Sensors and Actuators A 297 (2019) 111541
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Sensors and Actuators A: Physical journal homepage: www.elsevier.com/locate/sna
Quality factor improvement of piezoelectric MEMS resonator by the conjunction of frame structure and phononic crystals Fei-Hong Bao a , Jing-Fu Bao a,∗ , Joshua En-Yuan Lee b , Lei-Lei Bao c , Muhammad Ammar Khan a , Xin Zhou a , Qi-Die Wu d , Ting Zhang a , Xiao-Sheng Zhang a,∗ a
School of Electronic Science and Engineering, University of Electronic Science and Technology of China, 611731 Chengdu, China State Key Laboratory of Millimeter Waves and the Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China c Institute of Industrial Science, University of Tokyo, Meguro, 153-8505 Tokyo, Japan d Yingcai Honors College, University of Electronic Science and Technology of China, 611731 Chengdu, China b
a r t i c l e
i n f o
Article history: Received 1 May 2019 Received in revised form 23 July 2019 Accepted 2 August 2019 Available online 5 August 2019 Keywords: Piezoelectric resonator MEMS Quality factor Phononic crystals Energy dissipation
a b s t r a c t Recently, piezoelectric resonators fabricated by using MEMS (i.e., micro-electro-mechanical systems) technology have received increasing attention in a large and diverse set of applications, including sensors, filters and timing references. One of the critical challenges for the actual application of MEMS resonators is further improving their quality factors (Qs) to respond the urgent demand of performance enhancement. Herein, a strategy by employing suspended frame structure and phononic crystals (PnC) was proposed to reduce the energy dissipation, and thus AlN-on-SOI MEMS resonators with high Q were successfully implemented. The suspended frame structure isolates the mechanical vibration between the resonant body and the anchoring substrate, while PnC arrays serve as a frequency-selective reflector to reduce the energy leakage. The multi-physics finite-element-analysis (FEA) and the experimental comparison were employed to systematically investigate the underlying mechanisms of the energy dissipation reduction of the proposed strategy. The unloaded Qs (i.e., Qu ) of proposed resonators achieved maximum 7.8-fold and 1.5-fold improvements compared with that of bared resonators and that of those with only suspended frame structure, respectively. © 2019 Elsevier B.V. All rights reserved.
1. Introduction In the past decade, micro/nano-electro-mechanical systems (M/NEMS) technologies have shown promising prospects in autonomous sensor network and wireless communication [1–4]. In particular, thin-film aluminum nitride on silicon-on-insulator (AlN-on-SOI) MEMS resonator has been rapidly developing because of its excellent properties, such as complementary metal oxide semiconductor (CMOS)-process compatibility, moderate effective electromechanical coupling coefficient (keff 2 ), high power handling capacity and lithographically defined resonant frequency (namely a multiple-frequency design can be realized on a single chip) [5,6]. Even so, to truly affect a large and diverse set of practical applications (e.g., high-precision phononic frequency combs, low-loss RF band-pass filters, high-sensitivity sensors, and low-phase-noise oscillators), the quality factor (Q) of AlN-on-SOI MEMS resonator
∗ Corresponding authors. E-mail addresses:
[email protected] (J.-F. Bao),
[email protected] (X.-S. Zhang). https://doi.org/10.1016/j.sna.2019.111541 0924-4247/© 2019 Elsevier B.V. All rights reserved.
