Polarized Transmittance-Reflectance Scatterometry Measurements of 2D Trench Dimensions on Phase-Shift Masks

Transcription

1 Poaid Tansmittanc-Rctanc Scattomt Masumnts o D Tnch Dimnsions on Phas-Shit Mass John C. am, Aand Ga, Raa How, Stan Chn n& Tchnoog, nc., Santa Caa, CA 9554 Phsics Dpatmnt, Univsit o Caionia at Davis, CA 9566 ASTRACT Fo th ist tim, poaid boadband tansmittanc (T) pus ctanc (R) masumnts, combind with th Rigoous Coupd-Wav Anasis (RCWA) and th Foouhi-oom dispsion quations o n and, w usd to masu D tnch dimnsions. This is in contast to taditiona scattomt, which is basd on ctanc-on masumnts. T and R w masud om 9 to nm in on-nanomt intvas. ncusion o th tansmittanc masumnts povd to b advantagous, bcaus th is a gat snsitivit o th T spcta to th sub-nanomt stuctua and/o matia vaiations, which a diicut to dtct with R-on masumnts. Futhmo, th intnsit o T is much high than th intnsit o R, suting in a much impovd signa-to-nois atio, sinc intnsit is popotiona to numb o photons aching th dtcto, which in tun is popotiona to th signa. Thus, th high th intnsit, th high th signa-tonois, and th btt th patabiit and poducibiit o th suts. Fo th cunt stud, D aas o squa and cicua contact hos o vaious pitchs w masud on an At-Can-nspction (AC) phas-shit mas, using a spctophotomt-basd instumnt, capab o cocting ou continuous spcta duing on masumnt two poaid ctanc spcta (R s and R p ) and two poaid tansmittanc spcta (T s and T p ). Th masud spcta w anad using th Foouhi- oom dispsion quations, in conjunctions with RCWA agoithm, appid simutanous to R and T poaid spcta. Th mthod povidd accuat and patab suts o contact ho dpths, citica dimnsions im thicnsss and n and spcta. High-soution uniomit maps w obtaind o a th paamts mntiond abov. wods: Optica scattomt, citica dimnsions, D tnch stuctus, RCWA. NTRODUCTON: SNSTVTY AND RSOUTON OF TH RFCTANC-ASD AND TRANSMTTANC-ASD OPTCA MASURMNTS Th qustion o snsitivit o th optica scattomtic masumnts o th citica dimnsions o gating stuctus had bn invstigatd pvious (Ga and am, 6). t had bn dtmind that o most gating stuctus taditiona ctanc-basd scattomt might not b snsitiv nough to sov Angstom-v stuctua changs in gating gomtis. Th act that th samps in qustion (MoSi phasshit mass) a smi-tanspant in th DUV, visib and NR angs o th spctum bings us an advantag o bing ab to aso masu spcta tansmittanc in this boadband wavngth ang. Th pvious wo concntatd on th masumnts o D in gatings, and o that pupos RCWA tchniqu was appid o th ist tim to th anasis o th masud tansmittanc spcta in th wavngth ang btwn 9 and nm. t was shown that o most gating stuctus th tansmittanc Photomas and Nt-Gnation ithogaph Mas Tchnoog XV, ditd b Hidhio Watanab, Poc. o SP Vo. 667, 667, (7) X/7/$8 doi:.7/ Poc. o SP Vo

2 intnsit spctum is mo snsitiv to th stuctua and matia changs in th gating and tho is instumnta in dtmining th citica dimnsions, such as pitch, in width, dpth and poi. n th cunt stud w invstigatd th cts o CD vaiations in th D gating stuctus, such as ound and squa contact hos o vaious pitchs. Th pupos o th stud was to s i th incusion o th tansmittanc spcta into th anasis o th D gating stuctus impovs th snsitivit and tho soution o th masumnt. n addition, in od to obtain th suts, a non-ina gssion agoithm basd on th RCWA in conjunction with th Foouhi-oom dispsion ations o n and was catd and appid o th ist tim to ana boadband poaid ctanc and tansmittanc spcta masud using a boadband spctophotomt-basd instumnt. Fist, th snsitivit o th boadband poaid ctanc spcta (9 nm) to th changs in D gating dimnsions was invstigatd using RCWA simuations. Th oowing igu iustats th tpica vaiation in th poaid ctanc spcta (R s and R p ) du to 4 nm vaiation in th contact ho diamt o a 8 nm pitch D gating. Th R s spcta and th R p spcta a pottd - cosponding to th diamts o 38, 4 and 4 nm. Cotct Ho Diat 8 38 nm 4 nm 4 nm Wavnoh (n 8 Figu : Tpica vaiation in th poaid ctanc spcta (R s and R p ) du to 4 nm vaiation in in width o a 8 nm pitch D contact ho aa. t can b obsvd that most o th snsitivit occus aound th wavngths o 6 7 nm, and that th maimum inducd chang in th intnsit o th ctd ight is ~.% at 6 nm. Nt, th snsitivit o th boadband poaid tansmittanc spcta (9 nm) was invstigatd o th sam D gating gomt. Th oowing igu iustats th tpica vaiation in th poaid tansmittanc spcta (T s and T p ) du to 4 nm vaiation in th contact ho diamt o a 8 nm pitch D gating. Th T s spcta and th T p spcta a pottd - cosponding to th diamts o 38, 4 and 4 nm. Poc. o SP Vo

