A Tunable-Gain Transimpedance Amplifier for CMOS-MEMS

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Article A Tunable-Gain Transimpedance Ampliﬁer for CMOS-MEMS Resonators Characterization

Rafel Perelló-Roig 1,2, Jaume Verd 1,2,* , Sebastià Bota 1,2 and Jaume Segura 1,2

1 Electronic Systems Group (GSE-UIB), University of the Balearic Islands, 07122 Palma, Spain; [email protected] (R.P.-R.); [email protected] (S.B.); [email protected] (J.S.) 2 Health Research Institute of the Balearic Islands, IdISBa, 07010 Palma, Spain * Correspondence: [email protected]; Tel.: +34-971-172006

Abstract: CMOS-MEMS resonators have become a promising solution thanks to their miniaturization and on-chip integration capabilities. However, using a CMOS technology to fabricate microelectromechanical system (MEMS) devices limits the electromechanical performance otherwise achieved by specific technologies, requiring a challenging readout circuitry. This paper presents a transimpedance amplifier (TIA) fabricated using a commercial 0.35-µm CMOS technology specifically oriented to drive and sense monolithically integrated CMOS-MEMS resonators up to 50 MHz with a tunable transimpedance gain ranging from 112 dB to 121 dB. The output voltage noise is as low as 225 nV/Hz1/2—input-referred current noise of 192 fA/Hz1/2—at 10 MHz, and the power consumption is kept below 1-mW. In addition, the TIA amplifier exhibits an open-loop gain independent of the parasitic input capacitance—mostly associated with the MEMS layout—representing an advantage in MEMS testing compared to other alternatives such as Pierce oscillator schemes. The work presented includes the characterization of three types of MEMS resonators that have been fabricated and experimentally characterized both in open-loop and self-sustained configurations using the integrated TIA amplifier. The experimental characterization includes an accurate extraction of the electromechanical parameters for the three fabricated structures that enables an accurate MEMS-CMOS circuitry co-design. Citation: Perelló-Roig, R.; Verd, J.; Bota, S.; Segura, J. A Tunable-Gain Keywords: transimpedance amplifier; RF MEMS; oscillator; CMOS-MEMS Transimpedance Amplifier for CMOS-MEMS Resonators Characterization. Micromachines 2021, 12, 82. https://doi.org/10.3390/ 1. Introduction mi12010082 Microelectromechanical systems (MEMS) resonators are becoming more and more Received: 30 December 2020 used nowadays for RF and sensing applications. The use of these devices as the frequency- Accepted: 12 January 2021 determining element in an oscillator circuit is a common demand in RF signal processing Published: 15 January 2021 systems, leading to a reduction in area and power consumption [1]. Thanks to their small size and miniaturization capabilities, MEMS elements can prevent the use of discrete Publisher’s Note: MDPI stays neu- elements such as inductors and quartz crystals [2–5]. On the other hand, system-on-chip tral with regard to jurisdictional clai- applications demand the integration of not only the MEMS signal conditioning circuitry, but ms in published maps and institutio- also the electronics required to drive the mechanical system at resonance while continuously nal affiliations. tracking its resonant frequency [6]. In this sense, the use of an oscillator circuit has additional advantages given its inherent capability of providing a pseudo-digital output signal rather than an analog one. Various approaches can be found in the literature to implement resonators. It has been Copyright: © 2021 by the authors. Li- censee MDPI, Basel, Switzerland. proven that resonant MEMS structures can be fabricated using standard CMOS processes This article is an open access article combined with surface micromachining [1,6–11]. This approach enables the possibility of distributed under the terms and con- developing monolithically integrated systems that use electrostatic actuation and capacitive ditions of the Creative Commons At- readout to drive and sense, respectively. the motion of a mechanical resonator, with benefits tribution (CC BY) license (https:// in terms of area reduction and noise performance. creativecommons.org/licenses/by/ However, when using CMOS technology, both the materials available to fabricate 4.0/). the MEMS structures as well as the technological design rules to define the MEMS sizes

Micromachines 2021, 12, 82. https://doi.org/10.3390/mi12010082 https://www.mdpi.com/journal/micromachines Micromachines 2021, 12, x 2 of 17

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However, when using CMOS technology, both the materials available to fabricate the MEMS structures as well as the technological design rules to define the MEMS sizes limit thelimit electromechanical the electromechanical performanc performancee [10,12,13]. [10 In,12 the,13]. case In theof resonators, case of resonators, the scaling-down the scaling- trenddown in the trend new in generation the new generation of MEMS of usually MEMS results usually in results a reduction in a reduction of the coupling of the couplingcapac- capacitance between the moving structure and the sense electrode (Csense), an increase in itance between the moving structure and the sense electrode (𝐶), an increase in the the resonant frequency, and a decrease in the quality factor. In addition, the maximum resonant frequency, and a decrease in the quality factor. In addition, the maximum DC DC voltage (V ) applied between the moving and the ﬁxed electrodes is limited by the voltage (𝑉 ) applieddc between the moving and the fixed electrodes is limited by the pull- pull-in voltage, or in any case, by the resonator linear operation range. As a consequence, in voltage, or in any case, by the resonator linear operation range. As a consequence, the the capacitive signal current, Isig, injected in the sense electrode, capacitive signal current, 𝐼, injected in the sense electrode,

𝜕𝐶∂Csense 𝐼Isig =𝑉= Vdc , (1) (1) 𝜕𝑡∂t is isreduced reduced to very to very low low values. values. A transimpeda A transimpedancence amplifier amplifier (TIA) with (TIA) large with gain large and gain small and input-referredsmall input-referred noise, is noise,typically istypically used to convert used to 𝐼 convert to a voltageIsig to a feed voltage at subsequent feed at subsequent stages [14].stages This [ 14voltage]. This is voltage often applied is often appliedback to backthe resonator to the resonator input with input appropriate with appropriate gain and gain phaseand to phase generate to generate self-excited self-excited oscillations oscillations operat operatinging as parallel as parallel or series or seriesoscillators oscillators [6,8]. [6,8]. FromFrom these these considerations, considerations, the the motivation motivation of this workwork isis toto develop develop a a transimpedance transimped- anceamplifier amplifier suitable suitable to driveto drive monolithically monolithically integrated integrated capacitive capacitive CMOS-MEMS CMOS-MEMS resonators reso- natorsoperating operating up toup ~50 to ~50 MHz MHz and and exhibiting exhibiting large large transimpedance transimpedance gain gain (in (in the the range range of 66 −1 1 of10 10 VV·A·A ) )with with a neglectable a neglectable dependence dependence on on𝐶Csense. The. The last lastprovides provides a reliable a reliable tool for tool anfor accurate an accurate experimental experimental characterization characterization of MEMS of MEMSresonators resonators in the design in the stage, design which stage, mightwhich present might an present unknown an unknownor hard-to-predict or hard-to-predict equivalent equivalent parasitic capacitance parasitic capacitance value at thevalue sense at node, the sense mostly node, associated mostly with associated the MEMS with resonator the MEMS layout resonator [15]. layoutThus, achieving [15]. Thus, a transimpedanceachieving a transimpedance gain independent gain independentof the fabricated of the structure fabricated is helpful structure for iscompleting helpful for ancompleting accurate design an accurate and further design parameter and further extraction parameter during extractionthe redesign during iterations the accom- redesign plishediterations to optimize accomplished the CMOS-MEMS to optimize therequired CMOS-MEMS performance. required performance. InIn this this work, work, three three MEMS MEMS resonators resonators comprehending comprehending a broad a broad range range of of dimensions dimensions (Figure(Figure 1)1 )were were designed, designed, fabricated, fabricated, and and ex experimentallyperimentally characterized characterized by by the the addressed addressed TIATIA amplifier amplifier obtaining obtaining its electromechanical its electromechanical parameters parameters and comparing and comparing them themwith a with the- a oreticaltheoretical model. model. Section Section 2 of 2this of thispaper paper is devoted is devoted to tothe the TIA TIA amplifier, amplifier, the the theoretical theoretical modelmodel for for the the resonators resonators is ispresented presented in inSectio Sectionn 3,3 and, and the the fabrication fabrication process process is isaddressed addressed in inSection Section 4.4 .Finally, Finally, Section Section 55 showsshows the the experimental experimental data data collected collected and and a summarya summary of theof thework, work, and and final final conclusions conclusions and and are are given given in in Section Section6. 6.

50 µm 50 µm 50 µm

(a) (b) (c)

FigureFigure 1. 1.OpticalOptical image image of ofthe the fabricated fabricated microelectromechanical microelectromechanical system system (MEMS) (MEMS) resonators: resonators: (a) ( aPR1;) PR1; (b ()b PR2;) PR2; (c) ( cPR3.) PR3.

