Thin Film Lamb Wave Resonators in Frequency Control and Sensing Applications: A Review Ventsislav Yantchev and Ilia Katardjiev Uppsala University, Dept. Engineering Sciences, Uppsala, Sweden Email
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Abstract— This work makes an overview of the progress made during the last decade with regard to a novel class of piezoelectric microwave devices employing acoustic Lamb waves in micromachined thin film membranes. This class of devices is referred to as either thin film Lamb wave resonators or piezoelectric contour-mode resonators both employing thin film aluminum nitride membranes. These devices are of interest for applications in both frequency control and sensing. High quality factor Lamb wave resonators exhibiting low noise, low loss and thermally stable performance are demonstrated and their application in high resolution gravimetric and pressure sensors further discussed. A specific emphasis is put on the ability of these devices to operate in contact with liquids. Future research directions are further outlined.
in the lower GHz range but is quite sensitive to technological tolerances which limits the development of fully integrated systems. In an attempt to fill this technological gap a new class of micromachined electroacoustic devices employing plate guided waves propagating in micromachined AlN thin film membranes has been recently developed. Electrical excitation of the wave is also achieved, as in the SAW case, by IDTs and hence retains the robustness of the SAW technology. Device fabrication, on the other hand, employs the FBAR technological platform and is hence IC compatible. This unique combination makes the Lamb wave technology an IC compatible alternative to the commercially established SAW technology.
Index Terms— Thin film, Resonator, Oscillator, Sensor, Microwave, Contour-mode
I. INTRODUCTION Microwave electro-acoustics offers unique features in terms of low losses and small form factors for filter applications as well as low noise frequency sources. At the same time this technology enables fabrication of highresolution sensors for chemical, physical and biochemical sensor applications. Two general types of electroacoustic technologies are currently used in commercial application in a concurrent manner. Namely, the thin film bulk acoustic wave resonator (FBAR) technology and the microwave surface acoustic wave (SAW) technology. The FBAR technology employs thin piezoelectric, polycrystalline aluminum nitride (AlN) films on Si substrates which are acoustically isolated from the substrate typically by micromachining (Fig. 1a). The FBAR technology is a planar technology and as such is fully compatible with the IC technology. The SAW technology employs single crystal substrates with high mechanical quality and high electromechanical coupling. Typical examples are LiTaO3 and LiNbO3. The main building blocks of a SAW resonator are the interdigital transducer (IDT) (Fig. 1b) and the reflector gratings (the end gratings of the SAW resonator in Fig. 1b). Both approaches have specific advantages and shortcomings. For example, the SAW technology offers robust designs with low sensitivity to technological tolerances on the one hand while being inherently incompatible with the IC technology on the other because of the use of single crystalline substrates. The FBAR technology is IC compatible and has demonstrated impressive performance
Figure 1. Sketches of common piezoelectric resonator topologies a) FBAR b) SAW resonator The development of the Lamb wave resonator (LWR) technology was initiated about 8 years ago with the demonstration of the first thin film based resonator employing the lowest order symmetric Lamb wave (S0) [1]. Currently the S0 mode in AlN membranes has mostly been explored because of its unique combination of extremely high velocity, low dispersion and moderate piezoelectric coupling. In Figure 2 illustrates the two Lamb wave resonator topologies which only differ in the way the acoustic energy is confined within the cavity. Specifically, the grating type Lamb wave resonators employ reflective gratings (spatially distributed (Bragg)
reflectors) in an identical manner as in most of the SAW resonators (see Figure 1b). The edge type Lamb wave resonators employ reflection from the suspended edges of the membrane (spatially fixed reflectors). Most generally the edge type LWRs are smaller in size as compared to the grating-type LWR. Such a type of reflection was previously employed in some shear SAW resonators [2] as well as in various resonant microelectromechanical systems (MEMS) [3]. Accordingly, the term contourmode-resonators (CMR) is sometimes adopted to specify Lamb wave resonators employing suspended edges [4]. For simplicity, Lamb wave resonators will be referred to in this work as grating-type and edge-type LWR, respectively.
type is the so called shear acoustic plate modes which exhibits a shear or quasi-shear polarization. In here, focus is primarily on Lamb waves.. Generally, the plate supports a number of these waves depending on the plate thickness to acoustic wavelength ratio. Each type of plate waves consists of two different modes. These are the symmetric and the asymmetric modes respectively indicating the symmetry of the particle displacements associated with the wave relative the median plane of the plate (see Figure 3). For simplicity the different plate modes are denoted with symbols. Thus the nth order symmetric Lamb wave is denoted as Sn, while the nth order asymmetric Lamb wave is denoted as An, where ”n” is an integer ranging from 0 to infinity and represent the number of standing waves along the plate thickness. In this context, a Lamb wave has two characteristic wavelengths, one along the plate thickness and another along the plate surface. Throughout this overview we will refer only to the latter one and denote it by λ.
Figure 3. Lamb acoustic modes
Figure 2. Sketches of Lamb wave resonator topologies employing a) Grating reflectors b) Edge reflectors Most of the experimental data presented here refers to a specific set of LWR design parameters. These are AlN film thickness d=2μm and acoustic wavelength λ=12 μm. The demonstrated characteristics are found in a good agreement with the results obtained independently by other researchers, thus revealing the underlying Lamb wave properties which in turn determine the observed performance improvements.
II. THE LOWEST ORDER SYMMETRIC LAMB WAVE (S0) The AlN membrane, usually employed in FBARs itself represents a plate in which laterally propagating plate modes are allowed. Most generally, the plate waves are divided into two groups with respect to the acoustic wave polarization. The first type is the so called Lamb waves which exhibit an elliptical polarization while the second
Figure 4. Theoretical dispersion presented in coordinates normalized to the wavelength λ and the shear velocity V S. Figure 4 shows the typical dispersion of the first few Lamb modes in c-textured AlN as a function of the relative plate thickness d/λ. Unlike their first order counterparts the zero-th order symmetric and asymmetric Lamb waves do not exhibit critical “cut-off” frequencies at zero wavenumber (infinite λ). More specifically, the
lowest order symmetric Lamb wave S0 demonstrates an almost linear dependence of frequency for small values of the relative membrane thickness. In other words the S0 mode exhibits a low velocity dispersion when propagating in acoustically thin membranes. It should be noted that the cut-off frequencies of the A1 and S1 modes coincide with the fundamental resonance frequency of the thickness excited shear and longitudinal modes, respectively. Thus, the S1 Lamb wave represents a more general “2D-wavenumber” presentation of the one dimensional thickness excited FBAR mode. At the cutoff frequency, the mode has an infinite λ, which represents exactly the thickness excited mode.
resonators less sensitive to AlN technological thickness tolerances, while enables the elimination the frequency sensitivity towards small variations in transducer electrodes thickness [9]. Further, the electromechanical couplings achievable in the low dispersion region are of the order of up to 3%. In Figure 5(b), the electromechanical couplings of two basic types of transducers are shown. Here, the electromechanical coupling is defined as twice the fractional change of the velocity of the S0 mode propagating under electrically open and shorted top surface, respectively. The dashed line represents the electromechanical coupling corresponding to excitation with a standard IDT, while the dotted line represents the electromechanical coupling to an IDT transducer with an additional bottom electrode. In the latter case, the electric field is confined predominantly in the vertical direction, thus giving rise to lateral field excitation (LFE) of the longitudinal wave (LW) polarization through the e31 piezoelectric coefficient. III. S0 MODE LAMB WAVE RESONATORS A. LWR Design and Microfabrication As mentioned above LWRs are classified in the way the energy is confined but also they can be classified in accordance to the transducer topology used. Three major transducer topologies are used as shown in right corner of Figure 6.
