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Nano-gap micro-electro-mechanical bulk lateral resonators with high quality factors and low motional resistances on thin silicon-on-insulator q N.D. Badila-Ciressan * , M. Mazza, D. Grogg, A.M. Ionescu Laboratory of Micro and Nano-electronic Devices (LEG2), Ecole Polytechnique Fédérale de Lausanne, Switzerland article info Article history: Available online 2 June 2008 The review of this paper was arranged by Jurriaan Schmitz abstract The design, fabrication and experimental investigation of 22–25 MHz fragmented-membrane MEM bulk lateral resonators (BLR) with 100 nm air-gaps on thin (1 and 6 lm) silicon-on-insulator (SOI) are reported. Quality factors as high as 120,000 and motional resistances of as little as 60 kX are measured under vacuum at room temperature, with 12 V DC bias and low AC power. The temperature influence on the resonance frequency and quality factor is studied and discussed between 80 K and 320 K. Significant quality factor increase and motional resistance reduction are reported at cryogenic temperature. The paper shows that high-quality factor MEM resonators can be integrated on partially depleted thin SOI, which can be a substrate of choice for the fabrication of future integrated hybrid MEMS–CMOS integrated circuits for communication applications. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Today’s consumer electronics based on a large variety of time- keeping and frequency reference applications is based on quartz- crystal oscillators, because of their excellent performances in terms of quality factor, thermal and frequency stability. However, macro- scopic size and CMOS incompatibility of quartz-crystal resonators draw a major limit on the miniaturization of wireless communica- tion applications. For this reason, silicon micro-electromechanical (MEM) resonators are considered promising candidates to replace quartz-oscillators in VLSI communication systems, due to their compactness, design flexibility and CMOS process compatibility. Preliminary breakthroughs in MEMS resonators and related oscillators have been reported by Nguyen with comb-drive design [1], but their resonance frequencies and quality factors were not suitable for GSM and satellite communication specifications. Re- cently, a particular focus has been on bulk-mode MEMS resonators, using length-extensional modes [2]. These modes are typically placed at higher frequency (tens of MHz to GHz) and could achieve much higher quality factors compared to flexural modes. In addi- tion, the quality factor of bulk-mode resonators is less sensitive to air pressure [2], resulting in lower vacuum requirements for the package and hence, in a lower cost technology. Thick SOI MEM resonators with quality factors larger than 10 5 have been reported by VTT [3]. However, thick SOI (the term thick SOI is employed here for silicon film thicknesses larger than 10 lm) is not a very appropriate substrate for SOI ICs where par- tially depleted or totally depleted MOSFETs are based on much thinner silicon layers (from 1 lm down to tens of nm). Thin-film resonators are though limited in terms of quality fac- tor since it mirrors the stored mechanical energy, which is propor- tional to their (small) volume. For this reason, thin film resonator optimized design (optimization of losses) becomes a major issue in order to find a good trade-off between miniaturization, perfor- mances and partially depleted SOI CMOS technology. Another chal- lenge of MEM resonators is the reduction of their motional resistance in the order of tens of kXs or less, to meet oscillator de- sign requirements, this being translated into the technological challenge of fabricating actuation gaps of less than 100 nm. In this context, our paper proposes an original design and investigation of nano-gap MEM resonators thin SOI (with silicon thickness ranging from 1 lm to 6 lm) and resonance frequencies in the 22–25 MHz range, expected to meet GSM oscillator specifications. 2. Design and technology 2.1. Fragmented-membrane MEM BLR design Fig. 1a shows a fragmented-membrane BLR MEM resonator, fab- ricated on SOI substrate, and operated with capacitive detection. Two SOI wafer thicknesses of 1.5 lm and 6.25 lm were used, resulting in two groups of resonators: we will further on classify as type-A the resonators built on 1.5 lm SOI and type-B the ones on 6.25 lm SOI. The MEM structure in Fig. 1a is a type-B resonator, with a simple suspension arm, functioning in a 24.46 MHz bulk mode, as shown by ANSYS simulations in Fig. 1b. The MEM resonator is composed of a rectangular membrane fragmented by parallel rectangular holes, which serve a double 0038-1101/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.sse.2008.04.022 q This work was supported by IST project NanoTIMER. * Corresponding author. E-mail address: [email protected] (N.D. Badila-Ciressan). Solid-State Electronics 52 (2008) 1394–1400 Contents lists available at ScienceDirect Solid-State Electronics journal homepage: www.elsevier.com/locate/sse

