towards qantitative determination of the spring constant of a scanning force microscope cantilever w

IOP P UBLISHING M EASUREMENT S CIENCE AND T ECHNOLOGY Meas.Sci.Technol.21(2010)015103(8pp)doi:10.1088/0957-0233/21/1/015103Towards quantitative determination of the spring constant of a scanning force microscope cantilever with a microelectromechanical nano-force actuatorSai Gao1,Zhikai Zhang2,Yong Wu3and Konrad Herrmann11Physikalisch-Technische Bundesanstalt,Berlin,Germany2Fachhochschule Braunschweig/Wolfenb¨u ttel,Wolfenb¨u ttel,Germany3Tianjin University,Tianjin,People’s Republic of ChinaE-mail:Sai.Gao@ptb.deReceived7May2009,infinal form5October2009Published16November2009Online at /MST/21/015103AbstractThe calibration of the performance of an SFM(scanning force microscope)cantilever hasgained more and more interest in the past years,particularly due to increasing applications ofSFMs for the determination of the mechanical properties of materials,such as biologicalstructures and organic molecules.In this paper,a MEMS-based nano-force actuator with aforce resolution up to nN(10−9N)is presented to quantitatively determine the stiffness of anSFM cantilever.The principle,structure design and realization of the nano-force actuator aredetailed.Preliminary experiments demonstrate that the long-term self-calibration stability ofthe actuator is better than3.7×10−3N m−1(1σ)over1h.With careful calibration of thestiffness of the actuator,the MEMS actuator has the capability to determine the stiffness ofvarious types of cantilevers(from100N m−1down to0.1N m−1)with high accuracy.Inaddition,thanks to the large displacement and force range(up to8μm and1mN,respectively)of the actuator,the calibration procedure with our MEMS nano-force actuator features simpleand active operation,and therefore applicability for different types of quantitative SFMs.Keywords:scanning force microscope,cantilever,spring constant,microelectromechanicalnanoforce actuator,calibration(Somefigures in this article are in colour only in the electronic version)1.IntroductionScanning force microscopes,including atomic force microscopes(AFM),have become indispensable tools in the field of nano-technology,due to their outstanding spatial resolution,especially in lateral aspects.Although in most cases AFMs have been applied for the determination of the (geometrical)topography of an object under test,it is worth noting that the demands for further applications of AFM, such as quantitative determination of small forces in the range from micronewton(10−6N)down to several tens of piconewton(10−12N),are essential for many research tasks. These applications of low force actuation/sensing range from determination of the mechanical properties of nano-materials, biological structures and organic molecules,e.g.thinfilms [1],polymer[2,3],micro-organisms[4],living cells[5],to the force spectroscopy in thefield of biology[6]and pulling molecules and proteins[7].All these applications of an AFM depend,to a great extent,on the mechanical performance of the used cantilevers.U(a)(b)Figure1.Basic actuation mechanism of the nano-force actuator.(a)Fundamental principle of the lateral comb drive and(b)electrical potential around one pair of combfingers.The calibration of the mechanical performance of an AFMcantilever has therefore gained more and more interest inthe past years,yielding several types of methods.Mainlythese methods can be classified as dimensional methods,staticexperimental methods and dynamic experimental methods.Indimensional methods[8],either using a equation or usingfinite element analysis,the accurate material and geometricalproperties of the cantilever are essential to determine thespring constant.Dynamic experimental methods determinethe spring constant via measuring the resonant frequency.Forexample,Cleveland et al[9]have measured the resonantfrequencies after adding small end masses to an AFMcantilever.Sader et al[10–12]immersed an AFM cantileverinto a liquid medium with known viscosity and densityand obtained the corresponding resonant frequency of thecantilever.Hutter et al[13]developed a thermal method todetermine the spring constant of an AFM cantilever.Staticexperimental methods are direct methods,which measure