Electrothermal actuation of silicon carbide ring resonatorsEnrico Mastropaoloa� and Rebecca CheungSchool of Engineering, Scottish Microelectronics Centre, The University of Edinburgh, King’s Buildings,Edinburgh EH9 3JF, United Kingdom

Anne Henry and Erik JanzénDepartment of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping, Sweden

�Received 29 June 2009; accepted 14 September 2009; published 7 December 2009�

Silicon carbide �SiC� ring resonators have been designed, simulated, and fabricated in order toachieve higher resonant frequency compared to beam resonators. The resonant frequency as afunction of the ring radius and central hole radius, as well as the influence of the electrode designon the actuation efficiency have been investigated. Aluminum �Al� electrodes have been fabricatedon top of the structures in order to study the electrothermal actuation of the structures. The bimorphAl/SiC ring resonators have been constructed by etching the SiC in inductively coupled plasma. Therelease of the Si sacrificial layer has been performed with a XeF2 chemical etching. The radialrelease and area release have been characterized as a function of the central hole dimension atchamber pressure of 1 and 2 Torr, whereby the release rates have been found to increase as the holedimensions and the etching pressure increases. In addition, the release process has shown to begoverned by aperture effects. The rings fabricated with different dimensions have been actuatedmechanically and electrothermally, and the resonant frequency detected optically. The resonantfrequency has been shown to increase as the ring radius decreases and the hole radius increases, both

theoretically and experimentally. © 2009 American Vacuum Society. �DOI: 10.1116/1.3244622�

I. INTRODUCTION

In the past decade, the growth of wireless applications hasled to the improvement of radio frequency �rf� transceivers.Since most of the superheterodyne receivers employ off-chipfilters and mixers, attention has been focused on solutions forthe full on-chip transceiver integration. In particular, for theminiaturization and integration of high performance rf trans-ceivers, improvements for solving issues related to powerconsumption, impedance matching, operating frequency, andquality factor are needed. Recently, as a solution to theseissues, microelectromechanical system �MEMS� resonatingstructures performing filtering and mixing functions haveshown to be a challenging alternative to complementarymetal oxide semiconductor circuitry.1–3 In general, micro-beam resonators are used commonly due to their high Qfactors and simple fabrication process. However, beam de-signs suffer from frequency and dimensional limitationsleading to the need of new structures and materials forachieving higher resonant frequencies.4 Silicon carbide �SiC�is a good candidate for robust and high frequency MEMS.Given the same dimensions, SiC resonators achieve higherresonant frequencies compared to Si devices because of thehigh Young’s modulus, relatively low mass density and highacoustic velocity associated with SiC.5 In addition, SiC ismore inert than Si, therefore less prone to contaminant at-taching onto the devices surfaces so that higher Q factors areachievable under similar environmental conditions. In thepast years, great progress has been made in the fabrication ofSiC MEMS due to the improvement of the epitaxial growth

a�Author to whom correspondence should be addressed; electronic mail

e.mastropaolo@ed.ac.uk

3109 J. Vac. Sci. Technol. B 27„6…, Nov/Dec 2009 1071-1023/2009

methods6 and dry etching techniques for bulk and surfacemicromachining.7 Combining simple fabrication process andrelatively low power consumption compared to other formsof actuation methods, electrothermal excitation represents apromising alternative to the widely used electrostatictechnique.8–11 In addition, electrothermal excitation requiresa simple heating resistor that could be designed to match the50 � of the input/output network thus overcoming the issuesrelated to the high impedance typically associated with thecapacitively actuated devices. Furthermore, the simple layoutof electrothermal actuators allows the integration of addi-tional piezoresistive or piezoelectric electrodes that could beused for electrical sensing of the output signal.

In this work, we report on SiC ring resonators to achievehigher resonant frequencies compared to beam resonators.Aluminum �Al� electrodes have been designed on top of theSiC resonators in order to actuate the structures electrother-mally. Finite element simulations �FEMs� have been per-formed to study the modal behavior of SiC rings and thedegree of deflection induced electrothermally by the top Alelectrodes. The Al/SiC bimorph ring resonators have beenfabricated successfully by etching the SiC in inductivelycoupled plasma �ICP� with a mixture of sulfur hexafluorideand oxygen �SF6 /O2�. The release of the silicon �Si� sacrifi-cial layer has been performed and characterized with a xenondifluoride �XeF2� chemical etch. The fabricated rings resona-tors have been actuated mechanically and electrothermally toobtain out-of-plane deflections and the resonant frequency asa function of the structures’ dimensions has been investi-

gated.

