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A novel optical waveguide microcantilever sensor for the detection of nanomechanical forces

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A novel optical waveguide microcantilever sensor for the detection of nanomechanical forces
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  2132 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 5, MAY 2006 A Novel Optical Waveguide Microcantilever Sensorfor the Detection of Nanomechanical Forces Kirill Zinoviev, Carlos Dominguez, Jose Antonio Plaza, Víctor Javier Cadarso Busto, and Laura M. Lechuga  Abstract —This study presents a novel generic multipurposeprobe based on an array of 20 waveguide channels with micro-cantilevers acting as optical waveguides operated in the visiblerange. The principle of operation is based on the sensitivity of energy transfer between two butt-coupled waveguides to theirmisalignment with respect to each other. The technique can beconsidered an alternative to the known methods used for thereadout of the nanomechanical response of microcantilevers to theexternal force exerted on them. The cantilever displacement canbe detected with a resolution of 18 fm / √  Hz. The limit is generallydefined by the shot noise of a conventional photodetector used forthe readout of the output signal. Real-time parallel monitoring of several channels can be realized. In contrast to devices based onthe atomic force microscope detection principle, no preliminaryalignment or adjustment, except for light coupling, is required.The detection of the cantilever deflection at subnanometer rangewas demonstrated experimentally.  IndexTerms —Beam-propagationmethod,microcantilevers,mi-crooptoelectromechanical system (MOEMS), optical waveguide,silicon technology. I. I NTRODUCTION U LTRATHIN microcantilevers produced by standard sili-con technology possess low spring constants and allowhigh sensitivity while combined with a detection system basedon the atomic force microscopy (AFM) principle in which alaser beam reflected off the cantilever surface is monitoredwith a position-sensitive photodetector (PSD) located somedistance off the chip. Subangstrom resolution provided by themethod allows the detection of changes in deflection or inresonant frequency of the cantilever caused by any kind of reaction occurring on its surface. The principle has recentlybecomewidelyusedinbiologicalresearchand,inparticular,forthe readout of the nanomechanical response of microbeams tobiospecific interactions produced on one side of the cantileversthat result in the bending of the beams [1], [2]. In general, the systems using PSD work very well. Thetypical value of sensitivity defined as a fractional change in thedetected output signal per unit displacement of the cantileveris about  10 − 3 nm − 1 [3]. The typical value of deflection noise Manuscript received July 28, 2005; revised January 17, 2006. This work wasdone within the Optonanogen project supported by the EC under Grant IST-2001-37239.K. Zinoviev, C. Dominguez, J. A. Plaza, and V. J. Cadarso Busto arewith the Instituto de Microelectronica de Barcelona, Centro Nacional deMicroelectronica, Consejo Superior de Investigaciones Científicas, CampusUniversidad Autónoma de Barcelona, Barcelona 08193, Spain (e-mail: Kirill.Zinoviev@cnm.es).L. M. Lechuga is with Instituto de Microelectronica de Madrid, Madrid28760, Spain.Digital Object Identifier 10.1109/JLT.2006.872315 density (DND) is in the range of 100–1000 fm / √  Hz. To ourknowledge, the best noise density obtained in experiments,reported by Fukuma  et al.  [4], was 17 fm / √  Hz. However,to reach this sensitivity, one requires high stability in thefunctionality of each unit: the source, the sensor, and thedetector. Temperature and vibration control are essential inthe experiments. Chip replacement normally requires readjust-ment and realignment. As long as the transducer (cantilever)and the monitor (PSD) are separated in space, the systempossesses too many degrees of freedom, which introducesambiguity in the interpretation of its behavior.Among the other principles used for the detection of can-tilever displacement, the highest sensitivity was demonstratedwith optical interferometers [5], where DND was 6 fm / √  Hz.However, this principle has not been used in commerciallyavailable AFMs [4]. Cantilevers with piezoresistive readoutsare less sensitive, with their typical sensitivity being in theorder of   10 − 6 nm − 1 [6], but have the advantage of permittingintegrated devices requiring less adjustment and alignment.Spatial integration of the system, which implies placing all oras many components as possible on one chip, would help toincrease the reliability and repeatability of the measurements.The arrays of cantilevers with piezo are compact and frequentlyfacilitate operation in nontransparent liquids [6], [7]. Integrated optical sensor systems are small, relatively easy toproduce, sensitive and versatile tools [3], [8]–[10]. Integrated optics sensors with cantilevers have been realized before basedon the following: 1) a fiber cantilever used to detect displace-ments with 600 fm / √  Hz DND [9], 2) optical microcantileversintegrated with multimode interferometer [10], and 3) a con-ventional GaAs cantilever integrated with a Bragg grating as aphotoelastic strain sensor with a sensitivity of   10 − 3 nm − 1 [3].Availability of arrays of the cantilevers allows more versatileand sophisticated experiments to be performed. The probabilityofresultsbeingmisinterpretedcanbesignificantlyreducedwiththe presence of reference channels. Several different reactionscan be conducted and monitored on one chip [11], [12]. In this paper, we propose an integrated waveguide cantileversensor composed of an array of 20 independent waveguidechannels designed for monitoring biospecific reactions. Thesensor can work in static or dynamic modes, either by monitor-ing the deflection or by monitoring the changes in the resonancefrequency of the cantilever. The principle of operation is basedon the dependence of coupling efficiency between two butt-coupled waveguides on their misalignment with respect toeach other. The advantage of the device is that the transduceris integrated with the receptor on one chip, and the exter-nal photodetector is only used for optical power readout. No 0733-8724/$20.00 © 2006 IEEE  ZINOVIEV  et al. : WAVEGUIDE MICROCANTILEVER SENSOR FOR DETECTING NANOMECHANICAL FORCES 2133 Fig. 1. Schematic view of the sensor. preliminary alignment or adjustment is needed, except for lightcoupling into the chip, which does not seriously affect theperformance of the device if the coupler is well designed. Inthis paper, there were two main objectives that we aimed toachieve, namely 1) to prove experimentally that the device canbe fabricated with waveguide cantilevers being flat so that theirinitial deflection is less than 1  µ m and are initially aligned withstatic waveguides and 2) to demonstrate that the sensitivity of the device is comparable to the one of the AFM principle-basedinstruments.II. P RINCIPLE OF  O PERATION AND  T HEORETICAL A NALYSIS OF  S ENSITIVITY The “heart” of the sensor is an optically transparent can-tilever beam of submicrometer thickness acting as an opticalwaveguide. Light from the cantilever is injected into the outputwaveguide, called the receptor, separated from the cantilever’sfree end by a short gap  ∆ X   (see Fig. 1). Both the cantilever andreceptor are total internal reflection (TIR) waveguides, and onlythis type of waveguide is treated in this paper. If the gap  ∆ X   isin the order of several micrometers, the energy transmitted intothe receptor changes dramatically with the displacement of thecantilever’s free end in the transversal direction z . The idea wasto monitor the changes in the power transmitted into the outputwaveguide to register the deflection of the cantilever.To study the potential abilities of the device, single-modeoperation was analyzed. We modeled the performance for thezero- and first-order waveguide modes separately, considering afreestanding waveguide cantilever able to move in a transversaldirection and