thedeflection upon static loading of the cantilever.For example,Torii[15]has developed a large-scale cantilever as referencespring and introduced a laser interferometer for displacementmeasurement to calibrate the AFM cantilever;Gates[16]has developed a reference cantilever array of known springconstants to calibrate the working cantilever;A nano-indenterwas used to load force to the cantilever tip by Holberyet al[17].Recently a cantilever on cantilever technique[18–20]was reported,in which a set of calibrated micro-fabricated reference springs,potentially traceable to the SIunit system with a relative uncertainty of5%,can be usedas reference springs.A comparison of the above-mentionedmethods has reported that each method has its own meritsand disadvantages,but the uncertainties in the methods rangefrom5%to25%[8].Moreover,none of the above-mentionedstatic methods have their own force loading and/or positionsensing system.They need a force loading system,either acalibrated piezo-stage or commercial instrument such as nano-indenter,and also a position sensing system for displacementmeasurement of the cantilever.Therefore,an easy andaccurate method,with its own force loading and sensingsystem,suitable for on-site cantilever calibration is urgentlyneeded.In this paper,a MEMS nano-force actuator is presented tocalibrate the quasi-static mechanical properties of an AFMcantilever of any type,i.e.rectangular or triangular form,with/without reflective coating.The active operation nano-force actuator,working as a reference spring,has its own forceloading and position sensing system.The spring constant ofthis force actuator was traceably calibrated using a nano-forcecalibration device based on a high-resolution compensationbalance at Physikalisch-Technische Bundesanstalt(PTB),Germany.The nano-force actuator,which can generate upto1mN output force with nanonewton resolution,can beused to calibrate a cantilever with a normal stiffness from0.01N m−1to100N m−1.For cantilevers with stiffnesshigher than0.1N m−1,the measurement uncertainty is betterthan5%.2.A MEMS-based nano-force actuator2.1.Actuation mechanism of the nano-force actuatorThe nano-force actuator is developed based on the principle ofa lateral electrostatic comb drive[21].As shown infigure1,the comb-drive actuator consists of two interdigitatedfingerstructures,in which one isfixed and the other is movable.Inthe case of micro-structures having high aspect ratio,i.e.thevertical height of the combfingers h is far larger than thefingergaps d,a two-dimensional model(as shown infigure1(b))canbe well employed to predict the performance of the actuator.Then the force generated by each comb pair during electricalactuation can be analytically expressed as follows[22]:F act=ε0hd(U2−U1)2(1)in whichε0=8.854×10−12F m−1is the permittivity constant,U1and U2are the bias and drive signals applied to the movableandfixedfingers,respectively.2.2.Structural designA multi-functional nano-force actuator based on theaforementioned comb-drive actuation mechanism is to bedeveloped with the expected maximum force range up to1mN(1×10−3N)and the force sensitivity up to1nN(1×10−9N).Furthermore,it is expected that the nano-force actuator wouldwork mainly for one-dimensional applications,e.g.calibrationof various force sensors,determination of the mechanicalxy zEn g a g ement/Scanarea(b )Figure 2.Practical design of the nano-force actuator.(a )Basic structure of the nano-force actuator and (b )V-shaped test head for cantilever calibration.xF o r c e , m NDisplacement, µm(b )(a )Figure 3.Suspending system design of the force actuator.(a )Inner stress within the springs and (b )comparison of the spring constant of the actuator along x and y axes,respectively.properties of small volumes of materials by means of nano-indentation or the nano-tensile testing method.As shown in figure 2,the actuator has a left–right symmetric structure,in which the movable part is suspended by a folded spring system.All the movable fingers are mounted on the beams coming from the main trunk and electrically connected to the electrode U 1,through which a bias voltage is applied.The fixed fingers are connected to the electrode U 2.With those widely applied bulk micro-machining processes,especially