Influence of a Tailored Oxide Interface on the Quality Factor of Microelectromechanical Resonators

Piezoelectric microelectromechanical systems (MEMS) are used as sensors, actuators, energy harvesters, accelerometers, and communication modules. Aluminum nitride (AlN) is an especially attractive piezoelectric material because its fabrication process allows it to be integrated into semiconductor circuitry to deliver a fully integrated solution. Microelectromechanical resonators with AlN sandwiched between n‐type silicon (Si) and top metal electrode with and without a silicon oxide layer are designed and fabricated. The effect of the oxide film is up to a fourfold increase in quality factor (Q) that is consistent from very high frequency (VHF) to super high frequency (SHF). This effect is demonstrated using thin plate bulk acoustic wave modes from 70–80 MHz using the second contour mode and first width extensional mode and from 9.5–10.5 GHz using high overtone thickness modes. To explore potential applications of AlN‐transduced Q‐enhanced MEMS devices in harsh environments, measurements from −200 °C to +200 °C are performed. The Q enhancement is persistent across a wide temperature range for both VHF and SHF resonators with the added oxide layer. Furthermore, AlN‐on‐Si resonators that have a comparable temperature coefficient of frequency to silicon carbide‐based resonators in commercial applications are demonstrated.


Introduction
Piezoelectric materials have been widely used to facilitate efficient electromechanical transductions in a variety of important applications ranging from energy harvesting, [1][2][3] signal processing, [4][5][6] health, [7][8][9] automotive, [10,11] robotics, [12,13] to defense and aerospace environments. [14,15] When compared to other common microelectromechanical systems (MEMS) transduction methods such as thermal/piezoresistive, [16][17][18] capacitive, [19][20][21][22] and electrostatic [23][24][25] schemes, piezoelectric materials have a higher energy density, better frequency scaling, lower power configurations, and are easier to characterize and content) and it does not require a post-deposition poling step. [47] Furthermore, AlN can be doped with scandium to increase electromechanical coupling while maintaining a high quality (Q) factor [53] or to add ferroelectric behavior. [54] As a piezoelectric, AlN has been successfully implemented in transducers for a wide range of devices including energy harvesters, acoustic devices, sensors, actuators, RF filters and duplexers, [47,55,56] and accelerometers. [14] AlN has also been successfully implemented as part of the gate dielectric in thin film transistors. [57] The integration of CMOS and MEMS devices on a single chip reduces die size, power consumption, and manufacturing costs. [47] In many applications, it is most important that the piezoelectrically transduced resonant devices have extremely high Q. A narrower bandwidth at resonance enables a higher sensitivity and resolution for precision sensing tasks. High Q resonant devices have a lower loss for signal processing and energy harvesting. Lower loss results in a strong signal in RF processing and higher output in energy harvesting applications. In general, the lower Q the resonator has, the higher the system noise and interference. [19] Q enhancement has focused on reducing both intrinsic losses from material and resonator dimensions and extrinsic losses such as support and air/fluid losses. Enhancement methods include the use of phononic crystals, dispersion-engineered resonators, support transducer topologies, micromachined reflectors, [19] and doping. [53] Largely due to their small size and low power consumption, these devices are seen as well suited for aerospace and power applications. Piezoelectric accelerometers used in inertial sensors for air and spacecraft navigation systems are subject to extreme vibration and loading. Resonant devices in spacecraft communication systems are subject to large temperature fluctuations (−230 °C to +180 °C) [58] and a wide range of radiations (electron, proton, neutron, and electromagnetic). [59] Piezoelectric sensors used for temperature and vibration monitoring [14] in nuclear reactors are exposed to extreme gamma and neutron radiation. Significant research has gone into demonstrating these devices maintain functionality these in harsh thermal, [60] pressure, [61] and radiation environments. [14] We designed AlN transduced thin plate resonators with and without a silicon oxide (SiO 2 ) layer. FEA harmonic analysis is used to predict resonant frequencies and mode shapes of the two designs. The designs were sent to a commercial foundry, MEM-SCap, for fabrication. To explore potential applications of these devices in harsh environments, we performed RF characterization from −200 °C to +200 °C as illustrated in Figure 1. The effect of the added oxide layer is up to a fourfold increase in Q that is consistent across a wide frequency range (VHF-SHF) and temperature range. This effect is demonstrated using bulk acoustic wave (BAW) modes from 70-80 MHz using the second contour mode (CM) and first width extensional mode (WEM) and from 9.5-10.5 GHz using high overtone thickness modes (TM). Furthermore, we have demonstrated AlN resonators on a silicon substrate that have a comparable temperature coefficient of frequency (TCF) to silicon carbide (SiC). [62] The TCF at room temperature was ≈−30 ppm °C −1 for the VHF resonators and −35 ppm °C −1 for the SHF resonators. TCFs of less than ±50 ppm °C −1 are considered suitable for time-keeping in handheld wireless devices. [63]

