GeneralizedApproachtowardModeling ResistPerformance

Transcription

1 Reprited from AICHE JOURNAL, December 1991 GeeralizedApproachtowardModelig ResistPerformace David H. Ziger aj;)dchris A. Mack SEMATECH, Ic., Austi, TX A geeralized techique for modelig resist performace is outlied. I this approach, the fractio of resist remaiig after developmet as a fuctio of icidet dose, or characteristic curve, is related to the developmet rate which is assumed to be a power law of a domiat soluble species. Soluble species are either photochemically cosumed for egative resists or geerated for positive. Expressios for the depedece of characteristic curves o exposure dose ad chemistry are derived for various resist systems, which are cosistet with curret models. For similar chemical kietics, egative resists yield fewer lumped parameters to describe their developmet rate ad characteristic curves tha positive. Uder coditios of egligible surface ihibitio, lumped parameters ca be extracted from characteristic curves ad used to simulate lithography. A geeralized method to correct for absorptio i the resist ad reflectios is outlied. Exposure latitude was accurately predicted for a commercial egative chemically amplified resist. However, predictio of liewidths from characteristic curves of positive resists is complicated by surface ihibitio effects. Itroductio Resists are radiatio-sesitive polymers which are spi-coated to form thi films ad the pattered by exposure ad developmet. Exposed regios dissolve i developer for positive actig resists, while the uexposed regios dissolve for egative resists. For overviews of lithography practices ad fudametals, see Moreau (1988) or Thompso et ai. (1983). Positive ad egative resists at various actiic wavelegths have bee used for microlithography. For example, ovolac ad polyviylpheolic resis i both toes are used extesively i microelecroics for high-resolutio lithography. Sice the chemistries of these systems differ, various mechaisms have bee proposed to describe their lithographic behavior. I covetioal positive toe lithography, a photoactive compoud (PAC) is mixed with a ovolac matrix to ihibit the mixture's solubility i base. Sice irradiatio destroys the ihibitio effect, the resist system yields a positive image of the mask after developmet i base. Typically, the photochemistry is modeled as first order i PAC cocetratio, ad Correspodece cocerig this article should be addressed to D. H. Ziger, who is presetly at AIT Bell laboratories, Alletow, PA various models have bee proposed to describe the base developmet (see, for example, Dill et ai., 1975; Mack, 1985; Trefoas ad Daiels, 1987; Hirai et ai., 1987). Recetly, polyviylpheolic resis have bee applied toward 248-m ad e-beam lithographies yieldig sub 0.5-j.tm resolutio both for positive ad egative toes (Ito ad Willso, 1983; Ito ad Willso, 1984; Ito, 1988; Ito et ai., 1990; Thackeray et ai., 1989). SNR248, a egative resist (Shipley Co., Newto, MA), uses a photogeerated acid to catalyze reactio with polyviylpheol that reduces solubility i base. Thackeray et ai. (1989) have proposed that acid-catalyzed resi polymerizatio is the primary explaatio for solubility differeces i the exposed ad uexposed regios. Seligso et ai. (1988) ad Das et ai. (1990) correlated bake kietics for these resists by proposig the effective dose cocept. Fukuda ad Okazaki (1990) also proposed a model based o polymerizatio for egative chemically-amplified resists. Furgese et ai. (1990) ad Tam et ai. (1990) have used FTIR ad DRM techiques to measure kietic parameters ad simulate DUV lithography usig the multiplestate SAMPLE model. Fially, polyviylhydroxy-tert-butyl (t- HOC) resis have bee formulated to yield positive actig highresolutio resists whe combied with photogeerated acids. AIChE Joural December 1991 Vol. 37, No

2 Ito ad Willso (1983, 1984) suggested that acid catalyzes decompositio of the tert-butyl fuctioality leavig the remaiig polyviylpheol soluble i a base such as tetramethylammoium hydroxide (TMAH). Spece ad Ferguso (1991) ivestigated the extet of deblockig of t-boc with FTIR techiques ad postulated that the differet photoacid geerators ca have differet competig reactios durig the post-exposure bake. Oe problem with havig specific resist models is fidig geeral techiques to measure parameters for the lithographic models. For example, a covetioal positive photoresist usually requires the Dill ABC exposure parameters ad parameters for a specific develop model. Ultraviolet absorptio istrumets ad developmet rate moitors (DRM) are most ofte used for these measuremets. Developmet rate measuremets are ofte tedious to obtai. Additioally, chemically amplified resists require their ow parameters to model the post -exposure bake chemistry. I this article, we propose geeral chemical models for positive ad egative resists based o a commo develop model which assumes that developmet is cotrolled by the cocetratio of a domiat soluble species. Due to the specific chemistry, the dose depedece of developmet rate assumes various forms depedig o the toe, photochemistry, ad post-exposure bake chemistry. Although parameters are determied best usig developmet rate data, uder coditios of miimal absorptio ad surface ihibitio, these parameters ca be extracted from covetioal cotrast curves. These curves show remaiig resist thickess after develop as a fuctio of exposure dose. PROLITH/2 (FINLE Techologies, PIao, TX) was used to aalyze assumptios i the model for covetioal ad chemically-amplified positive ad egative resists. We show a geeralized method to correct these parameters for absorptio ad reflectios. Simulated exposure latitude is compared