3 Contact Ho Diamt 38 nm 4 nm 4 nm Wavncib (nnt Figu : Tpica vaiation in th poaid tansmittanc spcta (T s and T p ) du to 4 nm vaiation in in width o a 8 nm pitch D contact ho aa. t can b obsvd that th vaiation in th spcta intnsit o th tansmittanc spctum is compaab to th vaiations in th ctanc spctum, aching ~.% at 8 nm. A dint ct is obsvd o D stuctus o sma pitch. Th oowing igu iustats th tpica vaiation in th poaid ctanc spcta (R s and R p ) du to 4 nm vaiation in th contact ho diamt o a 5 nm pitch D gating. Th R s spcta and th R p spcta a pottd - cosponding to th diamts o 4, 6 and 8 nm. Pitch 5 nm MoS Quat Contact Ho Diamt.8% 4 nm 6nm 8,m 3 4d 5 6 Wavnoth (nnt ida OO do Figu 3: Tpica vaiation in th poaid ctanc spcta (R s and R p ) du to 4 nm vaiation in in width o a 5 nm pitch D contact ho aa. Poc. o SP Vo

4 Maimum vaiation o on about.8% s obsvd o th ctanc intnsit at 4, 5 and 64 nm. Th nt igu iustats th tpica vaiation in th poaid tansmittanc spcta (T s and T p ) du to 4 nm vaiation in th contact ho diamt o a 5 nm pitch D gating. Th T s spcta and th T p spcta a pottd - cosponding to th diamts o 4, 6 and 8 nm. 8 6 F- 4 Wavnoh (n Figu 4: Tpica vaiation in th poaid tansmittanc spcta (T s and T p ) du to 4 nm vaiation in in width o a 5 nm pitch D contact ho aa. t is vad that o sma-pitch D stuctus, th snsitivit o th tansmittanc spctum bcoms mo signiicant (~.5% at 64 nm), cosponding to th 4% incas in snsitivit compad to th ctancon masumnt. A simia phnomnon was obsvd o on-dimnsiona gating stuctus: th snsitivit o th tansmittanc spctum to th sma changs in stuctu gomt bcoms high as th pitch o th gating bcoms sma. As dmonstatd b simuations, incusion o th tansmittanc spcta into th anasis wi impov th snsitivit and soution o th CD masumnts. Howv, in od to b ab to ana th pimnta data, th RCWA mthod omuatd b Mohaam in 995 (Mohaam and Gann, 995) has to b modiid and adoptd o th anasis o th tansmittanc spcta coctd on th D gating stuctus. Th oowing sction givs th ovviw o th nw omuation. RCWA MTHOD FOR TH ANAYSS OF ROADAND TRANSMTTANC SPCTRA OF D GRATNG STRUCTURS n RCWA mthod o D gating, as in, th and componnts o th ctomagntic id in th gating gion can b wittn as a Foui pssion [ S, mn () S, mn ( ) ] p( jσ mn ) and () m, n Poc. o SP Vo

5 () () [ ] ( ) m n mn mn mn j U U j H H,,, p σ µ ε, () wh ( ) ( ) n m mn n m σ. (3) m and n a th diaction numbs in th and diction spctiv, and () ( ) ( ) [ ] { } P i ti d q c q c w S p p, (4) () ( ) ( ) [ ] { } P i ti d q c q c v U p p. (5) N M P, and M, N a th maimum vaus o m, n. Th vcto S ti consists o two MN vctos S, S spaat, as is th cas o U ti. Simia to th D gating cas, Maw s quations in th gating gion can b sovd b inding th ignvau o th mati: Q W W, (6) wh W and Q a ignvcto and ignvau matics spctiv, and q W V, (7) wh q is a diagona mati with mnts o positiv squa oot o that in Q, and ( ) ( ) inv inv (8) ( ) [ ] ( ) [ ] { } ( ) [ ] { } ( ) [ ] D inv inv inv inv, (9) and, D, and Λ Λ Λ. () Th dinitions o th oth matics a sam as in D gating. Fo th muti-a pobm, simia to th D cas, in th ist a th bounda at ads to C C X V V W X W C g D D, () wh, jz g, t R C, and Poc. o SP Vo