should be further improved (the state-of-art Q is generally around 1000) in comparison with quartz-based resonators and capacitively transduced resonators (Q is usually larger than 100,000) [7–11]. Previous research has shown that a large portion of mechanical energy dissipation through the supporting tethers of MEMS resonator is the major factor leading to low Q, namely, anchor loss [12–14]. Moreover, it is highly urgent to develop effective strategies to reduce the energy leakage dissipating from resonant body, thereby significantly improving the Q of resonator. Thus far, many strategies have been proposed to reduce the energy dissipation for thin-film piezoelectric-on-substrate (TPoS) resonators (piezoelectric material is not limited to AlN and substrate is not limited to silicon) to improve the Q factor [15–22]. For instance, Zou et al. proposed a butterfly-shaped AlN lamb wave resonator, and showed the great effectiveness of the butterfly-shaped structure in reducing the mechanical energy leakage through tethers, with the unloaded Q (Qu )being increased from 3348 to 5352 [23]. Binci et al. presented a strategy of surrounding the resonant body using ring-shaped phononic crystals (PnC) unit cells to reduce the anchor loss of the AlN-on-SOI resonator, and they achieved the maximum Q of 5369 [24]. Mohammadi et al. demonstrated a line defects design in a 2D
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PnC slab to confine the acoustic energy in the cavity region of zinc oxide (ZnO) micromechanical resonators and the measured Q was increased to more than 6000 [25]. Furthermore, a recent approach to effectively enhance the Q in AlN-on-SOI MEMS resonators is to apply suspended frame structure on tethers to capture more acoustic energy in the resonant body [26]. However, this literature [26] only investigated the Q enhancement of MEMS resonators with different widths of a frame structure in x-direction, while the underlying physical mechanism has not yet been clearly evidenced. In addition, another effective strategy of exploiting multi-stage PnC structure including two periodicity PnC unit cells has also been presented to significantly reduce the anchor loss, thereby improving Q, though the transmission characteristics of one-stage PnC structure have not been determined [27]. Given this, the underlying physical mechanism of suspended frame and transmission characteristics of one-stage PnC remains to be elucidated. In this research, a novel strategy by the conjunction of suspended frame structure and phononic crystals was proposed to reduce the energy dissipation of piezoelectric MEMS resonators. The extra physical frame structure was designed to rearrange the vibration field within the resonator. More specifically, multiphysics finite-element-analysis (FEA) simulation was performed, and simulation results showed that the frame structure isolates the mechanical vibration between the resonant body and the anchoring substrate and hence reduce the dissipation. Indeed, this strategy is emulated from the delay lines with PnC, and with the solid silicon slab (i.e., solid line) as the transmission mediums between interdigital transducers (IDTs), verifying the existence of acoustic bandgaps formed by the PnC structure [28,29]. In summary, this research demonstrates the transmission characteristics of the proposed onestage PnC structure with and without holes. Subsequently, the underlying physical mechanism of energy dissipation reduction by the suspended frame structure was elucidated through the mechanical vibrating systems-based theoretical analysis and multiphysics FEA simulation. Finally, three types of resonators (e.g., the MEMS resonator with suspended frame only, with frame as well as PnC structures and without either of structures) were fabricated to verify the effectiveness of the suspended frame structure and PnC structure in significantly reducing the energy dissipation and indicating a strategy that the resonator combining with suspended frame and PnC structures could realize the optimal Q.
2. Resonator design The resonant body of AlN-on-SOI MEMS resonators was formed by the piezoelectric film of AlN (0.5 m thick) sandwiched with the metal film of Al (1 m thick) and the silicon film, while the top film of the SOI substrate adopted the 10 m thick p-type doped silicon to act as the ground electrodes for both input and output electrodes. It is noteworthy that the thickness of the suspended frame and PnC structure was identical to that of the silicon layer of tethers and the resonant body (10 m) as shown in the zoom-in view of Fig. 1(a). In this research, the MEMS resonators were designed to work in the fundamental lateral-extension mode at 52 MHz. Moreover, as shown in Fig. 1(b), three types of MEMS resonators comprise of the same resonant body configuration were fabricated following a foundry AlN-on-SOI MEMS process, in order to verify the significant effectiveness of the suspended frame and PnC in reducing the energy dissipation, thereby improving Q. Prefix ‘C’ represents the conventional resonator and ‘F’ means the resonator with suspended frame structure only. Also, prefix ‘FP’ refers to the resonator with both frame and PnC structure.