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Solid-State Electronics 52 (2008) 1394–1400

Contents lists available at ScienceDirect

Solid-State Electronics

journal homepage: www.elsevier .com/locate /sse

Nano-gap micro-electro-mechanical bulk lateral resonators with high qualityfactors and low motional resistances on thin silicon-on-insulator q

N.D. Badila-Ciressan *, M. Mazza, D. Grogg, A.M. IonescuLaboratory of Micro and Nano-electronic Devices (LEG2), Ecole Polytechnique Fédérale de Lausanne, Switzerland

a r t i c l e i n f o

Article history:Available online 2 June 2008

The review of this paper was arranged byJurriaan Schmitz

0038-1101/$ - see front matter � 2008 Elsevier Ltd. Adoi:10.1016/j.sse.2008.04.022

q This work was supported by IST project NanoTIME* Corresponding author.

E-mail address: [email protected] (N.D. Badil

a b s t r a c t

The design, fabrication and experimental investigation of 22–25 MHz fragmented-membrane MEM bulklateral resonators (BLR) with 100 nm air-gaps on thin (1 and 6 lm) silicon-on-insulator (SOI) arereported. Quality factors as high as 120,000 and motional resistances of as little as 60 kX are measuredunder vacuum at room temperature, with 12 V DC bias and low AC power. The temperature influence onthe resonance frequency and quality factor is studied and discussed between 80 K and 320 K. Significantquality factor increase and motional resistance reduction are reported at cryogenic temperature. Thepaper shows that high-quality factor MEM resonators can be integrated on partially depleted thin SOI,which can be a substrate of choice for the fabrication of future integrated hybrid MEMS–CMOS integratedcircuits for communication applications.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Today’s consumer electronics based on a large variety of time-keeping and frequency reference applications is based on quartz-crystal oscillators, because of their excellent performances in termsof quality factor, thermal and frequency stability. However, macro-scopic size and CMOS incompatibility of quartz-crystal resonatorsdraw a major limit on the miniaturization of wireless communica-tion applications. For this reason, silicon micro-electromechanical(MEM) resonators are considered promising candidates to replacequartz-oscillators in VLSI communication systems, due to theircompactness, design flexibility and CMOS process compatibility.

Preliminary breakthroughs in MEMS resonators and relatedoscillators have been reported by Nguyen with comb-drive design[1], but their resonance frequencies and quality factors were notsuitable for GSM and satellite communication specifications. Re-cently, a particular focus has been on bulk-mode MEMS resonators,using length-extensional modes [2]. These modes are typicallyplaced at higher frequency (tens of MHz to GHz) and could achievemuch higher quality factors compared to flexural modes. In addi-tion, the quality factor of bulk-mode resonators is less sensitiveto air pressure [2], resulting in lower vacuum requirements forthe package and hence, in a lower cost technology.

Thick SOI MEM resonators with quality factors larger than 105

have been reported by VTT [3]. However, thick SOI (the term thickSOI is employed here for silicon film thicknesses larger than10 lm) is not a very appropriate substrate for SOI ICs where par-

ll rights reserved.

R.

a-Ciressan).

tially depleted or totally depleted MOSFETs are based on muchthinner silicon layers (from 1 lm down to tens of nm).

Thin-film resonators are though limited in terms of quality fac-tor since it mirrors the stored mechanical energy, which is propor-tional to their (small) volume. For this reason, thin film resonatoroptimized design (optimization of losses) becomes a major issuein order to find a good trade-off between miniaturization, perfor-mances and partially depleted SOI CMOS technology. Another chal-lenge of MEM resonators is the reduction of their motionalresistance in the order of tens of kXs or less, to meet oscillator de-sign requirements, this being translated into the technologicalchallenge of fabricating actuation gaps of less than 100 nm. In thiscontext, our paper proposes an original design and investigation ofnano-gap MEM resonators thin SOI (with silicon thickness rangingfrom 1 lm to 6 lm) and resonance frequencies in the 22–25 MHzrange, expected to meet GSM oscillator specifications.