Figure 5. Calculated characteristics of the S0 Lamb wave in c-oriented AlN: (a) acoustic wave velocity and (b) electromechanical couplings. Unlike the FBAR, LWRs are mostly employing the lowest order symmetric Lamb wave S0. The physical characteristics that make the lowest order Lamb wave attractive for practical use are the possibility of employing simultaneously high velocity, weak dispersion, and moderate electromechanical couplings [5], as also predicted theoretically using the Adler’s matrix approach [6] and Green’s function formalism [7, 8]. In Figure 5(a), the calculated dependence of the acoustic velocity on the AlN film thickness for the lowest symmetric Lamb mode (S0) in a thin c-oriented AlN membrane is shown. Clearly the S0 mode exhibits low dispersion for a membrane thickness d smaller than 0.4λ where λ is the acoustic wavelength, offering at the same time an acoustic wave velocity of up to around 10000 m/s. This unique feature makes the Lamb wave
Figure 6. Calculated harmonic admittances of common LWR transducer configurations. These are respectively an IDT over floating bottom electrode, a longitudinal wave (LW) transducer formed by a periodic array of a half wavelength wide metal strips over grounded bottom electrode, and a classical IDT configuration. In Figure 6 the harmonic admittances of each transducer configuration is shown for the case of d/λ=0.1 as calculated with COMSOL finite element frequency response analysis (FEA). The fractional frequency shift between the resonance fR and the antiresonance fA is related to the effective transducer coupling kEFF2=0.25π(fR-fA)/fR. Evidently, the IDT/floating electrode transducer offers a much higher
transduction coefficient at relatively small platethickness-to-wavelength ratios. Thus, the use of a given transducer architecture is application specific. If stronger electromechanical couplings are pursued, the IDT /floating electrode configuration is to be preferred [10], since the maximum achievable effective device coupling in this case approaches 3.5% (see in Figure 6). On the other hand LWRs with reduced technological complexity employ classical IDTs at the expense of reduced effective transducer couplings. The LW transducer could be advantageous when the resonant frequency of the first order asymmetric Lamb wave A1 is close to the resonance frequency of the S0 Lamb mode since LW transducers on c-textured AlN do not couple to anti-symmetric Lamb waves. Most generally, the device technology resembles to a very large extent the FBAR technology. The devices are typically fabricated on a micromachined free-standing AlN membrane. In the specific case of edge type LWRs suspended edges of the AlN membrane are additionally formed by etching the AlN employing a SiO2 hard mask to ensure vertical edges with fine quality. Here we illustrate the general process flow of such a device including also an electrical contact to the bottom electrode. All other configurations require a reduced number of lithographic steps and processes.
of the (002) X-ray rocking curve should be bellow 2˚ to ensure good material properties of the active layer. Contact via-holes through the AlN film are then dry etched by reactive ion etching (RIE) (see Fig. 7c). Thick contact metallization pads are subsequently formed on top of the AlN (see Fig. 7d). The top electrodes are defined by a standard deposition/lithography/dry etch steps (see Fig. 7e). Finally, the Lamb wave devices are acoustically isolated from the supporting Si substrate by etching the Si substrate from the backside using a standard, three-step, dry etch Bosch process (see Fig. 7f). Alternatively, surface micromachining can be employed as in FBARs. Note that the fabrication of IDT-based LWRs needs only the last three of the above six lithographic steps.
Figure 7. LWR micromachining. a) Bottom electrode b) Etch stop c) Via holes d) Contact pads e) Top electrodes f) micromachining of the substrate. As a supporting substrate, a Si wafer is used. After cleaning the substrate, a thin metal film is sputter deposited, then patterned (see Fig. 7a). This structure serves as a bottom electrode of the LWR and should be continuous throughout the device to eliminate macrodefects evolving from the electrode edges. Subsequently, an etch stop layer is grown, and subsequently a 1-2 μm thick c-textured AlN film having a slightly tensile stress is deposited by reactive sputtering onto the bottom electrode ( See Fig. 7b). The full width at half maximum
Figure 8. Top view of the fabricated devices. a) IDTbased LWR. b) LW-Transducer based LWR. Figure 8 represents a top view of grating types oneport LWRs as fabricated, employing both classical IDTs and LW transducers respectively. Specifically, S0 Lamb
waves with a 12 μm central wavelength are excited in 2 μm thick AlN membrane. The central wavelength is defined by the 6-μm pitch of the reflecting grating used in the LWRs. The thickness of the Al strips is 300 nm and the reflecting gratings have 50–60 aluminum strips. More specifically, the IDT-based WLR (see Fig. 8a) consists of 53 reflecting strips in each reflective grating, 79 strips in the IDT, and a 40 wavelengths aperture. The LW transducer based LWRs (see Fig. 8b) consists of 62 reflecting strips in each reflector, 30 half-wavelength wide strips forming the LW transducer and a 30 wavelengths aperture. The Al bottom electrode (see Fig. 7f) has a thickness of 300 nm. B. Performance of LWR Both edge type and grating type LWR have demonstrated comparable performances at similar frequencies Table I summarizes the results regarding the Qxf product achieved by various research groups. TABLE I. LWR Q FACTORS
LWR topology Resonant Frequency Edge type (CMR) [11] 1.17GHz Biconvex Edge type [12] 591.8MHz Grating type [13] 884MHz
electrode topology is preferred because of its higher effective coupling [10]. Classical IDT based 900 MHz LWRs have demonstrated an input admittance at resonance as low as 20Ω while the LW transducer based 900 MHZ LWR have demonstrated an input admittance at resonance as low as 7 Ω [13]. Figure 9 illustrates the performance of a high Q grating type one-port LWR employing classical IDT. This specific design uses a quarter wavelength shift introduced inside the regular electrode IDT (hiccup geometry), while the grating reflectors are placed synchronously around the IDT. More specifically, the fabricated device (similar in topology to that in Figure 8a) employs a 2 μm thick AlN membrane, has a central wavelength λ=12μm, 50λ-wide aperture, reflectors consisting of 62 strips, and an IDT consisting of 62 electrodes with an internal gap of 2.25λ. The Q factor of the LWR considered is determined through the phase slope of the impedance as Q=0.5·f·∂φZ/∂f. The measured device Q at resonant frequency approaches 3000 at a frequency of about 875 MHz.
