Understanding Lens Aberration and Influences to Lithographic Imaging

Understanding lens aberration and influences to lithographic imaging

Bruce W. Smith and Ralph Schlief Rochester Institute of Technology, Microelectronic Engineering Department 82 Lomb Memorial Drive, Rochester, NY 14623- 1732, [email protected]

ABSTRACT

Lithographicimaging in the presenceof lens aberrationresults in uniqueeffects, depending on feature type, size,phase, illumination, andpupil use. As higherdemands are placed on optical lithographytools, a betterunderstanding of the influenceof lens aberrationis required. The goal of this paperis to develop some fundamental relationships and to address issues regarding the importance, influence, and interdependenciesof imagingparameters and aberration.

Keywords: Aberrations,optical lithography,resolution enhancement

1. INTRODUCTION

It is generally true that there is no universal impact of lens aberration. This is especiallyso for microlithographicimaging. We havedemonstrated in earlier reportshow the influenceof lens aberration dependson illumination method,masking approach, and specificutilization of the objectivelens pupil (for a projectionlithography tool using Kohler illumination) [ 1, 21. As valuesof kl below 0.5 arepursued, an understandingof the impact of lens aberrationfor specific imaging situationsis important. Establishing tolerancelimits and relationshipsfor currentand future conditionsof optical lithographyis challenging, leavingthe lithographerwith concernsthat arenot easilyaddressed using conventionaloptical description. Historically, during the designand fabrication of an optical system,decisions about imaging capability and performancecould be carried out using generalmodulation calculations combined with actual resist performancedata. This has changeddramatically over the past few yearsas lithographydemands have pushedimaging to levels approachingincoherent diffraction limits. Methodsof image assessmentnow include specific featurecharacterization and the evalmtion of sensitivity to uniqueaberration types [3, 4, 51. Theseadvanced characterization techniques can make generalizations difficult andcan lead away from the developmentof underlying relationships. In this paper, we describesome of the fimda.mentaI relationshipsthat govern such things as feature specific aberration sensitivity, resist capability and aberrationtolerancing, illumination and maskinginfluences, and the bestutilization of an aberratedlens pupil. Additionally, we developa predictivelink betweenfrequency plane and imageplane distributions and presentpupil statisticsto model the primary influencesof aberrationon imaging. Theseanalytical techniquesand methodshave been incorporated into a lithographysoftware tool, which is alsodescribed.

2. PROXIMITY AND ABERRATION

Isolatedfeatures do not respondthe sameto lens aberrationas densefeatures do. This is a classical and important exampleof how the impact of lens aberrationdepends on the geometrybeing imaged. Closerexamination can leadto a betterunderstanding about optical performanceand limitations. Figure la showsan aerial imagesimulation for line/spacefeatures of sizekl=O.35 at duty ratiosranging from 4: 1 to 1:4 using a perfectlens for partial coherencevalues from 0.5 to 0.9 (wherea 1:1 duty ratio implies equal line/spacefeatures). A high NA scalarmodel was used for the simulations(Prolith/2 v. 6.05d). This plot showshow NILS generallyincreases for more isolatedfeatures, which is expectedas the corresponding pitch value increases.Figure lb showsa similar plot for an imaging systemwith 0.05 wavesof spherical aberration,a reasonablysmall level but significant by today’s standards.The impact of this aberrationis realized in the plot in Figure lc, where the fractional loss in NILS is shown. The impact of spherical aberrationis greatestas line isolation increasesand also at low levels of partial coherence.As will be

Proc. of SPIE Vol. 4000, Optical Microlithography XIII, ed. C. Progler (Mar, 2000) Copyright SPIE 294 shown,this is a direct result of phaseerrors between zero and higherfrequency terms in the objectivelens pupil. Analysis hasalso been carried out for otheraberration types suggesting similar effects.

25. 1 a

05. 0.5 0 w-qcc)qcvLc) -qcuqmIs,* ‘aqmqnlq ~qNqCr)qd c9 N cv c9 c’) N N m DutlJ ratio; :X) Duti ratio i :X)

Figure la&. NILS vs. duty ratio vs. partial coherencefor kl=0.35 features. Duty ratio variesfrom 4: 1 (lines) to 1:4 (spaces).A perfectlens (a) is comparedto a lens with 0.05 wavesof sphericalaberration (b).