2. 2.Transimpedance Transimpedance Amplifier Ampliﬁer A Atransresistance transresistance amplifier ampliﬁer uses uses a resistor a resistor (passive (passive or active) or active) as the as primary the primary gain ele- gain mentelement to convert to convert the theMEMS MEMS capacitive capacitive current current into into a voltage. a voltage. For For high high transresistance transresistance gains,gains, the the oscillator oscillator noise noise perf performanceormance is isusually usually quite quite poor poor and and is isdominated dominated by by the the input input resistorresistor noise noise [10,16,17]. [10,16,17 Thus,]. Thus, the the two two main main types types of ofCMOS CMOS oscillator oscillator topologies topologies that that have have found practical applicability to MEMS resonators are the TIA-based oscillator [17] and the Pierce oscillator [18–21]. The TIA circuit converts the input current Isig into an output

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Micromachines 2021, 12, 82 found practical applicability to MEMS resonators are the TIA-based oscillator [17] and3 of the 16 Pierce oscillator [18–21]. The TIA circuit converts the input current 𝐼 into an output voltage 𝑉 that is used to self-excite the MEMS based oscillator circuit. The main challenge when designing a resonator-based oscillator is the quite large resonator-equivalent mo- voltagetional resistanceVo that is used𝑅 (the to self-excite circuit oscillates the MEMS as long based as the oscillator forward circuit. gain of The the main TIA overcomes challenge whenthe resonator designing series a resonator-based loss represented oscillator by 𝑅 is). the quite large resonator-equivalent motional resistanceThe otherRM (the alternative, circuit oscillates the Pierce as longoscillator as the [18], forward uses gaina capacitive of the TIA input overcomes to integrate the resonatorthe current series from loss the represented resonator and by RconvertM). it into a voltage at the sense node. The Pierce circuitThe topology other alternative, is, in general, the Pierce superior oscillator in term [18s ],of uses the aoscillator capacitive noise input figure to integrate since it theex- currenthibits an from extremely the resonator high input-impedance and convert it into [22, a voltage23]. Thus, at the the sense gain node.is provided The Pierce by a circuit noise- topologyless capacitive is, in input general, element superior rather in termsthan a oflossy the resistive oscillator element. noise figure One of since the drawbacks it exhibits anof the extremely Pierce oscillator high input-impedance topology is its inherent [22,23]. Thus,dependence the gain of the is provided open-loop by gain a noiseless with the capacitive input element rather than a lossy resistive element. One of the drawbacks of the parasitic capacitance 𝐶 at the sense node. This drawback does not represent a real limi- Piercetation oscillatorwhen thetopology design is iscustomized its inherent for dependence a well-known of the resonator open-loop working gain with under the adequate parasitic capacitance C at the sense node. This drawback does not represent a real limitation when operating conditionsp but lacks in versatility to deal with resonators with different charac- the design is customized for a well-known resonator working under adequate operating teristics since its contribution to 𝐶 is hard to accurately estimate from the resonator lay- conditions but lacks in versatility to deal with resonators with different characteristics since out. Moreover, they are difficult to interface with high-impedance MEMS devices [17]. its contribution to C is hard to accurately estimate from the resonator layout. Moreover, Figure 2 illustrates thep expected dependence of the transimpedance gain vs. the parasitic they are difficult to interface with high-impedance MEMS devices [17]. Figure2 illustrates capacitance 𝐶 for a both the TIA with capacitive feedback [17] like the one designed in the expected dependence of the transimpedance gain vs. the parasitic capacitance Cp for this work and the behavior of the well-known dependence shown for a Pierce-based to- a both the TIA with capacitive feedback [17] like the one designed in this work and the behaviorpology amplifier. of the well-known dependence shown for a Pierce-based topology amplifier.

FigureFigure 2.2. Open-loopOpen-loop gain gain from from theoretical theoretical prediction prediction for fo ther the two two ampliﬁer amplifier topologies topologies as as a function a function of 𝐶 theof the capacitance capacitanceCp. .

InIn thisthis work,work, wewe designeddesigned ad-hocad-hoc aa commercialcommercial 0.35-0.35-µmµm 3.33.3 VV CMOSCMOS technologytechnology TIATIA amplifieramplifier constitutedconstituted byby aa firstfirst stage,stage, basedbased onon thethe schemescheme fromfrom [[16],16], andand aa second second stagestage inin whichwhich wewe addedadded aa controlcontrol signalsignal toto tune tune the the overall overall transimpedance transimpedance gaingain asas shown shown in in FigureFigure3 .3. The The circuit circuit behavior behavior is is closer closer to to the the ideal ideal characteristic characteristic of of Figure Figure2 in2 in terms terms of of sensitivitysensitivity toto thethe sensesense nodenode parasiticparasitic capacitance.capacitance. In the first stage, Cp corresponds to the resonator capacitance (including the routing components). RG1 and RG2 ensure that transistors M1 and M2 are saturated by appropri- ately biasing the transistor gate; given their high nominal values (they are in the range of GΩ), these devices have been implemented by two nMOS transistors, in anti-parallel configuration, working in their sub-threshold regions and consequently exhibiting an extremely high resistance [20]. In this design, we included a diode-connected pMOS transistor (M4) with an equivalent small-signal resistance given by RD ≈ 1/gm,M4. The transfer function can be written as Vo(s) Iout(s) C1 = RD ≈ 1 + RD, (2) Isig(s) Isig(s) C2

6 −1 to obtain a gain close to 2.5 × 10 V·A with RD = 36 kΩ, C2 = 6 pF and C1 = 90 fF. The second stage is a pMOS-based source follower with shunt-shunt feedback implemented through a nMOS device working in the linear region. The gate voltage is externally Micromachines 2021, 12, 82 4 of 16

controlled through Vcontrol, which can take values between 0.5 and 2.5 V. This nMOS plays the role of variable resistance, providing tunable input resistance in terms of Vcontrol. This variable input resistance affects the output resistance of the ﬁrst stage and consequently its gain (Figure3)[19]. Several simulation analyses were carried out to characterize the performance of the proposed circuit. Figure4a shows the frequency response of the transimpedance gain (magnitude and phase). A maximum gain of 1.17·106 V·A−1 (121 dB) was achieved over a bandwidth of 50 MHz. We notice that this value is lower than the 2.5·106 V·A−1 obtained from Equation (2) given the moderate voltage gain for the ﬁrst stage used in our design. Figure4a also reports the dependence of the gain with Vcontrol (a very low impact has been observed in the phase plot in Figure4b). The gain can be adjusted between 112 and 121 dB, varying Vcontrol between 0 and 3.3 V. Figure5 shows the input-referred current noise, having a mean value of 192 fA·Hz−1/2 at frequencies around 10 MHz (equivalent Micromachines 2021, 12, x to 225 nV·Hz−1/2 at the output). A low power consumption value of 930 µW for a4 3.3of 17 V voltage supply was obtained.

Figure 3. SchematicSchematic of of the the fabricated fabricated two-stage two-stage transimpedan transimpedancece amplifier ampliﬁer (TIA) (TIA) including including an additional an additional 50-Ω output 50-Ω output buffer for testing purposes. The biasing resistors 𝑅 and 𝑅 have been implemented by two nMOS transistors in anti-parallel buffer for testing purposes. The biasing resistors RG1 and RG2 have been implemented by two nMOS transistors in configuration. anti-parallel conﬁguration.

InTable the1 first compares stage, 𝐶 this corresponds TIA design to to the prior resonator works [capacitance14,17,24–27 (including]. As stated the earlier, routing in components).addition to the 𝑅 gain and insensitivity 𝑅 ensure to thatCp, atransistors significant 𝑀 advantage and 𝑀 ofare the saturated proposed by solution appro- priafeaturestely biasing a tunable-gain the transistor option. gate; Finally, given a Figuretheir high of Merit nominal (FoM) values is devised (they are to comparein the range the ofcircuit 𝐺Ω), design these devices effort in have series-resonant been implemented oscillators by with two various nMOS oscillatingtransistors, frequencies in anti-parallel and configuration,resonator characteristics working in [14 their]: sub-threshold regions and consequently exhibiting an extremely high resistance [20]. In this design,k weT BWincluded2R2 a diode-connected pMOS transis- FoM = B M , (3) 𝑀 2 𝑅 1/𝑔 tor ( ) with an equivalent small-signal resistanceVon P given by ,. The transfer function can be written as where kB is the Boltzmann constant, T is the absolute temperature, Von is the output noise, BW is the TIA bandwidth,𝑉𝑠RM is𝐼 the𝑠 TIA transimpedance𝐶 gain, and P is the power = 𝑅 1+ 𝑅, (2)23 consumption. The amplifier developed𝐼𝑠 𝐼 in𝑠 this work exhibits𝐶 an FoM value of 3.04·10 , which is absolutely competitive with the reported state of the art as shown in Table1. For to obtain a gain close to 2.5 × 106 V·A−1 with 𝑅 = 36kΩ, 𝐶 = 6 pF and 𝐶 = 90fF. comparison with the Pierce oscillator topology, an FoM value of 1.06·1027 was achieved for aThe highly second compact stage Pierce-basedis a pMOS-based amplifier source integrated follower with together shunt-shunt with a seesaw feedback resonator implemented through a nMOS device working in the linear region. The gate voltage is externally controlled through 𝑉, which can take values between 0.5 and 2.5 V. This nMOS plays the role of variable resistance, providing tunable input resistance in terms of 𝑉. This variable input resistance affects the output resistance of the first stage and consequently its gain (Figure 3) [19]. Several simulation analyses were carried out to characterize the performance of the proposed circuit. Figure 4a shows the frequency response of the transimpedance gain (magnitude and phase). A maximum gain of 1.17·106 V·A−1 (121 dB) was achieved over a bandwidth of 50 MHz. We notice that this value is lower than the 2.5·106 V·A−1 obtained from Equation (2) given the moderate voltage gain for the first stage used in our design. Figure 4a also reports the dependence of the gain with 𝑉 (a very low impact has been observed in the phase plot in Figure 4b). The gain can be adjusted between 112 and 121 dB, varying 𝑉 between 0 and 3.3 V. Figure 5 shows the input-referred current noise, having a mean value of 192 fA·Hz−1/2 at frequencies around 10 MHz (equivalent to 225 nV·Hz−1/2 at the output). A low power consumption value of 930 µW for a 3.3 V voltage supply was obtained. Micromachines 2021, 12, 82 5 of 16

