Impact of thin film metrology on the lithographic performance of 193nm bottom antireflective coatings

Transcription

1 Impact of thi film metrology o the lithographic performace of 193m bottom atireflective coatigs Chris A. Mack a, Dale Harriso b, Cristia Rivas b, ad Phillip Walsh b a Lithoguru.com, Austi, TX b MetroSol, 101 Doley Drive, Suite 101, Austi, TX USA ABSTRACT The performace eeds of a bottom atireflectio coatig (BARC) used i advaced optical lithography are extremely demadig, with reflectivities as low as 0.1% ad eve lower ofte required. BARC thickess ad complex refractive idex values ( = + iκ) must be highly optimized, requirig accurate kowledge of the BARC, resist ad substrate optical properties. I this paper, we have performed a theoretical aalysis of the BARC optimizatio process with respect to the propagatio of BARC ad κ measuremet errors. For several realistic cases, specificatios o the measuremet accuracy of these optical parameters will be derived ad the lithographic cosequeces of BARC metrology errors will be explored. Approaches to improvig the measuremet of BARC thickess ad refractive idex will be suggested. Keywords: Bottom atireflectio coatig, BARC, refractive idex measuremet, vacuum ultra-violet reflectometry, PROLITH 1. Itroductio At 65m device geeratios ad below, requiremets for bottom atireflectio coatig (BARC) performace are extremely striget. Reflectivities less tha 0.1% are ofte required. BARC thickess ad complex refractive idex values must be highly optimized for the specific resist, film stack, ad eve for the feature size ad lithographic imagig parameters beig used. Implicit i the optimizatio procedure is the assumptio that the optical properties of the BARC have bee measured to sufficiet accuracy so that the ucertaity i the measuremet of these BARC properties will ot have a sigificat impact o the lithographic performace of the resultig optimized BARC. I this paper, we will perform a theoretical aalysis of the BARC optimizatio process with respect to the propagatio of BARC ad κ (the real ad imagiary parts of the refractive idex) measuremet errors. For several realistic cases, specificatios o the measuremet accuracy of these optical parameters will be derived ad the lithographic cosequeces of BARC metrology errors will be explored. Next, the impact of measuremet oise o the ucertaity of ad κ measuremets will be studied for the case of spectral reflectace-based measuremets. I particular, the ifluece of measuremet wavelegth rage will be show to have a sigificat impact o the propagatio of measuremet oise to ucertaity i BARC ad κ values. Fially, the lithographic impact of BARC measuremet choices will be show as a propagatio of measuremet ucertaity to a icrease i fial substrate reflectivity. The goal of this paper is to preset a comprehesive method for evaluatig the impact of measuremet oise o the lithographic performace of BARC materials.

2 . Theory of BARC Optimizatio The goals of film stack optimizatio are to miimize stadig waves i the resist, ad to reduce the sesitivity of the process to film stack variatios (icludig resist, but other layers as well). By far the most commo way to accomplish all of these goals is by usig a optimized BARC. Whe optimizig a litho process for reflectivity, there are three basic tasks: 1) optimize the BARC, ) optimize the resist thickess (from a swig curve perspective), ad 3) uderstad the sesitivity to BARC, resist, ad film stack variatios. For the first task, there are two classes of BARC problems: BARC o a absorbig substrate (such as metal) the goal is to reduce the reflectivity (the thickess of the metal or what s udereath does t matter) BARC o a trasparet substrate (such as silico dioxide) reduce the sesitivity to oxide thickess variatios (while also keepig reflectivity low) There is a ufortuate problem i that the substrate reflectivity experieced by the photoresist caot be measured. Measurig the reflectivity of the substrate whe ot coated by photoresist is ot useful to this task, ad oce coated the reflectivity becomes hidde from measuremet. Thus, the approach that must be used is to calculate the reflectivity from measured fudametal parameters, amely the thickess ad complex refractive idex of each layer i the film stack. There are three BARC parameters available for optimizatio: the thickess of the BARC, ad the real ad imagiary parts of its refractive idex. The treatmet below follows that give i Referece 1. BARC o a Absorbig Substrate The electric field reflectio coefficiet (the ratio of reflected to icidet electric fields) at the iterface betwee two materials is a fuctio of the complex idices of refractio for the two layers. For ormal icidece, the reflectio coefficiet of light travelig through layer i ad strikig layer j is give by i j ρ ij = (1) i + j where is the complex refractive idex ( = + iκ). For the case of a bottom atireflectio coefficiet (BARC), assume the BARC (layer ) is sadwiched betwee a resist (layer 1) ad a very thick substrate (layer 3). The total reflectivity lookig dow o layer icludes reflectios from both the top ad bottom of the BARC film. The resultig reflectivity, takig ito accout all possible reflectios, is R total ρ1 + ρ3τ = ρ D total = () 1 + ρ1ρ3τ D where the iteral trasmittace, τ D, is the chage i the electric field as it travels from the top to the bottom of the BARC, give by for a BARC of thickess D. τ iπ D / λ D = e (3)