0.99 0.97 Y 0.95 7 g 0.93 ‘9 0.91 L 0.89 0.87 0.85 ~Lqcc)qcv~ ~~cu~c’>Lqd- c9 nl N c9 Duk ratio b:X)

Figure lc. Loss is NILS with 0.05waves of sphericalaberration, increasing with line isolationand with partial coherence.

3. SIMPLE COHERENT ANALYSIS

To gain insight into the reasonsfor the imaging differencesbetween dense and isolatedfeatures, their difFractiondistribution in the lenspupil needsto be explored.Figure 2 depictstwo maskfunctions - a denseline (1:1) maskfunction md(x)and a moreisolated line (1:4) maskfunction mi(X)(a duty ratio of 1:4 or greaterwill be usedto representline isolation).It is convenientto representthese functions using a linear systemsdescription, the convolutionof a singlespace function (rect)with an impulsetrain function (comb) with a fundamentalfrequency of the maskpattern (I/‘):

mP(x) = rect(x.OSp) * comb(x/p) mi(x) = rect(xdl.8p) * comb(x/p)

Proc. SPIE Vol. 4000 295 wherep is the maskpitch and the scalingfactor in the denominatorof the rect functionscorrelates to the spacewidth. The diffraction patternsresulting from coherentillumination are Fourier Transformsof these maskingfunctions:

i&(i) = OSsinc(id2) x comb(u) Mi(u) = 0.8sinc(4u/5) x comb(u)

whereM(U) is the Fourier Transformof m(x) and u is spatialfrequency, I/x. The magnitudevalues of the zero and first ordersfor the denselines are 0.5 and 0.318 and for the isolatedlines, valuesare 0.8 and 0.187, as shown in Figure 3 for a lens pupil collecting only theseorders (pitch - ?JNA). The resulting coherentimage amplitudefunction for the isolatedlines is biasedquite differently from the denseimage amplitude function. Figure 4a depicts the situation where image amplitude functions at the wafer, representedas:

m&ix) = 0.5 + 0.63 7cos(21zx/p) mi’(L) = 0.8 + 0.3 ~~cos(~~x/P).

Squaringthe image amplitude functions results in intensity or aerial image functions [I(x)], shown in Figure 4b:

&(-i-i)= r0.5 + 0.63 7cos(2xdp) Jz Ii(X) =[ 0.8 + 0.3 ~~cos(~YE..)]~

rect(x/O.5p)*comb(tip) rect(x/O.8p)*comb(x/p) 1.5 I i

-05’. -055. Figure 2. Mask functionsanalyzed, (left) equaldense lines and (right) 19 isolated hes.

Figure 3. The diffraction field for denseand isolatedlines showing orderscollected in the lens pupil NA-Up. Zero andfirst order magnitudevalues are 0.5 and0.3 18 for densefeatures and 0.8 and0.187 for isolatedfeatures. The defocus aberrationfunction acrossthe lens pupil is also shown.

296 Proc. SPIE Vol. 4000 ae I 21- b Intensity 55% threshold 30% threshold,

I -0 I 1 I I I 1 I I I 1 . 5 1 Figure 4. Amplitude and aerialimage (intensity) functions for denseand isolated(1:4) lines with pitch - ?JNA. The denselines arethe lower curves,the isolatedlines arethe uppercurves. A 55% resist amplitudethreshold and a 30% resistintensity threshold values are indicated.

