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Ultrasonic Monitoringof Photoresist Prebake Using TOF Measurement S.L. Morton, *A. Hansson, andB.T. Khuri-Yakub Edward L. Ginzton Laboratory, Stanford University, Stanford, CA 94305 *Information Systems Laboratory Abstract - We have measured the time of flight (TOF) through a 4 silicon wafer with and without a 1 . 8 ~ m coating of Shipley 1813 positive photoresist. The TOF change from hare to coated wafer was measured three times on a single wafer; the average the of three experiments was a TO
  Ultrasonic Monitoring of Photoresist PrebakeUsing TOF Measurement S.L. Morton, *A. Hansson, andB.T. Khuri-YakubEdward L. Ginzton Laboratory, Stanford University, Stanford, CA 94305*Information Systems Laboratory Abstract - We have measured the time of flight (TOF) through a 4 silicon wafer with and without a 1.8~mcoating of Shipley 1813 positive photoresist. The TOFchange from hare o coated wafer was measured threetimes on a singlewafer; the verageof he hreeexperiments was a TOF of 14.311s (+/-Z.Sns), consistentwith the calculated expected results. In order to increasethe precision of the TOF measurement to the level neededfor prehake monitoring, we have applied a least squaresalgorithm to estimate the transfer function between theechoandreceived waveforms. Results of pulsed datadeviation of the TOF measurement from 2.93ns to 2.5311sstudies indicate that we can get a decrease in the standardby determining heTOF rom the estimated ransferfunction. In current -line and deep-UV ithography, in situ INTRODUCTION monitoring of photoresist processing is not required tosurpasses sub-quarter micron, it is expected that the resist meet designbjectives.However,seatureize materials will be more sensitive to processing conditionssuch as prebake and postbake time and temperature. It isnecessary o prehake photoresist prior o ithographicexposure so that the solvent initially added to decreaseresist viscosity can he evaporated, and the resin polymerchains can relax into an ordered array. If the solvent isn'tfully evaporated or if the prehake time is too long, thenthe feature size may not he as small as expected.the prebake process. Metz, et al. (1991) performed real-There has been some research in endpoint detection oftime measurement of resistfilm hicknessonsilicon They determined resist thickness versus spin and bakewafers using multi-wavelength reflection interferometry.time. This method was used to monitor non-uniformitiesfor tatisticalprocesscontrol. In 1992,Metz, et al. reported on similarxperiments itheal-timephotoresist monitoring to optimize the hake time and spinspeed.have pplied ltrasonicechnologytomonitoringAt the Edward L. Ginzton Laboratory,several authorssemiconductor rocesses.Lee, et al. (1993, 1996)developed an ultrasonic echnique in order to measuretemperatureduring rapidhermal rocessing.Lamb waves were excited in the wafer, and the change in wavevelocity was monitored as the wafer temperature varied.Thewavevelocitydecreased inearlyas emperature increased. In relatedwork,Degertekin, et al. (1993,effect of thinfilms on this ultrasonicmeasurement of1994)appliedultrasonic hermometry to measure thewafer temperature.This echnology will be useful in monitoring resist prehake since the wafer temperatureand resist ilm hickness will change as thewafer sheated and the solvent evaporates.First,weonductedxperiments in ordero METHOD characterize the wave velocity in the coated and prehakedfunctions that described the relationship between the echowafer.Thenwedentified ontinuous-timeransfer and received acoustic signals. The transfer function wasused to calculate an estimated TOF that was expected tohe more precise than the current zero crossing techniquefor determining TOF. &sist Cha In order to characterize the effect of a thin film of racterization BY Time of Flieht Measurement photoresist on Lambwavepropagationvelocity in silicon, we measured the TOF change before and after thewafer was coated with resist.The method or TOF measurement was described previously by Lee, et al. (1996). Briefly, Lamb waves were excited in a siliconwafer by aquartzpinpiezoelectric ransducerand detected by an identicalransducer.The TOF wasdetermined by the time differencebetween a chosen zerocrossing in the echo waveform reflected from thepin/wafer nterfaceand he eceivedwaveform hatpropagates through the wafer to the second transducer. A Interval Counter wasused to measure the time differenceStanfordResearchSystemsSR620UniversalTime between the two zerocrossings. Figure I: Experimental setup with two quartz transducerpins contacting a 4 wafer placed on an aluminum plate. 