2. Design and technology

2.1. Fragmented-membrane MEM BLR design

Fig. 1a shows a fragmented-membrane BLR MEM resonator, fab-ricated on SOI substrate, and operated with capacitive detection.Two SOI wafer thicknesses of 1.5 lm and 6.25 lm were used,resulting in two groups of resonators: we will further on classifyas type-A the resonators built on 1.5 lm SOI and type-B the oneson 6.25 lm SOI. The MEM structure in Fig. 1a is a type-B resonator,with a simple suspension arm, functioning in a 24.46 MHz bulkmode, as shown by ANSYS simulations in Fig. 1b.

The MEM resonator is composed of a rectangular membranefragmented by parallel rectangular holes, which serve a double

Fig. 1. (a) Optical image of a fabricated type-B fragmented-membrane bulk-mode MEM rectangular resonator with 20 parallel connected beams, (b) ANSYS simulationshowing the mode shapes for a 24.6 MHz fragmented-membrane resonator and (c) anchor-loss optimization: ‘simple-arm’ (top) vs. ‘T-arm’ (bottom).

N.D. Badila-Ciressan et al. / Solid-State Electronics 52 (2008) 1394–1400 1395

purpose: (i) they enable the resonator to be designed as a multi-beam structure (with all the beams connected in parallel, whichincreases the lateral actuation width), based on beam and BLR res-onator theory [3,4], and (ii) they allow easier sacrificial layeretching.

As it will be shown later, this design answers the task of obtain-ing a high frequency resonator with large spring constant, lowmass and high quality factor. In order to further reduce the losses,design variations were investigated (e.g. different types of suspen-sion arms for lower anchor losses). Fig. 1c shows two different armtypes, a ‘simple-arm’ (top) and a ‘T-arm’ (bottom).

The one dimensional model of fundamental vibration frequency[3] is corrected with the mass loading corresponding to beam par-allel connections, resulting in the following expression:

fres ¼1

2p

ffiffiffiffiffiffiffiffiffikeff

meff

sffi b

2L

ffiffiffiffiEq

sð1Þ

where b = 0.942 is a correction factor, which reflects the keff/meff ra-tio deviation from the single-beam model, due to the added mass, Lis the resonator length and E and q are silicon Young’s modulus anddensity.

Based on Eq. (1), the resonance frequency for the device sum-marized in Table 1 is calculated to be 24.62 MHz, which showsgood agreement with the measurements (24.46 MHz) and theANSYS simulations.

Another critical resonator parameter is the motional resistance,Rm, which, for a MEM BLR, is given by [5]:

Rm /g4

V2DCQhwL

ð2Þ

Table 1Design parameters of fragmented-membrane MEM resonators

Resonator type A, simple-arm B, simple-arm B,T-arm

E (GPa), Si Young’s modulus 125a 165 165q (kg/m3), Si density 2330 2330 2330L (lm), resonator length 161 161 161Lh (lm), hole length 151 151 151wh (lm), hole width 5 5 5wb (lm), beam width 5 5 5Nb, nb. of parallel beams 20 20 20Larm (lm), arm length 20 10 30/70w (lm), electrode width 183 183 183g (nm), gap width 250b 100 100h (lm), SOI thickness 1.3c 6.25 6.25

Resonator type refers to the SOI thickness. Type-A stands for 1.5 lm SOI, and Type-Bfor 6.25 lm SOI wafers.

a Reduced Young’s modulus as result of silicon galvanic corrosion.b Reduced gap width as result of silicon galvanic corrosion.c Reduced thickness as result of silicon galvanic corrosion.

where VDC is the applied DC bias, g the air-gap width, h and w theheight and width of the electrode. Therefore, in order to meet thespecifications of practical oscillator applications, it is essential todecrease the gap width as much as possible (in our case, 100 nmgap is targeted).