3 If the role of layer is to serve as a atireflectio coatig betwee materials 1 ad 3, oe obvious requiremet might be to miimize the total reflectivity give by equatio (). If the light reflectig off the top of layer (ρ 1 ) ca cacel out the light that travels dow through layer, reflects off layer 3, ad the travels back up through layer (ρ 3 τ D), the the reflectivity ca become exactly zero. I other words, Rtotal = 0 whe ρ 1 + ρ3τ D = 0 or ρ1 = ρ3τ D (4) Whe desigig a BARC material, there are oly three variables that ca be adjusted: the real ad imagiary parts of the refractive idex of the BARC, ad its thickess. Oe classic solutio to equatio (4) works perfectly whe the materials 1 ad 3 are o-absorbig: let τ D = -1 ad ρ 1 = ρ 3. This is equivalet to sayig that the BARC thickess is a quarter wave (D = λ/4 ), ad the o-absorbig BARC has a refractive idex of = 13. While this BARC solutio is ideal for applicatios like atireflective coatigs o les surfaces, it is ot particularly useful for commo lithography substrates, which are ivariably absorbig. Will a solutio to equatio (4) always exist, eve whe the resist ad substrate have complex refractive idices? Sice all the terms i equatio (4) are complex, zero reflectivity occurs whe both the real part ad the imagiary part of equatio (4) are true. This requiremet ca be met by adjustig oly two of the three BARC parameters (, κ, ad D). I other words, there is ot just oe solutio but a family of solutios to the optimum BARC problem. Expressig each reflectio coefficiet i terms of magitude ad phase, i ij ρ ij = ρij e θ (5) equatio (4) ca be expressed as two equalities: λ ρ3 λ D = l = ( θ1 θ3) (6) 4πκ ρ1 4π Ufortuately, the seemigly simple forms of equatios (4) ad (6) are deceptive: solvig for the ukow complex refractive idex of the BARC is exceedigly messy. As a cosequece, umerical solutios to equatio (4) or (6) are almost always used. Note that a secod-miimum BARC ca be optimized usig equatio (6) by addig π to the agle differece o the right had side of the equatio. Cosider a commo case of a BARC for 193m exposure of resist o silico. The ideal BARC is the family of solutios as show i Figure 1, which gives the ideal BARC ad κ values as a fuctio of BARC thickess. Each solutio produces exactly zero reflectivity for ormally icidet moochromatic light. Withi this family of solutios, available materials ad the acceptable rage of BARC thickesses (usually costraied by coatig ad etch requiremets) will dictate the fial solutio chose.

