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Compensation, Tuning, and Trimming of MEMS Resonators Farrokh Ayazi, Roozbeh Tabrizian, Logan Sorenson Center for MEMS and Microsystems Technologies Georgia Institute of Technology Atlanta, GA, USA [email protected] Abstract—Fundamental characteristics of MEMS resonators such as acoustic velocity and energy dissipation may have strong temperature and process dependencies that must be carefully compensated in applications requiring high degrees of stability and accuracy. This paper presents an overview of compensation, tuning, and trimming techniques for MEMS resonators. The use of these techniques in implementation of high precision and high performance MEMS resonators is described, and the benefits and challenges of different approaches are discussed and compared.
I. INTRODUCTION As microelectromechanical resonators evolve from research labs to commercial products, maintaining high precision and repeatability across many performance parameters becomes increasingly important. The major performance metrics of MEMS resonators include their center frequency (f0), temperature coefficient of frequency (TCF), quality factor (Q), and motional resistance (Rm). Additional aspects such as power handling and linearity may be considered as appropriate to the application.
step and are referred to as wafer-level techniques. In this paper, an overview of compensation, tuning, and trimming techniques applied to MEMS resonators will be presented. II.
COMPENSATION TECHNIQUES IN MEMS RESONATORS
A. Compensation for Thermal Effects MEMS resonators typically show much larger temperature sensitivity compared to their quartz crystal counterparts. The temperature sensitivity of f0 can be defined and related to the temperature sensitivity of the resonator’s material properties by its TCF:
(1)
Depending on the specific application of the MEMS resonator, one or more of its metrics may require compensation [1]. While stringent control and device-todevice repeatability of f0 is required for nearly all of the applications of MEMS resonators to varying degrees of accuracy, the temperature sensitivity of f0 (and hence the TCF) is of major importance for resonators serving as analog signal processors and timing references, as well as environmental sensors, and must be kept within acceptable limits. Furthermore, cost restrictions place boundaries on the precision of fabrication processes used to implement these devices, imposing additional uncertainties on their performance.
where TCE, the temperature coefficient of Young’s modulus, and CTE, the coefficient of thermal expansion, are intrinsic material properties. The large TCF of the MEMS resonators is mainly a result of high TCEs of the materials commonly used to implement these devices. For silicon resonators, the large native TCF of 30 ppm/°C results in a frequency drift as large as 3750 ppm across the industrial temperature range of 40°C to 85°C. Major applications of MEMS resonators, such as temperature compensated crystal oscillators (TCXO) and thermally-stable sensors, often require sub-ppm instability levels, mandating a radical decrease in the TCF of these devices to facilitate full compensation through active electronic methods. Therefore, passive TCF compensation techniques are of great interest. Some examples of passive techniques are the compensation of material TCE through engineering of device geometry and/or doping profile, as well as the addition of a compensating material with a TCE of opposite sign to form a composite structure with reduced TCF.
The large amount of research invested in precise control of MEMS resonator metrics can be categorized into three groups: compensation, tuning, and trimming. Techniques developed under each of these categories may address resonator control at the device or system level and are applied in the design stage and/or post-fabrication. The most preferred techniques can be applied in batch across an entire wafer at once or in one
Figure 1 shows the SEM image of a TCF-compensated concave silicon bulk acoustic resonator (CBAR) in comparison with a rectangular geometry silicon bulk acoustic resonator (SiBAR). By opting for concave resonator geometries instead of the conventional circular or rectangular geometries, the TCF has been considerably reduced while the Q of the device has also been improved due to efficient
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Figure 1. Geometry-engineered TCF-compensated concave SiBAR (CBAR). Device shows a TCF of 6 ppm/°C at 105MHz with a Q of 100,000 [2].
compensation of energy leakage from the resonator towards surrounding substrate [2]. This device demonstrates the geometry engineering approach to compensation. Another group of TCF compensation techniques are based on selective introduction of dopants into the silicon substrate to reduce its large TCE by modifying the electronic energy levels. These techniques can be broadly termed doping profile engineering. Different works falling under this category include utilization of heavily P-doped [3,4] and N-doped silicon substrates [5,6], thermomigration of aluminum atoms into the silicon substrate [7], and carrier depletion of the device using multiple PN junctions [8]. More traditional TCF compensation techniques rely on addition of a compensating material. In these approaches, the large negative TCE of native silicon is compensated by addition of a material with positive TCE (usually silicon dioxide). Adding the correct amount of silicon dioxide to the silicon resonator forms a composite Si/SiO2 structure with temperature-compensated TCE. Figure 2 illustrates this concept schematically. The compensating silicon dioxide can be added in layers parallel to the resonator stack [9,10]. However, since a comparable amount of silicon dioxide is required for full TCF compensation, this technique is mostly applicable to thin substrates and low frequency flexural mode resonators, but
Figure 3. (top) Temperature-compensated SilOx bulk acoustic resonator with thin AlN transduction. (bottom) Temperature characteristic of f0 and Q [12].