3109/27„6…/3109/6/$25.00 ©2009 American Vacuum Society

3110 Mastropaolo et al.: Electrothermal actuation of silicon carbide ring resonators 3110

II. THEORY

A. Resonant frequency of circular structures

By solving the wave equation for flexural-mode beamsand disks, it is possible to perform a comparison between thenatural resonant frequencies obtainable with these two differ-ent structures. The analytical formula for the resonant fre-quency of clamped-clamped beams and for circular disks isgiven by fB and fD, respectively,12

fB = 1.03�E

�

t

L2 , �1�

fD = 1.65�E

�

t

D2 , �2�

where E and � are the material’s Young’s modulus and massdensity, respectively, t is the thickness of the structure, L isthe length of the beam, and D is the diameter of the disk. Bycomparing Eqs. �1� and �2�, it can be seen that for similardimensions, disks present a resonant frequency �1.6 timeshigher than clamped-clamped beams. However, formulas �1�and �2� give only an analytical prediction of the natural fre-quency of the structures. In fact, effects such as internal andresidual stresses due to the resonator’s material, its design,and the fabrication process can affect the resonant frequencymeasured experimentally.

B. Electrothermal actuation

Electrothermal excitation is a technique based on the elec-trically induced thermal expansion of the material that is tobe actuated. In the case of bimorph resonators, the top ma-terial can be used as an actuating electrode and the bottomone as the main structure. By applying a voltage across thetop electrode, an electrical current is generated through theresistor so that the Joule heating is dissipated within thestructure. This heating dissipation leads to a temperature in-crease in the bimorph structure that causes the resonator ma-terial to expand. In addition, the mechanical strain is en-hanced by the difference of the two materials’ thermalexpansion coefficient �TCE� as a result of the temperaturegradient generated through the structure. If an ac alternatingvoltage �Vac� is applied, temperature oscillations will be ex-perienced within the materials forming the resonators so thatthe structure will start to vibrate.8 Resonance is achieved ifthe applied frequency �fac� equals the half of the natural fre-quency �f0� so that fac= 1

2 f0.10 However, when the ac signal issuperimposed to a dc bias voltage �Vdc�, the device will bedriven into resonance if the applied frequency fac= f0.10

III. EXPERIMENTAL DETAILS

A. Design and simulations

Figure 1 shows the schematic of the designed SiC ringresonators. Single, double and interdigitated �IDT� electrodeshave been designed on top of the rings. The FEM analysis

has been performed by simulating out-of-plane deflections

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using COVENTORWARE. The thickness �t� of the structure hasbeen fixed at 2 �m and the side of the disk fixed as anchor.In order to study the dependence of the resonant frequencyon the ring radius, R has been varied in a range between 20and 200 �m. Moreover, structures with h=0 �m �disks�and with h=6, 15 �m have been simulated so that the influ-ence of the central hole on the resonant frequency can bestudied.

In addition, the electrothermal behavior of the Al/SiCrings has been investigated by applying a dc voltage of 1 Vacross the top electrodes, with the temperature at the sideanchor being fixed at 300 K. The actuation efficiency of thedifferent electrode configurations has been investigated byobserving the simulated induced displacements and amountof deflected area.

B. Fabrication and measurements

The rings have been fabricated using the same dimen-sional variations as in the simulations. A 2 �m thick singlecrystal SiC layer has been grown by hot-wall chemical vapordeposition13 on top of a silicon �Si� substrate. After deposit-ing a thin passivation layer �100 nm� of silicon dioxide�SiO2� by plasma enhanced chemical vapor deposition�PECVD�, a 500 nm thick Al layer has been sputtered on topof the SiO2. Afterward, the electrodes have been patterned byphotolithography and reactive ion etching. At this point, a3 �m thick PECVD layer of SiO2 has been deposited inorder to mask the SiC layer during the etching step. Holeswith different radii have been photolithographically pat-terned on the oxide mask and then the exposed material re-moved with a CF4 /H2 reactive ion etching plasma. After-ward, the exposed SiC has been etched in inductivelycoupled plasma with a SF6 /O2 gas mixture.7,13 In order torelease the rings, a XeF2 chemical etching step14,15 has beenused and the Si release has been investigated. The remainingmasking SiO2 has been removed with CF4 /H2 plasma. Fig-ure 2 shows the schematic side view of the fabricated Al/SiCring resonators. Figures 3�a� and 3�b� show two of the fab-ricated structures with double and IDT electrode configura-

FIG. 1. �Color online� Schematic of the ring resonators design with a singleelectrode on top �insets: different designed electrode configurations�.

tions, respectively. Typical resistance values in the range be-

3111 Mastropaolo et al.: Electrothermal actuation of silicon carbide ring resonators 3111

tween 5 and 20 � have been measured for the electrodes ofsingle and double configurations. However, the IDT elec-trodes have shown a higher resistance in the range of100–200 k� due to the open-circuit layout.

