We present an optical technique to detect cantilever deflection of an array using Fraunhofer diffraction patterns. Application areas include probe-based data storage. Intensity profiles of different cantilever arrays are captured on a CCD camera and compared with our model. These measurements are in excellent agreement with the Fraunhofer theory, less than 3% deviation is found. Each cantilever can either be deflected by a fixed amount or undeflected. Based on noise measurements on our setup and intensity patterns simulations, we predict that this method allows the measurement of 1nm deflections in an array of six cantilevers with an SNR of 35dB

Abelmann, Leon

Elwenspoek, Michael Curt

Koelmans, W.W.

Pjetri, O.

Siekman, Martin Herman

University of Twente Research Information

USING DIFFRACTION TO DETECT DEFLECTION OF THE CANTILEVERS IN AN ARRAYO. Pjetri1, W. W. Koelmans1, L. Abelmann1, M. H. Siekman1, and M. C. Elwenspoek1,21Transducers Science and Technology, MESA+ Institute for Nanotechnology, University of Twente, Enschede, the Netherlands2Freiburg Institute for Advanced Studies (FRIAS), Albert-Ludwigs-Universität Freiburg, Freiburg im Breisgau, GermanyAbstract — We present an optical techniqueto detect cantilever deflection of an array usingFraunhofer diffraction patterns. Application areasinclude probe-based data storage. Intensity profilesof different cantilever arrays are captured on aCCD camera and compared with our model. Thesemeasurements are in excellent agreement withthe Fraunhofer theory, less than 3% deviation isfound. Each cantilever can either be deflected bya fixed amount or undeflected. Based on noisemeasurements on our setup and intensity patternssimulations, we predict that this method allows themeasurement of 1nm deflections in an array of sixcantilevers with an SNR of 35dB.Keywords — Cantilever array, diffraction, opticalreadout, probe storageI – IntroductionCantilever arrays are used in many applications likeprobe-based data storage [1], probe based nano-lithography and nano-manufacturing. In many casesfeedback of the cantilever position is needed. A com-mon way to achieve this is by integrating a sensor onevery cantilever like piezoelectric [2], thermal [3] andmagnetoresistive. These techniques present complexityof fabrication and constrains on the cantilever design.Optical readout on the other hand is separated from thearray, does not put any constrains on the fabrication andcantilever design, and is simple to incorporate.Sensing of cantilever deflection using diffraction pat-terns was first introduced by [4], by fabricating a gratinginside a cantilever which creates a diffraction pattern.Later, this technique is extended to parallel operationand capturing on separate detectors [5]. We present anew scheme where the cantilevers themselves form anoptical grating so that the state of deflection of each can-tilever within the array determines the diffraction pat-tern, as is shown in figure 1. We consider the situationswhere the cantilevers can only be in two states: unde-flected or deflected by a fixed amount.Detection of the diffraction patterns can be performedby comparing measured patterns with calculated pat-terns stored in a look-up table. This is, however, notthe most efficient way. In [6], fast, low complexity de-tection algorithms are presented to retrieve the state ofthe cantilevers from the measured intensity profiles. Inthis paper we focus on the experimental verification andquantification of the change in the diffraction patterns.polymer sampleRDetectorw p n-th probeLaser beamθS0101Figure 1: Schematic of the optical readout using Fraunhoferdiffraction patterns. A line shaped laser beam illuminates thearray. The reflected light from the cantilevers will give riseto a diffraction pattern which is captured by a CCD camera.Small deflections of the cantilevers will result in different in-tensity patterns.II – TheoryWhen coherent laser light is focused on the array,the phase of the reflected light waves depends on theamount the cantilevers are deflected. This change inphase results in a different interference on the screenthus changing the intensity pattern. To be in the Fraun-hofer region it must hold: F  1, where F is [7]:F =a2Rλ(1)where a is the radius of the aperture, λ the wavelengthand R the distance between the array and the camera.Because the thickness of the line shaped beam incidenton