0-7803-3615-1/96/$5.00 0 996 IEEE 1996 WEE ULTRASONICS SYMPOSIUM - 013  The wave propagation velocity can then be determinedfrom the TOF and the spacing between theins.fabricated by epoxy bonding a cylinder of 5H PZT, 5mmFor heseexperiments,200kHz ransducerswere in height and 3mm in diameter, to a 4 long quartz pin3mm in diameter. The tip of the quartz pins were cut to a radius of curvature of lOcm to provide good contact forhigh signal transmission without the problem f multiplecontact sites. The pin was designed to be 4 long so thatthere would be at least 5 cycles of 2M)kHz signal beforereflections from the pidwafer contact ould be seen.The experimental setup is shown in Figure 1. A 4 silicon wafer <]M)> doped with boron to a resistivity of 8-12 ohm-cmwasplaced on an aluminumplateandcontacted from above by the two transducers. A voltagepulse (-4M)V) was applied to the transmitting transducerand the echo and received signals monitored. The TOF was hen determined using he zero crossing method;measurements were taken with the transducers raised andcoatedwith .8pmofShipley1813photoresist o a lowered between each data point. The wafer was thenplanarityof +/- SO,& along hesignalpath.After he cleanroom to the measurement setup in a dark containerwaferwas rebaked,twasransferredromhe to prevent exposure. The resist side was placed downonto the aluminum plate with the pins contacting theopposite side. Double-side polished wafers were used tomaintain a reproducible contact. The measurement wasrepeated and the delta TOF from hare wafer to resist-coated wafer calculated. The wafer was then stripped ofresistand heexperiment epeated womore imes. Results were compared with expected results calculatedfrom heory.Wafer hicknesswasmeasuredusing aThicknesswasmeasured t S locations longheLeitz height gauge with 1M)mm range and lpm accuracy.propagation path and averaged.change in TOF through a wafer with and without resist;The goal of these measurements is to determine theexpected values are in the range of 12-14ns, depending on the wafer thickness. Transfer Function Estimation Our goal is to measure the changen TOF as the resistchanges rom a liquid o olidduringprebake.The expected change in TOF for this 90 second process is - 2ns, much ower han he change from bare wafer oresist above. The 2ns includes changes n resist thicknessand changes in the elastic properties of the resist. A TOF distinguish this change.resolution of less han0.lnsec will be equired to measurement, we have developed Least Squares fit to aInorder o ncrease heprecisionof heTOF continuous-timeransferunctionmodel of therelationship between the echo and received signals.A set of sample signals to be modeled are shown in Figures 2 and 3. The echo signal in Figure 2 will be hemodelinput. u(t), and the received signal in Figure 3 will be themodel output, y(t). Data was collected with a at 2SOMHz 8 bit digitizer. In the time domain, the model s set up as follows: A(p)dr) = B(p)u(r - ) + E(f) -3 0 10 20 30 40 50 60 Time (vs) Figure 2: Sample echo signal for modeling 0 10 20 10 40 50 60 Time (bs) Figure 3: Sample received signal for modelingwherep s hederivativeoperator, ~(t) s the esidualerror and, where: ~(p) pn + I, p -' +...+a, B(p) = b,,p + b,p -' + ... + b, In the Laplace domain: Y(s) = G(s)e' 'U(s) + E(s), where C(s) = - Theparameters to beestimatedare .=[R, ... b = [b, __. ,] , and Z. he input and output signals willbe filtered with a bandpass filter C,(s) to give: B($) A(s) T u,(t) = C,fp)u(f) Y,(d = C,(P)Y(C The filtered equation reads: A(P,)Y,(I)=B(P)LI,(I-~T)+&,(~) and can be ewritten as a linear regression: 1014 - 996 IEEE ULTRASONICS SYMPOSIUM  o=[-aT b'] For a fixed Z is a leastsquaresproblemwhichcanbesolved in astraightforward way (Johansson 1993).The functionV(Z) has several local minima, but it islocally quasi-convex. By evaluating Figures 2 and 3, it is possible o determine in which nterval hereexists alocal minimum that captures the time-delay Z betweenthechondeceivedignals.Toindheocal minimum once the nterval is known, a polynomialinterpolationmethodcombinedwithGoldenSearch techniques was used (Gill et al., 1981). The filtration ofthe signals was performedn Matlab using a Runge-Kuttaordinary differential equation (ODE) solver. Data pointsobtainedby inear nterpolation.Optimizationof 7, inbetween hoseproduced by theODEsolverwere U, and b was performed for pulsed transducer excitationsignals. The model order used here was n = m = 4, and of pointswas imited oprevent he nclusion of 8000 points were included in the estimation. The