For the isolatedline case,the increasedbias from the zerodiffraction order comparedto the first order gives rise to problems. A photoresistprocess is generallyoptimized when it samplesan aerialimage at a thresholdpoint near a 30% intensity value. This correlatesto a 55% amplitudethreshold. This is appropriatefor denselines sinceit is closeto the intensity bias value. For isolatedlines, the situation is problematic. The isolatedintensity and amplitudefunctions are sampledby the photoresistnear image positionsthat will vary the most- the peakor nodalpositions of the biasedcosine functions. Sensitivity to image processvariation for small isolatedlines is now predictable. By comparison,the denselines samplingpoint is nearthe infectionpoint of the amplitudeor intensityfunctions. Photoresistmaterials and processeshave historically beentuned to denseline performance.This situationalso suggestspossibilities for materialsto be gearedmore specificallyfor isolatedline performance(which are also in use). The connectionto aberrationsensitivity is now a logical step. If any perturbationexists that will influence the diffraction orderswithin the lens pupil, it would be expectedthat the effectsmay be more noticeablefor small isolatedlines than for small denselines. Aberrationin the lens pupil causesphase error in the diffraction ordersthat are collectedby the lens. A phaseerror in the zero diffraction order aloneis of no consequencesince it hasno frequencycontent. As morethan the zeroorder exists in the lens pupil however,phase error will impact order interferenceand ultimately the integrity of the resulting image. To demonstratethis point, symmetricalaberration is considered.Defocus and sphericalaberrations are examplesof symmetricalaberration, as is astigmatismif consideredalong a single axis. The impact describedusing a defocusaberration (p*, shownin Figure 3) can be shown to be commonacross other symmetricalaberration types. If we considerdefocus and its influenceon coherentdiffraction orders,we recognizethe phaseerror in the first diffraction order measuredagainst the phaseof the zero diffraction order. For a peakdefocus aberration, Ad, the impacton first diffraction ordersat the edgeof the lens pupil will be a correspondingphase error. For a real and evenfunction, this can be a simple cosineamplitude dependenceof the aberrationleading to a modulationof the first diffraction order:

md’(x)= 0.5 + cos(Ad)O.63 ~cos(~xx..) mi’(i) = 0.8 + COS(A~)0.3 ~~COS(~ZU’JJ)

As an example,we will consider0.10 wavesof peak defocusaberration or 0.628 radiansof phaseerror. The cosine projection of this aberrationonto the first order results in an effective amplitude loss correspondingto cos(O.628)= 0.809. Figure 5 showsthe image resultsfor denseand for isolatedlines. Sincethe defocusphase error impactsthe first diffraction orderwith respectto the zero order,the biasing factor for either casedoes not changebut demodulationof the first order cosinesdoes occur This will havethe most significant

Proc. SPIE Vol. 4000 297 I:4 amplitude 1: 1 amplitude

2 2

15. 15.

1 1

05. --a-w--05. c-

0 I I I I I I I I I I I I I I I I 0 1 1

Figure 5. Imageamplitude and intensity for denseand isolatedfeatures, showing the impact of 0.1 wavesof defocusaberration.

impact in situationswhen the resultingimage is not samplednear the inflection point of the biasedcosine (which is the bias value itself). In the caseof small denselines, 0.1 wavesof defocusmay still produce usefulimages since it may havelittle impactat the resistthreshold point. For small isolatedlines, however, the resist is likely sampledat a positionin the imagethat varies significantly with defocus,making useful imaging unlikely. Other generalizationscan also be made. The analysissuggests that an isofocalpoint could exist for denselines, where a featurewould remain a near constantsize through focus. This is unlikely as feature isolation increases. It could also be concludedthat densefeatures would exhibit a resemblanceof an “iso-aberration”point where imaging would be least sensitiveto aberrations. This would alsobe moredifficult for isolatedfeatures. For this example, featureshave been exarnined with correspondingpitch valuesnear UNA (with first diffraction ordersjust within the lens pupil). The isolatedline size is thereforesubstantially smaller than the denseline size. For isolatedlines equalin sizeto the denselines, higherdiflkaction orders may be collected. This would reducethe impact of the zero order weighting (sinceit would be weightedagainst morethan just the first orders)and reduce the sensitivityto aberration,including defocus.Figure 6 showsa summaryof aerial imageswith and without defocusaberration. Threeconditions are shown: denselines on a pitch itlvA &=OS), 1:4 isolatedlines on a pitch MtA, and 1:3 semi-isolatedlines on a pitch 2;t/NA. Aberrationintroduced for eachcase is 0.1 wavesof defocus. This type of analysisleads to someuseful insight. Although defocusaberration has been studied, generalizationsmade can be extendedto higher aberrationorders as long as the specificcharacter of the aberrationis taken into account. Although not shownhere, a similar analysiswas carriedout for 3rdorder coma, resulting is similar conclusionsregarding image placementerror and line isolation. The analysis shownhere is basedon coherentillumination. Increasingpartial coherencereduces the discretecharacter of d.i@actionorders and lessensthe impactof defocusand aberration (see for instanceReference 6). From this analysis, it can be seen why simple biasing will not gain much with respect to isolated line performance.If a line is biased,the zerodiffraction orderweighting can be reduced.