the bonding-DRIE (deep reactive ion etching)technology [23]in the Chemnitz University of Technology (Germany),the typical parameters in figure 1can be h =50μm,d =3μm,t =3μm and x 0=5μm.The total output force is F act =N ·f act ,in which N is number of finger pairs within the actuator.In order to meet the desired specifications,i.e.F act 1mN,in the case that the maximum differential-driven voltage is limited to |U 2−U 1|max 70V ,here the number of finger pairs of the actuator is chosen to be 1500.Therefore,the electrostatic force generated by the actuator will reach 1.08mN in the case of U 2−U 1=70V .A well-designed actuator should feature not only outstanding specifications,but also adequate convenience for practical application.Here,a V-shaped test head is designed for the stiffness calibration of the cantilever:a tipped cantilever can be engaged on the top surface of either of the prongs of the fork,and the other prong can be used for in situ monitoring of the spatial relationship between the cantilever to be calibrated and the actuator with an optical method(e.g.microscopes).Furthermore,this specially designed test fork helps to minimize the potential influence of a parasitic capacitance between the cantilever to be tested and the electrostatic actuator,as mentioned in [24].With the help of commercial finite element analysissoftware (ANSYS R),the mechanical structure of the actuator has been carefully designed.Obviously,smaller stiffness of the actuator along the sensing direction means,in general,a higher force sensitivity of the actuator.However,when the dynamic performance of the actuator has to be considered,the actuator’s stiffness could not be chosen freely.The spring constant of the actuator along the x -axis was finally determined to 12.8N m −1,resulting in a resonant frequency of the actuator of 1.74kHz.Figure 3(a )shows the inner stress distribution of the spring within the actuator during the maximum in-plane one-axis movement of the trunk,in which the maximum stress is smaller than the allowable stress of the silicon.Figure 3(b )demonstrates the stiffness of the spring system along x and y directions,respectively.It can be seen that the spring constant of the y -axis is more than 80times larger than that of x ,which ensures that the whole structure moves along the x -axis symmetrically.In addition,the potential influence of the lateral offset of the test force in the order of 1μN is negligible which is proved by FEA simulation.Figure 4shows the dynamic performance of the force actuator when the damping ratios are 0and 0.05,respectively.The damping ratio of this force actuator in air,which can be roughly estimated [25],is smaller than 0.05.Freq u ency, Hz10002000300040005000A r b i t r a r y un i t s25002000150010005000(a ) damping ratio =0.Freq u ency, Hz10002000300040005000A r b i t r a r y u n i t s8006404803201600(b ) damping ratio =0.05.Figure 4.Simulation of the dynamic performance of the force actuator.(a ) Photograph of the force actuator. (b ) Testing fork for cantilever calibration.Figure 5.Micro-machined prototype of the nano-force actuator.(a )Photograph of the force actuator and (b )testing fork for cantilever calibration.3.Prototyping3.1.FabricationThe designed MEMS-based nano-force actuator is fabricated using the bonding and deep RIE (B-DRIE)process [23]developed at TU Chemnitz,in which two wafers (one for the structure layer and the other for the substrate)are first bonded together,and then the structure layer is processed by the deep RIE technology.One of the outstanding features of this process is that the structural layer is purely composed of single crystalline pared with other bulk micromachining technologies,such as SCREAM technique [26],in which the functional structures consist of at least three layers of materials (i.e.single crystalline silicon +silicon oxide +metallic coating),this feature of B-DRIE technology greatly simplifies the numerical simulation of the MEMS actuator,and therefore provides a quite good possibility for precise estimation of the mechanicalspecifications of the designed structure.The overall size of the actuator chip is about 2.5mm ×5mm.The typical structural thickness of the prototype is 50μm,the fixed and