an soi-mems piezoelectric torsional stage with bulk...

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JSEN.2017.2686643, IEEE SensorsJournal

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An SOI-MEMS Piezoelectric Torsional Stage withBulk Piezoresistive Sensors

Mohammad Maroufi, Member, IEEE, S. O. Reza Moheimani, Fellow, IEEE

Abstract—This paper presents a micro-electromechanical stagefor out-of-plane positioning of microcantilevers designed foratomic force microscopes. The stage produces an out-of-planedisplacement using a torsional mechanism that exploits piezoelec-tric clamped-guided beams as actuators. To measure the torsionaldisplacement of the stage, novel differential piezoresistive sensorsare implemented. These sensors feature clamped-guided beamsthat exploit the bulk piezoresistivity of silicon. Using this sensingconcept eliminates the requirement to fabricate highly-dopedregions on the flexures. An analytical model is provided thatdescribes the sensor’s linearity. The sensor, the microcantilevers,and the mechanical features of the stage are experimentallycharacterized. The first resonance frequency of the stage islocated at 7.8 kHz, and a static out-of-plane displacement of morethan 1.2µm is obtained. In addition, the piezoresistive sensorcaptures the dynamics of the stage within a bandwidth of 13 kHzwith a 1σ-resolution of 3 nm.

Index Terms—MEMS nanopositioner, Piezoelectric actuation,Piezoresistive sensing, Cantilever probe, Atomic force microscope.

I. INTRODUCTION

Achieving a precise out-of–plane displacement is a necessityfor numerous applications in a variety of fields in scienceand technology. Optical systems and atomic force microscopes(AFMs) are amongst the most prominent applications for thesetypes of stages. Spectroscopy and interferometery are the mostcommon examples of optical systems which make extensiveuse of macro-sized single axis positioning stages [1], [2].

In AFMs, the out-of–plane nanopositioners have the crucialrole of precisely positioning the probe with respect to thesample. These positioners should be initially used to land theprobe on the sample. Then, depending on the imaging mode,a nanopositioner may be used by the feedback controller toprecisely position the probe above the sample in order togenerate the topography [3]. To perform this task, numerousstate-of-the-art macro-scale nanopositioners are proposed inthe literature and are also available in the market [4].

Micro-electromechanical systems (MEMS) technology hasbeen extensively used for implementation of out-of-planestages predominantly for the realization of micromirrors re-quiring a piston-like out-of-plane motion. Electrothermal [5]–[8], electromagnetic [9], and piezoelectric [10], [11] actuationmethods have been used to realize these devices [5]–[8]. Afew sensing techniques such as LC circuits [12] have alsobeen implemented for measuring the vertical displacement ofmicromirrors.

Mohammad Maroufi and S. O. Reza Moheimani are with the De-partment of Mechanical Engineering, University of Texas at Dallas,Richardson, TX 75080 USA (e-mail: [email protected],[email protected]).

MEMS stages can also be used for in-plane or out-of-plane positioning of AFM probes during imaging [13]–[15].The MEMS stages designed for such a task should normallyoperate in closed loop in almost all AFM modes of imaging.This necessitates the incorporation of a sensing mechanism tomeasure the out-of-plane displacement of the MEMS nanopo-sitioner. In addition, as the AFM is typically used for imagingmicro- and/or nano-sized specimens, the vertical displacementrange of approximately ±1µm is adequate for most imagingapplications assuming the initial landing of the probe has beenperformed by another positioner. The required mechanicalbandwidth of the stage, on the other hand, can be determinedbased on the intended imaging speed [16], [17].

In [18], we reported an XY stage for lateral positioning ofan AFM microcantilever. The device features a microcantileverwhich is excited to vibrate in the out-of-plane direction usinga sputtered aluminum nitride (AlN) piezoelectric layer. Thepiezoelectric transducer is used for simultaneous sensing andactuation and the device is implemented for AFM imagingin tapping mode. No out-of-plane mechanism, however, isincorporated to vertically position the microcantilever relativeto the sample. Hence, the device relies on an external Z-positioner for AFM imaging. In the device reported in [15],out-of-plane positioning is achieved through electrothermalactuation. This, however, limits the bandwidth and increasespower consumption of the device.

In this paper, we present an out-of-plane MEMS nanopo-sitioner with built-in microcantilevers. The mechanism isintended to be ultimately used in a miniaturized AFM. Atorsional mechanism incorporating piezoelectric actuators isimplemented to produce out-of-plane displacement. Piezo-electric actuation mechanism is selected as its realizationis straightforward in a standard silicon on insulator (SOI)microfabrication process. In addition, the process allows usto deposit a layer of AlN on the microcantilever, enabling itsfuture use in dynamic mode AFM.

