Micromachined Resonators: a Review

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Review Micromachined Resonators: A Review

Reza Abdolvand 1, Behraad Bahreyni 2,*, Joshua E. -Y. Lee 3 and Frederic Nabki 4

1 Dynamic Microsystems Lab, Department of Electrical and Computer Engineering, University of Central Florida, Orlando, FL 32816, USA; [email protected] 2 School of Mechatronic Systems Engineering, Simon Fraser University, Surrey, BC V3T 0A3, Canada 3 State Key Laboratory of Millimeter Waves, City University of Hong Kong, Kowloon, Hong Kong, China; [email protected] 4 Department of Electrical Engineering, École de Technologie Supeérieure, Montreal, QC H3C 1K3, Canada; [email protected] * Correspondence: [email protected]; Tel.: +1-778-782-8694

Academic Editor: Joost Lötters Received: 2 June 2016; Accepted: 25 July 2016; Published: 8 September 2016

Abstract: This paper is a review of the remarkable progress that has been made during the past few decades in design, modeling, and fabrication of micromachined resonators. Although micro-resonators have come a long way since their early days of development, they are yet to fulfill the rightful vision of their pervasive use across a wide variety of applications. This is partially due to the complexities associated with the physics that limit their performance, the intricacies involved in the processes that are used in their manufacturing, and the trade-offs in using different transduction mechanisms for their implementation. This work is intended to offer a brief introduction to all such details with references to the most influential contributions in the field for those interested in a deeper understanding of the material.

Keywords: resonance; microresonators; micro-electro-mechanical systems

1. Introduction Microelectromechanical systems (MEMS) are a disruptive technology, much like lasers or integrated circuits. As such, MEMS have an overarching applicability and impact in several sectors such as telecommunications, consumer electronics, transportation, building automation and healthcare. The MEMS market is expected to sustain continued growth made possible by many technological revolutions fueled by, among others, the Internet of Things and wearable electronics, and it is expanding at an increasing rate, projected to almost double from $11B in 2014 to $21B in 2020 with MEMS resonator representing a growing market share [1]. The concept of MEMS resonators, mechanically resonating micro-structures that are electrically brought into resonance, along with some of their advantages and applications were introduced in their early form in the 1960s [2]. Today, amidst the widespread use of MEMS, MEMS resonators are generating significant research and commercial interest, and are poised to capture a significant portion of the MEMS market because of their numerous large volume and high impact applications. These include sensing applications, where changes in a resonant element are used to monitor a given quantity [3], timing applications, where a resonant element is used within an electronic system to generate a high quality clock signal [4], or in filtering applications, where resonant structures implement filters that can be of use in radiofrequency wireless transceivers [5]. MEMS resonators are expected to become prevalent in these applications because they are well-suited to low-cost batch fabrication, being manufactured with fabrication techniques similar to those widespread in integrated circuit manufacturing. Moreover, unlike other resonant elements such as quartz crystals, MEMS resonators have the potential for higher levels of integration with microelectronics at the

Micromachines 2016, 7, 160; doi:10.3390/mi7090160 www.mdpi.com/journal/micromachines Micromachines 2016, 7, 160 2 of 56 die or package level [6]. These advantages can lead to reduced cost and form-factor systems that can have enhanced performance and more functionality. However, before MEMS resonators can completely replace other types of resonant elements, some challenges remain such as material limitations, temperature stability, packaging or batch integration with electronics. MEMS resonators have been the subject of several reviews that covered various aspects of the field from the devices themselves to their various applications, e.g., [7–12]. This paper is aimed at surveying a wide range of topics and prior work related to MEMS resonators in order to provide readers with a better understanding of their operation and to give an overview of their evolution over the last thirty years towards achieving their foreseen potential, among which their penetration of the aforementioned applications. Specifically, the paper first details the operating principles of MEMS resonators, covering modeling, properties, resonance modes, damping mechanisms and transduction mechanisms. It then discusses techniques and challenges behind the manufacturing of MEMS resonators, touching on materials and processes that have been used in their fabrication, including their fabrication using complementary metal oxide semiconductor (CMOS) processes. Current and emerging applications of MEMS resonators, namely their use in timing, sensing and radio-frequency systems are then described. This includes an overview of the operating principles, performance metrics, design considerations and latest developments in MEMS resonator-based oscillators, a key MEMS resonator-based block suitable for sensing and timing applications. Where appropriate, the paper surveys the latest research developments and directions pertaining to MEMS resonators and discusses them. In addition, it provides information on the design and the use of MEMS resonators standalone and within systems.

2. Basic Model and Properties In a vibrating mechanical system, the kinetic and potential energies are continuously converted to each other. Most systems exhibit a frequency dependent response where this transfer of energy is optimum at certain frequencies (i.e., losses are minimum), known as the resonant frequencies of the system. For low enough damping, the system response shows peaks at these particular frequencies. Additionally, each resonant frequency corresponds to a particular pattern of motion for the components of the mechanical system which is known as a mode shape. To exhibit resonance, a mechanical system must possess the capacity to store both kinetic and potential energies. Therefore, the basic resonator structure is a mass-spring system. In physical systems, additionally, there are always energy loss mechanisms. A simple mode for mechanical losses is a damper. This combination of mass-damper-spring system represents the simplest model for a resonator, as shown in Figure1. Using Newton’s laws of motion, the relationship between the displacements of the mass and input force can be found from: ∂2x ∂x M + ζ + K x = F (1) e f f ∂t2 e f f ∂t e f f in where Fin is the input force, Me f f is the effective mass of the system, Ke f f is the effective stiffness, and ζe f f represents the effective total losses in the system. The system transfer function is given by ! X(s) 1 1 ω2 H(s) = = = 0 (2) ( ) 2 + + 2 ω0 2 Fin s Me f f s ζe f f s Ke f f Ke f f s + Q s + ω0 where s is the complex frequency, ω0 is the undamped resonant frequency of the system (i.e., natural frequency) and Q is the quality factor. For a second order system, the undamped resonant frequency is: s Ke f f ω0 = 2π f0 = (3) Me f f Micromachines 2016, 7, 160 2 of 55

have enhanced performance and more functionality. However, before MEMS resonators can completely replace other types of resonant elements, some challenges remain such as material limitations, temperature stability, packaging or batch integration with electronics. MEMS resonators have been the subject of several reviews that covered various aspects of the field from the devices themselves to their various applications, e.g., [7–12]. This paper is aimed at surveying a wide range of topics and prior work related to MEMS resonators in order to provide readers with a better understanding of their operation and to give an overview of their evolution over the last thirty years towards achieving their foreseen potential, among which their penetration of the aforementioned applications. Specifically, the paper first details the operating principles of MEMS resonators, covering modeling, properties, resonance modes, damping mechanisms and transduction mechanisms. It then discusses techniques and challenges behind the manufacturing of MEMS resonators, touching on materials and processes that have been used in their fabrication, including their fabrication using complementary metal oxide semiconductor (CMOS) processes. Current and emerging applications of MEMS resonators, namely their use in timing, sensing and radio-frequency systems are then described. This includes an overview of the operating principles, performance metrics, design considerations and latest developments in MEMS resonator-based oscillators, a key MEMS resonator-based block suitable for sensing and timing applications. Where appropriate, the paper surveys the latest research developments and directions pertaining to MEMS resonators and discusses them. In addition, it provides information on the design and the use of MEMS resonators standalone and within systems.

Micromachineswhere2016 , 7 is, 160 the input force, is the effective mass of the system, is the effective stiffness, 3 of 56 and represents the effective total losses in the system. The system transfer function is given by

Keff

Micromachines 2016, 7, 160 Fin 3 of 55 Meff () 1 1 ω ( ) = = = ω (2) () ζ +ζ+ + +ω eff

where is the complex frequency, ω is the undamped resonantx frequency of the system (i.e., natural frequency) and is the quality factor. For a second order system, the undamped resonant Figure 1. A mass-spring-damper system. frequency is: Figure 1. A mass-spring-damper system.

The quality factor is defined as: ω =2π = (3) Average energy stored The quality factor is defined Qas:= 2π (4) Energy lost per cycle Average energy stored =2π (4) Parameters ω0 (or f0) and Q are the twoEnerg significanty lost per performance cycle metrics in the microresonator domain. Due to their sizes, the resonant frequencies of microdevices are typically in kHz to MHz Parameters ω (or ) and are the two significant performance metrics in the rangemicroresonator but can be in thedomain. GHz Due range to their for properly sizes, the designed resonant frequencies devices [13 of–15 microdevices]. For a device are thattypically is intended in to bekHz used to asMHz a microresonator, range but can be inQ theranges GHz fromrange thousandsfor properly to designed millions devices depending [13–15]. on For the a device operating conditionsthat is intended and device to be design used as [16 a– microresonator,18]. Many applications ranges benefitfrom thousands from maximizing to millions depending both the resonant on frequencythe operating and quality conditions factor and of device a resonator design even [16–18]. though Many there applications is some benefit trade-off from between maximizing the two. both the resonant frequency and quality factor of a resonator even though there is some trade-off Consequently, their product, f0·Q, is a common figure of merit stated for resonators [19,20]. between the two. Consequently, their product, ∙, is a common figure of merit stated for The relationship between the resonant frequency, ωr, and the undamped natural frequency, ω0, resonators [19,20]. of a second order system is [21]: The relationship between the resonant frequency,s ω, and the undamped natural frequency, ω 1 , of a second order system is [21]: ω = ω 1 − (5) r 0 2 Q2 1 ω =ω 1− (5) It can be seen that, for large quality factors, as is2 the case for most micromachined resonators, ωr ≈ ω0. By running a single frequency response measurement, one can estimate the resonant frequencyIt of can a microresonatorbe seen that, for large by locating quality thefactors, peak as in isthe the frequencycase for most response micromachined while the resonators, quality factor ω ≈ω (for Q 1) can. Bybe running estimated a single from: frequency response measurement, one can estimate the resonant frequency of a microresonator by locating the peak in the frequency response while the quality factor (for ≫1) can be estimated from: f ω d H(ω) Q = 0 = 0 ^ (6) ∆ f− ω2 d∢H(ω)dω Q= 3dB = (6) Δ 2 dω where ∆ f− dB is the −3dB bandwidth around the resonant frequency. In addition to a narrower where 3Δ is the −3 bandwidth around the resonant frequency. In addition to a narrower bandwidth, high- Q systems exhibit a higher peak amplitude at resonance that is Q times the low bandwidth, high- systems exhibit a higher peak amplitude at resonance that is times the low frequencyfrequency response response (see (see Figure Figure2). 2).

Figure 2. Time and frequency response of resonant systems. Figure 2. Time and frequency response of resonant systems.

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While the basic second-order model of the resonator is quite useful to study a device response near its resonant frequency, it is often rather simplistic. Most mechanical systems, even those composed of discrete components, have numerous different mode shapes and corresponding resonant frequencies. If the resonant frequencies are far from each other, the device response can be analyzed using the basic mass-spring-damper method around each resonant frequency. Otherwise, a higher order model needs to be constructed that can potentially include the coupling between different modes. Some continuous mechanical systems can be broken into simpler subsystems, allowing for the treatment of the system as a lumped one. This is particularly helpful when it is possible to estimate concentrated masses and the effective stiffnesses of bodies that connect them to each other within the structure. In many cases, however, the whole system needs to be treated as a distributed mass-spring system. Dynamics of such systems is studied using the acoustic wave propagation models and theories [22]. Distributed systems, in theory, have inﬁnite mode frequencies and shapes. In practice, however, a limited number of these modes need to be studied in a frequency band of interest. The basic spring-mass-damper model can once again be used if one estimates the effective mass and stiffness of the system for the particular mode shape of interest. Rayleigh’s method is a fairly robust and yet simple technique to estimate the effective mass and stiffness of a system once good estimates for the mode shape of the device are available [23,24]. If the losses can be ignored, the resonant frequency of the nth mode of the system can be found from:

−→0 −→ 2 [x] [K][x] ωn = −→0 −→ (7) . . [x] [M][x]

−→ −→ . where [K] and [M] are the stiffness and mass matrices for the system and [x] and [x] are the displacement and velocity vectors for the nth mode shape of interest, respectively.

3. Electric Circuit Representation In a typical microresonator application, the micromechanical structure is forced into vibrations by converting an input electrical signal into a force and applying it to the device. Vibrations of the structure are then picked up and often converted back to the electrical domain through various transduction techniques. Consequently, from the point of view of interrogating instruments, the device is assumed electrical. On the other hand, it is common to use the analogy between electrical and mechanical resonators to build an equivalent electrical circuit for a micromachined resonator [21,24–26]. Such a model is often built from a set of experimental measurements and then is used in electric circuit simulators. This approach is particularly useful if the resonator needs to be modelled with the drive or sense electronics, allowing for co-simulation of the entire system within the electrical domain. To represent a mechanical device with electrical elements, proper mapping of mechanical to electrical quantities is needed. A common set of mapping rules is summarized in Table1[24–26].

Table 1. Correspondence between electrical and mechanical domains.

Mechanical Domain Electrical Domain Force, F Voltage, V . Velocity, x Current, I Displacement, x Charge, q Compliance, 1/K Capacitance, C Mass, M Inductance, L Damping, ζ Resistance, R

In most cases, a resonant device is modelled as a series Resistance-Inductance-Capacity (RLC) circuit. The transductions from the electrical to mechanical domain and vice versa are modelled with Micromachines 2016, 7, 160 5 of 56 transformers with proper winding ratios or controlled voltage or current sources. Other elements, especiallyMicromachines parasitic 2016, 7 and, 160 feedthrough capacitors, may be added to the equivalent circuit so5 of that 55 the model produces results similar to experimental measurements. Figure3 illustrates an equivalent especially parasitic and feedthrough capacitors, may be added to the equivalent circuit so that the electrical model for a microresonator with electrostatic input and output ports. The transformer at the model produces results similar to experimental measurements. Figure 3 illustrates an equivalent inputelectrical port converts model for an a input microresonator voltage to with a force electros andtatic applies input it and to theoutput mechanical ports. The system transformer represented at by thethe series inputRLC portcircuit. converts At an the input output, voltage another to a transformerforce and applies converts it to velocities the mechanical of the mechanicalsystem structurerepresented back toby anthe electricalseries RLC current. circuit. At Similar the output, models another can transformer be developed converts for velocities other transduction of the mechanismsmechanical such structure as piezoelectric back to an orelectrical thermal current. devices Similar considering models can the be mechanisms developed for involved other in convertingtransduction the electrical mechanisms signal such toa as mechanical piezoelectric one or and thermal vice versa.devices In considering all cases, the the electromechanical mechanisms involved in converting the electrical signal to a mechanical one and vice versa. In all cases, the coupling coefficients, ηin and ηout, need to be defined according to the employed transduction mechanism.electromechanical It is common coupling practice coefficients, to simplify η and η the, modelneed to furtherbe defined by according removing to the the employed transformers transduction mechanism. It is common practice to simplify the model further by removing the and scaling the equivalent circuit values accordingly. Note the inclusion of the feedthrough capacitance transformers and scaling the equivalent circuit values accordingly. Note the inclusion of the in the model. This parasitic capacitance in many cases poses a challenge in a proper measurement of feedthrough capacitance in the model. This parasitic capacitance in many cases poses a challenge in resonatora proper response measurement as the feedthroughof resonator response current as that the travels feedthrough through current it can that be travels significantly through larger it can than the currentbe significantly produced larger by thethan resonator. the current produced by the resonator.

If ζ η L=Meff C=1/Keff R= eff η :1 I Vin 1: in out out . x Fin Cpi Cpo

FigureFigure 3. Equivalent 3. Equivalent electrical electrical representation representation of an electrostatic resonator resonator including including the feedthrough the feedthrough capacitor and parasitic capacitors and . capacitor Cf and parasitic capacitors Cpi and Cpo. Modelling of Nonlinearities Modelling of Nonlinearities There can be several sources of nonlinearities in micromechanical resonators [27–33]. Elastic Thereproperties can beof most several materials sources are of nonlinearitiesa function of stre insses micromechanical applied to them. resonators Even brittle [27– materials33]. Elastic such properties as of mostsilicon materials exhibit some are a stress-dependent function of stresses behavior applied under tolarge them. stresses Even [34]. brittle On the materials other hand, such internal as silicon exhibitstresses some produced stress-dependent from large behavior displacements under can large alter stresses the stiffness [34]. of On the the structure, other hand, as is internalthe case for stresses producedthe stiffening from large of beams displacements under large loads. can alter Both theof these stiffness phenomena of the affect structure, the dynamic as is theresponse case forof the the device. In many cases, for instance where electrostatic or thermal actuators are used, the stiffening of beams under large loads. Both of these phenomena affect the dynamic response of the actuation mechanism itself is inherently nonlinear. Even when the actuation mechanism is linearized device. In many cases, for instance where electrostatic or thermal actuators are used, the actuation for small displacements, for example by adding a large DC signal to the AC actuation signal in mechanismelectrostatic itself resonators, is inherently there nonlinear. can be other Even sources when of the nonlinearities. actuation mechanism For example, is the linearized electrostatic for small displacements,force produced for by example a voltage by applied adding between a large two DC parallel signal electrodes to the AC can actuation be found signalfrom: in electrostatic resonators, there can be other sources of nonlinearities.1 For example, the electrostatic force produced = (8) by a voltage applied between two parallel electrodes 2 can be found from: where is the gradient of the capacitance between1 the two electrodes and is the voltage F = ∇CV2 (8) applied between them. While the nonlinear dependence 2 e on input voltage is apparent, in many cases the gradient term is a function of the separation between the electrodes, and hence can vary wherenonlinearly∇C is the as gradient the two electrodes of the capacitance move with between respect to the each two other electrodes [29]. and V is the voltage applied betweenA them. well-known While consequence the nonlinear of nonlinearities dependence is on a jump input phenomenon voltage is apparent,in the frequency in many response cases the gradientof the term device is a as function the resonant of the separationfrequency of between the device the will electrodes, depend andon the hence signal can amplitude. vary nonlinearly This as the twophenomenon electrodes is moveknown with as bifurcation. respect to If each the otherdevice [ 29response]. is studied through frequency sweeps, one will observe different device responses for upward or downward sweeps. For nonlinearities that A well-known consequence of nonlinearities is a jump phenomenon in the frequency response increase the stiffness of the structure, the resonant frequency shifts up while those which soften the of the device as the resonant frequency of the device will depend on the signal amplitude. structure (e.g., electrostatic nonlinearities), the resonant frequency moves towards lower frequencies This phenomenon[35]. Nonlinearities is known in resonators as bifurcation. has been If thestud deviceied extensively response for is studiedmacro- and through micro-scale frequency device sweeps, one will[21,29,36,37]. observe The different resonator device nonlin responsesearities are formodelled upward by adding or downward higher order sweeps. terms to For the nonlinearities effective that increase the stiffness of the structure, the resonant frequency shifts up while those which Micromachines 2016, 7, 160 6 of 56 soften the structure (e.g., electrostatic nonlinearities), the resonant frequency moves towards lower frequenciesMicromachines [35 2016]. Nonlinearities, 7, 160 in resonators has been studied extensively for macro- and micro-scale6 of 55 device [21,29,36,37]. The resonator nonlinearities are modelled by adding higher order terms to the effectivespring springconstant constant of the of structure the structure and andsolving solving the theresulting resulting nonlinear nonlinear equation equation of ofmotions. motions. PerturbationPerturbation analysis analysis is often is often employed employed to analyze to an thealyze behavior the behavior of the systems of the with systems small nonlinearities.with small It hasnonlinearities. been shown It has that been the shown total that nonlinear the total behavior nonlinear of behavior the system of the cansystem be can modiﬁed be modified by taking by advantagetaking advantage of the different, of the anddifferent, sometimes and someti opposite,mes interactionsopposite, interactions between different between mechanisms different of nonlinearitymechanisms of [38 nonlinearity,39]. [38,39].

4.4. Resonance Resonance Modes Modes

4.1.4.1. Flexural Flexural Modes Modes FlexuralFlexural mode mode vibrations vibrations are are characterized characterized by bending of of the the structure structure along along its its length length (l) (suchl) such thatthat the the motion motion in the in transversethe transverse direction direction perpendicular perpendicular to the to length. the length. Flexural Flexural modes modes can be excitedcan be in bothexcited beam in and both plate beam structures. and plate In structures. the case of In beams, the case the of motion beams, couldthe motion be within could the be plane within of the fabrication plane (i.e.,of alongfabrication its width (i.e., alongw) or its out width of plane ) or (i.e., out along of plane its (i.e., thickness along tits). Forthickness beam structures,). For beam the structures, vibration modethe shapevibration is determined mode shape by is the determined boundary conditionsby the boundary applied conditions to the structure. applied Various to the examplesstructure. of flexuralVarious mode examples shapes of areflexural illustrated mode inshapes Figure are4 alongillustrated with in the Figure corresponding 4 along with boundary the corresponding conditions boundary conditions applied to the beam. The resonant frequency of a given mode for a beam applied to the beam. The resonant frequency of a given mode for a beam resonator of length L and resonator of length L and thickness t vibrating out of plane can be generalized according to the thickness t vibrating out of plane can be generalized according to the following formula: following formula: s t E f = β=β (9) (9) L2 ρ wherewhereβ is β ais dimensionless a dimensionless coefficient coefficient that that is is determined determined by by the the shape shape of of the the vibration vibration mode,mode, whichwhich in turnin isturn depends is depends on the on respective the respective boundary boundary conditions conditions applied applied to the structure.to the structure. Equation Equation (9) assumes (9) thatassumes the beam that is the fabricated beam is fabricated with one with material one material whereby wherebyE denotes E denotes the Young’s the Young’s modulus modulus and ρ andis the density.ρ is the As density. can be seenAs can from be Equationseen from (9), Equation the resonant (9), the frequency resonant isfrequency independent is independent of the beam of widththe whenbeam it iswidth vibrating when in it theis vibrating thickness in direction. the thickness Figure direction.4 summarizes Figure the4 summarizes most common the most flexural common modes basedflexural on beam modes structures, based on classified beam structures, according classified to the boundary according conditions to the boundary applied. conditions The corresponding applied. valuesThe corresponding of β have been values referenced of β have from been [40]. referenced from [40]. As depicted in Figure 4a, a cantilever such as the ones reported in [41–45] is defined by a beam As depicted in Figure4a, a cantilever such as the ones reported in [ 41–45] is defined by a beam that that is clamped at one end and free on the other such that the maximum deflection takes place at the is clamped at one end and free on the other such that the maximum deflection takes place at the tip of tip of the beam furthest away from the clamped end. As illustrated in Figure 4b the the beam furthest away from the clamped end. As illustrated in Figure4b the clamped-clamped clamped-clamped or doubly-clamped beam such as the ones reported in [46–49] is defined by both or doubly-clamped beam such as the ones reported in [46–49] is defined by both ends of the ends of the structure clamped such that the maximum deflection takes place at mid-length. Both structure clamped such that the maximum deflection takes place at mid-length. Both cantilever cantilever and clamped-clamped beams are commonly adopted structures for mass sensing andapplications clamped-clamped due to their beams structural are commonly simplicity adopted and potential structures for realizing for mass small sensing proof applications masses [50,51]. due to theirFinally, structural as shown simplicity in Figure and 4c potential it is also for possi realizingble to realize small proofa flexural masses mode [50 free-free,51]. Finally, beam as whereby shown in Figureboth4 cends it is are also free possible [52]. toThe realize beam ahere flexural is clam modeped free-free at two positions beam whereby along the both length ends arewhere free the [ 52 ]. Thedeflection beam here is zero is clamped [18]. at two positions along the length where the deflection is zero [18].

(a) (b)(c)

Figure 4. Common flexural mode beams classified according boundary conditions: (a) cantilever, β = Figure 4. Common flexural mode beams classified according boundary conditions: (a) cantilever, 0.16154; (b) clamped-clamped beam, β = 1.02792; (c) free-free beam, β = 1.02792. β = 0.16154; (b) clamped-clamped beam, β = 1.02792; (c) free-free beam, β = 1.02792. Figure 5 illustrates the fundamental modes observed in membrane structures, most of which areFigure square5 orillustrates circular. The the fundamentaledges of the membra modesnes observed are clamped in membrane and the maximum structures, deflection most of occurs which areat square the center or circular. of the membrane. The edges ofThe the resonant membranes frequencies are clamped of plate and structures the maximum follow the deflection form of occurs the at theEquation center (9). of theMembrane membrane. resona Thetors resonant are commonly frequencies used ofto plateimplement structures micromachined follow the ultrasonic form of the transducers (MUTs) [53,54].