the array is much smaller than the length of the can-tilevers, we consider the one dimensional Fraunhoferintegral. The equation of the intensity profile on thecamera is then given by:I (x) = I (0)sinc2(qw2)∣∣∣∣∣N−1∑n=0 e−i(2ks+qnp)∣∣∣∣∣2(2)where I (0) is the irradiance at the center of the screenwith no cantilever deflected, s the deflection, k thewavenumber, w the cantilevers width, p the cantileversperiod, n the cantilever index and q = kxR with R beingbe the distance between the array and the screen wherethe diffraction pattern is measured while x representsthe coordinate on the screen.A. A figure of merit for diffraction patternsIn order to quantitatively evaluate the difference be-tween two intensity patterns, a figure of merit is pro-posed based on the area between two intensity profiles,Page 278∆IP =√√√√√√√∫profile[IP1(θ)− IP2(θ)]2 dθ∫profileIP1(θ)2dθ100% (3)where IP1 and IP2 are the two intensity profiles to becompared.III – ExperimentalA schematic of the setup is shown in figure 3. The spotfrom a laser diode with a wavelength of 635nm and3mW power is expanded five times using a beam ex-pander. This expanded beam is then passed through arectangular shaped aperture of 15mm width and 10mmheight. The resultant beam is focused on the array by acylindrical lens with a focal length of 200mm. This wayall cantilevers are illuminated by a line-shaped coherentbeam of 15mm wide and 80µm thick. Because the laserspot is not exactly at the tip end of the cantilever, themeasured deflection is smaller than the deflection at thetip.The diffraction pattern created by the reflected lightfrom the array is reflected by a second prism onto an-other cylindrical lens with a focal length of 60mm androtated 90◦ with respect to the first lens. The diffractionpattern is then projected onto a CCD camera positionedin the back focal plane of the second lens. By placingthe image plane in the back focal plane of the lens, theFraunhofer diffraction pattern can be observed indepen-dently of the distance between the array and the lens:the image plane is placed effectively at infinity [8]. Us-ing a lens has several advantages: the size of the diffrac-tion pattern can be tuned with the focal length of the lensand also the optical path can be shortened using a lenswith a shorter focal length. The camera has a resolutionof 2048x1536 pixels and a pixel size of 5µm.The cantilever array is mounted on two slip-stick mo-tors on top of each other: one allows the adjustmentof the roll-angle of the array and the other allows thecourse positioning in the z-direction (normal to the sam-ple surface).Measurements were performed with arrays withouttips as these are easier to fabricate. Because this methodis based on the phase shift introduced by the differencein height of the reflective surface of the cantilevers, it isvery important that the cantilevers thickness be as uni-form as possible and that their surface be as coplanar aspossible. The cantilevers are etched out of the devicelayer of a SOI wafer, which therefore determines theuniformity of the reflecting surface height of the can-tilevers. The fabrication process is similar to that de-scribed in [9], with exclusion of the steps that define thetips. A SEM photo of an array with four cantilevers,14µm wide, 250µm long and 3µm thick, is shown infigure 2.In order to deflect certain cantilevers in an array, amedium was fabricated consisting of a silicon wafer50 µmFigure 2: Scanning electron micrograph of an array with fourcantilevers 15µm wide and a pitch of 25µm used to measurethe patterns shown in figure 4, 7 and 6PrismsMediumLaser CCDSlitCylindricallensf1 = 200mmCylindricallensf2 = 60mmzCantileverarray4°Figure 3: Schematic of the setup used to measure diffractionpatterns. An expanded laser beam is first passed through arectangular shaped aperture and then focused by a cylindricallens on the array. The second cylindrical lens projects thediffraction pattern on a CCD camera.with etched pits of varying size in order to match thecantilevers width and pitch. The medium is mountedon a xyz stage used for fine positioning. By moving themedium in the z-direction, certain cantilevers are de-flected when they touch the medium, while others fallinto the pits, thus remaining undeflected.A. Analyzing CCD imagesIn the recorded CCD images the angle of diffraction,which is approximately equal to x/R (with x and R be-ing defined