298 Proc. SPIE Vol. 4000 0.60

0.30

0.00

- Dense ---- Dense defocus - I:4 pitch VNA ---- I:4 pitch VNA defocus ~ I:3 pitch 2VNA - - - - I:3 pitch I/NA defocus

Figure 6. Comparisonof aerialimages of denseand isolatedfeatures with and without aberration.

In order to print to size, however,additional exposure is needed,which will movethe resist thresholding point in the oppositedirection. The use of optical proximity correctioncan be useful howeversince additional frequencyinformation is actually addedin the lens pupil to reducethe weighting of the zero order. A combinationof biasing and OPC usually provesto be most practical. It is also interestingto realizehow featuretype might influencelens performancegoals. For densefeatures, the lens NA is most importantin orderto print as small a pitch aspossible. If only densefeatures are printed, the sensitivityto aberrationmay be lessimportant that achievinghigh NA. For more isolatedline structures,NA becomes less importancesince thesefeatures will likely be set on a larger total pitch than denselines would be. Aberrationsare, however,very critical. This may suggestdifferent lens criteria for different applications. Although not discussedin detail here, it becomesevident that resist processmodifications can greatly influenceprocess capability and aberrationsensitivity. In summary, a principle goal for a robustimaging processis to match the inflection point of an amplitudeimage with the resist processthresholding point. As a processgets closer to this goal, its toleranceto aberrationswill improve.

3. PREDICTIVE MODELING - APPLICATIONS IN IMAGING

The fundamentaldescription so far has been useful to help understandthe role of aberrationsin lithographic imaging. To anaIyzemore realistic situations,further descriptionis needed.The frequency descriptionof aberrationinfluence can be extendedto situationsof partial coherence,phase shift masking, modified illumination, and optical proximity correction(OPC) and this descriptioncan be usedto develop predictivemodels. Pupil metricshave recently been introduced to help predict the capabilityof an imaging systemin the presenceof lens aberration[ 1, 21. Descriptive statisticshave beendeveloped that measurethe phase variancein the lenspupil asit is weightedby diffraction energy. Variance,RMS, or similar measurements aremade across the utilized pupil wherea weightedpupil canbe definedas:

Weighted pupil = W(p, 8) x [M(u, v) *S(u,v)] x H(u, v) where W(p,8) is the aberrationfunction, M(u,v) is the maskdiffraction pattern, S(u,v)is the illumination function, and H(u,v) is the pupil function. A weightedvariance or PMS OPD measurementhas proven usefulfor instanceduring the illumination or phasemasking design [ 11.

Proc. SPIE Vol. 4000 299 Although useful for evaluatingresolution enhancement methods where zero difRaction order is limited, a simple weighted calculation of RMS OPD is not suflicient to describegeneral imaging performanceand such calculationscan sometimesbe misleading. The shortcomingsof using a simple RMS calculationare realizedusing an examplesimilar to the onein the previoussection where UNA pitch featuresare imagedwith 0.10 wavesof defocusaberration. As partial coherenceincreases, the weighted RMS OPD measurementcould suggestthat isolated line performancesuffer less consequencefrom aberrationthan denselines do, which is counterintuitiveand doesnot occur.