3. Transmission characteristics of one-stage PnC To simulate the acoustic bandgaps associated with the proposed PnC structure, Bloch-Floquet boundary conditions were applied to the surfaces along the repetition direction of the PnC structure [30]. The propagation of elastic waves in an anisotropic material (namely, acoustic waves in the silicon of this research) and the Bloch–Floquet theorem of displacements were expressed as [30]:
∂ ∂u (cilkl k ) = u¨ i (i, j, k, l = 1, 2, 3) ∂xj ∂xl
(1)
u(x + a) = eik.a u(x)
(2)
where xj (j = 1, 2, 3) denotes the x, y and the z axes. cijkl is the elastic tensor and ui is the displacement components ux , uy or uz . The k, , and a are the wave vector, mass density, and lattice constant of the associated PnC, respectively. Fig. 2 shows the investigation of two types of phononic crystals (PnC) structure based on 3D finite-element-analysis (FEA) simulations. Fig. 2(a) shows the proposed PnC with and without circular-shaped holes (i.e., the diameter of circular-shaped holes is 3 m). The lattice constant of these two types PnC is the same as 46 m. Moreover, Fig. 2(b) depicts the dispersion relations of an infinite periodic 1D PnC structure with and without holes. The corresponding eigenmode shapes of these two types PnC of the 7th -14th frequency band structures with ka/2 = 0.25 are displayed in Fig. 2(c). The eigenmode shapes of these two types of PnC are roughly the same, but the frequency is different, in particular in the frequency of high order band structures. It is known that the bandgap for out-of-plane mode also is a complete bandgap, as it is fully contained in the in-plane bandgap [31]. However, for the bulk acoustic wave device, the in-plane bandgap is a partial bandgap. For example, the 7th -9th frequency band structures are out-of-plane mode, which means an in-plane bandgap can be achieved between the frequency of 6th band structure and the frequency of 10th band structure. To verify the existence of acoustic bandgaps can be formed by the proposed one-stage PnC structure, transmission parameters (i.e., S21) of delay lines were performed. As shown in Fig. 3(a), PnC with holes line, PnC without holes line, and beam line (i.e., has different transmission mediums between drive electrodes and sense electrodes) were developed to investigate the transmission characteristics of proposed PnCs. In addition, the Perfectly Matched Layers (PML) were performed at the ends of delay lines in the x-direction to minimize the effects of reflected acoustic waves, thereby avoiding unexpected spurious peaks formed in the transmission spectrum [26,29]. The drive and sense electrodes of delay lines were identical to the input and output electrodes of MEMS resonators in this research. Besides, the S21 in decibels is expressed as: S21(dB) = 10log10
P
out
Pin
(3)
where Pout and Pin are the values of output and input power in the delay line and solid line, respectively. The initial Pin is 0 dB m. Moreover, S21 is the S-parameter of transmitted waves, and represents the power transmission coefficient from the input port to the output port. As shown in Fig. 3 (b), the transmission S21 spectrum with a finite PnC structure (i.e., only one-stage PnC), suggesting that acoustic bandgaps were successfully formed by the proposed PnC structure. The presented transmission characteristics show a wide acoustic bandgap of 68–120 MHz formed by the proposed PnC with a BG% (i.e., BG% is the ratio of the bandwidth to the mid gap frequency [31]) of 55%, which is contributed by the complete bandgaps and partial bandgaps. Furthermore, the transmission S21 in a narrow frequency range of 80–110 MHz and 50–60 MHz
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Fig. 1. (a) 3D illustration of the proposed AlN-on-SOI MEMS resonator with a suspended frame structure and one-stage phononic crystals (PnC) strips on each of supporting tethers. Zoom-in inset shows the thickness of the resonant body, supporting tethers, PnC structure, and suspended frame structure of the resonator is the same as 10 m. (b) Microscope images of three types of fabricated resonators with a zoom-in view of a PnC. Prefix ‘C’ refers to the conventional resonator, ‘F’ refers to the resonator with suspended frame structure only, and prefix ‘FP’ refers to the resonator with frame and PnC structure. In principle, the suspended frame structure can isolate the mechanical vibration from resonant body to the anchoring substrate, thereby reducing energy dissipation. The PnC structure also serves as a frequency-selective reflector to decline the energy leakage out of MEMS resonant body.
Fig. 2. Investigation of band structures of phononic crystals (PnC) structures based on 3D finite-element-analysis (FEA) simulations. Schematic view of the PnC unit cell (a) with and without circular-shaped holes, with diameter of 3 m. (b) Dispersion relations of the one-stage PnC with and without holes. (c) Corresponding eigenmode shapes of two types PnC of the 7th -14th frequency band structures with ka/2 = 0.25.
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Fig. 3. Investigation of transmission characteristics of PnCs based on 3D finite-element-analysis (FEA) simulations. In this research, simulated transmission S21 of (a) beam line, PnC without holes line, and PnC with holes line were performed, verifying that the existence of acoustic bandgaps formed by the proposed PnC structure. (b) Transmission spectrum (i.e., S21) of beam line, PnC without holes line, and PnC with holes line in the frequency range of 0–150 MHz, 80–110 MHz, and 50–60 MHz, showing the reduction of acoustic wave dissipation with varying degrees by the proposed PnC with and without holes. (c) Illustration of the displacement distribution in z-direction of beam line, PnC without holes line, and PnC with holes line at the frequency of 52 MHz, 56 MHz, 85 MHz and 106 MHz, respectively. In general, the presented transmission characteristics show a wide acoustic bandgap of 68–120 MHz formed by the proposed PnCs with a BG% of 55%, which is contributed by the complete bandgaps and partial bandgaps.
