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Design and development of a MEMS capacitive bending strain sensor

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2006 J. Micromech. Microeng. 16 935

(http://iopscience.iop.org/0960-1317/16/5/009)

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INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF MICROMECHANICS AND MICROENGINEERING

J. Micromech. Microeng. 16 (2006) 935–942 doi:10.1088/0960-1317/16/5/009

Design and development of a MEMScapacitive bending strain sensorJ Aebersold1, K Walsh2, M Crain2, M Martin2, M Voor3,J-T Lin2, D Jackson2, W Hnat1 and J Naber2

1 Department of Mechanical Engineering, University of Louisville, Louisville, KY 40292,USA2 Department of Electrical and Computer Engineering, University of Louisville, Louisville,KY 40292, USA3 Department of Orthopaedic Surgery, University of Louisville, Louisville, KY 40292, USA

Received 29 October 2005, in final form 1 March 2006Published 30 March 2006Online at stacks.iop.org/JMM/16/935

AbstractThe design, modeling, fabrication and testing of a MEMS-based capacitivebending strain sensor utilizing a comb drive is presented. This sensor isdesigned to be integrated with a telemetry system that will monitor changesin bending strain to assist with the diagnosis of spinal fusion.ABAQUS/CAE finite-element analysis (FEA) software was used to predictsensor actuation, capacitance output and avoid material failure. Highlydoped boron silicon wafers with a low resistivity were fabricated into aninterdigitated finger array employing deep reactive ion etching (DRIE) tocreate 150 µm sidewalls with 25 µm spacing between the adjacent fingers.The sensor was adhered to a steel beam and subjected to four-point bendingto mechanically change the spacing between the interdigitated fingers as afunction of strain. As expected, the capacitance output increased as aninverse function of the spacing between the interdigitated fingers. At theunstrained state, the capacitive output was 7.56 pF and increased inverselyto 17.04 pF at 1571 µε of bending strain. The FEA and analytical modelswere comparable with the largest differential of 0.65 pF or 6.33% occurringat 1000 µε. Advantages of this design are a dice-free process without theuse of expensive silicon-on-insulator (SOI) wafers.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Modern medical science has emerged with a need tomonitor physiological functions (i.e., intravascular pressure,intraocular pressure, etc) [1–4]. A variety of these monitoringdevices require that their tasks be performed wirelessly andimplanted for indefinite terms to allow for patient mobility,continuance of daily activities and avoidance of costlysurgeries to remove the systems after utilization is complete.

One area of need is a system that would assist orthopedicsurgeons with the diagnosis of lumbar arthrodesis or spinalfusion. Lumbar arthrodesis or lumbar spinal fusion is asurgical procedure performed to immobilize affected vertebraeof the spine from deformity (i.e., scoliosis), degenerativeconditions (i.e., degenerative disc disease), trauma and tumorsto reduce or eliminate back pain usually originating in the

lumbar region. This pain can be caused by discogenicpain, degenerative disc disease, spondylolisthesis, facet jointdegeneration, fracture, infection, tumors and scoliosis [5].Over a period of 6–12 months, the grafted bone is expectedto fuse with the adjacent vertebrae to form a collective bonesegment. Spinal instrumentation is often implanted across theaffected vertebrae to provide stability and to promote fusiondevelopment. Figure 1 shows spinal rods and pedicle screwsimplanted on a demonstration spine model.

The current method to assess fusion is the evaluation ofradiographic images. Relative motion across fusion levelsis evaluated by comparing standing flexion and extensionstances. However, image obstructions often prevent a cleardetermination of relative motion. The primary problem withthe method of evaluation is that it is subjective and does notprovide objective data that can conclusively determine the

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Figure 1. Illustrations of spinal fusion instrumentation implemented on a demonstration spine model.

presence of fusion. Nor can it offer supplemental informationabout the rate of fusion progression. Therefore, developmentof a system that offers objective data is needed.

