502 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 23, NO. 3, JUNE 2014

JMEMS Letters

Displacement Sensing With Silicon Flexuresin MEMS Nanopositioners

Ali Bazaei, Mohammad Maroufi, Ali Mohammadi,and S. O. R. Moheimani

Abstract— We report a novel piezoresistive microelectromechanicalsystem (MEMS) differential displacement sensing technique with a min-imal footprint realized through a standard MEMS fabrication process,whereby no additional doping is required to build the piezoresistors.The design is based on configuring a pair of suspension beams attachedto a movable stage so that they experience opposite axial forceswhen the stage moves. The resulting difference between the beamresistances is transduced into a sensor output voltage using a half-bridge readout circuit and differential amplifier. Compared with a singlepiezoresistive flexure sensor, the design approximately achieves 2, 22,and 200 times improvement in sensitivity, linearity, and resolution,respectively, with 1.5-nm resolution over a large travel range exceeding12 μm. [2014-0076]

Index Terms— Displacement sensor, nanopositioning, SOI-MEMS,piezoresistivity.

I. INTRODUCTION

Recent advances in micro-electromechanical systems (MEMS)such as scanning probe microscopy, probe-based data storage,microgrippers, and gyroscopes necessitate rapid development ofin-situ sensors with reduced footprint, noise, and drift and increasedbandwidth and dynamic range [1]–[3].

The piezoresistive effect refers to variations of the electrical con-ductivity in a material due to the mechanical stress. Semiconductorpiezoresistivity has extensively been used to measure various physi-cal quantities such as pressure, shear stress, acceleration, velocity,deflection, and displacement. However, fabrication of the requi-site sensors usually involves expensive custom processes to createpiezoresistors in selectively doped zones [4]. Few works have beenreported on solid-state piezoresistive displacement sensors fabricatedby standard micro-machining processes, where custom fabricationsteps are not available to incorporate the conventional piezoresistorsinto the flexures. In [5], piezoresistive position transducers werefabricated through standard micro-machining processes in a variety ofpolysilicon beam shapes, where considerable nonlinear behavior wasreported for bending beam sensors. In [6], a piezoresistive sensor wasmicro-machined adjacent to an electrothermal micro-actuator usinga standard process with n-type polysilicon. Since the piezoresistorsin [6] experience similar stresses, the sensor exhibits a nonlinearresponse. In [7] and [8], piezoresistivity of T-shaped flexures wereused to detect vibration of the resonators fabricated through standardSOI-MEMS processes over extremely small displacement ranges.

Manuscript received March 7, 2014; revised April 2, 2014; accepted April6, 2014. Date of publication April 29, 2014; date of current version May 29,2014. This work was supported in part by the Australian Research Counciland in part by the University of Newcastle. Subject Editor P. Sarro.

The authors are with the School of Electrical Engineering andComputer Science, University of Newcastle, Callaghan, NSW 2308, Australia(e-mail: ali.bazaei@newcastle.edu.au; mohammad.maroufi@uon.edu.au;mohamadi@ieee.org; reza.moheimani@newcastle.edu.au).

Color versions of one or more of the figures in this letter are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JMEMS.2014.2316325

This letter reports the fabrication of a novel displacement sensor ina flexure-guided MEMS nanopositioning through a standard single-crystal silicon SOI-MEMS fabrication process (SOIMUMPs [9])based on the differential piezoresistive effect, where two piezoresis-tors experiencing axial forces with opposite signs are simultaneouslyemployed. The piezoresistors also serve as structural flexures tosuspend a scan table. Thus, the sensor footprint is almost zero.The proposed differential approach utilizes orientations of the sus-pension beams to exert opposite stresses on the piezoresistor pairrather than the differential method in [8], where piezoresistors havesimilar stresses and an interface circuit cancels the feedthrough signalfrom actuator to sensor. In contrast to the traditional sensors thatuse stresses generated on the surface of implanted piezoresistors[10]–[12], we employ the inherent axial forces generated in theexisting suspension beams. This removes the need for doping certainzones to generate the piezoresistive effect. Note that in the few worksusing piezoresistors with axial forces, the displacement direction isin parallel with the axial force, significantly limiting the travel range[7], [8], [13]. However, the axial force and displacement directionsare almost orthogonal to each other in the proposed design, allowingmuch larger strokes. Compared with the sensing method reportedin [6], the differential operation demonstrates considerable improve-ment in sensitivity and linearity as well as lower noise and drift.Furthermore, our design benefits an electrostatic actuation mechanismwith a larger stroke and a higher bandwidth without the adverseeffect of thermal coupling from the actuator. Using an advancedMicro-System-Analyzer (MSA), we investigate the dynamic responseof the sensor and compare it with the actual displacement.

II. SENSING MECHANISM

Figures 1(a) and (b) show SEM image and schematics of theproposed sensor in a nanopositioner, where two straight suspensionbeams, designated as piezoresistors Rp1 and Rp2, differentiallymeasure the x-axis displacement of the stage. The stage is movablealong the x-axis in both directions by comb drives. As shown inFig. 1(b), the undeflected sensing beams have an angle of δ = 0.86°with respect to the y-axis in opposite directions so that the lowerends of the piezoresistors are oppositely displaced by � = 15 μmalong the x-axis, which is more than the expected stroke limitsof ±10 μm. This inclination was selected to allow for a large travelrange and avoid buckling suspensions. As the stage is displaced,one piezoresistor experiences axial tensile force while the other iscompressed; see Fig. 1(b); thus, their resistances change, oppositely.The resistance difference is amplified as the measured displacementby the readout circuit in Fig. 2. A pair of similar suspensions on theother side of the stage serve to complete the guidance mechanismalong the x-axis. On top of these suspensions and the stage, we optedto deposit a 500 nm gold layer to electrically ground the movingcombs and the lower ends of the piezoresistors. A pair of similarpiezoresistors are available on the chip as dummy resistors, whichexperience no mechanical stresses and complete the Wheatstonebridge legs in the readout circuit.