operating at frequencies below the 1-MHz range [21]. Despite the fact that it provides better performance compared to the present work, this would be rapidly degraded for higher operating frequencies and particularly for larger resonator parasitic capacitances. Similarly, in [23], a Pierce oscillator has been also demonstrated to achieve GSM noise requirements speciﬁcally oriented to phase noise optimization with a solution fabricated using the very same technological approach as this current work.

Table 1. Performance comparison with state-of-the-art reported works based on a TIA topology.

TIA [24][14][25][17][26][27] This Work Bandwidth 280 MHz 20 MHz 60 MHz 1.8 MHz 1.2 MHz 90 MHz 50 MHz 25.0 kΩ– 12.0 kΩ– 12.5 kΩ– 330 kΩ– Gain 316 kΩ 56.0 MΩ 7.94 MΩ 89.0 kΩ 69.0 kΩ 794 kΩ 1.17 MΩ Output 790 3.64 199 3.18 225 -- Voltage noise µV/Hz1/2 µV/Hz1/2 nV/Hz1/2 µV/Hz1/2 nV/Hz1/2 Input- Referred 192 -- Current fA/Hz1/2 Noise CMOS 0.18 µm 0.35 µm 0.18 µm 0.18 µm 0.35 µm 65 nm 0.35 µm Technology 14 21 22 20 23 MicromachinesFoM 2021, 12, x - - 4.04·10 7.28·10 6.65·10 1.66·10 3.045 ·of10 17 Power Con- Micromachines 20211.57, 12,mW x 6.90 mW 5.90 mW 436 µW 150 µW 900 µW5 930of 17µW sumption

(a)( a) ((bb) )

FigureFigureFigure 4. 4.Bode Bode 4. Bode plots plots plots of of amplitude amplitudeof amplitude ((aa) )( a andand) and phase phase ( (b b(b)) )of ofof the thethe proposed proposed proposed TIATIA TIA at atthe the 𝑉𝑉 V node. node.o node. Results Results Results have have have been beenbeen obtained obtained obtained under under under nominalnominal biasing biasing conditions conditions with with 𝐶 𝐶 = 20 = 20 fF. fF. nominal biasing conditions with Cp= 20 fF.

Figure 5. Simulation results for the input-referred current noise of the current TIA design. FigureFigure 5.5. Simulation results results for for the the input-referred input-referred current current noise noise of ofthe the current current TIA TIA design. design. Table 1 compares this TIA design to prior works [14,17,24–27]. As stated earlier, in additionTable to1 comparesthe gain insensitivity this TIA design to 𝐶 , toa significantprior works advantage [14,17,24–27]. of the proposedAs stated solutionearlier, in additionfeatures to a thetunable-gain gain insensitivity option. Finally, to 𝐶 ,a a Figure significant of Merit advantage (FoM) is ofdevised the proposed to compare solution the featurescircuit adesign tunable-gain effort in option.series-resonant Finally, oscill a Figureators ofwith Merit various (FoM) oscillating is devised frequencies to compare and the circuitresonator design characteristics effort in series-resonant [14]: oscillators with various oscillating frequencies and resonator characteristics [14]: 𝑘 𝑇 𝐵𝑊𝑅 𝐹𝑜𝑀 = , (3) 𝑉 𝑃 𝑘𝑇 𝐵𝑊 𝑅 𝐹𝑜𝑀 = , (3) where 𝑘 is the Boltzmann constant, 𝑇 is 𝑉the absolute𝑃 temperature, 𝑉 is the output noise, 𝐵𝑊 is the TIA bandwidth, 𝑅 is the TIA transimpedance gain, and 𝑃 is the where 𝑘 is the Boltzmann constant, 𝑇 is the absolute temperature, 𝑉 is the output power consumption. The amplifier developed in this work exhibits an FoM value of noise, 𝐵𝑊 is the TIA bandwidth, 𝑅 is the TIA transimpedance gain, and 𝑃 is the 3.04·1023, which is absolutely competitive with the reported state of the art as shown in powerTable consumption.1. For comparison The with amplifier the Pierce developed oscillator intopology, this work an FoM exhibits value an of 1.06·10FoM value27 was of 23 3.04·10achieved, which for a ishighly absolutely compact competitive Pierce-based with amplifier the reported integrated state together of the withart as a shownseesaw in Tableresonator 1. For operatingcomparison at frequencieswith the Pierce below oscillator the 1-MHz topology, range an[21]. FoM Despite value the of 1.06·10fact that27 wasit achievedprovides for better a highly performance compact compared Pierce-based to th amplifiere present integratedwork, this wouldtogether be with rapidly a seesaw de- resonatorgraded for operating higher operating at frequencies frequencies below and the pa 1-MHzrticularly range for larger [21]. resonatorDespite the parasitic fact that ca- it providespacitances. better Similarly, performance in [23] ,compared a Pierce oscillator to the present has been work, also thisdemonstrated would be to rapidly achieve de- gradedGSM noisefor higher requirements operating specifically frequencies oriented and pa torticularly phase noise for optimization larger resonator with parasitica solution capacitances.fabricated Similarly,using the veryin [23] same, a technologicalPierce oscillator approach has been as this also current demonstrated work. to achieve GSM noise requirements specifically oriented to phase noise optimization with a solution fabricated using the very same technological approach as this current work.

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Table 1. Performance comparison with state-of-the-art reported works based on a TIA topology.

TIA [24] [14] [25] [17] [26] [27] This Work

Bandwidth 280 MHz 20 MHz 60 MHz 1.8 MHz 1.2 MHz 90 MHz 50 MHz 25.0 kΩ– 12.0 kΩ– 12.5 kΩ– 330 kΩ– Gain 316 kΩ 56.0 MΩ 7.94 MΩ 89.0 kΩ 69.0 kΩ 794 kΩ 1.17 MΩ

Output Voltage 790 3.64 199 3.18 225 - - noise µV/Hz1/2 µV/Hz1/2 nV/Hz1/2 µV/Hz1/2 nV/Hz1/2

Input-Referred 192 - - Current Noise fA/Hz1/2

CMOS Technol- 0.18 µm 0.35 µm 0.18 µm 0.18 µm 0.35 µm 65 nm 0.35 µm ogy

FoM - - 4.04·1014 7.28·1021 6.65·1022 1.66·1020 3.04·1023

MicromachinesPower Consump-2021, 12, 82 6 of 16 1.57 mW 6.90 mW 5.90 mW 436 µW 150 µW 900 µW 930 µW tion

3.3. OscillatorOscillator ElectromechanicalElectromechanical ModelModel TheThe oscillatoroscillator is is constituted constituted by by the the MEMS MEMS resonator, resonator, represented represented by its lumpedby its lumped equivalentequivalent RLC circuitRLC circuit and the and feedthrough the feedthrough capacitance capacitance between between the actuation the actuation and readout and driversreadout [ 28drivers], connected [28], connected in series in to series the TIA to asthe shown TIA as in shown Figure in6. Figure In addition, 6. In addition, an output an bufferoutput for buffer testing for purposestesting purposes was also was included also included in the integrated in the integrated circuit scheme. circuit scheme.

FigureFigure 6.6. Oscillator schematic: MEMS MEMS resonator resonator (represent (representeded by by its its lumped lumped electrical electrical equivalent equivalent model)model) andand thethe transimpedancetransimpedance ampliﬁeramplifier (TIA).(TIA).