by the PnC with holes line, PnC without holes line, and beam line were calculated, showing the reduction of acoustic wave dissipation with varying degrees by the proposed PnC with and without holes. Fig. 3(c) shows the displacement distribution in zdirection of beam line, PnC without holes line, and PnC with holes
line at the frequency of 52 MHz, 56 MHz, 85 MHz and 106 MHz, respectively. The results indicate that the proposed one-stage PnCs have superior wave attenuation and vibration isolation mechanisms. In particular, As depicted in the Fig. 3(c), the one-stage PnC with holes has a significant vibration isolation at 106 MHz com-
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Fig. 6. (a) Transmission S21 of delay lines with and without frame structures in the frequency range of 50–54 MHz. (b) Illustration of the displacement distribution in z-direction of delay lines with and without frame structure working in the frequency of 52 MHz, and a significant isolation of mechanical vibration was observed. Furthermore, to systematically explore the frame structure, the transmission S21 of delay lines under different dimensions of frame and resonant body were performed (i.e., are displayed in Fig. 7), revealing that the presence of frame helps to trap the acoustic energy in the resonant body and frame, while less energy dissipating through tethers. Accordingly, a higher quality factor can be achieved. Fig. 4. Measured S21 of (a) 85 MHz and (b) 56 MHz PnC based MEMS resonators.The measurement results agree with the simulation results, verifying that the PnC structure without holes can reduce more energy dissipation of the resonator at 85 MHz and 56 MHz compared with that of the PnC with holes. Given this, the delay lines indicate a huge potential that could be used to indicative resonator designs.
pared with that of PnC without holes, which is also proved in [27]. To prove the simulated transmission characteristics of proposed one-stage PnC structures, two groups of 85 MHz and 56 MHz PnC based MEMS resonators were fabricated. It is noted that the resonators are electrically characterized by a network analyzer and a Cascade probe station to obtain the S21 parameters. Before
measurements, a standard short-load-open-through calibration is performed, while all of the measurements are done at room temperature and atmospheric pressure. As shown in Fig. 4(a), the loaded Q of PnC without holes resonator achieved as 7745.85 at 85 MHz, upwards 8.4% over PnC with holes resonator which owns a loaded Q of 7146.05. Moreover, the PnC without holes resonator enables a loaded Q of 2918.19 at 56 MHz as shown in Fig. 4(b), representing 43% improvement in Q in comparison with the PnC with holes resonator. The measured results are well consistent with the simulation results, verifying that the PnC structure without holes can reduce more energy dissipation of the resonator at 85 MHz and 56 MHz compared with that of the PnC with holes, which indicating
Fig. 5. Investigation of the effects of mechanical vibration isolation between resonant body and the anchoring substrate by suspended frame structure based on mechanical vibrating systems analyses and 3D FEA simulations. (a) Schematic view of a mass-spring-damper model for the conventional MEMS resonator. (b) Schematic view of a mechanical vibration isolation model, where the isolated resonant body is represented as mass mr . Moreover, the intermediate mass, namely the suspended frame structure, is represented as mass mf . (c) Side view of delay lines with and without a suspended frame on tethers as the transmission medium.
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Fig. 7. Investigation of energy dissipation reduction by the suspended frame structure under different dimensions of frame and resonant body based on 3D FEA simulations. A multiphysics FEA model (as shown in Fig. 5(c)) based on single variable method was adopted to predict the energy dissipation reduction under different parameters. Moreover, the variables are (a) frequency, (b) width of the supporting tethers (Wt ), (c) length of the tether inside of frame (Ltin ), (d) length of the tether outside of frame (Ltout ), (e) width of the frame in x-direction (Wfx ), (f) length of the frame in y-direction (Lfy ), (g) width of the frame in y-direction (Wfy ) and (h) length of the resonant body (Lr ), respectively. Note that the initial values of the dimensions of suspended frame and resonant body are listed in the Table 1. Finally, through considerable simulations, Lfy and Wfy (due to the relatively orderly transmission curves) showed great potentials to achieve the optimal quality factors of the resonator.
that the delay lines have the huge potential that could be used to indicate resonator designs. By definition, a PnC comprises a periodicity of several unit cells [24,27]. In [27], the resonator with five-stage PnC has can reduce the anchor loss and thus improve Qu to 9744.1. However, a resonator with only one-stage PnC can already improve Q, though not as effective as a periodicity of unit cells. By connecting several cells as described in [27] to realize a periodic array (i.e. the common definition of a PnC), further enhancement of Qu can be expected.