movable fingers have a width of 3μm,and the finger gap is 3μm.Figure 5(a )shows an SEM image of the wired prototype of the device,in which the testing forkFigure 6.Prototype of the nano-force actuator with a PCB package in comparison to Euro cent coin.protrudes about 500μm from the edge of the substrate,and figure 5(b )shows the test head in detail.Figure 6shows the final prototype of the nano-force actuator with a PCB package.The package size along the detecting axis is about 2mm,ensuring that the testing fork ofEquation: y = a*x +b Experimental data Linear regression4 05 1 2 3 Slope: 12.86843 Standard deviation: 0.00362Sum of square error: 0.01451 10502070304060Deflection, µmF o r c e , µN6Figure 7.Typical calibration curve of the force actuator’s stiffness.the actuator is fully accessible.In addition,due to its compact packaging,the MEMS actuator can be applied directly with most commercially-available AFMs.3.2.Stiffness calibration of the force actuatorBefore the MEMS-based nanoforce actuator could be used for the calibration of other objects,the stiffness of the actuator itself has to be carefully calibrated.The stiffness of the force actuator has been calibrated with an experimental setup developed at PTB and detailed in [27],one of whose key components is a precise compensation balance (Sartorius SC2),which has a measuring range of 20mN with 1nN resolution, 2.5nN reproducibility,9nN linearity deviation and an uncertainty of 0.1μN.A piezo-stage with capacitive feedback (PIFOC,Physik Instrumente)is employed to engage the MEMS actuator to the balance.Figure 7shows one typical calibration curve of the measured force by the balance when the actuator is pushed linearly to the balance after engagement.Under the condition that the temperature was set to 20.5◦C and the relativeUU sUTime, sS e n s o r o u t p u t , V(b )(a )Figure 8.The control and sensing system for the force actuator and its performance.(a )Schematic of the control and sensing system and (b )sensor output when the main shaft of the actuator realizes 1nm in-plane displacement.humidity was adjusted to 32.0%,18measurements have been done to calibrate the stiffness of the actuator.Taking into account the uncertainty contributors to the calibration,such as thermal drift,the stiffness of the experimental setup,the uncertainty of the balance and so on,finally,the force actuator has a stiffness of (12.909±0.054N m −1),which coincides quite well with our simulation result in section 2.2.3.3.Control and sensing s y stemThe performance of the control and sensing system for the MEMS electrostatic actuator would,to a great extent,determine the actual metrological capabilities of the actuator.Figure 8(a )shows the control and sensing system designed for the force actuator.A dc driving signal U d added with a 60kHz sinusoidal signal U s is amplified,and then applied to the MEMS actuator.The output current from the actuator is converted to the detecting voltage by an I/U converter,and finally demodulated with the help of a lock-in amplifier (SR830,Standford Research Systems,Inc.)to determine the capacitance variation due to the in-plane displacement of the main shaft of the actuator.Since the test head (and the movable structures)of the MEMS actuator is virtually grounded by the converter,the potential influences of the parasitic capacitance induced by the cantilever to be measured or other sources can then be well eliminated,ensuring the actuator has high sensitivity for in-plane displacement whilst being robust to the measurement circumstances.Figure 8(b )shows the output signal of the sensing system when the in-plane displacement is 1nm.The actual resolution of the electrostatic force generated by the actuator is,in principle,determined by the stability of the differential driving voltage U 2−U 1applied to the actuator,i.e.δF act =N ·c f ·εhd·[δ(U 2−U 1)]2,(2)where c f is a correction coefficient due to the fabrication errors.It was determined that the final differential driving voltage in our electrical system has a stability of 3mV over the whole range (70V).Suppose that c f =1.0,then the resolution of the actuator’s electrostatic force amounts to F act =0.002nN.Time, sSelfCalibrationDeviation,N/mFigure9.Long-term self-calibration stability of the nano-force actuator(σ=0.0037N m−1).PSISAFM headForceact u atorP ositionin gsystemzyx(a)ator(b)Figure10.Experimental setup of the cantilever calibration systemand the equivalent model.