Several research groups have investigated quantitativeapproaches to help address this issue. Kanayama performedposterolateral fusion on 24 sheep to observe the biomechanical,radiographic and histological properties of the fusion massand the load-sharing characteristics of the instrumentationover a period of time [6]. He found that the implantedrods were mainly subjected to bending stress rather than axialstress and the load-sharing properties of spinal instrumentationdecreased as the fusion mass developed. In addition, the axialstress on the rod was quite small compared to the bendingstress and changes in axial stress were small throughout thepostoperative period. A key finding was that as the fusion massdeveloped and became stiffer, the bending moments on theinstrumentation began to decrease and loading was transferredto the fused segment. Based upon this premise, changes inbending strain can offer insight and objective data for thepresence of fusion and the rate of fusion progression.

Rohlmann has performed many studies using modifiedspinal instrumentation that can measure three axial forcecomponents and three moments acting on the implant [7, 8].He has discussed application of the fixator for many studies todetermine trunk muscle forces, loads on the implant duringwalking, comparison of intradiscal pressure and loads forvarious positions and exercises and comparison of loadsin vivo and in vitro conditions [9–12]. Rohlmann has statedthat after stabilizing the spine with the implant, spinal load isshared in the bridged region by both the spine and implant.The bending moment on the implant strongly depends on thestiffness of the bridged region and the surgical procedure [13].

In particular, one specific study by Rohlmann monitoredin vivo loads with the modified fixator over a temporal course inan attempt to pinpoint the occurrence of fusion [14]. Findingsfrom the trial found that loads on the fixators often variedfrom one measuring session to the next because of differentmuscular loads. However, as flexion bending moment datawere collected for the supine and standing positions it wasnoted that the difference in the bending moment data showeda strong decrease during the temporal course for four patients, amoderate decrease for four other patients. A negligible changewas found for two patients that exhibited low flexion bendingmoments throughout the study, but these were the only twocases where the bridged region was compressed. Rohlmannalso comments that the stiffness of the bridged region increasedwith time as indicated by the decreasing difference between

Figure 2. Spinal rod undergoing bending.

the flexion bending moments for standing and lying positions[14]. This method of comparing the differential of bendingmoment data in the supine and standing positions over a periodof time is the intended method to monitor the progression ofspinal fusion.

The discussion presented, henceforth, is the design anddevelopment of a MEMS (micro-electro-mechanical systems)capacitive bending strain sensor to be eventually incorporatedwith a batteryless implantable telemetry system. Thesensor design utilized a comb drive or interdigitated fingers,which have been used to generate variable capacitance byelectrostatic actuation or frequency tuning, which has becomeintegral parts of RF and wireless communications [15–23].Due to dimensional limitations of the housing, the sensor couldnot be longer than 10 mm or wider than 4 mm and capacitivetransduction was preferred to minimize power consumption.Telemetry components required a minimal resting capacitanceof 5 pF at zero bending strain. However, it was desired togain a capacitance output as large as possible yet not to exceed100 pF at the maximum anticipated strain of 1000 µε.

2. Design concept

The main function of the sensor was to change capacitance,while attached to a rod or beam experiencing bending strain. Inaddition, it was sought to mechanically amplify actuation dueto small deformations. Figure 2 represents rod deformationunder pure bending where L is the length of the rod, δ is the

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change in length of the rod, ρ is the radius of curvature, θ is theangular curvature and c is the radius of the rod. Deformationand the change in rod length is small, therefore, sensitivity ofthe sensor throughout the entire strain range was an importantconsideration during the design process

In an effort to anticipate strain values occurring from thebending moments on the spinal rods, Gibson performed adiscectomy on an excised spine from a cadaver [24]. The spinewas constrained and loaded in a material testing system (MTS)to simulate a 113.4 kg patient resulting in rod bending strainvalues of approximately 1000 µε. Calculations of bending andaxial strain show that more than 90% of total strain developedis attributed to bending strain.