TheThe equivalentequivalent admittanceadmittance ((Y𝑌eq)) inin termsterms ofof thethe lumpedlumped elementselements is:is: 1 −1 𝑌 =𝑗𝜔𝐿 +1 +𝑅 + 𝑗𝜔𝐶, (4) Yeq = jωLM + 𝑗𝜔𝐶+ RM + jωC0, (4) jωCM where the feedthrough capacitance (𝐶) has also been included. The open-loop configura- wheretion amplifier the feedthrough output voltage capacitance is obtained (C0) has from also the been equivalent included. admittance The open-loop and the config- trans- urationconductance amplifier gain ( output𝐺), which voltage is accurately is obtained determined from the from equivalent the TIA amplifier admittance post-layout and the transconductancesimulations: gain (G), which is accurately determined from the TIA amplifier post- layout simulations: Vo 𝑉= =𝐺𝑌GYeq.. (5)(5) The main goal of this work is to determine these parameters for any specific resonator from an open-loop response by model fitting considering that the amplifier gain roughly depends on the resonator driver parasitic capacitance. From a practical point of view, it is

advisable to use Q and ω0 as ﬁtting parameters, together with RM, instead of CM and LM, which can be computed afterward. Therefore, using these deﬁnitions from the RLC branch,

1 Q = , (6) ω0RMCM 1 ω0 = √ , (7) LMCM

the output voltage is ﬁtted from the open-loop response in terms of ω0, Q, C0, and RM:   ω j ω R Q V = G 0 M + jωC  (8) o  2 0 1 − ω + j ω ω0 ω0Q

Therefore, the resonator is fully characterized by first fitting the parameters in Equation (8) and subsequently computing the remaining parameters (CM and LM). The motional resistance represents the crucial parameter as it determines the ampliﬁer gain constraints for a self-sustained oscillator. Micromachines 2021, 12, 82 7 of 16

4. MEMS Fabrication and Design The mechanical resonators measured in this work were fabricated using a commercial CMOS 0.35-µm technology with an additional post-CMOS step consisting of a mask-less wet-etching performed at our laboratory. This additional step is aimed to release the resonators by removing the sacrificial oxide layer underneath, obtaining a fully integrated CMOS-MEMS solution [29]. The CMOS process used provides two polysilicon layers and a stack of four metal layers (TiN-Al-TiN) interconnected by Tungsten (W) vias. This fabrication approach based on a CMOS commercial technology provides a wide range of benefits as detailed in [9,10]. However, only the materials available in the manufacturing process can be considered as structural layers, and the manufacturer design rules must also be conformed to [10,12,30]. Thus, the resonator performance is constrained in some issues as a poor-quality factor (Q) compared to specific MEMS fabrication processes, reduced capacitive coupling between the resonator and the readout driver due to fixed layer thickness and minimum distance, and a relatively high device temperature sensitivity. Three design options, shown in Figure7, were considered in this work, called Plate Resonator 1 (PR1), Plate Resonator 2 (PR2), and Plate Resonator 3 (PR3). All of them consist of an anchored plate resonator with a two-driver configuration with electrostatic actuation and capacitive readout to make it feasible to combine the MEMS with the readout circuitry in the same IC for a monolithic integration [31]. The large motional resistances exhibited by the resonators (as a consequence of the aforementioned relatively small capacitive coupling) is compensated by the high-gain, low-noise integrated TIA and a significant reduction of the parasitic contributions. The MEMS resonators were designed by means of a two-layer strategy, similar to that in [32], so that the coupling capacitance became larger compared to single-layer geometries, i.e., decreased the motional resistance. The coupling can be improved by either reducing the resonator-driver gap or by increasing the composite material thickness. Therefore, the first two structures presented here exploit each one of these alternatives for design optimization. Additionally, a composite material in the form of metal–oxide–metal reduces its overall temperature sensitivity because the oxide relative stress when increasing the operating temperature changes opposite to that of the metal layer [33]. This fact is also a key aspect for MEMS resonators design when considering the final oscillator stability as an important figure of merit directly related to the sensor limit of detection. In this sense, the PR1 structure benefits from MET3-OX-MET4 and MET3-VIA-MET4 layers (see Figure7a), while the PR2 was designed to have a MET-VIA stack as in Figure7b. On behalf of PR3, it inherits most of the design strategy developed for PR2 shown in Figure7c. It scales up its platform dimensions so as to provide a solution suitable for inkjet deposition; one of the possible applications for this resonator is to operate as a gravimetric gas sensor thanks to its outstanding distributed mass sensitivity [31] together with a proper functionalization process with a specific layer to capture the target molecules. A detailed discussion of each structure is presented next.

4.1. Plate Resonator 1 This design, shown in Figure7a, consists of a four-anchored plate resonator com- posed of two materials: (i) the resonator main body is designed to be manufactured with a MET3-OX-MET4 (MOM) compound so that the overall effective mass growth is minimum compared to using the VIA layer required in the anchors and drivers for coupling requirements; (ii) the anchors combine the previous stack with a MET-VIA-MET (MVM) composite to get an increase in the readout coupling thanks to the larger thickness when including MET4. However, the minimum distance between two MET4-adjacent layers is 600 nm, worsening the overall coupling when compared to a gap of 500 nm available by design rules when using VIA or lower metal layers. To investigate this option, we created the second structure (Figure7b), where the MV composite is not used in the whole beam to avoid an excessive increase of the whole resonator mass density [32]. Micromachines 2021, 12, x 8 of 17

also a key aspect for MEMS resonators design when considering the final oscillator stability as an important figure of merit directly related to the sensor limit of detection. In this sense, the PR1 structure benefits from MET3-OX-MET4 and MET3-VIA-MET4 layers (see Figure 7a), while the PR2 was designed to have a MET-VIA stack as in Figure 7b. On behalf of PR3, it inherits most of the design strategy developed for PR2 shown in Figure 7c. It scales up its platform dimensions so as to provide a solution suitable for inkjet deposition; one of the possible applications for this resonator is to operate as a gravimetric gas sensor

Micromachines 2021, 12,thanks 82 to its outstanding distributed mass sensitivity [31] together with a proper func- 8 of 16 tionalization process with a specific layer to capture the target molecules. A detailed discussion of each structure is presented next.

(a)

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(b)

(c)

Figure 7. SchematicFigure 7.designSchematic of the designfabricated of the MEMS fabricated resonators MEMS including resonators the different including layers the different that layers that have been used:have (a been) PR1, used: (b) PR2 (a) PR1,and ( (cb)) PR3. PR2 and (c) PR3.

4.1. Plate Resonator 1 This design, shown in Figure 7a, consists of a four-anchored plate resonator com- posed of two materials: (i) the resonator main body is designed to be manufactured with a MET3-OX-MET4 (MOM) compound so that the overall effective mass growth is minimum compared to using the VIA layer required in the anchors and drivers for coupling requirements; (ii) the anchors combine the previous stack with a MET-VIA-MET (MVM) composite to get an increase in the readout coupling thanks to the larger thickness when including MET4. However, the minimum distance between two MET4-adjacent layers is 600 nm, worsening the overall coupling when compared to a gap of 500 nm available by design rules when using VIA or lower metal layers. To investigate this option, we created the second structure (Figure 7b), where the MV composite is not used in the whole beam to avoid an excessive increase of the whole resonator mass density [32].

Micromachines 2021, 12, 82 9 of 16

4.2. Plate Resonator 2 The device shown in Figure7b is a six-anchored plate resonator with the four outer anchors conceived to provide large coupling and vibration stability, while the two inner ones increase the overall stiffness to achieve higher oscillation frequency. Similarly to the previous design, it also combines various material aggregates: (i) the main body and the inner anchors were made of a single MET4 (M) layer as it does not play any role in the coupling capacitance—not requiring an increased thickness—while the overall mass is reduced, thus decreasing the motional resistance; (ii) the outer anchors merge the MOM composite with a MET3-VIA composite at the driver side to reduce the resonator-driver gap since MET3 and VIA layers can have a separation of only 500 nm. A reduction in the gap has a higher impact on the coupling than the overall thickness does. In any case, the coupling thickness of this structure will be smaller than the one of the previously described structure. Notice that, depending on the metal and via combinations, the thickness of each layer may vary [34]. The structure depicted in Figure7c takes the design strategy from PR2 and implements some improvements in the pursuit of a large enough platform to enable inkjet deposition featuring droplets with diameter in the order of 70 µm. It combines the same material mixtures with a single metal layer approach: (i) the main body material is the MET4 layer to reduce the overall mass and, in consequence, the motional resistance, as well as to allow for regularly spaced holes for release purposes; (ii) the beams combine the MOM composite in the center for temperature insensitivity with the MV in both sides to increase the stiffness and improve the capacitive coupling; and (iii) the perimeter of the structure also features the MV composite to provide an increased stiffness to the overall platform and avoid vertical bending under self-loading effects. According to manufacturer fabrication parameters, the readout electrode parasitic capacitance featured for this structure is in the order of 80 fF; 8× the value found for a minimum-size MEMS resonator fabricated with the same 0.35-µm technology [15]. Thus, one would expect for the Pierce topology alternative to have its open-loop gain reduced, similar to the possibility of failing to compensate for the motional resistance losses and, consequently, not being able to operate as a self-sustained oscillator. In such a case, it is the TIA alternative that provides a huge advantage, having an open-loop gain that does not diminish with increased input capacitance. Therefore, in this work, we will also provide electrical characterization for this structure obtaining a parameter extraction with an accuracy that, otherwise, would have been not feasible with a Pierce scheme-based ampliﬁer.