Experiment
We performed a systematic study to see the influence of thin oxide film on TCF, Q, motional resistance (R m ), and effective electromechanical factor ( eff 2 k ) of bulk mode resonators. We chose rectangular thin-plate resonators for this study. The rectangular thin-plate resonators are designed to be driven in different BAW modes by applying an RF signal across the top and bottom electrodes thereby activating the d 31 [64,65] or d 33 vibrational modes in the AlN. The specific BAW vibrations investigated in this work are the first WEM, second contour We have demonstrated AlN resonators on a silicon substrate that have comparable TCF to SiC. [62] www.advmatinterfaces.de mode (CM), [28] and high overtone TM. The first WEM and second CM vibrations are in-plane and the high overtone TM vibrations are out of the plane. The layout and key dimensions of the rectangular flat plate resonator are presented in Figure 2. The frequency equation for rectangular plate CM vibrations is given by the transcendental equation: [28] cot 2 and E eq , ρ eq , and µ eq are the equivalent Young's modulus, equivalent density, and equivalent Poisson's ratio of the material stack suspended in the resonator, respectively. W and L are the width and length of the rectangular plate, respectively, and ω is the angular frequency. In the case where L ≫ W, the solution to the rectangular plate CM converges such that the resonance frequency (f r ) of the can be approximated by: [19,38,46] 2W f E r eq eq κ ρ = where κ is a dimensionless constant that is dependent upon the mode shape. [19] When κ = n, Equation (2) predicts the resonant frequency for the nth WEM vibration. The same approximation may be made for the nth TM vibration by replacing W with thickness, t. [19] Qualitative illustrations of the vibrational modes are presented in Figure 3. FEA simulations were accomplished with Ansys Mechanical to predict the resonant frequency and mode shapes using the material properties presented in Table S1 (Supporting Information). The BAW vibrational modes and their corresponding resonant frequencies are presented in Table S2 (Supporting Information).
The resonator designs were built using MEMSCap's Piezo-MUMPs fabrication process (see Figure S4, Supporting Information section). [66] The resonators built for the experiment were designed to not exceed a 400 × 200 µm footprint, to include the contact electrodes. The resonators are suspended in the air by two anchors and are ≈220 × 60 µm across and 12 µm thick. The rectangular thin plate consists of a 10 µm thick n-type Si (100) layer with a 0.5 µm thick AlN transduction  layer. The structural n-Si also acts as the bottom conductor. A 1.0 µm Al and 20 nm chrome (Cr) stack is used as the top electrode. We designed devices with and without an oxide layer such that the top electrode and AlN layers were identical. Scanning electron micrographs of the completed resonators are presented in Figure 4. The first design has the SiO 2 layer sandwiched between the AlN and Si (Figure 4b), and the second only uses the SiO 2 as an insulation layer between the top and bottom electrodes (Figure 4a). The device dimensions are summarized in Table 1. Cross-sectional SEM images of the devices are provided in Figure S5 (Supporting Information) section. The imagery shows the Al, Cr, AlN, SiO 2 , and n-Si layers are uniform and well-defined.
Two-port scattering parameters (S-parameters) of the resonators operating in the different modes were measured under vacuum using a Lake Shore cryogenic probe station. An Agilent/Keysight N5222A PMA microwave network analyzer was used to record the S-parameters. The two-port S-parameters were recorded in 10 °C increments from −200 °C to +200 °C at 1.0 (±0.3) µTorr. The network analyzer RF input power was 0 dBm. Two-port short-open-load-through calibration was accomplished to correct line and probe errors. Three randomly selected AlN-on-SiO 2 resonators and three AlN-on-Si resonators were measured to capture variance. An illustration of the experimental setup is presented in Figure 5.
S-parameter data was post-processed to measure f r , Q, motional resistance (R m ), and one port effective electromechanical factor ( eff 2 k ). Q was measured using: [46] where BW 3dB is the bandwidth at 3 dB less than the peak. R m and one port eff 2 k were calculated using the following equations, respectively: [19,46] where Z o is the termination impedance, IL is the insertion loss at the resonant frequency, and f a is the frequency at anti-resonance. The temperature coefficient of frequency (TCF) is calculated using: [46] TCF 1 f where T is temperature, and the units of TCF are presented as ppm °C −1 .

