Applying laser Doppler vibrometry to probe anchor losses in MEMS AlN-on-Si contour mode resonators

Sensors and Actuators A 263 (2017) 188–197

Contents lists available at ScienceDirect

Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna

Applying laser Doppler vibrometry to probe anchor losses in MEMS AlN-on-Si contour mode resonators C. Tu a , A. Frank c , S. Michael c , J. Stegner d , U. Stehr d , M. Hein d , J.E.-Y. Lee a,b,∗ a

Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong State Key Laboratory of Millimeter Waves, City University of Hong Kong, Hong Kong IMMS Institut für Mikroelektronik- und Mechatronik-Systeme gemeinnützige GmbH, Ilmenau, Germany d IMN MacroNano ® Technische Universität Ilmenau, Ilmenau, Germany b c

a r t i c l e

i n f o

Article history: Received 28 April 2017 Accepted 1 June 2017 Available online 4 June 2017 Keywords: MEMS resonators Contour mode Piezoelectric-on-substrate Anchor loss Laser doppler vibrometry

a b s t r a c t This paper reports the application of high frequency laser Doppler vibrometry to observe the surface profile of waves at the boundaries of contour mode aluminum nitride (AlN) on silicon (Si) resonators. The findings provide better understanding of the nature of the losses at the anchoring regions. These losses set the quality factors of these resonators. We have applied the technique to three groups of resonators to correlate the findings from laser vibrometer measurements to the measured quality factors (and thus also anchor loss). The three groups of resonators differ in their resonant frequencies, which are determined by the resonator dimensions, in order to provide a range of frequencies for enhanced testing reliability. Each group includes a flat-edge resonator and a biconvex resonator of the same resonant frequencies but largely different quality factors (at least by a factor of six: e.g. 12000 vs. 2100) in order to accentuate differences observed by vibrometry. Experimental vibrometer results for all resonators consistently show starkly different surface wave profiles (i.e. out of plane direction) despite the fact that the vibration modes are primarily lateral. The vibrometer wave profiles show strong confinement in the biconvex resonators while the waves in the normal flat edge resonators are spread out uniformly to the boundaries. The vibrometer results match well with the finite-element models. In summary, we find a strong correlation between the out-of-plane displacement profiles and anchor loss, which allows us to verify and consequently exploit the simulations in the course of analyzing anchor losses in AlN-on-Si contour mode resonators. Finally, our results show that varying the support tether length has neither any effect on the wave profile nor the quality factor. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Thin-film Piezoelectric-on-Silicon (TPoS) microelectromechanical resonators have, particularly over the last decade, been explored for integrated high-frequency oscillators [1], radio frequency (RF) filters [2] and low-power resonant sensors [3]. In all these applications, a high quality factor (Q) is desired or even required. In the case of oscillators, the Q-factor determines the close-to-carrier phase noise. In RF filters, the Q-factor determines the steepness of the skirts in the frequency response. In the case of resonant sensors, higher Q benefits detection resolution. TPoS resonators offer both high Q and low motional resistance because these types of

∗ Corresponding author at: Department of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong. E-mail addresses: [email protected] (C. Tu), [email protected] (A. Frank), [email protected] (U. Stehr), [email protected] (J.E.-Y. Lee). http://dx.doi.org/10.1016/j.sna.2017.06.003 0924-4247/© 2017 Elsevier B.V. All rights reserved.

resonators combine the advantages of piezoelectric transduction using a thin piezoelectric film like Aluminum Nitride (AlN) (which offers strong electromechanical coupling) and a single-crystal silicon (Si) substrate (which provides low intrinsic damping) [4–10]. As such, TPoS resonators are known to show higher electromechanical coupling efficiencies compared to capacitive resonators. Their quality factors are also generally higher than those of resonators whose bodies comprise only a piezoelectric film, when compared in the same frequency range. While Q of TPoS resonators can be further enhanced by increasing the thickness ratio of the Si device layer to the piezoelectric film [11], the improvement is ultimately limited by the dispersion of Lamb waves when the acoustic wavelength () becomes comparable to the device thickness [12]. Hence, to increase Q without compromising the electromechanical coupling efficiency, better understanding of the underlying dissipation mechanisms in TPoS resonators is necessary.

C. Tu et al. / Sensors and Actuators A 263 (2017) 188–197

It is widely perceived that anchor loss and electrode-related loss are the most significant sources of dissipation that set Q in TPoS resonators [13–15]. Thus, neglecting less significant sources of dissipation, Q of TPoS resonators can be expressed as [13]: 1 1 1 + = Q Qanchor Qelectrode

(1)