to experimetal results for a egative chemically-amplified resist. We call this approach the geeralized characteristic model for Lithography (GCM). Theory I geeral,the remaiigresistthickessafter developmet, TN'ormalized to the iitial thickess, is give by: TN= 1 - dtpeb - dtoev where dtpebis the ormalized thickess loss attributed to the post-exposure bake, ad dtoevis the ormalized thickess chage due to developmet. Both of these cotributios deped o the film compositio. Sice dtpebad dtoevca be readily measured, we wish to model these quatities to extract physical parameters for use i lithographic modelig. For both egative ad positive aqueous developable resist systems, we model the resist as a mixture of a base soluble species, S], ad a isoluble species, M]. Thickess loss durig post-exposure bake, dtpeb'is modeled as a liear fuctio of the extet of reactio of isoluble species ito soluble (Eq. 2a) or soluble to isoluble (Eq. 2b) for positive ad egative resist chemistries, respectively: 1864 dtpeb =dt(e=o) + ( ~ (Mo] ) G (1) (2a) LlrPE. ~ dt(e_o)+ (I - ~o~)g (2b) Here dt(e=o) is the thickess loss due to PEB at zero-exposure eergy, ad G is the fractioal volume chage for complete coversio. (Note that G is egligible for covetioal diazoaphthoquioe systems but ca be substatial for other resist chemistries. Also, S] is derived for various examples later i this sectio.) We derive expressios for dtoevfrom the geeralized rate of thickess loss durig developmet: dtoev r'de" J0 TOEvdt where TOEVis the developmet rate at time t, D is the iitial resist thickess, ad toevis the developmet time. We assume that the developmet rate is proportioal to the cocetratio of the relevat soluble species raised to a power of : D (3) TOEV= koevsr (4) where is a coordiatio umber for the average umber of base soluble groups that act i cocert to affect solubility rate. Larger values of imply more iteractio betwee eighborig S] groups. I the absece of surface ihibitio, absorptio ad stadig wave effects (see the Discussio sectio), TDEV may be cosidered idepedet of film thickess. I that case: A TOEvtoEv koevtoevsr ~TOEV= D - D Both LlTOEVad dtpebdeped o S]. I the followig sectios, S] is derived for both covetioal positive diazoaphthoquioe resists ad chemically-amplified positive ad egative base developable systems. Positive D N Q resists For covetioal positive DNQ resists, exposure at actiic radiatio decomposes a diazoapthoquioe moiety to a idee carboxylic acid that destroys the base bulk ihibitio effect. Therefore, S] is the cocetratio of carboxylic acid groups. Assumig first-order photochemistry, we derive the cocetratio of carboxylic acid groups (which are assumed to be proportioal to the cocetratio of deblocked ovolac). ds] de = kpholo(mo]- S]) where Mo]= S]+ M] is the iitial PAC cocetratio, E is the exposure eergy at a particular poit i the resist film, ad kphoiois the exposure rate costat (equivalet to the Dill C parameter, Dill et ai., 1975). Assumig o absorptio, bleachig, or reflectios, E becomes the icidet eergy. Itegratig Eq.6: December 1991 Vol. 37, No. 12 AIChE Joural (5) (6)

3 8] = Mo](1- e-kpho,oe) Substitutig ito Eq. 1 ad Eq. 5 yields: koevtoe V M. ] 7N= 1- d 7 PEB - 0 D (1 - e-kph,oe) (7) If acid loss via side reactio (that is, termiatio) ad diffusio are miimal, the H+] ca be assumed to stay costat durig the post-exposure bake. Itegratig this pseudo-firstorder reactio yields: (8) S] = So]e-kpEBH'jIPEB (12) The clearig dose, Eo, is defied as the dose at which 7Nis just O. Cosequetly, we ca solve Eq. 8 for (koeytoeymo])/di terms of Eo to obtai 7Nad roey,respectively: where 1 - e-kpholoe TN= 1 - A7PEB - (1- d7peb.ej 1 - e-kphotoeo ( ) (9a) roey = Rmax(1- e-kph,oe) (9b) d7peb = A7(E=0) + (1- Eo= e-kphotoe)g I/ I 1- (1- koeytoeymo] d7peb,ejd) ] kphoto ( D (1- A7PEB,EJ RMAX = toev )(1- e-kphoioeo) ad A7PEB.Eorefers to the thickess loss after post-exposure bake at E =Eo ad Rmax is a costat that ca be calculated from parameters regressed from the characteristic curve. Equatio 9a relates the ormalized thickess as a fuctio of exposure dose to the chemistry ad develop coditios i the bulk resist. Note that Rmaxad are itesive properties of the resist oly. Oce determied, roevca be modeled for ay resist thickess o ay substrate. If A7PEBis egligible, the Eq. 9a simplifies to: 1 - e-kphoioe 7N= 1-. ( ) 1 - e - kpholoeo (10) Equatio 10 was derived by Trefoas ad Daiels (1987) based o polyphotolysis studies where was related to the umber of PAC groups attached to each ballast molecule. The photoacid ~eerator decomposes upo radiatio to form protos (PAG":'H+). Assumig first-order decompositio photochemistry: Itegratig yields: dpag] = -kphoiopag] de (13) PAG] = PAGo]e-kphO,oE (14) where PAGo] is the iitial PAG cocetratio. Acid catalysis is sesitive to residual amie cotamiats. For a give amie cocetratio i the photoresist, a equal amout of acid will be cosumed i the eutralizatio reactio. Thus, the actual acid cocetratio will be H+]= PAGo] - PAG] - amies]. We ca relate amies] to a effective ihibitio dose, Eihib, which is required to geerate eough acid to eutralize the amies. From Eq. 14, amies] = PAGo](I-e-kphOIoEihib). Thus, the acid cocetratio which is available to catalyze the base isolublilizig reactio will be: H+] = P AGo] (e-kphoioeihib)i - e-kphlo(e-eihib)] (15) Substitutig Eq. 15 ito Eq. 12yields the cocetratio of S]: S] = So]e- PAGo]e-kphOloEihib kpebtpebil - e- kphlo(e -Eihib)j (16) Combiig Eqs. 16, 5 ad 1 yields the complete ormalized thickess curve: - 1 A koevtoevsot ( -ae-kpholoeihibl-e-kpholo(e-eihibl] ) 7N- - L.l7PEB- ~ e where (17) Negative chemically-amplified resists Photolysis for egative chemically-amplified resists geerates H+ that catalyzes a base isolublizatio reactio. The base soluble species, 8], for these resists is, therefore, the ureacted base soluble polymer (such as, polyviylpheol) prior to developmet. Assumig the host polymer reacts via acid catalysis, we obtai S] from the extet of reactio for the postexposure bake (PEB) process: ds] dtpeb= - kpebs]h+] where tpebis the post-exposure bake time, H+] is the photoacid cocetratio, ad kpebis the rate costat. (11) ex = P AGo]kPEBtpEB At E=Eo, 7N=0. Cosequetly, we ca solve for (koeytoeysot ID) i terms of Eo ad substitute back ito Eq. 17: where 7N= 1 - d7peb - (1 - d7 PEB,Eo)e-a(e-kphOloEo_e-kphO'OE) (18a) roey = Rmaxe-a(l-e-kph,oE) (18b) d7pfb = d7(~;;o) + ( 1 - e-ae-kpholoeihibll-e-kpho,oie-eihibl]) G AIChE Joural December 1991 Vol. 37, No