numberonset of unwanted reflections from the in and the waferreflections. In Figures 2 and 3, the primary signal and theedgeredentified.heeflectionsccurring immediatelyafter he ignalsrcinate rom he pingeometry and are included in the estimation. In Figure 3, I,~ and C,?,& are he nitial and final values used in theof the received signal at bout 20~s. he finalvalue wasestimation. The former was countedfrom thebeginningchosen based on the point at which edge reflections wereseen in the signal. The total number of points in eachsignal as plotted s 15,000. Resist Characteriaztion Figure 4 shows the change in TOF through 4.5cm of a single wafer before and after it was coated with resist.The first ten trials are measurements without resist andthe second ten trials were obtained after the wafer wascoated with resist and prebaked. Noise of about +/-3ns occurred when the 1.8$m film of resist wasspun onto thewas measured. An abrupt change in TOFof about 1411s wafer.Thisvaluewas lose o hat xpected rom theoretical alculationsFigure 5) forhe 30pmthickness of this wafer.Figure S is a plot of expected change in TOF uponaddition of photoresist for different wafer thicknesses.This plot was used to determine the expected value forthe 53Opm thick wafer. The expected ncrease can beseenoebout 13.211s. Theveragefhree RESULTSexperiments on the same 530pm thick wafer was 14.3ns valuewere within the noise rangedeterminedabove. witha variation of +/-2Sns. Errors from he expected Transfer Function Esiimation estimationcangive an estimateof 7 with a standardResults ndiiate hat heuse of transfer unctiondeviation that is less than that associated with the use ofstandard deviation of the Z stimates for 10 sets of echothe zero crossing method for determining the TOF. Theand received signal waveforms was found o be as low as 2.53ns. This is compared with a value of 2.96ns standarddeviation found by applying the zero crossing method tothe same waveforms. It should be noted that the valuesof 7 andTOF renot xpected to be he ame.However, he actual value of the estimated TOF wascalculated from separate theory not presented here andresulted in the same standard deviation as that of T . CONCLUSIONS Results of photoresist haracterization tudiesindicate that the measured change in TOF of 14.311s +/- 2.5ns is withinmeasurement oise ange of theexpected value of about 13.2ns for the 30wm 4 wafer,Results of transfer functionestimation indicate that 16.245 16.24 3 6.235 E 16.225 6.23 m ella TOF = 14 ns h 1 16.22 04 8 I2 16 20 Trial # Figure 4: TOF results from single wafer, first 10 trialsarewithoutresist,second IO are after resist has beencoatedhaked. 13 l,, , ,-, , ,, , , , ,, ,I :, ,y 12s 510 515 520 525 530 535 540WuferTlickne% Urn) Figure 5: Results of three experiments on same wafer,theoreticalandexperimental esultsare hown.Each experimental result is the average of ten measurements. 1996 IEEE ULTRASONICS SYMPOSIUM - 015  determining TOF by transferfunctionestimationcan predict he value of TOF with greater precision hanwhen t s determined by the zero crossing echnique.The standard deviation was decreased by 14% with theleast squares tit estimation. The deviations obtained were for data digitized with an 8 bit digitizer and would beexpected to be lower in both cases with an increase insignal o noise ratio. The analog measurement is stillmore precise (to <0.5ns) but we hope o mprove hedigitization and signal processing to obtain digital resultsthatreetterhanheorrespondingnalog measurements.ACKNOWLEDGEMENTSdeveloping he heoretical nalysis of LambwaveWe would like to acknowledge F.L. Degertekin for propagation that was used in this research. This researchwas supported by a multidisciplinary research initiativegrant from ARPA and by the Swedish Research Council for Engineering Science contract #S-838. REFERENCES [I] Degertekin, F.L., et al. Proc. 1993 IEEE UItrusonics Symposium, Part 1, Vol. I, 1993, pp. 375-377. Symp, Vol. 3, 1994, pp. 1337-1341. Press, London: 1981, p. 92.[2] Degertekin,F.L., t al. 1994 IEEE Ultrasonics [3] Gill, P.E., et al. vs, cademic [4] Johansson, R. “LinearRegression,” Chapter 5 in1dentification.Prentice Hall, Inc., Englewood Cliffs,NJ, 1993.. Meeting, pp. 187-190. Control, and Clustering, SPIE, Vol. 1594, 1991, [S] Lee, Y.J., et al. 1993 IEEE In? Electron Devices [6] Metz, T.E.. et al. Process Module Metrology, pp. 146-152.[7] Metz, T.E., et al. Semic. InternationaI, Feb 1992, [8] Lee, Y.J.. et al. IEEE Trans Semic Munuf, Vol. 9, pp. 68-9. No. 1,Feb 1996,pp. 115-121. 1016 - 996 IEEE ULTRASONICS SYMPOSIUM
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