Q Factor 2200 3280 3100
Q factors of about 3000 at a frequency of about 900MHz have been demonstrated determining a Qxf product of about 2.7 1012 Hz [14]. Further improvements are still feasible by reducing, for example, acoustic leakage through wave diffraction. A significant increase of this figure in edge-type LWRs can be achieved by reducing wave coupling to the supporting beams through bi-convex reflecting edges [12] or acoustic isolation of the supported beams [3]. Initial experimental data have demonstrated Q.f=4.6 1012 Hz at 4.7GHz [15] i.e scaling of this product with operation frequency. The possibility to scale Q.f product with frequency should be further studied.
Figure 9. Close-to-resonance characteristics of 12-μm wavelength WLR employing a “hiccup” geometry. The input impedance of the LWRs can easily be tailored for each transducer type through the number of strips in the transducers and the transducer aperture. When low impedances at resonance are required the IDT/floating
Figure 10. A 12-μm wavelength 2-port LWR. a) top view as fabricated b) Close-to-resonance S21 measurement
LWR maximum effective device coupling of about 2% has been demonstrated [16] although the IDT/Floating electrode configuration enables effective device couplings of up to 3.5%. Accordingly, LWRs having Qxf products in excess of 3x1012 Hz and electromechanical couplings of about 3% are feasible in the lower GHz frequency range. Another common LWR topology is the 2-port LWR which inherits the topology of the 2-port SAW resonators. Such LWR types can be used, for example, in low-noise integrated feedback loop oscillators (FLO) [17] or as integrated narrowband coupled-resonator filters [18]. Figure 10 shows a 2-port 12μm wavelength LWR as fabricated along with its close-to-resonance response. The response shown in Fig. 10b corresponds to a device employing a 2 μm thick AlN membrane with central wavelength λ=12μm, 41 strips in each IDT and 52 strips in the reflectors, a cavity length L =1.125λ and an aperture of 50λ. The device has an insertion loss of IL = 3.87 dB, a loaded QL = πfτ (f = frequency, τ = group delay) of 1110, and a corresponding unloaded Q U = QL/(1-10−IL/20) of 3150 at 885.7MHz resonance frequency. The demonstrated QU.f product of 2.79 1012 Hz is comparable to the Q.f products demonstrated by the one-port LWRs. C. Analysis of LWR The design of LWRs with given specifications requires the development of adequate analytical tools. The physical models commonly used in SAW analysis are found applicable to the analysis of LWRs. The LWR response can be roughly estimated by a 1D Mason network model [19] assuming a 1D nature of the propagating mode. The Mason model is among the simplest and has found broad application in the analysis of both FBAR and SAW resonant devices although with a limited accuracy. Accordingly, 2D models which take into account the Lamb wave energy distribution across the membrane thickness were shown to be more accurate [20,21]. Specifically, the Coupling-of-Modes (COM) theory has shown excellent agreement with experiment [22]. Most generally, COM is a phenomenological model for guided wave propagation and excitation, which is widely employed for the design of high-performance SAW devices [23, 24]. The analysis based on the COM model gives very simple and analytical solutions with a surprisingly good accuracy provided that the COM parameters are properly determined. The COM model has been used with success to describe also dispersive SAWs in layered structures [25] as well as Leaky SAWs [24]. In comparison to the latter, the S0 Lamb wave demonstrates weak dispersion and well-defined waveguiding. Conversion losses induced by reflection are known to be suppressed in acoustically thin plates, thus presuming relative simplicity of the loss mechanisms. This specific feature made possible the design of high-Q contourextensional-mode resonators employing free-edge reflections [26, 27]. Accordingly, the use of the COM approach toward the analysis of S0 Lamb wave FPARs seems convincingly justified.
The COM equations used in this study are [24]:
dR ( x ) jR ( x ) jk 12S( x ) jV dx dS( x ) , jk 12R ( x ) jS( x ) jV dx dI( x ) 2 jR ( x ) 2 jS( x ) jCV dx
(1)
where R(x) and S(x) are slowly varying fields describing the amplitudes of the forward and the backward propagating modes, k12 is the COM reflectivity parameter, α is the COM transduction coefficient, C is the transducer capacitance per unit length, V is the applied voltage and δ=ω/V(ω)-(π/p)-jγ is a detuning parameter describing the effects of the unperturbed velocity dispersion and the propagation losses induced by the material viscosity and the wave diffraction. Here ω is the angular frequency, V(ω) is the dispersive unperturbed velocity, p=λ/2 is the grating pitch and γ is the acoustic attenuation. For convenience here we present the COM parameters described above in a normalized fashion: • k P k12 - dimensionless reflectivity per finger pair; • VS0 – S0 Lamb wave unperturbed velocity in AlN at central frequency ; • n - normalized COM transduction coefficient,
, where W is the device aperture; W / • P 0 – attenuation per wavelength [Np/λ];
n
• D — dimensionless velocity ( V ( ) VS 0 (1 D( 0 ) / 0 ) )
dispersion
• Cn - Normalized Capacitance Cn C0 / W [F/m] (per IDT pair, per unit aperture).