an output waveguide fixed to a substrate. Thestructure was assumed to be surrounded by air. Only transverseelectric (TE)-polarized modes (electric field is parallel to the Y  -axis, see Fig. 1) were analyzed. All the simulations weredone for 0.7- µ m-thick silicon oxide cantilever (refractive in-dex, 1.46) and 0.12- µ m-thick silicon nitride output waveguide(refractive index, 2.0).The built cantilevers are wide (40  µ m) and so are the low-order longitudinal modes, which, after exiting the cantilever,suffer negligible divergence in the horizontal plane (XOY). Atthe same time, highly confined transversal modes diverge veryquickly in the vertical plane (XOZ) so that the energy densitybecomes inversely proportional to the distance. Using the finite-difference beam-propagation method (FDBPM) [13], [14], we built a two-dimensional (2-D) distribution of the electric fieldin the vicinity of the cantilever exit and approximated it by theLorentzian function. Approximation for the zero-order modewas given by the expression E  0 ( z,x ) = 2 A 1 ( x ) π   A 2 ( x )4 z 2 + [ A 2 ( x )] 2   (1)where  A 1 ( x ) = 0 . 6 x + 1 . 24  and  A 2 ( x ) = 1 . 02 x − 0 . 07 . Itwas assumed that  x  = 0  at the cantilever end. The field of thefirst-order mode was approximated by the two Lorentzian peaks E  1 ( z,x )= 2 A 1 ( x ) π ×   A 2 ( x )4( z + A 3 ( x )) 2 +[ A 2 ( x )] 2 −  A 2 ( x )4( z − A 3 ( x )) 2 +[ A 2 ( x )] 2  (2)where  A 1 =2 . 82+9 . 64 exp( − 0 . 21( x − 4 . 2) 2 ) ,  A 2 = − 0 . 35+1 . 87 x − 0 . 08 x 2 , and  A 3  = − 0 . 167 + 0 . 657 x − 0 . 216 x 2 +0 . 027 x 3 . Both approximations are valid for  x  containing in therange from 1 to 6  µ m.The electric field of the fundamental mode of the outputwaveguide was built on the basis of a solution of Maxwell equa-tions and the propagation constants derived from the dispersionequation [15].The coupling efficiency was calculated using the overlapintegral [16] η ( z, ∆ X  ) =   ∞   −∞ f  ( z, ∆ X  ) g ∗ ( z ) dz  2 ∞   −∞ f  ( z, ∆ X  ) f  ∗ ( z ) dz ∞   −∞ g ( z ) g ∗ ( z ) dz (3)where  f  ( z, ∆ X  )  is the distribution of the electric field of lightexiting the cantilever at the distance  ∆ X   off the cantileverend, and  g ( z )  is the distribution of the electric field of thefundamental mode of the receptor.Sensitivity, which is defined as the change in couplingefficiency per unit cantilever displacement, is given by theexpression [17] S   =  ∂η∂z.  (4)Thesensitivitydependsbothonthegap ∆ X   andontheinitialdisplacement of the cantilever, as denoted in Fig. 1 by  z 0 . Thesensitivity was numerically calculated and plotted in Fig. 2 asa function of   ∆ X   and  z 0 . There is a small asymmetry on thegraphs due to nonsymmetrical distribution of the fundamentalmode of the output waveguide. The coupling efficiency takenat the points of maximum sensitivity is plotted versus thegap width in Fig. 3. As expected, the coupling efficiency andthe sensitivity decrease quickly as the gap  ∆ X   increases. Toachieve high sensitivity with a short gap, the cantilever must beinitially displaced to a certain position with precision of severalhundred nanometers. Deflection of the cantilever out of this  2134 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 5, MAY 2006 Fig. 2. Sensitivity  S   versus initial displacement and the gap width. (a) Zero-order mode. (b) First-order mode. range would result in significant decrease in sensitivity. Thewider the gap, the lower the precision in the initial deflectionis required. The gap width  ∆ X   is a tradeoff: A short gap allowsfor high sensitivity and efficiency, whereas a wide gap makestolerance limits of the initial displacement less strict, whichfacilitates fabrication of the sensors.The minimum detectable deflection (MDD) is limited bythe shot noise of the photodetector, Johnson noise of the loadresistor, the noise in the acquisition system, the cantilevervibration due to the thermal noise, and the noise produced bythe laser source. The root-mean-square (rms) shot noise currentgenerated by the photodetector is given by the expression [9]  i sn  =   2 eP  out γ  ∆ f   (5a)  i sn  =   2 eηP  in γ  ∆ f   (5b)where  e  = 1 . 