where Qanchor and Qelectrode represent the quality factors set by anchor loss and electrode-related loss respectively. On this note, it has often been found that anchor loss dominates over electroderelated loss in piezoelectric resonators [14,15]. Anchor loss occurs when acoustic waves propagate from the resonator to the surrounding substrate through the supporting tethers. It was reported that anchor loss can be minimized by placing the supporting tethers at the nodal points of the resonator and using small cross-sectional dimensions for the tether [16]. However, there are limitations on the minimum realizable width of the supporting tether, though it is possible to design the length of the tether to minimize anchor loss. It was reported in [16] that setting the length of the tether to a quarter of the acoustic wavelength (/4) has the effect of an acoustic reflector. This is at least the case for resonators fabricated only of silicon (i.e. homogeneous structure). But reports by [17,18] have demonstrated that this argumentation does not hold for the multilayer TPoS resonators. The /4 wave reflection argument assumes only in-plane elastic wave propagate along the supporting tethers. In contrast, we have previously reported in [18] that significant out-of-plane bending motion occurs in the TPoS resonator body and supporting tethers. This notable bending is due to the differences in the stiffness between the piezoelectric thin film and the silicon substrate. As such, anchor loss seems to be unavoidable in TPoS resonators and approaches towards analyzing and reducing anchor loss are thus of great interest. To date, most of the works in the literature have analyzed anchor loss in TPoS resonators almost solely using Q-factors derived from measured transmission responses in the frequency domain [17–20]. The limitation of this approach is that the measured Q represents the combined effect of different sources of dissipation according to (1). Therefore, the error in using this method to evaluate Qanchor becomes larger as anchor loss becomes less dominant over other dissipation mechanisms. It was reported by [21] that, by using Finite-Element (FE) analysis, we can compute the ratio of strain energy stored in the resonator over the strain energy stored in the supporting tether as an indicator to quantitatively compare the anchor losses between different resonator designs. However, this method does not compute the exact value of Qanchor . Recently, another numerical method based on perfectly matched layers (PML) has been proposed to predict the exact value of Qanchor [22]. PML has the property of absorbing incident elastic waves without reflection. By applying PML to the outside boundary of the resonator, the stored elastic energy in the resonator and the average dissipated power over one cycle can be obtained, which enables the exact value of Qanchor to be computed [22]. However, it was also reported that the PML-based method could lead to significant errors in predicting Qanchor when the undercut anchoring region starts to influence the vibration mode shape of the resonator [23]. In addition, all three methods mentioned above have a common problem as they do not provide direct evidence on how anchor loss occurs in the resonators. Each of them rests purely on simulations and models while it would be highly useful to be able to directly measure the physical state of the resonator at resonance. These visualizations could then be correlated to the simulated and/or measured Q-factors to make further inroads into the actual nature of anchor losses in TPoS resonators. Our previous work reported in [25] presented a novel application of high-frequency laser Doppler vibrometry which allows us to map the actual out-of-plane displacement profile on the top

189

surface of two 106 MHz AlN-on-Si contour mode resonators that were designed to have largely different quality factors (2100 vs. 12000) by curving the edges of the resonator [18]. It was found that the measured out-of-plane displacement profiles of those two resonators could be used to explain differences in Q. In this work, we extend our initial findings by including a larger body of experimental data for resonators with resonant frequencies that are higher (141 MHz) and lower (70 MHz) than the devices used previously [25]. These frequencies were chosen to provide a reasonably wide parameter range to study anchor loss effects. The choice of the upper limit of resonant frequency is based on previous experimental findings that biconvex resonators with resonant frequency of 208 MHz do not enhance Q for the fabrication technology we have used [18]. As such, we have chosen the next lowest resonant frequency previously tested that showed a significant increase in Q, which is 141 MHz. It should be noted that the upper limit of the frequency range described in this paper is due to the choice of resonators we have chosen to use as test beds. The proposed method based on laser Doppler vibrometry should work in any frequency that is allowed by the laser Doppler vibrometer setup. We have showed previously in [18] that the measurements of quality factor are highly repeatable and consistent across multiple samples for the family of resonators we have chosen to use as test beds in this work to apply laser vibrometry. Given that the sample-to-sample variation in quality factor for these devices is much smaller compared to the level of enhancement due to design changes (from flat-edge to biconvex), these devices are therefore highly suitable as test beds for applying the proposed method of using laser vibrometry to study anchor losses. On a further note, the use of high-frequency laser Doppler vibrometry in measuring the out-of-plane displacement of conventional flat-edge piezoelectric resonators was previously reported in [23,24], where the focus was on the subtle effect of the undercut in the anchoring regions on Q. In this work, the resonators under test were specifically engineered to have vastly different Q for the chief purpose of accentuating differences in the acoustic wave profiles and their effect on anchor loss for this comparative study. In addition, we have also applied the proposed method based on laser vibrometry to the same pair of resonators (flat-edge and biconvex) but with supporting tethers of different lengths to investigate the effect of varying the tether length as observed by vibrometry.

2. Devices under test and Finite-Element Analysis 2.1. Description of devices under test Fig. 1(a) and (b) show the scanning electron micrographs (SEM) of the two resonator shapes under test in this work: a flat-edge resonator and a biconvex resonator. The symbols denoting the lateral dimensions of the resonators are also labelled in Fig. 1. As shown in Fig. 1 (a), the flat-edge resonator is a rectangular plate with length and width denoted by Lr and Wr respectively. The plate is supported by free-standing tethers that have lateral dimensions of 30 ␮m × 16 ␮m. It is worth pointing out that 16 ␮m is the minimum achievable width for the required multi-stack structure (Al-AlN-Si) allowed by the fabrication process. The TPoS resonator is electrically addressed with interdigital electrodes that cover the full length of the plate. The length and width of each electrode are denoted by Lef and We respectively. The center-to-center pitch between two adjacent electrodes is denoted by Wp . As shown in Fig. 1(b), the biconvex resonator adopts convex edges with a width change from the center to the sides of resonator denoted by W. Our previous work has shown that the biconvex design can confine acoustic energy to the center of the resonator and, consequently, to significantly enhance Q [18]. In contrast to the flat-edge resonator,

190

C. Tu et al. / Sensors and Actuators A 263 (2017) 188–197

Fig. 1. Scanning electron micrograph (SEM) of the (a) flat-edge resonator and (b) biconvex resonator with the lateral dimensions labelled.

Fig. 2. Perspective-view schematic of the AlN-on-Si resonator. The thickness for each composite layer is given in the brackets. The one-port electrical characterization setup applied to all devices is also shown.