Figure 11. Measured vs COM-fitted LWR admittance To demonstrate the applicability of the COM approach, we first extract the COM parameters by fitting to the close-in-resonance response of a 12μm wavelength synchronous one-port FPAR (identical to the one shown in Figure 8a). The experimental curves (solid lines) in Figure 11 are fitted to the COM model (dashed lines) by means of least squares fitting. Table II shows the values
of the COM parameters extracted from the fitting procedure in Figure 11. These parameters can alternatively be theoretically deduced by modal and Green’s function analyses as discussed elsewhere [20,22]. The agreement between theory and experiment was found excellent. To further demonstrate the applicability of the COM approach, the extracted parameters are used in the analysis of the 2-port LWR shown in Figure 10. The simulated COM frequency response is shown in Figure 12. The result is in a very good agreement with the experimental response in Figure 10. TABLE II. VALUES OF THE EXTRACTED COM PARAMETERS
Layout: 2μm thick AlN, 270nm thick Al electrodes, λ=12μm COM Parameters: Value S0 unperturbed velocity (VS0 [m/s]) 10435.05 Velocity dispersion (D) 3.5·10-2 Normalized Reflection Coefficient (kP) 16.5 ·10 -2 Normalized Capacitance (Cn [pF/m]) 81.9 Normalized Transduction Coefficient (αn [Ω-1/2]) 13.3 ·10-5 Attenuation (γP [Np/λ]) 9.48 ·10-4 Parasitic Electrical Resistance (RS [Ω]) 1.81
function analyses. FEA can be used also to accurately deduce the COM parameters in view of improving their accuracy. In its 3D form FEA is found a quite useful tool especially for the edge-type LWRs because of their generally smaller dimensions. Grating type LWRs can also be simulated in 3D but require increased computer power. IV. LWR STABILIZED OSCILLATORS IC compatibility and integration of S0 Lamb wave resonators has been successfully demonstrated in system on-chip frequency references [11]. Currently, the thin film Lamb wave technology allows easy integration of high-Q acoustic resonators on Si for oscillators with a low close-in phase noise. Lamb wave based oscillators in the frequency band 200MHz – 1GHz have shown a phase noise of about -90 dBc/Hz at 1 kHz offset frequency independently on the LWR topology used. Close-in phase noise of various LWR based oscillators are summarized in Table III. TABLE III. PHASE NOISE AT 1KHZ OFFSET
LWR topology Central Frequency Noise [dBc/Hz] Edge type (CMR) 222MHz -88 [16] Edge type (CMR) 483MHz -88 [29] Edge type (CMR) 583MHz -93 [30] Grating type 888MHz -92 [31] Edge type (CMR) 1.05GHz -81 [11]
The thermal noise floor (TNF) in these resonators is dependent to a very large extent on the LWR power handling abilities. Most generally, TNF is a function of the loop power P0, the overall loop loss G and the noise figure (NF) of the sustaining amplifier as follows [32]: TNF [dBc/Hz] = −174 − P0 + NF + G. Figure 12. Calculated COM response of a 12-μm wavelength 2-port LWR. It is further noted the ability to extend the method towards the analysis of edge type LWRs utilizing multiwavelength transducers and free edge reflections. In such structures the periodic transducer can be analyzed through the COM model including charge distribution and propagation effects, while the reflection from the suspended membrane edges can be defined by their amplitude and phase [21]. Last but not the least the COM approach has been developed to also account for the specific waveguiding in transversal direction, i.e. assuming changing wave amplitude along the device aperture [28]. Thus, the COM approach provides an opportunity to analytically describe LWR in a 3D fashion, which seems to be beneficial especially for the design of edge type LWRs. Recently, finite element analysis (FEA) has also been applied to the analysis of SAW, FBAR and LWR devices. In a 2D approximation FEA agrees very well with the 2D analytical techniques employing COM and Green’s
(2)
Thus oscillators with higher power in the loop demonstrate lower TNF provided that the LWR can sustain sufficiently high powers. This can be achieved by making the device area sufficiently large while providing efficient heat dissipation at the same time. It is noted that AlN is a material with high thermal conductivity which allows for efficient heat dissipation. In this respect the use of beam supporters (in edge type LWRs) must be avoided. Instead, only two, instead of four, free-standing edges may be utilized, as suggested earlier [33] In this way the heat can dissipate through the complete device length unlike the case of edge type LWRs employing beam supporters. Here we discuss the specific realization of a grating type LWR stabilized clock in the 900 MHz range running at up to 27 dBm (0,5W) loop power and exhibiting a phase noise of –92dBc/Hz at 1 kHz [31]. The close-in phase noise 1Hz intercept point of the oscillator was measured as £(1Hz )=-2dBc/Hz which was then used to determine the LWR flicker noise constant αR=2.1 10-36/Hz [34]. This value is comparable with some of the best SAW resonators built to date and suggests that
the LWR technology is a low noise one. This conclusion has been further supported by an independent study where a 222MHz edge-type LWR has demonstrated a phase-noise as low as -110dBc/Hz at 1kHz offset [16]. The two-port LWR shown in Figure 10 is connected in a feedback oscillator loop, as shown in Figure 13, with a sustaining RF amplifier capable of generating 27 dBm (0.5 W) of RF power at the 880 MHz resonant frequency. In this power oscillator configuration the FPARs were operated at an incident power level of 24 dBm (250 mW) for five weeks [34]. The power dissipated resulted in a o moderate temperature increase of about 6-7 K. An inspection under an optical microscope and a detailed analysis of their electrical characteristics prior to and after the power test did not show any measurable performance degradation or any evidence of electromigration and ageing effects..
irreversible degradation due to acoustically induced migration at stress peak levels exceeding 6·107N/m2 [20]. In the same experiment, SAW resonators on Quartz using a similar geometry would fail within a few seconds at a power of 24 dBm as a result of metal electro-migration in the transducer electrode structure.
Figure 14. WLR vibration mode at resonance The demonstrated high power handling of the S0 LWR is attributed to the favorable combination between the specific mode of vibration (see Figure 14), where the deformation is symmetric within the electrodes resulting in a zero net momentum induced in them, and the high thermal conductivity of the AlN. V. LWR THERMAL STABILITY
Figure 13. Block and level diagram of the power oscillator loop The feasible TNF=-186dBc/Hz that can be achieved in this configuration has been estimated by eq. 2 taking into account the experimentally obtained loop power P 0=27 dBm, the overall loop loss G = 8 dB (5 dB loss in the two-port LWR used and 3 dB output coupler loss) and the noise figure of the sustaining amplifier NF=7 dB. The LWR driving power level Pd=250mW can be further related to the longitudinal peak stress
LWR are appicable in low noise frequency sources and low loss narrow band filters with 3-dB bandwidth of up to about 3%. Both applications require compenstion of the thermal drift. LWR typically exhibit a teperature coefficient of frequency (TCF) of about -23ppm [14] which requires the development of a specific temeprature compensation scheme. Here we discuss LWR toplogies with intrinsic zero first order TCF. In the proposed designs composite membranes consisting of reactively sputtered AlN and thermally grown SiO2 are used as a platform for the design of temperature compensated LWR since the two materials exhibit opposite TCF [36-38]. A schematic view of a grating type LWR employing such a composite membrane is illustrated in Figure 15.