(a)Experimental setup of the calibrationsystem and(b)simplified mechanical model for the cantilever andactuator after engagement.However,the actual resolution of the output forceδF bythe actuator is defined byδF=N·c f·εhd·[δ(U2−U1)]2−k x·δx,(3)in which x is the displacement of the main shaft of the actuator,and k x is the spring constant along the x-axis.As showninfigure8(b),with our currently designed electronics thedisplacement of the trunk could be sensed with a resolutionof0.2nm(1σ),therefore the actual resolution of the MEMSactuator can reach2.6nN.With this control and sensing system,the long-termstability of the nano-force actuator has been investigated.Alow-frequency(e.g.0.1Hz)dc signal is applied to the actuatorto carry out self-calibration.Figure9shows the long-term self-calibration results.It can be seen that within1h the standarddeviation of the self-calibration amounts to3.7×10−3N m−1,which corresponds to a relative uncertainty of3×10−4(1σ).4.Preliminary experimental results of the stiffnesscalibration of AFM cantilevers4.1.Preliminar y experimental resultsAn experimental setup has been built for the determination ofthe stiffness of an AFM cantilever with a prototype of the nano-force actuator.As shown infigure10(a),the force actuatoris mounted on an x–y–z stage,which is used for alignment ofthe AFM tip and the force actuator.The Z-axis of the stageis driven by a stepper motor.The cantilever to be calibratedis mounted on an AFM head from Surface Imaging SystemsGmbH(Germany)[29],which employs afibre interferometerto monitor the cantilever’s deflection.Figure10(b)shows the equivalent static mechanicalmodel of the calibration system after engagement,in whichthe electrostatic force generated by the actuator F is balancedby the cantilever(with stiffness k cantilever)and the suspendingsystem of the actuator(with stiffness k actuator),i.e.F−k actuator· z=k cantilever· z,(4)where z is the relative deflection/displacement of thecantilever–actuator system.Finally,we getk total=k actuator+k cantilever.(5)Here the dimension and the strength of the fork are carefullydesigned to ensure that the influence of the deviation from thecentral axis and the deformation of the fork could be omitted[28].The calibration procedure was realized as follows:first,the force actuator is coarsely adjusted under the AFM tipby the x–y–z micro-stage,especially until the distance betweenthe force actuator and the cantilever is small enough to get intothe measurement range of the actuator.The force actuatoris then linearly driven to approach the cantilever and to testthe cantilever.During the whole test procedure,the drivingvoltage U driven,the sensor output signal U sensor of the forceactuator and the interferometer output signal from the AFMhead are acquired simultaneously.Two kinds of cantilevers,i.e.a non-contact modecantilever(SSS-NCLR-20,Nanosensors TM,nominal forceconstant48N m−1,specified range:21–98N m−1)anda contact mode cantilever(PPPZEILR-50,Nanosensors TM,nominal force constant 1.6N m−1,specified range:0.6–3.9N m−1)[30],have been measured with the newlydeveloped force actuator.Calibration results are shown infigure11,in which the blue curves(which are marked withk1and k2)and the green ones are the sensor output signal andthe interferometer output signal versus driving voltage of theactuator,respectively.Here k1and k2are defined as the inverse slope of theU2driven–U sensor curve(i.e. U2driven/ U sensor)measured by theS e n s o r o u t p u t , VDriven Volta g e, V 2I n t e r f e r o m e t e r o u t p u t , VDrivin g volta g e, U 2A c t u a t o r S e n s o r O u t p u t , U A F M I n t e r f e r o m e t e r O u t p u t , UA c t u a t o r S e n s o r o u t p u t , VDriven Volta g e,V 2-0.35-0.25-0.15-0.05A F M I t f t t t V Drivin g volta g e, U2A c t u a t o r S e n s o r O u t p u t , U A F M I n t e r f e r o m e t e r O u t p u t , UFigure 11.Calibration results of different AFM cantilevers.