2.2. Nano-gap MEM resonator technology

A three-layer deposition process is used to create the resonatorhard mask, employing a sacrificial-layer technique. First, a TEOSlayer with thickness of 500 nm (for type-A)/1 lm (for type-B) isdeposited and patterned by dry etching, in order to form the reso-nating structure and anchors. Polysilicon (100 nm) and 1.5 lm sec-ond TEOS layer are subsequently deposited. At this step, the cross-section looks as in Fig. 2a. The polysilicon film will act both asnano-gap spacer and as protection for the first oxide during dry-etch patterning of the second one.

The second TEOS layer is back-etched using a combination ofchemical–mechanical polishing (CMP) and wet-etch, until the toppolysilicon covering the resonating structures is revealed. A photo-lithography step, followed by dry etching is used to pattern the res-onator electrodes, as shown in Fig. 2b.

Third cross-section, depicted in Fig. 2c is obtained by transfer-ring the mask into the SOI layer by a high aspect-ratio deep RIE(SHARP) process, as previously described [4].

In the end, the oxide hard mask is removed using a buffered HFsolution, contacts are opened in the undoped polysilicon layer, themetallization is done and the resonators are released. A cross-sec-tion of the finalized structure is shown in Fig. 2d.

A typical gap of 110 nm, obtained with this technology, is de-picted in Fig. 3. At our knowledge, this is one of the smallest actu-ation gaps results reported to date for SOI MEM resonators. Theroughness of vertical and lateral gaps was optimized. As shownin Fig. 3a, the scalloping-induced vertical roughness is limited onthe top of the gap to 30 nm, and is decreasing with depth. The lat-eral roughness, generated mainly by photolithography, sidewallthickness-variation and etching is quasi-negligible (<10 nm;Fig. 3b).

After the last fabrication step of type-A structures, an unex-pected compatibility issue has been noticed between the metalli-zation gold and the n+, low resistivity wafers used, which causedgalvanic corrosion [6] of all structures when dipped in the finalBHF release bath. Due to this effect, the actual gaps were increasedto around 250–300 nm and the film was slightly thinned downfrom 1.5 lm to �1.3 lm.

The corrosion problem was solved when fabricating type-B res-onators by using aluminum metallization and by replacing the fi-nal release BHF with a silox-etch solution. Fig. 4a shows anFIB cross-section through the transduction gap separating the

Oxide-2

SOI active layerBOX

SOI-bulk

Oxide-1 PolySi

SOI active layerBOX

SOI-bulk

Oxide-1Oxide-2PolySi

ResonatorBOX

SOI-bulk

MetalOxide-1Oxide-2

Resonator

SOI-bulk

ElectrodeMetal

BOX BOX

a

b

c

d

Fig. 2. Main steps of the process flow: (a) formation of the hard-mask by successive TEOS and polysilicon depositions, (b) electrode patterning; at this step, the HARD mask isfinalized, (c) hard-mask transfer via dry-etch in the SOI device layer and (d) cross-section through a complete resonator, after metallization and release.

Fig. 3. (a) FIB cross-section of a typical 110 nm-wide transduction gap of a type ‘A’device and (b) top view of the gap before release.

1396 N.D. Badila-Ciressan et al. / Solid-State Electronics 52 (2008) 1394–1400

electrode and the resonator, and Fig. 4b shows an SEM top-viewimage of the successfully released fragmented-membrane resona-tor. Further optimization of the process is needed in order to elim-inate the notch visible on the gap-top in Fig. 4a, which reducedslightly the resonator performance. This notch is generated by asmall tilt of the vertical polysilicon wall which acts as gap-spacer(�5� deviation from vertical position), combined with the long-etch time needed to completely open the gaps.

3. Resonator characterization

3.1. Resonator figures of merit at room temperature

Resonators have been measured using a PMC-150 vacuum cryo-genic prober using a HP8753D network analyzer without ANYadditional pre-amplification. Bias voltage has been applied viathe same equipment at both input and output electrodes, whilethe resonating structure and the bulk silicon of the SOI wafer wereconnected to ground, as shown in Fig. 5.

