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Understanding Lens Aberration and Influences to Lithographic Imaging

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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 higher demandsare placed on optical lithographytools, a better understandingof 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 current and future conditionsof optical lithographyis challenging, leavingthe lithographerwith concernsthat are not easilyaddressed using conventionaloptical description. Historically, during the designand fabricationof 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 years as 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 makegeneralizations difficult and can leadaway from the developmentof underlying relationships. In this paper, we describesome of the fimda.mentaI relationships that 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 lead to a betterunderstanding about optical performanceand limitations. Figure la showsan aerial imagesimulation for line/spacefeatures of sizekl=O.35 at duty ratios rangingfrom 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 usedfor 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 higher frequencyterms 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 0.05 wavesof 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 mask pitch 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, values are 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 and first 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 aerial image(intensity) functions for denseand isolated(1:4) lines with pitch - ?JNA. The denselines are the 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 zero diffraction order comparedto the first order gives rise to problems. A photoresistprocess is generallyoptimized when it samplesan aerial image at a threshold point 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, phaseerror 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 impact on first diffraction ordersat the edgeof the lens pupil will be a correspondingphase error. For a real and evenfunction, this can be a simple cosineamplitude
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