6 · 10 − 19 C is the electron charge,  γ   = 0 . 4  A/Wis the photodetector responsivity,  P  out  is the optical power of light projected on to the photodetector,  P  in  is the optical powerof light exiting the cantilever, and  ∆ f   is the spectral bandwidth.The noise currents of the other srcins are either muchsmaller, like, for example, resistor Johnson noise [17], or dif- Fig. 3. Coupling efficiency between the cantilever and the output waveguidetaken at the points of maximum sensitivity versus the gap width. ficult to predict because they are dependent on the design of theinstrument. Some of noise can be filtered or compensated usingdifferentialmeasurementsandlock-inamplificationtechniques.The signal-to-noise ratio (SNR) can be found as [9], [17] SNR  = ( ∂i out /∂z ) 2  i 2sn   (6)where  i out  is the current generated by the photodetector inresponse to the output signal.MDD is defined by an SNR equal to unity [17]. For the givenSNR, the MDD can be calculated asMDD  = 1 √  SNR  =   2 eη ∆ f S  2 P  in γ   (7)or in terms of DNDDND  =  MDD √  ∆ f   =    2 eηS  2 P  in γ   (8)Taking the zero-order mode values of   η  and  S   correspondingto 3- µ m gap between the cantilever and the receptor (Figs. 2and 3) at the position of maximum sensitivity, the expression(8) gives the DND of 80 fm / √  Hz if the power  P  in  = 1  mW issupplied to the cantilever. The calculations for the 1- µ m-widegap give the density of 18 fm / √  Hz, which is comparable withthe deflection noise densities for the common techniques [4].III. D ESIGN In the embodiment of the built sensor, the cantilever and theoutput waveguides are located at the same level, although thecantilever’s free end and the facet of the output waveguide aremisaligned by a fraction of a micrometer. This implies that thecantilever, which is several hundred micrometers long, must bemade flat if no other technique for initial biasing correction isapplied during the operation of the sensor.The cantilevers may be fabricated from a single material oras a multilayer structure. The monolayer structure is preferable:It is much easier to find a material that is free of stress  ZINOVIEV  et al. : WAVEGUIDE MICROCANTILEVER SENSOR FOR DETECTING NANOMECHANICAL FORCES 2135 Fig. 4. Coupling efficiency between the input Si 3 N 4  waveguide and the SiO 2 cantilever versus the IWG thickness. gradient suitable for the production of straight cantilever beamsthan to find a combination of two or more different materialsresulting in no bimetallic effect that would not bend the beams.Unfortunately, in microelectronics, it is not a trivial problemto find dielectric material free of stress gradient that could beused for waveguide fabrication. Our experiments with low pres-sure chemical vapor deposition (LPCVD) or plasma enhancedchemical vapor deposition (PECVD) silicon nitrides failed dueto the stress gradient in the first one and high absorption lossesin the second one. The material we found to fit our requirementswas the thermally grown silicon dioxide. The film is perfectlytransparent and demonstrates low stress gradient if the bottomlayer of a few hundred nanometers is eliminated.As the refractive index of the silicon dioxide is low andthe film is grown on silicon substrate, it cannot form a TIRwaveguide over the substrate, unlike the SiO 2  cantilever inair. Therefore, over the substrate, light was delivered to thecantilever along a silicon nitride waveguide, called the inputwaveguide (IWG). At the anchoring area, the IWG beingdeposited over the silica buffer forms a junction with thecantilever beam, and the latter is an extension of the buffer(see Fig. 1). Generally speaking, nearly 100% of light can becoupled from Si 3 N 4  to the cantilever if the IWG was tapered atthe junction. If no taper is provided, light partially radiates in airat the point where the IWG ends. However, relatively low radia-tion loss can be achieved without taper because a big part of thefundamental mode of a thin Si 3 N 4  waveguide