Fig. 6 presents the typical peak resonance responses of the S21

transmission parameters for two simple-arm MEM resonators:the type-A device has a silicon thickness of 1.3 lm while thetype-B device has a silicon thickness of 6.25 lm, as previouslysummarized in Table 1. The measured resonance frequencies are21.72 MHz for the type-A and 24.46 MHz for type-B, respectively.Quality factor, Q = 33,000 (calculated from the transmissionparameter, as the 3 dB bandwidth over the center frequency) andmotional resistance, Rm = 582 kX are extracted for the type-A de-vice at 20 V DC bias voltage and 25 dBm AC power, andQ = 67,000 and Rm = 113 kX, are extracted for the type-B deviceat 12 V DC bias voltage and �20 dBm AC power; both measure-ments were performed at room temperature and in vacuum(<10�5 mbar). These results demonstrate a quality factor increaseby factor of 2 and motional resistance decrease by a factor of morethan 5 that can be obtained by the use of thicker silicon thickness.

Nevertheless, it is also shown that very good quality factors(>10,000) and relatively acceptable motional resistance (500 kXat low applied voltage) can be still achieved for 1 lm-thick MEMbulk resonators, with appropriate gap scaling and optimizeddesign.

S21 transmission parameter peaks for simple-arm and T-arm de-signs of the type-B device are compared in Fig. 7. We can notice theresonator performance improvement due to anchor-loss optimiza-tion: for the T-arm resonator: Q = 122,000 and Rm = 59 kX, ex-tracted at 12 V DC bias voltage and �25 dBm AC power, at roomtemperature and in vacuum (<10�5 mbar). The measured reso-nance frequency is fres = 24.48 MHz for the T-arm, slightly differentthan the simple-arm design value.

Finally, type-A and type-B resonator parameters are summa-rized in Table 2.

Fig. 8 shows the quality factor (Q) degradation with respect tothe vacuum level for a type-A, simple-arm resonator; it is observedthat, for our nano-gap device, the air damping becomes negligiblebelow approximately 0.1 mbar.

While the DC bias voltage has relatively little influence on thequality factor (less than 10–15% experimental variation), it is con-

Fig. 4. (a) FIB cross-section of a typical transduction gap through a type ‘B’ device and (b) top view of the resonator after release.

-90

-85

-80

-75

-70

-65

-60

-55

-50

24.446 24.451 24.456 24.461 24.466Frequency, f [MHz]

Tra

nsm

issi

on p

aram

eter

, S 2

1 [d

B]

21.710 21.715 21.720 21.725 21.730Frequency, f [MHz]

fres = 21.72 MHz Q = 33,000 Rm = 580 kΩtSi=1.3μm

fres = 24.46 MHz Q = 67,000 Rm = 113 kΩtSi=6.25μm

Type-B device Type-A device

A

B

Fig. 6. Comparison between experimental S21 scattering parameter data at reso-nance frequency for MEM resonators with silicon thickness of 1.3 lm (type-A de-vice) and 6.25 lm (type-B device), both with simple arm design, at appliedVDC = 12 V and PAC = �25 dBm and �20 dBm, respectively. Black curves are smoo-thed lines while grey curves correspond to measured data.

Fig. 5. Two-port resonator measurement setup.

-90

-85

-80

-75

-70

-65

-60

-55

-50

24.446 24.451 24.456 24.461 24.466

Frequency, f [MHz]

Tra

nsm

issi

on p

aram

eter

, S 2

1 [d

B]

24.471 24.476 24.481 24.486 24.491Frequency, f [MHz]

S

fres = 24.46 MHz Q = 67,000 Rm = 113 kΩtSi=6.25μm

Spl-arm device fres = 24.48 MHz Q = 122,000 Rm = 59 kΩtSi=6.25 μm

T-arm device

T

Fig. 7. S21 scattering parameter for a simple-arm, type-B device at resonance fre-quency is compared to the one of a T-arm, type-B resonator.