The bulk piezoresistivity of the silicon is exploited tomeasure the out-of-plane displacement of the MEMS nanopo-sitioner. We previously reported on the use of the bulk piezore-sistivity of silicon in tilted beam flexures for measuring in-plane displacement of a 1-degree of freedom (DOF) MEMSstage in [19], [20] and in a 2-DOF MEMS nanopositionerin [21]. The sensor relies on the axial mechanical stress fordisplacement measurement and is expected to be insensitiveto out-of-plane motions. In this paper, the measurement of theout-of-plane displacement of the stage in differential modeis made possible through a novel sensor design. The sensingmechanism is realized by employing the bulk piezoresistivityof silicon through the implementation of double-sectioned



2

clamped-guided beams.The paper continues as follows. In the next section, design

and fabrication of the out-of-plane nanopositioner is presented.The physical concept and the readout circuit configuration ofthe piezoresistive sensors are discussed in Section III. Here,by proposing an analytical model, the linearity of the sensoris also investigated. The MEMS stage and the sensors arefully characterized in the time and in frequency domainsin Section IV. The characterization of the microcantileversare detailed in Section V. Finally, the conclusion and thefuture work are presented in Section VI and in Section VII,respectively.

II. NANOPOSITIONER DESIGN AND FABRICATION

A scanning electron microscope (SEM) image of the stageand its schematic are shown in Fig. 1a and Fig. 1b, re-spectively. The stage is designed to provide an out-of-planedisplacement for AFM microcantilevers incorporated on itsopposite sides. Each microcantilever comprises two sectionswith different widths. An AlN layer is deposited on bothsections, enabling simultaneous actuation and sensing [22].Straight beam flexures are exploited on both sides of the stage,three on each side, functioning as the mechanical suspension.These beams also provide paths for electrical routing tothe piezoelectric layer on the microcantilevers and electricalground connection to the stage. The straight beams connectedat the middle of the stage have a width of 19µm and are calledtorsion bars as the stage is designed to rotate around them.

Two double-sectioned beams with AlN layers are fabricatedon either side of the stage that serve as actuators. The AlNlayers are deposited only on the wider section of these beamsso that by applying an electrical voltage, the beam producesan out-of-plane displacement. Thus, by applying actuationvoltages with opposite polarities to the actuators on the topand bottom of the straight beams, the stage rotates around thetorsion bars. The torsional mechanism, in fact, amplifies theout-of-plane displacement of the actuators at the base of themicrocantilevers.

To measure the torsional displacement of the stage and,as a result, the out-of-plane displacement at the base of themicrocantilevers, two piezoresistive sensors are implemented.Each sensor consists of two double-sectioned beams located onopposite sides of the torsion bars. These beams are designatedby S1 and S2 in Fig. 1b. When the stage rotates, the electricalresistance of the beams varies oppositely due to the piezore-sistivity of the silicon. These variations are translated to anoutput voltage using a readout circuit. On the contrary to theconventional piezoresistive sensors where the implementationof highly-doped regions on the flexures are required, thissensing mechanism relies on the bulk piezoresistivity of thesilicon. Further details on the design of the sensor and itsassociated readout circuit are provided in Section III. Thegeometrical properties of the stage are summarized in Table I.

The standard microfabrication process known asPiezoMUMPs provided by MEMSCAP is used to implementthe nanopositioner [26]. As shown in Fig. 2, the fabricationprocess starts with a silicon-on-insulator (SOI) wafer with

TABLE ITHE GEOMETRICAL AND MATERIAL PROPERTIES OF THE PROPOSED

MEMS NANOPOSITIONER.

Young’s modulusSilicon [23] Es = 169GPa

Aluminum [24] Ea = 25GPaAlN [25] Ep = 300GPa

CantileverNarrow section Width:30µm, Length:180µmWide section Width:50µm, Length:200µm

Stage Width 700µm to 1134µm, Length: 1097µmFlexure beams Width: 11µm , Length: 1050µm

Torsion bar Width: 19µm , Length: 1050µmPiezoelectric Narrow section Width:5µm, Length:115µm

actuation beams Wide section Width:260µm, Length:935µmPiezoresistive Narrow section Width:3.5µm, Length:222µmsensing beams Wide section Width:11µm, Length:398µm

10µm-thick device layer. The doping at the top surfaceof the device layer is further enhanced by deposition of aphosphosilicate glass layer followed by an annealing process.A 0.2µm thermal oxide is grown and patterned to functionas an insulating layer. The 0.5µm-thick AlN layer is thendeposited by reactive sputtering and patterned using the wetetch process. Afterwards, a metal stack consisting of 20 nmchrome and 1µm aluminum is deposited and patterned toobtain electrical routing. The mechanical structure is thenrealized by patterning the device layer using the deep reactiveion etching (DRIE) process. The back-side of the wafer isthen etched via reactive ion etching (RIE) and DRIE. Finally,the buried oxide layer underneath the moving structure isetched and the device is released.

As visible in Fig. 1, double-sectioned clamped-guidedbeams are used to realize both piezoelectric actuators andpiezoresistive sensors. The analytical model for these beamsis discussed in the next section, which is followed by a finiteelement modeling of the MEMS stage.