VHF Vibrational Modes
S-parameters were experimentally measured for VHF resonant modes of the rectangular flat plate from −200 °C to +200 °C at 1.0 (±0.3) µTorr. Mode shapes and resonant frequencies were predicted using FEA harmonic analysis. The FEA harmonic analysis of the VHF regime is presented in Figure S3a (Supporting Information). Extensional and contour modes are dominant in the VHF regime. Illustrations of the second CM and first WEM are provided in Figure S1 (Supporting Information). As a general trend, R m for the first WEM is greater than that of the second CM. In both modes f r and Q decrease and R m increases as temperature increases. Q values of the resonator with the oxide layer are consistently greater than those of the  device without the oxide layer, even at high temperatures. An example of the enhanced Q, the shift in frequency, and peak broadening with increasing temperature are clearly illustrated in Figure 6.
The TCF, R m , Q, and one port eff 2 k for the first WEM vibrations from −200 °C to +200 °C are presented in Figure 7a-d, respectively. TCF at room temperatures are −29.8 ± 1.0 ppm °C −1 for the baseline resonator (no SiO 2 layer) and −31.2 ± 2.0 ppm °C −1 . for the resonator with the SiO 2 layer. TCF is not significantly different between the two designs across all evaluated temperatures. The SiO 2 layer increases R m by ≈2.3 kΩ and decreases eff 2 k by 0.2% at room temperature. However, adding the oxide layer increases Q by up to 7000 points in some cases. At room temperature, Q for the baseline resonator is 1410 ± 810 and 8040 ± 800 for the resonator with the SiO 2 layer. The addition of the oxide layer increased Q by 5.7 times. Statistical analysis shows the difference in Q is significant within a 90% confidence interval (α = 0.1) up to +180 °C. Quality factors over 10 000 are achieved at cryogenic temperatures.
Results for the second CM are presented in Figure 8. Baseline TCF at room temperature is −26.4 ± 1.2 ppm °C −1 and −28.4 ± 1.4 ppm °C −1 for the device with the oxide layer. Overall, there are no significant differences in TCF behavior. Similar to the first WEM vibration, R m is roughly doubled by adding the SiO 2 layer. The effective electromechanical coupling of the device with the SiO 2 layer is consistently below the baseline device, but the difference does not exceed the 90% confidence interval threshold of statistical significance. At room temperature, baseline Q is 412 ± 61. Adding the oxide layer increases Q to 2400 ± 250, 5.8 times greater than baseline. Statistical analysis demonstrates the Q enhancement is significant within a 90% confidence interval across the entire evaluated temperature range.