more difficult to use for full TCF compensation of bulk acoustic wave (BAW) devices with thick substrates that offer high Q and superior power handling and linearity [3]. Alternatively, TCF compensation of silicon BAW resonators has been achieved by embedding a 2D array of silicon dioxide pillars inside the resonator [11]. Uniform distribution of silicon dioxide inside the silicon body of the resonator forms a homogenous composite material (a SilOx matrix); the addition of silicon dioxide does not degrade the main resonator characteristics such as Q, insertion loss (IL), and power handling. Careful design of the silicon dioxide distribution pattern across the resonator results in full cancellation of linear term of f0 thermal behavior [12]. Figure 3 shows the SEM picture of a 27 MHz length-extensional (LE) mode SilOx resonator with thin aluminum nitride (AlN) transduction layer (Q~7500, IL~15dB), showing 40-fold improvement in overall frequency drift across the temperature range of -20°C to 100°C. B. Compensation for Fabrication Process Uncertainities The resonance frequency f0 of resonators in arbitrary modes is described by the following equation:
Figure 2. Schematic representation of compensating a silicon resonator with silicon dioxide. When first order compensation has been achieved, a residual quadratic characteristic remains due to higher order residuals [11,12].
where L is a generalized length parameter dependent on the geometry of the device, Va is the effective acoustic velocity corresponding to L, and keff and meff are the effective stiffness and mass, respectively. Hence, variations in the resonance frequency can arise due to process-induced variations in the device geometry and material properties which affect the
compensated for in the resonator design. Process compensation is achieved when the effective stiffness to mass ratio in (2) is maintained, even under geometric changes to the device. Several methods have been taken to affect this condition in silicon resonators. For low frequency 32 kHz resonators, slots have been designed in the proof mass so that the effective mass changes in accordance with the effective stiffness of the flexural beams as they are subject to process variations [15]. For micromechanical I-shaped bulk acoustic resonators (IBAR), properly-designed tapered flanks can be used to balance the contribution of mass and stiffness changes [14,16]. In contrast, for high frequency SiBARs, perforations have been introduced which accommodate these dimensional variations [17]. Figure 4 shows a process-compensated thinpiezoelectric-on-substrate (TPoS) resonator design in which 4 μm by 4 μm perforations have been introduced to balance the stiffness to mass changes. This is evidenced by the middle plot of Figure 4, in which the relationship between frequency variation and lithographic process bias offset has been calculated for the design using finite element (FE) simulations. It can be seen that the 4 μm by 4 μm square perforations slightly overcompensate the design (indicating a negative trend with process bias) vs. the uncompensated design, even for different combinations of the piezoelectric transduction stack. Interestingly, the difference between the magenta firstorder analytical model from equation (2) and the blue circles from FE simulation of the structure is exactly explained by the addition of support tethers, indicating that the tethers themselves have a slight compensating effect.
Figure 4. (top left) Uncompensated TPoS resonator. (top right) Processcompensated 27 MHz TPoS resonator with a line of specially-designed 4 μm by 4 μm perforations. (middle) Frequency trends for 27 MHz TPoS resonators vs. DRIE trench critical dimension bias (delta). (bottom) Frequency trends of TPoS resonator vs. SOI device thickness for ±0.3 μm layer tolerance [17].
acoustic velocity. For instance, angular misalignment of ±0.1° from the [110] axis of silicon can theoretically affect the acoustic velocity (and frequency) of longitudinal acoustic waves by 1.8 ppm. Doubling the misalignment to ±0.2° increases the frequency shift to 7.3 ppm. Further impacting the repeatability of the acoustic velocity is dependence on doping levels. Similarly, sensitivity of Q to angular misalignment in SiBARs has been reported [13]. The acoustic velocities only experience change of less than 1% when switching from intrinsic to heavily phosphorous-doped silicon [14], so excellent control over the dopant contribution and angular misalignments is crucial. If the material contributions to initial frequency spread can be made negligible, then the remaining contributions come from the geometrical variations in the device. In silicon-based MEMS resonators, the Bosch DRIE process is typically used to create high aspect ratio trenches which define the in-plane dimensions of the resonator. Often, for in-plane resonators, the resonance frequency strongly depends on one or more of these trench-defined dimensions. Therefore, systematic changes in these dimensions must be well-understood so that they can be
In addition to lithographic process compensation, attention must be given to the thickness dependencies as well. Although the thickness has a negligible effect for plain SiBARs in certain thickness regimes [18], this assumption does not hold for TPoS resonators. Since these resonators are formed from a composite stack of materials, including the silicon layer as the bulk of the device, the AlN piezoelectric layer, and molybdenum top and bottom electrode layers, the effective acoustic velocity is a composite parameter of these layers, depending on the relative stack thicknesses. Since the AlN and Mo layers are formed by thin film deposition, their thicknesses can be controlled to high accuracy. Therefore, the dominant variations will come from the SOI wafer, which are often toleranced to ±0.3 μm from the vendor. Substituting these numbers into a first order analytical model which takes into account the relative thickness of each layer, it is found that increasing the nominal silicon thickness can significantly reduce the resonators’ sensitivity to the silicon layer thickness (Fig. 4, bottom). C. Compensation for Quality Factor In certain applications of MEMS resonators, control and compensation of Q are paramount to obtaining reliable performance. For the case of MEMS vibratory gyroscopes, it can be desirable to operate at high frequencies so that high Q devices can be used to get large sensitivity, while at the same time maintaining large bandwidth for high dynamic range. One example of this approach is the Q-controlled spoke gyroscope, in which the Q was purposefully limited by the thermoelastic damping (TED) in the central spoke region [19]. Since the coupling between the thermal and elastic domains is
Figure 5. AlN-on-silicon TPoS bulk acoustic resonator with linear acoustic bandgap (LAB) structures as supports providing Qsupport compensation [28].
