Thin-Film Piezoelectric-on-Silicon Resonators for High-Frequency ...
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Thin-Film Piezoelectric-on-Silicon Resonators for High-Frequency Reference Oscillator Applications Reza Abdolvand, Hossein M. Lavasani, Gavin K. Ho, and Farrokh Ayazi Abstract—This paper studies the application of lateral bulk acoustic thin-film piezoelectric-on-substrate (TPoS) resonators in high-frequency reference oscillators. Low-motionalimpedance TPoS resonators are designed and fabricated in 2 classes—high-order and coupled-array. Devices of each class are used to assemble reference oscillators and the performance characteristics of the oscillators are measured and discussed. Since the motional impedance of these devices is small, the transimpedance amplifier (TIA) in the oscillator loop can be reduced to a single transistor and 3 resistors, a format that is very power-efficient. The lowest reported power consumption is ~350 µW for an oscillator operating at ~106 MHz. A passive temperature compensation method is also utilized by including the buried oxide layer of the silicon-on-insulator (SOI) substrate in the structural resonant body of the device, and a very small (−2.4 ppm/°C) temperature coefficient of frequency is obtained for an 82-MHz oscillator.
I. Introduction
M
icromachined high-Q frequency-selective components with small form-factor are in high demand to replace quartz crystal resonators in temperature-stable, low-phase-noise oscillator applications. Significant progress has been made in developing oscillators that utilize silicon-micromachined capacitive resonators with Q values comparable to that of a quartz resonator [1], [2]. However, high-frequency capacitive resonators require relatively high dc polarization voltages (5–20 V) for operation, which complicates the design of the oscillator in low-voltage CMOS circuits. Moreover, the motional impedance of capacitive resonators is much larger than for quartz resonators and their power handling is usually lower. These resonators are operated at low pressures (mTorr regime), which makes their packaging process costly and challenging. Also, the temperature compensation techniques demonstrated so far usually lose efficiency at high frequencies [3]. Thin-film piezoelectric-on-substrate (TPoS) resonators, which the authors have investigated in previous work [4], [5], are a class of lateral extensional resonators with the potential to address some of the issues just mentioned. These resonators, similar to other micromachined piezo-
Manuscript received February 4, 2008; accepted June 30, 2008. R. Abdolvand is with the School of Electrical and Computer Engineering at Oklahoma State University (e-mail: reza.abdolvand@ okstate.edu). H. Mirilavasani and F. Ayazi are with the Georgia Institute of Technology, Atlanta. Digital Object Identifier 10.1109/TUFFC.2008.976 0885–3010/$25.00
electric resonators [6], [7], benefit from the large coupling factor of piezoelectric transduction, which provides for very small motional impedance at relatively high frequencies. The realized lower motional impedance eliminates the need for multiple gain stages in oscillator applications. Moreover, the use of low-loss substrates in TPoS resonators (e.g., single crystal silicon) leads to improved structural integrity while requiring a very thin (less than 1 μm) layer of piezoelectric. Also, the residual stress in the film is more tolerable. The contribution of squeezefilm damping on the quality factor of TPoS resonators is also significantly less compared to capacitive resonators with ultra-narrow transduction gaps [8]. Therefore, vacuum packaging may not be necessary, which makes the technology more cost-competitive. Also notably, the power handling in TPoS resonators is high due to inclusion of high power-density material such as silicon in the resonant structure (compared with the same device solely made of a thin piezoelectric film) [9], [10]. Consequently, the far-from-carrier phase noise in TPoS-based oscillators can be further reduced by increasing the oscillation power. Another important advantage of TPoS resonators over capacitive devices is that no bias voltage is necessary for their operation, a very attractive feature considering the low operating voltage of modern integrated circuits. In this work, application of high-frequency TPoS resonators in frequency reference oscillators (at VHF band) is studied. An arraying technique for systematically reducing the motional impedance of high-frequency TPoS resonators is introduced and compared with the conventional high-order designs. Also, the benefit of including the silicon substrate in the resonant structure on reducing the phase noise of TPoS-based oscillators is experimentally demonstrated. Furthermore, the temperature coefficient of frequency (TCF) of TPoS resonators is shown to be reduced by incorporating the buried oxide (BOX) layer of the silicon-on-insulator (SOI) substrate in the resonator structure. The large positive TCF of the oxide layer [11] compensates for the negative TCF of the rest of the material in the resonant structure and enables near-zero-TCF devices, provided the thickness of the layers is controlled. II. Resonator Structure A TPoS resonator comprises a thin-film piezoelectric layer sandwiched between 2 metallic electrodes stacked on top of a relatively thick substrate layer. The substrate
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Fig. 2. The third-order lateral-extensional resonance mode-shape of a block resonator simulated in COMSOL.