4 Refractive Idex - real BARC Thickess (m).8 κ (a) Refractive Idex - imagiary Refractive Idex - real κ Refractive Idex - imagiary Figure BARC Thickess (m) (b) Optimum BARC refractive idex (real ad imagiary parts, ad κ) as a fuctio of BARC thickess for ormal icidece illumiatio (resist idex = i ad silico substrate idex = i.778) at 193m. a) First miimum BARCs, ad b) secod miimum BARCs. Aother criterio for choosig the optimum BARC is the sesitivity to BARC thickess variatios. Ofte, BARC layers are coated over topography ad are partially plaarizig. This meas that BARC thickess variatios across the device are ievitable. Is oe BARC solutio from the family of solutios give i Figure 1 better from a BARC thickess sesitivity perspective? Cosider oly small errors i

5 BARC thickess about the optimum value, so that D = D opt + where D opt is the optimum thickess give by equatio (6). Sice equatio (4) is true at the optimum thickess, + = + i4π λ = 4π / λ ρ ρ τ ρ ρ τ / i ρ 1 3 D 1 3 e 1 1 e Dopt (7) Usig a similar operatio o the deomiator of the reflectivity expressio () gives 4π / λ ρ1 1 i e R = (8) i4π / λ 1 ρ1e Assumig is small, keepig oly the first two terms of a Taylor s expasio of the expoetial i the umerator gives π 1 1 R (9) λ 1 As ca be see, the reflectivity icreases approximately quadratically about the optimum BARC thickess. Differet BARC solutios will have differet sesitivities, depedig o how close the ratio / 1 is to oe. For the first miimum BARC example i Figure 1, the ~50m BARC thickess solutio has the miimum sesitivity to BARC thickess errors. Similarly, variatios i refractive idex of a BARC ca cause the reflectivity of a otherwise optimal BARC solutio to icrease. For the case of the optimal ormal-icidece BARC, the reflectivity for a give chage is BARC idex (which ca be a error i real ad/or imagiary parts) will be approximately ρ1 1 + ρ1 1 ρ R i4πd / λ 1 ρ 1 1 (10) 3 Note that is the sum of the squares of the errors i the real ad imagiary parts of the idex. The sesitivity to BARC errors, either i thickess or i refractive idex, are show i Figures ad 3 for the case of the BARC solutios of Figure 1. Note that for this case, practical first miimum BARC solutios have thickesses i the 0 50 m rage. Thus, for this case, thicker BARCs are less sesitive to thickess errors but more sesitive to refractive idex errors. Assumig that a reflectivity of 0.1% ca be tolerated, a 0 m optimal BARC ca tolerate 1 m of thickess error, or a chage i refractive idex. A 40 m optimal BARC ca tolerate m of thickess error, or a 0.04 chage i refractive idex. Roughly, if the BARC thickess has o error, the real part of the refractive idex of these BARCs must be cotrolled to.5% assumig o error i the imagiary part, or the imagiary parts must be cotrolled to 8% for o error i the real part. Likewise, if the refractive idex has o error, the BARC thickess must be cotrolled to roughly 5% for the give 0.1% reflectivity tolerace.

6 R/ (1/m ) R/ Optimum BARC Thickess (m) (a) Optimum BARC Thickess (m) Figure Sesitivity of substrate reflectivity for the optimum BARCs of Figure 1a as a fuctio of a) BARC thickess errors, or b) BARC refractive idex errors. (b) R/ (1/m ) Figure Optimum BARC Thickess (m) (a) R/ Optimum BARC Thickess (m) Sesitivity of substrate reflectivity for the optimum secod miimum BARCs of Figure 1b as a fuctio of a) BARC thickess errors, or b) BARC refractive idex errors. (b) BARC o a Trasparet Substrate The secod type of BARC optimizatio problem ivolves the use of a BARC o a trasparet substrate, such as a oxide film. For such a case, the overall substrate reflectivity will be a fuctio of the oxide thickess ad oe of the goals of the BARC desig is to reduce the sesitivity to uderlyig film thickess variatios. As ca be see from Figure 4, usig the BARC at a first miimum results i a very large sesitivity to uderlyig oxide thickess variatios. I fact, the thickest BARC films provide the most robust behavior whe a wide rage of oxide thickesses are expected. Thus, the preferred desig approach for this case is to determie the maximum allowed BARC thickess from a itegratio perspective, the optimize the ad κ values of the BARC to miimize the maximum reflectivity over the rage of expected oxide thickesses.