directly proportional to the absolute temperature, this mechanism has a strong temperature dependency. It also depends strongly on the mode shape of the resonator, with high frequency bulk acoustic modes generally being less subjected to TED than their low-frequency flexural beam counterparts [20]. However, selective addition of release holes can introduce additional TED by modifying the overall effective thermal paths [21]. Another important source of energy dissipation in MEMS resonators is energy leakage through their supporting tethers [21-24]. These tethers connect the released resonant structure to its surrounding substrate. Since point supports are desirable, the finite size of these tethers limited by photolithography precision increase the energy leakage from the resonator. However, proper design of these supports can provide passive compensation for support loss mechanism. A group of these methods focus on reflection of leaked waves back in to the resonator by creating acoustic mismatch at support region [25,26]. Although these techniques provide considerable improvement in Qsupport, substantial elimination of support leakage at the resonance frequency requires the engineering of phononic band structure of the material. This has been realized by implementation of acoustic bandgap structures [27,28]. These structures provide a frequency band in which phonons cannot be propagated. By selectively engineering the bandgap to include the resonance frequency of the resonators, full compensation of support loss can be achieved. Figure 5 shows an AlN-on-Si bulk acoustic resonator with linear acoustic bandgap supports as well as the corresponding phononic band diagram, where the bandgaps are shaded in blue. In addition to these passive compensation techniques, new research has emerged based on using the acoustoelectric effect in semiconductor piezoelectric resonators to provide an active means for Q compensation [29]. In this method, interactions
Figure 6. A 20 MHz IBAR with large frequency tuning range [33].
between phonons and free charge carriers [24] are used to amplify the acoustic waves propagating through the microresonator, compensating the attenuation due to different loss mechanisms [21] and thereby improving the Q. D. Compensation for Polarization Voltage Capacitive resonators require a DC polarization voltage (VP) for operation. This translates in to the requirement of additional circuitry resulting in incompatibility of these resonators with low-voltage CMOS processes. Moreover, since several characteristics of these devices are sensitive to the VP, stringent control is required to provide a constant DC voltage on-chip over all resonator operating conditions, which adds further complexity to the CMOS interface. Several techniques have been introduced for VP compensation based on charge trapping inside the electrically-isolated resonant silicon microstructures [30,31]. III. TUNING METHODS Although TCF and process compensation techniques considerably reduce the amount of temperature and processinduced frequency drifts and uncertainties, full compensation of residual f0 deviations as well as drifts caused by aging effects requires dynamic adjustment which is provided by tuning mechanisms. Frequency tuning can be addressed in both device and system levels. A. Device-Level Tuning These tuning mechanisms provide electronic f0 tuning for individual resonators through electromechanical transducers
IBARs [34]. Although application of electrostatic tuning is convenient in capacitive resonators, since the motional resistance of these devices is highly sensitive to their VP, electronic tuning of f0 results in fluctuations of the resonator’s IL, which is usually not desirable. This problem has been solved by separation of the capacitive tuning electrodes from the AC electromechanical transducer [35]. Figure 7 shows a 32 kHz flexural resonator with AlN piezoelectric transduction and electrostatic tuning. Having a large tuning pad which jointly serves as a frequency-loading mass enables large f0 tuning capable of covering the temperature-induced frequency drift across the entire oscillator industrial temperature range.
Figure 7. A 32 kHz flexural-mode resonator with AlN piezoelectric transduction and electrostatic tuning [35].
and by changing the effective equivalent stiffness of the micromechanical resonator. Electrostatic tuning has traditionally been the most commonly employed device-level tuning mechanism. In this technique, an electrical spring whose stiffness is tunable via DC voltage is added in series with the mechanical stiffness of the resonator and provides continuous f0 tuning with a quadratic characteristic. While small stiffness of the electrical spring, resulting from low-efficiency electrostatic transduction, makes this tuning technique more appropriate for low frequency flexural mode resonators [32], large tuning ranges have also been reported for high frequency bulk acoustic devices with efficient sub-μm capacitive gaps [14,33]. Figure 6 shows a high frequency (20 MHz) IBAR designed for maximum tunability. Temperature-compensated oscillators have been built using this tuning mechanism in
Figure 8. System diagram of a 27 MHz temperature-stable MEMS oscillator with sub-ppm instability using SilOx resonator and system-level tuning [12].