All the fabricated SiC resonators have been tested undervacuum and actuated mechanically with a piezodisk. Thestructures have been actuated electrothermally by applyingan ac signal �Vac=6 V� superimposed on a dc bias �Vdc

=2 V� to the top electrodes. Under these conditions, theJoule heating is generated due to the electrical current dissi-pated across the electrodes in the single and double electrodeconfigurations and through the conductive SiC in between

FIG. 2. Schematic side view of the fabricated ring resonators.

FIG. 3. �Color online� Optical pictures of the fabricated Al/SiC ring resona-

tors. �a� Double electrode; �b� interdigitated electrode.

JVST B - Microelectronics and Nanometer Structures

the electrode arms in the IDT layout. The resonant frequencyhas been detected optically with the use of a Polytec OFV3000 laser vibrometer that can measure frequencies up to 3.5MHz.

IV. RESULTS AND DISCUSSION

A. Release characterization

As mentioned in Sec. III B, the bulk Si underneath theSiC has been used as a sacrificial material and removedthrough the holes patterned in the SiC. The Si release withXeF2 chemical etching has been characterized by measuringthe radial release and calculating the released area as a func-tion of the process time. The release of rings with h=2, 6,and 15 �m has been performed at chamber pressures of 1and 2 Torr and by fixing the flow rate at 100 SCCM �SCCMdenotes cubic centimeter per minute at STP�. As shown inFigs. 3�a� and 3�b�, with our release process the circularshape of the patterned central hole is transferred to Si so thata ring structure is obtained. Rings with radius R in the rangebetween 15 and 200 �m have been fabricated.

1. Radial release rate

Figure 4�a� shows the obtained radial release rate as afunction of the etching time for the different values of h. Thesize of the central hole influences the etching rate of the

FIG. 4. �Color online� Release rates as a function of process time for h=2, 6,and 15 �m with XeF2 chamber pressures of 1 and 2 Torr. �a� Radial releaserate; �b� area release rate.

sacrificial layer increasing the radial release rate as the hole

3112 Mastropaolo et al.: Electrothermal actuation of silicon carbide ring resonators 3112

radius increases. As the hole’s size increases, the access ofthe gas species into the aperture and the removal of the etch-ing products are enhanced. The increase in the chamber pres-sure from 1 to 2 Torr does not affect the release rate for holeradius of 2 �m. However, when the pressure is increased, arelatively small increase and a larger one is observed for holeradii of 6 and 15 �m, respectively. This behavior is prob-ably due to the fact that by increasing the pressure, the meanfree path of the gas species decreases leading to a higheramount of species able to access the aperture. This results inan increase in the probability of chemical reaction with Si,hence increasing the radial release rate. However, it is be-lieved that the mean free path of the species is not reducedenough to enhance the access through the aperture with h=2 �m so that the increase in the radial release rate is notobserved for this aperture size.

2. Area release rate

The effect of the hole size and the increase in the etchingpressure can be better observed if the released area formingthe annular ring is considered. Figure 4�b� shows the calcu-lated area release rate as a function of the etching time fordifferent hole radii at the chamber pressure values of 1 and 2Torr. It can be seen that a higher area release rate is evidentwith increasing h. The larger area release rate for h=15 �m at higher pressures suggests the dominance of theaperture effects in the etching mechanism. In addition, thearea release rate is found to increase initially and then todecrease after some time. This effect is probably due to thefact that at the beginning, the amount of gas species able toenter in the hole is higher than the actual amount needed toremove Si. As Si is etched and removed, a larger amount ofSi is exposed and consequently a larger area is released re-sulting in an increase in the area release rate. As time goeson, the concentration of exposed Si becomes higher than theconcentration of gas species available to etch it, hence thearea release rate starts to decrease due to the depletion of thegas species.