Micromachines 2016, 7, 160 7 of 56

Equation (9). Membrane resonators are commonly used to implement micromachined ultrasonic transducersMicromachines 2016 (MUTs), 7, 160 [53 ,54]. 7 of 55

(a) (b)

Figure 5. Common flexural mode membrane resonators: (a) square membrane; (b) circular Figure 5. Common flexural mode membrane resonators: (a) square membrane; (b) circular membrane. membrane. 4.2. Bulk Modes 4.2. Bulk Modes In contrast to flexural mode resonators, bulk mode resonators are characterized by deformation of In contrast to flexural mode resonators, bulk mode resonators are characterized by deformation the structure through planar expansions or contractions rather than bending. In terms of geometrical of the structure through planar expansions or contractions rather than bending. In terms of dependence, the resonant frequencies of bulk modes only depend on the lateral physical dimensions of geometrical dependence, the resonant frequencies of bulk modes only depend on the lateral physical the structure (e.g., width or length). In other words, the lateral features of the structure alone determine dimensions of the structure (e.g., width or length). In other words, the lateral features of the the acoustic wavelength (λ) of the vibration mode. As such, the resonant frequencies of bulk mode structure alone determine the acoustic wavelength (λ) of the vibration mode. As such, the resonant resonators can be generalized by the following form: frequencies of bulk mode resonators can be generalized by the following form: s β E β bulk fbulk == (10)(10) λλ ρρ wherewhereE Ebulkbulkis is the the effective effective modulus modulus of theof the plate plate structure struct definedure defined for a givenfor a given axis of axis motion. of motion. Bulk modes Bulk resonatorsmodes resonators have been have reported been reported for beams for [55beams–57], [ rectangular55–57], rectangular plates [ 58plates,59], square[58,59], platessquare [ 60plates,61], and[60,61], circular and circular disks [ 62disks,63]. [62, In63]. the In case the ofcase bars/beams, of bars/beams,Ebulk Ebulksimplifies simplifies to to the the Young’sYoung’s modulus.modulus. InIn comparisoncomparison to to flexural flexural mode mode resonators, resonators, bulk bulk mode mode resonators resonators are much are stiffermuch for stiffer the samefor the physical same dimensionphysical dimension scales. This scales. in turn This translates in turn totranslates higher frequenciesto higher frequencies for the same for physical the same dimensions. physical Asdimensions. such, bulk As mode such, resonatorsbulk mode are resonators favored are over favored flexural over mode flexural resonators mode forresonators higher frequencyfor higher applicationsfrequency applications owing to their owing more to efficient their more frequency-to-size efficient frequency-to-size scaling characteristic. scaling The characteristic. mode shapes The of variousmode shapes examples of various of bulk examples mode resonators of bulk reportedmode reso innators the literature reported are in illustrated the literature in Figure are illustrated6. In the casein Figure of bulk 6. modes,In the case the standingof bulk modes, waves inthe the standi solidng structures waves in are the longitudinal solid structures waves. are It longitudinal can also be seenwaves. that It everycan also part be of seen the that structure every undergoes part of the either structure compression undergoes or either expansion compression apart from or theexpansion center. Theapart center from of the the center. structure The iscenter the most of the obvious structure choice is the to clampmost obvious the structure choice wherever to clamp possible the structure from thewherever viewpoint possible of the from fabrication the viewpoint from the of perspectivethe fabrication of minimizingfrom the perspective losses to theof minimizing supports. It losses should to bethe noted supports. that theIt should lateral be bulk noted modes thatdescribed the lateral in bu Figurelk modes3 can described each be excited in Figure at higher3 can each order be modesexcited ofat vibration.higher order This modes is rather of vibration. commonly This the is case rather for thecommonly length-extensional the case for (LE) the length-extensional and width-extensional (LE) (WE)and width-extensional modes. As an example, (WE) themodes. 5th order As an mode example, of the the WE 5th mode order of mode vibration of the is WE illustrated mode of in vibration Figure7, whichis illustrated can be describedin Figure as7, which having can 5 nodal be described lines. Higher as having order 5 modes nodal are lines. particularly Higher order common modes in theare caseparticularly of piezoelectric common resonators in the case [64 of]. Lateralpiezoelectric bulk modesresonators of resonance, [64]. Lateral particularly bulk modes when of appliedresonance, to piezoelectricparticularly when resonators, applied are to referred piezoelectric to as contour resonators, modes are [65 referred] wherein to as the contour acoustic modes radiation [65] patternswherein arethe viewedacoustic as radiation contours patterns in the plane are ofviewed fabrication. as contours This is in in the contrast plane toof thickness fabrication. vibration This ismodes in contrast that areto thickness typically viewedvibration by modes devices that such are as thetypically film bulk viewed acoustic by devices resonator such (FBAR) as the [66 film]. bulk acoustic resonator (FBAR) [66].

Micromachines 2016, 7, 160 8 of 56 Micromachines 2016, 7, 160 8 of 55 Micromachines 2016, 7, 160 8 of 55

(a) (b) (a) (b)

(c) (d) (c) (d) Figure 6. Bulk mode shapes based on rectangular plates, square plates, and circular disks: (a) FigureFigure 6.6. BulkBulk mode mode shapes shapes based based on on rectangular rectangular plates, plates, square square plates, plates, and and circular circular disks: disks: (a) length-extensional (LE) mode, β = 1, λ = 2L; (b) width-extensional (WE) mode, β = 1, λ = 2W; (c) (length-extensionala) length-extensional (LE) (LE) mode, mode, β =β 1,= λ 1, = λ2L;= 2L;(b) (width-extensionalb) width-extensional (WE) (WE) mode, mode, β =β 1,= λ 1, = λ2W;= 2W; (c) square-extensional (SE) mode, β = 1, λ = 2L; (d) radial breathing mode, β = 1, λ = 2R. (square-extensionalc) square-extensional (SE) (SE) mode, mode, β =β 1,= λ 1, =λ 2L;= 2L;(d) (radiald) radial breathing breathing mode, mode, β =β 1,= λ 1, = λ2R.= 2R.

Figure 7. Displacement profile of the 5th order width-extensional (WE) mode of vibration. Figure 7. Displacement profileprofile of the 5th orderorder width-extensionalwidth-extensional (WE)(WE) modemode ofof vibration.vibration. 4.3. Shear Modes 4.3.4.3. Shear Modes Shear mode resonators are similar to bulk mode resonators in that their acoustic wavelength is ShearShear modemode resonatorsresonators areare similarsimilar toto bulkbulk modemode resonatorsresonators inin thatthat theirtheir acousticacoustic wavelengthwavelength isis also determined only by the lateral features of the structure. However, in contrast to bulk modes, alsoalso determineddetermined only by thethe laterallateral featuresfeatures ofof thethe structure.structure. However, in contrast to bulk modes, shear modes are defined by shear waves instead of longitudinal waves. As such, their stiffness shearshear modesmodes areare defineddefined byby shearshear waveswaves insteadinstead ofof longitudinallongitudinal waves.waves. AsAs such,such, theirtheir stiffnessstiffness constants are defined by the shear modulus of the structural material rather than the Young’s constantsconstants areare defined defined by by the the shear shear modulus modulus of the of structural the structural material material rather thanrather the than Young’s the modulus.Young’s modulus. Therefore, the resonator frequency of lateral shear modes is given by the shear modulus G, Therefore,modulus. Therefore, the resonator the frequencyresonator offrequency lateral shear of lateral modes shear is given modes by is the given shear by modulus the shearG modulus, instead ofG, instead of the Young’s modulus: theinstead Young’s of the modulus: Young’s modulus: s ββ β G fshear== (11)(11) =λλ ρ (11) λ ρ This featurefeature of of being being defined defined by by shear shear is evident is evident when when one considersone considers the mode the shapes.mode shapes. In square In This feature of being defined by shear is evident when one considers the mode shapes. In plates,square shearplates, modes shear that modes have that been have observed been observ includeed the include Lamé [the67– 69Lamé] and [67–69] face shear and (FS)face [ 70shear] modes, (FS) square plates, shear modes that have been observed include the Lamé [67–69] and face shear (FS) which[70] modes, are depicted which are in Figure depicted8a,b in respectively. Figure 8a,b Inrespec bothtively. cases, In the both direction cases,of the motion direction is always of motion equal is [70] modes, which are depicted in Figure 8a,b respectively. In both cases, the direction of motion is andalways opposite equal betweenand opposite two orthogonal between two axes orthogonal within the axes plane within of fabrication. the plane In of other fabrication. words, while In other the always equal and opposite between two orthogonal axes within the plane of fabrication. In other structurewords, while is defined the structure by expansion is defined in one by axis,expansion it is simultaneously in one axis, it definedis simultaneously by contraction defined in theby words, while the structure is defined by expansion in one axis, it is simultaneously defined by orthogonalcontraction axis.in the In orthogonal every part axis. of the In plate, every the part in-plane of the strainplate, componentsthe in-plane arestrain equal components and opposite, are contraction in the orthogonal axis. In every part of the plate, the in-plane strain components are therebyequal and cancelling opposite, each thereby other cancel out whenling summedeach other up. out As when such, summed the volumetric up. As change such, the is theoretically volumetric equal and opposite, thereby cancelling each other out when summed up. As such, the volumetric zerochange everywhere is theoretically across zero the everywhere square plate. across This isochoricthe square property plate. This leads isochoric to the interestingproperty leads feature to the of change is theoretically zero everywhere across the square plate. This isochoric property leads to the interesting feature of lateral shear modes having theoretically no thermoelastic damping (TED). TED interesting feature of lateral shear modes having theoretically no thermoelastic damping (TED). TED

Micromachines 2016, 7, 160 9 of 56 lateral shear modes having theoretically no thermoelastic damping (TED). TED arises from irreversible Micromachines 2016, 7, 160 9 of 55 heat ﬂowMicromachines between 2016 regions, 7, 160 of expansion and contraction, and since there is no volume change9 of during55 the operation of the resonator TED is thus zero in principle. Low TED allows for resonators with arises from irreversible heat flow between regions of expansion and contraction, and since there is arises from irreversible heat flow between regions of expansion and contraction, and since there is high qualityno volume factors change in during the millions. the operation Consequently, of the resonator adding TED holes is thus in zero the in structure principle. for Low the TED purpose of no volume change during the operation of the resonator TED is thus zero in principle. Low TED fabricationallows breaks for resonators the isochoric with high property quality andfactors introduces in the millions. TED, resultingConsequently, in a adding substantial holes dropin the in quality allows for resonators with high quality factors in the millions. Consequently, adding holes in the factorstructure [71,72]. for The the shear purpose wave of fabrication appears 45breaks◦ to the the isochoric primary property axis of and deformation. introduces TED, In eitherresulting case of the structure for the purpose of fabrication breaks the isochoric property and introduces TED, resulting Laméin and a substantial FS modes, drop nodes in quality appear factor at speciﬁc [71,72]. The points shear along wave the appears edges 45° of to the the square primary plate, axis of where the in a substantial drop in quality factor [71,72]. The shear wave appears 45° to the primary axis of structuredeformation. can be conveniently In either case clampedof the Lamé to minimizeand FS modes, support nodes losses appear where at specific the displacementpoints along the is zero but deformation.edges of the squareIn either plate, case where of the the Lamé structure and FScan mo bedes, conveniently nodes appear clamp ated specificto minimize points support along the thereedges islosses some ofwhere rotation.the squarethe displacement For plate, elastically where is zero the anisotropic but structure there is materialssomecan be rotation. conveniently like For single-crystal elastically clamp anisotropiced silicon, to minimize thematerials relevant support shear moduluslosseslike issingle-crystal where given the by displacement thesilicon, axis the of relevant the is zero shear shear but wave. there modulus is some is given rotation. by the For axis elastically of the shear anisotropic wave. materials like single-crystal silicon, the relevant shear modulus is given by the axis of the shear wave.

(a) (b)

Figure 8. Lateral shear modes based on a square plate resonator: (a) Lamé mode , β = 1, λ = √2 L; √ Figure 8. Lateral shear modes(a based) on a square plate resonator: (a()b Lamé) mode , β = 1, λ = 2L; (b) FS mode, β = 1.283, λ = 2 L (b) FSFigure mode, 8.β Lateral= 1.283, shearλ = modes 2L. based on a square plate resonator: (a) Lamé mode , β = 1, λ = √2 L; (bShear) FS mode, modes β have= 1.283, also λ =been 2 L realized in circular disks as shown in Figure 9, from which we can Shearsee once modes again havethat the also motion been in realized one axis inis circularequal and disks opposite as shownto the orthogonal in Figure axis.9, from This whichis we commonlyShear modes referred have to as also the winebeen glassrealized mode in [73,74].circular Given disks the as shownsymme tryin Figureof the structure, 9, from which the same we can can see once again that the motion in one axis is equal and opposite to the orthogonal axis. This is seeelliptical once againmode shapethat the can motion occur in in two one axes axis 45° is apequalart. In and isotropic opposite solids, to the twoorthogonal modes share axis. theThis is commonlycommonlysame frequency, referred referred towhich asto theas is theknown wine wine glassas glass mode mode mode degenerac [[73,74].73,74y.]. In Given Given anisotropic the the symme symmetry solids,try the of twothe of the structure,modes structure, occur the at same the same ◦ ellipticalellipticalslightly mode differentmode shape shape frequencies can can occur occur [75]. in in two two axes axes 4545° apart.apart. In In isotropic isotropic solids, solids, the the two two modes modes share share the the samesame frequency, frequency, which which isknown is known as as mode mode degeneracy. degeneracy. In In anisotropic anisotropic solids, solids, the the two two modes modes occur occur at at slightlyslightly different different frequencies frequencies [75 [75].].

Figure 9. Wine glass mode observed in a circular disk resonator.

4.4. Torsional Modes Torsional modeFigure Figureresonators 9. Wine9. Wine are glass glass most mode mode typically observedobserved found in in ain a circular circularthe form disk disk of resonator. paddle resonator. resonators, which comprise a plate that is supported on two opposite ends by beams. The paddle resonator oscillates 4.4. Torsional Modes 4.4. Torsionalby means Modes of rotating about the axis along which the supporting beams lie as illustrated in Figure 10. The Torsionalsupporting mode beams resonators are clamped are mostat the typically ends an dfound experience in the aform twisting of paddle motion resonators, as the plate which Torsionalcompriseoscillates aabout modeplate thethatresonators axis is supported of rotation. are on The mosttwo beams opposite typically undergoing ends found by torsionbeams. in thethusThe paddle form the ofresonator spring paddle of oscillates the resonators, whichbyresonator comprise means ofand rotating a thereby plate about that define isthe supportedthe axis spring along constant which on two thwhilee opposite supporting the rotating ends beams plate by lie beams.approximates as illustrated The paddleto in a Figurerigid resonator 10. oscillatesThe supporting by means ofbeams rotating are clamped about the at axisthe alongends an whichd experience the supporting a twisting beams motion lie as as the illustrated plate in

Figureoscillates 10. The about supporting the axis beamsof rotation. are clamped The beams at theundergoing ends and torsion experience thus form a twisting the spring motion of the as the plateresonator oscillates and about thereby the axisdefine of rotation.the spring The constant beams while undergoing the rotating torsion plate thusapproximates form the to spring a rigid of the resonator and thereby deﬁne the spring constant while the rotating plate approximates to a rigid body

Micromachines 2016, 7, 160 10 of 56

Micromachines 2016, 7, 160 10 of 55 that deﬁnesbody that the defines proof the mass proof of themass resonator of the resonator [76]. Torsional [76]. Torsional mode mode paddle paddle resonators resonators have have been been applied Micromachines 2016, 7, 160 10 of 55 to sensingapplied applications to sensing applications that include that electrometers include electrometers [77] and [77] magnetometers and magnetometers [78]. [78]. body that defines the proof mass of the resonator [76]. Torsional mode paddle resonators have been applied to sensing applications that include electrometers [77] and magnetometers [78].

FigureFigure 10. 10.A A torsional torsional mode paddle paddle resonator. resonator.

4.5. Coupled Resonators 4.5. Coupled Resonators Figure 10. A torsional mode paddle resonator. The above examples of this section have included only single resonators so far. Single Theresonators4.5. Coupled above can examplesResonators in turn be of mechanically this section havecoupled included to realize only an singlearray of resonators identical resonators. so far. Single Assuming resonators can inthe turn sameThe be vibrationabove mechanically examples mode for coupled of each this resonator, tosection realize thehave an nu arraymberincluded of of modes identicalonly possiblesingle resonators. resonators in an array Assuming soincreases far. Single with the same vibrationtheresonators size mode of canthe for array.in each turn Ifresonator, be the mechanically resonators the number arecoupled coupl of toed modesrealize to each an possible other array strongly, of in identical an arraythe resonators.frequency increases separationAssuming with the size of thebetweenthe array. same Ifvibrationthe the modes resonators mode gets for widened. are each coupled resonator, This to approach the each nu othermber is ofparticularly strongly, modes possible the favorable frequency in an arrayfor separationthe increases purpose with between of the modesincreasingthe size gets of thethe widened. outputarray. Ifsignal Thisthe resonators streng approachth of are MEMS is coupl particularly resonatorsed to each favorable byother creating strongly, for arrays the the purpose of frequency the same of separation increasingresonator, the outputsynchronizedbetween signal the strength modesto vibrate of gets MEMS at widened. the resonators same This frequency byapproach creating [79]. is arraysThisparticularly is ofparticularly the favorable same resonator,useful for inthe lowering synchronizedpurpose the of to insertion loss of filters [80,81] as well as reducing the phase noise of MEMS oscillators [82,83]. Strong vibrateincreasing at the samethe output frequency signal streng [79].th This of MEMS is particularly resonators by useful creating in arrays lowering of the the same insertion resonator, loss of mechanicalsynchronized coupling to vibrate has at been the sademmeonstrated frequency using [79]. couplingThis is particularly structures usefulwith lengthsin lowering that arethe filters [80,81] as well as reducing the phase noise of MEMS oscillators [82,83]. Strong mechanical multiplesinsertion loss of the of filtersacoustic [80,81] half-wavelength as well as reducing (i.e., the, where phase n noise = 1,2,3,…) of MEMS [84,85]. oscillators An illustration [82,83]. Strong of an coupling has been demonstrated using coupling structures with lengths that are multiples of the arraymechanical of square coupling plate hasresonators beennλ dem mechanicallyonstrated usingcoupled coupling together structures for synchronized with lengths oscillation that are is acoustic half-wavelength (i.e., , where n = 1, 2, 3, ... )[84,85]. An illustration of an array of square providedmultiples inof Figurethe acoustic 11. Note half-wavelength that2 all the resonators (i.e., , inwhere the array n = 1,2,3,…) are vibrating [84,85]. in Anthe illustrationLamé mode of and an plate resonators mechanically coupled together for synchronized oscillation is provided in Figure 11. thearray phase of squarebetween plate the resonatorsresonators aremechanically the same [85] coupled. While togetherstrong coupling for synchronized pushes the modesoscillation apart, is Note that all the resonators in the array are vibrating in the Lamé mode and the phase between the weakprovided coupling in Figure results 11. Notein closely that allseparate the resonators modes, suchin the as array in defining are vibrating a narrow in the passband Lamé mode in filters and resonators[86].the phase Weak are between the mechanical same the [85 couplingresonators]. While is strong aresimilarly the couplingsame achieved [85]. pushes While by using strong the coupling modes couplingapart, structures pushes weak withthe coupling modes lengths apart, resultsthat in closelyare separate odd multiples modes, of such a quarter as in defining of the acoustic a narrow wavelength passband in(i.e., filters [86λ, ].where Weak nmechanical = 1,2,3,…) [80]. coupling weak coupling results in closely separate modes, such as in defining a narrow passband in filters is similarlyAlternatively,[86]. Weak achieved mechanical the byelectrostatic using coupling coupling spring is similarly tuning structures achieved effect with that by lengths arisesusing fromcoupling that the are nonlinearitystructures odd multiples with in alengths ofcapacitive a quarter that of − the acousticgapare oddtransducer wavelengthmultiples can of be (i.e.,a usedquarter2n to1 λ of,realize where the acoustic an weak= 1, 2, wavelengthspring 3, ... )[that80 (i.e.,].is Alternatively,a functionλ, where of thevoltage n = electrostatic 1,2,3,…) across [80]. the spring 4 tuningtransducer.Alternatively, effect that This arisesthe electrostaticelectrostatic from the spring nonlinearity tuningis used effect inas a the capacitivethat mechanical arises from gap coupling transducerthe nonlinearity element can in bebetween a used capacitive to the realize a weakresonatorsgap spring transducer that[87].is Tuningcan a function be the used voltage of to voltage realize across across athe weak tran the sducerspring transducer. changesthat is This thea function coupling electrostatic of spring, voltage spring which across is in used turn the as the mechanicaltunestransducer. the coupling separation This electrostatic element of the passband between spring [88]. theis usedWeakly resonators as coupledthe [87mechanical]. resonators Tuning coupling the are voltageparticularly element across interesting between the transducer thefor sensing applications through exploiting mode localization, which involves manipulation of energy changesresonators the coupling [87]. Tuning spring, the which voltage in across turn tunesthe tran thesducer separation changes of the the coupling passband spring, [88]. which Weakly in turn coupled between two coupled modes [89]. This approach has been found to be beneficial for enhancing resonatorstunes the are separation particularly of the interesting passband for[88]. sensing Weakly applicationscoupled resonators through are exploitingparticularly modeinteresting localization, for sensitivitysensing applications by a few ordersthrough of exploitingmagnitude mode [90] inlocalization, comparison which to conventional involves manipulation resonant sensing of energy that which involves manipulation of energy between two coupled modes [89]. This approach has been dependsbetween ontwo the coupled perturbation modes of[89]. frequency This approach while at has the beensame found time rejeto ctingbe beneficial common-mode for enhancing effects found to be beneficial for enhancing sensitivity by a few orders of magnitude [90] in comparison to [91].sensitivity by a few orders of magnitude [90] in comparison to conventional resonant sensing that conventionaldepends resonanton the perturbation sensing that of frequency depends onwhile the at perturbation the same time of reje frequencycting common-mode while at the effects same time rejecting[91]. common-mode effects [91].

Figure 11. Array of Lamé mode resonators realized through mechanical coupling.

Figure 11. Array of Lamé mode resonators realized through mechanical coupling. Figure 11. Array of Lamé mode resonators realized through mechanical coupling.

Micromachines 2016, 7, 160 11 of 56

4.6. Other Modes Based upon the WE mode, modiﬁcations to the geometry of the resonator have been made with the aim of concentrating the acoustic energy towards the center of the bulk mode resonator in order to reduce the energy distributed at the clamped ends of the resonator. Reducing the energy at the clamped ends of the resonator ultimately reduces leakage of energy to the substrate, thereby improving the quality factor of the resonator. Modiﬁcations with the aim of acoustic engineering include curving of the free edges of the resonator [92] or introducing steps [93].

5. Damping A portion of the elastic energy stored in an electromechanical resonant system could escape the system in the form of acoustic or electromagnetic waves (acoustic phonons or photons) or irreversibly transform to heat (thermal phonons) within the structure. In this chapter we brieﬂy describe the major mechanisms for such energy loss (i.e., damping) processes. Given the energy loss through all damping mechanisms is known, the overall quality factor of a resonator can be found by summing up the dissipated energies [94]: − 1 1 Qtotal = ∑ (12) Qi where Qi corresponds to damping from each potential loss mechanism.