Another electronic device-level tuning mechanism which is capable of providing large tuning ranges is based on ovenization of the microresonator via Joule heating. In this technique, a tunable DC current passing through a heater element results in increased resonator temperature and hence controllable frequency changes due to the large TCF of uncompensated resonators [36-38]. The highest efficiency and agility of thermal tuning has been achieved by selfovenization of silicon resonators. In this technique, the heating current passes through the device and the resonator serves as the micro-oven simultaneously [37,38]. In addition to electrostatic and thermal tuning techniques, a tuning mechanism which is applicable to piezoelectricallytransduced MEMS resonator is the piezoelectric stiffening effect. In this technique the stiffness of the piezoelectric film is controlled by tuning its electric termination at the tuning port [39,40]. B. System-Level Tuning System-level tuning and frequency control mechanisms are applied to the systems where MEMS resonator serves as the frequency reference. These techniques include the use of phase-locked loops [41] or addition of tunable electrical impedances and phase-shifters in series and/or in parallel with the resonator [12,42,43]. Systems employing these techniques can tune out the residual frequency drifts and uncertainties of TCF and process compensated resonators, to form highlystable frequency references. Figure 8 shows the schematic design of a 27 MHz oscillator implemented from the TCFcompensated SilOx resonator of Figure 3 in addition to tunable capacitors and phase-shifters embedded in series with the resonator in the oscillator loop. IV. TRIMMING METHODS Trimming refers to the permanent shift of a device parameter, usually performed after fabrication. Commonly, trimming is achieved using selective addition (e.g., metal deposition [44]) or removal of material, such as with laser ablation [45]. Emerging methods include localized growth of oxide on thermally-actuated silicon resonators [46] and metal diffusion via formation of metal-silicon eutectic alloys at elevated temperatures [47,48]. The latter is achieved by passing a controlled DC current through the body of the silicon resonator, causing its temperature to increase via Joule heating. This is an especially attractive technique because it allows post-vacuum-packaging trimming at the wafer or
well as reconfigurable arrays of MEMS filters. Further research is required to study the accuracy and stability limits of trimming techniques for MEMS resonators. Fabrication processes that enable simultaneous realization of compensation, tuning and trimming of MEMS resonators are of great interest and need to be developed. ACKNOWLEDGMENT The authors wish to acknowledge contributions from current and former members of the Integrated MEMS Laboratory. The work on compensation, tuning and trimming of MEMS resonators at Georgia Tech Integrated MEMS Laboratory and CMMT has been made possible through support from DARPA, NSF, ST Microelectronics, and Integrated Device Technology (IDT). Enhanced stiffness dominates
Resonance Frequency of the SiBAR at 25 C (in MHz)
100
REFERENCES
Pre-Joule Heating
99.8
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Heating at 30 mA for 1 hour before cooling to 25C Heating at 30 mA for 2 hours before cooling to 25C
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Heating at 30 mA for 3 hours before cooling to 25C
Diffusion time
99.4
[2]
Heating at 30 mA for 4 hours before cooling to 25C
40% Mass loaded SiBAR shifts up by 240 kHz
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Mass loading dominates
80% Mass loaded SiBAR shifts up by 17 kHz
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98.6 0
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[3] 100
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Figure 9. (top: a-d) Schematic representation of gold-diffusion-based trimming in gold-coated SiBARs. When a current is passed through the SiBAR body, the temperature is raised above the Au-Si eutectic temperature, allowing the gold layer to diffuse into silicon. (bottom left) Frequency uptrimming is achieved with Au-Si eutectic, since the Au-Si bond is stronger than the Si-Si bond. (bottom right) Frequency down-trimming achieved with Al-Si thermomigration, since Al-Si bonds are weaker than Si-Si bonds [48].
individual device levels. No material is vaporized within the vacuum package, allowing the package to maintain a high vacuum. Use of different metals allows either up or down trimming. For Au, the resonance frequency increases after running the thermal current, since the Au-Si bond is higher in strength than the Si-Si bond. For Al, the resonance frequency decreases after trimming because the Al-Si bond is lower in strength than both Au-Si and Si-Si bonds. Al was also found to be preferred from a trimming time standpoint, since Al thermomigrates against thermal gradients, whereas Au-Si bonding requires reaching the eutectic temperature to activate the trimming process. V. CONCLUSION Compensation and tuning of MEMS resonators has enabled their successful commercialization in the timing market, with the range of products and specifications expanding rapidly [49]. While the majority of temperature compensation effort so far has concentrated on system-level techniques that are power consuming, a significant opportunity lies in device-level compensation techniques that consume little to no power, promising the realization of low power reference oscillators with ppb inaccuracies. Significant research is underway to improve and control the quality factor (Q) and motional resistance (Rm) of MEMS resonators at both low and high frequencies in the presence of temperature and process variations. This will enable new classes of ultra-stable integrated devices such as angle measuring gyroscopes, accelerometers, magnetometers, and environmental sensors as