4. Physical mechanism of suspended frame It is known that the dissipated bulk acoustic waves are propagated from the resonant body to the anchoring substrate through supporting tethers, and the acoustic energy stored in the tethers and the anchoring substrate are inevitable wasted. Given this, inspired by the fact that in our daily life, walls can insulate the sound noise from large machines, the suspended frame structure was developed to effectively isolate the mechanical vibration between the resonant body and the anchoring substrate of MEMS resonators [26], thereby reducing the energy dissipation. However, the under-
lying physical mechanism has not been clearly evidenced, and the laws of energy dissipation reduction remains to be investigated. The conventional MEMS resonator can be represented as a simplest mass-spring-damper vibrating mechanical system as shown in Fig. 5(a) [32]. Moreover, the relationship between the displacements of the mass and force following the laws of Newton motion can be described as follows in line with its expressions. 2
mr
∂ d ∂d +c + kd = F ∂t 2 ∂t
(4)
where mr stands for the mass of resonant body, d represents the displacements of the mass, c is the damping coefficient, k refers to the stiffness and F denotes the force. Furthermore, the complex excitation force (Fejωt ) transmitted to the foundation of the conventional resonator (FT ) and the transmissibility (TF ) of the system is given by: FT = d(k + jωc) TF =
FT F
(5) (6)
where the complex variables have a real and imaginary part, namely, an amplitude and phase relative to the excitation force
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Fig. 8. Comparisons of the anchor loss and maximum displacement in the undercut regions of three types MEMS resonators, including (a) the conventional resonator, (b) with only suspended frame structure and (c) with both frame and PnC structures. In brief, the lower displacement in the undercut regions and the anchoring substrate mean lower anchor loss of the resonator, that is, it will have lower acoustic energy dissipation. Accordingly, a higher Q of the resonator can be achieved.
(Fejωt ). Also, ω is the angular resonance frequency of the excitation force. Moreover, as shown in Fig. 5(b), the MEMS resonator with a suspended frame structure can be interpreted as a mechanical vibration isolation system, in particular, the resonant body (mr ) is isolated by the intermediate mass of frame structure (mf ). Further on, the equations of this isolation system can be written as: 2
mr
∂ d1 ∂d1 ∂d2 + c1 ( − ) + k1 (d1 − d2 ) = F ∂t 2 ∂t ∂t
mf
∂ d2 ∂d2 ∂d1 ∂d2 + c2 + k2 d2 − c1 ( − ) − k1 (d1 − d2 ) = 0 ∂t 2 ∂t ∂t ∂t
(7)
2
(9)
Furthermore, according to the law of conservation of energy, the displacement of the frame is caused by the vibration of the resonant body, and the d2 is definitely smaller than the d in a conventional resonator if a same voltage is applied on them. Thus, it is expected that a higher Q can be achieved in the MEMS resonators designed with suspended frame structure by reducing the force transmissibility compared with that the conventional one. Besides, in order to quantify the effects of energy dissipation reduction by the frame structure, the energy transmissibility (TE ) in decibels is expressed as: TE = 10 ∗ log10 (TF ∗ TD ) = 20 ∗ log10 TF
Variable (Symbol)
Initial value (unit)
Simulated resonant frequency (f0 ) Width of the tether (Wt ) Length of the tether inside of frame (Ltin ) Length of the tether outside of frame (Ltout ) Width of the frame in y-direction (Wfy ) Length of the frame in y-direction (Lfy ) Width of the frame in x-direction (Wfx ) Length of the resonant body (Lr )
52 (MHz) 10 (m) 46 (m) 46 (m) 42 (m) 252 (m) 10 (m) 100 (m)
(8)
where mf stands for the mass of the suspended frame structure, d1 and d2 represent the displacements, c1 and c2 represent the damping coefficient, k1 and k2 represent the stiffness of the resonant body and frame, respectively. Therefore, the excitation force transmitted to the foundation (FfT ) of the system is expressed as: FfT = d2 (k2 + jωc2 )
Table 1 Investigation of energy dissipation reduction by the suspended frame under different parameters of the frame and resonant body based on 3D FEA simulations.