4 Eo=E mhlb I 1+ I D(1-~IPEBE ) kdeytdeys~]~ kpholo ae kphotoeihib D R =-(1-~, )e-a(e-kpholoeo-i) max tdey PEB,Eo Note that Rmaxis obtaied by solvig Eq. 18b for the maximum develop rate that occurs at E= 0 for egative resists. As before, Rmaxis itrisic properties of the resist. As a special case of. Eq. 18a, we cosider whe e-kphotoe=:; l-kpholoe, Eihib=:;0, ad ~'PEB =:;O. I this evet, Eq. 18a simplifies to: where 'N= 1- e-akpho,o(e-eo) Eo I(kDEytDEySo] / D) kpholoa ]j (19) ~TpEB = ~T(E=O) + ( 1 - e-ae-kphotoeihib1-e-kphoto(e-eihiblj) G ti (1- ~IPEB.EJD I\1- Eo=Emhib- k:. I 1+ l ::D:~::~OJ") D Rmax= - t DEY ( 1- e 1- ~ I (PEB.Eo» - ae- kphotoeihib I I - e- kphotoleo- Eihib») ) ad a is defied as before. As a special case of Eq. 23a, cosider whe 1 - e-kphoto(e-eihib) =:; kphoio (E - Eihib), Eihib::= 0, ad ~'PEB =:;O. I this case, we obtai: (1 - e-akphotoe) TN= 1- (1- e-akphotoeo) ] ] ] (24) Note that Eq. 24 assumes the same mathematical form as covetioal positive photoresists (Eq. 10) where a effectively amplifies the dose. Positive chemically-amplified resists Irradiatio geerates acid for positive chemically-amplified resists as with egative acid hardeed resists. I oe positive applicatio, the acid cotet cleaves a t-boc protectig group from the polyviylpheol host polymer durig the post-exposure bake leavig polyviylpheol, which is soluble i base. Cosequetly, S) is the cocetratio of polyviylpheol after post-exposure bake, while M] is the cocetratio of the blocked fuctioality. We derive S) from the relevat chemical kietics: Itegratig Eq. 20. yields: ds] dtpeb=kpeb(mo] - S)H+] S] = Mo](1- e-kpebiw)tpeb) where the post-exposure bake is agai pseudo-first order, sice H+] fuctios as a catalyst. We obtai H+] from the photolysis as for egative chemically-amplified resists ad derive a expressio for S]: S] = Mo] ( 1 - e- PAGo)e-kp/lotoEihib kpebtpebi-e-kpholoie-eihib») Substitutig Eq. 22 ito Eqs. 5 ad 1, ad solvig i terms of Eo as before yields: 'N= 1 - ~'PEB (1 - e- ae-kphotoeihibi - e-kphoto(e-eihit>!j) ~1(pEB.Eo>] (1 - e-ae-kphotoeihib(i -e-kphotoleo-eihib~) where ] (20) (21) (22) (230) rdey = Rmax ( 1 - e-ae-kphoioeihibl-e-kphotoie-eihit>!j) (23b) Experimetal Studies Results predicted by the geeralized approach outlied i the last sectio were ivestigated by two techiques. First, computer simulatios were used to ivestigate extractig lumped parameters from the characteristic curves ad usig these parameters for lithographic modelig. PROLITH/2 (FINLE Techologies, PIao, TX) is a lithographic simulatio program that ca model effects of resist absorptio, bleachig, ad ouiform developmet rates o developed liewidths ad characteristic curves. These effects are eglected i the GCM approach. Cosequetly, by comparig parameters used to simulate 'N ad those extracted, we ca measure ad correct the effect of GCM assumptios o lithographic simulatio. For covetioal positive resists, we wated to determie the effect of ouiform developmet rates o the accuracy of GCM simulatio. I particular, ihibitio effects ca drastically affect the characteristic curve (Mack, 1991). Characteristic curves were simulated for covetioal positive photoresist for coditios that varied the ratio of the dissolutio rate at the surface to the bulk (rs) from 1 to For these simulatios, we assumed a hypothetical resist o a oreflectig substrate, i which bleachig, absorptio, ad resist shrikage durig PEB were egligible. Table 1 summarizes the resist ad develop parameters that were used i the PROLITH/ 2 simulatio. Surface ihibitio is ot observed with egative chemicallyamplified resists (see Discussio). Simulatios of these resists were doe to quatify the effect that absorptio ad reflectios have o the accuracy of GCM parameters (that is, a ad Eo) extracted from characteristic curves. Cosequetly, we wated to simulate characteristic curves for a egative resist with optical properties similar to SNR248, extract a ad Eo, ad compare these values to the simulatio iputs. The method used was as follows. We varied iputs to PRO- LITH/2 over a wide rage, ad characteristic curves were the simulated for a particular resist (see Table 2, optical parameters 1866 December 1991 Vol. 37, No. 12 AIChE Joural