7 Substrate Reflectivity Thickess Layer # (m) Oxide Thickess Figure 4 Substrate reflectivity versus BARC thickess over a rage of uderlyig oxide thickesses (oxide o top of a silico substrate). A thick BARC solutio ca be thought of as a BARC that completely absorbs all of the light that may reflect off the substrate ad is thus isesitive to chages i the substrate stack. For this case, the product of BARC thickess ad the imagiary part of its refractive idex (κ ) must be sufficietly high. Maximum BARC thickess is usually determied by process cosideratios, thus fixig the miimum κ. Assumig the imagiary part of the resist refractive idex is sufficietly small, the resultig reflectivity is 1 i i = ( 1 ) + κ ( + ) + κ κ R total = ρ1 = (11) κ The optimum real part of the BARC refractive idex to miimize reflectivity will the be 1 The resultig reflectivity is = 1 + κ (1) 1 1 κ 1 + R = (13) + 4 κ Obviously, the thick BARC solutio is isesitive to BARC thickess variatios by desig. The sesitivity to errors i BARC refractive idex ca be obtaied from equatio (11). For a small chage i the real part of the BARC refractive idex,

8 R R 1 1 = 1 κ (13) For a small chage i the imagiary part of the BARC refractive idex, R κ R κ 1 (14) BARC Performace How critical is BARC optimizatio? How low must the substrate reflectivity be before acceptable CD cotrol ca be expected? There is o sigle aswer to these questios, sice they are process ad feature depedet. But cosider the example show i Figure 5. Here, 100 m lies o a 80 m pitch are simulated (usig PROLITH v9.3) with a stepper usig aular illumiatio, with a ceter sigma give by σna = As ca be see, a substrate reflectivity of less tha 0.1% still leads to a oticeable swig behavior. 130 Resist Feature Width, CD (m) R = 0.07% R = 0.43% Resist Thickess (m) Figure 5 CD swig curves (100m lies with a 80m pitch are prited with a stepper usig aular illumiatio, with a ceter sigma give by σna = 0.54) for two differet BARCs with differet levels of optimizatio, as give by the resultig substrate reflectivity R. (Simulatios usig PROLITH v9.3.) A commo approach to characterizig the impact of substrate reflectace (that is, the impact of a o-ideal BARC) is to relate reflectivity i the presece of film thickess variatios to effective dose errors. Cosider a resist thickess D = D mi ± where D mi is the thickess at the swig curve miimum ad is

9 small compared to the swig period. Assumig a reasoably good BARC, the effective dose error due to the resist thickess variatio is ( π ) E αd α + 4 ρair resist ρresist substrate e resist λ E (15) The dose error comes from a bulk absorptio term (α ) plus a fractio of the swig amplitude. Cosider the stadard 193 m resist o BARC o silico case described above, with α = 1. µm -1, D = 00m, resist = 1.7, ad ρ air-resist = 0.6. For i aometers, E ρ resist substrate (16) E For a 8.3 m icrease i resist thickess, the bulk effect causes about a 1% effective dose error. The swig effect will cause aother 1% effective dose error for that 8.3 m resist thickess error if the substrate reflectivity is 0.33%. The maximum allowed substrate reflectivity is a fuctio of the rage of resist thickess that must be tolerated ad the amout of effective dose error oe is willig to accept. Specificatios of substrate reflectivity ear 0.1% are ot ucommo. 3. Simulatig Errors i Thi Film Metrology The thickess ad optical properties of photoresist ad BARC films are routiely characterized usig reflectometry ad/or ellipsometry. I practice, may varieties of both techiques exist. Regardless of the specific method employed, the uderlyig approach typically ivolves recordig the optical respose through wavelegth from a sample ad the aalyzig this data i order to obtai values for the thickess ad optical properties of the film of iterest. The calculated respose is usually described usig the Fresel equatios i combiatio with oe or more models to describe the optical properties of the material comprisig the sample. Oce the resist ad BARC thickesses ad optical properties are determied, the methods of the precedig sectio ca be used to compute substrate reflectivity. For reflectace measuremets, the discrepacy betwee the measured ad calculated data sets is characterized by the weighted merit fuctio N 1 1 χ = [ yi y( xi, a) ], (17) N M i= 1σ i which is miimized through use of a iterative optimizatio or fittig procedure such as the Leveberg- Marquardt method []. I equatio (17), the y i are the measured data (i.e., reflectace), the x i are the idepedet variable (the wavelegth, λ, correspodig to data poit y i ), σ i is a estimate of the ucertaity i y i, a is the set of model parameters, N is the umber of data poits, ad M is the umber of parameters i the set a that are to be optimized. The best fit parameters are defied as those that give the smallest value for χ. Assumig the substrate refractive idex ad thickess ca be regarded as kow, a typical sigle film o substrate measuremet requires the determiatio of N+1 ukows (film thickess plus N pairs of ad κ). This is geerally ot possible with oly N measured data poits. Dispersio models that parameterize the behavior of ad κ with respect to wavelegth are ormally used to reduce the total