(10)
where TF and TD mean the force and displacement transmissibility of the vibration system, respectively. In the case of MEMS resonators, TF is generally considered to be identical to TD , thus
the equation of energy transmissibility can only relate to the force transmissibility. To represent a micromechanical device with electrical elements, a series resistance-inductance-capacity (RLC) circuit is the most frequently-used method to map mechanical quantities to electrical ones [32], i.e., describing the correspondence between the force (F) in mechanical domain and voltage (V) in electrical domain. Also, S21 is the S-parameter of the transmitted wave, and represents the voltage (or power) transmission coefficient from the input port to the output port. Thus, it is expected that multiphysics FEA simulation models can be adopted to simplify this research. As shown in Fig. 5(c), a multiphysics FEA simulation model was developed to systematically explore the frame structure, and to further verify that the energy dissipation can be reduced in varied degrees through the suspended frame structure with different parameters. Fig. 6(a) shows the simulated transmission S21 of delay lines with and without frame on tethers in a narrow frequency range of 50–54 MHz, indicating that the proposed frame structure can significantly reduce the energy loss by 23.1 dB at 52 MHz. To a more intuitive view of the displacement distribution, as depicted in Fig. 6(b), the domain of the sense electrodes place of the delay line with frame shows lower displacement than that with the conventional one, which has also been proved by the numerical calculation
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of MEMS resonators (i.e., for the 52 MHz fundamental lateralextension mode MEMS resonator, the Wr is /2). Subsequently, through considerable simulations by the proposed multiphysics model, the length of tethers inside and outside of the frame can be designed as /4. Finally, the width of the frame in x-direction, the length of the frame in y-direction (i.e., cannot be smaller than the Wr ) and the width of the frame in y-direction can be set as /16, and /16, respectively. 5. Results and discussions In this research, all the simulation models of MEMS resonators were obtained according to the boundary conditions of perfectly matched layers (PMLs) to absorb the dissipated acoustic waves, and these models have the same dimensions of the undercut region (because Qanc will be affected by the undercut regions) compared with the corresponding fabricated resonator [33]. In addition, Fig. 8 shows the comparisons of anchor loss (Qanc ) and the maximum displacement in undercut regions of these MEMS resonators. The anchor loss (Qanc ) of MEMS resonators is calculated by [34]: Qanc =
Fig. 9. Measured transmission S21 in a wide frequency span of 8 MHz of (a) the MEMS resonator without either frame or PnC structure, (b) the resonator with only frame structure, and (c) the resonator with both frame and PnC structures. Moreover, the inserted images give the higher-magnification view of the measured S21 and MBVD model fitted curves in a narrow frequency span of 500 kHz. In summary, the measured results are well consistent with the simulation results, verifying that the suspended frame and PnC structures can significantly reduce the energy dissipation of the resonator, thereby improving Q.
of simulation results (e.g., 2.8e-13 J elastic strain energy of frame one and 1.4e-10 J of normal one). Moreover, the eight variables of the frame structure and resonant body are discussed in Fig. 7, and the initial values of the dimensions are listed in Table 1. In general, due to the relatively orderly transmission curves, the length of the frame in y-direction (Lfy ) and the width of the frame in y-direction (Wfy ) showed great potentials to achieve the optimal quality factors of the MEMS resonator with targeted resonant frequency. For instance, when the desired resonant frequency of MEMS resonators is set as 52 MHz, the wavelength () will be approximate as 163 m (i.e., the sound velocity of doped silicon is 8500 m/s). Firstly, the width of tethers is depended by the rule of fabrication process, and it is designed as 10 m in this research. Moreover, the width of resonant body (Wr ) is depended by the targeted resonant frequency as well as resonant mode orders
Re(ω) 2Im(ω)
(11)
where ω is the eigenfrequency of the desired resonant mode of AlN-on-SOI MEMS resonators. The design C shows the lowest Qanc of 608.64, indicating a large part of mechanical energy loss through tethers. The design F shows a relatively higher Qanc of 2870, and the design FP with both frame and PnC structures shows the most significant displacement suppression in undercut regions as well as anchoring substrate, with the Qanc was up to 8110. In this research, the lumped parameters were extracted from the S21 by fitting a Modified Butterworth-Van Dyke (MBVD) equivalent circuit model [35,36]. Moreover, as predicted in the FEA simulations, the measured Q of the AlN-on-SOI MEMS resonator using both frame and PnC structures, and that using only frame was both higher than the conventional one. As shown in Fig. 9(a) and (b), the unloaded Q (Qu ) of design C and F reached 606.7 at 51.93 MHz and 3257.7 at 51.84 MHz, while the resonant peak value significantly decreased by 13 dB in the resonator with frame structure. The Qu of