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[33] G. K. Ho, K. Sundaresan, S. Pourkamali, and F. Ayazi, "Micromechanical IBARs: Tunable High-Q Resonators for Temperature-Compensated Reference Oscillators, IEEE Journal of Microelectromechanical Systems, Vol. 19, Issue 3, pp. 503-515. [34] K. Sundaresan, G.K. Ho, S. Pourkamali, and F. Ayazi, “Electronically temperature compensated silicon bulk acoustic resonator reference oscillators,” IEEE Journal of Solid-State Circuits, Vol. 42, No. 6, June 2007, pp. 1425-1434. [35] D. E. Serrano, R. Tabrizian, and F. Ayazi, "Electrostatically Tunable Piezoelectric-on-Silicon Micromechanical Resonator for Real Time Clock," IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 59, Issue 3, March 2012, pp. 358-365. [36] A. Tazzoli, M. Rinaldi, and G. Piazza, “Ovenized high frequency oscillators based on aluminum nitride contour mode MEMS resonators,” in Proc. IEEE IEDM, Dec. 2011, pp. 481–484. [37] K. Sundaresan, G. K. Ho, S. Pourkamali, and F. Ayazi, “A Low Phase Noise 100MHz Silicon BAW Reference Oscillator,” IEEE Custom Integrated Circuits Conference, 2006 (CICC ’06), pp. 841–844. [38] R. Tabrizian and F. Ayazi, "Reconfigurable SiBAR Filters with Sidewall Aluminum Nitride Signal Transduction," Solid-State Sensors, Actuators, and Microsystems Workshop (Hilton Head 2012), Hilton Head, SC, June 2012, pp. 98-99. [39] M. Shahmohammadi, D. Dikbas, B.P. Harrington, and R. Abdolvand, “Passive Tuning in Lateral-Mode Thin-Film Piezoelectric Oscillators,” in Proc. 2011 Joint Conference of the IEEE International Frequency Control Symposium(IFCS) and European Frequency and Time Forum(EFTF), San Francisco, CA, May. 2011, pp. 1-5. [40] R. Tabrizian and F.Ayazi, "Tunable Silicon Bulk Acoustic Resonators with Multi-Face AlN Transduction," Proceedings of the 2011 Joint IEEE International Frequency Control Symposium & European Frequency and Time Forum (IFCS/EFTF 2011), San Francisco, CA, May 2011, pp. 749-752. [41] J. Salvia, R. Melamud, S. Chandorkar, S. F. Lord, and T. W. Kenny, "Real-Time Temperature Compensation of MEMS Oscillators Using an Integrated Micro-Oven and a Phase Lock Loop," Journal of Microelectromechanical Systems, Vol. 19, No. 1, pp. 192-201, 2010. [42] H.M. Lavasani, W. Pan, F. Ayazi, "An electronically temperaturecompensated 427MHz low phase-noise AlN-on-Si micromechanical reference oscillator," 2010 IEEE Radio Frequency Integrated Circuits Symposium (RFIC), pp. 329-332, 2010. [43] H. M. Lavasani, W. Pan, B. Harrington, R. Abdolvand, and F. Ayazi, "Electronic Temperature Compensation of Lateral Bulk Acoustic Resonator Reference Oscillators using Enhanced Series Tuning Technique" IEEE Journal of Solid-State Circuits, Vol. 47, Issue 6, pp. 1381-1393. [44] C. G. Courcimault and M. G. Allen, “High-Q mechanical tuning of MEMS resonators using a metal deposition-annealing technique,” The Conference on Solid-State Sensors, Actuators and Microsystems, 2005. (TRANSDUCERS’05), pp. 875–878. [45] W.-T. Hsu and A. R. Brown, “Frequency trimming of MEMS resonator oscillators,” IEEE Int. Freq. Control Symp., 2007, pp. 1088–1091. [46] A. Hajjam, K. Dietrich, A. Rahafrooz, and S. Pourkamali," A SelfControlled Frequency Trimming Technique for Micromechanical Resonators," Solid-State Sensors, Actuators, and Microsystems Workshop (Hilton Head 2012), Hilton Head, SC, June 2012, pp. 74-77. [47] A. K. Samarao and F. Ayazi, “Post-Fabrication Electrical Trimming of Silicon Bulk Acoustic Resonators using Joule Heating,” in Micro Electro Mechanical Systems, 2009. MEMS 2009. IEEE 22nd International Conference on, 2009, pp. 892–895. [48] A. K. Samarao and F. Ayazi, "Postfabrication Electrical Trimming of Silicon Micromechanical Resonators via Joule Heating," IEEE Journal of Microelectromechanical Systems, Vol. 20, Issue 5, October 2011, pp. 1081 - 1088. [49] H. Bhugra, Y. Wang, W. Pan, D. Lei and S. Lee, " High Performance pMEMS™ oscillators - The next generation frequency references," IEEE International Electron Devices Meeting (IEDM 2011), Washington, DC, Dec. 2011, pp. 477-480.
I. INTRODUCTION As microelectromechanical resonators evolve from research labs to commercial products, maintaining high precision and repeatability across many performance parameters becomes increasingly important. The major performance metrics of MEMS resonators include their center frequency (f0), temperature coefficient of frequency (TCF), quality factor (Q), and motional resistance (Rm). Additional aspects such as power handling and linearity may be considered as appropriate to the application.
step and are referred to as wafer-level techniques. In this paper, an overview of compensation, tuning, and trimming techniques applied to MEMS resonators will be presented. II.
COMPENSATION TECHNIQUES IN MEMS RESONATORS
A. Compensation for Thermal Effects MEMS resonators typically show much larger temperature sensitivity compared to their quartz crystal counterparts. The temperature sensitivity of f0 can be defined and related to the temperature sensitivity of the resonator’s material properties by its TCF:
(1)
Depending on the specific application of the MEMS resonator, one or more of its metrics may require compensation [1]. While stringent control and device-todevice repeatability of f0 is required for nearly all of the applications of MEMS resonators to varying degrees of accuracy, the temperature sensitivity of f0 (and hence the TCF) is of major importance for resonators serving as analog signal processors and timing references, as well as environmental sensors, and must be kept within acceptable limits. Furthermore, cost restrictions place boundaries on the precision of fabrication processes used to implement these devices, imposing additional uncertainties on their performance.
where TCE, the temperature coefficient of Young’s modulus, and CTE, the coefficient of thermal expansion, are intrinsic material properties. The large TCF of the MEMS resonators is mainly a result of high TCEs of the materials commonly used to implement these devices. For silicon resonators, the large native TCF of 30 ppm/°C results in a frequency drift as large as 3750 ppm across the industrial temperature range of 40°C to 85°C. Major applications of MEMS resonators, such as temperature compensated crystal oscillators (TCXO) and thermally-stable sensors, often require sub-ppm instability levels, mandating a radical decrease in the TCF of these devices to facilitate full compensation through active electronic methods. Therefore, passive TCF compensation techniques are of great interest. Some examples of passive techniques are the compensation of material TCE through engineering of device geometry and/or doping profile, as well as the addition of a compensating material with a TCE of opposite sign to form a composite structure with reduced TCF.