3.1 Predictive modeling using frequency term evaluation The problemwith attemptingto use a simple weightedpupil RMS OPD calculationis that the zero diffraction order overwhelmsthe pupil phasemeasurement. Image modulation and image placement responsesdepend on phasedifferences between frequency terms. This was shown earlier for a coherent casewhere the phaseerror in the first diffraction orderis measuredagainst the phaseof the zerodiffraction order. This descriptionis valid alsofor non-coherentconditions and where mask and illumination structure is more complex. A weightedpupil function is shownin Figure7a for densek&).4 featuresimaged with a partial coherencevalue of 0.7. The full pupil aberrationis shownin Figure 7b, which is basedon a real lens file with full pupil RMS OPD of 0.0377waves, a reasonablegood lens from an aberrationstandpoint. The pupil weighted RMS OPD is 0.0356, a value slightly lower than that for full pupil use but any interpretationbeyond this generalizationis difficult. By separatingthe frequencyterms from the zero diffraction order,additional description should be possible.

Weighted Pupil OPD Weighted Pupil OPD Weighted Pupil OPD 1 _..._.__._.____._.._.----.--.--..---.-...... _..-.._.._...._-...... -....-...... - . _....-...... _._.._.-...... -....-....-...... _...... _..-...... --...... -..-. .._...._...... _...*...... -...... _...... _...... -...---...-.---- . _.-.._-..--._...-.._.-..--..-..---..--..--. .._...... _._.--..-...... -.-..--..-

0.6

0.4

02 - > 0

0.4

0.0 0 8 .-.~~-.-.-.-.~.-.-~-.-.~~~.-.~.~~-.-.-.~.~.~.-~~.~~-.-~-.-.-~-.-~-.-~-~-.-~-.-~-.-..-.-.-.-.'.-.-~-.-.-.-.'.‘~-~-.-~-.-.-.-~~.-.-~-.~.-.-.~.-~-.-.-~-~-~-.-.-.-.-.-.-~ .-..-..-...---.-...... -.-.-.-.-.-----.-.--...--.-...-.-.-.-.-...-...-.-.....-.-...------.---..---...... ---..---..-..- ..__.._.._...... __..-...--....-.-.-...... _.._...... -.-...... -...-.-.... -1-1 05 05 4 I _._.__....=~____..._=_..__.._._.-.-..____.----*---- .05 ---~*~'~ IY..-...... --.-..... 05 1 -1 0.5 05 1

Figure 7a The separationof weighteddiffraction ordersfor densekl-0.4 featuresimaged with a partial coherencevalue of 0.7 in an aberratedlens.

Lens Pupil OPD ,:‘: .:- . . :.’ : __ _.:,:: _.:-.._.i I..

Figure 7b. Full pupil aberrationplot (OPD in waves)used for imaging example.

To further explorethe ideaof performingpupil statisticson individual weightedorders, individual aberrationterms are considered.Typically, 37 Zernikepolynomials are used to describean aberratedpupil with 37 associatedZemike coefficientterms. Eight of thesecoefficients will be usedfor this analysis, specificallyeven terms: defocus (24), astigmatism(Z5), spherical(Z9), 5thorder astigmatism (212), and5* order spherical (216) and odd terms : x-coma (27) x-3 point (ZlO), and 5th order x-coma (214). LensMapper[7] imaging andaberration analysis software was used for modelingand statistical analysis of J~=0.5geometry (1: 1) using a 248nmwavelength, and a 0.62NA lens , with a partial coherencevalue of 0.7. Mean and RMS OPD valueswere calculated for individual ordersand are plotted in Figures8a and 8b. The meanwavefront aberration plot (Figure8a) showsthat thereis a large differencebetween the first

300 Proc. SPIE Vol. 4000 di.B?actionorders and the zero order for defocus,astigmatism, and spherical. Figure 9 is a plot of the differencesbetween the meanof the first diffraction ordersand the meanof the zeroorder. This plot gives insight into the sensitivityof this specificimaging situation to eachindividual aberration.Even aberrations result in equivalenteffects for both first diffraction orders while odd aberrationsresult in asymmetry betweenthe orders. The value of this descriptioncan be realizedwhen theseresults are comparedto data presentedfrom earlier work basedon full aerialimage simulation [i], shownin Figure 10. This plot shows the sensitivity to focus shift for thesesame aberrations under similar imaging condition. Comparisonof kI=0.5 results shows good correlation. Since focus shift does not describeasymmetrical deviations, additionaltesting using the simulationmethod is requiredto capturethe full effectof oddaberrations. This information is alreadycontained in the frequencyplane analysis. The frequencyplane or weightedpupil methoddescribed here provides quick, interactiveassessment of the sensitivityto aberrations.