SHF Vibrational Modes
S-parameters were experimentally measured for SHF resonant modes of the rectangular flat plate from −200 °C to +200 °C at 1.0 (±0.3) µTorr. Mode shape and resonant frequencies were predicted using FEA harmonic analysis. The FEA harmonic analysis of the SHF regime is presented in Figure S3b (Supporting Information). In the SHF regime, the higher-order CM and WEM vibrational modes have completely decayed and the resonance is dominated by TM vibrations. The measured high overtone TM vibrations were between 9.5 to 10.5 GHz. Illustrations of the high overtone TM shapes are provided in Figure S2 (Supporting Information). As a general trend, f r and Q decrease with increasing temperature. Unlike the VHF vibrational modes, R m decreases with increasing temperature in the SHF thickness mode vibrational regime; however, the noise floor also increases. This is because the RF signal at SHF easily leaks via the feedthrough capacitance, causing the entire noise floor to go up. Some Q enhancement is still present, although less apparent from a qualitative perspective than the VHF vibrational modes. Notably, a high-frequency "ringing" is present in this frequency range across all measured devices. The ringing is more prevalent at lower temperatures. The magnitude of the

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ringing is much smaller for the resonator with the SiO 2 layer than the device without the oxide layer. A deeper study into the reduction of the ringing in the device with an oxide layer is beyond the scope of this paper; however, it merits further investigation. The frequency shift and spurious mode damping are clearly illustrated in the example presented in Figure 9.
TCF, R m , Q, and one port eff  Figure 10, Figure 11, and Figure 12 for the 9.65, 10.0, and 10.35 GHz vibrations, respectively. Across all three modes, the average TCF at room temperature was −34.0 ± 3.1 ppm °C −1 for the baseline device and −37.9 ppm °C −1 ± 4.4 for the device with the added SiO 2 layer. Similar to the first WEM and second CM vibrations, the addition of the oxide layer increased R m , with the average baseline at 5.2 ± 0.1 kΩ and average R m for the device with the oxide layer at 7.3 ± 0.1 kΩ at room temperature. At low temperatures, some Q enhancement was observed. Devices with an oxide layer exhibited Q as high as 700 at temperatures less than −100 °C. At similar temperatures, the highest demonstrated Q for devices without the oxide layer was 350.

Discussion
The overall Q of a system is found by summing the dissipated energies. This is more commonly written as the sum of quality factors associated with each source of loss (Q i ): [46,67,68] Sources of loss are divided into intrinsic and extrinsic sources. Intrinsic losses are solely dependent upon the materials and dimensions of the resonator and include dielectric, piezoelectric, phonon-phonon interaction, and phononelectron interaction losses. Extrinsic losses are those losses not fundamentally bound to material properties and include anchor, fluid, surface, and ohmic losses. [46] With the exception of the added SiO 2 layer, the resonators are identical in geometry, anchor design, and environment. Therefore, we identify the primary cause of Q enhancement as an improvement in acoustic impedance mismatch between the AlN and Si layers.
The characteristic specific acoustic impedance, Z o , is given by the product of acoustic velocity, c, and mass density. [69] Using the densities, acoustic velocities, and characteristic specific acoustic impedances as presented in Table 2; without the oxide layer there is a large acoustic impedance mismatch between the dielectric layer and the silicon (|ΔZ o | = 12.8). With the oxide layer, the AlN-SiO 2 dielectric layer has an average acoustic impedance of 22.8 MPa s m −3 (|ΔZ o | = 3.1). Thus, at VHF range, Q improves when the oxide layer is added.
Akhiezer-type phonon-phonon interaction losses become dominant in the SHF range. [46,70] Akhiezer loss describes the interaction between thermal phonons and vibrational phonons when phonon scattering time is much shorter than one period of vibration (i.e., τ s ≪ τ v ). Irreversible loss occurs as phonons interact with each other. Q AKE associated with this loss is found using the formula: [46,71] where ρ is the material density, c is the acoustic velocity, f is the frequency of vibration, γ avg is the average Grünesen's parameter, Figure 6. A measured VHF frequency response for a rectangular flat plate resonator a) without an oxide layer and b) with an oxide layer. The resonator with the oxide layer exhibits significantly greater Q for both modes.
As a general trend, as the temperature increases, Q and resonant frequency decrease and R m increases.