A. Double-sectioned Beams

Fig. 3 shows the schematic of a clamped-guided beamwith the total length of L experiencing an out-of-plane dis-placement. The guided end displacement (v) is assumed tobe known. The beam comprises two sections with the firstsection having a length of a and Young’s modulus of E1 andthe second area moment of I1. Corresponding parameters ofthe second section, with the length of b, are designated asE2 and I2. The mechanical moments along the beam in thefirst section (M1) and in the second section (M2) obey thefollowing: M1 = M0 − F0x1

M2 = M0 − F0 (x2 + a)(1)

where F0 and M0 are the unknown reaction force andmoment at the clamped end, respectively. These unknownsas well as the deflection functions of both beam sections(i.e. y1(x1) and y2(x2)) are obtained in the appendix usingEuler-Bernoulli beam theory. Considering the beam’s curva-ture, it is expected that the bending moment becomes zero at a



3

(a)

(b)

Flebea

onr

Narrow section of actuator beam

Piezoresistive

Microcantilever

Piezoelectric and aluminum layers

Aluminum layer

Double-sectioned actuator beam

Fig. 1. a) SEM image of the 1-DOF piezoelectric MEMS nanopositioner. Double-sectioned structure of a sensing beam and the narrow section of an actuatorbeam are highlighted in the close-up views. b) A schematic of the stage. Two sensors are incorporated, each comprising of two piezoresistive sensing beamsannotated by S1 and S2. Green areas on the wider section of piezoelectric actuator beams and microcantilevers show the AlN layer.

point along the beam and changes its sign. This point is in-factthe inflection point of the beam’s deflection function, and wedenote its distance from the anchor point by linf . As a designcriterion for both piezoelectric actuator and piezoresistivesensor, the lengths of the beam’s sections, a and b, shouldbe determined such that the inflection point coincides withthe point where the two sections are met i.e. a = linf . Usingthe analytical model presented in the appendix, this conditionleads to a quadratic equation with respect to a, which has thefollowing solutions:

a =L

1±√X

(2)

where

X =E2I2E1I1

(3)

while only the plus sign is acceptable. Equation (2) isemployed for the design of the piezoelectric actuators and thepiezoresistive sensors, which are explained in the next sectionand Section III, respectively.

B. Piezoelectric Actuators

In the MEMS device, double-sectioned beams, with apiezoelectric layer on their wider section, enable the actuation.The structure of one of the actuation beams is schematicallyshown in Fig. 4a. The beam is comprised of silicon, AlN,and aluminum layers, thus it can be considered as a multi-morph piezoelectric structure [27]. The actuation voltage isapplied between the silicon and the aluminum layers as top andbottom electrodes, respectively. As is clear in Fig. 4b, upon theapplication of the actuation voltage to a piezoelectric actuator,a mechanical moment is produced that bends the beam in theout-of-plane direction [28], [29]. In order to increase the outputdisplacement of the actuator, the length of the first sectionwith piezoelectric layer (i.e. a) should be selected so that thesign of the mechanical moment along this section remainsunchanged. Here, this criterion is met by exploiting the resultof the analytical model presented in (2).

Dimensions of the piezoelectric actuators and the Young’smodulus of their structural materials are presented in Table I.To achieve a higher actuation force, the width of the firstsection, accommodating the piezoelectric layer, is chosenmuch larger than the second section. Since the first section alsofeatures a composite structure with three layers, the equivalent



4

Thermal oxide

Substrate

Device layer

(1) (2)

(4)(3)

Buried oxide layer

Piezoelectric layer

(5)

Metal layer

(6)

Fig. 2. The fabrication process sequence. Thermal oxide and AlN layers aredeposited and patterned using wet etch process in (1) and (2), respectively.Metal layer is patterned by lift-off in (3). DRIE of the device layer isperformed in (4). Patterning of the substrate using RIE and DRIE and releasingof the device are respectively shown in (5) and (6).

v

y

L

y

x

M0

Clamped end

F0

F0

M1

x1 x2a b

I11

E ,

I22

E ,

Beam segment

Fig. 3. The schematic of a double-sectioned beam enduring a known out-of-plane displacement. x1 and x2 are denoting the coordinate systems for thefirst and the second section, respectively. The free-body diagram of a segmentof the beam is also presented.

bending rigidity of the section (EIeq) is used instead of E1I1in (3). Obtaining EIeq is straightforward while the equivalentarea method is used [30].

Note that, due to the limitations imposed by the microfabri-cation process [26], the width of the AlN and aluminum layersare selected to be 10µm and 16µm smaller than the siliconbeam’s width, respectively. Since the thickness of these layersis also much smaller than silicon, they have an insignificanteffect on the first section’s bending rigidity. Further analyticalanalysis of the piezoelectric actuator is performed using thesimilar approach for modeling of cantilevers with piezoelectricactuator layers previously discussed in the literature [28], [29].

Other parameters such as the resonance frequencies ofthe stage should also be considered in the design of thepiezoelectric actuators. In addition, the Euler-Bernoulli beamtheory becomes less accurate due to the large width sizeof the first section. Hence, an iterative method is employedbetween the analytical and finite element models to performmore accurate dimensional tuning. The results of the finiteelement modeling are explained next.