FP (namely 4743.6) was improved by 7.8 times, compared with that of the resonator without either of the structures. In brief, the measured results agree with the simulation results, verifying that the suspended frame and PnC structures can significantly reduce the energy dissipation, and further improving Q. It is worth to be noted that the effective electromechanical coupling coefficient (keff 2 ) was decreased because of the presence of frame in the MEMS resonators, yet spurious modes seemed to be suppressed with its decrease. This is because the suspended frame structure contributed to capturing more mechanical energy, namely increasing the total stored energy to improve Q. However, the mechanical energy stored in the frame could not be converted into electric energy by the piezoelectric effect. Therefore, the effective electromechanical coupling coefficient of the resonator with frame would be lower compared with the conventional one. Nevertheless, this situation indicates the huge potential that the suspended frame could be used in a resonator with a strong keff 2 but relatively lower Q, such as the resonator reported in [37], where the X-cut lithium niobate MEMS resonator exhibited a maximum quality factor (Q) around 1200 but a strong keff 2 was up to 30%. In addition, one side effect of the frame structure is the resulting larger footprint of the resonator. And to avoid unwanted spurious modes introduced by the frame due to mechanical noise, the mechanical resonant frequency of the frame structure must be
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designed to be far from the desired resonant frequency of the resonator. Besides, the frame structure has a salient trait that can isolate the mechanical vibration from resonant body to the anchoring substrate, which means it can isolate resonator from the outside vibrations conversely. Furthermore, we can also integrate the PnC unit cells onto the frame to realize an ultra-high Q, which will not reduce the keff 2 as previously shown by FEA simulations in [38]. Numerical simulations indicate that integrating PnCs in the frame is more effective in reducing anchor loss compared with conventional PnC-based tethers or utilizing PnC plates as anchoring substrates. The results indicate potential of this approach in improving Q, thus systematic studies will be carried out in the future. 6. Conclusions In summary, a suspended frame structure and PnC structure were introduced in AlN-on-SOI MEMS resonators to significantly reduce the energy dissipation. FEA simulation and measurement experimental were performed to verify the effectiveness of the introduced structures. To be more specific, multiphysics FEA simulation models were developed to systematically explore the frame and PnC structures, and further verified that the energy dissipation can be reduced in varied degrees through the suspended frame and PnC structures with different parameters. The measured maximum unloaded quality factor (Qu ) of the fabricated resonator with both frame and PnC structures reached 4743.6 at 51.75 MHz and yielded a 7.8 times improvement in Qu compared with the conventional one. Finally, by acting on the device geometry, a higher quality factor of MEMS resonators can be obtained and expected, indicating the promising prospect of this technology in wireless communications and autonomous sensor networks. Acknowledgments This work is financially supported by National Natural Science Foundation of China (No. 61804023), Key R&D Program of Sichuan Province (No. 2018GZ0527). References [1] R.P. Middlemiss, A. Samarelli, D.J. Paul, J. Hough, S. Rowan, G.D. Hammond, Measurement of the earth tides with a MEMS gravimeter, Nature 531 (March (7596)) (2016) 614–617. [2] S.H. Baek, J. Park, D.M. Kim, et al., Giant piezoelectricity on Si for hyperactive MEMS, Science 334 (November (6058)) (2011) 958–961. [3] V. Flauraud, R. Regmi, P.M. Winkler, D.T.L. Alexander, H. Rigneault, N.F. Hulst, M.F. García-Parajo, J. Wenger, J. Brugger, In-plane plasmonic antenna arrays with surface nanogaps for giant fluorescence enhancement, Nano Lett. 17 (March (3)) (2017) 1703–1710. [4] X. Zhang, M. Han, R. Wang, F. Zhu, Z. Li, W. Wang, H. Zhang, Frequency-multiplication high-output triboelectric nanogenerator for sustainably powering biomedical microsystems, Nano Lett. 13 (March (3)) (2013) 1168–1172. [5] Z. Li, Y. Hao, D. Zhang, T. Li, G. Wu, An SOI–MEMS technology using substrate layer and bonded glass as wafer-level package, Sens. Actuators A Phys. 96 (January) (2002) 34–42. [6] R. Abdolvand, B. Bahreyni, J.E.-Y. Lee, F. Nabki, Micromachined resonators: a review, Micromachines 7 (September (9)) (2016) 160–216. [7] A. Ganesan, C. Do, A. Seshia, Phononic frequency comb via intrinsic three-wave mixing, Phys. Rev. Lett. 118 (January (3)) (2017), 033903. [8] C.T.-C. Nguyen, MEMS technology for timing and frequency control, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54 (February (2)) (2007) 251–270. [9] J.T.M.V. Beek, R.J. Puers, A review of MEMS oscillators for frequency reference and timing applications, J. Micromech. Microeng. 22 (December (1)) (2011), 013001. [10] R.A. Johnson, M. Borner, M. Konno, Mechanical Filters-A review of progress, IEEE Trans. Sonics Ultrason. 18 (July (3)) (1971) 153–168. [11] D.F. Sheahan, R.A. Johnson, Crystal and mechanical filters, IEEE Trans. Circuits Syst. CAS-22 (February (2)) (1975) 69–89.