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T is temperature, and k is thermal conductivity. As frequency increases, Q AKE decreases proportionally and the loss improvement given by the oxide layer is overcome by Akhiezer phonon-phonon interaction losses. This explains the dissipation of the Q enhancement for the high-overtone TM vibrations as T and f increase.

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Other loss sources such as thermoelastic damping (TED), squeeze film damping, surface losses, and air damping are less significant. TED describes the process of phonon diffusion from sections of higher temperature to lower temperature spots. TED in bulk-mode resonators is considered negligible in the frequency range for which they are utilized. [46] Squeeze film damping is negligible because there are no small air gaps around the resonator. Surface losses can be considered negligible because the surfaces do not change between the VHF and SHF regions. Finally, air damping can be ignored because the devices were measured in a vacuum for both VHF and SHF cases.
This experiment was limited to an SiO 2 layer thickness of 200 µm. The analytical solutions presented by Chandrahalim, et al. [38] provide some indications to the changes in resonator performance as the oxide layer is changed. Resonant frequency will be modified as , motional resistance will change as / . The Young's modulus of SiO 2 thin films is much less than Si while their mass densities are comparable. [72] Therefore, it is expected that f r will decrease with increasing oxide layer thickness and R m is dependent upon both layer thickness and elasticity. These effects are demonstrated using FEA mechanical simulation and the results are presented in Figure S6 (Supporting Information). In this case, f r and IL decrease linearly with increasing oxide layer thickness. Dielectric losses are not captured by mechanical-only FEA models. The dielectric loss tangent of AlN thin films is less than that of pure SiO 2 films. [73,74] As the thickness of the oxide layer increases, the dielectric loss due to the higher loss tangent of the oxide film will overcome the benefit of the acoustic impedance matching and reduce the device's quality factor. Future work will focus on validating this experimentally.

Conclusion
This paper presents a low-cost, CMOS-compatible method to enhance resonator Q factor ranging from VHF to SHF applications. Piezoelectric MEMS resonators are used in numerous engineering, aerospace, and communication systems and are used for timing, filters, sensors, and inertial navigation devices. High Q resonators are needed as higher sensitivity and resolution devices are required. Reducing the effects of system noise and interference are a key motivation of Q enhancement research.
We intentionally designed resonators to assess the Q enhancement caused by adding a silicon oxide thin film to a rectangular thin plate resonator. FEA techniques were used to evaluate resonator design operating in VHF (second CM and first WEM) and SHF (high overtone TM) vibrational modes. To validate the FEA results, an experiment was designed to demonstrate Q enhancement across a wide temperature range. The resonators were built using the PiezoMUMPs fabrication process. The S-parameters of the second CM, first WEM, and high overtone TM were measured from −200 °C to +200 °C in high vacuum conditions. Significant Q enhancement was present at VHF modes and some Q enhancement was observed in SHF modes at low operating temperatures. Q enhancement is caused by the oxide layer reducing the impedance mismatch between the dielectric and silicon layers. The Q enhancement is overcome at high frequencies and high temperatures by Akhiezer-type phonon-phonon interaction losses.
The TCF of our devices is comparable to the TCF of SiCbased resonators. [62] Furthermore, AlN is CMOS compatible and is also considered operationally stable in harsh shock, temperature, and pressure environments. This allows designers to fabricate devices on Si, which is more Figure 9. A measured SHF frequency response for a rectangular flat plate resonator a) without an oxide layer and b) with an oxide layer. The resonator with the oxide layer exhibits a greater Q as well as a reduction in the magnitude of the higher frequency noise.
www.advmatinterfaces.de economical, supported by CMOS electronics, and easier to process than SiC. Thermal growth or sputtering of the SiO 2 layer can be integrated into the CMOS process. This work merits further research into other thin films that will also reduce acoustic impedance mismatch and can be incorporated into CMOS processing steps.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.