A differential actuation mechanism allows us to compensate for thequadratic nonlinearity in the electrostatic force-voltage characteristicsof the comb drives [14], [15]. Since the stage and rotor combsare electrically grounded, we augment the actuation signals ±va by

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BAZAEI et al.: DISPLACEMENT SENSING WITH SILICON FLEXURES IN MEMS NANOPOSITIONERS 503

Fig. 1. (a) SEM image of MEMS nanopositioner with suspensions function-ing as piezoresistive sensors. (b) Differential axial forces under deflectionsinduced by stage displacement.

Fig. 2. Circuit diagrams of sensor and actuator. Potentiometers with smallresistance values are initially used to tune the output voltage at zero.

an identical bias voltage Vq ; see Fig. 2. As the comb drives arefabricated on a symmetrical layout around y-axis, the dominant elec-trostatic net force applied to the stage and suspensions is proportionalto Vqva .

III. CHARACTERIZATION

For static characterization of the sensor output voltage vo versus theMSA measured displacement, we apply a slowly varying triangularwaveform as the actuation signal with Vq = 30 V and Vb = 4 V.The voltage-displacement characteristics corresponding to rising andfalling periods of the triangular actuation are shown in Fig. 3. Notethat the sensor output voltage linearly changes with the displacementin a travel range exceeding 12 microns with no hysteresis.

To confirm that the linear response of the sensor is achieved by thedifferential sensing, we bypass one of the piezoresistive suspensions

Fig. 3. Static characteristics of the position sensor. We characterized thenonlinearity by NL = 104 (1 − |ρ|) with ρ standing for Pearson correlationcoefficient, whose magnitude is closer to 1 for more linear data [16].

Fig. 4. Normalized frequency responses with respect to the differentialactuation signal va .

in the Wheatstone bridge. Since the piezoresistive suspensions arenot removable, we apply a constant voltage source to one midpointof the bridge to null any voltage variation due to piezoresistivity atthe amplifier’s non-inverting input, as indicated in Fig. 2. For thisexperiment, we opted to use primary cells as the constant voltagesources of the bridge. Using two switching power supplies in thebridge creates excessive noise at the sensor output due to theiruncorrelated switching noises, which are amplified by the readoutcircuit. With a bias voltage of Vb = 6.3 V for the modified bridge,the resulting static characteristic of the sensor is shown in Fig. 3,where that of the original bridge biased by the same cells is alsoincluded. Clearly, the differential sensing significantly improves thelinearity and sensitivity of the sensor.

As a reference for dynamic characterization, we measured thefrequency response of the stage from the differential actuation signalva to the actual displacement detected by the MSA, directly. Fig. 4shows the results along with those of the differential piezoresistivesensor output with Vb = 4 V, where similar actuation signals wereused during both tests. As the frequency is increased, the sensorresponse closely follows the displacement up to 7 kHz, indicating asensing bandwidth well above the useful mechanical bandwidth ofthe nanopositioner, which is below its 3 kHz resonant frequency.

As the frequency increases, the sensor response gradually deviatesfrom the displacement as indicated in Fig. 4. This is mainly dueto non-zero resistance of the suspensions with gold layers (≈5�)connecting the piezoresistors to the ground and also the reductionof comb drive impedances with increasing frequency. To confirmthis assertion, we switched off the bias voltages (Vq = 0) in thedifferential actuation system to keep the displacement virtually zerowhile measuring the sensor response to the actuation signal. Asshown in Fig. 4, the frequency response of the sensor under the zero

504 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 23, NO. 3, JUNE 2014

Fig. 5. Output noise in differential and non-differential sensors biased by6.3 V primary cells.

TABLE ISENSITIVITY AND RESOLUTION OF THE SENSORS

displacement condition matches well with the original sensor databeyond the sensor bandwidth. Hence, the deviation is mainly due tothe electrical coupling from the actuator to the sensor rather than adynamic relationship between the displacement and the axial forces inthe piezoresistors. Similar electrical couplings from electrothermal orpiezoelectric actuators to built-in piezoresistive sensors are reportedin [6] and [17].

Fig. 5 shows the time histories of the sensor output with zeroactuation signal using the differential and non-differential sensingapproaches with the bridge biased by the foregoing batteries. Thesensitivities and resolutions of these sensors are reported in Table I.Compared with the non-differential method, the differential approachreduces the sensor noise and drift and improves on sensitivity andresolution, considerably. Furthermore, due to the highly doped natureof the top layer of the SOI chip [9], [18] and the sensing bridge beingfabricated on chip, the resulting sensor is expected to be robust withrespect to environmental temperature variations [4].

IV. CONCLUSION

A built-in differential displacement sensor with almost zero foot-print was presented based on the piezoresistivity of entire suspensionbeams employed in a flexure guided nanopositioner, which can befabricated through standard micro-machining SOI-MEMS processes.The differential action was achieved through a novel design of aflexure pair experiencing opposite axial forces orthogonal to themeasured displacement while avoiding buckling. Compared withthe non-differential approach, considerable improvement on linearity,sensitivity, resolution, and reduction of noise and drift are obtained bythe differential method. Although, electrical coupling from actuatorto sensor limits the sensor bandwidth to 7 kHz, it is well above themechanical bandwidth of the device.

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