms.. Smaller silion hydride moleules have een investigated in numerous studies that will not e reviewed here. A large numer of small to mediumsized silion hydride moleules were investigated y Katzer et al. wx 2 using an empirially orreted a initio sheme. Theoretial studies of strained, polyyli silion hydrides were presented y Zhao and Gimar wx 3, and y Nagase and o-workers w4,5 x. To our knowledge, the somewhat larger and less-strained moleules onsidered here have not previously een studied. 2. Methodology The GAUSSIAN 94 wx 6 suite of programs was used for the alulations presented here. The CBS-4 omplete asis set method wx 7 was used for the energy alulations. This is the least expensive of the omplete asis set methods presented y Ohterski and o-workers wx 7. In enhmark tests that they presented, this method predited the atomization energies of the 55 moleules in the G2 test set with a mean asolute error of 7.1 kj mol y1. The geometry optimization and frequeny alulation in this method are done at the HFr3-21GŽ. d level, and the strutures otained at that level are presented here. The total energy is omputed in a multistep proedure that uses progressively smaller asis sets for higher order alulations of the orrelation energy. Using the CBS-4 energies, the heats of formation of these strutures were omputed ased on the homodesmoti reation Si mq nh 2 mqn qž mq3r2n. Si 2H 6 m Si H qn iso-si H. Ž In Eq. Ž. 1, m is the numer of SiH 2 units in the luster, and n is the numer of SiH units in the luster. The heats of formation of Si 2H 6, Si 3H 8, and iso-si 4H10 were taken from the work of Katzer et al. wx Results The strutures of the eight ompounds studied are shown in Fig. 1. Geometri parameters for the strutures are given in Tale 1. The silion hydrogen ond lengths Ž not listed in Tale 1. were all 1.48" 0.01 A, whih is the same as their value in the smaller silanes. The silion silion ond lengths are also lose to their values in the smaller silanes Ž2.34 A in disilane at this level of theory.. Most of the Si Si ond lengths omputed here are longer than the orresponding ond in disilane. Silion silion onds appear to e lengthened y silyl sustitution for hydrogen and appear to e shortened when they are part of a highly strained ring. The Si Si Si ond angles are tightly onstrained y the polyyli geometry and many of them are far from the ideal tetrahedral angle Ž aout The H Si Si ond angles ome as lose to the tetrahedral angle as possile, given the positions of the silion atoms. Tale 2 summarizes the alulated thermohemial properties of the speies. The heat of formation per silion atom is aout 40 kj mol y1 for ayli polysilanes. The highly strained lusters ontaining six or seven silion atoms have muh higher heats of formation per silion atom, due to the ring strain. One reasonale measure of the total strain energy of a luster is the energy released when the luster is onverted to ayli moleules via reation Ž. 1. This energy is given in the last olumn of Tale 2. From alulations on the monoyli polysilanes w3,8 x, the strain energies for three-, four-, five-, and six-memered rings are expeted to e aout 160, 70, 23, and 0 kj mol y1, respetively. The strain energies alulated here are sustantially smaller than what would e predited y addition of those individual ring strain energies, partiularly for the six- and sevensilion ontaining lusters that are made up of highly strained three- and four-memered rings. This is Fig. 1. Strutures of the hydrogenated silion lusters studied in this work. Atom numering orresponds to geometri parameters in Tale Ž. 1. Atoms with the same numer are idential interhangeale y symmetry operations.