Fig. 3. Coupled-domain 3D FE simulation showing the resulting vibration mode shape for device F60 (flat-edge device with  = 60 ␮m); (a) deformed mode shape of the 5th order WE mode where the colored contours denote the y-direction displacement; (b) plot of the out-of-plane (z-direction) displacement on the top surface where the colored contours also represent the z-direction displacement. Material properties of the constituent layers used in the FE simulation can be found in [20]. The value of Q was preset to 900 in the simulations in accordance with the experimental frequency response measurement result presented in Section 3. Analysis is only performed on a quarter section of the device to exploit the symmetry of the vibration mode.

the biconvex resonator uses a shorter length of electrode (Lec ) with the aim to suppress the spurious modes excited by the convex edges [18]. As the electrode lengths are different between the biconvex and flat-edge resonators are different, we have used different subscripts associated with each of their electrode lengths (Lef for flat-edge and Lec for biconvex). Fig. 2 depicts the perspective-view schematic of a flat-edge resonator showing the various constituent layers in the AlN-on-Si structure and their respective thickness in brackets. Note that the structural layers are the same for both the flat-edge and biconvex resonators: Al electrodes (1 ␮m thick), AlN film (0.5 ␮m) and SCS resonator body (10 ␮m). All resonators considered in this work were designed to be transduced in the 5th order width-extensional (WE) mode whose mode shape is illustrated by the finite-element (FE) simulation result shown in Fig. 3(a). The fifth-order resonant frequency (fo ) of the resonator is determined

by the center-to-center electrode pitch (Wp ), which corresponds to 1/5 of the total width of the plate (Wr ) and 1/2 of the acoustic wavelength (): fo =

v 2Wp

(2)

where v is the velocity of the acoustic wave. The working principle of laterally-vibrating TPoS resonators is detailed in [4]. As shown by Fig. 1, only 60% of the resonator width (3/5) is covered by electrodes due to the reduction in area resulting from the convex edge. We designed three groups of resonators that differ from each other with respect to Wr and thus Wp to realize three different resonant frequencies. Each group of resonators contains a biconvex resonator and a flat-edge resonator that have same Lr , Wr and . Table 1 summarizes the lateral dimensions of the six resonator

C. Tu et al. / Sensors and Actuators A 263 (2017) 188–197

191

Table 1 Summary of the lateral dimensions for three groups of devices (units are all in ␮m). The lateral dimensions of supporting tethers are identical for all devices under test: 30 ␮m × 16 ␮m. The spacing between the electrodes for all resonators is the same (2 ␮m: the minimum allowed by the fabrication process). Device

Acoustic wavelength

Resonator length

Resonator width

Width change

Electrode length

Electrode width

Electrode pitch

Symbol F120/B120 F80/B80 F60/B60

 120 80 60

Lr 600 400 300

Wr 300 200 150

W 19.4 12.9 9.7

Lef /Lec 578/272 378/175 276/128

We 56 36 26

Wp 60 40 30

designs considered in this work. The prefix “F” refers to flat-edge resonators, while the prefix “B” refers to biconvex resonators with the number that follows representing the respective value of . For example, B120 refers to a biconvex resonator with  = 120 ␮m. According to (2), the calculated values of resonant frequencies for the three resonator groups are 70.8, 106.3 and 141.7 MHz respectively.

Table 2 Summary of the simulated maximum z-direction displacement components in the resonator body (Dr ) and supporting beam tether (Dt ) for all the resonator designs.

2.2. Finite-Element Analysis

have found that the maximum z-direction displacement in the resonator body (6 pm) is about 1/5 of the y-direction displacement component (33 pm), given the vibration mode is primarily lateral. Fig. 4(a) and (b) show the coupled-domain 3D FE simulation plot of the y- and z-direction displacement components for the resonator design B60. The preset value of Q is 14000 for resonator B60. The y-direction displacement pattern shown in Fig. 4(a) illustrates the 5th order WE mode. By comparing Figs. 4 (a) and 3 (a), we see that the biconvex resonator confines much more energy in the resonator body than the flat-edge resonator. For the resonator design F60, the z-direction displacements in the resonator body and tether are comparable (6 pm vs. 2 pm). For the biconvex resonator, the zdirection motion in the resonator body is confined to the center and becomes much larger than the z-direction motion in the tethers. Fig. 4(b) shows that the maximum z-direction displacement components in the resonator body and supporting tether are 60 pm and 2 pm respectively, differing by a factor of about 30. The maximum z-direction displacement of the resonator body is also about 1/5 of the maximum y-direction displacement component shown in Fig. 4(a) (340 pm), as in the case of resonator design F60, as the cross-sectional profiles of B60 and F60 are the same. The same FE simulation was carried out for the other two resonator groups (i.e. F120/B120 and F80/B80). By comparing the simulated y- and z-direction displacement profiles from the flatedge and biconvex resonators in the same group, we consistently found for all the models that the biconvex resonators confine the acoustic energy to the center of the resonator and suppressing the out-of-plane movement on the tethers. Since the simulated y- and z-direction displacement patterns from F120/B120 and F80/B80 are similar to F60/B60 shown in Figs. 3 and 4, we have omitted them to avoid repetition. The simulated maximum z-direction displacement components in the resonator body (Dr ) and supporting tether (Dt ) for all resonator designs are summarized in Table 2. We will show in Section 3 that the z-direction displacement profiles obtained from FE simulation can be reproduced by laser Doppler vibrometry and the measured z-direction displacement profiles can be strongly correlated with the FE simulations.