5.1. Viscous Losses Anytime a resonator operates inside a fluidic (gaseous or liquid) medium the resonator boundaries/surfaces continuously push against the surrounding molecules and transfer a portion of the resonator kinetic energy to the surrounding. This mode of energy loss is known as viscous loss or more particularly air damping (when the resonator operates in air). Viscous losses are a dominant source of loss in micromachined resonators as the surface to volume ratios become significantly larger at micro-scales [95]. The air damping is dependent on a variety of parameters including the resonator dimensions, the distance between the moving body of the resonator and the surrounding fixed surfaces (such as the electrodes in capacitive resonators or package walls), the frequency of operation, the resonance mode (i.e., how surfaces move relative to each other), and the gas pressure surrounding the resonator. Considering such complexity, one characteristic parameter that is commonly used to analyze the air damping is the Knudsen number (Kn). In this context, Kn is defined as the ratio of the fluid molecular mean free path to the separation between the resonator and the fixed surrounding structures. The Kn > 1 range is of practical significance as the majority of vacuum packaged resonators operate under this condition. In this regime of operation, the interaction of air molecules could be ignored as the collision of the air molecules with the resonator plays a dominant role. There have been several attempts to model the air damping in this regime with reasonable success [96–98] but an accurate prediction of the loss appears to be yet out of reach. In practice, the air damping is often avoided by packaging the resonators in partial vacuum. The Q vs. pressure graphs for micro-resonators typically follow a trend similar to what is shown in Figure 12. As seen in this figure, beyond a certain vacuum level, the effect of pressure (air damping) is negligible and other sources of loss dominate the effective quality factor. This is exactly the range targeted by the manufacturers as the sharp change of Q as a result of the variation in pressure could be detrimental to the performance and should be avoided. Micromachines 2016, 7, 160 12 of 56 Micromachines 2016, 7, 160 12 of 55 Micromachines 2016, 7, 160 12 of 55

FigureFigure 12. 12. AA typical typical measured measured Quality Quality factor factor vs. vs. pressure pressure plot plot for for micro-scale micro-scale (MEMS) (MEMS) resonators. resonators. Figure 12. A typical measured Quality factor vs. pressure plot for micro-scale (MEMS) resonators. 5.2. Anchor Losses 5.2. Anchor Anchor Losses Losses Most resonators have to be suspended through mechanical connection(s) commonly known as Most resonators have to be suspended through mechanical connection(s) commonly known as anchorsMost that resonators attach the have resonator to be suspended to a supporting throug frame.h mechanical At resonance connection(s) the elastic commonly waves trapped known asin anchors that attach the resonator to a supporting frame. At resonance the elastic waves trapped in the anchorsthe resonator that attach can leak the throughresonator these to a samesupporting connect frame.ions and At resonancepropagate theto theelastic frame waves causing trapped loss inof resonator can leak through these same connections and propagate to the frame causing loss of energy. theenergy. resonator This typecan leakof loss through is often these called same anchor/support connections and loss propagate (Figure 13). to theFrom frame this causingdefinition loss it ofis This type of loss is often called anchor/support loss (Figure 13). From this definition it is perceived that energy.perceived This that type anchor of loss loss is oftenis strongly called anchor/supportdependent on theloss location(Figure 13).and Fromthe size this ofdefinition the anchor. it is anchor loss is strongly dependent on the location and the size of the anchor. Analytical prediction of perceivedAnalytical thatprediction anchor ofloss anchor is strongly loss is dependentcomplicated on and the is location accomplished and the for size a limitedof the classanchor. of anchor loss is complicated and is accomplished for a limited class of resonator (mainly beams) [99,100]. Analyticalresonator (mainly prediction beams) of anchor[99,100]. loss However, is complicated finite element and ismodels accomplished capable offor capturing a limited the class anchor of However, finite element models capable of capturing the anchor loss are developed in recent years resonatorloss are developed (mainly beams) in recent [99,100]. years However, and are finite findi elementng increasing models popularity capable of capturingamong designers the anchor to and are finding increasing popularity among designers to suppress the anchor loss during the design losssuppress are developedthe anchor lossin recent during years the design and arephase findi [101,102].ng increasing popularity among designers to suppressphase [101 the,102 anchor]. loss during the design phase [101,102].

Figure 13. 2-D model of a third harmonic lateral-extensional resonator. The strain is color-coded on Figure 13. 2-D model of a third harmonic lateral-extensional resonator. The strain is color-coded on theFigure resonator 13. 2-D and model the of substrate a third harmonic but the lateral-extensional color intensity is resonator.not a true The representation strain is color-coded of the onstrain the the resonator and the substrate but the color intensity is not a true representation of the strain intensityresonator as and it is the manipulated substrate but on the the color substrate intensity region is not to enhance a true representation visibility. of the strain intensity as intensity as it is manipulated on the substrate region to enhance visibility. it is manipulated on the substrate region to enhance visibility. A universal guideline for mitigation of anchor loss is to reduce the cross sectional dimensions of the anchor-to-resonatorA universal guideline connection for mitigation relative of anchorto the ac lossoustic is to wave-length reduce the cross and to sectional align the dimensions center of the of the anchor-to-resonatorA universal guideline connection for mitigation relative of to anchor the ac lossoustic is towave-length reduce the crossand to sectional align the dimensions center of the of anchorsthe anchor-to-resonator to the nodal points connection of the resonance relative to mode the acoustic where the wave-length particle displacement and to align on the the center resonator of the anchorsbody is minimumto the nodal [18,103]. points However, of the resonance there are mode limitations where thein implementation particle displacement of this onguideline the resonator due to bodyanchors is minimum to the nodal [18,103]. points However, of the resonance there are mode limitations where in the implementation particle displacement of this guideline on the resonator due to fabricationbody is minimum imperfections [18,103 ].such However, as misalignment there are limitations [63] and as in the implementation acoustic wavelength of this guidelinereduces beyond due to fabricationthe smallest imperfections feature sizes practicallysuch as misalignment feasible (for [63] high and frequency as the acoustic devices). wavelength reduces beyond the smallestAn alternative feature sizesapproach practically explored feasible by researchers (for high frequency is to add devices).features around the resonator that effectivelyAn alternative reflect a approachportion ofexplored the radiated by researchers elastic energy is to add back features to the aroundresonator. the resonatorSuch acoustic that effectively reflect a portion of the radiated elastic energy back to the resonator. Such acoustic

Micromachines 2016, 7, 160 13 of 56 fabrication imperfections such as misalignment [63] and as the acoustic wavelength reduces beyond the smallest feature sizes practically feasible (for high frequency devices). An alternative approach explored by researchers is to add features around the resonator that effectively reﬂect a portion of the radiated elastic energy back to the resonator. Such acoustic reﬂectors could simply be trenches etched into the substrate [104,105] or phononic crystal structures that are tuned to block a narrow band centered around the frequency trapped in the resonant cavity [106,107]. Phononic crystals can also be embedded in the design of the suspension tether [108,109].

5.3. Material Losses Both viscous and anchor losses share the same characteristic in that the resonator elastic energy leaves the resonator for both mechanisms. In contrast there are a variety of mechanisms through which the elastic energy irreversibly turns into heat within the body of the resonator; hence categorized as material losses. The most fundamental and general approach to understanding such losses is through a quantum mechanical view. In quantum mechanical terms, the quanta of vibration energy are called phonons. Based on this definition, the elastic energy stored in a resonator is carried by phonons (elastic phonons). Similarly, heat energy, which is basically the random vibrations of particles, is embodied by phonons as well (thermal phonons). With this brief introduction, it can be envisioned that elastic phonons interact with other quantum mechanical particles inside the resonators including thermal phonons and electrons through a scattering process [110]. The end result of such intercalations is transformation of elastic energy to heat within the resonant body. The loss associated with the phonon-electron interaction is understandably not significant in dielectric and lightly-doped semiconducting material which are commonly used as the bulk of the micromachined resonant body. In all resonators, depending on the relative values of the mean phonon scattering time (τs), elastic vibration period (τv), and the thermal transport time constant (τth) a certain phonon-phonon interaction process could become dominant [111]. In flexural resonance modes of beams when τv ≈ τth (i.e., the average time it takes for phonons to transport between the local hot and cold spots is equal to the vibration period), elastic phonons efficiently interact with thermal phonons through a diffusion process. This process is classically described as thermoelastic damping (TED) [112]. TED in bulk mode resonators is insignificant and is practically absent in shear mode devices. A great body of effort exists on analytical and numerical modeling of TED [112–116]. Researchers have also attempted to reduce the effect of TED by engineering τth to be as far from τv as possible [117,118]. Apart from TED, in all resonators the periodic change of atomic spatial arrangement will disturb the equilibrium phonon distribution and as long as τs < τv it results in a redistribution of phonons through phonon-phonon scattering. This process is known as Akheiser loss and sets a fundamental limit on the quality factor that could be achieved in a resonator depending on the material chosen for the resonator [110]. This loss is proportional to vibration frequency and becomes more significant at high frequencies ( f > 100 MHz for most relevant acoustic material). It should be noted that Akheiser loss is no longer effective for τs > τv (very high frequencies) and the limit of quality factor could be relaxed at such frequencies [119]. This new regime of high frequency loss was first described by Landau and Rumer and the onset of this loss process (i.e., τs = τv) could greatly vary between different materials (Figure 14). Micromachines 2016, 7, 160 14 of 56 Micromachines 2016, 7, 160 14 of 55

Figure 14. Limit of f.Q for a wide range of frequencies imposed by phonon scattering in diamond and Figure 14. Limit of f.Q for a wide range of frequencies imposed by phonon scattering in diamond and <100> Silicon. <100> Silicon. 5.4. Other Damping Sources 5.4. Other Damping Sources There are several other pathways for the elastic energy to turn into heat including (but not Therelimited are to): several ohmic otherlosses pathwaysdue to electrical for the currents elastic energypassing tothrough turn into resistive heat includingpaths, dielectric (but notlosses limited to): ohmic[120] due losses to established due to electrical electriccurrents fields across passing dielectric through films, resistive and surface paths, losses dielectric [121] lossesdue to [120] due tonon-idealities established associated electric fields with surface across dielectricroughness films,and contaminations and surface lossesand electromagnetic [121] due to non-idealitiesradiation associatedlosses due with to surface variation roughness of electric fields. and contaminations Ohmic and dielectric and losses electromagnetic are relatively radiation straight forward losses to due to predict and manage, however, the physics of surface losses are rather complicated. Regardless of variation of electric fields. Ohmic and dielectric losses are relatively straight forward to predict and such complexities it is been practically shown that the surface losses could be minimized through manage, however, the physics of surface losses are rather complicated. Regardless of such complexities vacuum annealing and avoiding large surface to volume ratios [122]. it is been practically shown that the surface losses could be minimized through vacuum annealing and avoiding6. Transduction large surface Mechanisms to volume ratios [122].

6. TransductionIn most Mechanismsapplications, micromachined resonators are interfaced with electronic circuits. Therefore, the mechanical vibration in the resonator should be excited and sensed by an electrical Insignal most (i.e., applications, change in a micromachinedvoltage or a current). resonators The choice are interfacedof mechanism with through electronic which circuits. the electrical Therefore, the mechanicalenergy is reciprocally vibration converted in the resonator to elastic energy should (i.e., be mechanical excited and vibration) sensed plays by ana critical electrical role in signal (i.e., changethe overallin a performance voltage or a of current). a product The that choice contai ofns mechanism the resonator. through Factors which associated the electrical with the energy is reciprocallytransduction converted mechanism to such elastic as energyefficiency (i.e., of th mechanicale energy conversion vibration) (i.e., plays coupling a critical coefficient), role in the implementation simplicity, and power consumption should be carefully considered and analyzed. overall performance of a product that contains the resonator. Factors associated with the transduction In this chapter the most commonly used transduction mechanisms are briefly discussed and their mechanism such as efficiency of the energy conversion (i.e., coupling coefficient), implementation main properties are highlighted. simplicity, and power consumption should be carefully considered and analyzed. In this chapter the most6.1. Capacitive commonly used transduction mechanisms are briefly discussed and their main properties are highlighted. A voltage applied between two conducting plates separated by an insulating medium generates a force that could move the plates given one is free to move. Reversely, change of capacitance as a 6.1. Capacitive result of movement induces an electrical current given a constant voltage is applied to the Aconducting voltage applied plates of between the capacitor. two conductingThis is the original plates mechanism separated exploited by an insulating in capacitive medium resonators. generates a forceCapacitive that could transducers move the platesare relatively given oneeasy is to free impl toement move. as Reversely, there is no change special of requirement capacitance on as the a result of movementchoice of inducesmaterial anexcept electrical for high current electrical given conduc a constanttivity voltageof the electrode is applied plates. to the With conducting this, it is plates no of the capacitor.surprise that This the is first the originalpublished mechanism micromachined exploited mechanical in capacitive resonators resonators. operated based Capacitive on capacitive transducers transduction [2] and it continues to be a very common choice for implementation of such resonators. are relatively easy to implement as there is no special requirement on the choice of material except for The essential components in a capacitive beam resonator are schematically shown in Figure 15 high electricalfor a two-port conductivity configuration. of the The electrode alternating plates. input With electrical this, it issignal no surprise in this diagram that the firstis applied published micromachinedthrough a fixed mechanical electrode resonators on one side operated to excite basedthe mechanical on capacitive vibration transduction and on the [2 other] and side it continues the to be a very common choice for implementation of such resonators. The essential components in a capacitive beam resonator are schematically shown in Figure 15 for a two-port configuration. The alternating input electrical signal in this diagram is applied through a fixed electrode on one side to excite the mechanical vibration and on the other side the mechanical Micromachines 2016, 7, 160 15 of 56 Micromachines 2016, 7, 160 15 of 55 movementmechanical ismovement converted is back converted to an electricalback to an current electrical in current a symmetric in a symmetric design. A design. DC voltage A DC labeledvoltage Vlabeledp (polarization Vp (polarization or bias voltage)or bias voltage) is connected is connected to the resonator to the resonator body to body establish to establish the required the required initial electricinitial electric field. field.

(a) (b)

Figure 15. The schematic representation of a two-port capacitive beam resonator (a) and the scanning Figure 15. The schematic representation of a two-port capacitive beam resonator (a) and the scanning © electronelectron micrographmicrograph ofof aa capacitivecapacitive polysiliconpolysilicon diskdisk resonatorresonator ((bb)[) [62].62]. © 20052005 IEEE.IEEE. ReprintedReprinted withwith permissionpermission fromfrom High-QHigh-Q UHFUHF micromechanicalmicromechanical radial-contourradial-contour modemode diskdisk resonators resonators by by J. J.R. R. ClarkClark inin J.J. Microelectromech.Microelectromech. Syst.Syst.,, 2005.2005.

As seen in the above schematic diagram, the resonant body usually constitutes one of the As seen in the above schematic diagram, the resonant body usually constitutes one of the electrodes in a capacitive resonator. Therefore, the material used for the resonant body is required to electrodes in a capacitive resonator. Therefore, the material used for the resonant body is required be highly conductive. In the past, doped silicon/polysilicon [13,123] and doped polycrystalline to be highly conductive. In the past, doped silicon/polysilicon [13,123] and doped polycrystalline diamond [124] have been the most common choices of material for a capacitive micro-resonator. diamond [124] have been the most common choices of material for a capacitive micro-resonator. Silicon and polysilicon are the most natural choice considering that the micro-fabrication industry is Silicon and polysilicon are the most natural choice considering that the micro-fabrication industry mainly developed around processing silicon-based material. Silicon is coincidentally an excellent is mainly developed around processing silicon-based material. Silicon is coincidentally an excellent choice of material for its excellent mechanical properties including, low loss and exceptional choice of material for its excellent mechanical properties including, low loss and exceptional mechanical/chemical stability (i.e., negligible change of properties over time). Some of the highest mechanical/chemical stability (i.e., negligible change of properties over time). Some of the highest f.Q f.Q products measured from MEMS resonators are reported for capacitive resonators as the resonant products measured from MEMS resonators are reported for capacitive resonators as the resonant body body could be fabricated from a single material which eliminates any interfacial loss existing in could be fabricated from a single material which eliminates any interfacial loss existing in multi-layer multi-layer resonators [125,126]. resonators [125,126]. It can be shown that the electromechanical coupling factor for a capacitive resonator, defined as It can be shown that the electromechanical coupling factor for a capacitive resonator, deﬁned as the ratio of the output mechanical force over the input electrical voltage, is derived from [94]: the ratio of the output mechanical force over the input electrical voltage, is derived from [94]: d η =V (13) ddC η = V (13) p dx where Vp is the polarization voltage, C is the transducer capacitance, and x is the resonator wheredisplacement.Vp is the From polarization this equation voltage, one couldC is theconclude transducer a number capacitance, of basic andpropertiesx is the of capacitive resonator displacement.transduction. First, From it thisis observed equation that one the could electr concludeomechanical a number coupling of basic at microscale properties is ofa very capacitive small transduction.number (e.g., First,η≅10 it isfor observed Vp = 10 that V, theCapacitive electromechanical Area = 10 coupling−9 m2, Capacitive at microscale Gap is= a10 very−6 m, small and ∼ −7 −9 2 −6 numberassuming (e.g., a parallelη = plate10 displacementfor Vp = 10 V,in Capacitivevacuum). This Area implies = 10 thatm capacitive, Capacitive transduction Gap = 10 is notm, andinherently assuming an a parallelefficient plate energy displacement coupling invacuum). mechanism. This impliesSecondly, that capacitiveit is observed transduction that is notthe inherentlyelectromechanical an efﬁcient coupling energy could coupling be improved mechanism. by in Secondly,creasing it the is observedpolarization that voltage the electromechanical and increasing couplingthe rate of could capacitance be improved change bywith increasing respect to the disp polarizationlacement which voltage is proportional and increasing to the the capacitive rate of capacitancearea and inversely change proportional with respect to displacementthe second po whichwer of is capacitive proportional gap. to Several the capacitive approaches area have and inverselybeen explored proportional by designers to the to second improve power the ofenergy capacitive coupling. gap. These Several range approaches from simply have beenincreasing explored the bycapacitive designers area to improve[58] or reducing the energy the coupling. gap size These to extremely range from smal simplyl values increasing [127]. theBoth capacitive of these areaapproaches [58] or reducingencounter the limitations gap size to when extremely the freque smallncy values of operation [127]. Both is ofpushed these approachesbeyond 100’s encounter of MHz limitationsas the acoustic when wavelength the frequency is excessively of operation reduced is pushed and beyond so should 100’s the of MHzresonator’s as the acousticcritical dimensions. wavelength isThe excessively alternative reduced solution and for so improving should the the resonator’s coupling criticalat higher dimensions. frequency The is by alternative coupling solution a large number of resonators to each other [79]. This approach although very effective adds to the fabrication complexity and may lower the fabrication yield.

Micromachines 2016, 7, 160 16 of 56 for improving the coupling at higher frequency is by coupling a large number of resonators to each other [79]. This approach although very effective adds to the fabrication complexity and may lower the fabrication yield. A different approach to implement capacitive transduction is to use a solid dielectric to ﬁll the gap between the electrode and the resonant body [128]. This class of resonators is relatively simple to fabricate as the deposition and removal of sacriﬁcial material within the capacitive gaps which is a major source of failure is completely eliminated. Solid dielectric gap resonators have been demonstrated with reasonably high-Q at frequencies well beyond 1 GHz [129]. However, the use of a dielectric material with large permittivity will directly contribute to a large feedthrough capacitance that masks the resonance signal and will complicate the usage of such resonators in applications such as oscillators.

6.2. Piezoelectric Piezoelectric resonators operate based on the direct conversion of electric polarization to mechanical stress (and vice versa) in a certain class of crystalline materials known as piezoelectric materials [130]. Piezoelectric resonators such as Quartz have been in use for many decades and are still the most prevalent technology in electronic applications. The main attractions of the piezoelectric transduction are the self-generating nature (there is no need for an electrical bias or power consumption) and the relatively large coupling coefficient indicative of efficient reciprocal conversion of electrical and mechanical energy. The main technical difficulty in working with piezoelectric material at micro-scale is their incorporation into mainstream microelectronics fabrication processes. Single crystalline piezoelectric material such as quartz and lithium niobate cannot be simply grown on a silicon surface in the form of thin functional film. Therefore, alternative deposition techniques for deposition of properly oriented polycrystalline piezoelectric material should have been developed before piezoelectric micromachined resonators could be considered relevant. Moreover, many piezoelectric materials contain metals with high diffusivity or toxicity (e.g., Zinc oxide (ZnO) and Lead Zirconate Titanate or (PZT)) which cannot be tolerated in microfabrication facilities. Some of the earliest instances of micromachined resonators were fabricated based on RF sputtered ZnO thin-film deposited on silicon substrate [131]. However, ZnO is a chemically-unstable material and resonators fabricated of ZnO have not been successfully commercialized. It was until the development of RF sputtered piezoelectric Aluminium nitride (AlN) [132] that the thin-film piezoelectric material slowly gained acceptance in microfabrication industry. In contrast to ZnO, AlN is a chemically stable material with excellent acoustic properties such as large stiffness and low loss. More importantly aluminum, the only metallic ingredient in AlN, is commonly used for metallization in microelectronics. Thin-film piezoelectric micro-resonators could be divided into two main categories. The first category is the devices that use the thin-film piezoelectric layer mainly as a transducer to generate/sense the acoustic waves in a second substrate material [131,133,134]. Such devices are sometimes referred to as thin-film piezoelectric-on-substrate (TPoS) resonators (Figure 16) and can significantly benefit from the proper choice of the substrate material to improve certain features of the resonator characteristic such as the quality factor and linearity [135]. In addition to common choices of substrate material such as Silicon, polycrystalline Diamond has been demonstrated to be an excellent choice for high frequency applications [136,137]. The combined high-Q and low motional resistance offered by TPoS devices enabled the demonstration of some of the best oscillator performances achieved from MEMS resonators [138,139]. The trade-off in using a substrate under the piezoelectric layer in a TPoS resonator is the compromised coupling factor. Micromachines 2016, 7, 160 17 of 56 Micromachines 2016, 7, 160 17 of 55

(a) (b)

FigureFigure 16. 16.Scanning Scanning electron electron micrograph micrograph (SEM) (SEM) of anof an AlN-on-Silicon AlN-on-Silicon ﬁfth-order fifth-order lateral-extensional lateral-extensional © modemode (a )(a and) and an an AlN AlN contour-mode contour-mode rectangular rectangular resonator resonator (b )[(b135) [135].]. © 2007 2007 IEEE. IEEE. Reprinted Reprinted with with permissionpermission from Enhancedfrom Enhanced Power Handling Power and Hand Qualityling Factor and in Thin-FilmQuality Piezoelectric-on-SubstrateFactor in Thin-Film ResonatorsPiezoelectric-on-Substrate by R. Abdolvand inResonators Proceedings by ofR. the Ab IEEEdolvand Ultrasonics in Proceedings Symposium, of 2007.the IEEE Ultrasonics Symposium, 2007.

TheThe second second class class of of micromachined micromachined piezoelectric piezoelectric resonators resonators utilizes utilizes the the piezoelectric piezoelectric film film both both asas the the transducer transducer and and the the acoustic acoustic media. media. This This category category conceptually conceptually include include the the very very mature mature thickness-modethickness-mode film film bulk bulk acoustic acoustic resonator resonator (FBAR) (FBAR) technology technology [66 [66]] as as well well as as the the more more recently recently developeddeveloped contour-mode contour-mode devices devices [65 [65,140,140]. Devices]. Devices of of this this category category offer offer low-motional low-motional resistances resistances at at veryvery high high frequencies frequencies that arethat unmatched are unmatched by any otherby any MEMS other resonator MEMS technologyresonator andtechnology are specifically and are usefulspecifically for filter useful applications for filter [141 applications,142]. However, [141,142]. the quality However, factor the of quality such resonators factor of such is inferior resonators to the is f < capacitiveinferior resonatorto the capacitive and TPoS resonator resonators and especially TPoS atresonators lower frequencies especially ( at 500lower MHz). frequencies (< 500 MHz 6.3. Thermal/Piezoresistive).