3 M.T. Swihart, S.L. GirshikrChemial Physis Letters

4 530 M.T. Swihart, S.L. GirshikrChemial Physis Letters Tale 1 Geometri parameters a Si6H 8 Si6H10 Si 7H 8 Si7H10 Si8H12 Si9H14 Si10H14 Si10H16 Si Si ond lengths Ž A. R 2.36 R 2.37 R 2.36 R 2.39 R 2.41 R 2.36 R 2.39 R ,5 4,5 6,4 2,4 2,2 2,4 1,2 3,4 R 2.33 R 2.39 R 2.39 R 2.39 R 2.37 R 2.35 R ,6 5,5 6,7 2,6 2,3 4,6 1,4 R 2.38 R 2.37 R 2.35 R 2.36 R 2.36 R ,7 4,4 6,8 8,4 6,8 3,4 R 2.32 R 2.37 R 2.36 R 2.38 R ,7 9,7 8,6 8,8 3,3 R 2.36 R 2.33 R 2.36 R ,6 8,9 9,4 6,4 R 2.37 R ,8 6,6 R5, R2, Bond angles Ž degrees. /1,4,5 117 /1,4,5 114 /1,4,6 111 /1,2,6 126 /1,2,2 115 /1,2,4 109 /7,1,2 116 /1,4,3 110 /3,4,5 113 /2,4,5 115 /5,4,6 119 /4,2,6 89 /3,2,2 103 /4,2,4 112 /4,1,2 105 /3,4,3 109 /6,4,5 85 /4,4,5 90 /4,6,7 90 /2,4,8 90 /4,3,2 115 /3,4,6 114 /8,2,1 115 /4,3,4 110 /2,5,4 121 /3,5,4 118 /2,6,7 126 /3,4,8 118 /2,3,2 93 /2,4,6 109 /5,2,1 103 /2,3,4 110 /7,5,4 90 /5,5,4 90 /8,6,7 84 /9,4,8 110 /6,4,6 100 /9,4,1 116 /4,5,4 103 /4,5,4 109 /3,7,6 125 /7,8,4 111 /5,6,4 113 /3,4,1 108 /4,6,7 92 /9,7,6 93 /11,8,4 117 /7,6,4 110 /6,4,1 92 /8,6,7 129 /6,7,6 84 /6,8,4 90 /8,6,4 101 /3,3,4 103 /6,6,7 59 /6,8,9 95 /5,6,2 126 /9,8,6 114 /11,3,4 111 /9,7,6 135 /10,8,9 130 /8,6,2 90 /8,8,6 105 /13,3,4 111 /5,7,6 84 /8,8,9 59 /10,9,4 111 /6,8,6 105 /14,6,4 118 /6,7,6 61 /7,9,8 85 /12,9,4 117 /6,6,4 103 /8,9,8 61 /4,9,4 90 /5,6,4 97 /11,9,8 134 /2,5,6 93 / /12,5,6 115 a Ž. Ž. Geometries at the HFr3-21G d level. Atom numering is shown in Fig. 1. Silion hydrogen ond lengths not shown were 1.48" 0.01 Å. This is the same as their length in the smaller silanes. Virational frequenies and more detailed strutural information at this level are availale upon request from the authors. Tale 2 CBS-4 thermohemistry Speies CBS-4 enthalpy Entropy Heat of formation Total strain energy Ž hartrees. Ž y1 y1 J mol K. Ž y1 kj mol. Ž y1 kj mol. a 2 6 a Si H y Si 3 H 8 y a Si H y Si H y d 6 8 Si H y d 6 10 Si H y d 7 8 Si H y d 7 10 Si H y d 8 12 Si H y y6.5 d 9 14 Si10 H14 y d Si10 H16 y y32.5 d a These moleules were used as referene ompounds for alulating the heats of formation using the homodesmoti reation Ž. 1 given in the text. From Ref. wx 2. Taken to e zero y definition. d Enthalpy hange for the homodesmoti reation Si H qž mq3r2n. mq n 2 mqn Si 2H 6 msi 3H 8qniso-Si4H 10.

