ILSim A compact simulation tool for interferometric lithography

Transcription

1 LSm A compact smulaton tool fo ntfomtc lthogaphy Yongfa an, Anatoly Bouov, Lna Zavyalova, Janmng Zhou, Anw stoff, al Laffty, Buc W. Smth Rochst nsttut of Tchnology, Mcolctonc ngnng Dpatmnt 8 Lomb Mmoal Dv, Rochst, Y 463 ABSTRACT ntfnc magng systms a bng us mo tnsvly fo R&D applcatons wh A manpulaton, polaaton contol, latv bam attnuaton, an oth paamts a plo an pocton magng appoachs may not st. To facltat ntfomtc lthogaphy sach, w hav vlop a compact smulaton tool, LSm, fo stuyng mult-bam ntfomtc magng, nclung flu mmson lthogaphy. Th smulato s bas on fullvcto ntfnc thoy, whch allows fo applcaton at tmly hgh A valus, such as thos poct fo us wth mmson lthogaphy. n ths pap, LSm s monstat fo us wth two-bam an fou-bam ntfomtc mmson lthogaphy. Th smulaton tool was wttn wth Matlab, wh th thn flm assmbly ambnt, top coat, sst lay, BARC lays, an substat an llumnaton contons wavlngth, polaaton stat, ntfnc angl, moulaton, A can b fn. Th lght ntnsty stbutons wthn th sst flm fo posu o -pass posu a splay n th gaph wnow. t also can optm BARC lay thcknss an top coat thcknss. Kywos: ntfomtc lthogaphy, Hgh-A, Molng, ull vcto magng thoy. TRODUCTO n a convntonal lthogaphc magng systm, th pattns on th mask a poct though a st of lnss on a waf coat wth photosst wh th mag of th pattns s co. ntfnc lthogaphy poucs poc pattns n a photosst flm by th ntfng of two cohnt las bams. o a fw spcal cass, ffacton-lmt pocton magng s analogous to ntfnc magng. Th fst cas s th pocton magng of a phas shftng gatng mask : uty aton, altnatng 8º phas, % tansmsson wth cohnt llumnaton. Th gatng s th ffacton o s o. f th ptch of th gatng s such that only th ± st ffacton os a captu n th ntanc pupl, th sultng mag s smply th ntfnc fngs of two plan wavs wth oblqu angl half of th angl subtn by th lns at th mag plan. Th scon cas s th pocton magng of a : bnay gatng mask wth cohnt llumnaton. f th ptch of th gatng s such that only th th an ± st ffacton os a captu n th ntanc pupl, th sultng mag s th ntfnc fngs of th plan wavs, two bams wth oblqu angl, on nomal to th mag plan. Th th cas s th pocton magng of a : bnay gatng mask wth off-as cohnt llumnaton. f th ptch of th gatng s such that only th th an on of th ± st ffacton os a captu n th ntanc pupl, th sultng mag s th ntfnc fngs of two plan wavs of ffnt ampltus wth oblqu angl c th ampltu of th th o s ffnt fom that of th ± st os. o th abov cass wth patal cohnc llumnaton, th sultng mags stll can b cons as ntfnc fngs but wth wak ± st ffacton os c only pat of th ± st os s captu n th ntanc pupl. n a wo, magng of th abov gatng obcts fom an optcal pocton systm can b uc to th poblms of plan wav ntfnc. Th smblanc of pocton magng to ntfnc magng n th cass analy n th pcng paagaph has stmulat stus of optcal pocton systms ug an ntfomtc stup. Although thos a spcal cass, thy psnt a systm s soluton lmts, whch mostly fn th systm s capablty. An avantag of ug an ntfomtc stup s that th tly lnss a not n. At th sam tm, a gl ntfomtc stup posssss th flblty of mulatng vaous lnss. Th polaaton of bams can b convnntly manpulat, allowng stuy of polaaton ffcts. An ta flblty s that th latv ampltu of th bams can b asly contoll. n vw

2 of ths avantags, a goous analyss of plan wav ntfnc s pfom n th followng sctons to affo a btt unstanng.. THORY. ntfnc magng ntfnc fngs wll b fom n th ntscton gon of two o mo sts of cohnt monochomatc optcal plan wavs. ntfnc u to two o th pola cohnt monochomatc optcal plan wavs s analy h. Th bams n th followng scusson gnally f to monochomatc optcal plan wavs... Two-bam ntfnc wth T polaaton As llustat n th gu., two bams wth qual oblqu angl ntsct at a plan. Th lctcal vctos of th plan wavs a ppncula to th plan of th fgu T polaaton. Th ntscton ln s st as as wth ogn at th cnt of th bams. y as s th nomal cton. Wth th tm pnnc facto suppss an th ogn as phas fnc pont, th fls lft bam an ght bam at th ntscton as a functon of locaton can b pss spctvly as, wh k s th popagaton vcto, n. Th total fl at th ntscton s th sum of th two, Th ponng ntnsty s popotonal to th squa of th ampltu of th fl, ] ] 3 4 Th stbuton of ntnsty along cton s usoal, th ptch spatal po of whch s, p k n 5 o th phas shftng gatng cas scuss n th pvous scton,, th ntnsty stbuton s uc to, ] 4 6 o th cas of bnay gatng wth off as llumnaton scuss n th pvous scton, stbuton s uc to, 4 ], th ntnsty 7