Piezoelectric layer

Stage

Aluminum layer

a b

(a)

(b)

Vact

31

GND

Fig. 4. (a) The top view of one piezoelectric actuation beam is schematicallyshown. (b) An actuation voltage (Vact) is applied to the aluminum layer whichgenerates an electrical field along AlN thickness. The polar axis of the AlN isalong its thickness (designated by 3), thus, the AlN layer produces mechanicalstress along its length, denoted by 1, in the wider section of the beam in its31-actuation mode.

(a)

(b)

Fig. 5. (a) shows the first resonant modes of the stage. A high-frequencyresonant mode of the microcantilever is also presented in (b). In both modeshapes, the color codes show the magnitude of the modal displacement.

C. Finite Element Model

The CoventorWare software is used to construct the fi-nite element model (FEM) of the MEMS stage. Since thedevice generates out-of-plane displacement via a torsionalmechanism, the dimensional tuning is performed such thatfundamental mode of the stage is torsional. Consequently, thismode will be fully observable from the displacement sensors.As shown in Fig. 5a, the torsional mode of the device is locatedat 9.8 kHz.

When used in tapping mode, the microcantilever is forcedto oscillate at or near a resonance frequency [3]. The resonantmode located at 95.2 kHz, depicted in Fig. 5b, can potentiallybe used for this purpose.



5

ws

wbSensing segment Aluminum layer

Vc

Anchor Point

Stage

Doped silicon

N.A.

Cross section

zb

d ts

(a)

(b)

eI

GNDy

x1

v

M1>0 2M <0

x2

a b

Fig. 6. (a) The top view of the sensing beam and the direction of electricalcurrent (Ie) are schematically presented. (b) The schematic of a sensingbeam enduring an out-of-plane displacement. The close-up view presentsthe direction of the mechanical stress and an approximate distribution of thedopant concentration along the thickness.

In time domain analysis, actuation voltages with oppositepolarities are applied to the piezoelectric actuators above andbelow torsion bars inducing stage rotation. The FEM showsan out-of-plane displacement of more than 1µm at the tip ofthe microcantilevers with an actuation voltage of 3.1 V.

III. PIEZORESISTIVE SENSORS

In this section, we describe the piezoresistive sensors, andinvestigate their linearity.

A. The Sensor

In the MEMS device, although the doping level of thetop surface of the device layer is enhanced, the exact depth,concentration and profile of the doping is not strictly con-trolled. In addition, no extra fabrication steps for implementinghighly-doped regions on mechanical flexures are availablethrough the microfabrication process used here. Therefore, theproposed piezoresistive sensor is designed to utilize the bulkpiezoresistivity of the top surface of the device layer, whereit is doped, in a differential configuration.

The sensor consists of two double-sectioned beams locatedon either side of the torsional bars. One of these beams isschematically shown in Fig. 6. The double-sectioned beamfeatures a wide aluminum covered section and a narrower“sensing segment”. Due to the aluminum layer, the widesection has a negligible electrical resistance and it is short-circuited to the electrical ground via the stage.

As the stage rotates around the torsion bars, the guided endof the sensing beam displaces in the out-of-plane direction.

To achieve the sensing functionality with a high signal tonoise ratio, the dimensions of the beam should be selectedsuch that the polarity of the mechanical moment along thesensing segment remains unchanged for a given guided-enddisplacement. This is performed by employing the result ofthe analytical model presented in (2). The equivalent areamethod is also used to obtain the equivalent bending rigidityfor the aluminum covered section using the material propertiesin Table I.

For the selected dimensions it is expected that the mechan-ical moment has the same polarity along the entire sensingsegment as the beam’s guided end undergoes an out-of-planedisplacement as schematically shown in Fig. 6. Mechanicalstress distribution and an approximate estimate of the dopantdistribution in a cross section of the sensing segment arealso presented in the close-up view. Assuming pure bending,mechanical stress above the neutral axis (N.A.) in the dopedarea is unidirectional. This stress results in a change in theelectrical resistance of the sensing segment. The beam onthe opposite side of the torsion bar experiences a mechanicalmoment and consequently a mechanical stress of oppositepolarity. Hence, its electrical resistance changes in the oppositedirection allowing the sensor to function in the differentialmode.

B. Readout circuit

A variety of approaches may be used to convert theelectrical resistance change of the sensing segments to anoutput voltage [31]. The V-I transimpedance and Wheatstonebridge (in a half-bridge configuration) are amongst the moststraightforward methods that ensure adequate sensitivity. Thetransimpedance circuit is used here due to its better linearresponse [31].

The schematic of the readout circuit is shown in Fig. 7.The electrical currents flowing into the sensing resistances(Ie1,2) are initially converted to the voltage using operationalamplifiers (op-amps). The output of the op-amps are thendifferentially amplified using an instrumentation amplifier. Themagnitude of the change in the current flowing into the sensingsegment is designated by δIe and is assumed to be equal due tothe device symmetry. The output of the readout circuit shownin Fig. 7 can be easily written as:

Vout = 2ARfδIe (4)

where A is the gain of the instrumentation amplifier andRf is the feedback resistor. As is visible, the output of thecircuit is a linear function of the current changes in thepiezoresistors. For the realization, the high-precision low-noiseop-amp, OPA2227 [32], and the instrumentation amplifierINA128 [33] are used.