10 umber of optimizatio parameters. The measured parameter set a the cosists of the film thickess ad a usually small set of dispersio parameters. The optimized dispersio parameters are used to compute the ad κ values at the desired wavelegths at the ed of the fittig procedure. A example of a dispersio model is the Tauc-Loretz model [3]. The Tauc-Loretz model is based o a combiatio of the Tauc joit desity of states ad the Loretz oscillator. It has advatages over other available dispersio models i that it is Kramers-Kroig ad time-reversal symmetry cosistet, correctly describes the behavior of κ i the high frequecy limit, ad is capable of accurately characterizig the dispersio of a wide rage of materials [3]. For a simple 1-term Tauc-Loretz film, such as the 1-term resist example below, the parameter set a cosists of the resist thickess ad the Tauc-Loretz dispersio parameters E g, ε 1, A, E 0, ad C, for a total of 6 parameters to be determied from each reflectace measuremet. The complex idex of refractio = (E g, ε 1, A, E 0, C, λ) is calculated from the Tauc-Loretz model at the ed of the fittig procedure. Films havig a more complicated dispersio structure, such as the BARC example below, are characterized usig multiple Tauc-Loretz terms, each term represetig a peak i the material s absorptio spectrum. The total parameter set the cosists of the film thickess, the high frequecy costat term ε 1, ad four additioal parameters E g, A, E 0, ad C for each dispersio peak. The best achievable χ value is geerally limited by the applicability of the model, that is, the extet to which the dispersio model actually describes the optical properties of the material. Still, a good merit value is ot i itself sufficiet to esure that accurate results have bee obtaied. I practice, ucertaities i the derived results may also arise as a result of ambiguity or correlatios betwee parameters i the model, meaig that differet combiatios of dispersio parameters lead to idistiguishable reflectace spectra. These ambiguities i dispersio parameters ofte lead to ambiguities i the refractive idex values that are calculated from them. I additio, lack of sesitivity of the modeled data to parameter chages ca lead to ucertaities whe determiig parameter values. Geerally speakig, iter-parameter correlatio may be reduced by providig greater costrait to the fittig process. I reflectometry, greater costrait may be achieved by a variety of meas, icludig addig data measured at differet icidet agle ad polarizatio coditios ad/or multi-sample aalysis. I this paper, aother meas of providig greater costrait is explored, amely the extesio of covetioal m reflectometry ultra-violet to visible (UV-Vis) wavelegths ito the m vacuum ultraviolet (VUV) regio. The optical properties of may materials exhibit richer structure (i.e., peaks ad valleys) i the VUV regio tha at UV ad visible wavelegths. This ca aid both i ehacig sesitivity of reflectace data to chages i film parameters, as well as i reducig iter-parameter correlatios, yieldig more reliable ad κ measuremets, eve whe ad κ data are eeded oly for o-vuv wavelegths. It will be demostrated that there is cosiderable beefit associated with the extesio of reflectometry data sets ito the VUV whe usig such data i material characterizatio applicatios, particularly as they relate to the accurate determiatio of ad κ values at the 193 m wavelegth. To explore the effects of extedig covetioal reflectometry ito the VUV, several simulatios of 193 m resist ad BARC materials were cosidered. The optical properties of the resist ad BARC, based o actual represetative material measuremets ad show i Figure 6, were assumed to be perfectly described usig a oe-term ad three-term Tauc-Loretz model, respectively. The reflectace of a 900Å sigle layer of each material o a crystallie silico substrate was calculated from m wavelegth rage usig the assumed parameter values. These reflectace spectra were the used as the basis for creatig a series of similar data files with oise added accordig to a Gaussia distributio with stadard deviatios of 0.1% ad 0.%. I this sese, the origial oiseless data is cosidered to be the true reflectace of the sample, which ca ever be realized i a optical measuremet, while the data with added oise represets

