Application of Molecular Dynamics to the Simulation of Deposition P. Belsky 1, R. Streiter 2, H. Wolf 2

Transcription

1 Application of Molcula Dynamics to th Simulation of Dposition P. Blsky 1, R. Stit, H. Wolf 1 Chmnitz Univsity of Tchnology, Cnt fo Micotchnologis, Chmnitz, Gmany Faunhof IZM, Dpt. Mico Dvics and Equipmnt, Chmnitz, Gmany Intoduction Ulta thin films a ndd as contact lays, sd lays, and bais fo th fabication of psnt and futu Dp Submicon Intconnction Systms (DSM). As long as possibl th dposition of such thin mtal films is pfomd by Physical Vapo Dposition (PVD) o Ionizd Physical Vapo Dposition (IPVD). S Fig. 1 fo a simplifid illustation of th PVD / IPVD pocss. Confomal (homognous) dposition in vias and tnchs of incasing aspct atio as wll as unifom bottom and sidwall covag in th fatus acoss a lag waf diamt qui a na nomal incidnc of th filmfoming paticls. This can b achivd by a combination of a long tagt-to- waf distanc, a high dg of (post-) ionization, and waf bias voltags in th od of 100 V. Bcaus of thi incasd ngy th ions undgo vaious intactions with th sufacs thy hit: adsoption, flction, and sputting of on o mo film paticls. An optimization of th pocss conditions has to b suppotd by a multi-scal simulation of paticl gnation, tanspot, and dposition. Mtal tagt Mtallizd waf U ~ V (sputting) Coils fo additional ionization (IPVD) Agon plasma U bias up to ~ V (IPVD) Objctivs of PVD / IPVD simulation Fig. 1: A simplifid illustation of th PVD / IPVD pocss Th acto scal simulation compiss fistly calculation of tagt mission spcta using th Molcula Dynamic (MD) appoach and scondly simulation of tanspot at th acto scal by th Mont Calo (MC) appoach. Th goal of th acto scal simulation is to obtain th pofil of th film acoss th whol waf disgading th fatus, and th ngy and angula distibutions of paticls aiving on th waf. Th sults of th acto scal simulation sv as input fo th fatu scal simulation. Th fatu scal simulation compiss fistly simulation of tanspot at th fatu scal using th MC appoach, and scondly simulation of intactions of th aiving film-foming paticls with th film sufac using th MD appoach. Th main goal of th fatu scal simulation is to obtain th topogaphy of th film in th fatus (tnchs and vias) fo vaious positions on th th waf (fom waf cnt to waf dg), and thus to b abl to pdict fo givn pocss conditions whth th bottom and sidwall covag of th fatus will b sufficint o not. Paticl-sufac intactions A lot of sach has bn don in th fild of paticl-sufac intactions. In th nxt paagaph lt us summaiz som basic facts lvant fo this wok. Fo a dtaild analysis of this poblmatics w f to [1,]. As an incidnt ion in collisions with atoms and lctons of a mtal slows down, ngy in xcss of th lattic binding ngy (in th od of 10 V) may b tansfd to an atom of th mtal. Atoms movd fom thi oiginal sits a subsquntly slowd down in th solid as wll. Thy can also tansf ngy to oth atoms in th lattic. Thus, a so calld collision cascad dvlops. Collision cascad volution is influncd by th cystal lattic stuctu though channling, blocking, and focusing. Som atoms involvd in th collision cascad can b jctd out of th lattic. Th jctd atoms a calld as sputtd and th phnomnon of th jction of lattic atoms out of th cystal by paticl bombadmnt as sputting. Th pojctil itslf nd not b absobd in th cystal, it can b flctd and scap fom th lattic as wll. Sputting yild is th avag numb of atoms jctd fom th lattic by on incidnt pojctil. Th sputting yild and th pobability of pojctil absoption / flction and also th ngy and angula spcta of mittd atoms (sputtd mtal and flctd pojctil atoms) dpnd on th pojctil spcis, th composition of th mtal tagt, th txtu of th tagt, th pojctil ngy and th angl of pojctil incidnc. 74