6.3.Unlike Thermal/Piezoresistive capacitive and piezoelectric transducers, there are other transduction mechanisms that could only be used to either excite the vibration or sense the vibration (i.e., one-way transduction). Unlike capacitive and piezoelectric transducers, there are other transduction mechanisms that For example, thermal actuators could only be used for excitation of vibration and piezoresistive could only be used to either excite the vibration or sense the vibration (i.e., one-way transduction). elements could only be used to sense the change in the resistance as the resonator vibrates. Despite such For example, thermal actuators could only be used for excitation of vibration and piezoresistive relative deficiency both thermal and piezoresistive transducers are very attractive for their ease of elements could only be used to sense the change in the resistance as the resonator vibrates. Despite implementation. All that is required in both cases is a conductive material through which an electrical such relative deficiency both thermal and piezoresistive transducers are very attractive for their ease current is passed to either generate heat (in the case of the thermal actuation) or to measure resistance of implementation. All that is required in both cases is a conductive material through which an (in the case of the piezoresistive sensing). electrical current is passed to either generate heat (in the case of the thermal actuation) or to measure In a thermally-actuated resonator, an alternating current is passed through the resistive heating resistance (in the case of the piezoresistive sensing). elements to generate a dynamic heating power. This varying power will result in a dynamic In a thermally-actuated resonator, an alternating current is passed through the resistive heating temperature distribution (thermal wave) in the resonant structure which is the source of the desired elements to generate a dynamic heating power. This varying power will result in a dynamic actuation force. Once the frequency of the thermal wave matches the mechanical resonance frequency temperature distribution (thermal wave) in the resonant structure which is the source of the desired of the structure the mechanical vibration is efficiently excited [94]. Thermal actuation is specially actuation force. Once the frequency of the thermal wave matches the mechanical resonance desired for applications in which a large force is required for excitation of the vibration in liquid frequency of the structure the mechanical vibration is efficiently excited [94]. Thermal actuation is medium [143]. The efficiency of the thermal transduction (force to heat ratio) is dependent on the specially desired for applications in which a large force is required for excitation of the vibration in thermal time constant associated with the structure. Generally speaking, the equivalent model of liquid medium [143]. The efficiency of the thermal transduction (force to heat ratio) is dependent on a heat generator with a heat transfer path can be simplified to an R C circuit where R is the the thermal time constant associated with the structure. Generally THspeaking,TH the equivalentTH model of thermal resistance associated with the heat transfer and C is the thermal capacitance. In other words, a heat generator with a heat transfer path can be simplifiedTH to an circuit where is the the temperature (i.e., force) generated by an input alternating power reduces for higher frequencies. thermal resistance associated with the heat transfer and C is the thermal capacitance. In other This fundamental behavior has led to the traditional belief that thermal actuators are “slow” and words, the temperature (i.e., force) generated by an input alternating power reduces for higher can only be used for low frequency applications. However, there is a growing body of evidence frequencies. This fundamental behavior has led to the traditional belief that thermal actuators are pointing to the contrary. Based on some recent and original work on this topic, the thermal actuation “slow” and can only be used for low frequency applications. However, there is a growing body of evidence pointing to the contrary. Based on some recent and original work on this topic, the thermal actuation can be used for very high frequency applications [56]. It could be proved that the thermal

Micromachines 2016, 7, 160 18 of 56 Micromachines 2016, 7, 160 18 of 55 timecan beconstant used forfor verya specific high resonant frequency structure applications scales [ 56much]. It faster could (it be has proved second that order the dependency) thermal time thanconstant the resonant for a specific frequency resonant (liner structure dependency) scales much as the faster dimensions (it has second of the order structure dependency) reduce [144]. than theIn otherresonant words, frequency the temperature (liner dependency) of a structure as the dimensionsfollows the ofinput the structurepower much reduce faster [144 ].(less In other lag) as words, the dimensionsthe temperature are scaled of a structure down. A follows fundamental the input limitati poweron muchassociated faster with (less the lag) thermal as the dimensionsactuation that are continuesscaled down. to Aimpede fundamental its spread limitation is the associated required with power the thermalconsumption actuation to thatgenerate continues considerable to impede vibrationits spread amplitude is the required especially power at consumption higher frequencie to generates where considerable the structure vibration is stiffer amplitude and the amplitude especially ofat the higher alternating frequencies temperature where the is structurelower for is the stiffer same and input the amplitudepower. of the alternating temperature is lowerIn forthermal the same resonators input power. the mechanical vibration is commonly sensed through piezoresistivity whichIn is thermal the change resonators of resistivity the mechanical in response vibration to stress. is In commonly the most general sensed form through the piezoresistivity piezoresistivity inwhich material is the is change characterized of resistivity by a 6 in × response6 matrix toof stress.piezoresistive In the most coefficients general. form Semiconductor the piezoresistivity materials in suchmaterial as doped is characterized single crystalline by a 6 × silicon6 matrix possess of piezoresistive exceptionally coefficients. large piezoresistive Semiconductor coefficients materials [145] such whichas doped enables single an crystalline efficient siliconsensin possessg vehicle. exceptionally Piezoresistive large elemen piezoresistivets could coefficients be formed [ 145either] which by depositionenables an and efficient patterning sensing of vehicle. a thin film Piezoresistive or selectively elements doping could the surface be formed of the either silicon by substrate deposition [146] and separatepatterning from of a thinthe heating film or selectivelyresistor, or doping alternatively the surface be offormed the silicon from substrate the bulk [146 of] separatesilicon [147] from (Figurethe heating 17). resistor,The latter or is alternatively an attractive be approach formed from as the the same bulk ofheating silicon element [147] (Figure could 17 be). used The latteras the is piezoresistivean attractive approach sensing element as the same simplifying heating element the devic coulde interface be used (a as two-terminal the piezoresistive interface sensing as opposed element tosimplifying four-terminal). the device interface (a two-terminal interface as opposed to four-terminal).

(a) (b)

FigureFigure 17. 17. SEMSEM of of piezoeresistively-sensed piezoeresistively-sensed thermally-actuated thermally-actuated resonator: resonator: a a rotational rotational disk disk resonator resonator withwith boron-dopedboron-doped piezoresistivepiezoresistive readout readout element element (a) and(a) aand solid a singlesolid crystallinesingle crystalline silicon disk silicon resonator disk © resonatorwith combined with combined heater/piezoeresistive heater/piezoeresistive silicon beams silicon (b)[ beams147]. © (b2010) [147]. IEEE. 2010 Reprinted IEEE. withReprinted permission with permissionfrom Rotational from modeRotational disk resonators mode disk for resonators high-Q operation for high-Q in liquidoperation by A. in Rahafrooz liquid by inA. Proceedings Rahafrooz in of Proceedingsthe 2010 IEEE of Sensors,the 2010 2010.IEEE Sensors, 2010.

Piezoeresistive sensing has been also coupled with other actuation mechanism such as Piezoeresistive sensing has been also coupled with other actuation mechanism such as capacitive capacitive to improve the effective electromechanical coupling [148] as piezoresistive coupling can to improve the effective electromechanical coupling [148] as piezoresistive coupling can be enhanced be enhanced through increasing the readout current. Piezoresistivity is also the transduction of through increasing the readout current. Piezoresistivity is also the transduction of choice for extremely choice for extremely small scales [149–151] as other transducers lose efficiency while piezoresistivity small scales [149–151] as other transducers lose efﬁciency while piezoresistivity enhances [152]. enhances [152]. Piezoresistivity is also the most compatible transduction with mainstream CMOS Piezoresistivity is also the most compatible transduction with mainstream CMOS fabrication as fabrication as minimum alteration to the process is required [153]. minimum alteration to the process is required [153].

6.4.6.4. Other Other Transduction Transduction Mechanisms Mechanisms BeyondBeyond thethe mostmost common common transduction transduction schemes schemes discussed discussed above, severalabove, otherseveral energy other conversion energy conversionprocesses could processes be utilized could for be speciﬁc utilized applications. for specific For applications. example, electromagnetic For example, Lorentz electromagnetic forces have Lorentzbeen successfully forces have utilized been successfully to excite vibration utilized in to micromachined excite vibration resonator in micromachined [154,155]. Opticalresonator sensing [154] [155].is another Optical mechanism sensing thatis another is relatively mechanism popular that amongst is relatively researchers popular for detectionamongst ofresearchers the structural for detectionvibrations of as the the structural sensing apparatus vibrations is completelyas the sensing independent apparatus of is the completely resonant structureindependent and of can the be resonantused for structure a wide variety and can of resonatorsbe used for [156 a wide]. variety of resonators [156].

Micromachines 2016, 7, 160 19 of 56 Micromachines 2016, 7, 160 19 of 55 Micromachines 2016, 7, 160 19 of 55 7.7. Fabrication 7. Fabrication 7.1. Narrow Gaps 7.1. Narrow Gaps 7.1.As Narrow was Gaps previously described, the electromechanical behavior of a resonator oscillating in the As was previously described, the electromechanical behavior of a resonator oscillating in the linear regime can be modeled using an inductor-resistor-capacitance (LRC) series resonant circuit linearAs regime was previouslycan be modeled described, using the an electromechani inductor-resistor-capacitancecal behavior of a (LRC)resonator series oscillating resonant in circuit the representation. It has also been pointed out earlier that the motional resistance scales inversely with the representation.linear regime can It has be alsomodeled been usingpointed an outinductor-res earlier thatistor-capacitance the motional resistance (LRC) series scales resonant inversely circuit with fourth order of the capacitive transducer gap for resonators that are actuated and sensed by capacitive therepresentation. fourth order It ofhas the also capacitive been pointed transducer out earlier gap that for theresonators motional that resistance are actuated scales inversely and sensed with by transduction.capacitivethe fourth transduction. order Given of thethe importanceGivencapacitive the importancetransducer of narrowing gapof na theforrrowing transductionresonators the transduction that gap are in actuated order gap to in and reduce order sensed to motional reduce by resistance,motionalcapacitive resistance, methodstransduction. formethods fabricating Given forthe importancefabricating narrow gaps ofnarrow na atrrowing the gaps scale theat of thetransduction sub-microns scale of sub-micronsgap have in beenorder reported tohave reduce been for polysilicon-basedreportedmotional for resistance, polysilicon-based and methods silicon-on-insulator-based andfor fabricatingsilicon-on-insulator-based narrow fabrication gaps at processes. fathebrication scale of processes. sub-microns have been reportedInIn thethe for casecase polysilicon-based ofof polysiliconpolysilicon beamsbeams and silicon- thatthat werewereon-insulator-based designeddesigned to vibrate fabrication out of processes. plane that require require a a vertical vertical capacitivecapacitiveIn the gap,gap, case the theof gappolysilicon gap size size is is definedbeams defined that by by thewere the thickness designedthickness of to aof vibrate silicon a silicon out oxide oxideof plane layer layer typicallythat typically require grown a grown vertical by lowby pressurelowcapacitive pressure chemical gap, chemical the vapor gap vapor size deposition is deposition defined (LPCVD) by (LPCVD)the th thatickness actsthat asofacts a sacrificialsiliconas a sacrificial oxide layer layer layer [18 typically,86 [18,86].]. The grown oxide The oxide layerby low pressure chemical vapor deposition (LPCVD) that acts as a sacrificial layer [18,86]. The oxide canlayer be can made be made as thin as as thin 130 as nm. 130The nm.thin The sacrificialthin sacrificial oxide oxide layer layer is patterned is patterned (etched (etched away away where where the layer can be made as thin as 130 nm. The thin sacrificial oxide layer is patterned (etched away where anchoringthe anchoring region region are located),are located), followed followed bydeposition by deposition of the of polysiliconthe polysilicon structural structural layer. layer. After After the the anchoring region are located), followed by deposition of the polysilicon structural layer. After polysiliconthe polysilicon layer layer is patterned is patterned to form to theform beam the structures,beam structures, the oxide the layer oxide is layer etched isaway etched by away buffered by the polysilicon layer is patterned to form the beam structures, the oxide layer is etched away by hydrofluoricbuffered hydrofluoric acid (HF) acid to leave (HF) behindto leave a thinbehind air a gap thin between air gap thebetween beam the and beam the drive and the electrode. drive buffered hydrofluoric acid (HF) to leave behind a thin air gap between the beam and the drive Theelectrode. process The flow process for fabricating flow for verticalfabricating narrow vertical gaps narrow in a polysilicon-basedgaps in a polysilicon-based process is illustratedprocess is electrode. The process flow for fabricating vertical narrow gaps in a polysilicon-based process is inillustrated Figure 18 in. Figure 18. illustrated in Figure 18.

((aa)) ((bb)()(c)c )

FigureFigureFigure 18.18. 18. FabricationFabrication Fabrication of ofof verticalverticalvertical narrownarrow gaps gaps in in a a polysilicon-based polysilicon-based process: process: (a ( )a Growth)) Growth Growth of of ofsacrificial sacrificial sacrificial oxide;oxide;oxide; ( (b(bb))) Growth GrowthGrowth and andand patterning patterningpatterning ofofof polysiliconpolysilicon structural structural layer layer after after patterning patterning of of ofsacrificial sacrificial sacrificial oxide; oxide; oxide; (c(c()c) Release )Release Release of ofofpolysilicon polysiliconpolysilicon structure structure of ofof removalremovalremoval ofof sacrificial sacrificialsacrificial oxide. oxide.oxide.

WhileWhile thethe processprocess flow described inin FigureFigure 1818 isis suitablesuitable for for realizing realizing out-of-plane out-of-plane vibrating vibrating While the process flow described in Figure 18 is suitable for realizing out-of-plane vibrating beams beamsbeams that that requirerequire verticalvertical capacitive gaps, thethe procprocessess has has to to be be modified modified to to order order to to realize realize lateral lateral that require vertical capacitive gaps, the process has to be modified to order to realize lateral capacitive capacitivecapacitive gapsgaps forfor thethe case of laterally vibratinvibratingg bulkbulk modemode resonators. resonators. The The modification modification in in the the gapsprocessprocess for therequiresrequires case of extraextra laterally stepssteps vibrating to define bulk thethe narrow modenarrow resonators. lalateralteral gap gap The as as illustrated modificationillustrated in in Figure in Figure the process19. 19. As As can requires can be be extraseenseen steps fromfrom to FigureFigure define 19,19, the afterafter narrow the lateral polysilicon gap as stru illustratedstructurecture layerlayer in Figure thatthat defines19defines. As canthe the beresonator resonator seen from has Figurehas been been 19 , afterpatterned,patterned, the polysilicon aa conformalconformal structure side wall layer high that definestemperattemperat theureure resonator oxideoxide (HTO)(HTO) has beenfilm film patterned,coats coats the the whole awhole conformal structure structure side wall(including(including high temperature side side walls)walls) byby oxide LPCVD.LPCVD. (HTO) The film thicknessthickness coats the ofof wholethethe conformal conformal structure side side (including wall wall HTO HTO side film filmwalls) defines defines by the LPCVD.the gap gap Theseparationseparation thickness ofof of thethe the laterallateral conformal electrodes. side wall This HTO isis follfoll filmowedowed defines byby LPCVDLPCVD the gap low-stress low-stress separation polysilicon polysilicon of the lateral to to form electrodes. form the the Thissideside is electrodes,electrodes, followed by whichwhich LPCVD isis subsequently low-stress polysilicon patternedpatterned to toto form definedefine the thesidethe structure electrodes,structure of of whichthe the electrodes. electrodes. is subsequently The The patternedstructurestructure to isis define finallyfinally the releasedreleased structure by ofHF the etch, electrodes. thatthat alsoalso The removesremoves structure thethe is side finallyside wall wall released HTO HTO byto to leave HF leave etch, behind behind that alsoa a removesnarrownarrow air theair gap gap side asas wall thinthin HTO asas 30 to nm leave [62,63]. behind a narrow air gap as thin as 30 nm [62,63].

(a) (b) (c) (a) (b) (c) Figure 19. Fabrication of lateral narrow gaps in a polysilicon-based process: (a) Conformal growth of FigureFigure 19.19. FabricationFabrication ofof laterallateral narrownarrow gapsgaps inin aa polysilicon-based process: ( a) Conformal growth growth of of sacrificial oxide to define lateral gaps; (b) Growth and patterning of polysilicon electrodes; (c) sacrificialsacrificial oxideoxide to to define define lateral lateral gaps; gaps; (b) Growth(b) Growth and patterningand patterning of polysilicon of polysilicon electrodes; electrodes; (c) Release (c) Release of polysilicon structure after removal of sacrificial oxide. ofRelease polysilicon of polysilicon structure structure after removal after removal of sacrificial of sacrificial oxide. oxide.

Micromachines 2016, 7, 160 20 of 56

Micromachines 2016, 7, 160 20 of 55 Compared to micromachining MEMS resonators with polysilicon, fabricating MEMS resonators Compared to micromachining MEMS resonators with polysilicon, fabricating MEMS resonators based on silicon-on-insulator (SOI) wafers offers the advantage of having thicker structural layers based on silicon-on-insulator (SOI) wafers offers the advantage of having thicker structural layers available. The challenge for realizing thick structures in polysilicon lies in keeping the film stress available. The challenge for realizing thick structures in polysilicon lies in keeping the film stress low.low. In In an an SOI SOI process, process, the the resonator resonator structure structure isis almostalmost alwaysalways defineddefined by the silicon device device layer, layer, µ whichwhich comes comes available available in in a a variety variety of of thicknesses thicknesses even even up upto to 100100 µm.m. InIn thethe case of laterally vibrating resonators,resonators, thicker thicker structures structures are are desirable desirable for for the th reducinge reducing motional motional resistance. resistance. Narrow Narrow gaps gaps are stillare neededstill needed in SOI-based in SOI-based resonators resonators in order in toorder improve to improve electromechanical electromechanical coupling. coupling. In order In toorder realize to narrowrealize lateralnarrow capacitive lateral capacitive gaps in gaps an SOI in process,an SOI process, the approach the approach of using of conformalusing conformal side wall side oxide wall tooxide define to the define gaps the needs gaps to needs be modified. to be modified. As illustrated As illustrated in Figure 20in ,Figure the key 20, difference the key ofdifference fabricating of narrowfabricating gaps narrow in single-crystal gaps in single-crystal silicon is instead silicon of is growinginstead of a polysilicongrowing a polysilicon electrode, theelectrode, deposited the polysilicondeposited ispolysilicon used as a is filling used material.as a filling The material. lateral Th gape lateral is first gap formed is first by formed etching by vertically etching vertically through thethrough single-crystal the single-crystal silicon by deepsilicon reactive by deep ion reactive etch (DRIE). ion etch Although (DRIE). DRIE Although allows DRIE for high allows aspect for high ratio trenchaspect structures, ratio trench the structures, desired narrow the desired gaps demand narrow greater gaps demand precision greater not practical precision for not DRIE. practical Hence for the initialDRIE. gap Hence defined the initial by DRIE gap is defined narrowed by byDRIE first is depositingnarrowed by a conformalfirst depositing LPCVD a conformal HTO followed LPCVD by refillingHTO followed the HTO-coated by refilling trenches the HTO-coated with polysilicon. trenches Once with again,polysilicon. the electrode Once again, gap the is defined electrode by gap the thicknessis defined of by the the conformal thickness side of the wall conformal oxide. When side thewall sacrificial oxide. When oxide the is sacrificial removed byoxide HF is etch, removed a narrow by submicronHF etch, a air narrow gap is submicron formed [123 air,157 gap,158 is formed]. [123,157,158]. SomeSome research research groups groups have have exploredexplored thethe benefitsbenefits ofof definingdefining the gap with a solid dielectric, dielectric, substitutingsubstituting the the silicon silicon dioxide dioxide film film with with a a different different filmfilm thatthat hashas aa higherhigher dielectricdielectric constant, such as as siliconsilicon nitride. nitride. The The process process flow flow is theis the same same to to what what is depictedis depicted in Figurein Figure 20, 20, except except that that the the nitride nitride is not is etchednot etched away. away. The benefit The benefit of this approachof this approach is that it allowsis that thinnerit allows gaps thinner to be realized,gaps to be while realized, additionally while increasingadditionally the increasing capacitance the by capacitance means of theby means high dielectric of the high constant dielectric of theconstant film [ 159of the,160 film]. It [159,160]. has been foundIt has that been the found best that location the best on thelocation resonator on the to resonator place the to solid place gaps the issolid at thegaps points is at the of minimum points of displacementminimum displacement [128]. [128].

(a) (b) (c)

Figure 20. Fabrication of narrow gaps in a silicon-on-insulator-based process using polysilicon Figure 20. Fabrication of narrow gaps in a silicon-on-insulator-based process using polysilicon refilling refilling of the gaps etched into the silicon device layer by Deep Reactive Ion Etching: (a) Conformal of the gaps etched into the silicon device layer by Deep Reactive Ion Etching: (a) Conformal growth of growth of sacrificial oxide to define lateral gaps; (b) Growth, etch back and patterning of polysilicon sacrificial oxide to define lateral gaps; (b) Growth, etch back and patterning of polysilicon electrodes; electrodes; (c) Release of silicon structure after removal of sacrificial oxide. (c) Release of silicon structure after removal of sacrificial oxide.

Others have also shown notable reduction in motional resistance by using a partially filled gap wherebyOthers a havepart of also the shownair gap notablebetween reduction the structural in motional side walls resistance is filled by a using high-K a partiallydielectric. filled The gaphigh-K whereby dielectric a part film of thethus air increases gap between the dielectric the structural constant side of wallsthe gap is filledelectrode by a overall high-K while dielectric. still Theleaving high-K a thin dielectric air gap film [160]. thus This increases approach the aims dielectric to deliver constant high of quality the gap factor electrode by keeping overall an while air gap still leavingwhile improving a thin air gap the [coupling160]. This efficiency approach through aims to gap deliver reduction high qualityand increasing factor by the keeping overall andielectric air gap whileconstant improving of the gap. the coupling efficiency through gap reduction and increasing the overall dielectric constant of the gap. 7.2. Piezoelectric Layers 7.2. Piezoelectric Layers As mentioned in the previous section, fabrication of narrow gaps is essential to improving transductionAs mentioned in the in case the of previous capacitive section, resonators fabrication. This brings of narrow along gaps additional is essential complexity to improving to the transductionfabrication process. in the case Piezoelectric of capacitive transduction resonators. offers This an brings alternative along to additional achieve reduced complexity motional to the fabricationresistance process.while leveraging Piezoelectric on developments transduction in offersthe growth an alternative of piezoelectric to achieve thin films reduced owing motional to the resistancematurity whileand success leveraging of thin on film developments bulk acoustic in resonators the growth (FBARs). of piezoelectric Among thinpiezoelectric films owing thin tofilms the maturitythat have and been success applied of thin to MEMS film bulk resonators, acoustic AlN resonators [65,161–163], (FBARs). ZnO Among [133], piezoelectricand PZT [164] thin are films the thatmost have common been applied ones reported to MEMS in resonators,the literature. AlN On [65 this,161 note,–163 ],AlN ZnO has [133 become], and PZThighly [164 popular] are the due most to commonits compatibility ones reported with inexisting the literature. fabrication On tec thishnology note, AlNfor manufacturing has become highly integrated popular circuits. due toThe its cross section of AlN resonators generally comprises a thin AlN film that is sandwiched by bottom

Micromachines 2016, 7, 160 21 of 56 compatibility with existing fabrication technology for manufacturing integrated circuits. The cross section of AlN resonators generally comprises a thin AlN film that is sandwiched by bottom and top metal electrodes. The bottom electrode acts as a ground, and input AC voltage is applied to the top electrodes. This results in an electric field that is dropped across the thickness of the AlN structure. These AlN resonators are designed to vibrate primarily in the lateral modes, of which the frequency is defined by the lateral features of the resonators (as mentioned in Section 6.2 previously). Hence although the cross-sectional topology of the AlN MEMS resonator is similar to an FBAR, the modes of interest are different as the FBAR. The FBAR is designed to vibrate across the thickness of the film, which thus defines the resonant frequency. The motivation behind AlN MEMS resonators is to realize integrated resonators that are characterized by low motional resistance and resonant frequencies that can be lithographically defined towards a multiple-frequency on a single chip solution. As such, given that the electric field is applied across the thickness and the intended mode of vibration lies within the fabrication plane, the vibration modes are excited and detected through the d31 piezoelectric coefficient. FBARs in contrast are transduced through the d33 coefficient. Given that the d31 coefficient is typically lower than the d33 coefficient, the coupling efficiency of laterally-vibrating resonators is thus generally lower than an FBAR for the same piezoelectric material. Apart from realizing a piezoelectric resonator with only the piezoelectric film to define the structural layer, some research groups have implemented resonators comprising a thin piezoelectric film on a thick substrate layer. In this case, the structural layer is defined mainly by the substrate material, examples of which include single-crystal silicon [59,165–168], silicon carbide [169–171], and diamond [172,173]. Pursuant to reaching higher coupling coefficients towards realizing low insertion filters based on laterally vibrating resonators, some groups have turned to materials with higher piezoelectric coupling coefficients such as Lithium Niobate (LiNbO3). The process differs from the above as device is fabricated from the wafer itself as the material cannot be deposited as a thin film. MEMS resonators fabricated from LiNbO3 have been shown to exhibit much lower insertion losses compared to AlN resonators [174–177].