5. Electrical Characterization 5.1. Transimpedance Ampliﬁer Figure8 shows one the CMOS-MEMS devices fabricated in the IC using a CMOS 0.35-µm commercial technology. First, the CMOS TIA circuit was characterized in terms 1/2 of noise performance. A voltage noise at the Vo_50 node of 110 nV/Hz at 10 MHz was measured, providing a value that perfectly matches the simulation outcome (see Figure9 ). For clariﬁcation, Figure9 also depicts the simulated voltage noise at the Vo node (the output of the TIA 2nd stage), which is 225 nV/Hz1/2 at 10 MHz (see Table1). This node is the one used to drive the resonator excitation and closes the oscillator loop, but it cannot be experimentally tested since it was not designed to interface with the 50-Ω input laboratory benchtop equipment [20]. Notice that the noise at this node is higher than the one obtained at the tested node Vo_50 because of the attenuation introduced by the output buffer. Micromachines 2021, 12, x 10 of 17

also features the MV composite to provide an increased stiffness to the overall platform and avoid vertical bending under self-loading effects. According to manufacturer fabrication parameters, the readout electrode parasitic capacitance featured for this structure is in the order of 80 fF; 8× the value found for a minimum-size MEMS resonator fabricated with the same 0.35-µm technology [15]. Thus, one would expect for the Pierce topology alternative to have its open-loop gain reduced, similar to the possibility of failing to compensate for the motional resistance losses and, consequently, not being able to operate as a self-sustained oscillator. In such a case, it is the TIA alternative that provides a huge advantage, having an open-loop gain that does not diminish with increased input capacitance. Therefore, in this work, we will also provide electrical characterization for this structure obtaining a parameter extraction with an accuracy that, otherwise, would have been not feasible with a Pierce scheme-based amplifier.

5. Electrical Characterization 5.1. Transimpedance Amplifier Figure 8 shows one the CMOS-MEMS devices fabricated in the IC using a CMOS 0.35- µm commercial technology. First, the CMOS TIA circuit was characterized in terms of noise 1/2 performance. A voltage noise at the 𝑉_ node of 110 nV/Hz at 10 MHz was measured, providing a value that perfectly matches the simulation outcome (see Figure 9). For clarifi- cation, Figure 9 also depicts the simulated voltage noise at the 𝑉 node (the output of the TIA 2nd stage), which is 225 nV/Hz1/2 at 10 MHz (see Table 1). This node is the one used to drive the resonator excitation and closes the oscillator loop, but it cannot be experimentally Micromachines 2021, 12, 82 tested since it was not designed to interface with the 50-Ω input laboratory benchtop10 equip- of 16 ment [20]. Notice that the noise at this node is higher than the one obtained at the tested node 𝑉_ because of the attenuation introduced by the output buffer.

Micromachines 2021, 12, x 11 of 17

FigureFigure 8. OpticalOptical image image of the of CMOS-MEMS the CMOS-MEMS oscillator oscillator IC fabricated IC fabricated in a CMOS ina 0.35-µm CMOS commer- 0.35-µm commercialcial technology. technology.

𝑉 FigureFigure 9.9. TheThe measuredmeasured output output voltage voltage noise noise (blue (blue line) line) at atVo _50_is compared is compared to theto the simulation simulation results atresults the same at the node same (magenta node (magenta line) to showline) to that show both th valuesat both arevalues in good are in agreement. good agreement. Additionally, Addition- the ally, the simulated voltage noise at 𝑉 is depicted with a solid green line to show how the output simulated voltage noise at Vo is depicted with a solid green line to show how the output buffer buffer attenuates the voltage signal. attenuates the voltage signal. 5.2.5.2. PlatePlate ResonatorResonator 11 andand PlatePlate ResonatorResonator 22 TheThe CMOS-MEMSCMOS-MEMS resonatorsresonators werewere characterizedcharacterized inin bothboth open-open- andand closed-loopclosed-loop con-con- figurationsfigurations thanksthanks to to the the capacitive capacitive readout readout scheme scheme and and the the integrated integrated amplifier. amplifier. Figure Figure9 shows9 shows the measuredthe measured electromechanical electromechanical transmission transmission coefficient coefficient (obtained (obtained with a Keysight with a ENAKeysight E5061B ENAnetwork E5061B analyzer) network atanalyzer) low excitation at low powerexcitation (−35 power dBm) to(−35 keep dBm) the to resonators’ keep the operationresonators’ in operation the linear in regime the linear both regime for vacuum both for (below vacuum 10− 3(belowmbar) 10 and−3 mbar) ambient and pressure. ambient Additionally,pressure. Additionally, a sweep of a the sweep resonator of the DC resonator biasing DC voltage biasing from voltage 10 V to from 40 V 10 was V to performed 40 V was toperformed obtain the to motional obtain the resistance motional at resistance various values at various and experimentally values and experimentally observe the relation- observe shipthe relationship in which the in resistance which the is resistance inversely proportionalis inversely proportional to the squared to the DC squared voltage throughDC volt- theage electromechanical through the electromechanical coupling. coupling. TheThe experimentalexperimental response shown in in Figure Figure 1010 was was fitted fitted to to the the model model in in Section Section 3 3to toobtain obtain the the aforementioned aforementioned parameters. parameters. The The re resultingsulting resonance resonance frequency is plottedplotted inin f 2 = a − bV2 FigureFigure 1111 asas aa function of the biasing voltage voltage and and fitted fitted as as 𝑓 =𝑎−𝑏𝑉dc,, from from which which the the naturalnatural frequencyfrequency waswas computedcomputed (resonant(resonant frequencyfrequency at at 0 0 V V biasing).biasing). FigureFigure 12 12 illustrates illustrates an example of such fitting with the extracted values demonstrating high model accuracy, as it perfectly matches the measured transmission coefficient. Remarkably, this degree of precision in the parameter extraction procedure is only achievable thanks to having an amplifier open-loop gain that does not depend on the input capacitance and whose specific value was obtained from post-layout simulations. The parameters obtained for both resonators are listed in Table 2 for a biasing voltage of 25 V. We also obtained the motional resistance for all biasing voltages (plotted in Figure 13); the theoretical prediction is also included in solid lines as well as the linear fitting in logarithmic scale in dashed lines. Results show that the theoretical motional resistance prediction matches the experimental data with an error below 20% in the worst case; such a reliable calculation is also a direct consequence of the amplifier gain being accurately characterized. In any case, the remaining error could be attributed to the metal layers’ degradation caused by the etching step that is intended to remove only the sacrificial oxide but in practice has an impact on the metal layers as well [35]. Such a metal degradation can reduce the overall resonator-driving coupling capacitance, resulting in experimental motional resistances larger than expected. Furthermore, the fabrication process itself, together with the post-CMOS etching step, has been shown to produce a 10% error in the measured resonant frequency, which goes in line with the error also observed for the motional resistance.

Micromachines 2021, 12, 82 11 of 16

an example of such fitting with the extracted values demonstrating high model accuracy, as it perfectly matches the measured transmission coefficient. Remarkably, this degree of precision in the parameter extraction procedure is only achievable thanks to having an amplifier open-loop gain that does not depend on the input capacitance and whose specific value was obtained from post-layout simulations. The parameters obtained for both resonators are listed in Table2 for a biasing voltage of 25 V. We also obtained the motional resistance for all biasing voltages (plotted in Figure 13); the theoretical prediction is also included in solid lines as well as the linear fitting in logarithmic scale in dashed lines. Results show that the theoretical motional resistance prediction matches the experimental data with an error below 20% in the worst case; such a reliable calculation is also a direct consequence of the amplifier gain being accurately characterized. In any case, the remaining error could be attributed to the metal layers’ degradation caused by the etching step that is intended to remove only the sacrificial oxide but in practice has an impact on the metal layers as well [35]. Such a metal degradation can reduce the overall resonator-driving coupling capacitance, resulting in experimental motional resistances larger than expected. Micromachines 2021, 12, x Furthermore, the fabrication process itself, together with the post-CMOS etching step,12 of has 17 been shown to produce a 10% error in the measured resonant frequency, which goes in line with the error also observed for the motional resistance.

(a) (b)

Figure 10. ElectricalElectrical characterization characterization of of the the MEMS MEMS resonator resonator with with on-chip on-chip readout readout circ circuituit in open-loop in open-loop configuration. conﬁguration. Ex- perimental magnitude of frequency response for various MEMS bias voltages (Vdc): (a) plate resonator PR1 in ambient Experimental magnitude of frequency response for various MEMS bias voltages (Vdc): (a) plate resonator PR1 in ambient pressure; ((bb)) plateplate resonatorresonator PR1PR1 in in vacuum vacuum pressure; pressure; ( c()c) plate plate resonator resonator PR2 PR2 in in ambient ambient pressure; pressure; (d ()d plate) plate resonator resonator PR2 PR2 in in vacuum pressure. vacuum pressure.