The large amount of research invested in precise control of MEMS resonator metrics can be categorized into three groups: compensation, tuning, and trimming. Techniques developed under each of these categories may address resonator control at the device or system level and are applied in the design stage and/or post-fabrication. The most preferred techniques can be applied in batch across an entire wafer at once or in one
Figure 1 shows the SEM image of a TCF-compensated concave silicon bulk acoustic resonator (CBAR) in comparison with a rectangular geometry silicon bulk acoustic resonator (SiBAR). By opting for concave resonator geometries instead of the conventional circular or rectangular geometries, the TCF has been considerably reduced while the Q of the device has also been improved due to efficient
978-1-4577-1820-5/12/$26.00 ©2012 IEEE
Figure 1. Geometry-engineered TCF-compensated concave SiBAR (CBAR). Device shows a TCF of 6 ppm/°C at 105MHz with a Q of 100,000 [2].
compensation of energy leakage from the resonator towards surrounding substrate [2]. This device demonstrates the geometry engineering approach to compensation. Another group of TCF compensation techniques are based on selective introduction of dopants into the silicon substrate to reduce its large TCE by modifying the electronic energy levels. These techniques can be broadly termed doping profile engineering. Different works falling under this category include utilization of heavily P-doped [3,4] and N-doped silicon substrates [5,6], thermomigration of aluminum atoms into the silicon substrate [7], and carrier depletion of the device using multiple PN junctions [8]. More traditional TCF compensation techniques rely on addition of a compensating material. In these approaches, the large negative TCE of native silicon is compensated by addition of a material with positive TCE (usually silicon dioxide). Adding the correct amount of silicon dioxide to the silicon resonator forms a composite Si/SiO2 structure with temperature-compensated TCE. Figure 2 illustrates this concept schematically. The compensating silicon dioxide can be added in layers parallel to the resonator stack [9,10]. However, since a comparable amount of silicon dioxide is required for full TCF compensation, this technique is mostly applicable to thin substrates and low frequency flexural mode resonators, but
Figure 3. (top) Temperature-compensated SilOx bulk acoustic resonator with thin AlN transduction. (bottom) Temperature characteristic of f0 and Q [12].
more difficult to use for full TCF compensation of bulk acoustic wave (BAW) devices with thick substrates that offer high Q and superior power handling and linearity [3]. Alternatively, TCF compensation of silicon BAW resonators has been achieved by embedding a 2D array of silicon dioxide pillars inside the resonator [11]. Uniform distribution of silicon dioxide inside the silicon body of the resonator forms a homogenous composite material (a SilOx matrix); the addition of silicon dioxide does not degrade the main resonator characteristics such as Q, insertion loss (IL), and power handling. Careful design of the silicon dioxide distribution pattern across the resonator results in full cancellation of linear term of f0 thermal behavior [12]. Figure 3 shows the SEM picture of a 27 MHz length-extensional (LE) mode SilOx resonator with thin aluminum nitride (AlN) transduction layer (Q~7500, IL~15dB), showing 40-fold improvement in overall frequency drift across the temperature range of -20°C to 100°C. B. Compensation for Fabrication Process Uncertainities The resonance frequency f0 of resonators in arbitrary modes is described by the following equation:
Figure 2. Schematic representation of compensating a silicon resonator with silicon dioxide. When first order compensation has been achieved, a residual quadratic characteristic remains due to higher order residuals [11,12].
where L is a generalized length parameter dependent on the geometry of the device, Va is the effective acoustic velocity corresponding to L, and keff and meff are the effective stiffness and mass, respectively. Hence, variations in the resonance frequency can arise due to process-induced variations in the device geometry and material properties which affect the
compensated for in the resonator design. Process compensation is achieved when the effective stiffness to mass ratio in (2) is maintained, even under geometric changes to the device. Several methods have been taken to affect this condition in silicon resonators. For low frequency 32 kHz resonators, slots have been designed in the proof mass so that the effective mass changes in accordance with the effective stiffness of the flexural beams as they are subject to process variations [15]. For micromechanical I-shaped bulk acoustic resonators (IBAR), properly-designed tapered flanks can be used to balance the contribution of mass and stiffness changes [14,16]. In contrast, for high frequency SiBARs, perforations have been introduced which accommodate these dimensional variations [17]. Figure 4 shows a process-compensated thinpiezoelectric-on-substrate (TPoS) resonator design in which 4 μm by 4 μm perforations have been introduced to balance the stiffness to mass changes. This is evidenced by the middle plot of Figure 4, in which the relationship between frequency variation and lithographic process bias offset has been calculated for the design using finite element (FE) simulations. It can be seen that the 4 μm by 4 μm square perforations slightly overcompensate the design (indicating a negative trend with process bias) vs. the uncompensated design, even for different combinations of the piezoelectric transduction stack. Interestingly, the difference between the magenta firstorder analytical model from equation (2) and the blue circles from FE simulation of the structure is exactly explained by the addition of support tethers, indicating that the tethers themselves have a slight compensating effect.
Figure 4. (top left) Uncompensated TPoS resonator. (top right) Processcompensated 27 MHz TPoS resonator with a line of specially-designed 4 μm by 4 μm perforations. (middle) Frequency trends for 27 MHz TPoS resonators vs. DRIE trench critical dimension bias (delta). (bottom) Frequency trends of TPoS resonator vs. SOI device thickness for ±0.3 μm layer tolerance [17].