is concentrated inthe buffer. The efficiency of the coupling, which is calculatedusing the 2-D FDBPM [13], depends on the thickness of theSi 3 N 4  layer and may reach 75% value when the thicknessapproaches the 70-nm value corresponding to the cutoff condi-tion of the fundamental mode (see Fig. 4). Coupling efficiencyincreases with decreasing Si 3 N 4  thickness because the modedrops further into the SiO 2  layer. Production of a taper wouldrequire additional technological efforts, which were omitted inthis work where the objective was to prove the concept of thedevice, so light coupling into the cantilever was realized via theevanescent field of the fundamental mode of the IWG.The electric field of the transversal fundamental mode of the IWG is located off the cantilever symmetry axis, whereas Fig. 5. (a) Photograph of the fabricated chip. (b) Magnified photo of thecantilevers. the waveguide cantilever is a symmetrical structure with themodes distributed symmetrically. This results in light fromthe IWG coupling in all the modes existing in the cantilever.Multimode operation is actually a problem: Orthogonality of the modes implies their independent propagation with differentvelocities, depending on the parameters of the cantilever, andleads to an unpredictable distribution of light intensity both intransversal and longitudinal directions due to small variationsin the cantilever parameters. Therefore, multimode operation isbest avoided either by fabricating a single-mode cantilever orby filtering the unwanted modes in some way.Light coupling into the IWG can be realized either bydirectly focusing onto the waveguide facet or by meansof a diffraction grating coupler implemented on top of thewaveguide. The latter is the most convenient and, if the coupleris well designed, is a more effective method, as it does notrequire the fine alignment of direct focusing.IV. F ABRICATED  D EVICE The fabricated device presented in the photograph in Fig. 5contains an array of 20 waveguide channels. Samples with200- µ m-long cantilever beams were produced. The cantileverswere 500 nm thick and, in air, supported two guiding modes,according to the simulations. Silicon nitride input and outputwaveguides were 120 nm thick. The cantilevers on chip werelocated in a common cavity, which is a reach-through holelocated in the center. Both the cantilevers and the waveguideswere 40  µ m wide. The external facets of the input and outputwaveguides were made at the very edge of the chip. This helped  2136 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 24, NO. 5, MAY 2006 Fig. 6. Profiles of the cantilevers obtained with a confocal microscope. Inset:Scanning electron microscopy (SEM) images of the cantilevers. to avoid waveguide facet polishing and to provide relatively ef-ficientcouplingusingdirectfocusingintothechipandtocollectlight exiting the receptor using the full numerical aperture.V. C HARACTERIZATION A chip with 200- µ m-long cantilevers and 3- µ m-wide gapswas tested. The profiles of the cantilevers measured with aconfocal microscope are presented in Fig. 6. The cantileversare practically flat, so that the cantilever end and the outputwaveguide facet are misaligned by a few hundred nanometers.Fig. 7 shows a schematic view of the experimental setupused to measure the amplitude of modulation of the outputsignal induced by vibration of the cantilever at the resonancefrequency. The chip was located on a piezoelectric actua-tor (Piezomechanik PST150/10x10/18) connected to a sinewaveform synthesizer. Light from an He–Ne laser (632.8 nm,7.5 mW) was coupled into the chip using direct focusingwith an objective lens (40 × , numerical aperture (NA) 0.65)and was collected upon exiting by another objective (40 × ,NA 0.65) before being directed to a silicon photodetector (PD,Hamamatsu S1337-33BR) connected to an oscilloscope and anacquisition system for spectrum analysis through a low-noiseamplifier with bandwidth of 5–45 kHz at full-width at half-maximum (FWHM). Light from the same laser source aftersplitting was focused by a lens with a focal