B. Influence of ring design on resonant frequency

1. Mechanical simulations

Figure 5 shows the results obtained from the mechanicalsimulations. The resonant frequency has been plotted as afunction of the ring radius �R� for different hole radii �h=0,6, and 15 �m�. The resonant frequency is seen to increasewhen R decreases achieving values up to 30 MHz for R=20 �m and h=6 �m. Moreover, higher values have beenobtained for smaller rings reaching frequencies up to 145MHz for R=20 �m and h=15 �m. The quadratic behavioras a function of the radius length R is in good agreementwith the analytical formula reported for disk structure �2�. Inaddition, when R�80 �m the resonant frequency valuesobtained for the different hole sizes remain the same whilefor R�80 �m, the resonant frequencies obtained for h=15 �m �i.e., less wide ring size� are observed to be higher

than those obtained for h=0 and 6 �m.

J. Vac. Sci. Technol. B, Vol. 27, No. 6, Nov/Dec 2009

In order to deduce better the influence of the central holeon the modal behavior of the structure, the inset of Fig. 5shows the resonant frequency as a function of the hole radiush for ring radii R=30, 40, 80, and 100 �m. It can be seenthat for values of R�80 �m the resonant frequency remainsconstant despite the increase in the hole size. On the con-trary, for R�80 �m, the resonant frequency is observed toincrease as h increases from 6 to 15 �m, more so for smallerR. The impact of the size of the central hole h on the reso-nant frequency becomes more evident as R decreases �i.e., asthe width of the ring becomes smaller�.

As expected from the comparison between the analyticalformulas for bridge �1� and disk �2�, the simulated SiC ringsresonate at higher natural frequencies compared to flexural-mode vertical beam resonators with similar dimensions. Pre-vious studies reported measured resonant frequencies up to�30 MHz for a 20 �m long poly-Si bridge16 and�72 MHz for 8 �m long SiC bridge,17 and in our case, forR=20 �m, simulated resonant frequencies up to 145 MHzcan be reached.

2. Mechanical actuation: Experiment

Figure 6 shows the measured and simulated resonant fre-quency as a function of the radius R for the mechanicallyactuated SiC ring structures with h=6 and 15 �m. It can beseen that, in general, the measured resonant frequency ishigher than the simulated ones. It is well known that thepresence of stress in the structures results in an increase inthe resonant frequency.18 In our design, the internal stress inthe structures is not relieved through the side of the structure,as in a beam design, but only through the central hole thathas a relatively small size compared to the entire structure.This can result in a relatively large stress within the fabri-cated ring resonators. However, the observed quadratic trendin the measured values and the higher resonant frequenciesmeasured for rings with a larger hole are in good agreementwith the simulations results. Furthermore, it can be seen thatthe effect of the larger hole size �15 �m� serves to increasethe measured resonant frequency further at R�120 �m

FIG. 5. �Color online� Simulated resonant frequency as a function of the ringradius R for h=0, 6, and 15 �m �inset: resonant frequency as a function ofhole radius h for R=30, 40, 80, and 100 �m�.

�i.e., smaller rings�. The onset for the increase in the resonant

3113 Mastropaolo et al.: Electrothermal actuation of silicon carbide ring resonators 3113

frequency as a result of larger h can be seen to shift tosmaller R ��80 �m� in the simulations. This observationcould be attributed to the presence of stress in the fabricateddevices.

In order to confirm the effect of the internal stress on thefabricated SiC rings, additional simulations have been per-formed. By the use of parametric simulations as a function ofthe stress, a value of 500 MPa has been obtained as the bestfitting parameter. The simulated resonant frequencies as afunction of the radius �R� for SiC rings with h=6 �m havebeen plotted in Fig. 6 �dotted line�.

C. Influence of electrode design on displacement

1. Electrothermal simulations

In order to study the actuation efficiency of the single,double, and interdigitated electrode designs, their influenceon the induced displacement and the amount of deflectedarea has been investigated. From the simulations, the maxi-mum displacement has been observed to be always on thepart of the ring where the electrodes lie �not shown�. In thisarea, the mechanical stress and displacement are higher com-pared to the other parts of the structure due to the heatingeffect of the electrodes and to the difference in the TCEs ofthe two materials. However, the magnitude of the displace-ment and the deflected area depend on the different electrodeconfigurations. In general, the single electrode configurationhas shown to induce a higher displacement than the doubleelectrode and the IDT ones. The lowest displacement is in-duced by the IDT architecture. The difference in the inducedmagnitudes of displacement can be explained by observingthe simulated temperature induced by the electrodes. Figure7 shows the snapshots of the simulated temperature distribu-tion on the Al/SiC rings �R=100 �m and h=6 �m� ob-tained with the different electrode configurations. It has beenfound that the average temperature generated by the single�570 °K� and double �505 °K� electrode configurations ismuch higher than the one obtained with the IDT electrode

FIG. 6. �Color online� Measured �continuous line� and simulated �dashedand dotted lines� resonant frequencies �inset: resonant peak at �1.43 MHzof an electrothermally actuated SiC ring, R=125 �m, h=15 �m, and Q�12 000�.