Table 2Experimental electrical parameters for the fabricated SOI MEM bulk lateral resonators

Resonator type A simple-arm B simple-arm BT-arm

Vbias (V), DC bias voltage 20 12 12PAC (dBm), AC signal power �25 �20 �25fres (MHz), resonance frequency 21.72 24.46 24.48Q, quality factor 32,802 67,000 122,000Rm (kX), motional resistance 582 113 59Lm (H), motional inductance 140.0 49 46.8Cm (aF), motional capacitance 0.384 0.865 0.903C0 (fF), feed-through capacitance 25.90 107.91 107.9

N.D. Badila-Ciressan et al. / Solid-State Electronics 52 (2008) 1394–1400 1397

firmed that it has a significant impact on the resonance frequencyand on the motional resistance of BLR with fragmented electrodes.Fig. 9 shows the resonance frequency drift due to spring softening,for type-A, simple-arm resonator: when increasing the DC bias, theresonance peaks become higher, narrower and their resonance fre-quency decreases.

Fig. 10 confirms two key dependencies for the same device:

(i) the quadratic dependence of the resonance frequency withDC bias (spring softening), according to:

-70

-69

-68

[dB

] -20dBm-19dBm

-25, -30dBm

-80

-78

-76

-74

-72

-70

-68

-66

21.714 21.715 21.716 21.717 21.718 21.719 21.72 21.721

Frequency, f [MHz]

Tra

smis

sion

par

amet

er, S

21 [

dB]

32V30V28V26V24V22V

Fig. 9. Type-A, simple-arm resonator transmission parameter S21 response withvarying bias voltages and AC power set at �25 dBm.

10

20

30

40

50

60

70

80

Mot

iona

l res

ista

nce,

Rm

[kO

hm]

Fig. 10.resistan

0

10000

20000

30000

40000

1.0E-06 1.0E-04 1.0E-02 1.0E+00 1.0E+02

Pressure, P [mbar]

Qua

lity

fact

or, Q

Fig. 8. Quality factor experimental dependence on chamber pressure for a type-A,simple-arm resonator. Measurements are done using 20 V DC bias and �25 dBm ACpower. Severe degradation is observed for pressure beyond 0.1 mbar.

1398 N.D. Badila-Ciressan et al. / Solid-State Electronics 52 (2008) 1394–1400

x20 ¼

km� eAV2

bias

mg3 ; ð3Þ

-76

-75

-74

-73

-72

-71

smis

sion

par

amet

er, S

21 -18dBm-17dBm-16dBm-15dBm

(ii) the linear depence of the motional resistance, Rm, with 1/V2 � Q(V) (for the precision of the extraction, Q is extractedat each DC bias), as predicted by Eq. (2). It is worth notingthat the motional resistance can be greatly decreased from720 kX to nearly 300 kX by increasing VDC from 18 V to32 V.

-78

-77

Frequency, f [MHz]

Tra

n

21.701 21.7015 21.702 21.7025 21.703 21.7035 21.704 21.7045

ig. 11. Nonlinearity effects appearing when increasing AC input power from15 dBm to �30 dBm on a type-A, simple-arm resonator. Biasing voltage is 20 V.

3.2. Nonlinear effects

Linear behavior of the resonator is a key concern for grantingboth optimal energy transmission to the resonator and for obtain-ing non-distorted signal and hence lower phase-noise in an oscilla-

0

0

0

0

0

0

0

0

0

2.E-08 3.E-08 4.E-08 5.E-08 6.E-08 7.E-08 8.E-08 9.E-08 1.E-07

1/[V2*Q(V)]

21.716

21.7165

21.717

21.7175

21.718

21.7185

21.71918 20 22 24 26 28 30 32

DC bias, VDC [V]

Res

onan

ce f

requ

ency

, fre

s [M

Hz]

(a) Resonance frequency dependence on DC bias voltage and (b) motionalce dependence on 1/V2 � Q(V) for a type-A, simple-arm device.

tor. In [7] and [8], a detailed analysis of nonlinearity effects hasbeen proposed. Fig. 11 shows the peak shape degradation of atype-A, simple-arm resonator, with respect to the AC injectedpower: below �25 dBm, the curves are superposed, while at�20 dBm a slight deviation appears, and finally, at �15 dBm thebehavior becomes completely nonlinear.

In a similar way, in Fig. 12, we can see the peak shape degrada-tion of a type-B, T-arm resonator, with respect to the AC injectedpower, at VDC = 6 V. Nonlinearities appear beyond �2 dBm.