T11 P through a relatively simple one dimensional model, initially introduced to describe the stress levels in SAW resonators [35]. It is further noted that the S0 mode can be treated as one-dimensional with a sufficient accuracy when propagating in acoustically thin plates. Accordingly, the peak stress is given by [31]:
T11 P J m QU Pd /( L.W )
(3)
where J m V / / d 3310 / d , ρ is the AlN mass density, V is the S0 phase velocity, λ the acoustic wavelength, QU is the unloaded Q, L is the effective resonant cavity length and W is the effective cavity width determined by the profile of the fundamental waveguiding mode as W=3W0/8 (W0 – device aperture). Accordingly the peak stress level
T11 P in the WLR
operating at 250mw drive power is found to exceed 3·108N/m2. It is noted that Rayleigh SAW quartz resonators with pure aluminum metallization show
Figure 15. Topology of a thermally compensated LWR The TCF of the S0 mode in such composite structures is readily derived theoretically[36,37] as illustrated in Figure 16. Specifically, the TCF, defined as the relative frequency change per 1K of temperature variation, is shown as a function of the relative SiO2 layer thickness for different relative thicknesses of the AlN. It is noted that thicknesses are normalized with respect to the acoustic wavelength (λ) at room temperature as defined from the transducer grating pitch. The relative AlN thickness of interest lies in the range where the S0 mode exhibits low dispersion. In this specific range of AlN acoustic thicknesses temperature compensation can be
achieved with SiO2 of thicknesses smaller than that of the AlN. It is also noted the wide applicability of the results obtained with respect to the frequency of operation required. For a desired frequency of operation the optimal AlN/SiO2 combination is to be chosen among the range of solutions shown in Figure 16. From those solutions, the one that offers a reasonable trade-off between electromechanical coupling and robustness of fabrication is to be chosen.
Figure 16. Temperature coefficient of frequency as function of the SiO2 thickness for AlN plate of varying thicknesses relative to the wavelength (λ). Practical realizations of the proposed scheme were demonstrated for both type of topologies. It was further observed that the second order TCF2 tends to decrease with the thickness of the composite membrane. Thus, compensated LWR demonstrated a second order TCF2 of about -31ppb/K2 and -22ppb/K2, when employing AlN thicknesses of d=0.167λ [36] and d=0.09λ [37], respectivelly (see Figure 16). For comparison, the second order TCF2 demonstrated is slightly larger than that for temperature compensated AlN FBAR (TCF2= 20ppb/K2) [39] but smaller than that for Rayleigh SAWs on ST-cut quartz (TCF2=-34ppb/K2) [40].
where σY(τ)min is the minimum Allan deviation [41], while S is the normalized sensitivity defined as the fractional frequency variation per unit increment of the measurand M (S=Δf/(f·ΔM)). Here, M denotes any physical quantity being measured, for instance mass, pressure, temperature, etc. The theoretical limit of the LWR noise floor can be estimated by the Q factor through the empirical relation σY(τ)min=10-7/Q [42]. Thus, a LWR with a Q factor of about 1000 could demonstrate a noise floor down to 10-10. Practically achievable noise floors are larger, i.e in the range of 10-9 which makes the LWR technology comparable, in noise floor, to the commercially established SAW. A good SAW sensor exhibits a short term stability of about 5·10-9/s [43]. Accordingly, a sufficient improvement over the state of art of the sensor resolution is most likely to be achieved by improvements in sensitivity while preserving the LWR low noise performance. Bellow we summarize the sensitivity performance of the LWR with respect to pressure, mass and liquid loadings, respectively. A. LWR Pressure Sensors The use of a high aspect ratio membrane itself promotes higher stress levels in the membrane and thus an improved sensitivity to pressure. Grating type LWR configurations typically employ about 2μm thick AlN membrane with area of about 0.5mm2. The pressure sensitivity can be further scaled by improving the aspect ratio of the membrane – either by reducing the membrane thickness or by increase of the membrane area. Further, the S0 mode has been shown to be more sensitive than all other modes in the AlN membranes [44] making it a preferable choice when developing a high resolution pressure sensors. It is also noted that due to the low losses LWR as well as their SAW and BAW counterparts are well suited for low power wireless interrogation[45] thus making these devices preferable in remote sensing applications.
VI. LWR AS SENSORS As discussed above, the LWR technology offers robust thermal compensation along with low noise performance. Further, the specific membrane configuration (see Figure 2a) enables physical separation between the analyte and the transducer in e.g. biosensor applications. This feature is specifically advantageous when operation with liquid or aggressive environments is required. The specific advances regarding the use of the LWR platform in sensing applications should be considered through the possibility to achieve increased resolution as compared to the other alternative micro-acoustic technologies, namely SAW and FBAR. The resolution R is represented by
R
3 Y ( ) min , S
(4)
Figure 17. LWR Pressure sensitivity as a function of pressure differential Figure 17 shows the pressure sensitivity of a 900MHz S0 grating type LWR as measured experimentally. The device is a synchronous LWR with a 12 μm wavelength
employing a 2 μm thick AlN membrane having a 0.55mm2 surface area [44]. The measured fractional sensitivity of the S0 mode is found in excess of 6ppm/kPa. The LWR was measured in pressure differentials of up to 160kPa and have shown a hysteresis-free performance with good linearity and no degradation with time [44, 46]. B. LWR GrvimetricSensors The S0 Lamb wave platform appeared to be much more mass sensitive as compared to its SAW and FBAR counterparts [47, 48]. A common way to estimate the mass sensitivity is through the relative frequency shift caused by mass loading with thin layers. Figure 18 shows the calculated magnitude of the fractional frequency shifts as a function of the relative thickness h/λ of a mass-loading, glassy state polymer pp-HMDSO (plasma polymerized hexamethyl di-siloxane) for the four different cases, a S0 LRW and an FBAR both employing AlN membranes as well as the Love wave and SAW resonators both employing commercial AT cut Quartz substrates. In this specific calculation the relative membrane thickness d/λ for the S0 mode case is 0.166.
increases with the thickness of the sensing layer. This beneficial effect is in practice inhibited by the viscosity of the sensing layer. At relatively thicker sensing layers the S0 mode also exhibits an improved damping which in turn results in LWR performance degradation in terms of losses and, hence, Q factor. Figure 19 shows the S0 mode mass sensitivity taking into account the viscosity of the thin sensing layer. A very good agreement between theory and experiment is demonstrated. The gas sensitivity of a HMDSO coated LWR towards Xylene was measured and compared to that of Rayleigh SAW and Surface Transverse Wave (STW) Quartz resonators covered with the same sensing layer. The sensing mechanism in this study is mass-loading caused by the adsorption of the gas molecules onto the HMDSO surface. Table IV summarizes the calculated mass sensitivities of the three types of resonators towards Xylene. In order to compare the sensitivity values to the theoretical estimates, the relative sensitivity towards Xylene, defined as the ratio of the absolute sensitivity (in Hz/ppm) to the unloaded resonance frequency, was calculated for LRW, STW and SAW respectively. These sensitivities were found to be in relation 5.0/1.3/1.0 for LWR vs. STW vs. SAW, respectively, which is in good agreement with the theoretical expectations.