(a )Typical result when k cantilever >k actuator and (b )typical result when k cantilever <k actuator .force actuator before and after the engagement,respectively.Here the slopes are determined outside the regions of ‘jump-in’and ‘jump-out’.This will reduce the influence of the interaction between the cantilever tip and the force actuator on the measurement result.Therefore we havek cantilever =(k 2/k 1−1)×k actuator .(6)In figure 11(a ),k 2k 1=4.566(k 1=5.718,k 2=26.110),and in figure 11(b ),k 2k 1=1.110(k 1=5.634,k 2=6.254).It can be seen from figure 11that in the case of the cantilever stiffness being far larger than that of the force actuator,i.e.k cantilever k actuator ,the interaction between the cantilever and the force actuator could be clearly observed from the sensor output signal within the jump-in and jump-out region,while when the stiffness of the cantilever is much smaller than that of the force actuator,i.e.k cantilever k actuator ,this phenomenon is no longer observed so obviously from the sensor output signal,but from the SIS AFM interferometer output.The calibration results also show that the fibre interferometer output signal and the sensor output signal coincide with each other very well.4.2.Measurement uncertaint y estimationFrom equation (6),the uncertainty for measuring the stiffness of the cantilever can be deduced as follows:u 2c (k cantilever )= k 2k 1−1 2·u 2(k actuator )+k 2actuator k 1u 2(k 2)+k 2actuator ·k 22k 1u 2(k 1),(7)and the relative measurement uncertainty is expressed asfollows:u 2c (k cantilever )k 2cantilever =u 2(k actuator )k 2actuator+11−k 1k 2 2·u 2(k 2)k 22+1 1−k 1k 2 2·u 2(k 1)k 21.(8)For simplification,the relative uncertainties for the determination of k 1and k 2can be considered to be thesame,and equal to the relative stability of the self-calibrationprocedure,i.e.U(k 1)k 1=U(k 2)k 2=3×10−4.When the cantilever’s stiffness is far larger than that ofthe actuator (i.e.k 1/k 2 1),since U(k actuator )k actuator=4.2×10−3and U(k 1)k 1=U(k 2)k 2=3×10−4,from equation (8)one can estimate that the relative uncertainty for determining the stiffness of a cantilever is close to that of the actuator’s stiffness,i.e.U(k actuator )/k actuator =4.2×10−3.In this case,the stiffness uncertainty of the force actuator is the main contributor to the calibration result.For a cantilever with a stiffness of 100N m −1,for example,the calibration uncertainty amounts to 0.42N m −1.When the cantilever to be calibrated tends to be quite weak,i.e.k 1/k 2→1,the last two terms in equation (8)would increase quickly,thus the corresponding measurement uncertainty would increase quickly.As an example,for a cantilever with a spring constant of 0.1N m −1,the relative measurement uncertainty will amount to about 5%.For the cantilevers calibrated in figure 11,the spring constants are found to be (46.10±0.20)N m −1and (1.425±0.014)N m −1,respectively,and the corresponding relative uncertainties are 0.4%and 0.9%,respectively.5.SummaryIn this paper,a MEMS-based nano-force actuator for thecalibration of the AFM cantilever stiffness has been developed,which can generate a test force up to 1mN with a force resolution in the order of nanonewton.Due to its small size,the nano-force actuator is especially suitable for the on-site calibration of the spring constant of an AFM cantilever.This calibration method does not need any pre-knowledge of the cantilever.Preliminary experimental results verified that the force actuator can be used to calibrate different AFM cantilevers,such as contact mode or non-contact mode cantilevers,with a stiffness varying from 100N m −1to about 0.01N m −1.For hard cantilevers with a stiffness higher than that of the force actuator (12.9N m −1),the measurement uncertainty would be about 0.42N m −1(the relative uncertainty is better than 3.3%),For weak cantilevers with a stiffness higher than 0.1N m −1,the calibrationuncertainty would be better than5%.The relative calibration uncertainty for cantilevers with0.01N m−1stiffness will amount to about20%.AcknowledgmentsThis research was supported by DFG project HE2235/5-1. Dr K Hiller in TU Chemnitz is thanked for sharing her MEMS fabrication experience with the authors.The stiffness of the nano-force actuator was calibrated by Dr L D¨o ring and Dr U Brand,and the SEM images were taken by T Klein in