2 Th collision cascad spans ov lativly lag aas. If w want to poply modl a pojctil-sufac intaction by atomistic simulations, fo a pojctil ngy in th od of 100 V th tagt siz should b in th od of thousands of atoms. Molcula (Classical) Dynamics appoach It is tchnically impossibl to simulat a systm consisting of thousands of atoms fom fist pincipls, i.. by quantum mchanics. Th appoach of modlling th intactions on atomic scal is basd on th appoximation of quantum intactions by classical ons. Instad of solving th Schöding quation, a smimpiical modl of classical intaction btwn atoms is constuctd and thn th Nwton quations a solvd [3]. Fo MD simulations w us an ffctiv cod Kalypso wittn by Macus Kaolwski [4] dsignd fo simulating intactions of an atomic pojctil with a mtal cystal. Th intaction potntial usd consists of th pats. Th fist acts at a shot intatomic distanc and it is a paiwis pulsiv potntial, so calld scnd Coulombic potntial of Zigl-Bisack-Littmak typ []. E p = 1 åå i j i Z α 4 Z β πε o 4 å k = 1 c k b k / a (1) E p is th total ngy contibution sulting fom th paiwis pulsiv intactions. α and β dnot th atomic typs of th intacting atoms. Z is th atomic numb, is th distanc btwn atoms i and j; a, c k and b k a paamts. Th pulsiv pat is impotant fo high ngy collisions that tak plac at th bginning of th collision cascad. At lag intatomic distancs th intaction is modld by an attactiv potntial consisting of a paiwis pat and a many-body pat basd on so calld tight-binding appoximation [5]. E att = é åå ê i A p x å êë j> i j i ξ q x ù ú úû wh x = -1 o () E att is th total ngy contibution sulting fom th attactiv intactions. A, p, ξ, q and 0 a paamts dpnding on th typs of th intacting atoms α and β. Th squa oot is th many-body pat. Th xpssion und th adical sign psnts th local lcton dnsity at th sit of atom i. To simplify th matt, th squa oot accounts fo th fact that th total bond ngy dos not incas linaly with th numb of bonds. This is impotant fo a pop dsciption of intactions at th sufac. Thus, th sufac binding ngy should b automatically coct and it is not ncssay to intoduc an additional coction. An appopiat attactiv potntial is impotant fo a pop dsciption of th collctiv intaction in th collision cascad [,6]. Not that th potntial fom dfind by lations (1) and () dos not show any xplicit dictional dpndnc that is in accod with th bhaviou of tansition mtals. Bcaus of a diffusiv chaact of thi valnc f-obitals th tansition mtals do not fom bonds with a ponouncd dictionality. Th paamts in th intaction functions a usually obtaind by fitting on xpimntal data of th matial lik cohsiv ngy, lastic constants, phonon spcta, hat of sublimation, and oths o by fitting on data calculatd ab initio by quantum mchanics. Th tim stp fo intgation of th Nwton quations is in th od of fs. Th duation of th collision cascad is in th od of fs. Aft this tim th is not nough ngy fo futh atoms b sputtd. MD simulation of th tagt mission spcta Fig. shows kintic ngy distibutions of sputtd atoms fo diffnt facs of th hcp Ti cystal. It is obvious that th diffnc btwn th spcta fo th paticula facs is small. Not that dspit th high ngy of th pojctil th ngy of th most sputtd paticls dos not xcd 5 V. It is a gnal phnomnon. Th dpndnc of ngy spcta of sputtd paticls both on th pojctil spcis and ngy and vn on th tagt mtal is not stong. Th maximum always lis in th od of sval V (dpnding on th cohsiv ngy of th mtal cystal) and kintic ngy of th most sputtd atoms dos not xcd sval tns V. Though, sputting yild stongly dpnds on th matials usd and th pojctil ngy. On th oth hand, th pola angl distibutions of sputtd atoms can significantly diff dpnding on cystal stuctu and txtu. Fo a pfctly polycystallin tagt wh th cystallits a andomly ointd, th angula distibution of sputtd paticls has a cosin fom. In this cas th pobability of mission is popotional to th cosin of th pola angl of th sputtd atom. Though, fo paticula txtus th angula distibution can significantly diff fom th cosin distibution. S Fig. 3 fo compaison of th cosin distibution of a polycystallin tagt with angula distibutions calculatd by MD simulations fo diffnt facs of th hcp-ti tagt. Fo a pop simulation of th dposition pocss at th acto scal it is ncssay to know 75

3 th tagt txtu (th pcntag of cystallit ointations psnt on th tagt sufac) and th cosponding spctum of sputtd atoms sulting fom this txtu hcp-ti (001) hcp-ti (10) hcp-ti (103) hcp-ti (104) Pobability Pobability hcp-ti (001) hcp-ti (10) hcp-ti (103) hcp-ti (104) cos distibution Ekin [V] θ [dg] Fig. : Kintic ngy spctum of sputtd atoms, MD calculation (Pojctil: A+, 441 V, nomal incidnc) Fig.3: Pola angl spctum of sputtd atoms, MD calculation (Pojctil: A+, 441 V, nomal incidnc) MD simulation of sufac intactions fo th Fatu scal simulation Fig. 4 and 5 show th dpndnc of th (-)sputting yild on th incidnt kintic ngy Ekin and th incidnt pola (off-nomal) angl θ fo an agon atom (Fig. 4) o a mtal atom (Fig. 5) aiving on th sufac of th gowing thin film fo th diffnt mtal sufacs: bcc Ti (100), fcc Cu (111), and bcc Ta (110), as obtaind by MD simulations. A+ Ta Ta+ Ta Cu+ Cu Ti+ Ti A+ Cu A+ Ti Ekin [V] θ [dg] Fig. 4: Dpndnc of th (-)sputting yild on Ekin and θ fo A+ as pojctil (down Ti, middl Cu, up Ta) Ekin [V] θ [dg] Fig. 5: Dpndnc of th slf-(-)sputting yild on Ekin and θ (down Ti, middl Cu, up Ta) Excpt ths sputting spcta, also spcta fo flction a impotant fo a pop simulation of thin film dposition in high-aspct-atio fatus. It can b sn that th is a thshold fo sputting in th ang of sval tns V. Th sputting yild usually shows a maximum in th ang fom 40 to 50 dgs. Blow 40 th is a high pobability of pojctil absoption and abov 50 th pobability of flction stats to incas. 76