C. Analytical model

In this section, we are investigating the linearity of thesensor by obtaining the current change in the sensing segment(δIe) as a function of the displacement of the beam’s guidedend (v). The doping depth is assumed to be smaller than the



6

Vout

+

-

Rf

VC

Rs1

Rs2

GND

InstrumentationAmplifier

GND +

-

+

-

Rf

Ie1

Ie2

Fig. 7. The transimpedance readout circuit used to convert the resistancechange in the sensor to an output voltage.

half of the beam’s thickness. In Fig. 6, d indicates the distancefrom the neutral axis, above which the doping and conse-quently the electrical current becomes significant. Derivationsare based on an Euler-Bernoulli beam in pure bending, whilethe unknown reaction force (F0) and the moment (M0) atthe beam’s clamped end are obtained in the appendix. Byreplacing M0 and F0 respectively from (27) and (26) in (1),the mechanical moment along the sensing segment is foundas a function of v as:

M1(x1) =E1I1H

v

[2ab+ b2 + a2X

2 (b+ aX)− x1

](5)

where H is defined in (28). In the sensing segment, theneutral axis is located at the center of the cross section, andthus, the bending stress at the distance z from this axis is [30]:

σb (x1, z) =M1z

I1. (6)

To obtain the resistance change of the doped layer whileundergoing a mechanical stress, Ohm’s law is written alongthe sensing segment in (7) assuming a unidirectional current.

Ex1 = ρJx1. (7)

Here, ρ is the resistivity of the doped silicon, and Ex1 andJx1 are the electrical field and the current density along x1direction, respectively. Due to the silicon’s piezoresistivity, ρis a function of mechanical stress as:

ρ = ρ0 [1 + σb (x1, z)πl (z)] (8)

where πl (z) is the piezoresistivity coefficient of the siliconalong the beam (along the current direction) and ρ0 is theinitial resistivity of the silicon in the absence of mechanicalstress. The coefficient πl can vary as a function of thecrystallographic orientation, doping concentration, and thetemperature of the silicon [34]. Due to the diffusion procedure,the doping concentration is expected to be variable along thebeam’s thickness, thus for the piezoresistivity we have:

πl = π0 × f(z). (9)

In (9), f(z) is a function accounting for the variation of thepiezoresistivity with the dopant concentration along z, whileπ0 is the piezoresistivity coefficient at the top surface of thebeam. Since silicon is n-type and the device is fabricated in(100) plane, the maximum π0 which can occur along the beamin this plane is −1.02×10−9Pa−1at room temperature and atlow dopant concentration (Fig. 2 in [34]). Also, the magnitudeof f(z) can vary between 1 at low dopant concentration level(about 1015 cm−3) to about 0.35 at high concentrations (about1020 cm−3) [34]. Note that, by assuming a small bias voltage(Vc), the joule heating in the sensors is ignored. By replacing(8) and (9) in (7) we have:

Ex1 = ρ0

[1 +

M1z

I1π0 × f(z)

](10)

where the bending stress is replaced by (6). To calculate thecurrent density along the sensing segment (jx1), we may use:

Vc =

∫ a

0

Ex1dx1. (11)

Replacing (10) in (11) and integrating, jx1 is obtained asfollows:

jx1 =Vc

aρ0 [1 + vzT × f(z)](12)

where:

T =E1

2H

(ab+ b2

b+ aX

)π0. (13)

Having the current density (jx1) the electrical current in thedoped cross section of the sensing segment (Ie) is:

Ie =

∫ ts/2

d

jx(z)wsdz (14)

Equation (14) is rewritten in (15) by replacing jx1 from(12).

Ie =wsVcaρ0

∫ ts/2

d

1

[1 + vzT × f(z)]dz. (15)

Using the geometrical dimensions reported in Table (I), Tcan be evaluated from (13). Since both v and z are in themicrometer range while 0.35 . f(z) 6 1, we conclude thatvTzf(z) 1 and we may use:

1

1 + x∼= 1− x. (16)

Hence, the integral in (15), can be approximated by:

Ie ∼=wsVcaρ0

∫ ts/2

d

[1− vzTf(z)] dz (17)

or equivalently:

Ie ∼=wsVc(ts/2− d)

aρ0− wsVc

aρ0v

∫ ts/2

d

Tzf(z)dz. (18)

The first term in (18) is the initial current in the sensingsegment before the stage displacement, while the second



7

term represents the current variation (δIe) due to the guidedend displacement (v). This term also indicates that δIe is alinear function of v, regardless of the doping profile (f(z)).Revisiting the output of the readout circuit presented in (4),the sensor output is a linear function of the electrical currentchange (δIe) and consequently is a linear function of v.

The sensitivity of the sensor (S) is defined as the absolutevalue of the rate of the change in the sensor output (Vout) withrespect to the guided-end displacement (v). Using (18) in (4),the sensitivity is obtained as follows:

S =2ARfwsVc

aρ0

∫ ts/2

d

Tzf(z)dz. (19)

In order to calculate the sensor sensitivity in (19), knowingthe doping profile is necessary. Note that, in the case wherethe doped area extends below the neutral axis (i.e. d < 0), thesensor is still expected to function linearly. However, this candegrade the sensor’s sensitivity, and, in a special case, evenmakes it insensitive to the displacement.