�310 °K�. Furthermore, if the temperature is considered

JVST B - Microelectronics and Nanometer Structures

along with the heated up area, the double electrode configu-ration is found to be the most efficient design for actuationwith a relatively high average temperature and the largestheated up area, hence inducing a large and uniform deflec-tion of the structure.

2. Electrothermal actuation: Experiment

The rings have been driven into resonance successfully byelectrothermal actuation using the three different electrodeconfigurations. The inset of Fig. 6 shows one of the resonantpeaks measured at �1.43 MHz �Q�12 000� for a ring withR=125 �m and h=15 �m actuated electrothermally withthe single electrode configuration. It is worth pointing outthat the obtained Q factors �10 000–12 000� from our devicesare higher than the ones reported in literature, up to �1000and �10 000 for vertical beam Si and SiC resonators,respectively.17–19

In general, the resonant frequencies detected when actu-

FIG. 7. �Color online� Simulation snapshots for the temperature generated bydifferent electrode configurations applied on a ring with R=100 �m andh=6 �m. �a� Single electrode; �b� double electrode; �c� IDT electrode.

ating the structures electrothermally are slightly lower than

3114 Mastropaolo et al.: Electrothermal actuation of silicon carbide ring resonators 3114

the ones measured when actuating mechanically��2–3 kHz�. This is probably due to the fact that by apply-ing a driving voltage to the structures, the temperature in theresonators is increased. This temperature increase enhancesthe thermal tensile stress and leads to a decrease in Young’smodulus of the material forming the resonator.10,20 It is be-lieved that in our structures the decrease in Young’s modulushas a greater influence than the increase in the tensile stress,thus the resonant frequency is found to decrease.

The vibration amplitude of a ring with R=190 �m andh=15 �m has been investigated when actuating with thesingle, double, and IDT electrode designs. The amplitude hasbeen measured on a circular trajectory with a radius equal toR /2 �Fig. 1�. In the single electrode case, a maximum am-plitude of about 460 nm has been measured on top of the Aland a lower one of 180 nm has been measured on the part ofthe ring not covered by the electrode. On the contrary, con-stant vibration amplitudes of 460 and 10 nm have been de-tected on the measuring circumference for the double andIDT electrode cases, respectively.

V. CONCLUSIONS

The study of bimorph Al/SiC circular ring resonators hasbeen presented. Simulations have been performed with plaindisks and rings having a hole patterned in the center. Inagreement with the analytical model, the mechanical simula-tions for the ring resonators have been shown to resonate atfrequencies up to 145 MHz and that the resonant frequencyincreases as the structure’s radius decreases. In addition, thepresence of the central hole influences the modal behavior ofthe structures by increasing the resonant frequency as thehole size increases. The ring resonators have been fabricatedentirely with dry etching techniques by patterning circularholes in the SiC and by releasing the Si sacrificial layer un-derneath with XeF2 chemical etching. The rings have beenfabricated with a radius in a range between 20 and 200 �mand with hole radii of 6 and 15 �m. In general, an increasein the release rate has been observed when the chamber pres-sure and the aperture size increased. The etching mechanismhas been deduced to be governed by aperture effects. Byactuating the structures mechanically and electrothermally,resonant frequencies up to 3.3 MHz have been detected and

J. Vac. Sci. Technol. B, Vol. 27, No. 6, Nov/Dec 2009

Q factors of �12 000 have been obtained. In good agree-ment with the simulations, the measured resonant frequencyhas been shown to increase when the ring radius decreases.One significant finding is that for rings having a radius belowa certain threshold, the resonant frequency can be increasedby increasing the size of the central hole. The double elec-trode design has been found to be the best compromise be-tween induced vibration amplitude and deflected area com-pared to single electrode and IDT ones. The electrodes’heating efficiency and the uniformity of the heated up areaplay a key role in the electrothermal actuation of the de-signed bimorph ring resonators.

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