It was necessary to find the change in length of the rod’supper surface, δ, to determine the initial gap of the fingers of thecomb drive to avoid shorting or touching of the interdigitatedfingers during actuation. The relationship between the angleof curvature, rod length and the radius of curvature is givenby the radius of curvature equation from deflection by flexuralloading [25]:

θ = L

ρ= L + δ

ρ + c= L − δ

ρ − c(1)

where θ is the angle of curvature, L is the rod’s length and ρ

is the radius of curvature. The ratio of the rod’s radius to theradius of curvature as it relates to bending strain is given by

c

ρ= δ

L= ε = σ

E= Mc

EI(2)

where M is the applied bending moment, E is Young’s modulusfor 316L stainless steel and I is the area moment of inertia. Thefinal relationship to determine the radius of curvature is givenby

1

ρ= M

EI. (3)

Stainless steel 316L rods with a length of 38.10 mm, radiusof 3.18 mm and a Young’s modulus of 200 GPa were used asdimensional and material properties. Bending strain values of1000 µε gave a radius of curvature of 3.175 m. The angle ofcurvature for the rod, θ rod, was found to be 0.012 radians andits change in length, δrod, was 38.100 µm. However, the lengthof the sensor was restricted to 10 mm due to spacing allowedby the sensor housing. The angle of curvature spanned by thesensor, θ sensor, was calculated to be 0.003 radians, which gavea change in length for the sensor, δsensor, to be 10.0 µm.

The capacitance relationship for a parallel plate system isgiven by

C = ε0εrA

d(4)

where C is the generated capacitance in farads (F) and ε0 is thedielectric constant of free space equal to 8.85 × 10−14 F cm−1

[26, 27]. The second dielectric constant, εr, is the relativepermittivity for the medium between the two plates and isequal to 1 for air. The overlapping area between the two platesis A and d is the distance between the two plates [27]. Fromthis relationship, increasing or decreasing the overlapping areaof the plates would produce a linear difference in capacitance,whereas, adjusting the spacing between the two plates wouldresult an inverse response. The sensor’s response can beamplified by increasing the distance from the neutral axis of

Figure 3. An illustration of the elevated comb drive or interdigitatedfinger capacitive design with two independent anchors.

the rod to the sensor’s interdigitated fingers. Based uponthis approach, an initial design was developed as shown infigure 3.

Based upon an initial capacitance requirement of 5 pF forthe telemetry system and the anticipated change in the sensor’slength, dimensional characteristics could be determined. Theinitial gap between the interdigitated fingers was 25 µm and thefinger sidewall height was 150 µm resulting in an overlappinglength of 1705 µm. The anchor height was changed by addinga glass pad to achieve larger actuation, higher sensitivity and toprovide a large surface area for attachment to the rod. The finaldesign included an array of 89 interdigitated fingers. The largegap between the fingers was required to maintain a 10:1 aspectratio needed for the DRIE process to create the interdigitatedarray. Based upon this dimensional information and ignoringfringing effects, the initial capacitance was calculated to be8.01 pF.

3. Finite-element analysis

Finite-element analysis (FEA) using ABAQUS 6.5(Providence, RI) was performed to model actuation of thesensor to calculate capacitance output and avoid fracture ofthe materials due to developed stresses in the silicon or glasspads. Actuation or displacement of the interdigitated fingerswas used to calculate capacitance. Analysis of the systembegan by properly constraining the beam to produce acontinuous magnitude of strain across its surface whileundergoing bending. The sensor was modeled by positioningborosilicate (7740) glass to the bottom of the anchors andattaching the assembly to a beam using the constraints.This was performed to reduce stress concentrations and toprovide ample area to apply adhesive for final attachment tothe rod. The glass was represented as an isotropic materialwith a Young’s modulus of 63 GPa and a Poisson’s ratio of0.2 [28]. Silicon was represented as an isotropic materialwith a Young’s modulus of 150 GPa and a Poisson’s ratioof 0.23 [29]. The beam was meshed with 800 µm, 8-nodelinear bricks with reduced integration or C3D8R elements.The glass pads were meshed with similar 70 µm elements. Thesensor was modeled with 100 µm, 10-node modified quadratictetrahedrons or C3D10M elements. Brick elements wereconsidered for the sensor geometry, but exceptionally longfinger lengths as compared to the finger width would havecreated an unreasonably large number of small elements andextended computational time. Figure 4(a) shows the meshedmodel of the micro-machined silicon sensor, glass pads andtesting beam. To reduce computational time, the modelwas simplified to include fingers only in the middle and endsections, as seen in figure 4(b).