For this design, the condition vTzf(z) ≤ 0.1 will be validprovided that the displacement (v) remains below 10µm1.Note that, the pure bending condition is valid for smalldisplacements. Other loading conditions such as generationof an axial force [35] can become dominant above a certaindisplacement range leading to a deviation from linear at thesensor’s output. This can also impose an additional limitationfor the sensor’s measurable displacement range.

IV. CHARACTERIZATION

Adjustment of the bias voltage in the readout circuit (Vcin Fig. 7) is carefully performed as a large voltage can causeoverheating and possible buckling of the sensing segment. Thebias voltage of 1.4 V is chosen for all experiments, and themeasured initial electrical resistance of each sensing beam isapproximately 400 Ω.

A. Static Response

In order to test the dc-level displacement, the stage istorsionally driven by applying up to 9 V actuation signalswith opposite polarities to the piezoelectric beam actuatorsabove and below the torsion bars. The bottom layer of thepiezoelectric layers are electrically grounded via the stage.All displacement measurements are performed using a PolytecMicrosystem Analyzer MSA-100-3D.

The out-of-plane displacement of the stage at the microcan-tilever’s base as a function of the actuation voltage is presentedin Fig. 8a. A linear trend is observed between the actuationvoltage and the microcantilever’s base displacement. The baseand the tip displacements of the microcantilever are also mea-sured while the stage is being torsionally actuated. As shownin Fig. 8b, these displacements are linearly dependent asexpected. The stage at the cantilever’s base reaches more than1.2µm of peak-to-peak (Pk-Pk) displacement, which translatesto about 2.1µm for the tip. At the maximum displacement

1For the calculation, f(z) = 1, z = 5µm, and | π0 |= 1.02×10−9 Pa−1

are assumed.

-8 -6 -4 -2 0 2 4 6 8

Actuation Voltage (V)

-1

-0.5

0

0.5

1

Ba

se

Dis

pla

ce

me

nt

(µm

)

(a)

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

Base Displacement (µm)

-0.4

-0.2

0

0.2

0.4

Se

nso

r O

utp

ut

(V)

-2

-1

0

1

2

Tip

Dis

pla

cem

ent (µ

m)

(b)

Fig. 8. a) The out-of-plane displacement of the microcantilever base is shownversus the actuation voltage. b) The piezoresistive sensor output and the out-of-plane displacement of the microcantilever tip are shown as a function ofthe microcantilever’s base displacement. The slope of the tip displacementline is 1.598.

range of the stage, the tilting angle of the microcantileveris calculated to be 0.06. This angle is infinitesimal, and itspossible effect on the AFM imaging can also be canceled outdue to its deterministic property.

The output of the piezoresistive sensor is also recorded usingthe same test method, and is presented versus the displacementof the stage at the microcantilever base in Fig. 8b. Thecalibration factor defined as the slope of a fitted rectilinearline obtained using the least squares method is calculatedas 0.37 V/µm. To estimate the linearity of the sensor, thepercentage of the mapping error (M ) is defined as [36]:

M = ±100max | er |

FSR(20)

where the FSR is the full-scale range of the sensor outputand | er | is the distance between each experimental pointand the fitted line. M is obtained as 0.47 % for the sensoroutput versus input displacement indicating the highly linearbehavior of the sensor. Since, a linear relationship also existsbetween the displacement of the microcantilever base and itstip, the sensor output may also be used as a measure of themicrocantilever tip displacement.

B. Dynamic Response

The out-of-plane displacement of the stage is also tested inthe frequency domain using the MSA-100-3D. The measure-ment is performed at the base of the top microcantilever. Thefrequency response is presented in Fig. 9 indicating that thefundamental torsional mode of the stage is located at about7.8 kHz.

We recorded the frequency response of the piezoresistivesensor and compared it with the stage displacement response



8

103 104 105

-50

0

50M

agni

tude

(dB

)

Piezoresistive SensorMSA

103 104 105

Frequency (Hz)

-400

-200

0

Pha

se (

deg.

)

Piezoresistive Sensor

Fig. 9. Frequency response of the stage obtained by the MSA and thepiezoresistive sensor. The sensor completely captures the fundamental modeof the stage while the feedthrough from the actuation becomes dominant athigher frequencies. For the sake of clarity, the dc-gain of both responses areadjusted to unity.

101 102 103 104 105

Frequency (Hz)

-100

-90

-80

-70

Mag

nitu

de d

B (µ

m2 /H

z)

Fig. 10. The PSD of the piezoresistive sensor in a bandwidth of 100 kHz.

in Fig. 9. The sensor precisely captures the dynamics ofthe stage up to about 13 kHz of bandwidth. Beyond thisbandwidth, however, the feedthrough signal originating fromthe actuation becomes dominant. The parasitic impedancesbetween the actuation and sensing tracks are most likelyleading to this phenomenon. The feedthrough behavior inin-plane bulk piezoresistive sensors is further investigated in[19], [21] by proposing an analytical model based on parasiticimpedances. Methods such as modifying the design of thesensor’s signal routing [21] and/or implementing external feed-forward compensation [37] can be employed to alleviate thefeedthrough and consequently expand the sensor bandwidth.