6 D D D D M jd jdm ( cosψ cosθ sinφ sinψ cosφ) δ mδ n ( cosψ cosθ cosφ sinψ sinφ) δ δ jn jn m n ( cosψ cosφ cosθ sinψ sinφ) δ mδ n ( cosψ sinφ cosθ sinψ cosφ) δ δ and th dinition o spac ang φ, θ, ψ a th sam as in D gating. dining ( D g ) D and o ach a, a on obtains m n (), (3), (4) ( V g W ) ( V g W ) X, (5) ( V g W ) X ( V g W ) (6) g W V ( X a ) ( X a ), (7) unti th ast a (wh is th tota numb o as), b W X V X W a C b V C jz X V g W. On ina obtains Tt, (8) wh ( ) Tt ( g jz ) ( g W V ) X b ( g jz ). (9) Th tansmittanc T o an od is ppndicua with (th substat). Fo th oth od, on obtains wh T T T, (),,,, n sinθ cosφ, n sinθ sinφ, and n n sin θ a nown. Simia with th D cas (Ga and am, 6), on ina obtains th oth od tansmittanc wh RT [ MR t T t ] T s t, () MR T R R. () s R v is th vsd ctanc o th gating, and v ( n ) π m t p d s (3) λ cos_ i Poc. o SP Vo

7 is th attnuation o th id in th substat, cos_i is th cosin o th tansmittanc bam ang in th substat, and d s is th thicnss o th substat. MASURMNT TCHNQU AND RSUTS Th too usd to coct th data is a commcia avaiab n& Ana 57-CDRT, which is a spctophotomt-basd instumnt, capab o cocting ou continuous spcta duing on masumnt two poaid ctanc spcta (R s and R p ) and two poaid tansmittanc spcta (T s and T p ). Th ight souc o th spctophotomt is quippd with a otating poai, aciitating T and TM poaiations o th masumnt bam. Th masumnt wavngth ang is om 9 nm to nm, in on-nanomt intvas. Th coctd boadband poaid ctanc and tansmittanc spcta a anad using th RCWA agoithm dscibd in th pvious sction, in conjunction with th Foouhi-oom dispsion ations o n and (Foouhi and oom, 986). Th anasis mod gnats th simuatd poaid ctanc and tansmittanc spcta using nomina inputs o th gating dimnsions and matia poptis and thn uss a non-ina gssion agoithm to obtain th bst possib it btwn th simuatd and masud spcta. Th dimnsions obtaind upon th convgnc with th highst obtainab goodnss o it paamt a potd as th CD o th gating stuctu. Th mthod dscibd abov was usd o th chaactiation o squa and cicua contact hos in MoSi on quat substat. Th nomina thicnss o MoSi was 68Å, and th contact hos w tchd a th wa though th MoSi a to th quat substat. Th nomina sid ngth o th squa contact ho was 4 nm, with th gating pitch o 8 nm in and dictions. Th nomina diamt o th cicua contact ho was 6 nm, with th gating pitch o 5 nm in and dictions. ach atu was patd 385 tims on th mas. Tho, 385 cicua contact ho aas o 5 nm pitch w masud and 385 squa contact hos o 8 nm pitch w masud on th mas using th optica tchniqu dscibd abov. Th oowing igu iustats th uniomit maps obtaind as a sut o th masumnts. Poc. o SP Vo

8 tt ta , 4-4 C *4-6 -S a a a a a Figu 5: CD uniomit maps obtaind using th optica tchniqu dscibd abov. Th points mad with d cics w aso amind using a convntiona CD-SM. Th tm points (sma and ag vaus o CD) w amind with a convntiona CD-SM. Ths points a mad with d cics on th maps. Th vaus obtaind using th optica tchniqu and th CD- SM w compad to ach oth. Th oowing igu iustats th it btwn th pimnta and cacuatd poaid T s tansmittanc spcta (T s -p, and T s -ca) o th ag squa contact ho (pitch 8 nm) on th mas. 8 U, 6 4 sdo 6 Wavnth (nm Figu 6: Fit btwn th masud and cacuatd T s tansmittanc spcta o th ag squa contact ho (pitch 8 nm) on th mas. Th oowing igu iustats th compaison btwn th citica dimnsions obtaind using th optica tchniqu dscibd abov and th CD-SM. Poc. o SP Vo