Fig. 3(a) shows the coupled-domain three-dimensional (3D) FE simulation of the deformed shape of the resonator design F60 at resonance. The colored contours refer to only the y-direction (along the width of the plate) displacement component. As expected, the y-direction displacement pattern shown in Fig. 3(a) represents a typical 5th order WE mode. Note that the FE simulation model includes all three film layers (i.e. Al, AlN and Si layer) with material properties adopted from [26]. Analysis was performed on a quarter section of the device model to take advantage of the symmetry of the vibration mode while minimizing the computational complexity of the FE model. Fixed boundaries have been applied to the perimeter of the undercut anchoring region along which the entire free-standing structure (including the supporting beam tethers) is anchored to the handling substrate of the silicon-on-insulator (SOI) wafer. In order to solve for the displacement values through a coupled-domain 3D analysis (i.e. frequency domain stepped frequency sweep), we preset the damping based on the experimentally determined values of Q (presented later in Section 3): 900 for resonator F60. Note that all the simulations considered in this work were performed with COMSOL Multiphysics [27]. The mesh type used was tetrahedral. The maximum element size used was set to be ␭/10. The magnitude of the excitation AC voltage in the FE simulation was set to 0.1 V which also applies to the simulations conducted to other devices. It can be seen from Fig. 3(a) that the maximum y-direction displacement of the resonator is 33 pm. As the resonator vibrates along its width, there is also some out-of-plane (z-direction) motion occurring on the resonator body due to the different stiffness and Poisson’s ratio of the AlN film and the Si device layer [26]. Another possible contribution for this out-of-plane motion comes from the indirect piezoelectric effect in thickness direction via the d33 coupling coefficient. The out-of-plane motion can be seen in Fig. 3(b) which plots the FE simulated z-direction displacement component on the top surface of the Si layer (the z-direction displacement component is approximately constant across the thickness of the Al and AlN layers because the Al and AlN layers are much thinner than the Si layer). Given that the tether is a continuum structure that physically links the resonator plate and the undercut anchoring region, the z-direction movements are also transferred to the supporting beam tethers. Some of the energy in the vibrating beam tethers is inevitably transferred to the substrate via the undercut anchoring region as shown in Fig. 3(b). Fig. 3(b) also labels the maximum z-direction displacement components in the resonator body (Dr ) and supporting tether (Dt ), which are 6 pm and 2 pm respectively. As such, the displacement in the resonator body is comparable with the displacement in the beam tether. From FE analysis, we

Device

F120

B120

F80

B80

F60

B60

Preset Q Dr (pm) Dt (pm)

600 8 5

12000 50 2

2100 14 6.2

12000 60 0.8

900 6 2

14000 60 2

3. Experimental measurements 3.1. Electrical transmission measurements All six resonators considered in Section 2 were fabricated using a foundry AlN-on-SOI MEMS process as reported in [28]. We characterized these devices electrically in air using a network analyzer (Agilent E8361A). Short-open-load (SOL) calibration was performed prior to measuring the one-port scattering parameter (S11 ), from which the admittance (Y11 ) was derived. After remov-

192

C. Tu et al. / Sensors and Actuators A 263 (2017) 188–197

Fig. 4. Coupled-domain 3D FE simulation showing the resulting vibration mode shape for device B60 (biconvex device with  = 60 ␮m); (a) colored contours denote the y-direction displacement; (b) plot of out-of-plane (z-direction) displacement on the top surface. The value of Q was preset to 14000 in the simulations in accordance with the experimental frequency response measurement result presented in Section 3.

Fig. 5. (a) Modified Butterworth van Dyke model for a one-port measurement to obtain the admittance (Y11 ); (b) Measured magnitude of extracted Y11 frequency response for device F60 and B60; (c) Comparison of unloaded quality factors (Qu ) among all six devices (the repeatability of these results has been previously demonstrated in [18] where more samples were tested).

ing the electrical feedthrough from the inherent shunt capacitances of the devices, we obtained the magnitudes of the extracted Y11 , from which the key parameters such as resonant frequency (fo ), motional capacitance (Cm ) and Q of the device can be extracted based on a modified Butterworth Van Dyke (BVD) model [29]: a series-resonant circuit in parallel with a shunt capacitor as shown in Fig. 5(a). The motional capacitance Cm from the BVD model is considered in this work as it captures the electromechanical coupling efficiency of the resonator. Fig. 2 shows the one-port characterization configuration applied to all devices tested.

Fig. 5(b) compares the measured magnitude of the extracted Y11 frequency response (after feedthrough has been removed) for the intended 5th order WE modes of devices F60 and B60. It can be seen that Q of B60 is 16 times that of F60, increasing the resonant peak value by 20 dB. Fig. 5(c) plots the values of Q measured for all six devices. It can be seen that there is a consistent significant enhancement in Q from the flat-edge device to the biconvex device within each resonator group. It should be noted that the observed Q enhancements from the flat-edge devices to the biconvex devices agree well with the measured results reported in [18]. It was also found that the measured values of resonant frequency and

C. Tu et al. / Sensors and Actuators A 263 (2017) 188–197

193

motional capacitance agree well with the predictions from the FE simulation to within 1% and 7% respectively. Given that the FE simulation results of Cm agree well with the corresponding values of Cm extracted from the admittance measurements. As such we can thus refer to the verified FE model to obtain the relationship between the z-direction displacements and the lateral displacements. This is helpful as we are unable to measure lateral displacements using the vibrometer.

in z-direction displacements between vibrometer measurements and the FE simulations as well as (2) magnitude ratio between zdirection and y-direction displacements from FE simulations, we can therefore make inferences about the lateral displacements from the vibrometer measurements of the z-direction displacements.