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(a)

(b)

silicon anchor

interdigitated fingers

Figure 4. Illustrations from the ABAQUS FEA model before bending. (a) Overall view of the sensor model attached to the rod.(b) Close-up view of the end of the sensor demonstrating the fingers and anchor.

Figure 5. Illustration of the maximum principal stresses developed in the glass pads and sensor while attached to a beam undergoing1074 µε of bending strain. The beam is not shown.

Particular interest was given to the generated stresses toavoid failure of the materials. The mechanical strength of7740 borosilicate glass is 15 MPa [30], whereas the fracturestrength of silicon is significantly higher at 7 GPa [31].Figure 5 shows maximum principal stress values of 283 MPafor the glass pads and the silicon sensor undergoing 1074 µε

of bending strain from the beam. This value was generateddue to the 6000 N load couple applied to one end of the beamto generate a constant magnitude of strain on the surface where

the sensor would be attached. While these values exceed themechanical strength of the borosilicate glass it is believed thatthe glass is annealed during anodic bonding, which improvesits fracture strength [30].

While undergoing bending, the sensor will exhibita parabolic increase in capacitance due to its transverseactuation. The narrow gap developed on one side of theinterdigitated fingers dominates the sensor’s net capacitance.However, the sensor also exhibits vertical actuation resulting

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Design and development of a MEMS capacitive bending strain sensor

Figure 6. Front view of the capacitive strain sensor actuated fromthe rod undergoing bending.

in a reduction of the overlapping surface area. Figure 6 shows afront view of the sensor undergoing vertical actuation withoutthe glass pads.

Displacement results from figure 7 show transverse andvertical displacement of the sensor while attached to the beamundergoing 1653 µε of bending strain. This strain valuewas selected to clearly show the vertical displacement ofthe interdigitated fingers, which may not be visible at lowermagnitudes. The final small gap between the interdigitatedfingers was 4.3 µm, whereas, vertical displacement of theendmost fingers was 26.14 µm. However, this verticaldisplacement becomes smaller when approaching the midpointof the sensor. These results were used to predict a capacitanceof 10.11 pF at 1074 µε compared to the initial calculatedcapacitance of 8.01 pF at 0 µε. Increasing the height of theborosilicate glass pad amplified actuation of the sensor byaugmenting the distance from the neutral axis of the beam tothe sensor’s plane of interdigitated fingers. The height of theborosilicate glass pads is 300 µm.

4. Fabrication process

The fabrication process used double-sided polished 2′′,300 µm thick silicon wafers and a borosilicate glass wafer300 µm thick. The wafers were highly boron doped (p+)with a low resistivity of 0.001–0.005 � cm to replicate ametallic substrate and to avoid sputtering or electroplating ametallic layer. The glass wafer was diced into 3 mm squaresbefore fabrication. Processing began with base cleaning ofthe wafer to remove organic materials and wet oxidation todevelop an oxide thickness layer approximately 1 µm thick,as seen in figure 8(a). One side of the oxidized wafer waspatterned using a buffered oxide etching (BOE) solution tocreate the sensor’s anchors. The remaining oxide from the topsurface was removed and potassium hydroxide (KOH) was

Figure 7. Transverse and vertical displacement of the interdigitated fingers of the sensor, while attached to a beam undergoing 1653 µε ofbending strain.

used to reduce the overall thickness of the wafer, excludingthe anchors to 150 µm, as shown in figure 8(b).