In general, the MEM resonators experience mechanical andelectrical nonlinearities [7,8]; in order to distinguish between thetwo types of the nonlinearities one should model and analyze theirdependences (especially the critical power or critical current) onthe applied DC bias and AC power. Fig. 13 shows the maximumexperimental output current before nonlinearity with respect tothe applied DC bias for the same B-type, T-arm resonator. The insetof Fig. 13 depicts the general dependences of the output criticalcurrent (defined as the output current value at which one observesthe onset of the nonlinear effect) for mechanical, second order andthird order electrical nonlinearities, according to [7]. By comparingthe experimental dependence of Iout–VDC for the resonator reportedin Fig. 12, we observe a quasi-linear increase of the critical currentwith DC bias and we conclude that in the investigated voltagerange, our resonator operation is limited by mechanicalnonlinearities.

3.3. Temperature influence

Temperature drift of MEM resonator characteristics is of criticalimportance for their future success in circuit application. The res-onance frequency dependence on temperature is investigated herefrom 80 K to 320 K.

F�

-90.00

-80.00

-70.00

-60.00

24.485 24.486 24.487 24.488 24.489 24.490 24.491 24.492 24.493

Frequency, f [MHz]

Tra

nsm

issi

on p

aram

eter

, S21

[dB

]

-2dBm

-0dBm

1dBm

Fig. 12. Nonlinearity effects for a type-B, T-arm resonator, at different AC powers,with biasing voltage of 6 V.

1.50E-06

2.00E-06

2.50E-06

3.00E-06

3.50E-06

4.00E-06

4.50E-06

5.00E-06

5.50E-06

6.00E-06

0 2 4 6 8

Bias voltage, VDC [V]

Exp

erim

enta

l out

put c

urre

nt, I

out [

A]

VDC

I out

3rd order ElectricalNon-Linearity limited

2nd order ElectricalNon-Linearity limited

MechanicalNon-Linearity limited

Fig. 13. Maximum experimental output current before nonlinearity with respect tothe applied DC bias compared to the theoretical dependence of power handling onbias voltage (inset).

150000

200000

250000

ctor

, Q

measured values

Debye

N.D. Badila-Ciressan et al. / Solid-State Electronics 52 (2008) 1394–1400 1399

Fig. 14 shows the resonance frequency dependence with tem-perature for a type-B, T-arm MEM resonator. At temperatures be-yond 160 K, the measured resonance frequency values are ingood agreement with the ones calculated with Eq. (1). The temper-ature dependence is mainly controlled by Young’s modulus varia-tion, which follows Wachtman’s law [9] as follows:

E ¼ E0 � BTe�T0T ð4Þ

The parameter values corresponding to the reported fit,E0 = 164.4 GPa (Young’s modulus at 0 K), B = 12.5 MPa/K andT0 = 317 K (high temperature limit beyond which Young’s modulusdependence becomes linear), are in good agreement with publisheddata [10,11].

At high temperatures, as T approaches T0, Young’s modulus var-iation becomes quasi-linear, with a drift of �46 ppm/K [12]. FromEq. (1), we calculate:

f ðTÞ ffi 12L

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiEðT0Þ þ aEðT � T0Þ

q

sffi f ðT0Þ 1þ aE

2ðT � T0Þ

h ið5Þ

Based on our data, a linear approximation of fres(T) in the 170–320 Khas a slope of �24.5 ppm/K (black line in Fig. 12) which is in goodagreement with Eq. (7).

Between 140 K and 160 K, the frequency dependence on tem-perature has an inversed trend, probably due to the phase changeof an unknown material inside the vacuum chamber. The shift hasbeen noticed on all measured structures, independently of the res-

24.44

24.46

24.48

24.5

24.52

24.54

24.56

24.58

70 120 170 220 270 320

Temperature, T [K]

Res

onan

ce f

requ

ency

, fre

s [M

Hz]

-24.53ppm/deg

Linear fit at medium&high T

Wachtman's law

Experimental data

Fig. 14. Resonance frequency dependence on temperature for T-arm, type-B reso-nator, between 80 K and 320 K. The triangles correspond to experimental data; thedotted line corresponds to Wachtman’s equation and the black line is a linear fitthrough the values at medium and high temperature.

onance frequency. At temperatures below 140 K, the resonance fre-quency variation resumes the trend described by Wachtman’s law,with slightly lower values (compared to the extracted model)probably due to added mass.