3.2. Laser Doppler vibrometer measurements

4.1. Comparison of measured z-direction displacement profiles against FE simulations

Next, we measured the z-direction displacement profiles on the top surface of the devices using a Polytec UHF120 laser Doppler vibrometer. The excitation AC voltage from the voltage source was applied to all the devices using a chirped input with a frequency bandwidth of 2 MHz. To construct the surface profiles accurately, sufficient number of points were measured on the surface of the resonator body and beam tether respectively. The measurement resolutions for each of the devices under test are summarized in Table 3. We present the z-direction displacement profiles measured by the vibrometer around the resonant frequencies, where the response was the largest. Fig. 6(a) shows the z-direction displacement profiles measured on the top surface of the flat-edge resonator F60 at its resonant frequency of 140.64 MHz. From Fig. 6(a), we can see that the maximum displacement with opposite signs occurs alternately along the width of the resonator body, indicating a 5th order WE mode. Fig. 6(a) also shows that the zdirection displacement profile is generally uniform along the length of the resonator body, which allows z-direction motions in the resonator body to be transferred to the supporting tethers. The resultant notable bending motion of the supporting tether has also been picked up by the vibrometer measurement as shown in the inset of Fig. 6(a). We can see from Fig. 6(a) that the maximum zdirection displacement in the tether is comparable to the resonator body (3.4 pm vs. 6 pm). Fig. 6(b) shows the z-direction displacement profiles measured on the top surface of the biconvex resonator B60 at its resonant frequency of 140.85 MHz. As with Fig. 6(a), Fig. 6(b) shows that the maximum displacement with opposite signs occurs alternatively along the width of the resonator body. However, we can see a significant difference in the z-direction displacement profiles along the length direction between Fig. 6(b) and (a). In Fig. 6(b), the z-direction displacements are concentrated in the center of the resonator body rather than distributed uniformly along the length as shown in Fig. 6(a). The maximum z-direction displacement in Fig. 6(b) is also much larger compared to that in Fig. 6(a) owing to the higher Q (60 pm vs. 6 pm). Despite larger z-direction displacements within the body of the biconvex resonator, the vibrometer measurements show that the motion in the tether is smaller than in the flat-edge resonator tethers (1.4 pm vs. 3.4 pm). Figs. 7 and 8 show the z-direction displacement profiles measured for the other two resonator groups respectively (i.e. F80/B80 and F120/B120). As with Fig. 6, Figs. 7 and 8 show that the zdirection displacement within the body is comparable to that of the tether for flat-edge devices. In the case of the biconvex resonators, the z-direction displacement is always much larger than the displacements of the supporting beam tether along the same axis. In short, these vibrometer measurements confirm that the biconvex resonators concentrate the acoustic energy within the resonator body, thereby greatly reducing the out-of-plane motions in the tethers. It should be noted that although the acoustic confinement is meant primarily for the lateral displacements (which cannot be measured by the vibrometer) we see, from both the FE models and vibrometer results, that the confinement also applies to motion observable in the z-direction. As such, given (1) the good agreement

4. Discussion

By comparing the measured z-direction displacement profile shown in Fig. 6(a) with the simulated FE model in Fig. 3(b), we can see that the z-direction displacement profile measured by the vibrometer closely resembles the profile from the FE 3D coupleddomain analysis for device F60. Good agreement in z-direction displacement profiles between measurement and simulation can also be seen for device B60 by comparing Fig. 6(b) to Fig. 4(b). For easier comparison between the z-direction displacement profiles of flat-edge and biconvex devices, we used the ratio of the maximum z-direction displacement of the resonator body over the maximum vertical displacement of the tether ( = Dr /Dt ) as an indicator of energy stored in the tether relative to the resonator body. In the case of device F60, the simulated and measured values of  are 3.0 and 1.8 respectively. These values of  indicate that the out-ofplane motions in the resonator body and the supporting tether are of comparable magnitude. In comparison, the simulated and measured values of  are both larger by at least a factor of 10 (30.0 and 42.9 respectively) for device B60. This suggests that the amplitudes of out-of-plane motion in the resonator body are much larger than that in the supporting tether. As such, the significant (at least tenfold) increase of  in B60 relative to F60 is found in both the FE model and the vibrometer measurement. This increase in  is due to the combined effects of acoustic energy confinement in the resonator body and out-of-plane movement suppression in the tether. The measured z-direction displacement profiles of the other two resonator groups (i.e. F80/B80 and F120/B120) were also found to be in good agreement with the FE simulations. The simulated and measured values of  for all the devices are summarized in Table 4, from which we can see that the biconvex devices which have higher Q always have significantly larger values of  compared to flat-edge devices. We attribute discrepancies in the value of  between the vibrometer measurement and FE model, particularly for the biconvex designs, to the measurement resolution of the vibrometer setup when the displacements are in the range of pm (which is particularly the case for the biconvex designs); the smallest z-direction displacement (amplitude) among our vibrometer measurements is 1.4 pm. Another reason for discrepancies between the vibrometer measurements and FE simulations is the differences between the fabricated device and FE model (e.g. actual thickness of layers, fabrication tolerances, and actual boundary conditions), which would have a notable impact on the mode shape. This all the more illustrates the importance of selecting resonators with largely different Q-factors when carrying out such a comparative study. But overall, the vibrometer measurements are consistent with the FE simulation results. By comparing the maximum z-direction displacement of the resonator plates measured by the vibrometer to the corresponding value from FE simulation (Table 3), the results agree to within 20% except for the resonator design F120 where the maximum z-direction is the lowest among all the resonators. It is worth recalling that although the vibrometer can only provide information on the vertical motion on the top surface of the resonator, the z-direction displacement can be correlated to the primary axis of motion which is in the lateral plane (which the vibrometer in its current setup cannot measure). The relation between lateral

194

C. Tu et al. / Sensors and Actuators A 263 (2017) 188–197

Fig. 6. Measured z-direction displacement profile on the top surface of (a) device F60; (b) device B60. Insets show the zoom-in scan of the supporting tether.

Fig. 7. Measured z-direction displacement profile on the top surface of (a) device F80; (b) device B80. Insets show the zoom-in scan of the supporting tether.