5 Table 1. Positive Resist Exposure ad Developmet Parameters for PROLITH/2 Simulatios. Parameter A (pm-i) B (pm-i) kpholo(cm2/mj) Refractive Idex Resist Thickess, D (pm) tdev(s) Rmax (m/s) Rmi (m/s) M'h Ihibitio Depth (pm) rs Value ,0.1,0.001.Develop parameters are for the model discussed by Mack (1985). are those for SNR248). Sice PROLITH/2 accouts for bleachig, absorptio, ad reflectios, roevwill vary with depth ito the resist, which will affect the simulated characteristic curve. The simulated curve is the fit accordig to the GCM expressio for TN(Eq. 18awith ~TpEB=0). By comparig values of the iputs to PROLITH/2 vs. those extracted from simulated curves, we ca quatitatively correct for absorptio ad reflectio i a self-cosistet maer for a resist. The corrected parameters are idepedet of the substrate ad deped oly o the resist ad developmet coditios. Note that this procedure must be repeated if the optical parameters differ from those show i Table 2. To verify the GCM approach for a egative chemicallyamplified resist, characteristic curves ad liewidths were measured for SNR248 resist usig the test patter show i Figure 1. A patter of icreasig exposures was iterwoud with a serpetie of resolutio die (See Figure 1). I this maer, simulatios usig parameters extracted from the GCM model could be directly compared to resolved images uder the same coditios that were used to geerate the characteristic curves. Partial resist thickesses were measured usig a Ff500 (Prometrix, Sata Clara, CA) iterferometric thickess measurig istrumet. The effect of ucertaity i the optical parameters o absolute resist thickess was miimized, because oly relative differeces (~TpEBad ~TOEV)were aalyzed. All exposures were doe o a 0.35NA GCA Laserstep Stepper (GCA Corp., Adover, MA) operatig at 248 m. A orgaic atireflectio coatig, DUV-3 (Brewer Sciece, Rolla, MO), Table 2. Parameters for PROLITH/2 Simulatio of a Negative Chemically-AmplifiedResist. Parameter A (pm-i) B (pm-i) kpholo(cm2/mj) Refractive Idex tdev (s) a Rmax (m/s) Rmi (m/s) M'h Value " Develop parameters are for the model discussed by Mack (1985)...This has the effect of varyig Eo from 2 to 16 mj/cm2. ~ '0 0 0 ~...,.. OOOOOOOOb:6] ~OOOOOOOO l1=:li... OODOODOO~ ~OOOOOOOO 11={ Ope Frame. Re8olutlo Figure 1. Two-passtest structure. 8i=II a;:8 Characteristic curves ad liewidth measuremets could be obtaied o the same wafer. was used uder the SNR248 resist to elimiate reflectios at the actiic wavelegth. DUV-3 does ot iterfere with the Ff500 iterferometric resist thickess measuremets, because the coatig is very trasparet (absorptio < 0.05) at the wavelegths used for measuremet ( m). Sice we use a self-cosistet method to correct for absorptio ad reflectios, the purpose of atireflectio coatig uder the resist is basically to reduce the experimetal error i measurig the GCM parameters. By elimiatig substrate reflectios, four sources of experimetal error are reduced. First, substrate reflectios cause the eergy coupled ito the resist to deped strogly o resist thickess. Therefore, local resist thickess variatios may cause sigificat experimetal error i the measuremet of characteristic curves o reflectig substrates. This is especially true i the DUV (248 m), i which resist thickess variatios of 0.02 Jtm o reflectig substrates ca cause the eergy coupled ito the resist to chage by about 100"10.Secod, the substrate optical parameters may ot be accurately kow, ad diffuse reflectace, if preset, would cause additioal error i the calculated eergy distributio i the photoresist. third, reflectios could cause a staircase effect i the characteristic curve if a post-exposure bake does ot average out the stadig waves. GCM will fit a average curve through the staircase but at the expese of additioal error. A fial error is that stadig waves ca exaggerate surface effects, especially i positive resist systems. This happes if a stadig wave ode should occur at the resist surface. I that evet, developmet rate will be a miimum at the surface that exaggerates surface ihibitio effects. I geeral, it is better to accurately measure the lumped parameters o oreflectig film stacks (that is, atireflectio coatig o silico) ad use the results to evaluate roevthat ca the be used to simulate geeral cases. Oce we correct the extracted parameters for absorptio ad reflectios7 the resultig parameters ca be AIChE Joural December 1991 Vol. 37, No

6 TN PROLITH/2. GCM fit data Exposure Eergy (mj/cm2) 2a TN TN PROLITH/2 data. GCM fit Exposure Eergy (mj/cm2) 2b PROLITH/2 data. GCMfit Exposure Eergy (mj/cm2) 2c Figure 2. Characteristic curves simulated with PROLlTH/2 ad fitted with the GCM model for varyig surface ihibitio effects. The top O.I-llm dissolves a) the same (rs = I), b) 0.1 (rs= 0.1), ad c) (rs= 0.(01) times as fast as the bulk. used to simulate lithography o ay stackt provided the optical parameters are kow sufficietly well. Results Simulatio Figures2a-2c showsprolith/2 simulatiosof a positive oabsorbig photoresist with varyig surface ihibitio effects. These simulatioswere fit accordigto Eq, lot ad the 1868 parameters ad Eo were extracted. Table 3 summarizes these results. Note that both ad the lack of fit icrease as the ratio of surface to bulk developmet ratet rst decreases. I a extreme case i which rs=o.oolt the value of extracted from the characteristic curve is more tha twice that used to simulate the curve. I geeralt as discussed later t this implies that the surface ihibitio effect cofouds the estimatio of from characteristic curve data. Negative chemically-amplified resists were simulated to December 1991 Vol. 37, No. 12 AIChE Joural