C. Noise Performance

The power spectral density (PSD) of the noise in a band-width of 100 kHz is obtained as shown in Fig. 10. As clear, thelow frequency flicker noise is dominant at the sensor’s output.This characteristic is also previously reported for the outputnoise of the electrothermal displacement sensors in [38] andpiezoresistive sensors in [19], [39].

The output noise of the piezoresistive sensor was recordedin the time domain for 12.8 s with the sampling frequencyof 390 kHz. The noise is filtered using two SR560 low-noise preamplifiers each of them featuring a first-order band-pass filter with the lower and upper cutoff frequencies of0.03 Hz and 30 kHz, respectively. Using the recorded data,the 1σ-resolution of the sensor is obtained as 3 nm for thedisplacement of the base of the microcantilever and 4.8 nmfor its tip. The sensor’s calibration factor is used to convertthe resolution to the displacement. Since the bias voltage of

TABLE IITHE PEAK-TO-PEAK DISPLACEMENT AT THE TIP OF THE

MICROCANTILEVERS ACTUATED IN IN-PHASE AND OPPOSITE PHASES.

Freq. Actuation (Pk-Pk) Displ. (Pk-Pk)

In phase 126 kHz 154.5mV 214 nmOpposite phases 91.8 kHz 191.9mV 285 nm

the sensor simultaneously affects its calibration factor and thenoise level, further tuning may be performed on this voltageto improve the sensor resolution [21], [40].

V. MICROCANTILEVER PERFORMANCE

The microcantilevers in the device are characterized byapplying actuation signals to their piezoelectric layers. Theactuation can be performed either in-phase or in oppositephases. In the in-phase method, the same actuation signal isapplied to the top and bottom microcantilevers, while voltageswith 180 phase shift are used on the microcantilevers foractuation with opposite phases.

The frequency domain behavior of the top microcantileveris shown for the in-phase and the opposite phase actuationmethods in Fig. 11a and b, respectively. During the test,piezoelectric beam actuators are connected to the electricalground while the displacement of the tip of the microcantileveris measured by the MSA. In-phase actuation method results ina larger number of resonant modes with the first resonant modelocated at 48.9 kHz. In the opposite phase actuation, however,the fundamental mode of the system, i.e. the torsional modeof the stage, can also be excited. Hence, this mode becomesobservable in the microcantilever frequency response shownin Fig. 11b. Fewer number of modes are also observable herewithin the tested frequency range.

Using the in-phase actuation, the mode shape of the resonantmode with 126 kHz frequency is determined and presentedin Fig. 11c. The MSA is used to record the out-of-planedisplacement of many test points scattered on the stage andthe microcantilevers. The same experiment is also performed,while the microcantilevers are actuated in opposite phases atthe resonant frequency of 91.8 kHz. The mode shape obtainedvia this experiment is shown in Fig. 11d. In both mode shapes,the microcantilevers achieve the largest displacement whilethe stage shows a negligible motion. This indicates that theselected mode shapes can be suitable for tapping mode AFMimaging.

The microcantilevers’ tip displacement for the same modeshapes are reported in Table II. More than 200 nm dis-placement is obtained with both actuation methods and withrelatively small actuation signals. This displacement range islarger than the oscillation amplitude required for tapping modeAFM which is ranging from 20 nm to 100 nm [3]. Note that, inorder to implement the microcantilevers in the feedback loopfor tapping mode imaging, the self-sensing method should alsobe used [22].

VI. CONCLUSIONS

An out-of-plane MEMS nanopositioner is presented in thispaper. The device is realized using a torsional mechanism



9

(a)

(c)

(b)

(d)

40 60 80 100 120 140

-200

-180

-160

-140

-120

Magnitude (

dB

)

40 60 80 100 120 140

Frequency (kHz)

-200

-100

0

Phase (

deg.)

10 50 100

-200

-180

-160

-140

-120

Ma

gn

itu

de

(d

B)

10 50 100

Frequency (kHz)

-200

-100

0

Ph

ase

(d

eg

.)

Fig. 11. a) The displacement of the top microcantilever tip in the frequency domain while the microcantilevers are actuated a) in in-phase, and b) in opposite-phases. In (c), the stage mode shape at the resonance frequency of about 126 kHz is presented, while the microcantilevers are actuated using in-phase method.d) shows the mode shape of the stage while the microcantilevers are actuated in opposite phases at the resonance mode 91.8 kHz.

with piezoelectric actuator beams to vertically position twopiezoelectric microcantilevers. A sensing mechanism based onpiezoresistivity of silicon is also proposed to measure the out-of-plane displacement of the stage. The sensing mechanismfunctions based on the bulk piezoresistivity of the siliconeliminating the need for additional microfabrication steps.The proposed sensors can be implemented in various MEMSdevices where an out-of-plane displacement measurement isrequired and the use of a standard microfabrication processis also a must. More than 1.2µm dc-level displacement isobtained by the stage with the resonant frequency of 7.8 kHz.The sensor shows a highly linear behavior with a bandwidthof 13 kHz limited due to the feedthrough signal from the actu-ation. The MEMS stage is designed to precisely position twopiezoelectric microcantilevers. The microcantilevers are alsocharacterized with two different actuation methods showinga promising performance for potential use in tapping modeAFM.