(a) (b) Figure 11. Resonance frequency dependence with the resonator bias voltage obtained from experimental open-loop response data fitting. The linear fit for the frequency values is also included (dashed lines) to obtain the natural frequency at 0 bias voltage for each case: (a) PR1; (b) PR2.

Micromachines 2021, 12, x 12 of 17

(a) (b)

(c) (d) Figure 10. Electrical characterization of the MEMS resonator with on-chip readout circuit in open-loop configuration. Ex- perimental magnitude of frequency response for various MEMS bias voltages (Vdc): (a) plate resonator PR1 in ambient Micromachines 2021, 12, 82 12 of 16 pressure; (b) plate resonator PR1 in vacuum pressure; (c) plate resonator PR2 in ambient pressure; (d) plate resonator PR2 in vacuum pressure.

(a) (b)

Figure 11. Resonance frequencyfrequency dependence dependence with with the the resonator resonator bias bias voltage voltage obtained obtained from from experimental experimental open-loop open-loop response re- Micromachines 2021, 12, x 13 of 17 sponsedata ﬁtting. data Thefitting. linear The ﬁt linear for the fit frequencyfor the frequency valuesis values also included is also included (dashed (dashe lines) tod lines) obtain to the obtain natural the frequencynatural frequency at 0 bias atvoltage 0 bias forvoltage each case:for each (a) case: PR1; (ba) PR1; PR2. (b) PR2.

(a) (b)

Figure 12. Electrical characterization of the MEMSMEMS resonator with on-chip readout circuit in open-loop conﬁgurationconfiguration for RLC parameter extractionextraction byby meansmeans of of model model ﬁtting. fitting. The The experimental experimental data data corresponds corresponds to to PR1 PR1 using using a biasa bias voltage voltage of of 25 25 V inV in air air conditions: conditions: (a )(a magnitude) magnitude and and (b )(b phase.) phase.

Table 2. Extracted parameters from experimental open-loop response by model ﬁtting for both resonators in air and vacuum conditions.

Resonator f0 (MHz) Q RM (MΩ)CM (aF) LM (H) C0 (aF) PR1 (air) 1.152 110 18 † 72 † 280 † 210 PR1 (vac) 1.147 2100 1.2 † 56 † 360 † 210 PR2 (air) 3.789 210 63 † 3.4 † 530 † 890 PR2 (vac) 3.767 1600 7.7 † 3.3 † 520 † 890 PR3 (air) 0.402 132 662 § 4.5 § 34,000 § 96 † These values refer to a biasing voltage of 25 V. § These values refer to a biasing voltage of 8 V.

The PR1 structure was also measured in closed-loop conﬁguration to operate as an Figureoscillator 13. inMotional self-excited resistance mode computed in vacuum from conditions experimental obtaining open-loop the outputdata by voltagemeans of waveform the proposed model fit: the value is inversely proportional to the square of the resonator biasing voltage. shown in Figure 14a. The self-sustained oscillation started at a DC biasing voltage of 23 V, The obtained fit (dashed lines) matches the theoretical prediction (solid lines) for both structures V inand air atand dcvacuum= 25 V, conditions. the oscillator exhibited a frequency of 1.120 MHz and a peak-to-peak voltage of 273 mV. The measured Allan deviation (obtained with the frequency counter Table 2. Extracted parametersPendulum from experimental CNT-90) open-loop is also provided response by in model Figure fitting 14b forfor both integration resonators times in air ranging and vac- from −5 uum conditions. 5·10 s to 5 s, reaching a minimum value of 2 ppm for an integration time of 300 ms. The

The PR1 structure was also measured in closed-loop configuration to operate as an oscillator in self-excited mode in vacuum conditions obtaining the output voltage waveform shown in Figure 14a. The self-sustained oscillation started at a DC biasing voltage of 23 V, and at VDC = 25 V, the oscillator exhibited a frequency of 1.120 MHz and a peak-to- peak voltage of 273 mV. The measured Allan deviation (obtained with the frequency counter Pendulum CNT-90) is also provided in Figure 14b for integration times ranging from 5·10−5 s to 5 s, reaching a minimum value of 2 ppm for an integration time of 300 ms.

Micromachines 2021, 12, x 13 of 17

Micromachines 2021, 12, 82 (a) (b) 13 of 16 Figure 12. Electrical characterization of the MEMS resonator with on-chip readout circuit in open-loop configuration for RLC parameter extraction by means of model fitting. The experimental data corresponds to PR1 using a bias voltage of 25 experimental value for the oscillator stability is close to the one obtained in previous works V in air conditions: (a) magnitude and (b) phase. using a Pierce topology for the oscillator circuit [36].

Micromachines 2021, 12, x 14 of 17

FigureFigure 13. 13.Motional Motional resistance resistance computed computed from experimental from experime open-loopntal data open-loop by means of thedata proposed by means of the pro- modelposed ﬁt: model the value fit: the is inversely value is proportional inversely proportional to the square of to the the resonator square biasing of thevoltage. resonator The biasing voltage. The experimental value for the oscillator stability is close to the one obtained in previous obtainedThe obtained ﬁt (dashed fit (dashed lines) matches lines) the matc theoreticalhes the prediction theoretical (solid prediction lines) for both (solid structures lines) infor air both structures works using a Pierce topology for the oscillator circuit [36]. andin air vacuum and vacuum conditions. conditions.

Table 2. Extracted parameters from experimental open-loop response by model fitting for both resonators in air and vacuum conditions.

Resonator f0 (MHz) Q RM (MΩ) CM (aF) LM (H) C0 (aF) PR1 (air) 1.152 110 18 † 72 † 280 † 210 PR1 (vac) 1.147 2100 1.2 † 56 † 360 † 210 PR2 (air) 3.789 210 63 † 3.4 † 530 † 890 PR2 (vac) 3.767 1600 7.7 † 3.3 † 520 † 890 662 § 4.5 § 34,000 § 96 PR3 (air) 0.402 132 (a) † These values refer to a biasing voltage of 25 V. § These values (referb) to a biasing voltage of 8 V. FigureFigure 14.14. MEMSMEMS resonator resonator electrical electrical characteri characterizationzation with with on-chip on-chip CMOS CMOS amplifier ampliﬁer in ina closed-loop a closed-loop configuration: conﬁguration: (a) (oscillatora) oscillator output output voltage voltage in inthe the timeThe time domain domainPR1 forstructure for PR1 PR1 with with wasa abiasing biasing also voltage voltagemeasured of of 25V; 25V; in( (b)) closed-loopmeasured Allan configuration deviationdeviation asas aa to operate as an functionfunction ofof thethe integrationintegration timetimeoscillator inin ambientambient in temperaturetemperature self-excited and and pressure. modepressure. in vacuum conditions obtaining the output voltage wave-

5.3.5.3.form Plate shown Resonator in Figure 3 14a. The self-sustained oscillation started at a DC biasing voltage of 23 V,InIn thisandthis section, section,at VDC the the= extraction25 extraction V, the of oscillator electromechanicalof electromechanical exhibited parameters parameters a frequency for PR3for arePR3of also1.120 are obtained also MHz ob- and a peak-to- usingtainedpeak the usingvoltage capabilities the capabilitiesof 273 of the mV. TIA of the amplifierThe TIA measured amplifier addressed addressedAllan in this deviation work. in this The work. plate(obtained The resonator plate withreso- has the frequency anatorcounter 150 µhasm × Penduluma 150150µ µmm platform × 150 CNT-90) µm that platform features is also that a parasiticprovided features capacitance ain parasitic Figure due capacitance 14b to the for readout integration due driverto the times ranging onreadoutfrom the order5·10 driver−5 of s 80toon fF5 the estimateds, reachingorder of from 80 a minimum manufacturerfF estimated value from specifications. manufacturerof 2 ppm The foropen-loop specifications. an integration response The time of 300 ms. inopen-loop air conditions response is shown in air in conditions Figure 15 ais for shown a biasing in Figure voltage 15a that for ranges a biasing from voltage 4 V to 12that V. Additionally,ranges from 4 the V to Bode 12 V. plot Additionally, corresponding the toBode 8 V plot biasing corresponding is depicted to in 8 Figure V biasing 15b,c is and de- fittedpicted to in the Figure theoretical 15b,c and model fitted presented. to the theoreti It iscal clearly model shown presented. that bothIt is clearly the experimental shown that curveboth the and experimental theoretical model curve are and in theoretical good agreement model thanks are in togood having agreement the open-loop thanks gainto hav- of theing on-chipthe open-loop amplifier gain perfectly of the on-chip characterized amplifier and perfectly not depending characterized on the and aforementioned not depending parasiticon the aforementioned capacitance. Interestingly, parasitic capacitance. the feedthrough Interestingly, capacitance the feedthrough obtained for capacitance PR3 is 2× smallerobtained than for PR3 the oneis 2× featured smaller bythan PR1 the inone spite featured of having by PR1 a much in spite larger of having platform a much size. Actually,larger platform this is size. directly Actually, related this to is the directly fact that, related with to athe larger fact that, platform, with a the larger readout platform, and drivingthe readout electrodes and driving are further electrodes dissociated are further and, dissociated in consequence, and, in the consequence, parasitic capacitance the parasitic capacitance between them is smaller. Additionally, the obtained motional resistance for such a structure is well above the one presented for PR1—662 MΩ over 18 MΩ—as a consequence of the highly increased mass.