Figure 18. Theoretical mass sensitivity of S0 Lamb wave, BAW, Love wave, SAW and Love wave. Although mass loading causes a frequency downshift, absolute values are presented to underline the increase of sensitivity Evidently, the S0 mode demonstrates a considerably higher mass sensitivity as compared to the FBAR, RSAW and Love waves. This is explained by the fact that the S0 Lamb wave is typically confined in membranes with a smaller thickness to wavelength ratio (d/λ~0.1–0.2) as compared to the classical FBAR where d/λ=0.5 and to the SAWs where the depth of energy confinement is in the range of one wavelength d/λ~1. Therefore, sensitivity can easily be scaled by varying the membrane thickness [49]. However, an increased sensitivity may not necessarily be the best choice for a practical system. Generally, an improved mass sensitivity correlates with greater susceptibility to losses induced by the viscosity of the sensing layer [50]. This in turn deteriorates the noise performance and thus limits the sensor resolution. Figure 18 further suggests that mass sensitivity of the S0 mode
Figure 19. Experimental vs calculated LWR mass sensitivity as a function of the relative thickness h/λ of the HMDSO sensing layer. Layer losses are taken into account in the calculations through complex elastic constants C=C’+i*C”. TABLE IV. SENSITIVITY TO XYLENE OF HMDSO COATED RESONATORS
Mode SAW on Quartz STW on Quartz LWR on AlN
Frequency 430MHz 700MHz 890MHz
Sensitivity [Hz/ppm] 7.2 [51] 9.1 [51] 33 [47]
The results presented suggest that S0 mode resonators employing acoustically thinner sensing films are preferable in order to preserve the low noise and low loss
performance of the sensor [47] while benefitting from the improved sensitivity of the LWR technology. Most generally, the design of a gravimetric sensor employing the S0 Lamb wave in thin AlN membranes is application specific. Resolution, exceeding that of the other competing microacoustic technologies, is quite feasible. The design of high resolution sensor requires an optimal ratio between increased sensitivity and added noise by both the viscosity of the sensing layer and the analyte [47]. C. LWR In-Liquid Sensors In contact with a liquid the S0 mode couples weakly to the liquid due to its predominantly longitudinal polarization parallel to the plate surface. A small coupling to the liquid is induced by the weak vertical shear component of the S0 mode and by the shear viscosity stress gradient which is more pronounced in liquids with increased viscosity [52]. The observed frequency shift is mostly due to changes in the electric permittivity of the liquid and changes in the acoustic impedance of the liquid [46]. The S0 mode can be used as complementary to shear mode liquid sensors. Recently, a bio-chemical sensor employing the S0 Lamb wave in a thin GaN membrane has been demonstrated showing weak susceptibility to water and high mass sensitivity [53]. To further clarify the sensing mechanisms of LWR immersed in a liquid we used a frequency response finite element method analysis (COMSOL) to calculate the harmonic admittance of the LWR as a function of the dielectric and the acoustic loads caused by the liquid. The results obtained are then used to explain the experimental observations as follows. Figures 20a,b show the harmonic admittance of a LWR unit cell (an IDT pair of electrodes with applied periodic boundary conditions) calculated by means of COMSOL Multiphysics FEM frequency response analysis. Three physical modules, namely the piezoelectric strain module, the acoustic-structure interaction module and the quasistatic electric module, are simultaneously used in a complementary manner to describe the phenomena involved. The first module is used to describe the excitation of a 12 μm wavelength S0 mode in 2μm thick AlN membrane and is further coupled to the other two modules to describe acoustic and electric couplings to the liquid. The electrical condition at the bottom membrane surface is assumed to be that of an open electrical circuit. Figure 20a presents the effect of the acoustic loading by the liquid. The harmonic admittances are calculated assuming outside media having the dielectric permittivity of the water. The acoustic loading is simulated by coupling and decoupling the fluid-structure interaction module. It is seen that the admittance amplitude decreases significantly with the loading while the resonance frequency remains almost unaffected. The observed behavior is due to the acoustic radiation in liquid (shown in Figure 20a in terms of square root of the pressure) Figure 20b presents the effect of electrical loading by varying the dielectric permittivity of the liquid while the liquid acoustic properties are considered identical to those of water. An increase of the resonance frequency with
dielectric permittivity is observed while the amplitude of the response slightly drops. The latter is associated with the effective decrease of electromechanical coupling to the S0 mode since a significant part of the electric energy penetrates in to the liquid and does not contribute to wave excitation. By the same token, initial increase of the dielectric permittivity above the vacuum level causes an improvement in the vertical alignment of the electric field, which in turn promotes higher electromechanical coupling through the e31 piezoelectric coefficient.
Figure 20. COMSOL FEM Simulations a) Acoustic Loading b) Electric Loading A 12 μm wavelength LWR, identical to the one used in the pressure sensitivity study, in contact with liquid by dispensing a droplet on the membrane backside has been characterized with a Network Analyser [46]. The measurements indicate that the S0 mode has a performance comparable to that of the state of the art FBAR bio-sensors[54]. Figure 21 shows the measured S0-mode LWR responses, demonstrating Q-values of 1700 (in air), 150 (in water) and 70 (in 50% glycerol water solution), respectively. An initial 9.2 MHz (from air to water) and an additional 1.3MHz (from water to
50% glycerol solution) frequency shifts were observed. Further, the FPAR static capacitance increases by about 40% due to the dielectric permittivity of the water.