7 Table 3. Effect of Surface Ihibitio o GCM Parameter Extractio for a Covetioal Positive Photoresist Eo (mj/cm2) quatify the effect that absorptio ad reflectio have o the accuracy of extracted a ad Eo parameters usig the selfcosistet approach described i the previous sectio. The chemical amplificatio ad developmet rate models used i PROLITH/2 are quite similar to the models used i the GCM (Mack et ai., 1991). Parameters a ad are direct iputs ito PROLITH/2, while the developmet rate model requires that the maximum developmet rate, Rmax(see Eq. 18b), be specified. I the ideal case of o absorptio, bleachig or reflectivity, the eergy deposited i the photoresist film is equal to the icidet eergy. I this case, specifyig a,, ad Rmaxi PROLITH/2 will result i a characteristic curve that ca be fit exactly by the GCM if the regressio error is egligible. The extracted parameters will be the same a ad Eo correspodig to the iput values of a, ad Rmax.(Note that the product a cotrols the developmet rate as a fuctio of dose. Cosequetly, we varied a for all PROLITH/2 simulatios by holdig a costat ad varyig.) If, however, the deposited eergy ad the icidet eergy are ot equal, the values of a ad Eo extracted from the simulated cotrast curve will ot match the iput values. Table 4 shows the results of extractig a ad Eo from simulated cotrast curves for SNR248 over a variety of iput a ad Rmaxvalues. Table 2 summarizes the parameters used i these simulatios. We ca call the value of a used as a iput to PROLITH/2 the effective a, or aeff. Similarly, the iput value of Rmaxcorrespods to a effective Eo, or Eft. It is thus possible to correlate aeff ad E~ff used as iputs to the simulatio with the values extracted by fittig the characteristic curves to the GCM equatios. The results for the parameters show i Table 2 ad the data give i Table 4 are: Table 4. Values of Eo ad a from PROLITH/2 Simulated Characteristic Curves acff Values of Eo Values of a rs Simulatio Extracted Simulatio Extractio Rmax (m/s) E02 E~ff=0.93Eo-loo aeff = l.oo908a - 0.OOOI427Eo(a)2 (25a) (25b) It should be emphasized that the correlatios give by Eqs are valid oly for a resist whose optical parameters match those show i Table 2. However, the method show for estimatig the effect of absorptio o parameters extracted usig GCM is completely geeral. Over the full rage of data give i Table 4, the average stadard deviatio i predictig aeffis 1.4. This error is withi the regressio error for fittig a to characteristic curve data (Ziger ad Mack, 1991). The average stadard deviatio for fittig E~ffis 0.4 mj / cm2.this error is larger tha typical errors for fittig characteristic curve data to Eq. 18a (typical errors are mj/cm2, see Ziger ad Mack, 1991). However, the effect of this error is expected to be small sice it is oly 1070of the typical dose required to image the resist. Applicatio to a egative chemically-amplified resist Sice surface ihibitio is ot a factor for egative chemically-amplified resists (see the Discussio sectio), GCM parameters (a ad Eo) were extracted from SNR248 characteristic curves over a wide rage of PEB ad develop coditios. Figures 3a-3c show typical TN' ~TpEB'ad ~TDEV data for SNR248. I additio, Figures 3a ad 3c show fitted curves. (Note that ~TPEBwas ot fit, sice the absolute chage i thickess was too small.) These regressed parameters were the adjusted for absorptio ad reflectio effects usig Eqs. 25a ad 25b. We have reported elsewhere that liewidths simulated with extracted a ad Eo parameters agreed withi 150J0 of measured values over the etire experimetal rage that was studied (Ziger et ai., 1991). For example, Figure 4 compares the predicted ad experimetal exposure depedece of the photoresist profile for a wafer processed at a PEB time of 60 secods, PEB temperature of 130 C, ad developed for 90 secods t 0.135N TMAH. Discussios Form of GCM expressios The GCM approach forces TNad rdevto have the correct behavior at the extremes of the characteristic curves for all resist systems. At E = Eo, the developmet rate is D/tDEv,which is appropriately the average developmet rate for the dose i which the resist just clears for positive or begis to scum for egative. Coversely, as TN-I, rdev-ofor all resist systems. This coditio is obviously required to patter resist. Costraiig TN =0 at E =Eo also has the effect of lumpig parameters, some of which are difficult to measure, ito a easily measured quatity, Eo. It is iterestig to ote that egative resists yield fewer lumped parameters tha correspodig positive resist systems. For example, both positive ad egative chemically-amphfied resist systems were derived with similar assumptios cocerig PAG chemistry ad bake kietics. Yet, for egative toe, equatios for TNad rdevlump the post-exposure bake ad develop kietics ito two parameters, a ad Eo. (Note that Eihibis lumped ito Eo i thi~ ca~e.) It i~ ot ece~~ary to decompo~e AIChE Joural December 1991 Vol. 37, No

8 TN ~TpEB Exposure Dose (mj/cm2) 3a Exposure Dose (mj/cm2) 3b ~TDEV Exposure Dose (mj/cm2) 3c Figure 3. Experimetal a) 7th b) 47PEB' ad c) 47DEVdata for SNR248 processed at TpEB= 130 C, tpeb= 60 s, ad tdev= 90 S. GeM fitted curvesshow for TNad dtdev. these effects to do lithographicmodelig. Howevert the form of the positive chemically-amplified resist characteristic curve demads that the bake kietics, a, chemical ihibitio, Eihibt developmet coordiatio umbert t ad dose to c1eart EOt be kow separately. (Perhaps, the most attractive method to do this is to accurately measure 4TpEBad regress these parameters. However, this is difficult to do for most lithographically-attractive materials that are desiged to miimize G.). CosequetlYt there are oly two lumped parameters (a ad Eo) for egative chemically-amplified resistst while there are as may as four (a,, Eihib'ad Eo) for the positive toe. There is a fudametal reaso why egative systems yield fewer lumped parameters for the same chemistry tha positive. For egative resistst 8] is proportioal to a expoetial fuctio of the kietics. Raisig a expoetial fuctio to a power (to obtai rdev)lumps together with the chemical kietics. Meawhilet 8] is proportioal to oe mius a expoetial fuctio for positive resists. Cosequetly t for positive resistst parameters i 8] must be kow idepedet of. Mathematically this leads to other simplificatios for egative systems. For examplet sice Eihibis lumped oly ito Eo for egative resistst amie cotamiats dissolved i the resist 1870 AIChE Joural December 1991 Vol. 37, No. 12