(a)

Micromachines 2021, 12, x 14 of 17

The experimental value for the oscillator stability is close to the one obtained in previous works using a Pierce topology for the oscillator circuit [36].

(a) (b) Figure 14. MEMS resonator electrical characterization with on-chip CMOS amplifier in a closed-loop configuration: (a) oscillator output voltage in the time domain for PR1 with a biasing voltage of 25V; (b) measured Allan deviation as a function of the integration time in ambient temperature and pressure.

5.3. Plate Resonator 3 In this section, the extraction of electromechanical parameters for PR3 are also obtained using the capabilities of the TIA amplifier addressed in this work. The plate resonator has a 150 µm × 150 µm platform that features a parasitic capacitance due to the readout driver on the order of 80 fF estimated from manufacturer specifications. The open-loop response in air conditions is shown in Figure 15a for a biasing voltage that ranges from 4 V to 12 V. Additionally, the Bode plot corresponding to 8 V biasing is depicted in Figure 15b,c and fitted to the theoretical model presented. It is clearly shown that both the experimental curve and theoretical model are in good agreement thanks to having the open-loop gain of the on-chip amplifier perfectly characterized and not depending

Micromachines 2021, 12, 82 on the aforementioned parasitic capacitance. Interestingly, the feedthrough capacitance14 of 16 obtained for PR3 is 2× smaller than the one featured by PR1 in spite of having a much larger platform size. Actually, this is directly related to the fact that, with a larger platform, the readout and driving electrodes are further dissociated and, in consequence, the para- siticbetween capacitance them is smaller.between Additionally, them is smaller. the obtainedAdditionally, motional the obtained resistance motional for such aresistance structure foris well such above a structure the one is presentedwell above for the PR1—662 one presented MΩ over for PR1—662 18 MΩ—as M aΩ consequence over 18 MΩ—as of the a consequencehighly increased of the mass. highly increased mass.

Micromachines 2021, 12, x 15 of 17

(a)

(b) (c)

Figure 15. ElectricalElectrical characterization characterization of of the the MEMS MEMS resonator resonator with with on-chip on-chip readout readout circuit circuit in open-loop in open-loop configuration. conﬁguration. (a) Experimental magnitude of frequency response for various MEMS bias voltages (Vdc) for the plate resonator PR3 in ambi- (a) Experimental magnitude of frequency response for various MEMS bias voltages (Vdc) for the plate resonator PR3 in ambientent pressure. pressure. RLC RLCparameter parameter extraction extraction by means by means of model of model fitting; ﬁtting; the theexperimental experimental data data corresponds corresponds to a to bias a bias voltage voltage of 8 V in air conditions: (b) magnitude and (c) phase. of 8 V in air conditions: (b) magnitude and (c) phase.

6. Conclusions Conclusions The design of of capacitive capacitive readout readout circuits circuits specifically specifically oriented oriented to to CMOS-MEMS CMOS-MEMS reso- res- natorsonators that that operate operate in inthe the MHz-range MHz-range is a is demanding a demanding task task if state-of-the-art if state-of-the-art outcomes outcomes are toare be to achieved be achieved due to due moderate to moderate capacitive capacitive coupling coupling and rather and ratherpoor-quality poor-quality factor of factor fab- ricationof fabrication materials. materials. In this Inwork, this we work, have we provided have provided experimental experimental proof of proof a design of a that design not onlythat notenables only self-sustained enables self-sustained oscillation oscillation but also provides but also a provides great characterization a great characterization capability togethercapability with together tunable with gain tunable so as to gain keep so reso as tonators keep operating resonators in operating their linear in regime their linear that suitsregime a wide that suitsrange a of wide resonator range ofcharacteristics. resonator characteristics. We developed a versatile transimpedance amplifieramplifier (TIA) designed in a commercial 0.35-µm0.35-µm 3.3 V V CMOS CMOS technology technology specifically specifically oriented oriented to to monolithic monolithic CMOS-MEMS CMOS-MEMS reso- res- nators.onators. The The proposed proposed design design is clearly is clearly competit competitiveive with with the thestate state of the of art, the achieving art, achieving low power,low power, low noise, low noise, and a and high a gain high that gain enables that enables closed-loop closed-loop oscillation oscillation of MEMS of MEMSresonators res- thatonators have that been have experimentally been experimentally tested. tested.Moreover, Moreover, it offers it offerstunable tunable gain between gain between 112 and 112 121and dB 121 with dB witha dramatically a dramatically reduced reduced dependen dependencece on the on input the input parasitic parasitic capacitance capacitance com- paredcompared to other to other common common alternatives alternatives such as such the as Pierce the Pierce topology topology commonly commonly used in used previ- in ousprevious works works [37]. [37]. The TIA was applied to accurately characterize three MEMS resonators monolithically fabricated into the same CMOS die. The extraction of their electromechanical parameters using the theoretical model presented offers an extremely precise fitting, thus being able to obtain a correct value for the motional resistance thanks to having a parasitic capacitance independent gain. This value represents a key parameter in MEMS resonator and sustaining amplifier co-design, being of great importance in the design stage for future fabrication iterations and system improvement.

Author Contributions: Conceptualization: R.P.-R., J.V., and J.S.; investigation: R.P.-R. and S.B.; methodology: R.P.-R., J.V., S.B. and J.S.; supervision: J.V. and J.S.; writing—review and editing: R.P.-R., J.V. and J.S. All authors have read and agreed to the published version of the manuscript. Funding: This work has been supported by the Spanish Ministry of Economy and Competitive- ness under project TEC2017-88635-R (AEI/FEDER, UE). Acknowledgments: R. Perelló-Roig thanks his grant FPU-16/01758 from the Spanish Ministry of Education, Culture and Sport. Conflicts of Interest: The authors declare no conflict of interest.

Micromachines 2021, 12, 82 15 of 16

The TIA was applied to accurately characterize three MEMS resonators monolithically fabricated into the same CMOS die. The extraction of their electromechanical parameters using the theoretical model presented offers an extremely precise ﬁtting, thus being able to obtain a correct value for the motional resistance thanks to having a parasitic capacitance independent gain. This value represents a key parameter in MEMS resonator and sustaining ampliﬁer co-design, being of great importance in the design stage for future fabrication iterations and system improvement.