5 M.T. Swihart, S.L. GirshikrChemial Physis Letters onsistent with the alulations of Nagase wx 5, who onluded that strained rings were sustantially stailized y silyl sustitution for hydrogen. The overall thermodynamis for the formation of these silion hydride lusters from silane are summarized in Tale 3. Results for speies ontaining five or fewer silion atoms are ased on the alulations of Katzer et al. wx 2. Note that the reation enthalpies and entropies are given per mole of SiH 4. Formation of the highly strained lusters ontaining six or seven silion atoms is sustantially endothermi, while formation of ayli polysilanes and the less-strained lusters ŽSi5H10 and the lusters with eight or more Si atoms. is roughly thermoneutral. At the temperatures where signifiant silane dissoiation ours Ž) 700 K. the lustering proess is entropially driven. The entropy of reation for forming any luster that ontains at least one ring is positive, simply eause there is an inrease in the numer of moles of gas-phase speies. Prodution of the more highly strained lusters that ontain more rings also produes more H 2 as a y-produt. This results in higher entropies of reation for formation of the highly strained lusters. So, inreasing temperature favors lustering in general, and partiularly favors Tale 3 Overall thermodynamis of lustering a Moleules produed Enthalpy of Entropy of reation reation Ž y1 kj mol. Ž y1 y1 J mol K. 1r2 Ž Si. 2H6qH r3 Ž Si. 3H6q3H r3 Ž Si H q2h y1.7 1r4 Ž Si H q4h r4 Ž Si. 4H10q3H y4.3 1r5 Ž Si H q6h r5 Ž Si. 5H10q5H r6 Ž Si H q8h r6 Ž Si. 6H10q7H r7 Ž Si H q10h r7 Ž Si H q9h r8 Ž Si. 8H12q10H r9 Ž Si H q11h r10 Ž Si. 10 H14 q13h r10 Ž Si H q12h a Enthalpies and entropies of reation are for onversion of SiH 4 to the produts listed, at 298 K and 1 ar. Based on Ref. wx 2. Based on this work. formation of the strained ut less hydrogenated lusters ontaining six or seven silion atoms. At 1000 K and 1 ar, the free energy of reation for luster formation is positive for all the lusters in Tale 3 with six or fewer silion atoms exept for ylopentasilane, Si5H 10, and is negative for all lusters in Tale 3 that ontain seven or more silion atoms. The free energy of reation at this temperature does not vary smoothly with inreasing luster size, ut has a maximum at four silion atoms, a minimum at five silion atoms, a maximum at six silion atoms, and then dereases for larger sizes. In addition, there are energeti arriers to onversion from one struture to another that are not onsidered in this analysis. The free energy profile hanges with temperature, and this an move the positions of these maxima and minima, ut the data given in Tale 3 allow approximate alulation of the free energy profile for aritrary onditions. 4. Conlusions Strutures, enthalpies of formation, and standard entropies for eight seleted silion hydride lusters with six to ten silion atoms were alulated using a initio methods. Ring strain in these polyyli ompounds, partiularly those with highly strained three- and four-memered rings, was found to e sustantially smaller than would e predited y additivity of ring strain energies of the unsustituted monoyli polysilanes. Formation from silane of lusters ontaining seven or more silion atoms was found to e thermodynamially favorale at onditions typial of silion CVD. The free energy for luster formation did not vary smoothly with luster size. Aknowledgements This work was partially supported y Advaned Silion Materials, Moses Lake, WA, y the Semiondutor Researh Corporation, and y the Minnesota Superomputer Institute. We are grateful to Gernot Katzer and his olleagues at the University of Graz for helpful disussions and aess to unpulished details of their alulations.

6 532 M.T. Swihart, S.L. GirshikrChemial Physis Letters Referenes wx 1 M.T. Swihart, S.L. Girshik, J. Phys. Chem. B 103 Ž wx 2 G. Katzer, M.C. Ernst, A.F. Sax, J. Kalher, J. Phys. Chem. A 101 Ž wx 3 M. Zhao, B.M. Gimar, Inorg. Chem. 35 Ž wx 4 S. Nagase, T. Kudo, Organometallis 6 Ž wx 5 S. Nagase, K. Koayashi, M. Nagashima, J. Chem. So., Chem. Commun. Ž wx 6 GAUSSIAN94, Revision D.4, M.J. Frish, G.W. Truks, H.B. Shlegel, P.M.W. Gill, B.G. Johnson, M.A. Ro, J.R. Cheeseman, T. Kieth, G.A. Petersson, J.A. Montgomery, K. Raghavahari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challaome, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J. Defrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, Gaussian, Pittsurgh, PA, wx 7 J.W. Ohterski, G.A. Petersson, J.J.A. Montgomery, J. Chem. Phys. 104 Ž wx 8 R.S. Grev, H.F. Shaefer III, J. Am. Chem. So. 109 Ž