9 Table S. Compariso of TN Expressios for Various Resist Systems *.1 Negative. Positive 1- Covetioal Chemically Amplified. 1- e-kpholo(e- Eo) 1 - e-akphoio(e-eo) o-e-kphoioe) 1 - e - kpholoeo) ] e-akphotoe) 1 - e - akphotoeo) ]. Expressios valid whe: ]. ~TpEB== 0; 2. Eihib ==0; 3. e( - kpho,oe) ==] - kphotoe... The expressio for TNfor a covetioal egative resist is derived by a method idetical to that show i the sectio o Theory for other resist systems. Here, IS) i Eq. 5 is assumed to be cosumed by a first-order photochemical reactio with a rate costat of kphoio" Figure 4. -I; :-"-- ~.. Imm I I Simulated Ys.experimetal exposure latitude of O.S"lLmlies ad spaces. We used PROLITH/2 with developmet rate parameters extracted usig the GCM approach for SNR248 egative chemicallyamplified resist. should ot affect the shape of the characteristic curve. For positive chemically-amplified resists, both the shape ad Eo are expected to chage with dissolved amie impurities. It is iterestig to compare expressios for TN for various resist systems. To simplify this compariso, we ivestigate the case i which we eglect post-exposure film loss (.::ltpeb;::;: 0) ad bulk amie cotamiatio (Eihib;::;: 0), ad assume e( -kphotoe);::;: 1- kpholoe.table 5 summarizes these results. Note that the differece i expressios for TNis the presece of a AIChE Joural December 1991 i the chemical-amplified equatios. Therefore, as a first approximatio, chemical amplificatio is achieved oly if a> 1. GCM approximatios Several approximatios are cotaied i the GCM model. The most importat of these are: 1. The developmet rate is a fuctio oly of a sigle domiat soluble species ad is costat durig the develop cycle. 2. The photochemistry is first order. 3. Chemically-amplified resist systems exhibit ideal catalysis with pseudo-first-order kietics (H+] is assumed costat). The first assumptio eglects effects that chage the developmet rate with depth ito the resist. For example, the resist surface ca dissolve slower (surface ihibitio) or faster (surface ehacemet) tha the bulk resist. From Figures 2a-2c ad Table 3, we observe that icreasig surface ihibitio has the effect of icreasig the slope of TN i the viciity of Eo. Cosequetly, estimatio of will be cofouded by surface ihibitio (Figures 2a-2c). I a similar way, surface ihibitio causes resist cotrast, 'Y, to be overestimated. Previous studies have show that estimatio of is critical for simulatig lithography, sice it affects process latitude, resist sidewall agle ad exposure, ad focus latitude (Trefoas ad Mack, 1991). Therefore, the GCM approach must be modified to compesate for surface ihibitio (if possible) before it could be reliably applied toward predictig liewidths for positive resists i which surface ihibitio is importat. Although surface ihibitio ca have a large effect o the value of a, surface ehacemet, i geeral, is expected to have a lesser effect. Measurig a characteristic curve has the effect of averagig developmet rate over the developmet time. By its very ature, surface ihibitio icreases the amout of time required to dissolve the thi ihibitio layer. Thus, this slow developig regio is heavily weighted i the average developmet rate. O the other had, surface ehacemet will cause the thi ehacemet layer to be dissolved i very little time, so that it has relatively little effect o the average developmet rate. As a result, comparable amouts of surface ihibitio ad surface ehacemet do ot produce comparable chages i a. Other factors that affect the dissolutio rate are absorptio, bleachig, ad thi-film iterferece effects. However, as show i the Results sectio, these effects ca be accouted for by correctig the extracted parameters as show i the previous sectio for egative chemically-amplified resists.a Vol. 37, No

10 key poit of this correctio approach is that it is totally selfcosistet. A primary parameter model is used to simulate these effects, ad extracted parameters are compared with those etered ito the simulatio. The accuracy of the correctio depeds o the accuracy of the primary model (i this case, PROLITH/2) to predict these optical effects. The assumptio that developmet rate is a power fuctio of a sigle soluble species is cosistet with prior ivestigatios ad agrees with available developmet rate data (see, for example, Trefoas et al., 1987; Trefoas ad Mack, 1991; Ferguso et ai., 1990). The assumptio for first-order photochemistry has bee justified for covetioal positive photoresist systems ad is used i other simulatio programs (see, for example, Dill et al., 1975). Data for the photochemical decompositio of photo acid geerators have ot bee published. The assumptio of ideal acid catalysis i the GCM model has bee discussed elsewhere (Ziger et al., 1991). Basically; idirect evidece suggests that a quechig mechaism may be importat at elevated temperatures or exteded postexposure bake times. The GCM model predicts a to have a Arrheius temperature ad liear PEB time depedece. Ziger et al. (1991) measured a over a rage from 1l0-160 C ad observed that a saturates as a fuctio of both PEB temperature ad time. This suggests that either quechig becomes importat at higher acid cocetratios or that the acid catalyzed reactio becomes diffusio-limited. (Aother possibility is that the power depedece o solubility is temperaturedepedet above a threshold value.) The assumptio of ideal acid catalysis also implies that H+] is locally costat, that is, diffusio is egligible. I fact, diffusio is ot egligible uder ormal lithographic