Author Contributions: Conceptualization: R.P.-R., J.V., and J.S.; investigation: R.P.-R. and S.B.; methodology: R.P.-R., J.V., S.B. and J.S.; supervision: J.V. and J.S.; writing—review and editing: R.P.-R., J.V. and J.S. All authors have read and agreed to the published version of the manuscript. Funding: This work has been supported by the Spanish Ministry of Economy and Competitiveness under project TEC2017-88635-R (AEI/FEDER, UE). Acknowledgments: R. Perelló-Roig thanks his grant FPU-16/01758 from the Spanish Ministry of Education, Culture and Sport. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References 1. Nguyen, C.T.C. Integrated micromechanical radio front-ends. In Proceedings of the International Symposium on VLSI Technology, Systems, and Applications (VLSA-TSA) 2008, Hsinchu, Taiwan, 21–23 April 2008; pp. 3–4. 2. Nguyen, C.T.C.; Howe, R.T. CMOS micromechanical resonator oscillator. In Proceedings of the IEEE International Electron Devices Meeting, Washington, DC, USA, 5–8 December 1993; pp. 199–202. 3. Van Beek, J.T.M.; Puers, R. A review of MEMS oscillators for frequency reference and timing applications. J. Micromech. Microeng. 2012, 22, 013001. [CrossRef] 4. Pachkawade, V.; Li, M.H.; Li, C.S.; Li, S.S. A CMOS-MEMS resonator integrated system for oscillator application. IEEE Sens. J. 2013, 13, 2882–2889. [CrossRef] 5. Nguyen, C.T.C. MEMS technology for timing and frequency control. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 2007, 54, 251–270. [CrossRef][PubMed] 6. Verd, J.; Uranga, A.; Abadal, G.; Teva, J.L.; Torres, F.; López, J.; Pérez-Murano, F.; Esteve, J.; Barniol, N. Monolithic CMOS MEMS oscillator circuit for sensing in the attogram range. IEEE Electron Device Lett. 2008, 29, 146–148. [CrossRef] 7. Lo, C.C.; Chen, F.; Fedder, G.K. Integrated HF CMOS-MEMS square-frame resonators with on-chip electronics and electrothermal narrow gap mechanism. In Proceedings of the 13th International Conference on Solid-State Sensors, Actuators and Microsystems, 2005 Digest of Technical Papers TRANSDUCERS ’05, Seoul, Korea, 5–9 June 2005; pp. 2074–2077. 8. Huang, W.L.; Ren, Z.; Lin, Y.W.; Chen, H.Y.; Lahann, J.; Nguyen, C.T.C. Fully monolithic CMOS nickel micromechanical resonator oscillator. In Proceedings of the 2008 IEEE 21st International Conference on Micro Electro Mechanical Systems (MEMS), Wuhan, China, 13–17 January 2008; pp. 10–13. 9. Brand, O. Microsensor integration into Systems-on-Chip. Proc. IEEE 2006, 94, 1160–1176. [CrossRef] 10. Uranga, A.; Verd, J.; Barniol, N. CMOS–MEMS resonators: From devices to applications. Microelectron. Eng. 2015, 132, 58–73. [CrossRef] 11. Chen, W.C.; Fang, W.; Li, S.S. A generalized CMOS-MEMS platform for micromechanical resonators monolithically integrated with circuits. J. Micromech. Microeng. 2011, 21, 065012. [CrossRef] 12. Fedder, G.K.; Howe, R.T.; Liu, T.J.K.; Quévy, E.P. Technologies for cofabricating MEMS and electronics. Proc. IEEE 2008, 96, 306–322. [CrossRef] 13. Xie, H.; Erdmann, L.; Zhu, X.; Gabriel, K.J.; Fedder, G.K. Post-CMOS processing for high-aspect-ratio integrated silicon microstructures. J. Microelectromech. Syst. 2002, 11, 93–101. 14. Seth, S.; Wang, S.; Kenny, T.; Murmann, B. A -131-dBc/Hz, 20-MHz MEMS oscillator with a 6.9-mW, 69-kΩ, gain-tunable CMOS TIA. In Proceedings of the ESSCIRC (ESSCIRC) 2012, Bordeaux, France, 17–21 September 2012; pp. 249–252. 15. Verd, J.; Uranga, A.; Abadal, G.; Teva, J.; Pérez-Murano, F.; Barniol, N. High-sensitivity capacitive sensing interfacing circuit for monolithic CMOS M/NEMS resonators.√ Electron. Lett. 2007, 34, 1274. [CrossRef] 16. Razavi, B. A 622 Mb/s 4.5 pA/ Hz CMOS transimpedance ampliﬁer [for optical receiver front-end]. In Proceedings of the 2000 IEEE International Solid-State Circuits Conference, San Francisco, CA, USA, 9 February 2000; pp. 162–163. 17. Salvia, J.; Lajevardi, P.; Hekmat, M.; Murmann, B. A 56 MΩ CMOS TIA for MEMS applications. In Proceedings of the 2009 IEEE Custom Integrated Circuits Conference, Rome, Italy, 13–16 September 2009; pp. 199–202. 18. Lee, S.; Demirci, M.U.; Nguyen, C.T.C. A 10-MHz Micromechanical Resonator Pierce Reference Oscillator for Communications. In Proceedings of the 11th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS & EUROSENSORS XV) 2001, Berlin, Germany, 10–14 June 2001; pp. 1066–1069. Micromachines 2021, 12, 82 16 of 16

19. Sobreviela, G.; Uranga, A.; Barniol, N. Tunable transimpedance sustaining-amplifier for high impedance CMOS-MEMS resonators. In Proceedings of the 10th Conference on PhD Research in Microelectronics and Electronics (PRIME) 2014, Grenoble, France, 30 June–3 July 2014; pp. 1–4. 20. Verd, J.; Uranga, A.; Segura, J.; Barniol, N. A 3V CMOS-MEMS oscillator in 0.35 µm CMOS technology. In Proceedings of the 17th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS & EUROSENSORS XXVII) 2013, Barcelona, Spain, 16–20 June 2013; pp. 806–809. 21. Riverola, M.; Sobreviela, G.; Torres, F.; Uranga, A.; Barniol, N. Single-resonator dual-frequency BEOL-embedded CMOS-MEMS oscillator with low-power and ultra-compact TIA core. IEEE Electron Device Lett. 2017, 38, 273–276. [CrossRef] 22. Roessig, T.A.; Howe, R.T.; Pisano, A.P.; Smith, J.H. Surface-micromachined 1 MHz oscillator with low-noise Pierce configuration. In Proceedings of the 1998 Solid State Sensor and Actuator Workshop, Hilton Head, SC, USA, 1 June 1998. 23. Naing, T.L.; Rocheleau, T.O.; Alon, E.; Nguyen, C.T.C. Low-power MEMS-based Pierce oscillator using a 61-MHz capacitive-gap disk resonator. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 2020, 67, 1377–1391. [CrossRef][PubMed] 24. Li, M.H.; Li, C.S.; Hou, L.J.; Liu, Y.C.; Li, S.S. A 1.57 mW 99 dB CMOS transimpedance amplifier for VHF micromechanical reference oscillators. In Proceedings of the IEEE International Symposium on Circuits and Systems (ISCAS) 2012, Seoul, Korea, 20–23 May 2012; pp. 209–212. 25. Chen, T.T.; Huang, J.C.; Peng, Y.C.; Chu, C.H.; Lin, C.H.; Cheng, C.W.; Li, C.-S.; Li, S.-S. A 17.6-MHz 2.5V ultra-low polarization voltage MEMS oscillator using an innovative high gain-bandwidth fully differential trans-impedance voltage amplifier. In Proceedings of the IEEE 26th International Conference on Micro Electro Mechanical Systems (MEMS) 2013, Taipei, Taiwan, 20–24 January 2013; pp. 741–744. 26. Li, M.H.; Chen, C.Y.; Liu, C.Y.; Li, S.S. A sub-150-µW BEOL-embedded CMOS-MEMS oscillator with a 138-dB ultra-low-noise TIA. IEEE Electron Device Lett. 2016, 37, 648–651. [CrossRef] 27. Bouchami, A.; Elsayed, M.Y.; Nabki, F. A Sub-mW 18-MHz MEMS Oscillator Based on a 98-dBΩ Adjustable Bandwidth Transimpedance Amplifier and a Lamé-Mode Resonator. Sensors 2019, 19, 2680. [CrossRef][PubMed] 28. Senturia, S.D. Microsystem Design; Springer: New York, NY, USA, 2001. 29. Verd, J.; Uranga, A.; Teva, J.; López, J.; Torres, F.; Esteve, J.; Abadal, G.; Pérez-Murano, F.; Barniol, N. Integrated CMOS MEMS with on-chip readout electronics for high-frequency applications. IEEE Electron Device Lett. 2006, 27, 495–597. [CrossRef] 30. Fang, W.; Li, S.S.; Cheng, C.L.; Chang, C.I.; Chen, W.C.; Liu, Y.C.; Tsai, M.-H.; Sun, C. CMOS MEMS: A key technology towards the “More than Moore” era. In Proceedings of the 2013 Transducers & Eurosensors XXVII: The 17th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS & EUROSENSORS XXVII), Barcelona, Spain, 16–20 June 2013; pp. 2513–2518. 31. Perelló-Roig, R.; Verd, J.; Barceló, J.; Bota, S.; Segura, J. A 0.35-µm CMOS-MEMS oscillator for high-resolution distributed mass detection. Micromachines 2018, 9, 484. [CrossRef][PubMed] 32. Vidal-Álvarez, G.; Marigó, E.; Torres, F.; Barniol, N. Fabrication and measurement of a suspended nanochannel microbridge resonator monolithically integrated with CMOS readout circuitry. Micromachines 2016, 7, 40. [CrossRef][PubMed] 33. Liu, Y.C.; Tsai, M.H.; Chen, W.C.; Li, M.H.; Li, S.S.; Fang, W. Temperature-compensated CMOS-MEMS oxide resonators. J. Microelectromech. Syst. 2013, 22, 1054–1065. [CrossRef] 34. Riverola, M.; Vidal-Álvarez, G.; Torres, F.; Barniol, N. CMOS-NEM relay based on tungsten VIA layer. In Proceedings of the IEEE Sensors 2014, Valencia, Spain, 2–5 November 2014; pp. 162–165. 35. Michalik, P.; Fernández, D.; Wietstruck, M.; Kaynak, M.; Madrenas, J. Experiments on MEMS integration in 0.25 µm CMOS process. Sensors 2018, 18, 2111. [CrossRef][PubMed] 36. Perelló-Roig, R.; Verd, J.; Bota, S.; Segura, J. Frequency Fluctuations in CMOS-MEMS Oscillators: Towards the Thermomechanical Limit. In Proceedings of the 2018 IEEE International Symposium on Circuits and Systems (ISCAS), Florence, Italy, 27–30 May 2018; pp. 1–5. 37. Melero, A.; Verd, J.; Uranga, A.; Segura, J.; Barniol, N. A 24-MHz differential oscillator circuit for 5-MΩ CMOS-MEMS resonator. In Proceedings of the XXI Conference on Design of Circuits and Integrated Systems (DCIS) 2011, Albufeira, Portugal, 16–18 November 2011.