Mean wavefront aberration RMS wavefront aberration

5 -0.015 6 -0.02 -0.025 -0.03 24 z5 27 Z9 ZIO 212 214 Z16 24 25 27 z9 ZIO 212 214 Z16 Zernike # Zernike # Figure 8. Meanwavefront aberration and RMS wavefrontaberration plots of individual diffraction orders.

Aberration sensitivity ASMUZeiss data, 0.08 waves, 0.5 sigma*

-0.015 ’ 24 25 27 Z9 ZIO 212 214 Z16 24 z5 27 z9 ZIO 212 214 Z16 Zernike # Zernike # Figure 9. Aberrationsensitivity analysis using Figure 10. Full aerial imageanalysis of aberration frequencyplane or pupil description.The sensitivityfor comparison.Good agreement exists differencesbetween the first diffraction order acrossall terms. Only symmetricallyanalysis is meanand zeroorder mean are plotted. possible.

Proc. SPIE Vol. 4000 301 3.2 Evaluating the effects of sigma, OAI, and PSM

The method of image assessmentand aberration evaluation describedhere can be extendedto situationsinvolving optimizationof partial coherence,designing of phaseshift masking,or customizingof illumination. A few examplescan illustrate this.

3.2.1 The effect of partial coherence on imaging with aberrations

The influence of partial coherenceon aberrationeffects is demonstratedfor 130nmdense lines (1:l) imagedusing a 248nmwavelength and a 0.67 NA lens with the aberrationdescription of Figure 7. Weightedpupil plots are shownin Figure 11for sigmavalues from 0.7 to 0.9. Table 1 showsthe statistics on the individual ordersfor a singlepartial coherencecondition. Figure 12 showshow the calculatedRMS and meanOPD valuesvary with partial coherence. Minimization of the impact of aberrationresults with reducedaverage phase of the first diffractionorder, suggesting increased levels of partial coherencefor this situation.

Weighted Pupil OPD 0.9cr Weighted Pupil OPD 1 0.8~ 1

0.6 0.6

0.4 0.4

0.2 0.2

> 0 > 0

-cl2 -a2

-a4 -a4

-a6 -a6

-1 -1 -1 -a6 -a6 -a4 -a2 0 0.2 0.4 0.6 0.6 1 -1 -a6 -a6 -a4 -a2 0 0.2 0.4 0.6 04 1 -1 -as -a6 -a4 -a2 0 0.2 0.4 0.7 0.6 1 U U U

Figure 11. Weightedpupil plots for threelevels of partial coherence.Mask lines sizeis 13Onm(1: l), wavelengthis 248nmand NA is 0.67.

0.008 I 0.016 o*oo7 ~""------*~~~~~~ 0.007 - 0.4 0.014 3 0.006 - 0.012 T 9 5 g 0.005 - 0.010 z ti g 0.004 - 0.008 % x IE 0.003 - 0.006 i !G of 0.002 - -- 0.004 g - 0.001 l4 I---a---RMS -m + I . IAvgl -- 0.0020.0°2 -

0.000 I I I 0.000 0.5 0.6 0.7 0.8 0.9 Partial Coherence (sigma)

Figure 12. Plot of RMS andmean OPD vs. partial coherencefactor for the +first diffraction orderof Figure 11with sigrnavalues from 0.5 to 0.9.