C. Tu et al. / Sensors and Actuators A 263 (2017) 188–197

195

Table 3 Summary of the measurement resolution for all the resonators tested. Device

F120

B120

F80

B80

F60

B60

All

Area Dimension (␮m2 ) Points measured x-direction (␮m) y-direction (␮m) z-direction (pm)a

body 600 × 300 400 29.5 15.6 2

body 600 × 300 400 29.5 15.6 2

body 400 × 200 400 19.6 10.4 2

body 400 × 200 400 19.6 10.4 2

body 300 × 150 400 14.5 7.7 2

body 300 × 150 400 14.5 7.7 2

tether 30 × 16 35 5.3 2.7 2

Frequency resolution of 4.88 kHz for all measurements over a span of 2 MHz for F80/B80/F60/B60 (including corresponding scan of tethers) and 4 MHz for F120/B120 (including corresponding scan of the tethers). a Obtained by measuring the maximum noise over the surface of each resonator far from the resonance (1 MHz from the respective resonant frequency).

Fig. 8. Measured z-direction displacement profile on the top surface of (a) device F120; (b) device B120. Insets show the zoom-in scan of the supporting tether.

Table 4 Comparison of maximum z-direction displacement obtained by FE simulation and measured by laser vibrometer; resonator design B80T20 refers to a flat-edge resonator with a longer supporting tether (20 ␮m) than the other resonators (10 ␮m). kt 2 denotes the electromechanical coupling coefficient. Device Simulation

Measured

f0 (MHz) Dr Dt  = Dr /Dt f0 (MHz) Dr Dt  = Dr /Dt kt 2 Qu

F120

B120

F80

F80T20

B80

F60

B60

70.52 8 5 1.6 70.43 4 12 0.3 0.078% 600

70.70 50 2 25.0 70.65 40 4 10.0 0.071% 12000

105.86 14 6.2 2.3 105.64 17 8 2.1 0.075% 2100

105.80 14 5.9 2,4 105.61 13 5.8 2.2 0.070% 1700

106.05 60 0.8 75.0 106.03 69 2.6 26.5 0.073% 12000

140.55 6 2 3.0 140.64 6 3.4 1.8 0.066% 900

140.86 60 2 30.0 140.85 60 1.4 42.9 0.064% 14000

and vertical displacements is available from the FE simulations. This inference between vertical and lateral profiles is reasonable given the close agreement between the simulated and measured equivalent-circuit frequency response as well as the close match of vertical displacement profiles obtained by FE simulation and vibrometry.

4.2. Effect of tether length on the z-direction displacement profile As mentioned before, all the devices considered in the three groups (F60/B60, F80/B80 and F120/B120) have the same supporting tether dimensions (30 ␮m long × 16 ␮m wide). Given that one may argue that the differences are due to unmatched tether lengths,

196

C. Tu et al. / Sensors and Actuators A 263 (2017) 188–197

Fig. 9. Measured z-direction displacement profile on the top surface of device F80T20 (Device with acoustic wavelength of 80 ␮m and tether length of 20 ␮m). Insets show the zoom-in scan of the supporting tether.

we have also measured the surface profile of resonator design F80 with a quarter wavelength tether (i.e. 20 ␮m long) while keeping the tether width unchanged at 16 ␮m. Thus essentially the comparison is between a 3/8 and 1/4 wavelength tether and to see how this difference may be reflected using laser vibrometry. We refer to this device as F80T20. As such, the only difference between F80T20 and F80 is the length of the tether. It is worth pointing out that we chose a tether length of 20 ␮m as this length is exactly a quarter of the acoustic wavelength of F80. As such, if the tether length is to have an effect on the anchor loss and vibration mode, we should see some improvement in Q with F80T20 and some observable difference in the vibration profile compared to design F80. But none of this is observed under the vibrometer and the FE model. Fig. 9 shows the z-direction displacement profiles measured on the top surface of the device F80T20 at its resonant frequency of 105.61 MHz. It can be seen from Fig. 9 that the z-direction displacement profile of F80T20 resembles very closely that of F80 (shown in Fig. 7(a)). Just like F80, it is characterized by uniform z-direction displacements along the length of the resonator body and a comparable level of motion in the tether (see Fig. 7(a)). By comparing Fig. 9 with Fig. 7(a), we also see that the values of  for F80T20 and F80 deduced from the vibrometer measurements are very similar (2.2 and 2.1). This agreement is expected as the measured values of Q for both devices are comparable (1700 vs. 2100). The simulated results for F80T20 are also provided in Table 4; they agree with the vibrometer measurement results. By comparing both the vibrometer and FE model results for F80T20 and F80, we can see that the effect of the tether length on the z-direction displacement pattern is undetectable and thus much less significant compared to the effect of acoustic confinement by curving the sides of the resonator. Therefore, based on the vibrometer measurements, there is sufficient reason to conclude that in the case of our TPoS resonators, the length of the supporting tether is inconsequential to anchor loss compared to the much more pronounced effect of biconvex shaping of the plate, which we previously hypothesized in [18]. Given that the tether deformation profiles for the various flat-edge resonators tested here are similar, and their corresponding Qs are in the same range, it would appear that anchor losses for these flat-edge resonators are independent of frequency. 5. Conclusion In this work, we have shown that the small but measurable out-of-plane deformations of AlN-on-Si contour mode MEMS resonators allow us to map vibration profiles through laser Doppler vibrometry. Using laser Doppler vibrometry, we are able to visualize indications of bending in support structures that are closely associated with anchor loss. We have applied the technique to three resonator groups with different resonant frequencies. Each

group includes a flat-edge resonator and a biconvex resonator designed to have similar resonant frequencies but very different quality factors and notably distinct vertical displacement profiles. Strong correlation was found between the measured vertical displacement profiles and anchor losses. In addition, we show that vibrometer measurements are consistent with FE analysis. In short, all the presented results suggest that using laser Doppler vibrometry to measure out-of-plane deformations can provide an effective experimental approach to analyze anchor loss in TPoS resonators. Although the contour modes are characterized primarily by lateral displacements rather than out of plane displacements, the measurable information of vertical motion from the vibrometer can be used to analyze the lateral displacements (which cannot be measured by the vibrometer). This is possible given the excellent agreement between FE simulations of electrical characterization results as well as the close agreement between FE simulations and vibrometer measurements.