coditios. The more rigorous approach is to simultaeously solve the reactio ad diffusio equatios (Barouch et al., 1991). PROLITH/2 makes a simplificatio that diffusio occurs first ad the the reactio. The GCM approach eglects diffusio, sice its assumptio of costat rdevimplies that H+] does ot vary with positio withi the resist. This situatio is physically reasoable for very large exposed areas o a atireflectio film. Cosequetly, kietic parameters ca be extracted usig the GCM approach ad used i more rigorous models that take ito accout diffusio. Developmet rate expressios The developmet rate model proposed here for all photoresist systems (rdevocs])has bee previously applied to describe covetioal ovolac resist systems. Mack (1985) derived the followig expressio: where (a+ 1)(1- m) + Rmi rdev=rmaxa+ (l-m) - (+ 1)(1-Mth) a-(-l) (26) For may resist systems, M1h< 0, so that Eq. 26 simplifies to: rdev =Rmax(1- m t + Rmi (27) Sice 1- m] is the relative cocetratio of the base soluble carboxylic acid, the GCM develop model is cosistet with Mack's model, provided Rmiis egligible. Developmet rate expressios equivalet to Eq. 27 have bee proposed by Trefoas ad Daiels (1987) ad Hirai et al. (1987). Lastly, it should be oted that Rmica be accouted for i the GCM approach by measurig the thickess loss of regios exposed at very large doses for egative resists ad at zero dose for positive resists. The effect of Rmio TNca the be lumped ito dtpeb'for SNR248, Rmiwas about 0.23 m/s. Furguso ad coworkers (1990) used a similar fuctioal form for rdevto model egative DUV resists: TOEV=R. )- C6C'']' (28) where Ro, Co, ad a are regressed from developmet rate data, ad CE(cs) is obtaied from acid catalyzed cross-likig kietics. If 1- CE(cs/Co] is a effective soluble species cocetratio, the this model. is equivalet to the oe adopted for the GCM approach. Compariso with other approaches It is iterestig to compare oem assumptios ad results with other models. Equatios relatig the PAC decompositio with exposure dose used i the GCM model for positive photoresists were derived by Dill ad coworkers (1975) ad are used i simulatio programs such as SAMPLE ad PROLITH/2. Neglectig thickess loss due to post-exposure bakig, Trefoas ad Daiels previouslyderived the expressiofor TN (Eq. 10), though the depedece of Eo o processig coditios ad formulatio was ot explicitly stated. As stated i the Itroductio, the covetioal approach toward modelig acid catalyzed egative resists has bee to formulate the kietics of polymerizatio. Developmet rate parameters are regressed from DRM data that are the correlated to FTIR data. The geeralized characteristic model for lithography is a cosistet approach toward modelig resist performace that provides a outlie for characterizig resists, whether positive or egative, covetioal or chemically-amplified. Cosequetly, a advatage of the oem approach is that it provides a framework for uderstadig the similarities ad differeces betwee positive ad egative resists of complimetary chemistries. Liewidth simulatios For SNR248, we have reported elsewhere (Ziger et al., 1991) that the a ad Eo parameters extracted from characteristic curves were used to simulate liewidths withi 15% of experimetal values over a rage of postexposure bake temperatures ad times from 1l0-150 C ad 30-9Os, respectively, ad develop times from s. Figure 4 shows that exposure latitude was accurately predicted (Mack et ai., 1991). Cosequetly, the GCM approach is a viable predictor of lithographic respose over essetially the etire operatig rage 1872 December1991 Vol. 37, No. 12 AIChE Joural

11 of this resist. Furthermore, this techique is expected to work well for ay egative chemically amplified resist system primarily because of the lack of surface ihibitio i these systems. As metioed earlier, Eoad a parameters ca be corrected for both absorptio ad substrate effects. A rigorous test of this is to measure the developmet parameters o oe substrate to predict liewidths o aother. Figure 5 shows experimetal ad predicted liewidths for resist o silico. The rdevparameters were obtaied from a characteristic curve of resist o DUV-3 atireflectig coatig ad subsequetly corrected for absorptio usig Eqs. 25a-25b. Note that both experimet ad theory predict stepper sidewall profiles. This is due to substrate reflectios. Agreemet betwee experimet ad simulated liewidths was withi (a) Additioal work A challegig problem is to determie uder ~hat coditios the GCM approach ca be used to extract meaigful kietic parameters for positive resists from TN' We have show that surface ihibitio cofouds estimatio of bulk dissolutio properties from TN' However, there could be ways to estimate the ihibitio effect from the lack of fit of the GCM model with characteristic curve data for several develop times. Coclusios The geeralized characterizatio model for Lithography is a geeralized approach toward modelig resist performace. Characteristic curves for positive ad egative covetioal ad chemically-amplified resists ca be modeled usig cosistet assumptios. Positive systems usually require more lumped parameters to model characteristic curves ad developmet rates tha egative. I the absece of surface ihibitio, lumped parameters ca be extracted from characteristic curves to accurately model developmet rates as a fuctio of dose. Simulatio programs ca the be used to predict liewidths. This techique was applied to egative chemicallyamplified resists to successfully predict liewidths ad process latitudes. Ackowledgmet The authors wish to ackowledge the followig idividuals at SEMATECH for their cotributios: Romelia Distasio for experimetal work ad Orlado Castao for SEM work. Discussios with Dr. Charles Szmada ad Dr. Jim Thackeray (Shipley Co.) cocerig SNR248 chemistry were istrumetal toward the developmet of the GCM approach. We also ackowledge useful coversatios with Dr. Richard Ferguso, Prof. Adrew Neureuther ad Prof. William Oldham (Uiversity of Califoria, Berkeley), ad Prof. Eyta Barouch (Priceto Uiversity) ad Dr. Daiel Seligso (Itel). Notatio A,B D = E= Eo = Eihib = Eft = G = Dill model (1975) exposure parameters resist thickess prior to exposure dose i the resist dose at which the resist clears for positive resist ad begis scummig for egative effective dose required to geerate protos to eutralize basic cotamiats. effective Eo compesatig for absorptio fractioal resist thickess of volume chage for complete coversio after PEB AIChE Joural December 1991 (b) Figure 5. (a) Simulated YS.