in equation 2), is oriented horizontally. Thecaptured images are averaged over 200 lines in the ver-tical direction in order to minimize the influence of dustand particles. After this averaging, low pass filtering isperformed to remove high spatial-frequency noise. Allthe post-processing of the images is done in MatLabsoftware.IV – ResultsA. Diffraction patterns with no cantilever deflectionOur first experiment was performed in order to checkthe accuracy of our model. To avoid aberrations, thesecond lens in the optical path ( f2 = 60mm) was re-moved. The CCD camera was placed at a distance of70mm from the array. An array with five cantileverswas used having a width of 14µm and a pitch of 20µm.The array is not in contact with the medium underneathso that all cantilevers are undeflected. The measured in-Page 279−0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.0800.20.40.60.81Difraction angle (rad)Normalized intensity  MeasurementSimulation101Figure 4: Calculated and measured intensity profile of thediffraction pattern created by an array of five undeflected can-tilevers. The numbers near the maxima indicate the zeroth-and first-order maxima. The ∆IP between theory and mea-surement, as defined in equation 3 is 3%.tensity profile and calculated are shown in figure 4. Theerror of fit according to equation 3 is smaller than 3%,showing the measurements are in excellent agreementwith theory.B. Introducing cantilever deflectionIn the next set of experiments we introduce cantileverdeflection. Here we use an array of three cantilevers30µm wide and a pitch of 40µm where the outer twocantilevers are deflected by the same amount. Withincreasing deflection, the zeroth-order maximum de-creases while the first-order maxima increase (figure 4).The ratio of the zeroth-order and first-order maxima isused as a measure of cantilever deflection. Figure 5shows the calculated and measured ratio as a functionof deflection. These measurements are in good agree-ment with theory for deflections up to 440nm. Fur-thermore, figure 5 shows that the sensitivity of thistechnique changes based on the deflection point aroundwhich the cantilevers are operating. Maximum sen-sitivity is achieved when the cantilevers are operatingaround a deflection bias of 30nm and lowest sensitivitywhen operating around 159nm (1/4 λ ).C. Offset in deflectionsWe illustrate the effect of biasing using an array offour cantilevers having a width of 14µm and a pitch of25µm. The outer right cantilever is deflected in steps of50nm. The deflection at the center of the spot is cal-culated to be 23nm. For this array and deflected can-tilever, we calculated the most sensitive biasing pointto be 1/4 λ . First we measure two intensity profileswith 22nm biasing. These two profiles for h = 22nmand h = 45nm are shown in figure 6. The calculated∆IP for this pair is found to be 17.6%. Next, we mea-sure another pair with 136nm biasing: h = 136nm andh = 159nm. These two patterns are shown in figure 7.∆IP in this case is calculated to be 32.2%. This is a0 100 200 300 40010 010 1Deflection (nm)Ratio  MeasurementCalculationFigure 5: The ratio of the amplitudes of the zeroth mode max-imum to the first mode maxima as function of deflection foran array of N = 3 with the two side cantilevers bended. Themeasurements are in good agreement with the model.−0.06 −0.04 −0.02 0 0.02 0.04 0.0600.20.40.60.81Diraction angle (rad)Normalized intensity  22nm45nmFigure 6: Two normalized diffraction intensity profiles createdby an array of four cantilevers with its outright cantilever bentat 22nm and 45nm. The ∆IP as defined in equation 3 for thispair is 17.6%.factor 1.83 better compared to the case where 22nm bi-asing was used.D. Noise measurementIn order to give a quantitative evaluation of the capa-bility of this technique, noise measurements were per-formed on an array with six cantilevers, 19µm wide and30µm pitch. A hundred patterns were measured withone second interval and 9ms exposure time giving abandwidth of 111.1Hz. The patterns were corrected fordrift. Noise amplitude for each measurement was cal-culated using equation 3 with IP1 being the measuredintensity profile and IP2 the calculated profile. The stan-dard deviation of ∆IP (n) is a measure for the noise level.The signal amplitude of the same array is calculatedwith the outer right cantilever deflected at 159nm and160nm. We use equation 3 with