7.3. CMOS MEMS While the above processes involving silicon processing and deposition of AlN films are compatible with CMOS fabrication technology, some groups have been explored fabricating MEMS resonators based on standard CMOS technology. The key advantage of this approach, referred to CMOS MEMS, is monolithic integration of the MEMS structure with the interface electronics. Most demonstrations of CMOS MEMS resonators have been reported for either 0.35 µm or 0.18 µm technologies. There are several ways in which a MEMS structure can be realized from the layers of polysilicon, interlayer dielectrics, and metals included in a standard CMOS process. One approach is to use the polysilicon layers to define the MEMS resonator and electrodes. In the case of [178–182] where there are two polysilicon levels, one polysilicon level was used for the resonator while the other polysilicon level was used for electrodes. In this case, the oxide layer between the two polysilicon levels defines the lateral gap between the side electrode and beam resonator, allowing gaps as narrow as 40 nm to be realized. As such, the oxide layer here serves as a sacrificial layer. The thickness of the resonator is defined by the polysilicon thickness, which is typically a few 100 nm and therefore much thinner than the polysilicon resonators described in Section 6.1 previously. This in turn places a limit on the transduction efficiency. The other approach found from the literature is to use the top metal layer to define both the MEMS resonator and the electrodes [183,184]. In this case, the minimum achievable gap between the electrode and the MEMS structure is determined by the technology layout rules (i.e., the minimum gap between two features defined in the same metal level allowed in the process). In this case, as the MEMS resonator is defined in the metal layer, the thickness of the MEMS resonator will be determined by the thickness of the metal layer, which can be almost 1 µm. Compared the previously mentioned Micromachines 2016, 7, 160 22 of 56 approach of using a spacer, realizing the MEMS resonator with the top metal layer allows a thicker structure but with the drawback of a wider capacitive gap. The above two approaches define the resonator using the conductive layers that are available in the CMOS technology stack, of which only one layer is used. The last approach in contrast uses several of the layers that include both metals as well as interlayer oxide layers in order to realize a structure that is much thicker [185–187]. In this approach, the metal layers are physically and electrically connected to each other vertically through vias. These interconnected metal features are used to realize conducting sidewalls in both the beam resonator and the electrodes, embedded within an oxide matrix formed by the different layers of interlayer oxide. The other function of the interconnected metal features is to serve as vertical sacrificial features that extend through the entire thickness of the MEMS structure. These sacrificial metal features are exposed to the etching solution that selectively etches away the metal, while the metal sidewall features embedded in the oxide matrix are protected from the etchant. There is also the final option to release the structures from the underside by etching the exposed top side of the silicon substrate with XeF2. Out of plane vibration mode structures can also be realized using this approach and integrated with a MOS field effect transistor (FET) to implement a resonant gate FET [187] that has the advantage of incorporating intrinsic gain.

7.4. Packaging Adequate packaging of resonators for the purpose of extending reliability is essential given that these devices are extremely sensitive to the external conditions. The package provides a barrier against exposure of the device to dust and moisture. In the particular case of capacitive resonators, the device needs to be sealed at moderate vacuum pressure levels in order to reduce viscous damping. There are two main approaches that have been used to seal the device at the wafer-level. The first involves attaching a capping wafer onto the processed wafer with the resonator, which typically is either glass or silicon [188–191]. The capping wafer is typically processed by etching recesses into the wafer to create a cavity to accommodate the MEMS device to be encapsulated. The other approach involves depositing an encapsulation material directly on the wafer processed with the MEMS device. Prior to the deposition of the encapsulation layer, a sacrificial layer is deposited over the processed MEMS device. The encapsulation layer could be a polymer [192] or combination of a metal and organic film [193–195] where the sacrificial layer is also an organic film. The benefit of using metal and organic films as the encapsulation layer is that the process can be done at low temperatures and thus compatible as a post-processing step. An alternative to implementing encapsulation as a post-processing step is to integrate packaging into the process for fabricating silicon resonators, using encapsulation materials such as polysilicon [195] or epitaxial silicon [196]. In this case, silicon oxide is used as the sacrificial layer that is deposited over the SOI wafer which has been processed with the resonator. The first encapsulation layer is then deposited and etched through to create vents. The resonator is released from the substrate and encapsulation layer through vapor HF etching, followed by sealing the wafer with a second encapsulation layer that seals off the vents.

8. Applications

8.1. Timing For over a decade, MEMS resonator-based oscillators have moved towards commercialization for timing applications [8,10,12,197,198], mainly focusing on wired communications standards such as USB and on real-time clocks. The reason why MEMS oscillators are more slowly penetrating RF systems as frequency references is due to their fairly stringent phase noise requirements. These requirements stem from the synthesized carrier spectral purity speciﬁed by the majority of wireless standards. The close-in phase noise performance requirements are particularly challenging in wireless standards, as resonator non-linear behavior and somewhat lower-Q-factor than quartz usually degrades performance at close-in offsets to be as competitive for such applications. However, in serial communications, Micromachines 2016, 7, 160 23 of 56

Micromachines 2016, 7, 160 23 of 55 where clock-data recovery circuits filter close-in phase noise due to their feedback nature, close-in phase noiseresonator-based performance oscillators is relaxed, to allowing penetrate MEMS these resonator-based applications oscillatorsregardless to of penetrate their somewhat these applications lower regardlessclose-in phase of their noise somewhat performance lower [15,199]. close-in phase noise performance [15,199]. InIn addition to to phase phase noise noise perfor performance,mance, an animportant important requirement requirement of timing of timing applications applications is the is frequency stability of the oscillator. Recently, temperature compensation algorithms or resonator the frequency stability of the oscillator. Recently, temperature compensation algorithms or resonator fabrication techniques have allowed MEMS resonators to match the performance of quartz fabrication techniques have allowed MEMS resonators to match the performance of quartz temperature temperature compensated oscillators (i.e., TCXOs) with regards to temperature stability [199]. compensated oscillators (i.e., TCXOs) with regards to temperature stability [199]. Real-time clocks, Real-time clocks, requiring oscillators operating at 32.768 kHz are of particular interest such as requiring oscillators operating at 32.768 kHz are of particular interest such as demonstrated demonstrated in [200–203], where the resonator-based oscillator is interfaced with a phased-locked in [200–203], where the resonator-based oscillator is interfaced with a phased-locked loop to synthetize loop to synthetize the desired frequency output, and improve its temperature stability through the the desired frequency output, and improve its temperature stability through the use of a temperature use of a temperature sensor and calibration data. In [203], a phase-locked loop is not used for this sensor and calibration data. In [203], a phase-locked loop is not used for this purpose in order to reduce purpose in order to reduce power consumption, but a state machine determines the fractional power consumption, but a state machine determines the fractional division ratio of the oscillator output division ratio of the oscillator output based on the output of a temperature sensor and calibration based on the output of a temperature sensor and calibration data. This method achieves an output data. This method achieves an output frequency stability of ±10 ppm over 0 to 50 °C. In [202], a frequency stability of ±10 ppm over 0 to 50 ◦C. In [202], a resonator is placed in a Pierce oscillator loop resonator is placed in a Pierce oscillator loop shown in Figure 21a [202]. Its 524 kHz output is fed to a shown in Figure 21a [202]. Its 524 kHz output is fed to a dual-mode compensation circuit that can dual-mode compensation circuit that can generate the 32 kHz required output, shown in Figure 21b generate the 32 kHz required output, shown in Figure 21b [202]. In compensated mode, a modified [202]. In compensated mode, a modified fractional-N phase-locked loop can be activated to provide fractional-Nprecise temperature phase-locked compensation loop can by be modulating activated to its provide output precisefrequency temperature based on compensationthe output of a by modulatingtemperature its sensor. output This frequency allows basedto maintain on the outputthe output of a temperaturefrequency steady sensor. regardless This allows of frequency to maintain thedrift output due to frequency temperature steady in the regardless MEMS oscillator. of frequency In low-power drift due to mode, temperature the phase-locked in the MEMS loop oscillator. can be Inbypassed low-power in order mode, to the generate phase-locked an uncompensate loop can be bypassedd output infor order applications to generate that an do uncompensated not require outputcompensation for applications and which that can dobenefit not requirefrom the compensation reduced power and consumption. which can benefitIn low-power from the mode, reduced the powercurrent consumption. consumption is In of low-power0.6 μA (1.4 V mode, supply), the and current when consumption temperature iscompensated of 0.6 µA (1.4it is Vof supply),1.0 μA and(1.4 whenV supply). temperature The system compensated achieves a it ±100 is of ppm 1.0 µ frequencyA (1.4 V supply). stability The over system −40 to achieves85 °C in alow±100 power ppm ◦ frequencymode, and stability of ±3 ppm over in− temperature40 to 85 C in compensated low power mode, mode. and Note of ±that3 ppm the temperature in temperature compensation compensated mode.in this Notesystem that requires the temperature calibrationcompensation to allow for the in most this system effective requires compensation calibration of the to allowresonator’s for the mosttemperature effective characteristic. compensation of the resonator’s temperature characteristic.

(a) (b)

Figure 21. (a) A MEMS oscillator and (b) its compensation and frequency synthesis electronics [202]. Figure 21. (a) A MEMS oscillator and (b) its compensation and frequency synthesis electronics [202]. © 2015 IEEE. Reprinted with permission from A 3 ppm 1.5 × 0.8 mm2 1.0 µA 32.768 kHz MEMS-Based © 2015 IEEE. Reprinted with permission from A 3 ppm 1.5 × 0.8 mm2 1.0 µA 32.768 kHz MEMS-Based Oscillator by Zaliasl in J. Solid-State Circuits, 2015. Oscillator by Zaliasl in J. Solid-State Circuits, 2015. Similar efforts have also been done using phase locked loops to generate MHz range output frequenciesSimilar for efforts systems have targeting also been serial done communi using phasecations locked such loops as in to[204] generate where MHz a 5 MHz range MEMS output frequenciesresonator-based for systemsoscillator targeting is used as serial the frequency communications reference such of a asfractional-N in [204] where phase-locked a 5 MHz loop MEMS to resonator-basedgenerate output frequencies oscillator isranging used asfrom the 1 frequencyMHz to 110 reference MHz with of a a ±30 fractional-N ppm stability phase-locked from −40 °C loop to to85 generate°C. Another output design frequencies improves the ranging temperatur frome compensation 1 MHz to 110 to ±0.5 MHz ppm with accuracy a ±30 from ppm −40 stability °C to ◦ ◦ from85 °C− and40 widensC to 85 theC. output Another frequency design range improves from 0.5 the MHz temperature to 220 MHz, compensation consuming 3.97mA to ±0.5 from ppm a ◦ ◦ accuracy3.3 V supply from [205].−40 C to 85 C and widens the output frequency range from 0.5 MHz to 220 MHz, consumingAlternatively, 3.97 mA some from other a 3.3 temperature V supply [205 compensati]. on techniques rely on dual resonator devices that Alternatively,have different sometemperature other temperature coefficients compensationand are placed techniquesin a thermal rely feedback on dual loop. resonator These devicesattain thatfrequency have different stabilities temperature of ±1 ppm over coefﬁcients −20 °C to and 80 are°C in placed [206], in and a thermal of ±4 ppm feedback from − loop.40 °C Theseto 70 °C attain in [207], and interestingly do not require calibration, which is a significant advantage in order to reduce

Micromachines 2016, 7, 160 24 of 56 frequency stabilities of ±1 ppm over −20 ◦C to 80 ◦C in [206], and of ±4 ppm from −40 ◦C to 70 ◦C in [207], and interestingly do not require calibration, which is a signiﬁcant advantage in order to reduce device cost. However, these techniques require heating of the resonators, and thus will consume higher amounts of current that are on the order of a few milliamps. Considering wireless standards, in [208], while no temperature compensation loop is implemented, a fractional-N phase locked loop with a MEMS resonator-based oscillator running at 11.6 MHz is presented with an RF output frequency of 1.7–2 GHz and attempts at meeting the local RF oscillator wireless standards performance metrics of GSM, such that the reported phase noise attained is −122 dBc/Hz at a 600 kHz offset, and −137 dBc/Hz at a 3 MHz offset. Close-in phase noise performance precludes the system from meeting wireless phase noise standards (e.g., error vector magnitude), because of the relative low Q-factor of the resonator used.

8.2. MEMS Resonator-based Oscillators As was previously discussed, the electrical model applicable to all resonators is a series-resonant RLC circuit with capacitive feedthrough causing parallel resonance as well. If resonators are operated as channel-select filters such as in [209], typically no interface electronics are required to achieve the filtering operation. However, if present as filters in radiofrequency (RF) systems such as receivers, they may be embedded into electronic circuits such as mixers in order to reduce the impact of their typically higher insertion losses on the overall noise figure of the systems [15,210,211]. Typically, MEMS resonators are interfaced with sustaining amplifiers that allow for their use in electronic oscillators that generate an electrical signal at the resonant frequency of the resonator such as demonstrated in [211]. When used in sensors, resonators will usually operate through some functionalized MEMS resonator that varies its frequency in response to sensed element such as in [212]. When used in timing circuits as precision clocks [200] or as RF carriers [10], MEMS resonators are used as the frequency reference element. Whether MEMS resonators are used in sensing or in timing applications, the sustaining amplifier needs to carefully be designed to consider the particularities of MEMS resonators in order to enable high quality oscillation [213–216]. MEMS resonators, while similar in function to quartz crystals, have properties that require specific interface circuitry designs. For instance, unlike quartz crystals that can have milliamp scale output motional currents, the output motional current of a MEMS resonator is typically in the nano-ampere range [217,218]. In addition, their insertion losses, in the case of electrostatically driven resonators, can represent motional resistances in the 1 kΩ–100 kΩ range [18,62,218], which is significantly higher than quartz crystals (i.e., 25 Ω–200 Ω). Accordingly, the power handling ability of MEMS resonators is on the order of a few micro-Watts, and they will exhibit significant non-linearity beyond that drive level which can deteriorate performance or, if harnessed properly by the electronics, improve it [219–224]. In addition, the Q-factor of MEMS mechanical resonators is in the 104 range, and is generally strongly inversely proportional to the resonant frequency. This is lower than the Q-factors achieved by AT-cut crystals, which are typically in the range of 104–105 over a wide range of frequencies. Furthermore, the resonant frequency temperature dependence of an uncompensated MEMS silicon resonator is much higher (−30 ppm/◦C [197]) than that of an AT-cut crystal (±25 ppm from −40 to 85 ◦C). Mechanical or electronic temperature compensation is thus a must for MEMS resonators to match quartz temperature stability, a critical parameter in all timing applications. Regardless of their disadvantages, typical resonance frequencies of MEMS resonator can vary from the kHz range to the GHz range [63,203,225], which is much higher than what is attained by quartz crystals (~100 MHz), and they can be fabricated at relatively low cost and in some cases can be integrated monolithically with the electronics [12], which are significant advantages. Ultimately, a MEMS resonator exhibits a series and a parallel resonance, and a sustaining circuit is required to compensate its motional resistance and provide the suitable phase condition to allow for electronic oscillation. However, the higher motional resistance, non-linearity and in some cases Micromachines 2016, 7, 160 25 of 56 high operating frequencies increase the design complexity of the sustaining electronics. In addition, the mechanical noise of the resonator is an important factor to consider when designing an integrated circuit and several works have attempted to model it [221,226–228]. This section focuses on the Micromachinesparticularities 2016 of, 7, MEMS160 resonator-based oscillators, and discusses the circuitry that is interfaced25 of with 55 MEMS resonators in order to implement them. on the particularities of MEMS resonator-based oscillators, and discusses the circuitry that is interfaced8.2.1. Operating with MEMS Principles resonators in order to implement them. Oscillators are commonly used in RF systems in voltage controlled oscillators (VCOs) for high 8.2.1. Operating Principles frequency signal generation of carriers, or as low-frequency reference oscillators for PLLs. They can alsoOscillators be used standalone are commonly in timing used circuits, in RF suchsystems as in in electronic voltage controlled watches. Resonatorsoscillators (VCOs) are well for suited high to frequencycreating such signal oscillators, generation because of carriers, of their or high-Q-factorsas low-frequency and reference frequency oscillators filtering propertiesfor PLLs. They [6–8]. can also beThe used topology standalone in Figure in timing 22a circuits, illustrates such the as configuration in electronic watches. of a typical Resonators MEMS resonator-basedare well suited tooscillator, creating such with oscillators, a resonator’s because typical of their amplitude high-Q-factors and and phase frequency frequency filtering responses properties shown [6–8]. in FigureThe 22 topologyb [162]. Inin aFigurepositive 22afeedback illustrates loop, the aconfiguration sustaining amplifier of a typical with MEMS a frequency resonator-based dependent oscillator,gain, A(s), with an input-referred a resonator’s noisetypical and amplitude a non-linear and characteristicphase frequency has itsresponses frequency shown response in Figure filtered 22b by [162].a MEMS In aresonator positive feedback having aloop, frequency a sustaining dependent amplifier motional with resistance a frequency and dependent thus frequency gain, response,A(s), an input-referredβ(s)[228]. At powernoise and up, thea non-linear noise present characteristic in the positive has its feedback frequency loop response gets amplified filtered and by filtereda MEMS by resonatorthe resonator having after a multiplefrequency passes dependent around motion the loopal untilresistance the sustaining and thus amplifier frequency or theresponse, mechanical β(s) [228].resonator At power limit theup, signal the noise growth present because in the of positive non-linearity. feedback This loop reduces gets the amplified loop gain and A( sfiltered)β(s) such by the that resonatorin steady-state, after multiple the gain aroundpasses thearound loop (i.e.,the loop gain)until hasthe ansustaining effective valueamplifier of unity, or the and mechanical a sustained resonatorconstant oscillationlimit the signal can be growth observed. because Important of non-linearity. aspects of theThis loop reduces gain arethe thatloop forgain this A(s) constructiveβ(s) such thatpositive in steady-state, feedback to the occur, gainand around to allow the loop for an(i.e oscillation., loop gain) be has sustained, an effective thelinear value gainof unity, around and the a sustainedloop must constant be larger oscillation than unity, can usually be observed. with some Important safety margin aspects to of allow the forloop fast gain start-up are that and for design this constructivemargins (e.g., positive 1.5 times feedback the minimal to occur, gain and required), to allow and for the an phase oscillation shift around be sustained, the loop the must linear allow gain for aroundthe noise the waveform loop must propagating be larger than around unity, the usually loop to with constructively some safety grow. margin These to allow oscillation for fast conditions, start-up andfirst design defined margins by Heinrich (e.g., Georg1.5 times Barkhausen, the minimal can gain be expressed required), as: and the phase shift around the loop must allow for the noise waveform propagating around the loop to constructively grow. These oscillation conditions, first defined by Heinrich|A(s Georg)β(s)| Barkhausen,> 1 can be expressed as: (14)

|()β()|◦>1 (14) ∠(A(s)β(s)) = n360 , n = 0, 1, 2 . . . (15) ∠()β() = 360°, = 0,1,2 … (15)

Sustaining Amplifer

A(s)

Noise Non- linearity

β (s)

fs fp

f MEM Resonator (a)(b)

FigureFigure 22. 22. ((aa) )Typical Typical MEMS MEMS resonator-based resonator-based oscillator oscillator loop; loop; and and ( (bb)) typical typical resonator resonator transmission transmission characteristiccharacteristic amplitudeamplitude and and phase phase [162 ]. [162].© 2010 IEEE.©2010 ReprintedIEEE. Reprinted with permission with frompermission Multifrequency from MultifrequencyPierce Oscillators Pierce Based Oscillators on Piezoelectric Based on Piezoelectric AlN Contour-Mode AlN Contour-Mode MEMS Technology MEMS Technology by Zuo by in ZuoJ. Microelectromech. in J. Microelectromech. Syst., 2010.Syst., 2010.

As can be seen in the phase condition above, the phase shift around the loop must either be zero or a multiple of 360°. Typically, oscillators will either operate around a 0° phase shift or a 360° phase shift. In the former, the resonator’s series-resonance, when the resonator’s impedance is lowest, is used with a sustaining amplifier having sufficient bandwidth to add negligible phase shift to the loop, while in the latter, its parallel-resonance, when the resonator’s impedance is largest, is used with an amplifier providing 180° phase-shift around the loop. In that case, the rest of the phase shift is provided by electrical passive components, usually capacitors, such that the phase shift at a

Micromachines 2016, 7, 160 26 of 56

As can be seen in the phase condition above, the phase shift around the loop must either be zero or a multiple of 360◦. Typically, oscillators will either operate around a 0◦ phase shift or a 360◦ phase shift. In the former, the resonator’s series-resonance, when the resonator’s impedance is lowest, is used with a sustaining amplifier having sufficient bandwidth to add negligible phase shift to the loop, while in the latter, its parallel-resonance, when the resonator’s impedance is largest, is used with Micromachinesan amplifier 2016 providing, 7, 160 180◦ phase-shift around the loop. In that case, the rest of the phase shift26 of 55 is provided by electrical passive components, usually capacitors, such that the phase shift at a frequency frequency between the series and parallel resonances of the resonators is of 180°, yielding the total between the series and parallel resonances of the resonators is of 180◦, yielding the total required required 360°. Typically, series resonance provides more accurate oscillation frequency as it does not 360◦. Typically, series resonance provides more accurate oscillation frequency as it does not depend depend on electrical components that may be inaccurate in order to attain additional phase shift, on electrical components that may be inaccurate in order to attain additional phase shift, however, however, designing an amplifier with negligible phase shift can be a challenge [216,229,230]. designing an amplifier with negligible phase shift can be a challenge [216,229,230]. Provided that the Provided that the amplifier has enough gain to offset the loss of the resonator at resonance, and that amplifier has enough gain to offset the loss of the resonator at resonance, and that its bandwidth is wide its bandwidth is wide enough to contribute negligible phase shift to the loop, the circuit will oscillate enough to contribute negligible phase shift to the loop, the circuit will oscillate at the series-resonant at the series-resonant frequency of the resonator [230], otherwise, an offset in frequency will occur frequency of the resonator [230], otherwise, an offset in frequency will occur and the amplifier will and the amplifier will have to provide more gain to overcome the additional losses of the resonator have to provide more gain to overcome the additional losses of the resonator at a frequency offset from at a frequency offset from the series resonance. For parallel resonant circuits, a negative gain (i.e., a the series resonance. For parallel resonant circuits, a negative gain (i.e., a 180◦ phase shift) amplifier 180° phase shift) amplifier can also be used with additional phase shift, such as in Pierce oscillators can also be used with additional phase shift, such as in Pierce oscillators [163,215]. [163,215]. 8.2.2. Phase Noise 8.2.2. Phase Noise Because of the bandpass nature of the resonator, and the noise-shaping of the electronic amplifier noiseBecause caused of by the feedbackbandpass loop,nature the of spectral the resona densitytor, ofand the the output noise-shaping is a single of tone the that electronic has its amplifierfrequency noise purity caused compromised by the feedback by a “skirt” loop, around the spec it [231tral]. Thisdensity is shown of the in output Figure is 23 aa single [232], wheretone that the hasspectrum its frequency from a 27purity MHz compromised MEMS resonator by a “skirt” oscillator arou isnd shown. it [231]. The This corresponding is shown in Figure phase noise23a [232], plot whereshown the in Figurespectrum 23b from [232], a where 27 MHz the MEMS noise powerresonato relativer oscillator to the is oscillation shown. The power corresponding is plotted against phase noiseoffset frequenciesplot shown form in Figure the oscillation 23b [232], frequency. where the In the no timeise power domain, relative phase noiseto the can oscillation also be transposed power is plottedto the time against domain offset as frequencies jitter in the phaseform the of theoscillati outputon signal.frequency. In timing In the applications, time domain, jitter phase performance noise can alsois more be oftentransposed quoted to (e.g., the intime ps) domain instead ofas phasejitter in noise the performancephase of the (e.g., output in dBc/Hz signal. atIn atiming given applications,frequency offset), jitter butperformance both metrics is more and inherentlyoften quoted related (e.g., [ 233in ps)]. instead of phase noise performance (e.g., in dBc/Hz at a given frequency offset), but both metrics and inherently related [233].

(a) (b)

Figure 23. A 27 MHz MEMS resonator oscillator (a) output spectrum and (b) phase noise plot [232]. Figure 23. A 27 MHz MEMS resonator oscillator (a) output spectrum and (b) phase noise plot [232]. © IOP Publishing. Reproduced with permission. All rights reserved. © IOP Publishing. Reproduced with permission. All rights reserved.