The wafer was wet oxidized again, as seen in figure 8(c), toan oxide thickness of 1 µm, which served as a mask for deepreactive ion etching (DRIE) on the front side of the wafer.Oxide was removed from the backside of the wafer and the3 mm glass pads were anodically bonded to the anchors, asseen in figure 8(d). After anodic bonding, the top of thewafer was patterned using front to back alignment and thesilicon was etched in a Surface Technology System’s multiplexadvanced silicon etcher DRIE (Imperial Park, Newport, UK)system until the elevated interdigitated fingers were free, asseen in figure 8(e) without altering the glass pads. Beforeetching, thermally conductive grease was applied between thedevice and handling wafer to enhance cooling provided by thehelium-chilled chuck. Figure 8(f ) demonstrates attachmentof the wire leads and figure 8(g) is the sensor applied to abeam with the tethers broken. Tethers were incorporated inthe design to maintain alignment of the interdigitated fingersuntil application to the substrate. Figure 8(h) is the completedsensor adhered to a beam and ready for testing.

5. Experimental results and discussion

The sensors were attached to a steel beam using acyanoacrylate adhesive (M-Bond 200, Vishay Micro-Measurements, Raleigh, North Carolina) and tested for acapacitance change in four-point bending. Conductance andcapacitance of the sensor were measured using a Keithley590 CV Analyzer. Conductance was less than 2 µS when allsilicon materials were clear between the fingers and a changein capacitance could be measured. Figure 9 shows the MTSapplying bending strain and a sketch of the load diagram. Thesensor was placed between the loading points of the MTSfixture, where bending strain was constant.

Metal foil strain gages were mounted on the beamand upon adjacent materials not undergoing bending fortemperature compensation. The gages were connected to a2120A Measurements Groups strain gage conditioning unit.Following shunt calibration, the strain analog signal and loadcell output from the MTS were recorded using a customvirtual instrument developed using LabView version 6.1 anda National Instruments 6024 data acquisition card with asampling rate of 6.3 samples s−1. The capacitance sensor wasconnected to a Keithley CV Analyzer where the GPIB outputwas recorded with the same virtual instrument and collectionrate.

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(a)

(b)

(c)

(d)

( f )

(g)

(h)

wire lead wire lead

silver epoxy

break tethers

8 mm

silver epoxy

affix sensor to substrate

(e)

Figure 8. Fabrication process of the MEMS capacitive bending strain sensor. (a) Wet oxidation. (b) Wet etching the bottom of the wafer toform the anchors. (c) Re-oxidation of the wafer. (d) Anodic bonding of the glass pads to the anchors. (e) Deep reactive ion etching of theinterdigitated fingers from the top side of the wafer. (f ) Attachment of wire leads. (g) Application of the sensor to the substrate andbreaking of the tethers. (h) The completed sensor.

(a) (b)

Figure 9. Four-point bending in the (a) MTS fixture applying an equal strain magnitude across the surface of the beam. (b) Illustration ofthe loads applied by the MTS and placement of the sensors and strain gage on the bar.

A series of tests were developed to characterize thebehavioral response of the sensor. The first test applied acyclical load to generate 200–1010 µε at a frequency of0.0083 Hz for 5 h, for a total of 150 cycles, to determineif hysteresis was present. Application of a zero load was notselected to assure that the beam did not slip in the MTS fixture.The second test statically loaded the sensor for an extendedperiod of time to see if the capacitive output of the sensor would

drift over time. Optical micrographs of the micro-machinedcapacitive sensor are shown in figure 10. The first photograph,figure 10(a), shows equal spacing of the fingers before loading.Figure 10(b) shows movement of the interdigitated fingers afterbending was induced on the beam.