The quality factor dependence on temperature is plotted inFig. 15. At room temperature, the resonator shows a Q of around120,000. Quality factor values slowly fall while decreasing the tem-perature and reach a minimum around 220 K. Below this value, Qsharply rises reaching 200,000 at 80 K. The large spread of experi-mental Q data, especially for the very high values, is due to themeasurement precision, i.e. frequency steps are becoming compa-rable with the 3 dB bandwidth, resulting in a relative error of 33%.Similar Q–T curves have been previously observed in other works,such as [13,14], on flexural and torsional resonators. It has beensuggested that two main mechanisms could be responsible forsuch behavior: (i) internal friction losses and (ii) surface or nearsurface related phenomena. Silicon internal friction has been re-ported to present a maximum sharp peak (and hence a Q factorminimum) in the range 115–124 K.

The thermally activated internal loss mechanisms are governedby Debye’s relaxation equation [15]:

1Qdefects

¼ Dxs

1þ ðxsÞ2; s ¼ s0 � exp

EkBT

� �ð6Þ

where D is the relaxation strength, s is the relaxation time, E and s0

are defect activation energy and time constant, kB is Boltzmann’sconstant, T is the temperature and x is the resonance frequency.

In order to fit this trend to our experimental data, we have con-sidered that the internal friction effect dominates at medium tem-perature, while at low and high temperature other types of lossmechanisms limit the resonator quality factor. Thus, Q is calculatedas:

1Q¼ 1

Qdefectsþ 1

Q otherð7Þ

Fig. 15 shows a good agreement between the experimentallydetermined quality factor, Q(T) at different temperatures and

0

50000

100000

70 120 170 220 270 320

Temperature, T [K]

Qua

lity

fa

Fig. 15. Quality factor versus temperature for type-B resonator: measured values(triangles) and Debye’s analytical model.

Table 3Debye’s relaxation equation parameters

Parameter Value

s0 (s), defect activation time constant 0.8 � 10�12

Ea (eV), defect activation energy 0.17D, relaxation strength 4 � 10�5

Qother, quality factor due to other losses 180,000

-90

-85

-80

-75

-70

-65

-60

-55

-5024.540 24.542 24.544 24.546 24.548 24.550

Frequency, f [MHz]

Tra

nsm

issi

on p

aram

eter

, S21

[dB

] Temperature: 80Kfres = 24.544MHz

Q 200'000 Rm = 42kΩ

Fig. 16. S21 parameter at resonance frequency of the same type-B device, measuredat a temperature of 80 K with bias voltage of 12 V and AC-signal of �20 dBm.

1400 N.D. Badila-Ciressan et al. / Solid-State Electronics 52 (2008) 1394–1400

Debye’s relaxation equation (6), for the fitting parameters given inTable 3, which are consistent with other published values.

Fig. 16 presents the S21 peak, measured at 80 K temperature,showing an extracted quality factor, Q > 200,000 and a motionalresistance Rm = 42 kX for fres = 24.54 MHz.

4. Conclusion

The design, fabrication and experimental evaluation of 22–25 MHz MEM resonators on thin SOI (1 lm and 6 lm) with100 nm air-gaps have been presented. Quality factors as high as120,000 and motional resistances as low as 60 kX have been mea-sured at room temperature with DC bias voltages of 12 V and lowAC power levels. Suspension arm shape influence on losses wasinvestigated and it was concluded that T-shape arm design signif-icantly reduces the mechanical losses, which improves the qualityfactor. The resonator experimental linearity limits have beeninvestigated. An increase of quality factor value was observed atcryogenic temperatures (80 K) and an analysis on resonator tem-perature dependence was proposed.

Acknowledgments

This project has been funded by European Project IST NanoTI-MER. Many thanks are due to Dr. Dimitrios Tsamados for technicalsupport and useful discussions.

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