(b) experimetal liewidths for SNR248 for omial O.5'JLmdese lies o silico. Developmet rate parameters were obtaied from a characteristic curve o a oreflectig substrate. H+ = protos (geerated from PAG) kdev = rate costat for developmet kpeb rate costat for post-exposure bake kpbolo rate costat for photochemistry M = base isoluble species S = base soluble species dissolutio rate power PAC photoactive compoud (diazoaphthoquioe) PAG = photoacid geerator rdev= developmetrate rs = ratio of surface to bulk developmet rates Rmax,Rmi'M'h Mack model (1985) develop rate parameters tdev develop time tpeb = post-exposure bake time Greek letters a = lumped kietic parameter for chemically amplified resists = P AGoJkpEBtpEB TN = fial resist thickess after developmet ormalized to D ~TDEV = chage i ormalized resist thickess due to developmet Vol. 37, No

12 Subscript ~TpEB = chage i ormalized resist thickess due to postexposure bake aeff = effective value of a compesatig for absorptio ad reflectios Literature Cited 0 = iitial cocetratio Barouch, E., B. Bradie, U. Hollerbach, G. Kariadakis, ads. Orszag, "Comprehesive 3-D Notchig Simulator with Noplaar Substrates," Proc. SPIE, 1264, 334 (1990). Das, S., ad D. Seligso, "Characterizatio ad Process Cotrol of Thermally Activated Resists," Proc. It. Photopolymers Cof, Elleville, NY (1988). Das, S., J. Thackeray, M. Edo, J. Lagsto, ad H. Gaw, "A Systematic Ivestigatio of the Photorespose ad Dissolutio Characteristics of a Acid Hardeed Resist," Proc. SPIE, 1262, 60 (1990). Dill, F. H., W. P. Horberger, P. S. Hauge, ad J. M. Shaw, "Characterizatio of Positive Photoresist," IEEE Tras. Electro Devices, ED-22, 445 (1975). Ferguso, R. A., J. M. Hutchiso, C. A. Spece, ad A. R. Neureuther, "Modelig ad Simulatio of a Deep-Ultraviolet Acid Hardeig Resist," J. Vac. Sci. Techol., 88, 1423 (1990). Fukuda, H., ad S. Okazaki, "Kietic Model ad Simulatio for Chemical Amplificatio Resists," J. Electrochem. Soc., 137, 675 (1990). Hirai, Y., M. Sasago, M. Edo, K. Tsuj, ad Y. Mao, "Process Modelig for Photoresist Developmet ad Desig of DLR/sd Process," IEEE Tras. Computer-Aided Desig, CAD-6, 403 (1987). Ito, H., ad C. G. Willso, "Chemical Amplificatio i the Desig of Dry Developig Resist Materials," Polym. Eg. Sci., 23, 1012 (1983). Ito, H., ad C. G. Willso, Polymers i Electroics, ACS Symp. Ser., No. 242, T. Davidso, ed., Amer. Cher. Soc., Washigto, DC, 11 (1984). Ito, H., "Sesitive Resist Systems Based o Acid Catalysis: Chemical Amplificatio," Proc. KTI Microelectroics Semiar, 81 (1988). Ito, H., L. A. Pederso, K. N. Chiog, S. Sochik, ad C. Tsai, "Sesitive Electro Beam Resist Systems Based o Acid-Catalyzed Deprotectio," Proc. SPIE, 1086, 11 (1989). MacDoald, S. A., C. D. Syder, N. J. Clecak, R. Wet, C. G. Willso, C. J. Kors, N. B. Deyoe, J. G. Maltabes, ad J. R. Morrow, "Airbore Chemical Cotamiatio of a Chemically Amplified Resist," Proc. SPIE, 1466,2 (1991). Mack, C. A., "PROLITH: a Comprehesive Optical Lithography Model," Proc. SPIE, 538, 207 (1985). Mack, C. A., "Lithographic Optimizatio Usig Photoresist Cotrast," Microelectroics Mfg. Tech., 14, 36 (1991). Mack, C. A., E. Capsuto, S. Sethi, ad J. Witowski, "Modelig ad Characterizatio' of a O.5-pm-Deep Ultraviolet Process," J. Vac. Sci. Techol. B, i press (1991). Moreau, W., Semicoductor Lithography Priciples, Practices ad Materials, Pleum Press, New York (1988). Seligso, D., S. Das, H. Gaw, ad P. Piaetta, "Process Cotrol with Chemical Amplificatio Resists Usig Deep Ultraviolet ad X-Ray Radiatio," J. Vac. Sci. Techol. 86, 2303 (1988). Spece, C. A., ad R. A. Ferguso, "Some Experimetal Techiques for Characterizig the Performace of Photoresists," Proc. SPIE, 1466, 324 (1991). Tam, N. N., R. A. Ferguso, A. Titus, J. M. Hutchiso, C. A. Spece, ad A. R. Neureuther, "Compariso of Exposure, Bake ad Dissolutio Characteristics of Electro Beam ad Optically Exposed Chemically Amplified Resists," J. Vac. Sci. Techol., B8, 1470 (1990). Thackeray, J. W., G. W. Orsula, D. Caistro, E. K. Pavelcheck, L. E. Boga, A. K. Berry, ad K. A. Graziao, "DUV ANR Photoresists for 248-m Excimer Laser Photolithography," Proc. SPIE, 1086, 34 (1989). Thompso, L. F, C. G. Willso, ad M. J. Bowde, eds. Itroductio to Microlithography, ACS Symp. Ser., No. 219, Washigto, DC (1983). Trefoas, P., ad B. K. Daiels, "New Priciple for Image Ehacemet i Sigle-Layer Positive Photoresists," Proc. SPIE, 771, 194 (1987). Trefoas, P., ad C. A. Mack, "Exposure Dose Optimizatio for a Positive Resist Cotaiig Poly-fuctioal Photoactive Compoud," Proc. SPIE, 1466, 117 (1991). Ziger, D., C. A. Mack, ad R. Distasio, "The Geeralized Characteristic Model for Lithography: Applicatio to Negatively Chemically Amplified Resists," Proc. SPIE, 1466, 270 (1991). Mauscript received July 22, 1991, ad revisio received Oct 11, December 1991 Vol. 37, No. 12 AIChE Joural