The Leeson phase noise model is a linear model that gives and expression for the phase noise in an oscillator.The Leeson Leeson’s phase equa noisetion model is given is a linearby [231]: model that gives and expression for the phase noise in an oscillator. Leeson’s equation is given by [231]: ℒ(∆) =10log" 1 + 2!1+ dBc/Hz# (16) kTF2 2f0∆ ∆fC Lϕ(∆ f ) = 10 log 1 + 1 + ∆dBc/Hz (16) 2P 2Q ∆ f ∆ f where k is the Boltzmann constant, T Sis the operatingL temperature, F is the effective excess noise factor, mainly caused by the sustaining amplifier, PS is the signal power at the input of the amplifier, f0 is the oscillation frequency of the oscillator, Δf is the offset frequency at which the phase noise is measured, QL is the loaded quality factor of the resonator, and fC is the corner offset frequency at which the phase noise starts to increase at a rate of 30 dB per decade. The conceptual power spectral density of the phase noise shown in Figure 24 outlines that at far away offsets from the oscillation frequency, phase noise becomes white in spectrum, but within the half-bandwidth of the resonator (i.e., f0/2QL), the phase noise increases by 20 dB per decade until it reaches a point where it increases by 30 dB per decade below fC. Leeson’s model is somewhat empirical as F and fC are often obtained by measurements, since phase noise is often significantly affected by nonlinearities and time variance of the phase noise mechanisms in oscillators.

Micromachines 2016, 7, 160 27 of 56 where k is the Boltzmann constant, T is the operating temperature, F is the effective excess noise factor, mainly caused by the sustaining amplifier, PS is the signal power at the input of the amplifier, f0 is the oscillation frequency of the oscillator, ∆f is the offset frequency at which the phase noise is measured, QL is the loaded quality factor of the resonator, and fC is the corner offset frequency at which the phase noise starts to increase at a rate of 30 dB per decade. The conceptual power spectral density of the phase noise shown in Figure 24 outlines that at far away offsets from the oscillation frequency, phase noise becomes white in spectrum, but within the half-bandwidth of the resonator (i.e., f 0/2QL), the phase noise increases by 20 dB per decade until it reaches a point where it increases by 30 dB per decade below f C. Leeson’s model is somewhat empirical as F and f C are often obtained by measurements, since phase noise is often significantly affected by nonlinearities and time variance

Micromachinesof the phase 2016 noise, 7, 160 mechanisms in oscillators. 27 of 55

1/Δf3

1/Δf2

Phase Noise (dBc/Hz) Noise Phase kTF/2PS

fC f0/2QL Offset Frequency, ΔF (Hz)

Figure 24. TypicalTypical phase noise power spectral density (single sided).

More elaborate phase noise models exists such as that in [234], where a time-variant phase noise modelMore is proposed. elaborate phaseHowever, noise while models not exists predictive such as in that nature, in [234 the], whereLeeson a time-variantmodel can still phase provide noise importantmodel is proposed. insights with However, regards while to phase not predictivenoise performance. in nature, Notably, the Leeson a higher model resonator can still providequality factorimportant and insightsoscillation with power regards will to phaseimprove noise phase performance. noise performance Notably, a higherby tightening resonator the quality oscillator’s factor outputand oscillation spectrum, power and reducing will improve excess phase noise noise stemming performance from electronics by tightening will improve the oscillator’s the phase output noise floor.spectrum, It is andalso reducingof interest excess to reduce noise the stemming loading from of the electronics quality factor will improveof the resonator the phase by noise ensuring floor. It is also of interest to reduce the loading of the quality factor of the resonator by ensuring appropriate appropriate input and output resistances of the sustaining amplifier [235]. The 1/f3 corner frequency f 3 isinput often and attributed output resistancesto 1/f noise ofpresent the sustaining in the electronics, amplifier however [235]. The it is 1/ oftencorner different frequency in phase is noise often f plots,attributed notably to 1/ becausenoise of present the time in thevarying electronics, nature of however the phase it is noise often mechanism different in [234]. phase Degradation noise plots, ofnotably phase because noise ofdue the to time noise varying folding nature can ofalso the phaseimpact noise oscillator mechanism performanc [234]. Degradatione [236]. In addition, of phase complexitiesnoise due to noisecan arise folding because can also of impactnonlinearity oscillator [221] performance or the specificities [236]. In addition,of MEMS complexities resonators can deterioratearise because phase of nonlinearity noise. For [instance,221] or the mechanical specificities noise of MEMS can impact resonators performance can deteriorate depending phase on noise. the relativeFor instance, noise mechanicalperformance noise of the can sustaining impact performance amplifier [225]. depending Moreov oner, the resonant relative non-linear noise performance behavior canof the also sustaining cause close-in amplifier offset [225 ].noise Moreover, degradat resonantion and non-linear a higher behaviorthan 30 candB alsophase cause noise close-in slope [222,226,227].offset noise degradation This degradation and a higher of phase-noise, than 30 dB notably phase noise at low slope frequency [222,226 ,offsets227]. This has degradation pushed most of phase-noise,MEMS oscillator notably designs at low to frequencyemploy automatic offsets has gain pushed control most in the MEMS sustaining oscillator amplifier designs in to order employ to reduceautomatic the gain non-linear control inbehavior the sustaining of the amplifier MEMS inresonator, order to reduceand en thesure non-linear optimal behaviorclose-in ofoffset the performanceMEMS resonator, [209,231,237,238]. and ensure optimal The influence close-in of offset automatic performance gain control [209,231 on, 237the, 238oscillator]. The influencephase noise of isautomatic shown with gain controlregards onto thetime-domain oscillator phase frequency noise stability is shown in with Figure regards 25a to[208] time-domain and to phase frequency noise performancestability in Figure in Figure 25a [25b208 ][237], and tooutlining phase noisethe significant performance degradation in Figure in 25 oscillatorb [237], outliningperformance the whensignificant no automatic degradation gain in control oscillator is used performance to limit the when oscillation no automatic amplitude. gain control Notably, is usedsome to resonator limit the modelsoscillation have amplitude. been proposed Notably, to someenhance resonator the typical models RLC have model been which proposed does to not enhance allow thefor typicalcircuit designRLC model that takes which into does account not allow resonator for circuit nonlineari designty (e.g., that takes[223,228,239]), into account and resonatorother works nonlinearity have also (leveragede.g., [223, 228the,239 non-linearity]), and other of works resonators have alsoto en leveragedhance phase the non-linearitynoise performance of resonators by designing to enhance the phaseoscillator noise to performancetake advantage by of designing the Duffing the oscillatorbehavior of to the take resonator advantage (e.g., of the[139,221]). Duffing behavior of the resonator (e.g., [139,221]).

(a) (b)

Figure 25. (a) The effect of automatic gain control due to the nonlinearity of the resonator on time domain frequency stability of a MEMS oscillator [208]. © 2009 IEEE. Reprinted with permission from A Highly Integrated 1.8 GHz Frequency Synthesizer Based on a MEMS Resonator by Nabki in J. Solid-State Circuits, 2009; and (b) the effect of automatic gain (level) control on the phase noise performance of a MEMS oscillator [237]. © 2003 IEEE. Reprinted with permission from Influence of automatic level control on micromechanical resonator oscillator phase noise. by Lee in Proceedings of the IEEE International Frequency Control Symposium, 2003.

Micromachines 2016, 7, 160 27 of 55

1/Δf3

1/Δf2

Phase Noise (dBc/Hz) Noise Phase kTF/2PS

fC f0/2QL Offset Frequency, ΔF (Hz) Figure 24. Typical phase noise power spectral density (single sided).

More elaborate phase noise models exists such as that in [234], where a time-variant phase noise model is proposed. However, while not predictive in nature, the Leeson model can still provide important insights with regards to phase noise performance. Notably, a higher resonator quality factor and oscillation power will improve phase noise performance by tightening the oscillator’s output spectrum, and reducing excess noise stemming from electronics will improve the phase noise floor. It is also of interest to reduce the loading of the quality factor of the resonator by ensuring appropriate input and output resistances of the sustaining amplifier [235]. The 1/f3 corner frequency is often attributed to 1/f noise present in the electronics, however it is often different in phase noise plots, notably because of the time varying nature of the phase noise mechanism [234]. Degradation of phase noise due to noise folding can also impact oscillator performance [236]. In addition, complexities can arise because of nonlinearity [221] or the specificities of MEMS resonators can deteriorate phase noise. For instance, mechanical noise can impact performance depending on the relative noise performance of the sustaining amplifier [225]. Moreover, resonant non-linear behavior can also cause close-in offset noise degradation and a higher than 30 dB phase noise slope [222,226,227]. This degradation of phase-noise, notably at low frequency offsets has pushed most MEMS oscillator designs to employ automatic gain control in the sustaining amplifier in order to reduce the non-linear behavior of the MEMS resonator, and ensure optimal close-in offset performance [209,231,237,238]. The influence of automatic gain control on the oscillator phase noise is shown with regards to time-domain frequency stability in Figure 25a [208] and to phase noise performance in Figure 25b [237], outlining the significant degradation in oscillator performance when no automatic gain control is used to limit the oscillation amplitude. Notably, some resonator models have been proposed to enhance the typical RLC model which does not allow for circuit design that takes into account resonator nonlinearity (e.g., [223,228,239]), and other works have also Micromachinesleveraged2016 the, 7 ,non-linearity 160 of resonators to enhance phase noise performance by designing28 of 56 the oscillator to take advantage of the Duffing behavior of the resonator (e.g., [139,221]).

(a) (b)

FigureFigure 25. 25.(a) ( Thea) The effect effect of automaticof automatic gain gain control control due due to theto the nonlinearity nonlinearity of theof the resonator resonator on on time time © domaindomain frequency frequency stability stability of of a a MEMS MEMS oscillator oscillator [[208].208]. © 20092009 IEEE. IEEE. Reprinted Reprinted with with permission permission from fromA Highly A Highly Integrated Integrated 1.8 1.8GHz GHz Frequency Frequency Synthesi Synthesizerzer Based Based on ona MEMS a MEMS Resonator Resonator by by Nabki Nabki in J. in J.Solid-State Solid-State Circuits Circuits, 2009;, 2009; and and ( (bb)) the the effect ofof automaticautomatic gaingain (level) (level) control control on on the the phase phase noise noise © performanceperformance of aof MEMS a MEMS oscillator oscillator [237 [237].]. © 2003 2003 IEEE. IEEE. Reprinted Reprinted with with permission permission from from Inﬂuence Influence of of automaticautomatic level level control control on micromechanicalon micromechanical resonator resonator oscillator oscillator phase phase noise. noise. by Lee by inLee Proceedings in Proceedings of theof IEEE the InternationalIEEE International Frequency Frequency Control Control Symposium, Symposium, 2003. 2003.

Ultimately, the limited power handling capabilities of MEMS resonators compared to quartz crystals restricts phase-noise performance improvement through the increase of the oscillation amplitude, but the high-Q they provide allows competitive phase noise performance if proper gain control measures are taken to mitigate resonator nonlinearity. This is particularly true of electrostatic resonators which are inherently more non-linear due to their actuation mechanism [83]. However, piezoelectric resonators are also prone to non-linear behavior [220]. Overall, the output phase noise of a MEMS resonator-based oscillator thus depends on several factors:

• The higher the Q-factor of the resonator, the lower the phase noise in the MEMS oscillator because of the enhanced noise filtering. • The higher the power handling capability of the resonator, the lower the phase noise of the MEMS oscillator because of the increased sustainable amplitude of oscillation. • The higher the motional resistance, the higher the phase noise of the MEMS oscillator because of the higher gain sustaining amplifier is required, usually required more active devices that generate noise. • The lower the electronic noise of the sustaining amplifier, the better the phase noise because of the shaping of this noise that causes a significant portion of the overall phase noise.

8.2.3. Temperature Compensation A signiﬁcant issue for MEMS oscillators is their stability with changes in the ambient temperature. As was previously mentioned, the resonant frequency temperature dependence of an uncompensated MEMS silicon resonator is much higher than that of an AT-cut crystal (i.e., ~50 times worse). Many strategies can be adopted to reduce this sensitivity. Electrostatic tuning can be used to change the bias of the resonator in response to temperature changes [240–242]. Thermal stress compensation can also be used by creating composite resonating structures that feature materials such as silicon oxide that can compensate silicon’s temperature variability [242]. Direct thermal tuning can also be used to control the resonator’s frequency and improve its frequency stability, similarly to oven controlled crystals [243–245]. Other approaches involve the use of phase-locked loops in arrangements that can include mismatched temperature coefﬁcient resonators that result in a temperature stable operating point (e.g., [207,208]) or that can include temperature to digital converters that control the output frequency of the loop to compensate the resonator temperature variance (e.g., [203,206,207,246,247]). More recently, the use of electronics for compensation has precluded MEMS oscillators from operating Micromachines 2016, 7, 160 29 of 56 at power budgets that rival that of quartz oscillators. However, mechanically temperature compensated resonators using doped silicon or silicon oxide [243,248,249] are a current interest for commercial applications as they can preclude the need for heating or electronic compensation, allowing for lower power consumption and better phase noise performance due to the reduced complexity of the control electronics.

8.2.4. Sustaining Amplifiers As was previously discussed, MEMS resonators exhibit very high motional resistances compared to that of quartz crystals—typically in the order of several tens of kilo-Ohms for electrostatically actuated resonators, and a few kilo-Ohms for piezoelectrically actuated resonators. Accordingly, in order to operate at the series-resonance of the resonator, the motional current outputted by the resonator device needs to be amplified by a trans-impedance amplifier (TIA) having the following characteristics [215]:

• a high gain to offset the resonator losses (i.e., at least 1.5 times the resonator’s motional resistance); • a bandwidth which is an order of magnitude larger than the resonator’s frequency to ensure a small phase shift around the feedback loop; Micromachines 2016, 7, 160 29 of 55 • low input and output impedances to avoid loading the resonator’s Q-factor; • an automatic automatic gain gain control control capability capability to prevent to prevent large oscillations large oscillations from exerting from the exerting resonator’s the resonator’snonlinearities. nonlinearities.

All these specificationsspecifications are challenging to fulfill fulfill simultaneously, and require carefully designed circuitry. TheThe typicaltypical interconnection interconnection for for a trans-impedancea trans-impedance amplifier amplifier with with automatic automatic gain gain control control used toused bring to bring a clamped-clamped a clamped-clamped beam beam resonator resonator is shown is shown in Figure in Figure 26[241 26]. [241].

Figure 26.26.The The typical typical trans-impedance trans-impedance amplifier amplifier configuration configuration providing providing 0◦ phase 0° shift phase and shift sufficient and © gainsufficient around gain an around electrostatic an el resonatorectrostatic [241 resonator]. © 2007 [241]. IEEE. Reprinted 2007 IEEE. with Reprinted permission with from permission Electronically from TemperatureElectronically Compensated Temperature SiliconCompensated Bulk Acoustic Silicon ResonatorBulk Acoustic Reference Resonator Oscillators Reference by SundaresanOscillators by in J.Sundaresan Solid-State in Circuits J. Solid-State, 2007. Circuits, 2007.

In this configuration, an operational amplifier is put in shunt-shunt resistive feedback to In this configuration, an operational amplifier is put in shunt-shunt resistive feedback to provide provide a trans-impedance gain of −RAMP and a second stage provides an additional gain of −1 to a trans-impedance gain of −R and a second stage provides an additional gain of −1 to provide provide a total positive gain withAMP 0° phase shift and sufficient gain to offset the motional resistance a total positive gain with 0◦ phase shift and sufficient gain to offset the motional resistance of the of the resonator. Note that the resonator in this work has two transducer gaps, which reduces the resonator. Note that the resonator in this work has two transducer gaps, which reduces the feedthrough feedthrough capacitance and thus mitigates the parallel resonance of the resonator. A level control capacitance and thus mitigates the parallel resonance of the resonator. A level control circuit can circuit can modulate the gain by changing the feedback resistance, which is implemented with a modulate the gain by changing the feedback resistance, which is implemented with a triode transistor. triode transistor. Note that the use of a triode transistor can cause non-linear behavior of the circuit Note that the use of a triode transistor can cause non-linear behavior of the circuit and detract from and detract from phase noise performance [249]. In addition, the input resistance of the shunt-shunt phase noise performance [249]. In addition, the input resistance of the shunt-shunt feedback amplifier feedback amplifier is typically on the order of RF/A, where A is the gain of the operational amplifier is typically on the order of R /A, where A is the gain of the operational amplifier in the shunt-shunt in the shunt-shunt feedback. FThis implies that if very large gain is implemented with the amplifier or feedback. This implies that if very large gain is implemented with the amplifier or if it has insufficient if it has insufficient gain, the input impedance may increase sufficiently to significantly load the quality factor of the resonator and deteriorate phase noise performance, as later discussed. As for resonator nonlinearity mitigation, many different amplitude limiting schemes exist, ranging from hard limiting using comparators or saturating circuits to soft limiting using variable gain amplifiers [216,231,238,250–252]. In Figure 27, a topology using a trans-impedance input stage with a second voltage gain stage to provide sufficient gain is shown [215]. The advantage of splitting the gain stages into two is that more gain bandwidth can be achieved per stage to allow for series-resonant oscillation at up to 15 MHz in [208]. The shunt-shunt feedback is implemented in the variable gain amplifier. Again, an automatic gain control can regulate the gain to prevent resonator nonlinear limiting and enhance phase noise. This is implemented by varying the voltage stage gain in response to the amplitude detected at the output of the oscillator through the automatic gain control loop.

Micromachines 2016, 7, 160 30 of 56 gain, the input impedance may increase sufficiently to significantly load the quality factor of the resonator and deteriorate phase noise performance, as later discussed. As for resonator nonlinearity mitigation, many different amplitude limiting schemes exist, ranging from hard limiting using comparators or saturating circuits to soft limiting using variable gain amplifiers [216,231,238,250–252]. In Figure 27, a topology using a trans-impedance input stage with a second voltage gain stage to provide sufficient gain is shown [215]. The advantage of splitting the gain stages into two is that more gain bandwidth can be achieved per stage to allow for series-resonant oscillation at up to 15 MHz in [208]. The shunt-shunt feedback is implemented in the variable gain amplifier. Again, an automatic gain control can regulate the gain to prevent resonator nonlinear limiting and enhance phase noise. This is implemented by varying the voltage stage gain in response to the amplitude detected at the outputMicromachines of the 2016 oscillator, 7, 160 through the automatic gain control loop. 30 of 55

Figure 27.27. Typical trans-impedance amplifier ampliﬁer (TIA) (TIA) bloc blockk diagram, diagram, showing showing a resonator a resonator connected connected in inclosed-loop. closed-loop.

At the transistor level, the trans-impedance structure has been used both for electrostatic At the transistor level, the trans-impedance structure has been used both for electrostatic resonators (e.g., [201,217,231,242,245,253]) or piezoelectric resonators (e.g., [239]). Many designs resonators (e.g., [201,217,231,242,245,253]) or piezoelectric resonators (e.g., [239]). Many designs utilize a regulated cascode input stage to boost the current gain and reduce the input resistance of utilize a regulated cascode input stage to boost the current gain and reduce the input resistance of the the trans-impedance at the input, in order to reduce the Q-loading on the resonator. This is trans-impedance at the input, in order to reduce the Q-loading on the resonator. This is important as important as Q-loading in series-resonant oscillators is given by: Q-loading in series-resonant oscillators is given by: = (17) 1+(Q +UL )/ QL = (17) 1 + (Ri + Ro)/Rm where QUL is the unloaded Q-factor of the resonator, Rm its motional resistance, Ri the input whereresistanceQUL ofis the unloadedsustaining Q-factor amplifier of and the resonator, Ro its outputRm itsresistance. motional Moreover, resistance, inRi orderthe input to reduce resistance the ofQ-loading the sustaining of the ampliﬁerresonator, and all series-resonantRo its output resistance. circuits include Moreover, an output in order stage to reduce which theensures Q-loading a low ofoutput the resonator,resistance, allas series-resonantshown in Figure circuits 27. This include can be a an common-source output stage whichtype buffer, ensures or a series-shunt low output resistance,feedback buffer as shown circuit. in Figure 27. This can be a common-source type buffer, or a series-shunt feedback bufferThe circuit. regulated cascode circuit is shown in Figure 28 [215] and variants of it are used in works suchThe as [138,216,245,254]. regulated cascode Assuming circuit is R shown3 is large in Figureenough 28 so[ 215 that] andthe signal variants current of it are through used init workscan be suchneglected, as [138 the,216 low-frequency,245,254]. Assuming input impedaR3 is largence of enough this stage so thatcan be the shown signal to current be through it can be neglected, the low-frequency input impedance of this1 stage can be shown to be = (18) 1 + ( || ) 1 Ri = (18) gm1(1 + gm2(R2||ro2)) VDD

R1 R2 vout

iin M2

Figure 28. Regulated cascode trans-impedance amplifier stage.

It can be seen that the gain of the feedback loop increases the trans-conductance of transistor M1, and therefore lowers the input impedance of the amplifier beyond that of a traditional common-gate configuration biased at the same current. The trans-impedance gain of the stage is approximately R1, which can be selected independently to gm1 and gm2 with appropriate transistor sizing. This is in contrast to the shunt-shunt amplifier which imposes relationship between the

Micromachines 2016, 7, 160 30 of 55

Figure 27. Typical trans-impedance amplifier (TIA) block diagram, showing a resonator connected in closed-loop.

At the transistor level, the trans-impedance structure has been used both for electrostatic resonators (e.g., [201,217,231,242,245,253]) or piezoelectric resonators (e.g., [239]). Many designs utilize a regulated cascode input stage to boost the current gain and reduce the input resistance of the trans-impedance at the input, in order to reduce the Q-loading on the resonator. This is important as Q-loading in series-resonant oscillators is given by:

= (17) 1+( +)/

where QUL is the unloaded Q-factor of the resonator, Rm its motional resistance, Ri the input resistance of the sustaining amplifier and Ro its output resistance. Moreover, in order to reduce the Q-loading of the resonator, all series-resonant circuits include an output stage which ensures a low output resistance, as shown in Figure 27. This can be a common-source type buffer, or a series-shunt feedback buffer circuit. The regulated cascode circuit is shown in Figure 28 [215] and variants of it are used in works such as [138,216,245,254]. Assuming R3 is large enough so that the signal current through it can be neglected, the low-frequency input impedance of this stage can be shown to be 1 = Micromachines 2016, 7, 160 (18) 31 of 56 1 + (||)

VDD

R1 R2 vout

iin M2

Figure 28. Regulated cascode trans-impedance amplifier stage. Figure 28. Regulated cascode trans-impedance amplifier stage. It can be seen that the gain of the feedback loop increases the trans-conductance of transistor MIt1 can, and be therefore seen that lowers the gain the of input the feedback impedance loop of increases the amplifier the trans-conductance beyond that of a oftraditional transistor M1, and thereforecommon-gate lowers configuration the input biased impedance at the ofsame the amplifiercurrent. The beyond trans-impedance that of a traditional gain of the common-gate stage is configurationapproximately biased R1, which at the can same be current.selected independently The trans-impedance to gm1 and gain gm2 with of the appropriate stage is approximatelytransistor sizing. This is in contrast to the shunt-shunt amplifier which imposes relationship between the R1, which can be selected independently to gm1 and gm2 with appropriate transistor sizing. This is inMicromachines contrast to2016 the, 7, 160 shunt-shunt amplifier which imposes relationship between the achievable31 gain of 55 and the input resistance, as was previously discussed. To achieve a large gain, the size of R1 must beachievable maximized, gain but and the the voltage input resistance, drop across as it was must pr beeviously small enough discussed. to keep To achieveM1 in saturation a large gain, mode. the Thissize revealsof R1 must the be main maximized, advantage but of the the voltagegm-boosted drop topology, across it comparedmust be small to a enough simple common-gateto keep M1 in amplifier.saturation A mode. small This bias currentreveals canthe flowmain through advantageM1 ofand theR 1g,m allowing-boosted fortopology, a large trans-impedancecompared to a simple gain, whilecommon-gate the feedback amplifier. provided A small by M bias2 and currentR2 boosts can the flow trans-conductance through M1 and of RM1, 1allowingsuch that for the a inputlarge impedancetrans-impedance remains gain, small. while Note the feedback that the resistors provided can by beM2 implemented and R2 boosts asthe triode trans-conductance transistors as of well, M1 butsuch care that should the input be given impedance to the 1/remainsf noise small. performance Note that in thatthe case.resistors can be implemented as triode transistorsTypically as well, following but care the should regulated be given cascode to the is a1/ variablef noise performance voltage gain inamplifier that case. in shunt-shunt feedbackTypically using following a triode transistorthe regulated to vary cascode the gain is a suchvariable as in voltage [253], andgain shown amplifier in Figurein shunt-shunt 29[ 253] followingfeedback using a regulated a triode cascode transistor input to stage vary using the gain two such triode as transistors in [253], andM3 andshownM4 .in The Figure voltage 29 [253] gain amplifierfollowing thisa regulated case is composed cascode input of two stage inverters using two (M5 ,triodeM6 and transistorsM7, M8), M with3 and the M second4. The voltage inverter gain in shunt-shuntamplifier this feedback case is allowingcomposed for of controllable two inverters gain ( throughM5, M6 and the biasingM7, M8 of), with transistor the secondMf. Capacitor inverterC pkin isshunt-shunt included in feedback this case allowing in order tofor provide controllable a peaking gain through zero in the the frequency biasing of response transistor which Mf. Capacitor extends ◦ theCpk bandwidthis included ofin thethis amplifier case in order and ensures to provid a sufficiente a peaking bandwidth zero in tothe meet frequency the 0 phaseresponse condition which forextends series-resonant the bandwidth oscillation. of the Noteamplifier that theand first ensure inverters a sufficient in the voltage bandwidth amplifier to meet can be the difficult 0° phase to biascondition properly for becauseseries-resonant of the sensitive oscillation. nature Note of that the inverterthe first inputinverter node in tothe DC voltage bias. Asamplifier such in can [138 be], adifficult less sensitive to bias common properly source because voltage of the gain sensitive stage nature is used of before the inverter the shunt-shunt input node feedback to DC tunablebias. As voltagesuch in stage.[138], a less sensitive common source voltage gain stage is used before the shunt-shunt feedback tunable voltage stage.