acoustic velocity. For instance, angular misalignment of ±0.1° from the [110] axis of silicon can theoretically affect the acoustic velocity (and frequency) of longitudinal acoustic waves by 1.8 ppm. Doubling the misalignment to ±0.2° increases the frequency shift to 7.3 ppm. Further impacting the repeatability of the acoustic velocity is dependence on doping levels. Similarly, sensitivity of Q to angular misalignment in SiBARs has been reported [13]. The acoustic velocities only experience change of less than 1% when switching from intrinsic to heavily phosphorous-doped silicon [14], so excellent control over the dopant contribution and angular misalignments is crucial. If the material contributions to initial frequency spread can be made negligible, then the remaining contributions come from the geometrical variations in the device. In silicon-based MEMS resonators, the Bosch DRIE process is typically used to create high aspect ratio trenches which define the in-plane dimensions of the resonator. Often, for in-plane resonators, the resonance frequency strongly depends on one or more of these trench-defined dimensions. Therefore, systematic changes in these dimensions must be well-understood so that they can be
In addition to lithographic process compensation, attention must be given to the thickness dependencies as well. Although the thickness has a negligible effect for plain SiBARs in certain thickness regimes [18], this assumption does not hold for TPoS resonators. Since these resonators are formed from a composite stack of materials, including the silicon layer as the bulk of the device, the AlN piezoelectric layer, and molybdenum top and bottom electrode layers, the effective acoustic velocity is a composite parameter of these layers, depending on the relative stack thicknesses. Since the AlN and Mo layers are formed by thin film deposition, their thicknesses can be controlled to high accuracy. Therefore, the dominant variations will come from the SOI wafer, which are often toleranced to ±0.3 μm from the vendor. Substituting these numbers into a first order analytical model which takes into account the relative thickness of each layer, it is found that increasing the nominal silicon thickness can significantly reduce the resonators’ sensitivity to the silicon layer thickness (Fig. 4, bottom). C. Compensation for Quality Factor In certain applications of MEMS resonators, control and compensation of Q are paramount to obtaining reliable performance. For the case of MEMS vibratory gyroscopes, it can be desirable to operate at high frequencies so that high Q devices can be used to get large sensitivity, while at the same time maintaining large bandwidth for high dynamic range. One example of this approach is the Q-controlled spoke gyroscope, in which the Q was purposefully limited by the thermoelastic damping (TED) in the central spoke region [19]. Since the coupling between the thermal and elastic domains is
Figure 5. AlN-on-silicon TPoS bulk acoustic resonator with linear acoustic bandgap (LAB) structures as supports providing Qsupport compensation [28].
directly proportional to the absolute temperature, this mechanism has a strong temperature dependency. It also depends strongly on the mode shape of the resonator, with high frequency bulk acoustic modes generally being less subjected to TED than their low-frequency flexural beam counterparts [20]. However, selective addition of release holes can introduce additional TED by modifying the overall effective thermal paths [21]. Another important source of energy dissipation in MEMS resonators is energy leakage through their supporting tethers [21-24]. These tethers connect the released resonant structure to its surrounding substrate. Since point supports are desirable, the finite size of these tethers limited by photolithography precision increase the energy leakage from the resonator. However, proper design of these supports can provide passive compensation for support loss mechanism. A group of these methods focus on reflection of leaked waves back in to the resonator by creating acoustic mismatch at support region [25,26]. Although these techniques provide considerable improvement in Qsupport, substantial elimination of support leakage at the resonance frequency requires the engineering of phononic band structure of the material. This has been realized by implementation of acoustic bandgap structures [27,28]. These structures provide a frequency band in which phonons cannot be propagated. By selectively engineering the bandgap to include the resonance frequency of the resonators, full compensation of support loss can be achieved. Figure 5 shows an AlN-on-Si bulk acoustic resonator with linear acoustic bandgap supports as well as the corresponding phononic band diagram, where the bandgaps are shaded in blue. In addition to these passive compensation techniques, new research has emerged based on using the acoustoelectric effect in semiconductor piezoelectric resonators to provide an active means for Q compensation [29]. In this method, interactions
Figure 6. A 20 MHz IBAR with large frequency tuning range [33].
between phonons and free charge carriers [24] are used to amplify the acoustic waves propagating through the microresonator, compensating the attenuation due to different loss mechanisms [21] and thereby improving the Q. D. Compensation for Polarization Voltage Capacitive resonators require a DC polarization voltage (VP) for operation. This translates in to the requirement of additional circuitry resulting in incompatibility of these resonators with low-voltage CMOS processes. Moreover, since several characteristics of these devices are sensitive to the VP, stringent control is required to provide a constant DC voltage on-chip over all resonator operating conditions, which adds further complexity to the CMOS interface. Several techniques have been introduced for VP compensation based on charge trapping inside the electrically-isolated resonant silicon microstructures [30,31]. III. TUNING METHODS Although TCF and process compensation techniques considerably reduce the amount of temperature and processinduced frequency drifts and uncertainties, full compensation of residual f0 deviations as well as drifts caused by aging effects requires dynamic adjustment which is provided by tuning mechanisms. Frequency tuning can be addressed in both device and system levels. A. Device-Level Tuning These tuning mechanisms provide electronic f0 tuning for individual resonators through electromechanical transducers
IBARs [34]. Although application of electrostatic tuning is convenient in capacitive resonators, since the motional resistance of these devices is highly sensitive to their VP, electronic tuning of f0 results in fluctuations of the resonator’s IL, which is usually not desirable. This problem has been solved by separation of the capacitive tuning electrodes from the AC electromechanical transducer [35]. Figure 7 shows a 32 kHz flexural resonator with AlN piezoelectric transduction and electrostatic tuning. Having a large tuning pad which jointly serves as a frequency-loading mass enables large f0 tuning capable of covering the temperature-induced frequency drift across the entire oscillator industrial temperature range.