The sensor was tested under cycle loading and capacitanceversus strain data were collected using a customized LabViewprogram. The test was performed for a duration of 5 h or

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Design and development of a MEMS capacitive bending strain sensor

(a)

(b)

Figure 10. Visualization of the interdigitated fingers of the sensor.(a) Before bending strain is applied. (b) After bending strain isapplied the spacing between the fingers changes significantly.

7.00

7.50

8.00

8.50

9.00

9.50

10.00

10.50

11.00

0 100 200 300 400 500 600 700 800 900 1000 1100

Strain (µε)

Cap

acit

ance

(pF

)

Figure 11. Graphical results of 150 cycles of load testing for thesensor.

150 cycles with the sensor’s response shown in figure 11.It is evident from the graphical information that the responseof the sensor shows no hysteresis and is very repeatablethroughout cycle testing. However, the sensor was onlyloaded for the intended range of use, 100–1000 µε, anddoes not show the complete possible capacitance range ofthe sensor. Additionally, the data demonstrate the inverserelationship from equation (4) where the generated capacitanceincreases due to the reduction in spacing between theinterdigitated fingers. Three additional devices were testedand demonstrated comparable graphical behavior.

Sensor drift was evaluated by applying a static load fromthe MTS that generated 11.50 pF from the sensor. This valuewas beyond the capacitance range tested during cycle testing,but was selected due to increased sensitivity of the devicewhere drift would become more evident. Data were recordedin a similar manner as the cyclical test, but for a duration of10 h and are shown in figure 12. A minimal amount ofchange was seen during the static test; however, these small

10.00

10.50

11.00

11.50

12.00

12.50

13.00

0 1 2 3 4 5 6 7 8 9 10

Time (hours)

Cap

acita

nce

(pF)

Figure 12. Graphical results of static testing for the sensor.

6.00

8.00

10.00

12.00

14.00

16.00

18.00

0 200 400 600 800 1000 1200 1400 1600 1800

Strain (µε)

Cap

acita

nce

(pF)

FEA Model Experimental

interdigitated fingers touch

Figure 13. Graphical results of the entire capacitance range fromthe FEA model and experimental testing.

fluctuations were attributed changes in the load applied bythe MTS and not due to any change from the MEMS sensor.This was supported by load cell and strain gage data recordedsimultaneously from the MTS.

Maximum range of the sensor was determined byincreasing loading from the MTS to the beam until maximumcapacitance was achieved and conductance began to rapidlyincrease. This indicated that the fingers were in contactwith each other and no further actuation could be achieved.Figure 13 shows the change in capacitance from the FEAmodel and experimental data. A small differential is notedbetween the FEA model and experimental data between 500and 1300 µε, with the largest differential of 0.65 pF or6.33% at 1000 µε. This may be attributed to non-symmetricspacing between the interdigitated fingers of the sensor beforeapplication of bending strain and would explain the lowerthan anticipated capacitance value at 100 µε. Another itemnot taken into account was fringe effects incorporated inthe capacitance calculations from the FEA model, wherethe displacement data were used in a simple parallel platemodel. Further capacitive calculations could be performedwith the ABAQUS model, but deemed unnecessary given theencouraging results from the simple parallel plate model.

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6. Conclusions and recommendations

The following were derived from modeling, fabrication andtesting of the sensor. First, the sensor model developed inABAQUS simulated the longitudinal and vertical actuationof the fabricated sensor, which was verified by visualinspection of the fabricated sensor while undergoing actuation.Additionally, the sensor did not exhibit any drift characteristicsduring static testing or hysteresis during cycle testing. Finally,FEA modeling and experimental data results were comparableverifying efficacy of the ABAQUS model. The capacitiveresponse of the sensor performed as expected according to theinverse relationship of the spacing of the interdigitated fingers.It is recommended that additional ABAQUS capacitivemodeling is performed to account for fringe effects that wereomitted from calculations to better compare to quantitative andqualitative data.

Acknowledgment

Financial support from the National Science Foundation grantno 0097521 is gratefully acknowledged.

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