FigureFigure 29.29. VoltageVoltagegain gainstage stageused usedto toincrease increasethe thegain gainof ofthe theregulated regulated cascade cascade ampliﬁer amplifier [ 253[253].]. © © 20122012 IEEE.IEEE. ReprintedReprinted withwith permissionpermission fromfrom AA 1.571.57 mWmW 9999 dBdBΩΩ CMOSCMOS transimpedancetransimpedance ampliﬁeramplifier forfor VHFVHF micromechanicalmicromechanical referencereference oscillatoroscillator byby LiLi inin ProceedingsProceedings ofof thethe IEEEIEEE InternationalInternational SymposiumSymposium onon CircuitsCircuits andand Systems,Systems, 2012.2012.

Another amplifier structure which has been used is the capacitive feedback trans-impedance amplifier structure [218,255,256]. This structure is shown in Figure 30 [254] and includes an operational amplifier which is configured with capacitive feedback, allowing for a very large gain and very low noise since the capacitor element does not contribute any noise to the circuit, unlike the feedback resistor used in shunt-shunt configurations. This topology requires careful design of the frequency response of the circuit to ensure proper phase shift for oscillation.

Figure 30. Capacitive sustaining amplifier circuit [254]. © 2014 IEEE. Reprinted with permission from CMOS 0.18 µm standard process capacitive MEMS high-Q oscillator with ultra low-power TIA readout system by Kuo in Proceedings of the IEEE Sensors, 2014.

Micromachines 2016, 7, 160 31 of 55 achievable gain and the input resistance, as was previously discussed. To achieve a large gain, the size of R1 must be maximized, but the voltage drop across it must be small enough to keep M1 in saturation mode. This reveals the main advantage of the gm-boosted topology, compared to a simple common-gate amplifier. A small bias current can flow through M1 and R1, allowing for a large trans-impedance gain, while the feedback provided by M2 and R2 boosts the trans-conductance of M1 such that the input impedance remains small. Note that the resistors can be implemented as triode transistors as well, but care should be given to the 1/f noise performance in that case. Typically following the regulated cascode is a variable voltage gain amplifier in shunt-shunt feedback using a triode transistor to vary the gain such as in [253], and shown in Figure 29 [253] following a regulated cascode input stage using two triode transistors M3 and M4. The voltage gain amplifier this case is composed of two inverters (M5, M6 and M7, M8), with the second inverter in shunt-shunt feedback allowing for controllable gain through the biasing of transistor Mf. Capacitor Cpk is included in this case in order to provide a peaking zero in the frequency response which extends the bandwidth of the amplifier and ensures a sufficient bandwidth to meet the 0° phase condition for series-resonant oscillation. Note that the first inverter in the voltage amplifier can be difficult to bias properly because of the sensitive nature of the inverter input node to DC bias. As such in [138], a less sensitive common source voltage gain stage is used before the shunt-shunt feedback tunable voltage stage.

Figure 29. Voltage gain stage used to increase the gain of the regulated cascade amplifier [253]. © 2012 IEEE. Reprinted with permission from A 1.57 mW 99 dBΩ CMOS transimpedance amplifier for VHF Micromachinesmicromechanical2016, 7, 160 reference oscillator by Li in Proceedings of the IEEE International Symposium on32 of 56 Circuits and Systems, 2012.

Another amplifier amplifier structure which has been used is thethe capacitivecapacitive feedbackfeedback trans-impedancetrans-impedance amplifieramplifier structurestructure [218 [218,255,256].,255,256]. This This structure structure is shown is shown in Figure in 30Figure[ 254] and30 [254] includes and an includes operational an operationalamplifier which amplifier is configured which is with configured capacitive with feedback, capacitive allowing feedback, for aallowing very large for gaina very and large very gain low andnoise very since low the noise capacitor since the element capacitor does element not contribute does not anycontribute noise to any the noise circuit, to the unlike circuit, the unlike feedback the feedbackresistor used resistor in shunt-shunt used in shunt-shunt configurations. configurations. This topology This requirestopology careful requires design careful of thedesign frequency of the frequencyresponse of response the circuit of tothe ensure circuit proper to ensure phase proper shift phase for oscillation. shift for oscillation.

© Figure 30. Capacitive sustaining amplifier ampliﬁer circuit [[254].254]. © 20142014 IEEE. IEEE. Reprinted Reprinted wi withth permission from CMOS 0.180.18µ µmm standard standard process process capacitive capacitive MEMS MEMS high-Q high-Q oscillator oscillator with ultrawith low-power ultra low-power TIA readout TIA readoutsystem by system Kuo inby Proceedings Kuo in Proceed of theings IEEE of the Sensors, IEEE Sensors, 2014. 2014.

InMicromachines addition, 2016 the, Pierce7, 160 oscillator structure shown in Figure 31[ 214], often used in quartz32 oscillators, of 55 has also been used in MEMS resonator-based oscillators. In this architecture, one transistor is used to In addition, the Pierce oscillator structure shown in Figure 31 [214], often used in quartz provide negative gain, and load capacitance ensures minimal Q-loading of the resonator and optimal oscillators, has also been used in MEMS resonator-based oscillators. In this architecture, one phasetransistor shift. This is used configuration to provide negative utilizes gain, parallel and resonanceload capacitance of the ensures resonator minimal to attainQ-loading the of additional the phaseresonator shift required and optimal to attain phase oscillation. shift. This configuratio The Piercen utilizes structure, parallel due resonance to its reduced of the resonator achievable to gain is mostlyattain used the additional in piezoelectric phase shift MEMS required resonator-based to attain oscillation. oscillators The Pierce (e.g., structure, [163,215 due,257 to, 258its reduced]). However, this topologyachievable is lessgain usedis mostly in electrostatic used in resonators,piezoelectric as MEMS they generally resonator-based have too oscillators large of a(e.g., motional resistance[163,215,257,258]). to be overcome However, by the this one topology transistor is less stage used Pierce in electrostatic structure. resonators, Notably, someas they works generally involving electrostatichave too resonators large of a motional have been resistance able to to achievebe overcome Pierce-type by the one oscillators transistor stage by using Pierce relatively structure. small Notably, some works involving electrostatic resonators have been able to achieve Pierce-type electrostatic gap resonators in order to reduce the motional resistance sufficiently (i.e., 50 nm in [249]). oscillators by using relatively small electrostatic gap resonators in order to reduce the motional In thatresistance regard, sufficiently works have (i.e., shown 50 nm methodsin [249]). In of that reducing regard, theworks electrostatic have shown gap-size methods afterof reducing fabrication usingthe static electrostatic electrostatic gap-size actuation after fabrication of the resonant using stat structureic electrostatic towards actuation the of drive the resonant and sense structure electrodes, potentiallytowards allowing the drive for and more sense widespread electrodes, potentially use of the allowing Pierce structure for more widespread [259,260]. MEMS use of the oscillators Pierce can also operatestructure using [259,260]. parallel MEMS resonance oscillators though can also a operat highere using gain parallel inverting resonance amplifier though (e.g., a higher current gain starved inverterinverting in [201 amplifier]) and capacitive (e.g., current elements starved to provideinverter in additional [201]) and phase capacitive shift. elements to provide additional phase shift.

Figure 31. Typical Pierce oscillator configuration [214]. Reproduced with permission from Arndt et Figureal., 31. Sens.Typical Actuators Pierce Phys. oscillator; published conﬁguration by Elsevier, 2011. [214 ]. Reproduced with permission from Arndt et al., Sens. Actuators Phys.; published by Elsevier, 2011. It is important to note that while some oscillators feature single-ended sustaining amplifier Itstructures, is important many toalso note are implemented that while someusing different oscillatorsial structures, feature single-ended in order to reduce sustaining the impact ampliﬁer of structures,common-mode many also noise, are implementedand take advantage using of differential resonators having structures, differential in order resonant to reduce modes the which impact of can result in better phase noise performance (e.g., [256,260]).

8.2.5. Nonlinear Oscillators Some efforts have been carried out to operate MEMS resonators in their non-linear Duffing regime in order to achieve more than 1/f2 phase noise filtering, and significantly improve the close-in phase noise performance of MEMS oscillators [220]. Work in [220] and all of the previously discussed series and parallel resonant oscillators are harmonic in nature, such that a resonator, acting as a bandpass filter is put within a positive feedback loop to generate an oscillation at a frequency within the resonator’s series or parallel resonance frequencies. Recently, nonlinear oscillators, such as the parametric oscillator, originally introduced in RF and microwave applications (see [259]), have been applied to MEMS resonators [224,260–263,]. The simplest parametric oscillators operate on the modulation of a characteristic in a pumping loop at twice the required resonator resonant frequency [260]. When doing so, the resonator will generate a signal through its non-linearity that will provide the required output frequency. The fact that no electronics operating at the resonant frequency are required to close a harmonic loop around the resonator allows for these oscillators to feature low close-in phase noise performance (i.e., within the resonator bandwidth) since the electronic noise is not dominating at the resonant frequency [224,263,264].

Micromachines 2016, 7, 160 33 of 56 common-mode noise, and take advantage of resonators having differential resonant modes which can result in better phase noise performance (e.g., [256,260]).

8.2.5. Nonlinear Oscillators Some efforts have been carried out to operate MEMS resonators in their non-linear Duffing regime in order to achieve more than 1/f 2 phase noise filtering, and significantly improve the close-in phase noise performance of MEMS oscillators [220]. Work in [220] and all of the previously discussed series and parallel resonant oscillators are harmonic in nature, such that a resonator, acting as a bandpass filter is put within a positive feedback loop to generate an oscillation at a frequency within the resonator’s series or parallel resonance frequencies. Recently, nonlinear oscillators, such as the parametric oscillator, originally introduced in RF and microwave applications (see [259]), have been applied to MEMS resonators [224,260–263]. The simplest parametric oscillators operate on the modulation of a characteristic in a pumping loop at twice the required resonator resonant frequency [260]. When doing so, the resonator will generate a signal through its non-linearity that will provide the required output frequency. The fact that no electronics operating at the resonant frequency are required to close a harmonic loop around the resonator allows for these oscillators to feature low close-in phase noise performance (i.e., within the resonator bandwidth)Micromachines since 2016, the7, 160 electronic noise is not dominating at the resonant frequency [224,263,26433]. of 55 Electrostatic resonators are particularly well-suited for harmonic oscillators, as their spring Electrostatic resonators are particularly well-suited for harmonic oscillators, as their spring constantsconstants can can be be modulated modulated using using a variation a variation of theirof their bias bias voltages, voltages, such such as shownas shown in Figurein Figure 32a 32a [223 ] and[223] 32b and [261 Figure]. This 32b can [261]. be done This by can a speciallybe done by designed a specially oscillator designed operating oscillator at operating double the at resonatordouble resonator’sthe resonator frequency resonator’s [223], frequency or by putting [223], the or resonator by putting within the resonato a loop thatr within includes a loop a frequency-doubler that includes a andfrequency-doubler start-up source [ 261and]. start-up Parametric source oscillation [261]. Parame can alsotric be oscillation carried-out can with also piezoelectric be carried-out resonators, with butpiezoelectric the higher resonators, linearity of but the the piezoelectric higher linearity transducer of the piezoelectric has required transducer the use has of arequired voltage the varying use capacitorof a voltage (i.e., avarying varactor), capacitor in the (i.e., parametric a varactor), amplifier in the toparametric generate amplifier the harmonic to generate behavior the [harmonic262]. behavior [262].

(a) (b)

Figure 32. (a) Parametric pumping of a MEMS electrostatic resonator [223]; © 2014 IEEE. Reprinted Figure 32. (a) Parametric pumping of a MEMS electrostatic resonator [223]; © 2014 IEEE. Reprinted with with permission from A micromechanical parametric oscillator for frequency division and phase permission from A micromechanical parametric oscillator for frequency division and phase noise noise reduction by Rocheleau in the Proceedings of International Conference on Micro Electro reduction by Rocheleau in the Proceedings of International Conference on Micro Electro Mechanical Mechanical Syst., 2014; and (b) a typical parametric oscillator loop used with a nanoscale resonant Syst., 2014; and (b) a typical parametric oscillator loop used with a nanoscale resonant beam [261]. beam [261]. Reproduced with permission from Villanueva et al., Nano Lett.; published by American Reproduced with permission from Villanueva et al., Nano Lett.; published by American Chemical Chemical Society, 2011. Society, 2011. This approach notably has for advantage of allowing lower-Q-factor resonators to be used and deliverThis approachperformance notably akin hasto higher-Q for advantage devices, of allowing lower-Q-factorfor the design using resonators moderate to be Q-factor used and deliverresonator performance which may akin have to higher-Qpower handling devices, advantag allowinges forthat the can design reduce using far offset moderate phase Q-factornoise resonatorperformance which further, may havewhile power providing handling adequate advantages close-in thatphase can noise reduce performance far offset through phase noise a performanceparametric further,oscillator while configuration. providing adequate close-in phase noise performance through a parametric oscillator conﬁguration. 8.3. Sensing Operation of resonant sensors is based on transforming energy in from one domain to a change in the resonant frequency of a device. The change in resonant frequency can be detected by sweeping the frequency of an excitation signal around the resonant frequency of the device. A more practical method is to place a two-port resonant device within the feedback loop of a properly designed electronic circuit to form an oscillator. In this case, measurements of the quantity of interest will be carried through monitoring of the output frequency of the oscillator circuit. Resonant sensors are among the most sensitive and precise devices for many applications. This in great part is due to the variety of existing techniques for fast, precise, and accurate measurement of the frequency or period of a signal. It is relatively simple to measure the frequency of a signal with sub-ppm levels of precision while achieving a similar level of precision on a voltage or current measurement is typically a challenge. Accurate frequency references, from crystal oscillators to atomic clocks, offer better stability than typical voltage or current references. On the other hand, the signal from a resonant sensor is quasi˗digital since an analog˗to˗digital converter is not needed to measure a frequency. As the information is embedded in frequency rather than amplitude, the sensor signal is immune to noise and interference.

Recalling that ω = ⁄ , it can be seen that a shift in the resonant frequency of a structure is a consequence of a change in the effective mass or the effective spring constant of the structure:

Δ Δ Δ = − (19) 2

Micromachines 2016, 7, 160 34 of 56

8.3. Sensing Operation of resonant sensors is based on transforming energy in from one domain to a change in the resonant frequency of a device. The change in resonant frequency can be detected by sweeping the frequency of an excitation signal around the resonant frequency of the device. A more practical method is to place a two-port resonant device within the feedback loop of a properly designed electronic circuit to form an oscillator. In this case, measurements of the quantity of interest will be carried through monitoring of the output frequency of the oscillator circuit. Resonant sensors are among the most sensitive and precise devices for many applications. This in great part is due to the variety of existing techniques for fast, precise, and accurate measurement of the frequency or period of a signal. It is relatively simple to measure the frequency of a signal with sub-ppm levels of precision while achieving a similar level of precision on a voltage or current measurement is typically a challenge. Accurate frequency references, from crystal oscillators to atomic clocks, offer better stability than typical voltage or current references. On the other hand, the signal from a resonant sensor is quasi-digital since an analog-to-digital converter is not needed to measure a frequency. As the information is embedded in frequency rather than amplitude, the sensor signal is immune to noise and interference. q Recalling that ω0 = Ke f f /Me f f , it can be seen that a shift in the resonant frequency of a structure is a consequence of a change in the effective mass or the effective spring constant of the structure: ! f0 ∆Ke f f ∆Me f f ∆ f0 = − (19) 2 Ke f f Me f f where ∆Ke f f and ∆Me f f are disturbances in the effective stiffness and mass of the structure, respectively. The challenge, therefore, is the proper design of mechanical coupling structures to transform the information from the desired physical domain to a change in dynamic properties of a micromechanical device. Consequently, the design of resonant sensors involves the design of a (high-Q) resonator as well as coupling mechanisms that convert the quantity of interest into a mass or stiffness disturbance. The changes in stiffness are usually a consequence of developing internal stresses within the structure of the device. Obvious applications of resonant sensors are thus mass or strain sensing. Changes in resonant frequency can be measured in different ways. The most straightforward method, especially in a laboratory setting, is to sweep the frequency of the excitation signal around resonant frequency and monitor the changes in resonant frequency in response to disturbances. Another technique is to excite the resonator with a fixed stable signal at a frequency that is slightly different (typically higher) than the resonant frequency of the device. In this case, changes in the resonant frequency will be converted to changes in the amplitude of the output signal and can be related back to the measurand. A technique more suitable for general applications is to place the resonator in the feedback loop of an oscillator circuit and monitor its output frequency. In all these cases, higher quality factors result in better resolutions for the sensor. Therefore, maximizing the resonant sensor quality factor is another design and operation requirement. It should be noted that too high a Q can lead to large resonance amplitudes, and hence, make the resonator prone to nonlinearities. It is noteworthy that, as can be seen from Equation (5), changes in quality factor can also affect the resonant frequency of a device. However, quality factor of microdevices is often quite large and varies significantly from device to device. As such, both precision and accuracy advantages may be sacrificed to a great extent. If the parameter of interest affects the quality factor, changes in signal amplitude are typically easier to measure than changes in the resonant frequency. Additionally, a high quality factor often reduces the sensitivity of the resonator response to changes in quality factor.

8.3.1. Resonant Sensors Based Changes in Effective Mass Resonant mass sensing, also known as gravimetric sensing, has been a well-known application of resonators. The change in the effective mass of the structure can be due to settlement of particles and Micromachines 2016, 7, 160 35 of 56 objects on the resonators surface, deposition of thin films, or absorption of material into films on the surface of the device. Resonant mass sensors have therefore been used to detect particle concentration, deposition rate, chemical sensing, and bio-sensing. As can be inferred from Equation (9), to obtain a high mass sensitivity, one would like to use a device with a high resonant frequency f0, with a small effective mass, Me f f . Reducing device dimensions usually achieves both of these goals at the expense of complexity of input/output coupling to the device. Beam based structures, such as cantilevers and bridges, offer a simple structure, straightforward excitation, and various detection possibilities [48,265–271]. Figure 33 is an SEM image of a bridge-based mass sensor where sheets of platinum were deposited for controlled characterization of the device. Even single carbon nanotubes can be used as super-sensitive cantilever-based mass sensors [272,273]. To use these devices, the beam resonator is excited in its flexural, typically out-of-plane, mode of vibration using piezoelectric or electrostatic actuation. The resonant frequency of the beam is then monitored using optical or electrical techniques as to quantify the mass added to the structure. For flexural vibrations of a beam, the contributions of different segments of the structure to its effective mass vary depending on the beam geometry and the relative amplitude of vibration (see Equation (19)). The location of added mass onto the beam is thus another factor that affects the amount of shift in the resonantMicromachines frequency 2016, 7, 160 and must be taken into account in such studies [274,275]. 35 of 55

Figure 33. A resonant mass sensor based on coupled resonators. Note the addition of platinum sheets Figure 33. A resonant mass sensor based on coupled resonators. Note the addition of platinum sheets used for characterization of the sensor [269]. © 2016 IEEE. Reprinted with permission from Improving used for characterization of the sensor [269]. © 2016 IEEE. Reprinted with permission from Improving sensitivity of resonant sensor systems through strong mechanical coupling by M.S. Hajhashemi in J. sensitivity of resonant sensor systems through strong mechanical coupling by M.S. Hajhashemi in J.Microelectromech. Microelectromech. Syst. Syst., 2016., 2016.

To go beyond the capabilities of a simple cantilever structure without dealing with complexities To go beyond the capabilities of a simple cantilever structure without dealing with complexities of driving and sensing signals at the nano-scales, one can take advantage of bulk resonant modes of of driving and sensing signals at the nano-scales, one can take advantage of bulk resonant modes of structures. Bulk mode resonators, in general, offer higher resonant frequencies for similar structures. Bulk mode resonators, in general, offer higher resonant frequencies for similar dimensions dimensions as flexural devices. Furthermore, they often have higher quality factors, which improves as flexural devices. Furthermore, they often have higher quality factors, which improves the resolution the resolution of the sensors [274]. The structure of a bulk mode resonators is typically simple to of the sensors [274]. The structure of a bulk mode resonators is typically simple to reduce the effects reduce the effects of spurious modes and is usually based on a beam, square or circular plate, or a of spurious modes and is usually based on a beam, square or circular plate, or a ring. Any of surface ring. Any of surface acoustic wave [276–278], thickness shear [279,280], bulk acoustic wave [281,282], acoustic wave [276–278], thickness shear [279,280], bulk acoustic wave [281,282], or extensional or extensional modes [283,284] can be selected for mass sensing among several other modes of modes [283,284] can be selected for mass sensing among several other modes of vibration [283]. vibration [283]. The selection of the mode shape is usually influenced by fabrication capabilities and The selection of the mode shape is usually influenced by fabrication capabilities and the desired the desired transduction mechanisms. transduction mechanisms. One of the main applications of gravimetric sensors is chemical sensing, particularly in gaseous One of the main applications of gravimetric sensors is chemical sensing, particularly in gaseous phase [284]. In such applications, a thin film that selectively binds to the target chemical is applied to phase [284]. In such applications, a thin film that selectively binds to the target chemical is applied to the surface of the resonator. During the device operation, the analyte is adsorbed onto or absorbed the surface of the resonator. During the device operation, the analyte is adsorbed onto or absorbed into into this sensitive layer, causing an increase in the effective mass of the structure, among other this sensitive layer, causing an increase in the effective mass of the structure, among other potential potential effects. For instance, molecules absorbed into the film often produce a stress at the surface effects. For instance, molecules absorbed into the film often produce a stress at the surface of the of the structure, which besides affecting the resonant frequency of the resonator, modifies the structure, which besides affecting the resonant frequency of the resonator, modifies the surface losses surface losses in the structure and alter the quality factor of the resonator. The resonator, on the other hand, is usually placed in an oscillator loop and the changes in its resonant frequency are monitored. For a perfectly selective film, the changes in the effective mass can be directly related to the concentration of the particular chemical in the environment. In practice, however, various other phenomena may affect the resonant frequency of the device including variations in temperature, humidity, and other molecules that may also bind to the film. Cantilevers and bridges are among the more common types of resonators that are used for gravimetric gas sensing in gases [285–289]. The simple structure of these resonators makes it possible to fabricate high performance devices even when the manufacturing process is not optimal [290–292]. The large surface area of quartz microbalances or surface acoustic wave resonators makes them popular choices for gas sensing applications as the focus is placed on the thin film [293–296]. Gravimetric sensors based on nano-resonators are capable of detecting a single molecules of target analyte. Arrays of gravimetric gas sensors have been used in multi-gas sensors systems, also known as electronic-noses [297–299]. Resonant mass sensors are also used for the detection of biomolecules. In this case, the active surface of the resonator is coated with a protein that selectively binds to the target biomolecule. However, as most biological sensing needs to be carried within biofluids, most resonant modes are damped so heavily that they could no longer be used as gravimetric sensors. The resonant modes that can still result in high quality factors often rely on in-plane movements of the resonator relative to the liquid surface [148,274,279,300–302]. It is also possible to build micro- or nano-channels within the structure of the resonator (see Figure 34) [45]. Once the inside walls of these channels are

Micromachines 2016, 7, 160 36 of 56 in the structure and alter the quality factor of the resonator. The resonator, on the other hand, is usually placed in an oscillator loop and the changes in its resonant frequency are monitored. For a perfectly selective film, the changes in the effective mass can be directly related to the concentration of the particular chemical in the environment. In practice, however, various other phenomena may affect the resonant frequency of the device including variations in temperature, humidity, and other molecules that may also bind to the film. Cantilevers and bridges are among the more common types of resonators that are used for gravimetric gas sensing in gases [285–289]. The simple structure of these resonators makes it possible to fabricate high performance devices even when the manufacturing process is not optimal [290–292]. The large surface area of quartz microbalances or surface acoustic wave resonators makes them popular choices for gas sensing applications as the focus is placed on the thin film [293–296]. Gravimetric sensors based on nano-resonators are capable of detecting a single molecules of target analyte. Arrays of gravimetric gas sensors have been used in multi-gas sensors systems, also known as electronic-noses [297–299]. Resonant mass sensors are also used for the detection of biomolecules. In this case, the active surface of the resonator is coated with a protein that selectively binds to the target biomolecule. However, as most biological sensing needs to be carried within biofluids, most resonant modes are damped so heavily that they could no longer be used as gravimetric sensors. The resonant modes that can still result in high quality factors often rely on in-plane movements of the resonator relative to the liquid surface [148,274,279,300–302]. It is also possible to build micro- or nano-channels within the Micromachines 2016, 7, 160 36 of 55 structure of the resonator (see Figure 34)[45]. Once the inside walls of these channels are activated, activated,the biosample the biosample is flown through is flown the through channels. the Target channe biomoleculesls. Target biomolecules in the sample in bindthe sample to the channelbind to thewalls, channel increasing walls, theincreasing effective the mass effective of the mass resonator. of the resonator. This technique This technique allows for allows the use for ofthe various use of variousresonators resonators at the expense at the expense of increased of increased fabrication fabrication complexity. complexity.