Figure 7. A 32 kHz flexural-mode resonator with AlN piezoelectric transduction and electrostatic tuning [35].
and by changing the effective equivalent stiffness of the micromechanical resonator. Electrostatic tuning has traditionally been the most commonly employed device-level tuning mechanism. In this technique, an electrical spring whose stiffness is tunable via DC voltage is added in series with the mechanical stiffness of the resonator and provides continuous f0 tuning with a quadratic characteristic. While small stiffness of the electrical spring, resulting from low-efficiency electrostatic transduction, makes this tuning technique more appropriate for low frequency flexural mode resonators [32], large tuning ranges have also been reported for high frequency bulk acoustic devices with efficient sub-μm capacitive gaps [14,33]. Figure 6 shows a high frequency (20 MHz) IBAR designed for maximum tunability. Temperature-compensated oscillators have been built using this tuning mechanism in
Figure 8. System diagram of a 27 MHz temperature-stable MEMS oscillator with sub-ppm instability using SilOx resonator and system-level tuning [12].
Another electronic device-level tuning mechanism which is capable of providing large tuning ranges is based on ovenization of the microresonator via Joule heating. In this technique, a tunable DC current passing through a heater element results in increased resonator temperature and hence controllable frequency changes due to the large TCF of uncompensated resonators [36-38]. The highest efficiency and agility of thermal tuning has been achieved by selfovenization of silicon resonators. In this technique, the heating current passes through the device and the resonator serves as the micro-oven simultaneously [37,38]. In addition to electrostatic and thermal tuning techniques, a tuning mechanism which is applicable to piezoelectricallytransduced MEMS resonator is the piezoelectric stiffening effect. In this technique the stiffness of the piezoelectric film is controlled by tuning its electric termination at the tuning port [39,40]. B. System-Level Tuning System-level tuning and frequency control mechanisms are applied to the systems where MEMS resonator serves as the frequency reference. These techniques include the use of phase-locked loops [41] or addition of tunable electrical impedances and phase-shifters in series and/or in parallel with the resonator [12,42,43]. Systems employing these techniques can tune out the residual frequency drifts and uncertainties of TCF and process compensated resonators, to form highlystable frequency references. Figure 8 shows the schematic design of a 27 MHz oscillator implemented from the TCFcompensated SilOx resonator of Figure 3 in addition to tunable capacitors and phase-shifters embedded in series with the resonator in the oscillator loop. IV. TRIMMING METHODS Trimming refers to the permanent shift of a device parameter, usually performed after fabrication. Commonly, trimming is achieved using selective addition (e.g., metal deposition [44]) or removal of material, such as with laser ablation [45]. Emerging methods include localized growth of oxide on thermally-actuated silicon resonators [46] and metal diffusion via formation of metal-silicon eutectic alloys at elevated temperatures [47,48]. The latter is achieved by passing a controlled DC current through the body of the silicon resonator, causing its temperature to increase via Joule heating. This is an especially attractive technique because it allows post-vacuum-packaging trimming at the wafer or
well as reconfigurable arrays of MEMS filters. Further research is required to study the accuracy and stability limits of trimming techniques for MEMS resonators. Fabrication processes that enable simultaneous realization of compensation, tuning and trimming of MEMS resonators are of great interest and need to be developed. ACKNOWLEDGMENT The authors wish to acknowledge contributions from current and former members of the Integrated MEMS Laboratory. The work on compensation, tuning and trimming of MEMS resonators at Georgia Tech Integrated MEMS Laboratory and CMMT has been made possible through support from DARPA, NSF, ST Microelectronics, and Integrated Device Technology (IDT). Enhanced stiffness dominates
Resonance Frequency of the SiBAR at 25 C (in MHz)
100
REFERENCES
Pre-Joule Heating
99.8
[1]
Heating at 30 mA for 1 hour before cooling to 25C Heating at 30 mA for 2 hours before cooling to 25C
99.6
Heating at 30 mA for 3 hours before cooling to 25C
Diffusion time
99.4
[2]
Heating at 30 mA for 4 hours before cooling to 25C
40% Mass loaded SiBAR shifts up by 240 kHz
99.2
99
Mass loading dominates
80% Mass loaded SiBAR shifts up by 17 kHz
98.8
98.6 0
20
40
60
80
[3] 100
120
Incremental percentage of mass loaded area
Figure 9. (top: a-d) Schematic representation of gold-diffusion-based trimming in gold-coated SiBARs. When a current is passed through the SiBAR body, the temperature is raised above the Au-Si eutectic temperature, allowing the gold layer to diffuse into silicon. (bottom left) Frequency uptrimming is achieved with Au-Si eutectic, since the Au-Si bond is stronger than the Si-Si bond. (bottom right) Frequency down-trimming achieved with Al-Si thermomigration, since Al-Si bonds are weaker than Si-Si bonds [48].
individual device levels. No material is vaporized within the vacuum package, allowing the package to maintain a high vacuum. Use of different metals allows either up or down trimming. For Au, the resonance frequency increases after running the thermal current, since the Au-Si bond is higher in strength than the Si-Si bond. For Al, the resonance frequency decreases after trimming because the Al-Si bond is lower in strength than both Au-Si and Si-Si bonds. Al was also found to be preferred from a trimming time standpoint, since Al thermomigrates against thermal gradients, whereas Au-Si bonding requires reaching the eutectic temperature to activate the trimming process. V. CONCLUSION Compensation and tuning of MEMS resonators has enabled their successful commercialization in the timing market, with the range of products and specifications expanding rapidly [49]. While the majority of temperature compensation effort so far has concentrated on system-level techniques that are power consuming, a significant opportunity lies in device-level compensation techniques that consume little to no power, promising the realization of low power reference oscillators with ppb inaccuracies. Significant research is underway to improve and control the quality factor (Q) and motional resistance (Rm) of MEMS resonators at both low and high frequencies in the presence of temperature and process variations. This will enable new classes of ultra-stable integrated devices such as angle measuring gyroscopes, accelerometers, magnetometers, and environmental sensors as
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