11 realized, albeit simulated, represetatios of the true reflectace. It is importat to poit out that the oise model assumed for this iitial study is cosistet with assumig that errors i the raw data are due to radom ucorrelated processes, ad represets best-case performace for a give oise level sice systematic errors ad/or model shortcomigs are ot represeted here. Refractive Idex κ Wavelegth (m) Refractive Idex κ Wavelegth (m) Figure 6 (a) Optical properties used i simulatios of a) 1-term photoresist, ad b) 3-term BARC materials. (b) The simulated reflectace data files were aalyzed usig the Leveberg-Marquardt algorithm i a attempt to re-obtai the startig parameters. To seed the optimizatio routie, the thickess ad Tauc- Loretz startig parameters were offset by 1% from their omial values. The fial fit parameters were the fed back ito the Tauc-Loretz model ad used to calculate the determied values for ad κ at 193 m. The results of 100 such measuremets for each oise coditio were used to compute stadard 3-σ cofidece limits for thickess ad 193 m optical properties. The results from aalysis of the 1-term photoresist reflectace files are summarized i Table 1 ad Figure 7 below. The data correspodig to coditios 1 3 i Figure 7 correspod to fits performed o simulated data files with a oise level of 1σ = 0.%. The first two coditios were fit over the rage of m ad m, respectively. The third coditio correspods to fits extedig ito the VUV (10 800m). As is evidet from these results, the differeces betwee the first ad secod coditios are egligible. Hece, the extesio of the covetioal reflectace data set of the first coditio by 80 m at the log wavelegth ed (where the ad κ values are essetially flat) does othig to improve measuremet performace. The performace of coditio 3 however, wherei the data set of coditio 1 is exteded by 70 m ito the VUV (where the ad κ values exhibit cosiderable structure) yields a very differet result, reducig the 3σ ucertaity by a factor of 3.1 i ad 6.7 i κ. Coditios 4 6 preset the results of fits performed o data files with a reflectace ucertaity of 1σ = 0.1%. Agai the same treds are evidet - extedig the stadard ( m) reflectace data rage by 80m to loger wavelegth does othig to improve measuremet performace, while extedig by 70 m ito the VUV reduces the 3σ repeatability by a factor of 3.6 i ad 7.6 i κ.

12 Table 1 Summary of results obtaied from fittig 100 simulated reflectace files based o 900Å photoresist with ad κ values at 193 m equal to ad respectively. Photoresist Compariso Coditio Oscillators Rage (m) Added Noise (1σ) 0.0% 0.0% 0.0% 0.10% 0.10% 0.10% Mea Thickess (Å) Thickess 3σ Mea (193 m) σ Mea κ (193 m) κ 3σ Mea value Actual value Mea k value Actual k value at 193 m k at 193 m Coditio Coditio (a) (b) Figure 7 Mea value of a), ad b) κ at 193 m obtaied from fittig 100 simulated reflectace files based o a 900Å photoresist. Error bars represet +/- 3 sigma ucertaities. The ucertaities i the idex values are a direct cosequece of the ucertaities i the Tauc- Loretz parameters used to describe the film. Table compares the 3-σ ucertaities for each of the 5 Tauc- Loretz parameters for m ad m data rages for the 1 term resist example. The compariso shows that the ucertaities i Tauc-Loretz parameters are reduced for the m data by at least a factor of 4, ad i may cases by a order of magitude. The extet to which the Tauc-Loretz ucertaities propagate ito actual errors i measured ad κ values depeds o the amout of costrait provided by the reflectace itself. For thicker films, chages i these parameters ted to affect the reflectace spectra everywhere i the m rage, ad the additio of VUV wavelegth data serves to ehace sesitivity to chages i optical parameters ad to reduce iter-parameter correlatio, resultig i