IP1 and IP2 being thesimulated intensity profiles of the two deflections. To-gether with the noise level calculated above, this leadsto an SNR of 35dB.Page 280−0.06 −0.04 −0.02 0 0.02 0.04 0.0600.20.40.60.81Diraction angle (rad)Normalized intensity  136nm159nmFigure 7: Two normalized diffraction intensity profiles createdby an array of four cantilevers with its outer right cantileversbent at 136nm and 159nm. The ∆IP as defined in equation 3for this pair is 32.2%.0 0.1 0.2 0.3 0.4 0.50.20.40.60.811.21.41.6Deection bias (λ)ΔI P(%)  [101][011][11011][10111]Figure 8: Simulated ∆IP for 1nm deflection at different off-sets for different cantilever arrays. “1” and “0” representundeflected and deflected cantilevers respectively. Sensitivitydiffers per array and per set of deflected cantilevers.V – DiscussionMeasurements show that diffraction patterns are verysensitive to cantilever deflection. Sensitivity can be in-creased by biasing the cantilevers at a certain deflection.The simulations in figure 8 show that the exact amountof bias for optimal performance differs per array andalso per set of cantilevers that are deflected. Instead ofa CCD camera, a photodiode array could be used to in-crease bandwidth and resolution resulting in faster andmore accurate measurements.We expect thermal noise to be negligible comparedto shot noise, especially with increasing laser power.Moreover, when used in information storage, the can-tilevers will be supported by the sample where the datais stored, further reducing thermal noise.VI – ConclusionIn this work we show that parallel optical readoutof cantilever arrays can be achieved by analyzing thediffraction patterns created by such arrays when illu-minated by a line shaped laser beam. The diffractionpattern obeys the one-dimensional Fraunhofer theory.Noise measurements on our setup and intensity profilesimulations predict that a 1nm deflection of individualcantilevers can be detected with a SNR of 35 dB, in abandwidth of 111Hz.Sensitivity can be improved by biasing the cantileversdeflection. The exact amount of bias for optimalperformance differs per array and also per set ofcantilevers that are deflected. For an array of fourcantilevers, with the outer right cantilever deflected, wemeasured a signal improvement of a factor 1.83 whenthe cantilever is biased by 136nm.References[1] A. Pantazi et al., “Probe-based ultrahigh-densitystorage technology,” IBM J. Res. Dev., vol. 52, no.4-5, pp. 493–511, 2008, doi:10.1147/rd.524.0493.[2] C. S. Lee, H.-J. Nam, Y.-S. Kim, W.-H. Jin, S.-M. Cho, and J. uk Bu, “Microcantilevers in-tegrated with heaters and piezoelectric detec-tors for nano data-storage application,” Appl.Phys. Lett., vol. 83, no. 23, pp. 4839–4841, 2003,doi:10.1063/1.1633009.[3] W. P. King, T. W. Kenny, K. E. Goodson, G. Cross,M. Despont, U. Durig, H. Rothuizen, G. K.Binnig, and P. Vettiger, “Atomic force micro-scope cantilevers for combined thermome-chanical data writing and reading,” Appl. Phys.Lett., vol. 78, no. 9, pp. 1300–1302, 2001,doi:10.1063/1.1351846.[4] S. R. Manalis, S. C. Minne, A. Atalar, and C. F.Quate, “Interdigital cantilevers for atomic forcemicroscopy,” Appl. Phys. Lett., vol. 69, no. 25, pp.3944–3946, 1996.[5] T. Sulchek, R. J. Grow, G. G. Yaralioglu, S. C.Minne, C. F. Quate, S. R. Manalis, A. Kiraz,A. Aydine, and A. Atalar, “Parallel atomic forcemicroscopy with optical interferometric detection,”Appl. Phys. Lett., vol. 78, no. 12, pp. 1787–1789,2001, doi:10.1063/1.1352697.[6] J. Van Honschoten, H. W. De Jong, W. W.Koelmans, T. P. Parnell, and O. V. Zaboronski,“Information storage and retrieval for probe storageusing optical diffraction patterns,” submitted, 2011.[Online]. Available: http://arxiv.org/abs/1104.0871[7] E. Hecht, Optics. Addison-Wesley, 2002.[8] F. Träger, Springer Handbook of Lasers and Op-tics. Springer, 2007.[9] W. W. Koelmans, T. Peters, L. Abelmann, andM. C. Elwenspoek, “Fabrication of cantileverarrays with tips for parallel optical readout,” inProc. Micromechanics and Microsystems Europe,Enschede, The Netherlands, 26-29 Sept. 2010.Page 281

English

Using diffraction to detect deflection of the cantilevers in an array

NARCIS 

https://ris.utwente.nl/ws/files/5445284/MME_Pjetri.pdf

Using diffraction to detect deflection of the cantilevers in an array

Abstract

Similar works

Full text

Available Versions

University of Twente Research Information

NARCIS