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Biographies
Fei-Hong Bao received his B.E. degree from Shenyang Ligong University in 2013. He is currently pursuing the Ph.D. degree at the School of Electronic Science and Engineering, University of Electronic Science and Technology of China (UESTC), Chengdu, China. His research field covers the energy loss mechanism and spurious modes suppression of thin-film piezoelectric-on-silicon MEMS resonators.
Dr. Jing-Fu Bao is currently a Professor at University of Electronic Science and Technology of China (UESTC). He received the Ph.D. degree in Integrated Circuit and Microelectronic System from University of Electronic Science and Technology of China (UESTC) in 1996. From 1998 to 2005, He joined Sony Corporation in Tokyo as a research scientist. His research interests are focused on Frequency Synthesizer, Linear High Amplifier and Radio-frequency (RF) MEMS. He has published more than 130 peer-reviewed papers, including IEEE Transactions on Power Electronics, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, etc., and received several awards including the First-class Prize of Sichuan Province Science and Technology Progress in Electronic Industry and the Outstanding Science and Technology Youth Prize in Sichuan Province. Dr. Joshua En-Yuan 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, U.K. He joined the faculty of the Department of Electronic Engineering, City University of Hong Kong in June 2009, where is currently an Associate Professor and is affiliated with the State Key Laboratory of Millimetre Waves. He is also the Program Leader for Postgraduate Studies, in which capacity he is responsible for graduate affairs and admissions. In 2017, he was a visiting professor at University Grenoble Alpes in France. His research interests include the design, analysis, and characterization of Micro Electro Mechanical Systems (MEMS) for sensing and frequency control applications. Dr Lee is a Senior Member of the IEEE. He has served on the Technical Program Committees of various conferences including ISQED, IFCS, and Transducers. Lei-Lei Bao received her B.E. degree from University of Electronic Science and Technology of China in July 2017. She is currently a Master Course student in Precision Engineering, University of Tokyo, Japan, since October 2017. Her research field covers the microneedle technology and piezoelectric MEMS resonators.
Dr. Muhammad Ammar Khan received his Doctor degree in 2015 from UESTC Chengdu in the field of Engineering Physics. Currently he is working as Senior Research Fellow in School of Electronic Science Engineering, UESTC. His research interests include Polymers, Diodes, Organic Semiconductors, Electrical properties of Materials, Radio frequency devices, Phononic crystals MEMS/NEMS technology.
Xin Zhou was born in Henan province, China in 1995. He received the B.S. degree in electronic information science and technology from Changchun University of Science and Technology in July 2017. He is currently studying as a master student in the School of Electronic Science and Engineering, University of Electronic Science and Technology of China (UESTC). His research interests include MEMS resonators, especially the application of phononic crystal to reduce the energy loss of thin-film piezoelectricon-silicon (TPoS) resonator.
Qi-Die Wu is currently pursuing the bachelor degree at the Yingcai Honors College, University of Electronic Science and Technology of China (UESTC), Chengdu, China. His research field cover the energy loss mechanism of thin-film piezoelectric-on-silicon resonators.
Ting Zhang received the Bachelor’s degree in Electronics and Information Engineering from China Three Gorges University (CTGU) in 2013. Now he is pursuing his PHD degree in circuit and system from University of Electronic Science and Technology of China (UESTC). As a joint doctoral student training, he joined University of Technology Sydney (UTS) to research Millimeter-Wave Radio Frequency Integrated Circuits (RFIC) for 5G Communications: Part I RF Chain up-Conversion Link. His research interests include RF/microwave filter, oscillator, switch and amplifier. He has published several journal papers and conference papers. Dr. Xiao-Sheng Zhang is currently a Professor at University of Electronic Science and Technology of China (UESTC). He received the Ph.D. degree in Microelectronics and Solid-State Electronics from Peking University in 2014. And then he joined École Polytechnique Fédérale de Lausanne (EPFL), Switzerland, as a research scientist, and also served as a research associate at The University of Tokyo, Japan. His research field covers the micro/nano electronic science and technology, and especially its application for self-powered micro/nano electronics.