302 Proc. SPIE Vol. 4000 LENSMAPPER PUPILSTATISTICS (XOrientation)(Waves)

Order Mean RMS PV X-Asym Y-Asym +I0 0.004387-0.00651 0.0327010.00726 0.0463550.13995 -0.00327-0.00939 -0.00651-0.0002 Table 1. Pupil statisticson individual -1 -0.00324 0.028826 0.13184 -0.00327 0.003242 ordersfor a partial +2 0 0 0 0 0 coherencefactor of -2 0 0 0 0 0 0.9. No DC -0.00488 0.021062 0.13184 -0.00327 -0.00327 Full 0.002654 0.035592 0.20841 -0.00952 -0.00112

3.2.2 Evaluating custom illumination

Designing off-axis and custom illumination requires considerationof the distribution of diffraction energyin the pupil. Defocusand aberrationneeds to be accountedfor during the designstage since the minimization of their effects is a primary goal. As an example,Figure 13 shows248nm illumination of 150nmdense lines with strongquadrupole illumination (0,=0.7 and 0,=0.2). Sincezero diffraction energy doesnot exist in this instancewhere the illumination has been optimized for these features,statistics on the entire weightedpupil are most useful. In this example,an additionalmetric is included. The asymmetrystatistic measuresthe differencein the pupil and betweendiffraction orders alongvarious directions in the pupil [ 11. Figure 13 showsasymmetry results along an X direction.

Wavefrontaberration 0.03 Figure 13. Full pupil statistics 0.025 for strongquadrupole illumination of 15Onmdense F 0.02 lines. 5m 0.015 0 .-L 0.01 G E 0.005 .-E 3 0 k a2 -0.005

24 z5 27 Z9 ZIO 212 214 Zl6 Zernike #

3.2.3 Evaluating phase shift masking

Strong phase shift masking utilizes specific portions of a lens pupil. Figure 14 shows the differencesin pupil utilization for a binary mask vs. a strong alternatingphase shift mask for imaging 130nmdense features at 248nmwith 0.67NA. The diffraction energyfor this phaseshift maskcase does not distributediffraction energyinto the centerof the pupil, similar to the situationwith strongquadrupole illumination. The sensitivityto individual aberrationtypes is shownin Figure 15where the impactfrom

Proc. SPIE Vol. 4000 303 defocusis significantly reduced,as expectedwith this masktype. The sensitivityto odd aberrationtypes, especially3-point, is increasedsubstantially. Although this evaluationis unique to the specific imaging situation, it has generallybe demonstratedthat phaseshift masking is most sensitiveto theseaberration

weighted Pupil OPD ,...... :...... _:._. . 1‘...... -...... -...... I ...... Weighted Pupil OPD i j i f ; i i i f i i i : : : : ; : i : i i ...... 3...... I ...... i ...... i ...... i : ; : i i : : : : i Figure 14. Weighted o1 i : ; : : : : : : : . . . . i . i ...... i ...... L ...... pupil plots for 130nm densegeometry using binary (left) and alternatingphase shift (right) masking.

-1

-0 c

-1 -1 03 ae -0.4 -02 0 0.2 0.4 0.6 0.e 1 ll

Mean wavefront aberration 0.03 1 Figure 15. Full pupil statisticsfor 0.025 strongphase shift maskingof 0.02 130nmfeatures. 2 0.015 > sm 0.01 z 0.005 E 0 & -0.005 0z -0.01 -0.015 -0.02 -0.025 ’ I 24 z5 27 z9 ZIO 212 214 Z16 Zernike #

3.2.4 Evaluating optical proximity correction

Whenusing OPCassist features, a pair of sub-resolutionbars is placedon either sizeof an isolated featureso that the cosinusoidalfrequency distribution in the lens coincideswith the frequencypositions of denseline diffraction orders. As this cosinefunction is addedto the diffraction pattern for the isolate feature, the diffraction pattern more closely resemblesthat of the densefeatures, reducing proximity effects.Figure 16 demonstratesthe effectthat assistfeatures have on the distribution of a maskdiffraction field. Optimizationof OPC is mostappropriately carried out with the considerationof aberration.Figure 17 showsfor examplehow OPC assistfeatures used with isolatedspaces features can improve depth of focusby reducingsensitivity to the defocusaberration. As the numberof assistpairs areadded, RMS OPD acrossthe pupil is decreased.The separationdistance of the assistfeatures is determinedto minimize the

304 Proc. SPIE Vol. 4000 defocusaberration. This separationcorresponds to a distanceof NA/I or an equivalentfrequency of UNA in the lens pupil. Furtheroptimization is possibleas other aberrationsare considered.