Acknowledgements The work described in this paper was supported by a grant under the Germany/Hong Kong Joint Research Scheme by the Research Grants Council of Hong Kong (under project number GCityU106/14) and the German Academic Exchange Service (under project number 57137725) and a grant under the General Research Fund by the Research Grants Council of Hong Kong (under project number CityU 11206115).

References [1] R. Abdolvand, H.M. Lavasani, G.K. Ho, F. Ayazi, Thin-film piezoelectric-on-silicon resonators for high-frequency reference oscillator applications, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 55 (2008) 2596–2606. [2] W. Pan, R. Abdolvand, F. Ayazi, A low-loss 1.8 GHz monolithic thin-film piezoelectric-on-substrate filter, Roc. of the 21 St IEEE Int. Conf. on Micro Electro Mechanical Systems (MEMS 2008) (2008) 176–179. [3] J.L. Fu, R. Tabrizian, F. Ayazi, Dual-mode AlN-on-silicon micromechanical resonators for temperature sensing, IEEE Trans. Electron. Devices 61 (2014) 591–597. [4] G.K. Ho, R. Abdolvand, A. Sivapurapu, S. Humad, F. Ayazi, Piezoelectric-onsilicon lateral bulk acoustic wave micromechanical resonators, J. Microelectromech. Syst. 17 (2008) 512–520. [5] A. Jaakkola, P. Rosenberg, S. Asmala, A. Nurmela, T. Pensala, T. Riekkinen, J. Dekker, T. Mattila, A. Alastalo, O. Holmgren, K. Kokkonen, Piezoelectrically transduced single-crystal-silicon plate resonators, IEEE Ultrasonics Symposium (2008) 717–720. [6] C. Cassella, Y. Hui, Z. Qian, G. Hummel, M. Rinaldi, Aluminum nitride cross-sectional Lamé mode resonators, J. Microelectromech. Syst. 25 (2016) 275–285. [7] C. Cassella, N. Oliva, J. Soon, M. Srinivas, N. Singh, G. Piazza, Super high frequency aluminum nitride two-dimensional-mode resonators with kt 2 exceeding 4.9%, IEEE Electron. Device Lett. 37 (2016) 1344–1346.

C. Tu et al. / Sensors and Actuators A 263 (2017) 188–197 [8] C. Cassella, N. Oliva, J. Soon, M. Srinivas, N. Singh, G. Piazza, Super high frequency aluminum nitride two-dimensional-mode resonators with kt 2 exceeding 4.9%, IEEE Microwave Wireless Compon. Lett. 27 (2017) 105–107. [9] R.C. Ruby, P. Bradley, Y. Oshmyansky, A. Chien, Thin film bulk wave acoustic resonators (FBAR) for wireless applications, IEEE Ultrasonics Symposium (2001) 813–821. [10] L. Hung, C.T.C. Nguyen, Capacitive-piezoelectric transducers for high-Q micromechanical AlN resonators, J. Microelectromech. Syst. 24 (2015) 458–473. [11] R. Abdolvand, F. Ayazi, Enhanced power handling and quality factor in thin-film piezoelectric-on-substrate resonators, IEEE Ultrasonics Symposium (2007) 608–611. [12] H. Zhu, C. Tu, J.E.-Y. Lee, High-Q low impedance UHF-band AlN-on-Si MEMS resonators using quasisymmetrical lamb wave modes, in: Proc. of the 29th IEEE Int. Conf. on Micro Electro Mechanical Systems (MEMS 2016), Shanghai, China, 2016, pp. 970–973. [13] A. Frangi, M. Cremonesi, A. Jaakkola, T. Pensala, Analysis of anchor and interface losses in piezoelectric MEMS resonators, Sens. Actuators A: Phys. 190 (2013) 127–135. [14] C. Tu, J.E.-Y. Lee, Effects of cryogenic cooling on the quality factor of lamb wave mode aluminium nitride piezoelectric-on-silicon MEMS resonators, Sens. Actuators A: Phys. 244 (2016) 15–23. [15] J. Segovia-Fernandez, M. Cremonesi, C. Cassella, A. Frangi, G. Piazza, Anchor losses in AlN contour mode resonators, J. Microelectromech. Syst. 24 (2015) 265–275. [16] K. Wang, A. Wong, C.T.C. Nguyen, VHF free–free beam high-Q micromechanical resonators, J. Microelectromech. Syst. 9 (2000) 347–360. [17] B.P. Harrington, R. Abdolvand, In-plane acoustic reflectors for reducing effective anchor loss in lateral extensional MEMS resonators, J. Micromech. Microeng. 21 (2011) 085021. [18] C. Tu, J.E.-Y. Lee, VHF-band biconvex AlN-on-silicon micromechanical resonators with enhanced quality factor and suppressed spurious modes, J. Micromech. Microeng. 26 (2016) 065012. [19] H. Zhu, J.E.-Y. Lee, AlN piezoelectric on silicon MEMS resonator with boosted Q using planar patterned phononic crystals on anchors, in: Proc. of the 28th IEEE Int. Conf. on Micro Electro Mechanical Systems (MEMS 2015), Estoril, Portugal, 2015, pp. 797–800. [20] H. Zhu, J.E.-Y. Lee, Design of phononic crystal tethers for frequency-selective quality factor enhancement in aln piezoelectric-on-silicon resonators, Proc. Eng. 120 (2015) 516–519. [21] J.E.-Y. Lee, J. Yan, A.A. Seshia, Study of lateral mode SOI-MEMS resonators for reduced anchor loss, J. Micromech. Microeng. 21 (2011) 045010. [22] A. Frangi, A. Bugada, M. Martello, P.T. Savadkoohi, Validation of PML-based models for the evaluation of anchor dissipation in MEMS resonators, Eur. J. Mech. 37 (2013) 256–265. [23] J. Segovia-Fernandez, G. Piazza, Analytical and numerical methods to model anchor losses in 65-MHz AlN contour mode resonators, J. Microelectromech. Syst. 25 (2016) 459–468. [24] K. Gibson, K. Qalandar, C. Turner, Analysis of the impact of release area on the quality factor of contour-mode resonators by laser Doppler vibrometry, in: Proc. of 2015 Joint Conference of the IEEE International Frequency Control Symposium & the European Frequency and Time Forum, Denver, CO, 2015, pp. 709–712. [25] C. Tu, A. Lee, U. Schäffel, M.A. Hein, Probing anchor losses in AlN-on-Si contour mode MEMS resonators through laser Doppler vibrometry, in: Proc. of IEEE Sensors 2016, Orlando,FL, 2016, pp. 1–3. [26] C. Tu, J.E.-Y. Lee, A semi-analytical modeling approach for laterally-vibrating thin-film piezoelectric-on-silicon micromechanical resonators, J. Micromech. Microeng. 25 (2015) 115020. [27] Comsol Multiphysics 5.2. [Online]. Available: www.comsol.com. [28] A. Ali, J.E.-Y. Lee, Electrical characterization of piezoelectric-on-silicon contour mode resonators fully immersed in liquid, Sens. Actuators A: Phys. 241 (2016) 216–223. [29] J.D. Larson, P.D. Bradley, S. Wartenberg, R.C. Ruby, Modified Butterworth-Van Dyke circuit for FBAR resonators and automated measurement system, in: Proc. Ofthe 2000 IEEE Ultrasonics Symposium, San Juan, Puerto Rico, 2000, pp. 863–868.