PTB.References[1]Chowdhury S and Laugier M T2004Non-contact AFM with ananoindentation technique for measuring the mechanicalproperties of thinfilms Nanotechnolog y151017–22[2]Vanlandingham M R et al1997Relating elastic modulus toindentation response using atomic force microscopyJ.Mater.Sci.Lett.16117–9[3]Clifford C A et al2005Quantification issues in theidentification of nanoscale regions of homopolymers usingmodulus measurement via AFM nanoindentation Appl.Surf.Sci.2521915–33[4]Wang J et al2004Probing nanomechanical properties ofnickel coated bacteria by nanoindentation Mater.Lett.61917–20[5]Ho M S,Kuo F J,Lee Y S and Cheng C M2007Atomic forcemicroscopic observation of surface-supported humanerythrocytes Appl.Ph y s.Lett.91023901[6]Rief M et al1997Single molecule force spectroscopy onpolysaccharides by atomic force microscopy Science2751295–7[7]Rief M et al1997Reversible unfolding of individual titinimmunoglobulin domains by AFM Science2761109–12 [8]Clifford C A et al2005The determination of atomic forcemicroscope cantilever spring constants via dimensionalmethods for nanomechanical analysis Nanotechnolog y161666–80[9]Cleveland J P and Manne S1993A non-destructive methodfor determining the spring constant of cantilevers forscanning force miccroscopy Rev.Sci.Instrum.64403–5 [10]Sader J E et al1995Method for the calibration of atomic forcemicroscope cantilevers Rev.Sci.Instrum.663789–98 [11]Sader J E1998Frequency response of cantilever beamsimmersed in viscousfluids with applications to the atomicforce microsope J.Appl.Ph y s.8464–76[12]Sader J E,Chon J W M and Mulvaney P1999Calibration ofrectangular atomic force microscope cantilevers Rev.Sci.Instrum.703967–9[13]Hutter J L and Bechhoefer J1993Calibration of atomic-forcemicroscope tips Rev.Sci.Instrum.641868–73[14]Butt H J and Jaschke M1995Calculation of thermalnoise in atomic force microscopy Nanotechnolog y61–7[15]Torii A et al1996A method for determining the springconstant of cantilevers for atomic force microscopy Meas.Sci.Technol.7179–84[16]Gates R S et al2007Precise atomic force microscopecantilever spring constant calibration using a referencecantilever array Rev.Sci.Instrum.78086101[17]Holbery J D,Sarikaya M and Fisher R M2000Experimentaldetermination of scanning probe microscope cantileverspring constants utilizing a nanoindentation apparatus Rev.Sci.Instrum.713769[18]Cumpson P J and Hedley J2003Accurate force measurementin the atomic force microscope:a microfabricated array ofreference springs for easy cantilever calibrationNanotechnolog y14918–24[19]Cumpson P J and Hedley J2003Accurate analyticalmeasurements in the atomic force microscope:amicrofabricated spring constant standard potentiallytraceable to the SI Nanotechnolog y141279–88[20]Cumpson P J et al2004Quantitative analytical atomic forcemicroscopy:a cantilever reference device for easy andaccurate AFM spring-constant calibration Meas.Sci.Technol.151337–46[21]Tang W C,Nguyen C H and Howe R T1989Laterally drivenpolysilicon resonant microstructures Sensors Actuators A2025–32[22]Tang W C,Nguyen T-C H,Judy M W and Howe R T1990Electrostatic-comb drive of lateral polysilicon resonatorsSensors Actuators A21–23328–31[23]Hiller K et al2005Bonding and deep RIE—a powerfulcombination of high aspect ratio sensors and actuators Proc.SPIE571580–91[24]Fumagalli L et al2006Nanoscale capacitance imaging withattofarad resolution using ac current sensing atomic forcemicroscopy Nanotechnolog y174581–7[25]Borovic B et al2006The lateral instability problem inelectrostatic comb drive actuators:modeling and feedbackcontrol J.Micromech.Microeng.161233–41[26]Fr¨o mel J,Wiemer M and Gener T2005Packaging of MEMSstructures in SCREAM technology using anodic bondingProc.Micro S y stem Technologies(M¨u nchen,5–6October)pp99–104[27]Doering L,Peiner E,Behrens I and Brand U2003Calibrationof micro force setting standards using a new nano forcecalibration device Proc.MST(Micro S y stem Technologies)(M¨u nchen)pp492–4[28]Li Z,Gao S and Herrmann K2007Development of amicro-miniature nanoindentation instrument Proc.Conf.onHARDMEKO pp13–6[29]UltraObjective Operating Manual,Surface Imaging SystemsGmbH1996[30]NANOSENSORS Rue Jaquet-Droz1Case Postale216CH-2002Neuchatel Switzerland(/products catalog.html)。