VII. FUTURE WORK

The behavior of the piezoresistive sensors can be studied forvarious bias voltages. In addition, the fabrication of a sharp tipat the end of the microcantilevers is required to utilize themas an AFM probe. This can be performed by employing thefocused ion beam technique. A self-sensing method shouldalso be implemented for the piezoelectric microcantilevers toincorporate them within a feedback control system to realizethe tapping mode AFM imaging.

APPENDIX

Considering the schematic of the beam shown in Fig. 3, thedeflection functions for each section of the beam are obtainedin (21) using the Euler-Bernoulli beam theory [30].

y1 = M0

2E1I1x21 − F0

6E1I1x31 + C1x1 + C2

y2 = (M0−F0a)2E2I2

x22 − F0

6E2I2x32 + C3x2 + C4

. (21)

The deflection functions contain four unknown constants i.e.Ci (i = 1 to 4). Taking the reaction forces into account, thereare six unknowns in (21), which should be obtained by usingboundary conditions. The first condition is written in (22) forthe clamped end where the slope and the displacement of thebeam are zero.

y1 =dy1dx1

= 0 ⇒ C1 = C2 = 0 (22)

The continuity of the beam where two sections are met isalso used to obtain two extra boundary conditions as follows:

y1 |(x1=a)= y2 |(x2=0) &dy1dx1|(x1=a)=

dy2dx2|(x2=0) . (23)

Using (23), the unknown coefficients C3 and C4 are ob-tained as function of F0 and M0.

C3 = M0

E1I1a− F0

2E1I1a2

C4 = M0

2E1I1a2 − F0

6E1I1a3

(24)

For the boundary conditions at the guided end (i.e. x2 = b)we have:

y2 = v &dy2dx2

= 0. (25)

Using (25), the remaining unknowns, i.e. F0 and M0, canbe easily obtained as:



10

F0 =E1I1H

v (26)

and

M0 =F0

2

[2ab+ b2 + a2X

b+ aX

](27)

where X is defined in (3) and H is:

H =

(2ab+ b2 + a2X

)4X(b+ aX)

[b2 + aX (2b+ a)

]−[

b3 + 3ab (b+ aX) + a3X

6X

]. (28)

The inflection point of the beam’s curvature should coincidewith the point where two sections are met i.e. a = linf . Hence,using (27) and the moment distribution equation in (1) wehave: (

2ab+ b2 + a2X)

2 (b+ aX)= a. (29)

Knowing b = L − a, the solution of (29) is calculatedand presented in (2), which is used for the design of thepiezoelectric actuator and the piezoresistive sensor.

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11

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Mohammad Maroufi (M’16) graduated with theB.Sc. degrees in Mechanical Engineering and Ap-plied Physics as a distinguished student from Amirk-abir University of Technology (Tehran Polytechnic)in 2008. He continued his studies in a Masters inMechatronics at the same university, and graduatedin 2011. He finalized his PhD in Electrical Engi-neering at the University of Newcastle, Australiain 2015. He is currently a Research Associate inthe Department of Mechanical Engineering at theUniversity of Texas at Dallas. His research interests

include the design and control of MEMS nanopositioning systems, MEMSbased sensing and actuation, on-chip atomic force microscopy, and modelingof smart materials and structures.

S. O. Reza Moheimani (F’11) currently holdsthe James Von Ehr Distinguished Chair in Scienceand Technology in Department of Mechanical En-gineering at the University of Texas at Dallas. Hiscurrent research interests include ultrahigh-precisionmechatronic systems, with particular emphasis ondynamics and control at the nanometer scale, in-cluding applications of control and estimation innanopositioning systems for high-speed scanningprobe microscopy and nanomanufacturing, modelingand control of microcantilever-based devices, control

of microactuators in microelectromechanical systems, and design, modelingand control of micromachined nanopositioners for on-chip scanning probemicroscopy.

Dr. Moheimani is a Fellow of IEEE, IFAC and the Institute of Physics,U.K. His research has been recognized with a number of awards, includingIFAC Nathaniel B. Nichols Medal (2014), IFAC Mechatronic Systems Award(2013), IEEE Control Systems Technology Award (2009), IEEE Transac-tions on Control Systems Technology Outstanding Paper Award (2007) andseveral best paper awards in various conferences. He is Editor-in-Chief ofMechatronics and has served on the editorial boards of a number of otherjournals, including IEEE TRANSACTIONS ON MECHATRONICS, IEEETRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, and ControlEngineering Practice. He currently chairs the IFAC Technical Committee onMechatronic Systems.

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