Figure 21. FPAR in-liquid performance The large frequency downshift between air and water is primarily due to the large dielectric permittivity of water, while the contribution of the acoustic loading remains negligibly small. The acoustic loading in this case is mostly manifested by the moderate decrease of the LWR Q factor. The response of the LWR immersed in 50% glycerol solution is affected by the relative decrease of the liquid permittivity and the increase of the liquid acoustic impedance along with its viscosity. Using the developed COMSOL-multphysics model we have estimated theoretically that the decrease of the dielectric permittivity causes about -840ppm frequency shift, while the change in the acoustic impedance causes about 360ppm frequency shift. Thus, the total frequency shift is expected to be about -1200ppm. Experimentally we have observed a frequency shift of about -1485ppm which is in a very good agreement with the theoretical prediction. The subsequent decrease of the Q factor is explained by the improved acoustic coupling to the fluid due to increase of both the acoustic impedance and the viscosity of the fluid. In summary, the LWR technology is sensitive to both the mechanical and the dielectric properties of the liquid. A LWR design with metalized bottom side of the membrane would electrically isolate the WLR from the liquid (making the device sensitive to the liquid mechanical properties only) as well as further improve the electromechanical coupling, resulting in higher inliquid performance. Thus, LWR designs with Au backside metallization seem to be a promising candidate for biosensor applications. VII. CONCLUSIONS In summary the LWR technology has demonstrated a number of unique features stemming from the nature of the S0 Lamb wave propagating in silicon micromachined AlN membranes. These are as follow: Technologically compatible with IC; Very high velocity at low dispersion;
Moderate electromechanical coupling ≤3%; Low loss and low noise performance; Robust first order temperature compensation with a low second order temperature coefficient of frequency; Highly sensitive to mass and pressure. Sensitivity is inversely proportional to the membrane thickness; Able to operate in liquids, highly sensitive to liquid permittivity; LWR technology continues to develop simultaneously in several directions. The AlN/Si LWR platform is further developed employing AlN/SiC composite membranes aiming at increasing the device Q [55]. Other Lamb waves and principles of energy confinement are under investigation. Recently LWR employing other principles than reflection were demonstrated in proof of concept studies [56,57]. More specifically, these include the employment of the zero group velocity characteristic of the S1 Lamb wave as well as the conversion of the S0 mode into the fundamental thickness shear plate resonance. Further, new piezoelectric thin films[58] with increased piezoelectricity and retained mechanical quality are being employed towards boosting the electromechanical coupling and thus the bandwidths of the LWR based filters. Promising materials candidates are the Sc doped AlN films, and LiNbO3 thin plates released by means of smart cut technology. ACKNOWLEDGMENT This work was supported by the Swedish Research Council (VR) through the Forskarassistent grant "Thin Film Guided Microacoustic Waves in Periodical Systems: Theory and Applications" REFERENCES [1] Bjurstrom J, Katardjiev I, Yantchev V 2005 Lateral-fieldexcited thin film Lamb wave resonator Appl. Phys. Lett. 86 154103 [2] Kadota M, Ago J, Horiuchi H, Ikeura M 2002 Very small IF resonator filters using reflection of shear horizontal wave at free edges of substrate IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 49 1269-1279 [3] Harrington B P and Abdolvand R 2011 In-plane acoustic reflectors for reducing effective anchor loss in lateral– extensional MEMS resonators J. Micromech. Microeng. 21 085021 [4] Stephanou P J and Pisano A P GHz Contour Extensional Mode Aluminum Nitride MEMS Resonators Proc. 2006 IEEE Int. Ultrason. Symp., pp. 2401 –4 [5] Benetti M, Cannatà D, Di Pietrantonio F and Verona E Guided Lamb waves in AlN free strips Proc. 2007 IEEE Int. Ultrasonics Symp. pp. 1673–6. [6] Adler E 1990 Matrix methods applied to acoustic waves in multilayers IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37 485–490 [7] Joshi S and Jin Y 1991 Excitation of ultrasonic Lamb waves in piezoelectric plates J. Appl. Phys. 69 8018–8024,
[8] Yantchev V and Katardjiev I 2006 Quasistatic transduction of the fundamental symmetric Lamb mode in longitudinal wave transducers Appl. Phys. Lett. 86, 154103 [9] Yantchev V Zero Mass Loading Sensitivity of the S0 Lamb Wave resonance in Thin Film Plate Acoustic Resonators (FPAR) Proc. 2009 Int. IEEE Ultrasonic Symp. pp. 2181–4 [10] Lin C-M, Yantchev V, Chen Y-Y, Yen T-T, Felmetsger V and Pisano A Characteristics of AlN Lamb Wave Resonators with Various Bottom Electrode Configurations Proc. 2011 Int. IEEE Freq. Contr. Symp. pp. 505-9 [11] Zuo C, Van der Spiegel J and Piazza G 2010 1.05 GHz CMOS Oscillator Based on Lateral-Field-Excited Piezoelectric AlN Contour-Mode MEMS Resonators IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 57 82-7 [12] Lin C–M, Lai Y-J, Hsu J-C, Chen Y-Y, Senesky D G and Pisano A P 2011 High-Q aluminum nitride Lamb wave resonators with biconvex edges Appl. Phys. Lett. 99 143501 [13] Yantchev V and Katardjiev I 2007 Micromachined thin film plate acoustic resonators utilizing the lowest order symmetric lamb wave mode IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54 87–95. [14] Yantchev V, Arapan L, Katardjiev I 2009 Micromachined Thin Film Plate Acoustic Wave Resonators (FPAR): Part II IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56 2701 - 2710 [15] Rinaldi M, Zuniga C and Piazza G 5-10 GHz AlN contourmode nanoelectromechanical resonators Proc. 2009 IEEE MEMS Conference, pp. 916-9 [16] Zuo C, Sinha N, Van der Spiegel J and Piazza G 2010 Multifrequency pierce oscillators based on piezoelectric AlN contour-mode MEMS technology J. Microelectromech. Syst. 19, 570-580 [17] Avramov I, Walls F, Parker T and Montress G 1996 Extremely Low Thermal Noise Floor, High Power Oscillators Using Surface Transverse Wave Devices IEEE Trans. Ultrasonics, Ferroelectrics and Frequency Control 43 20-29 [18] Morgan D P 2004 Idealized analysis of SAW longitudinally coupled resonator filters IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 51 1165-70 [19] Joshi S, Zaitsev B and I Kuznetsova 2002 Reflection of plate acoustic waves produced by a periodic array of mechanical load strips or grooves IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 49 1730–1734 [20] Yantchev V and Katardjiev I 2005 Propagation Characteristics of the Fundamental Symmetric Lamb Wave in thin Aluminum Nitride Membranes with Infinite Gratings J. Appl. Phys. 98 084910 [21] Kuypers J and Pisano A 2009 Interpolation Techniques for fast analysis of surface acoustic wave and Lamb wave devices Jpn. J. Appl. Phys. 48 07GG07 [22] Yantchev V 2010 Coupling-of-Modes Analysis of Thin Film Plate Acoustic Wave Resonators utilizing the S0 Lamb mode IEEE Trans. Ultrason., Ferroelect., Freq. Contr. 57 801 - 807 [23] Chen D P and Haus H A 1985 Analysis of metal-strip SAW gratings and transducers IEEE Trans. Ultrason. Ferroelectr. Freq. Control SU-32 395–408 [24] Plessky V and Koskela J 2001 Advances in Surface Acoustic Wave Technology, Systems and Applications 2 (Singapore: World Scientific) pp. 1– 82. [25] Iriarte G, Engelmark F, Katardjiev I, Plessky V and Yantchev V 2003 SAW COM-parameter extraction in AlN/Diamond layered structures IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50 1542–1547