3 g... Two monochomc plan wavs wth T polaaton ntsct at a plan wth qual oblqu angl. Th ntscton ln s st as as wth ogn at th cnt of th bams. y as s th nomal cton... Two-bam ntfnc wth TM polaaton TM polaaton fs to th polaaton stat wh th lctcal vctos of th plan wavs a paalll to th plan of th fgu, as llustat n th gu.. o T polaaton, th total fl s smply th scala summaton of th two plan wavs c th lctcal vctos a paalll to ach oth. o TM polaaton, th lctcal vcto s a functon of oblqu angl, qung vcto opaton fo summaton. an can b pss spctvly as, ˆ ˆ 8 ˆ ˆ ˆ ˆ ˆ ˆ wh î an ĵ a unt vctos n an cton spctvly, subscpts, sgnat, componnts of th lctcal vctos. Th total fl thus s, ˆ ]ˆ Th ntnsty stbuton s valuat as, ˆ ˆ ]ˆ ] ] ˆ o th phas shftng gatng cas scuss n th pvous scton,, th ntnsty stbuton s uc to, 9

4 ] o th cas of bnay gatng wth off as llumnaton scuss n th pvous scton, stbuton s uc to,, th ntnsty ] 3 4 ˆ ˆ ˆ î g... Two monochomc plan wavs wth TM polaaton ntsct at a plan wth qual oblqu angl. Th ntscton ln s st as as wth ogn at th cnt of th bams. as s th nomal cton...3. Th-bam ntfnc wth T polaaton f th s a th bam that s nomal to th ntscton of th two bams as scuss n th pcng sctons, th ntfnc can b analy n a smla way. ot that th bam has a constant phas as th ntscton. o T polaaton, th total fl can b pss as, Th ntnsty stbuton thfo s, f, 4..4 Th-bam ntfnc wth TM polaaton Rgang to th-bam ntfnc wth TM polaaton, th total fl can b v smlaly,

5 ˆ ] ]ˆ ˆ ]ˆ ˆ ˆ ˆ ˆ Th ntnsty stbuton s: ] ] ] ] ] f 5. Lght popagaton though a stack of thn flms...tanmsson an flcton coffcnts of a thn-flm assmbly Tansmsson an flcton coffcnts of a thn-flm assmbly can b comput ug th wll stablsh thn-flm mat tchnqus bas on Maclo s wok. 3 Th optcal chaactstc of a lay of thn flm s pss ug a mat, δ δ δ δ M / 6 wh s phas facto an s th oblqu optcal amttanc, whch a fn spctvly as, fo T polaaton 7 fo TM polaaton 8 δ 9 Th chaactstc mat of an assmbly wth q lays s smply th pouct of th nvual matcs, sub q M C B wh subscpt sub nots th substat. Th tansmsson an flcton coffcnts of th thn flm assmbly a spctvly pss as, C B C C B τ B wh th oblqu optcal amttanc n th ncnt ma.

6 ... ntnsty stbuton wthn a thn flm lay A unfom mum s assum n th pcng analyss on ntfnc magng. Howv, photosst, th mag cong ma, s oftn n th fom of a lay of thn flm among an assmbly of thn flms. A typcal flm stack n mon lthogaphy may nclu a top coat lay, a sst lay an a BARC bottom antflctv coatng lay on a substat. Th top lay potcts th sst lay by solatng t fom th mmson flu n th contt of mmson lthogaphy. Th BARC lay functons to allvat stanng wavs u to flcton fom th substat. Th flm stack foms an nhomognous mum. Rflctons/factons at th ntfacs sult n stbuton of lght ntnsty wthn th photosst lay. Dons Gog lagllo analy th lght ntnsty stbuton wthn th sst flm whch s on th top of th flm stack. 4 Whn a top coat lay s psnt abov th sst flm, a smla analyss can b conuct to v th lght ntnsty stbuton wthn th sst flm. A ay ncnt on th flm stack s llustat n gu.3. Th total fl at any pont wthn th sst lay s th sum of th ownwa fl an upwa fl. Th ownwa fl an upwa fl at ntfac X a not as X an X, spctvly, wh X s a Roman numal fo an ntfac. Thn, th ownwa an upwa fls at ntfac a an, spctvly. Th ownwa fl an upwa fl at any pont wthn th sst lay can b pss as, wh s th stanc fom ntfac, th phas s fnc at ntfac. Th total fl n th sst lay at any pont s thfo, 3 Mum, Top coat, Rsst, 3 3 Bac, 3 V Substat, sub g..3. Thn flm stack on a substat wth ncnt plan wav. Th flm thcknsss, optcal constants, ntfacs, ncnt angls a not. Th optcal constants may b compl. t can b shown that an a lat to th ncnt fl at ntfac. Th tansmsson an flcton coffcnts at th ntfac a fn as:

7 sub 4 wh sub s th fl tansmtt at th last ntfac. Smlaly, th tansmsson an flcton coffcnts at ntfac, a fn as, sub 5 om th abov quatons, th followng latons can b v, sub 6 7 Th total fl at any pont wthn th sst lay s v by substtutng th abov quatons nto quaton 3, 8 uth substtut of 9 sults n, 3 wh s tm as flm functon. t scbs th stanng-wav bhavo u to th flcton fom blow th sst lay. valuaton of qus computng,,, whch can b on ug th quaton...3 lm uncton As scuss n th pcng scton, th flm functon scbs th stanng-wav ffcts wthn th sst lay u to flcton fom th low ntfac of th sst lay. om quaton 9, can b valuat ug coffcnts, an, whch a polaaton pnnt. o T polaaton, th flm functon s smply pss as, ] S S 3 S wh th subscpt S nots T S polaaton. n th cas of TM P polaaton, th ponng coffcnts comput ug stana thn flm mat tchnqus can not b appl to quaton 3 ctly n that a vcto summaton of th ownwa an upwa fls s n c th polaaton ctons a not paalll to ach oth. Dcomposton of th ncnt lctcal vcto nto an componnts whch a thn tat spaatly s ncssay. Th ponng functons a pss as, ] P P 3 P ] P 33 P P wh subscpts an not th lat composton componnts. Th coffcnts, an of componnts can b comput ug stana thn flm mat tchnqus but not th componnts. Howv, th latonshp btwn th coffcnts of an componnts can b stablsh ug gu.4.

8 t t t t g..4. A TM pola ncnt wav ncnt on a stack of thn flms wth angl ffacts nto a substat wth an angl t. Th lctcal vctos a compos nto an componnts. As llustat n gu.4, a TM pola ncnt wav ncnt on a stack of thn flms wth angl ffacts nto a substat wth an angl t. Th lctcal vctos of ncnt not wth subscpt an ffact wavs not wth subscpt t a compos nto componnt not wth subscpt an componnt not wth subscpt. Th flcton coffcnt of componnt s pss as, P 34 Th componnt s lat to th componnt by a smpl tangnt functon. Also, t s not that th s 8 out of phas wth. Thfo, tan P P tan 35 P P Smlaly, th tansmsson coffcnt of componnt s pss as, t P 36 An th componnt s lat to th componnt by a smpl tangnt functon. Along wth Snll s law, w hav, t tan tt t t t P tan t t t P τ 37 P t t Applcaton of th latonshps fom quaton 35 an 37 to quaton 33 yls th flm functon fo componnt of TM polaaton, ] P P 38 P quaton 3, 3 an 38 consttut th whol flm functon. Thy a summa h as:

9 ] S S S 3 ] P P P 3 ] P P P 38 Th lght ntnsty stbuton wthn th sst flm sultng fom ntfnc s foun smply by applyng th flm functon fn n th pcng paagaph. o ampl, applyng flm functon to quaton 6 an quaton, th ntnsty stbutons wthn th sst flm sultng fom two-bam ntfnc fo T an TM polaaton a foun spctvly as, ] T S T 39 ] 4 4 ] ] ] ] P P P P TM 4 scbs th stanng wav ffct n th vtcal cton, whch s not sabl n lthogaphc pactc. t s convnnt to pss n th fom of ϕ 4 wh s a al numb. Thn flm functon quaton 9 bcoms ϕ valuaton of gvs, ϕ ϕ ϕ t ncats that th usoal stanng wav has a ptch of R. Th ampltu of th stanng wav s tmn by. Complt suppsson of th stanng wav qus that vansh. 3. PUTS AD OUTPUTS SUMMARY Bas on th mol scb n th pcng scton, a smulato call LSm was bult wth Matlab fo hgh A molng of ntfomtc lthogaphy, allowng fo mag pcton an optmaton. LSM s nputs nclu optcal constants fo magng ma, thn flms fom th flm stack an substat, as wll as magng optcs such as wavlngth,