4 Futh, lt us point out th big diffnc in sputting yild fo titanium and copp on on sid and th havy tantalum on th oth sid. Th masss of Cu and Ti a simila (63.5 and 47.9 a.u.) whil Ta is much havi (180.9 a.u.). Th most ffctiv ngy tansf in an lastic collision occus if both collision patns hav th sam mass. This is ason why in th cas of Ta th sputting yild fo A + pojctil (39.9 a.u.) is th lowst on. But, vn fo th slf-sputting, th yild is lowst fo Ta (Ta sputting Ta). It can b xplaind by a long intaction tim of th slow Ta pojctil with th lattic atoms and with a high valu of lattic binding ngy of Ta. Thus, in a PVD pocss, wh th ngy of aiving paticls is low, ffctivly no film sputting occus. On th oth hand, in an IPVD pocss, wh th ngy of aiving ions is incasd by a bias voltag applid on th substat, sputting can occu. Th mtallization of th low pat of th sidwalls in vy highaspct-atio fatus occus pactically only du to th sputting of th bottom film bcaus on th sidwall only fw atoms aiv, moov if so, thy aiv und low angls with a high pobability of thi naly spcula flction. Th following figus show th sults of th fatu scal simulation using an in-hous dvlopd multiscal simulato T >35 E[V] Fig. 6: Engy dposition in V/atom, 3D psntation Fig. 7: Engy dposition in V/atom, D pofil Fig. 8: TEM micogaph of th film in th fatu Fig. 9: Engy dposition in V/atom, 3D psntation (without sputting and flction) Fig. 10: Engy dposition in V/atom, 3D psntation (with sputting and flction) 77

5 Figus 6 and 7 show th simulatd film pofil and th distibution of th ngy dposition (in V p dpositd mtal atom) fo a Ti dposition into a bottl-shapd tst stuctu using a Tikon Advancd Hi-Fill pocss [7]. To hav a good pictu how th atoms aiv on th sufac, sputting, flction, and diffusion modls in T hav bn switchd off dlibatly. Th absnc of diffususion and sputting ffcts is th ason fo th occunc of th shap spiks in th bottom film pofil. Fig. 8 is a TEM photo of an xpimntal film in th bottl-shapd fatu fo compaison. Fig. 9 shows th sam as Fig. 6, th fatu is just otatd so that also th clan upp wall can b sn. Fig. 10 shows again a 3D psntation fo th sam pocss whn sputting and flction vnts w switchd on in th simulation. It can b sn that thanks to ths ffcts also th upp wall gts mtallizd. Conclusions Th simulation of PVD and IPVD mtallization pocsss fo micolctonic applications at th acto scal quis th knowldg of th ngy and angula distibutions of sputtd paticls. If th mtal tagt has a txtu ths distibutions must b obtaind by atomistic simulations. Th simulation of th film pofils at th fatu scal fo an IPVD pocss tund out to b impossibl if th adsoption pobability of all aiving atoms is assumd to b 1. Th vy diffnt angls and an incasd ngy at which th atoms aiv on diffnt pats of th fatu mak it ncssay to consid flction and sputting vnts. Th pobabilitis of ths vnts must b obtaind by atomistic simulations. Rfncs [1] Sputting by Paticl Bombadmnt III, d. by R. Bhisch and K. Wittmaack, Topics Appl. Phys., Vol. 64, Sping, 1991 [] W. Eckstin, Comput Simulation of Ion-Solid Intactions, Sping Sis in Matials Scinc 10, Sping, 1991 [3] W. G. Hoov, Molcula Dynamics, Lctu Nots in Physics 58, Sping, 1986 [4] Hompag of M.A. Kaolwski, [5] M. A. Kaolwski, Tight-binding potntials fo sputting simulations with fcc and bcc mtals, Radiation Effcts and Dfcts in Solids, Vol. 00 (000), pp [6] D. Y. Lo, T. A. Tombllo, M. H. Shapio, B. J. Gaison, N. Winogad, and D. E. Haison J., Thotical studis of ion bombadmnt: Many body intactions, J. Vac. Sci. Tchnol. A, Vol. 6 (1988), pp [7] N. Ubansky, S. R. Bugss, S. Schmidbau, U. Hydnich, H. Donohu, I. Monciff, C. Gogns, Advancd Hi-Fill fo intconnct lin applications, Micolctonic Engining, Vol. 64 (00), pp