13 more reliable ad κ measuremets. As the film thickess decreases, the degree of ucertaity i ad κ icreases as chages i film optical properties ad thickess have less of a impact o m reflectace, to the poit that determiig both thickess ad optical properties for a < Å film requires m data, eve if we re oly tryig to measure the optical properties for wavelegths greater tha 190 m. Table 3-σ ucertaities for the 1 term resist Tauc-Loretz parameters calculated from the 100x data for m reflectace ad m reflectace. A radom oise error of σ i = 0.1% was assumed for the raw data i both cases. E g (ev) ε 1 ( ) A (ev) E 0 (ev) C (ev) m m The results from aalysis of the 3-term BARC reflectace files are summarized i Table 3 ad Figure 8. Coditios 1 ad i Table 3 correspod to fits performed o data files with a oise level of 1σ = 0.% ad fit over the rage of m ad m, respectively. As is evidet, the exteded VUV data set yields a sigificat reductio i measuremet ucertaity of both ad κ. The data correspodig to coditios 3 5 represet the result of fits performed o data files with a oise level of 1σ = 0.1%. Oce agai the m data set outperforms the stadard set of coditio 3. The data correspodig to coditio 4 results from fits performed usig a -term Tauc-Loretz dispersio rather tha a 3-term dispersio to model the m data. The motivatio for this coditio follows from a examiatio of the ad κ spectra ad simulated reflectace spectrum preseted i Figures 9 ad 10, which illustrate how structure i the VUV optical properties ca play a subtle role i optical measuremets performed at loger UV-Vis wavelegths. Table 3 Summary of results obtaied from fittig 100 simulated reflectace files based o 900 Å BARC film with ad κ values at 193 m equal to ad respectively. BARC Compariso Coditio Oscillators Wavelegth Rage (m) Added Noise (1σ) 0.0% 0.0% 0.10% 0.10% 0.10% Mea Thickess (Å) Thickess 3σ Mea (193 m) σ Mea κ (193 m) κ 3σ

14 at 193 m Mea value 1.71 Actual value Coditio Figure 8 (a) k at 193 m Mea k value Actual k value Coditio Mea value of (a) ad (b) κ at 193 m obtaied from fittig 100 simulated reflectace files based o a 900 Å BARC. Error bars represet +/- 3 sigma ucertaities. (b) The solid lies i Figure 9 are the real ad imagiary parts of the refractive idex for the 3-term BARC material. The structure associated with a oscillator cetered ear 146 m is apparet i the correspodig reflectace spectra, show as the solid lie i Figure 10. The correspodig curves for a - term BARC are show as dashed curves i Figures 9 ad 10. Above 190 m, the reflectace from the ad 3-term models appear quite similar. Hece, without prior kowledge of the presece of the third oscillator i the VUV, covetioal reflectometry users (oly collectig data dow to 190 m) may lack icetive to iclude a third term i their descriptio of the BARC. The results of this are show i Table 3, coditio 4. While the -term dispersio yields a better ucertaity statistic for the m case, the resultig systematic error causes the measured idex to be completely erroeous. Real Part of Refractive Idex term term Wavelegth (m) (a) Imagiary Part of Refractive Idex term term Wavelegth (m) Figure 9 Real (a) ad imagiary (b) parts of the refractive idex of BARC materials as described usig - term ad 3-term Tauc-Loretz model. (b)