9 CD-SM mag 3 5 Scattomt mag nm 368. nm Angstom (Å) 5 Pitch 8 nm 5 Angstom (Å) Figu 7: Compaison btwn th citica dimnsions obtaind using th optica tchniqu and CD-SM o th ag squa contact ho (pitch 8 nm) on th mas. Th oowing igu iustats th it btwn th pimnta and cacuatd poaid T s tansmittanc spcta (T s -p, and T s -ca) o th sma squa contact ho (pitch 8 nm) on th mas. 8 4 a 6d Wavoth (nm Figu 8: Fit btwn th masud and cacuatd T s tansmittanc spcta o th sma squa contact ho (pitch 8 nm) on th mas. Th oowing igu iustats th compaison btwn th citica dimnsions obtaind using th optica tchniqu dscibd abov and th CD-SM. Poc. o SP Vo

10 CD-SM mag 3 Scattomt mag nm nm Angstom (Å) 5 Pitch 8 nm 5 Angstom (Å) Figu 9: Compaison btwn th citica dimnsions obtaind using th optica tchniqu and CD-SM o th sma squa contact ho (pitch 8 nm) on th mas. Th oowing igu iustats th it btwn th pimnta and cacuatd poaid T s tansmittanc spcta (T s -p, and T s -ca) o th ag cicua contact ho (pitch 5 nm) on th mas. Tansmittanc Spcta T pimnta Cacuatd Pitch 5 nm // P J Wavoth (nm J J Figu : Fit btwn th masud and cacuatd T s tansmittanc spcta o th ag cicua contact ho (pitch 5 nm) on th mas. Th oowing igu iustats th compaison btwn th citica dimnsions obtaind using th optica tchniqu dscibd abov and th CD-SM. Poc. o SP Vo

11 CD-SM mag Scattomt mag 6.7 nm 6. nm Angstom (Å) 5 Pitch 5 nm Angstom (Å) Figu : Compaison btwn th citica dimnsions obtaind using th optica tchniqu and CD-SM o th ag cicua contact ho (pitch 5 nm) on th mas. Th oowing igu iustats th it btwn th pimnta and cacuatd poaid T s tansmittanc spcta (T s -p, and T s -ca) o th sma cicua contact ho (pitch 5 nm) on th mas. N) Ts(%, Figu : Fit btwn th masud and cacuatd T s tansmittanc spcta o th sma cicua contact ho (pitch 5 nm) on th mas. Th oowing igu iustats th compaison btwn th citica dimnsions obtaind using th optica tchniqu dscibd abov and th CD-SM. Poc. o SP Vo

12 CD-SM mag Scattomt mag 84.9 nm 85.5 nm Angstom (Å) 5 Pitch 5 nm Angstom (Å) Figu 3: Compaison btwn th citica dimnsions obtaind using th optica tchniqu and CD-SM o th sma cicua contact ho (pitch 5 nm) on th mas. SUMMARY ncusion o poaid tansmittanc spcta povd to b instumnta in impoving th soution o th CD masumnts o th D gating stuctus o sma pitchs. Futhmo, th incasd signa stngth du to high tansmissivit o th MoSi phas-shit mass aciitatd btt patabiit o th CD masumnts b incasing signa-to-nois atio o th masumnt. Two-dimnsiona aas o squa and cicua contact hos o vaious pitchs w masud using a spctophotomt-basd instumnt capab o cocting two poaid ctanc (R s and R p ) and two poaid tansmittanc spcta (T s and T p ) in th wavngth ang om 9 to nm (in nm intvas) at th sam ocation on th gating aa. n od to b ab to ana th pimnta data, th RCWA mthod omuatd b Mohaam in 995 was modiid and adoptd o th anasis o th tansmittanc spcta coctd on th D gating stuctus. Th suts dmonstatd cnt coation to convntiona CD-SM. ACNOWDGMNTS W woud i to than Jan Richt o AMTC o poviding th samps and th CD-SM imags o this stud. W woud aso i to than Gnnadi Poissi o Mton Tchnoog o poviding cnt psntation and suppot in uop. RFRNCS Foouhi, A. R. and oom,. (986). "Optica dispsion ations o amophous smiconductos and amophous dictics." Phsica Rviw 34(): 78. Poc. o SP Vo

13 Foouhi, A. R. and oom,. (988). "Optica poptis o cstain smiconductos and dictics." Phsica Rviw 38(3): 865. Ga, A., am, J.C., t a. (6). Nov tchniqu o citica dimnsion masumnts o phas-shit mass using boadband tansmittanc spcta in conjunction with RCWA. Photomas Tchnoog 6, Mont, CA, USA, SP. Mohaam, M.G., Gann,.., t a. (995). "Fomuation o stab and icint impmntation o th igoous coupd-wav anasis o bina gatings," J. Opt. Soc. Am. A, 68 Poc. o SP Vo