197

Biographies Cheng Tu received the B.E. and M.S. degrees in Electronic Engineering from the University of Electronic Science and Technology of China in 2008 and 2011 respectively, and the Ph.D. degree from City University of Hong Kong in 2016. He is currently a postdoctoral researcher in the University of Illinois Urbana-Champaign. His research interests include energy loss mechanisms and new transduction approaches in MEMS resonators. He is a member of the IEEE. Astrid Frank was born in Königs Wusterhausen, Germany, in 1981. She received her Diploma in Mathematics in 2009 from Technische Universität Ilmenau, Germany. Since 2009 she has been working at the IMMS Institut für Microelektronik- und Mechatronik-Systeme gemeinnützige GmbH, Ilmenau. Her current activities are MEMS simulation, design and control engineering in mechatronics Steffen Michael was born in Dresden, Germany, in 1967. He received his Diploma in Electrical Engineering in 1993 from Technische Universität Ilmenau, Germany. Since 2008 he has been working in the field of MEMS. His research priorities are optical non-destructive testing, finite element simulation and design of MEMS. Johannes Stegner received his M. Sc. degree in electrical engineering and information technology from Technische Universität Ilmenau in 2015. Currently, he is working towards his doctoral degree in electrical engineering at this University, in the “RF and Microwave Research Group” headed by Prof. Matthias Hein, on integrated MEMS oscillator circuits. Uwe Stehr received his Dipl-Ing degree from Technische Universität Ilmenau in 1991. After his studies, he worked for 15 years as scientific assistant in an institute of the University Duisburg-Essen. His main work areas concerned RF CMOS design of application-specific integrated circuits (ASIC), especially for frequency generation (VCO, PLL, XO circuit blocks). In July 2015, he joined the “RF and Microwave Research Group” at the Technische Universität Ilmenau were he coordinates interdisciplinary multi-physical research on efficient and reconfigurable RF MEMS circuits in the framework of the research unit MUSIK funded by the German Research Foundation (DFG). His main research interest is in the integration of the design flow of mechanical (MEMS–based) and electrical (e.g. CMOS) circuit functions using a compound silicon ceramics multilayer substrate technology. Since March 2015, he is part of the academic staff of the research unit MUSIK funded by the German Research Foundation (DFG). Matthias A. Hein received his diploma and doctoral degrees with honors from the University of Wuppertal, Germany, in 1987 and 1992. In 1999, he received a British Senior Research Fellowship of the Engineering and Physical Sciences Research Council (EPSRC) at the University of Birmingham, U.K. From 1998 until 2001, he headed an interdisciplinary research group of passive microwave electronic devices. In 2002, he joined the Technische Universität Ilmenau as the Head of the RF and Microwave Research Laboratory. He has authored and coauthored around 500 publications and delivered about 30 invited talks or tutorials at international conferences. He chaired the German Microwave Conference 2012, and served as co-organizer and convener of various international conferences. He is elected board member of the IEEE Joint German Chapter MTT/AP and of the EurAAP. In 2014, he became spokesman of the Thuringian Center of Innovation in Mobility, where one focus is on intelligent vehicular wireless sensor and communication systems and virtual test drives. His research interests focus on antenna and microwave engineering. Joshua E.-Y. Lee received the B.A. (Hons) and M.Eng. (Distinction) degrees in 2005, and the Ph.D. degree in 2009, all from the University of Cambridge. He joined the faculty of the Department of Electronic Engineering, City University of Hong Kong, in June 2009 as an Assistant Professor. He is currently an Associate Professor and is affiliated with the State Key Laboratory of Millimeter Waves. His research interests include the design, fabrication, and characterization of Microelectromechanical Systems (MEMS) for sensory and frequency control applications, as well as studying issues arising from interfacing MEMS with circuits. In 2008, he was awarded a Research Student Development Fellowship by the Royal Academy of Engineering, UK.