10 polaaton, moulaton, popagaton angl, numcal aptu, tc. Th Outputs nclu th mag n ma, -D mag n sst, 3-D mag n sst, two-pass posu mags, flcton fom top sufac an substat BARC, tc. Th nputs an outputs of LSm w summa n Tabl. Th ntactv ntfac to LSm s us to fn flm stack ata an magng contons. LSm gnats D an 3D ntnsty plot output fo ln/spac pattns two-an th-bam ntfnc an contact hols fou- an fv-bam ntfnc. Tabl 3.. Summay of LSm s nputs an outputs LSm nput lu popts Top coat Photosst Multlay BARCs Substat popts Wavlngth Polaaton Dmoulaton Popagaton angl umcal aptu Lsm Output mag n ma D mag n sst 3D mag n sst Two-pass posu top Two-pass posu s-scton Pola two-pass posu Top Sufac flcton Substat BARC flcton 4. SMULATO XAMPLS n ths scton, a numb of smulaton ampls w gvn to llustat vaous fatus of LSm. Th magng optcs contons an flm stack paamts a lst along wth th smulaton plots. n th plots,, y an a spacal coonats wth notng th pth nto th sst. 4. mag n mmson ma Th mag n mmson ma s th ntfomtc fng n a unfom ma n absnc of a flm stack. An ampl s shown n gu 4. wth th ponng smulaton paamts lst n Tabl 4.. Tabl 4. Smulaton paamts fo ampl 4. lm Assmbly Optcs Ma.437 Wavlngth 93 nm Top coat.437 Polaaton TM Rsst.437 A.5 Bac.437 Dmoulaton Substat D mag n sst Th -D mag n sst s th plot fo so-mag contous. An ampl s shown n gu 4.. wth th ponng smulaton paamts lst n Tabl 4.. A smulaton plot fo th sam smulaton paamts but wth TM polaaton s shown n gu 4... Tabl 4. Smulaton paamts fo ampl 4. lm Assmbly Optcs Ma.437 Wavlngth 93 nm Top coat.44, 4nm Polaaton T Rsst.7-.39, nm A. Bac.8-.34, 39nm Dmoulaton Substat

11 4.3 3-D mag n sst Th 3-D mag n sst s th sufac plot fo lght ntnsty stbuton wthn th sst. An ampl s shown n gu 4.3 wth th ponng smulaton paamts lst n Tabl mag contast n sst Th mag contast n sst s plott aganst th thcknss of th sst. An ampl s shown n gu 4.4 wth th ponng smulaton paamts lst n Tabl 4. but wth TM polaaton Pass posu wth othogonal/paalll polaaton Th waf s pos onc, thn t s tun 9 g fo a scon-pass posu. f th polaaton cton mans th sam fo th scon posu, t s call othogonal polaaton -pass posu confguaton. f th polaaton cton s tun 9g fo th scon posu, t s call paalll polaaton -pass posu confguaton. Th so-mag contous of a top-own vw o s-scton of th sst can b smulat as llustat n gu 4.5. an gu Th ponng smulaton paamts lst n Tabl Rflcton fom top sufac an substat BARC Th flcton fom th top sufac an th substat BARC as a functon of top lay thcknss o BARC thcknss can b smulat fo optmal thcknss. An ampl s shown n gu 4.6. an gu Th flcton fo both T an TM s shown. An optcal thcknss fo T polaaton s shown n th plot. Th ponng smulaton paamts lst n Tabl COCLUSO A compact smulaton tool, LSm, was bult fo stuyng mult-bam ntfomtc magng, nclung flu mmson lthogaphy. Th tool s bas on th full-vcto ntfnc thoy, allowng fo applcaton at tmly hgh A valus, such as thos poct fo us wth mmson lthogaphy. Th thn flm assmbly ambnt, top coat, sst lay, BARC lays, an substat an llumnaton contons wavlngth, polaaton stat, ntfnc angl, moulaton, A can b fn n th ntactv ntfac. Vaous smulatons ampls w monstat. LSm s a usful smulaton tool fo ntfomtc lthogaphy 6. RRCS. B. W. Smth, Optcs fo Photolthogaphy, n Mcolthogaphy Scnc an Tchnology, J. R. Shats, B. W. Smth, s. Macl Dkk, 998, pp Copans, A. Bouov, Y. an, A. stoff, L. Zavyalova, Synthss of pocton lthogaphy fo low k va ntfomty, n Optcal Mcolthogaphy XV, B. W. Smth., Poc. SP, 5377, PART 3, H. A. Maclo, Thn-flm optcal flts Macmllan Publshng Company, D. G. lagllo, Hgh numcal aptu magng n homognous thn fms, Ph.D. Dsstaton, Unvsty of Aona, 993

12 g. 4. mag n mmson ma. g D mag n sst. g D mag n sst. g D mag n sst. g. 4.4 mag contast n sst. g Pass, othogonal pol., top own. g Pass, othogonal pol., s-scton. g.4.6. Substat BARC flcton. g.4.6. Top sufac flcton.