(a) (b)

Figure 34. (a) Damping in liquid phase resonant mass sensors are reduced by using suspended Figure 34. (a) Damping in liquid phase resonant mass sensors are reduced by using suspended microfluidic channels as resonators; (b) Analytes are detected based on their mass density difference microﬂuidic channels as resonators; (b) Analytes are detected based on their mass density difference relative to the surrounding solution. [43]. Reproduced with permission from T.P. Burg, Appl. Phys. relative to the surrounding solution. [43]. Reproduced with permission from T.P. Burg, Appl. Phys. Lett.; Lett.; published by AIP, 2003. published by AIP, 2003.

8.3.2. Resonant Sensors Based Changes in Effective Stiffness 8.3.2. Resonant Sensors Based Changes in Effective Stiffness The stiffness of most mechanical structures is a function of the stress applied to them. A The stiffness of most mechanical structures is a function of the stress applied to them. A familiar familiar example is a guitar string whose natural frequency increases with tensile stress. Most example is a guitar string whose natural frequency increases with tensile stress. Most resonant sensors resonant sensors employ the flexural resonant modes of a structure. This in part is due to the fact employ the flexural resonant modes of a structure. This in part is due to the fact that it is fairly simple that it is fairly simple to couple an input stress onto a flexural spring without affecting other to couple an input stress onto a flexural spring without affecting other resonator parameters especially resonator parameters especially its quality factor. For a clamped-guided beam, a common element its quality factor. For a clamped-guided beam, a common element in MEMS structures. The effective in MEMS structures. The effective flexural spring constant of such a beam under axial force flexural spring constant of such a beam under axial force T (positive for tensile forces) is given by [302]: (positive for tensile forces) is given by [302]: γT 12EI 6T k = γ ≈ 12 +6 (20) b = γL ≈ 3 + γL − 2tanh γ L 5L (20) γ−2 2 5 2 where E is the Young’s modulus of the material, L and I are the length and the second moment of inertia where is the Young’s modulus of the material,√ and are the length and the second moment of the beam spring, respectively, and γ = T/EI. As can be seen, the flexural spring constant changes of inertia of the beam spring, respectively, and γ = . As can be seen, the flexural spring constant changes linearly for small axial forces (stiffens for tensile stress and softens for compressive). The extreme sensitivity of resonant sensors allows for the detection of strains on the order of pico- to nano-strains, and hence, a viable mechanism for detection of various phenomena. To maintain high quality factor, most resonant sensors are operated under vacuum. This encapsulation creates challenges for the coupling of the measurand to the resonator structure. Much like mass sensing, strain sensing is an obvious application of resonant sensors. A strain sensor, in its simplest form, is anchored at two locations which undergo some relative displacement during the device operation. The anchors transfer this strain to the resonator structure, and consequently, affect its resonant frequency [303–306]. Pressure sensors were among the early examples of resonant sensors. The design of these devices is based on anchoring a resonator to one side of a membrane that would deflect under pressure. The membrane deflections would then cause an axial strain onto the resonator, ultimately causing a change in its resonant frequency (see Figure 35). The required high quality factor was achieved through providing a stable, low-pressure ambient on the resonator side of the membrane [307–311]. Figure 36 shows such a device where coupled bridge resonators were enclosed in a micro-cavity and anchored to the top of a flexible membrane [312,313]. The device was placed within a fixed magnetic field produced by a permanent magnet. A current is used to produce a Lorentz force on one arm of the device whose dynamic deflections are picked up using the electromotive voltage produced across a coupled beam. The device was then placed within the feedback loop of an oscillator circuit.

Micromachines 2016, 7, 160 37 of 56 linearly for small axial forces (stiffens for tensile stress and softens for compressive). The extreme sensitivity of resonant sensors allows for the detection of strains on the order of pico- to nano-strains, and hence, a viable mechanism for detection of various phenomena. To maintain high quality factor, most resonant sensors are operated under vacuum. This encapsulation creates challenges for the coupling of the measurand to the resonator structure. Much like mass sensing, strain sensing is an obvious application of resonant sensors. A strain sensor, in its simplest form, is anchored at two locations which undergo some relative displacement during the device operation. The anchors transfer this strain to the resonator structure, and consequently, affect its resonant frequency [303–306]. Pressure sensors were among the early examples of resonant sensors. The design of these devices is based on anchoring a resonator to one side of a membrane that would deflect under pressure. The membrane deflections would then cause an axial strain onto the resonator, ultimately causing a change in its resonant frequency (see Figure 35). The required high quality factor was achieved through providing a stable, low-pressure ambient on the resonator side of the membrane [307–311]. Figure 36 shows such a device where coupled bridge resonators were enclosed in a micro-cavity and anchored to the top of a flexible membrane [312,313]. The device was placed within a fixed magnetic field produced by a permanent magnet. A current is used to produce a Lorentz force on one arm of the device whose dynamic deflections are picked up using the electromotive voltage produced across a coupled beam. The device was then placed within the feedback loop of an oscillator circuit. MicromachinesMicromachines 2016 2016, 7, 160, 7, 160 37 of 5537 of 55

Figure 35. Generation of axial strains in bridges anchored to a flexible membrane due to pressure. Figure 35. Generation of axial strains in bridges anchor anchoreded to a flexible ﬂexible membrane due to pressure.

Figure 36. The resonant pressure sensor by Ikeda et al. [311]: (a) the schematic of the resonator and circuitry around it and (b) cross-sectional view of one of the beams inside the cavity and the Figureencapsulation 36. The resonant film. © pressure1998 IEEE. sensor Reprinted by Ikedawith permission et al. [311]: from (a) theSilicon schematic Micromachined of the resonator Vacuum and Figure 36. The resonant pressure sensor by Ikeda et al. [311]: (a) the schematic of the resonator circuitryEncapsulated around Resonantit and ( bPressure) cross-sectional Sensors by K.view Ikeda of in one Proceedings of the beamsof International inside theMicroprocesses cavity and the and circuitry around it and (b) cross-sectional view of one of the beams inside the cavity and the and Nanotechnology© Conference, 1998. encapsulation film. ﬁlm. © 19981998 IEEE. IEEE. Reprinted Reprinted with with permission from Silicon Micromachined Vacuum Encapsulated Resonant Pressure Sensors by K. Ikeda in Proceedings of International Microprocesses EncapsulatedSeveral resonant Resonant magnetic Pressure field Sensors sensor by K. designs Ikeda inhave Proceedings also been of proposed International [304,314–316]. Microprocesses In a and Nanotechnology Conference, 1998. andtypical Nanotechnology design, the Lorentz Conference, force 1998. on a current-carrying beam is used to generate a stress on a resonator, whose resonance frequency then changes accordingly. Figure 37 illustrates a sample Several resonant magnetic field sensor designs have also been proposed [304,314–316]. In a Severaldesign where resonant the Lorentz magnetic force ﬁeld on sensortwo cross-bars designs was have transferred also been axially proposed to an [ electrostatic304,314–316 resonator]. In a typical typical design, the Lorentz force on a current-carrying beam is used to generate a stress on a design,[315]. the Thanks Lorentz to the force inherent on a current-carryingadvantages of resonant beam sensing, is used resonant to generate magnetic a stress sensors on typically a resonator, resonator,offer a whosehigh resolution resonance and frequency dynamic range then withouchanget sthe accordingly. need for any Figure special 37fabrication illustrates steps a sampleor whose resonance frequency then changes accordingly. Figure 37 illustrates a sample design where the designmaterials. where theSome Lorentz magnetic force sensors on two designs cross-bars employ was resonance transferred to enhance axially theto an sensor electrostatic response, resonator but Lorentz force on two cross-bars was transferred axially to an electrostatic resonator [315]. Thanks to the [315].their Thanks output to is the based inherent on a change advantages in signal of amplitude resonant rather sensing, than frequencyresonant magnetic[317–319]. sensors typically inherent advantages of resonant sensing, resonant magnetic sensors typically offer a high resolution offer a high resolution and dynamic range without the need for any special fabrication steps or and dynamic range without the need for any special fabrication steps or materials. Some magnetic materials. Some magnetic sensors designs employ resonance to enhance the sensor response, but their output is based on a change in signal amplitude rather than frequency [317–319].

Figure 37. A resonant micromachined magnetic field sensor [315]. A DC current is passed through the two metal coated cross-bars which generates a Lorentz force that results in an axial force on the beam springs of the electrostatic resonator.

Linear inertial forces on structures can also be coupled to a resonator structure to realize resonant accelerometers [320–322]. Figure 38 is an SEM image of a resonant accelerometer where Figure 37. A resonant micromachined magnetic field sensor [315]. A DC current is passed through

the two metal coated cross-bars which generates a Lorentz force that results in an axial force on the beam springs of the electrostatic resonator.

Linear inertial forces on structures can also be coupled to a resonator structure to realize resonant accelerometers [320–322]. Figure 38 is an SEM image of a resonant accelerometer where

Micromachines 2016, 7, 160 37 of 55

Figure 35. Generation of axial strains in bridges anchored to a flexible membrane due to pressure.

Figure 36. The resonant pressure sensor by Ikeda et al. [311]: (a) the schematic of the resonator and circuitry around it and (b) cross-sectional view of one of the beams inside the cavity and the encapsulation film. © 1998 IEEE. Reprinted with permission from Silicon Micromachined Vacuum Encapsulated Resonant Pressure Sensors by K. Ikeda in Proceedings of International Microprocesses and Nanotechnology Conference, 1998.

Several resonant magnetic field sensor designs have also been proposed [304,314–316]. In a typical design, the Lorentz force on a current-carrying beam is used to generate a stress on a resonator, whose resonance frequency then changes accordingly. Figure 37 illustrates a sample Micromachinesdesign where2016, 7, the 160 Lorentz force on two cross-bars was transferred axially to an electrostatic resonator38 of 56 [315]. Thanks to the inherent advantages of resonant sensing, resonant magnetic sensors typically offer a high resolution and dynamic range without the need for any special fabrication steps or sensors designs employ resonance to enhance the sensor response, but their output is based on a change materials. Some magnetic sensors designs employ resonance to enhance the sensor response, but in signaltheir amplitude output is based rather on thana change frequency in signal [317 amplitude–319]. rather than frequency [317–319].

Figure 37. A resonant micromachined magnetic field sensor [315]. A DC current is passed through Figure 37. A resonant micromachined magnetic ﬁeld sensor [315]. A DC current is passed through the the two metal coated cross-bars which generates a Lorentz force that results in an axial force on the two metalbeam springs coated cross-barsof the electrostatic which resonator. generates a Lorentz force that results in an axial force on the beam springs of the electrostatic resonator. Linear inertial forces on structures can also be coupled to a resonator structure to realize Linearresonant inertial accelerometers forces on [320–322] structures. Figure can also 38 is be an coupled SEM image to a resonatorof a resonant structure accelerometer to realize where resonant Micromachines 2016, 7, 160 38 of 55 accelerometers [320–322]. Figure 38 is an SEM image of a resonant accelerometer where displacements of proofdisplacements mass were of measured proof mass through were measured changes inthrough the resonant changes frequency in the resonant of the connectorfrequency of beam the [321]. It isconnector also possible beam to [321]. measure It is the also proof possible mass to displacements measure the proof through mass monitoring displacements the changethrough in the electrostaticmonitoring spring the change constant in inthe electrostatic electrostatic resonators spring constant [322]. in Even electrostatic though resonantresonators accelerometers [322]. Even are capablethough of achieving resonant accelerometers very high resolutions, are capable their of achiev relativelying very slow high response resolutions, times their makes relatively their applications slow response times makes their applications limited to special cases. Vibratory gyroscope designs are limited to special cases. Vibratory gyroscope designs are also based on microresonator structures. also based on microresonator structures. However, in typical designs, two resonators or two However, in typical designs, two resonators or two vibration modes of a single resonator are employed vibration modes of a single resonator are employed and the measurement of rate is based on change andin the signal measurement amplitudes of [323–327]. rate is based on change in signal amplitudes [323–327].

(a) (b)

Figure 38. A resonant accelerometer: (a) The structure was brought under resonance using a thermal Figure 38. A resonant accelerometer: (a) The structure was brought under resonance using a thermal actuator embedded at the base of connector beam (b). Strains were measured using doped actuator embedded at the base of connector beam (b). Strains were measured using doped piezoresistors [321]. Reproduced with permission from Aikele, M. Sens. Actuators Phys.; published by piezoresistors [321]. Reproduced with permission from Aikele, M. Sens. Actuators Phys.; published by Elsevier, 2001. Elsevier, 2001. Structures can be designed to convert a Columbic force to an axial stress. The Columbic force canStructures be generated can be from designed a field to produced convert aby Columbic an electric force charge. to an This axial concept stress. has The been Columbic employed force can be generateddesign and from fabricate a ﬁeld micromachined produced by resonant an electric charge charge. sensors This [328,329]. concept has been employed design and fabricate micromachined resonant charge sensors [328,329]. 8.4. Radio-Frequency Systems MEMS resonators have the potential to be used in RF systems as filters in various locations of the transceiver chain or as oscillator core elements to directly generate RF carriers or generate reference frequencies for LC RF oscillators in RF frequency synthesizers [7,86,330,331]. This is illustrated in Figure 39a, where MEMS resonators could replace the band-select, image-reject, or channel-select filters. They could also be used in the channel-select phase-locked loop as frequency references. The very high quality factor and GHz-range resonant frequencies attainable by MEMS resonators can also allow for receiver architectures that are not possible with other filter technologies. This is illustrated in Figure 39b, where electrostatic MEMS resonators resonating at RF frequencies can be used to filter the channel directly before the low-noise amplifier (LNA) [7,11,332–334]. Moreover, the MEMS resonators can be used as mixer-filters by leveraging their non-linearity to provide tuned carrier down-conversion [333], and the RF local oscillator can be implemented without a phase-locked loop [210]. Besides the inherent area and cost savings, the architecture in Figure 39b can be used to trade off high-Q for power consumption [330] as channel selection directly carried-out at RF yields a substantial advantage: the dynamic range and linearity requirements of the LNA and mixer in the receive path can be reduced. This is because high power interferers can be rejected not only at the band-level but also at the channel-level, only leaving the channel of interest to be amplified. Moreover, an RF-level channel-filter can relax the phase noise requirements of the RF oscillator relative to adjacent channel interferers, as these channels are already attenuated before the down-conversion.

Micromachines 2016, 7, 160 39 of 56

8.4. Radio-Frequency Systems MEMS resonators have the potential to be used in RF systems as filters in various locations of the transceiver chain or as oscillator core elements to directly generate RF carriers or generate reference frequencies for LC RF oscillators in RF frequency synthesizers [7,86,330,331]. This is illustrated in Figure 39a, where MEMS resonators could replace the band-select, image-reject, or channel-select filters. They could also be used in the channel-select phase-locked loop as frequency references. The very high quality factor and GHz-range resonant frequencies attainable by MEMS resonators can also allow for receiver architectures that are not possible with other filter technologies. This is illustrated in Figure 39b, where electrostatic MEMS resonators resonating at RF frequencies can be used to filter the channel directly before the low-noise amplifier (LNA) [7,11,332–334]. Moreover, the MEMS resonators can be used as mixer-filters by leveraging their non-linearity to provide tuned carrier down-conversion [333], and the RF local oscillator can be implemented without a phase-locked loop [210]. Besides the inherent area and cost savings, the architecture in Figure 39b can be used to trade off high-Q for power consumption [330] as channel selection directly carried-out at RF yields a substantial advantage: the dynamic range and linearity requirements of the LNA and mixer in the receive path can be reduced. This is because high power interferers can be rejected not only at the band-level but also at the channel-level, only leaving the channel of interest to be amplified. Moreover, an RF-level channel-filter can relax the phase noise requirements of the RF oscillator relative to adjacent channel interferers, as these channels are already attenuatedMicromachines before 2016, 7,the 160 down-conversion. 39 of 55

I 90º MEMS LNA MEMS MEMS IF resonator-based resonator-based resonator-based amplifier Q band-select filter image-reject filter channel-select filter

Channel select IQ oscillator freq. synth. MEMS MEMS resonator-based resonator-based oscillator oscillator

(a) I MEMS resonator-based mixer-filter 90º LNA IF amplifier Tunable MEMS Q resonator-based RF oscillator IQ oscillator Bias voltage Switchable bank of MEMS MEMS-based resonator-based resonators RF channel oscillator select filters

(b)

FigureFigure 39.39.( a)(a Super-heterodyne) Super-heterodyne architecture architecture with with off-chip off-c componentship components replaced replaced by integrated by integrated MEMS resonators;MEMS resonators; and (b) aand resonator-based (b) a resonator-based receiver receiver architecture. architecture.

With regards to filtering, MEMS resonators can be electrically viewed as bandpass filters with very small bandwidths, having center frequencies determined by their intended resonant mode. MEMS resonators can also be combined in order to create higher order bandpass filters which can potentially be integrated into transceiver front-ends by replacing costly, off-chip, narrow-bandwidth filters. In order to achieve a bandpass filtering function with sufficient bandwidth, MEMS resonators need to be coupled together as their quality factors are generally too high to provide a wide enough bandwidth standalone. This coupling between resonators to achieve the required flat enough passband can be done mechanically (e.g., [86,210,335–338]) using springs, typically implemented through torsional, flexural or extensional beams, or electrically using intrinsic capacitances (e.g., [64,88,141,339]). Band stop filters have also been proposed [338] and wideband filters have also been demonstrated [175]. An obstacle to the deployment of MEMS resonators as filters in RF systems is their insertion losses that can be on the order of several dBs [11], causing too much noise figure degradation if used before the low-noise amplifier. Moreover, the motional resistance of electrostatic MEMS resonators is usually on the order of several kilo ohms, which requires matching networks to be implemented in order to ensure correct filter terminations in 50 Ω RF systems [11]. This can be circumvented by using piezoelectric MEMS resonators (e.g., [64,141,142,340,341]) that can have lower motional resistances on the order of 50 Ω. Moreover, resonator arraying can mitigate the large motional resistance in the case of electrostatic resonators [79]. Other works include a post filter trans-impedance amplifier to increase the signal strength after the filter, at the cost of increased power consumption and no noise figure benefit [337,338]. Regardless of these challenges, piezoelectric bulk acoustic wave (BAW) MEMS resonators have successfully been demonstrated in receivers [15,211] to perform PLL-free frequency synthesis and channel selection at RF.

Micromachines 2016, 7, 160 40 of 56

With regards to filtering, MEMS resonators can be electrically viewed as bandpass filters with very small bandwidths, having center frequencies determined by their intended resonant mode. MEMS resonators can also be combined in order to create higher order bandpass filters which can potentially be integrated into transceiver front-ends by replacing costly, off-chip, narrow-bandwidth filters. In order to achieve a bandpass filtering function with sufficient bandwidth, MEMS resonators need to be coupled together as their quality factors are generally too high to provide a wide enough bandwidth standalone. This coupling between resonators to achieve the required flat enough passband can be done mechanically (e.g., [86,210,335–338]) using springs, typically implemented through torsional, flexural or extensional beams, or electrically using intrinsic capacitances (e.g., [64,88,141,339]). Band stop filters have also been proposed [338] and wideband filters have also been demonstrated [175]. An obstacle to the deployment of MEMS resonators as filters in RF systems is their insertion losses that can be on the order of several dBs [11], causing too much noise figure degradation if used before the low-noise amplifier. Moreover, the motional resistance of electrostatic MEMS resonators is usually on the order of several kilo ohms, which requires matching networks to be implemented in order to ensure correct filter terminations in 50 Ω RF systems [11]. This can be circumvented by using piezoelectric MEMS resonators (e.g., [64,141,142,340,341]) that can have lower motional resistances on the order of 50 Ω. Moreover, resonator arraying can mitigate the large motional resistance in the case of electrostatic resonators [79]. Other works include a post filter trans-impedance amplifier to increase the signal strength after the filter, at the cost of increased power consumption and no noise figure benefit [337,338]. Regardless of these challenges, piezoelectric bulk acoustic wave (BAW) MEMS resonators have successfully been demonstrated in receivers [15,211] to perform PLL-free frequency synthesis and channel selection at RF.

9. Conclusions In this review paper, we have endeavored to illustrate the diversity of progress made in the field of micromachined resonators and the divergence in approaches and applications that have been pursued over the last three decades. We began with a description of the basic model and properties of a generic micromachined resonator as the unifying and starting spring board from which the various key aspects of interest pertaining to resonator design and implementation were subsequently described. We have seen that there exists not only a great diversity in the vibration modes reported in the literature but also a plethora of approaches in the fabrication technology as well as materials. While the field of started off with single-crystal silicon and polysilicon processing dominating the literature, this review has shown the great diversity of process technologies that illustrate the divergence of the field today represented by piezoelectric thin films (e.g., AlN, PZT, ZnO) and bulk materials (e.g., LiNbO3) as well as micromachining in standard CMOS fabrication technology. We have also presented the variety of transduction mechanisms that have been actively employed during the progress of this field in addition to capacitive transduction that was the most common method in the early days of development. This variety of transduction mechanisms includes recent findings suggesting that thermal actuation has a place for actuation in high frequency resonators. While analytical modeling of damping mechanisms remains highly complex and out of reach, numerical methods for capturing specific energy loss mechanisms such as anchor loss have become highly popular among designers. Advancement in the field of microresonators has gone beyond the resonator itself to include interface electronics such as in the case of implementing oscillators. We have described key circuit topologies that have been employed to realize MEMS oscillators, as well as developments in addressing the issue of temperature compensation. With respect to applications, we have shown how resonators constitute key elements in radiofrequency frequency control, sensing (mass and force) and timing references. We envisage that the range of applications for resonators will expand further with increasing advancement in their fabrication, design and analysis. Micromachines 2016, 7, 160 41 of 56

Acknowledgments: This work was supported by a grant from the Hong Kong Research Grants Council under project number CityU 11206115, by grants of the Natural Sciences and Engineering Research Council of Canada (NSERC), and by a grant of the Research Funds of Quebec on Nature and Technologies (FRQNT). Author Contributions: The co-authors contributed equally to the writing of this article. Reza Abdolvand was in charge of Sections5 and6. Behraad Bahreyni was responsible for Sections2,3 and 8.3. Joshua Lee wrote Sections4 and7. Frederic Nabki contributed to Sections 8.1, 8.2 and 8.4. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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