[26] Volatier A, Caruyer G, Pellissier Tanon D, Ancey P, Defaÿ E and Dubus B UHF/VHF resonators using Lamb waves co-integrated with bulk acoustic wave resonators”, Proc. 2005 IEEE Int. Ultrasonics Symp. pp. 902-905 [27] Piazza G, Stephanou P and Pisano A 2006 Piezoelectric Aluminum Nitride Vibrating Contour-Mode MEMS Resonators J. Microelectromech. Syst 15 1406-1418 [28] Wagner K, Mayer M, Bergmann A, Riha G A 2D P-Matrix Model for the Simulation of Waveguiding and Diffraction in SAW Components Proc. 2006 IEEE Int. Ultrasonics Symposium pp. 380 – 388 [29] Rinaldi M, Zuo C, Van der Spiegel and J Piazza 2011 Reconfigurable CMOS Oscillator Based on Multifrequency AlN Contour-Mode MEMS Resonators IEEE Trans. Electron. Dev. 58 1281-1286 [30] Tazzoli A Rinaldi M and Piazza G Ultra-High-Frequency Temperature-Compensated Oscillators Based on Ovenized AlN Contour-Mode MEMS Resonators Proc. 2011 Int. Electron Devices Meeting (IEDM) pp. 20.2.1 - 20.2.4 [31] Avramov I, Arapan L, Katardjiev I, Strashilov V and Yantchev V IC-compatible Power Oscillators Using Thin Film Plate Acoustic Resonators (FPAR) Proc. 2009 Int. IEEE Ultrasonic Symp. pp. 20 - 23 [32] Rhea R W Oscillator design and computer simulation, (Noble Publishing Cooperation 2000) p 113 [33] Bjurstrom J, Yantchev V and Katardjiev I 2006 Thin Film Lamb Wave Resonant Structures - the First Approach, Solid State Electron. 50 322-326 [34] Arapan L, Avramov I and Yantchev V 2011 Thin film plate acoustic resonators for integrated microwave power oscillator applications Electron. Lett. 47 453-454 [35] Shreve W, Bray R, Elliot S and Chu Y Power dependence of aging in SAW resonator Proc. 1981 Int. IEEE Ultrason. Symp. pp. 94-99 [36] Wingqvist G, Arapan L, Yantchev V and Katardjiev I 2009 A Micromachined thermally compensated thin film Lamb wave resonator for frequency control and sensing applications J. Micromech. Microeng. 19 035018 [37] Lin C-M, Yen T-T, Lai Y-J, Felmetsger V, Hopcroft M, Kuypers J and Pisano A 2010 Temperature compensated aluminum nitride Lamb wave resonators IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 57 524-532 [38] Lin C, Yen T, Felmetsger V, Hopcroft M, Kuypers J and Pisano A 2010 Thermally compensated aluminum nitride Lamb wave resonators for high temperature applications Appl. Phys. Lett. 97 083501 [39] Pang W, Ruby R C, Parker R, Fisher P W, Larson J D III, Grannen K J, Lee D, Feng C and Callaghan L A thermally stable CMOS oscillator using temperature compensated FBAR Proc 2007 IEEE Ultrasonics Symp. pp 1041–4 [40] Lam C S, Wang C Y J and Wang S M A review of the recent development of temperature stable cuts of quartz for SAW applications 2008 Symp. on Piezoelectricity, Acoustic Waves, and Device Applications [41] IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology – Random Instabilities, IEEE Std. 1139, Jul. 1999 [42] J Vig, F Walls A review of sensor sensitivity and stability Proc. 2000 Int. IEEE Freq. Contr.l Symposium, pp. 30–33. [43] Avramov I, Kurosawa S, Rapp M, Krawczak P and Radeva E 2001 Investigations on plasma polymer coated SAW and STW resonators for chemical gas sensing applications IEEE Trans. Microw. Theory Tech. 49 827-837 [44] Anderås E Katardjiev I and YantchevV 2011 Lamb wave resonant pressure micro-sensor utilizing a thin-film aluminum nitride membrane J. Micromech. Microeng. 21 085010
[45] Friedt J, Droit C, Martin G and Ballandras S 2010 A wireless interrogation system exploiting narrowband acoustic resonator for remote physical quantity measurement Rev. Sci. Instrum. 81 014701 [46] Arapan L, Anderas E, Katardjiev I and Yantchev V 2011 Sensitivity Features of Thin Film Plate Acoustic Wave Resonators IEEE Sensors Journal 11 3330-3331 [47] Arapan L, Alexieva G, Avramov I, Radeva E, Strashilov V, Katardjiev I and Yantchev V 2011 Highly MassSensitive Thin Film Plate Acoustic Resonators (FPAR) Sensors 11 6942-6953 [48] Rinaldi M, Zuniga C, Nipun S Taheri M, Piazza G, Khamis S and Johnson A Gravimetric Chemical Sensor based on the direct integration of SWNT on AlN Contour mode MEMS Resonators Proc. 2008 IEEE Frec. Contr. Symp. pp 443 – 448 [49] G Piazza, Rinaldi M, Zuniga C Nanoscaled piezoelectric aluminum nitride contour-mode resonant sensors Proc. 2010 IEEE Sensors Conference pp. 2202-2207 [50] Yantchev V, Strashilov V, Rapp M, Stahl U and Avramov I 2002 Theoretical and experimental mass-sensitivity analysis of polymer-coated SAW and STW resonators for gas sensing applications IEEE Sens. J. 2 307-313. [51] Avramov I, Rapp M, Kurosawa S, Krawczak P, Radeva E 2002 Gas sensitivity comparison of polymer coated SAW and STW resonators operating at the same acoustic wave length IEEE Sens. J. 2002 2 150-159 [52] Zaitsev B, Kuznetsova I and Joshi S Propagation of Acoustic Waves in Plates Bordered with Viscous Load Proc. 1997 Int. IEEE Ultrason. Symp., pp. 381-384 [53] Lu X, Lee C M, Wu S Y, Ho A and Lau K M 2013 GaNbased S0-wave Sensors on Silicon for Chemical and Biological Sensing in Liquid Environments IEEE Sensors Journal, in print [54] Katardjiev I and Yantchev V 2012 Recent developments in thin film electro-acoustic technology for biosensor applications Vacuum. 86 520-531 [55] Lin C M, Chen Y-Yu, Felmetsger V, Senesky D and Pisano A 2012 AlN/3C–SiC Composite Plate Enabling High-Frequency and High-Q Micromechanical Resonators Advanced Materials 24 2722- 2724 [56] Yantchev V, Arapan L, Katardjiev I and Plessky V 2011 Thin-film zerogroup- velocity Lamb wave resonator Appl. Phys. Lett. 99 033505 [57] Arapan L, Katardjiev I and Yantchev V 2012 An intermode-coupled thin-film micro-acoustic resonator J. Micromech. Microeng. 22 085004 [58] Moreira M, Bjurström J, Katardjev I and Yantchev V 2011 Aluminum scandium nitride thin-film bulk acoustic resonators for wide band applications Vacuum 86 23-26