15 0.30 Reflectace term BARC 3 term BARC Wavelegth (m) Figure 10 Simulated reflectace spectra for a 900Å BARC film based o -term ad 3-term Tauc-Loretz model. 4. Discussio/Coclusios The results from the previous two sectios ca ow be combied to examie the ifluece of metrology ucertaity o the effectiveess of a BARC at cotrollig reflectivity. The BARC studied above, which was based o a actual BARC material, is close to but ot exactly a optimum secod miimum BARC for 193m resist o silico. However, assumig that the fractioal ucertaity i ad κ demostrated i the simulated BARC of Sectio 3 is costat, the ucertaity i the optimum 90 m secod miimum BARC of Sectio ca be used. Table 4 shows the relevat refractive idices ad ucertaities uder this assumptio. Table 4 Coversio of ad κ ucertaity from the simulated BARC of Sectio 3 (0.% oise case) to the optimum BARC of Sectio uder the assumptio of costat relative ucertaity for both ad κ. Simulated BARC Optimum BARC m rage m rage m rage m rage (193m) σ σ / κ (193m) σ κ σ κ /κ For the optimum 90 m thick secod-miimum BARC from Sectio, equatio (10) becomes R (18)

16 For a 1-σ error i both real ad imagiary parts of the refractive idex, the resultig reflectivity (at 193m) becomes R σ + σ κ (18) For a 3-σ error i both real ad imagiary parts of the refractive idex, the resultig reflectivity would be ie times larger. The results for reflectivity, for both the covetioal m metrology ad the VUV exteded m metrology, are summarized i Table 5. The exteded wavelegth rage results i a 7X reductio i the worst-case substrate reflectivity. For example, if a substrate reflectivity error of 0.01% is budgeted for BARC ad κ 3-σ metrology errors, the clearly the covetioal m wavelegth rage with 0.% added oise produces a uacceptably high reflectivity. Uder the same coditios, however, the exteded m wavelegth rage with its iheretly higher oise tolerace produces reflectivities well withi specificatios. Note that o BARC thickess errors were icluded i this aalysis, or errors i photoresist optical properties. Sice these errors will put the BARC film off of its miimum i reflectivity, the results preseted here are a best case sceario. Table 5 Resultig 1-σ ad 3-σ worst-case reflectivities for the 0.% added oise coditio m rage m rage σ σ κ σ R (%) σ R (%) The aalysis preseted above shows how measuremet oise propagates from the optical measuremet of BARC ad κ to the resultig reflectivity of a BARC material. I particular, we have show how the wavelegth rage used i optical measuremets ca impact the BARC optimizatio process. The aalysis shows that extedig the covetioal UV-Vis metrology to VUV wavelegths ca lead to a sigificat reductio of the substrate reflectivity error caused by metrology errors, showig that VUV metrology is a promisig optio for use i the characterizatio ad selectio of materials used i moder lithography. I additio, the distict spectral features that are preset i the vacuum ultraviolet regio of the material optical properties could be used, for example, as a meas of figerpritig differet lithography films that may otherwise appear to be idetical if ispected at loger wavelegths. Fially, we poit out that the improvemets of VUV metrology over covetioal metrology are expected to be eve more proouced for thier films used i the fabricatio of semicoductor devices. Further studies i this area would iclude the impact of high agles of icidece o BARC performace, ad the couplig of other error sources like photoresist ad substrate optical properties. 5. Refereces 1. C. A. Mack, Fudametal Priciples of Optical Lithography: The Sciece of Microfabricatio, Joh Wiley & Sos (i press).. W. H. Press, S. A. Teukolsky, W. T. Vetterlig, ad B. P. Flaery, Numerical Recipes i C: The Art of Scietific Computig, Secod Editio, Cambridge Uiversity Press (Cambridge, MA: 199). 3. G. E. Jelliso ad F. A. Modie, Parameterizatio of the optical fuctios of amorphous materials i the iterbad regio, Appl. Phys. Lett., Vol. 69 (1996) p. 371.