2.00 -

4.00 -

6.00 -

8.00 - a

Figure 16. The distributionof difEaction energyin a lens pupil for (a) denselines, (b) an isolatedline and (c) an OPC assistedisolated line.

21:1 space 0.05h w/l pair w/2 pairs w/3 pairs defocus hINA spacing l/2/3 h/NA spacing l/2/3 h/NA spacing

Weighted Pupil OPD Weighted Pupil OPD Weighted Pupil OPD Wei@ted Pupil OPD a05 ...... ~ . .._ o E...... oa5 ...... ~...... r ; f i ; f ; ; f 1

O,M . ;.~ *mo235x .; ...... aac ...... $PJJ).2~8x...... j......

o,m ...... _I ..;... ., oo3 ...... i......

I I o,a ,...... ; . . ..~...... { ..,.,...._,__. ___

.iy~ _____, i : i d , O.D, ::‘...... f. i _..._.____.~.. @.,, ; 1

il A._ : &$I 8 5 : ;f;$ v- ;.z . 0 ‘,.zRNG-~,<-..T: /+.,‘~ SC, ~.x<:,%.,- ‘$‘ >* ;p 1 I .A; < d/.2, ,

-0.02

-0.03

. . . . . _...... -0.04

-o.ffi m;-” ’ -1 -0.5 05 1 0.5 '. 0" 0.5 1 U

Figure 17. The effect of assistfeatures on the distribution of diEaction ordersin a lenswith defocus aberration. The weightedpupil OPDis plottedand RMS OPD is shownfor an isolatedspace and a space with oneto threepairs of assistfeatures, spaced VNA in the pupil.

Proc. SPIE Vol. 4000 305 4. CONCLUSIONS

Somegeneralization about imaging with aberrationcan be madebased on the conceptsdiscussed. The pupil statistics presentedbecome useful prediction methods if the consequencesto imaging are considered. More specifically, statistics on frequency terms weighted against a zero order can be predictive. The fundamentalfrequency is in most situationsmost important. Partial coherencecan reduce the overall impact of aberrationby spreadingdiffraction ordersbut the oppositemay be true for PSM and strong OAI. In general, small denseline geometryis more robust to aberrationthan small isolated geometry,leading to the possibilityof differentlens performancecriteria dependingon application. Resist thresholdingis an important factor in maximizing imaging toleranceto aberrationand modificationsto resistmaterials and processes have the potentialfor significant consequence.For lithographicapplications, defocusaberration will always be the greatestconcern as imaging is carried out over topographyand through a resistlayer. As optical lithographycontinues its extensiontoward smallerkl values,there is also an increasing needfor userinteraction with illumination design,phase mask optimization, and OPCcustomization. All of this should be carried out with the knowledgeand an understandingof the sensitivity to aberration. LensMapperTM,an imaging design,evaluation, and optimizationtool hasbeen developed to assistthe user with theseactivities [7].

5. REFERENCES

[l] B. W. Smith, “Variations to the influenceof lens aberrationinvoked with PSM and OAI,“SPlE 3679 (1999),30. [2] B. W. Smith, J.S.Petersen, “Influences of OAI on opticallens aberration,”J. Vat. Sci. Technol.B 16(6) (1998)3405. [3] D. Flagelloet al, “Towardsa comprehensivecontrol of full-field imagequality in optical photolithography,”SPIE 305 1 (1997)673. [4] C. Progler,D. Wheeler,“Optical lens specificationsfrom the user’sperspective,” SPlE 3334(1998) 257. [5] B. Smith et al, “Aberrationevaluation and tolerancing of 193nmlithography objective lenses,” SPIE 3334 (1998)269. [6] B. W. Smith, “Revalidationof the Rayleighresolution and DOF limits,” SPIE 3334(1998), 142. [7] LensMappei? is a productand trademark of LithographicTechnology Corp. (LTC), B.W. Smith (2000).

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