distance of 75 mmon the cantilever near its free end. The reflected beam wasprojected onto a two-sectional PSD to monitor the displacementof the cantilever. Assuming the reflected beam has Gaussianprofile (distortion due to the cantilever bending was neglected)given by P  ( x,y ) = 2 P  0 πσ 2  exp  − 2 x 2 + y 2 σ 2   (9)the difference in voltage generated by the PSD sections can berepresented by the expression ∆ V   = 12 P  0  erf   √  2  a − dσ  +  erf   √  2  a + dσ  Rs · R PSD (10)where  P  0  is the total intensity of the beam illuminating PSD, σ  =  L Θ max  is the size of the beam,  L  is the distance betweenthe cantilever and the PSD,  Θ max  is the divergence angleof the reflected beam defined by the focusing lens,  d  is half of the gap width between the photodetector sections, Rs is theresponsivity of the PSD,  R PSD  is the load resistors in the PSDcircuitry, erf is the error function, and  a  = (3∆ Z/L cant ) L  isthedisplacementofthespotatthePSDdefinedbythecantileverlength L cant  and by the cantilever displacement  ∆ Z  . Cantileverprofile corresponding to the fundamental resonance mode andexpressed by the formula  z  =  κx 3 / 2 was considered.CouplingefficiencyprovidedbydirectfocusingintotheIWGwas about 5%. According to the measurements, about 50% of that was coupled from the IWG into the cantilever. Thus, thelosses were about − 16 dB after the light reached the cantilever.The power of light exiting the output waveguide and measuredin direct current (dc) mode was 0.015 mW ( − 27 dB withrespect to the laser power), which corresponded to the 60-mV voltage generated by the photodetector on the load resistor ( R L  = 10  k Ω) . The noise amplitude registered in the experi-ment was 0.05 mV. The rms shot noise voltage density gen-erated by the photodetector was calculated as   i sn  R L  = 1 . 4 · 10 − 8 V / √  Hz. Working in the bandwidth of 40 kHz, the noiseproduced by the photodetector would be 2.8  µ V, which is al-most 20 times less than that experimentally observed. The rea-son was the mechanical vibration of the setup and no filtering of laser noise. The spectrum of the output signal when no voltagewas applied to the piezo actuator is presented in Fig. 8. There isa clear resonance behavior near 13 kHz with a  Q -factor of 12.When the excitation voltage of variable frequency and ampli-tude was applied to the piezo actuator, the output signal did notshow any oscillations when the cantilever was out of the reso-nance. In resonance mode, the photodetector demonstrated pe-riodical change in the photocurrent at a frequency of 13.1 kHz.The modulation amplitude of both the output voltage and thecantileverdisplacementlinearlyincreasedwiththeamplitudeof voltage supplied to the piezo actuator (see Fig. 9). The changein the output voltage per unit cantilever displacement was15  µ V/nm. The initial displacement of the cantilevers, definedby the fabrication, was about 0.4 µ m upward. Looking at Fig. 9,it can be concluded that the behavior of the coupling efficiencycurve near this point is quite linear.Working in the spectral range of 1 Hz with the noise onlygenerated by the photodetector, it would be possible to de-tect the cantilever displacement with a precision of   ± (1 . 4 · 10 − 8 V / √  Hz ) / (15 · 10 − 6 V/nm ) = 0 . 93 · 10 − 3 nm / √  Hz.The spectrum of the cantilever vibration when exciting thecantilever by the piezo actuator is presented in Fig. 10. Theexcitation voltage at 13.1 kHz applied to the piezo actuator was50 mV and corresponded to the cantilever oscillation amplitudeof about 1.7 nm. It is worth mentioning that some modulationof the output signal was due to coupling efficiency modulationresulting from the misalignment of the chip and the objectivelens 1. In the inset in Fig. 10, the spectrum of the outputsignal is presented. The driven voltage of the piezo actuator was50 mV at 11.1 kHz, and frequency was shifted out of thecantilever resonance. The amplitude of the output modulationsignal was comparable to the amplitude of the modulation
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