Fig. 1. The schematic viewgraph of a two-port third-order TPoS resonator.
layer, which usually comprises a large portion of the resonant structure, is chosen from low-acoustic-loss material such as single crystal silicon or nano-crystalline diamond (NCD) [12]. The metal electrodes are patterned to match the strain field in a targeted resonance mode-shape. The resonator can be configured in 1- or 2-port configurations. All the resonators discussed in this work are 2-port designs. By applying an alternating signal to the input electrode, a vertical alternating electric field is induced in the piezoelectric film and consequently a corresponding lateral stress is introduced in the structure due to the nonzero d31 coefficient of the piezoelectric film. This stress field is responsible for excitation of the lateral extensional resonance modes of the structure and the resulting vibration is converted back to electrical signal on the output electrodes [5]. With a careful electrode design, the coupling factor is optimized and the motional impedance of the resonator is minimized. The resonators used in this paper had bottom electrodes covering the entire resonant structure (e.g., a ground plane), although the bottom electrode can optionally be patterned to match the shape of the top electrode. A. High-Order Design The designed top electrode pattern for excitation of high-order lateral-extensional resonance modes of a rectangular plate resembles an interdigitated transducer (Fig. 1) [13]. The resonant frequency of the device can be approximated using
f =
1 2(W /n)
E eff 1 = v a,eff, r eff 2L p
(1)
where W is the total width of the block, Eeff is the effective Young’s modulus of the stack along the width direction, ρeff is the effective density of the stack, and n is the number of fingers. Alternatively, the equation can be written
as a function of Lp (finger pitch) and va,eff (effective acoustic velocity along the width of the block). The resonator is suspended by 2 beams attached to the middle of the structure on both sides. The resonator can be modeled as a simple series RLC circuit [5]. The motional impedance of a fundamental mode resonator with two electrodes covering the entire top surface [5] is
R1 »
pt tot E eff r eff 2 2d 31 E f2WQ
,
(2)
where ttot is the total thickness of the block, d31 is the transverse piezoelectric coefficient, Ef is the Young’s modulus of the piezoelectric film, and Q is the quality factor of the resonator. For a high-order device, it can be shown that the impedance is:
R 1,n »
R1 , N
(3)
where N = n for even n, and N = (n2 − 1)/n for odd n. Intuitively, this is very simple. As the number of regions or multiple of resonators is increased, the impedance decreases by N. The top electrode design matches the periodic strain field pattern of the block structure excited in the highorder lateral-extensional resonance modes. As an example, the third-order mode shape of a rectangular plate simulated in COMSOL is shown in Fig. 2. The color code in this picture demonstrates the strain field. Bluish colors present areas under compressive strain and reddish colors are representative of the tensile strain. At resonance, opposite charges are accumulated on the 2 electrodes because the strain polarity alternates from one finger to the other. Therefore, the output signal phase is 180° shifted relative to the input signal phase. It is worth mentioning that using the same electrode pattern, the fundamental resonance mode of the structure can also be excited, where strain field is uniform across the whole structure. However, we have shown that the sustained oscillation frequency can be selected between the 2 frequencies without the need for any mode-suppression circuitry
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Fig. 3. The schematic viewgraph of a two-resonator coupled-array TPoS resonator.
[14]. This is achievable by exploiting the dissimilar phase shift of the output signal, which is 0° for the fundamental mode and 180° for the third harmonic. Therefore, an inverting amplifier in the oscillation loop would only sustain the frequency of the third harmonic mode. B. Arrayed Design The motional impedance of the high-order TPoS resonators is reduced by increasing the resonance order (number of fingers) due to the proportional increase in the transduction area [13]. However, the small suspension beams located at 2 nodal points of a wide freestanding resonant structure are not constraining enough to prevent excitation of unwanted resonance modes. Therefore, an increase of spurious modes in the frequency response of a TPoS resonator is predicted to be observed as the resonance order is increased. The validity of this prediction will be proved experimentally in Section IV.A. A solution to this problem is suggested in Fig. 3, which shows a design for a coupled array of individual resonators in which each section of the resonant plate is supported with a separate set of support beams (corresponding to an individual resonator). This design improves the rigidity of the resonant structure and consequently suppresses the vibration amplitude of the spurious modes. The excited resonant mode in this design is the second harmonic lateral mode-shape of the plate, in which the input and the output signals are out-of-phase (area covered by one electrode is expanding while the other portion is contracting and vice versa). The motional impedance of a coupled-array resonator is ideally inversely proportional to the number of resonators in the array (combination of individual impedances in parallel). III. Fabrication Process The process flow for TPoS resonators fabricated on SOI is briefly described in Fig. 4. The important modifica-
Fig. 4. The schematic diagram of the process flow.
tion compared with the prior process described in [5] is in the release step. The buried oxide (BOX) layer in the SOI substrate is optionally etched from the top side in an inductively coupled plasma (ICP) etcher using the same mask layer that defines the device structure (mask 4), by which the BOX layer attached to the resonant structure is kept intact, thus improving the temperature stability of the resonator. The bottom metal electrode is chosen based on the piezoelectric film utilized. Sputtered ZnO and AlN are used for the resonators studied in this paper. Despite ZnO’s deposition simplicity, the resistivity of the film is hard to control. On the other hand AlN, which was deposited by an outside foundry, provides for an excellent insulation layer. Gold is the bottom electrode metal of choice for resonators fabricated with sputtered ZnO, both because the vertical alignment of the c-plane ZnO grains on gold was enhanced and also because gold does not react with the chemical etchant used for patterning the ZnO layer. Molybdenum is chosen for the AlN films because it is a high Q metal. The top electrode is made of Al for both ZnO and AlN devices. IV. Frequency Response Measurement To measure frequency response of the fabricated resonators, a Karl-Suss high-frequency probe station, Cascade GSG probes, and an E8364 Agilent network analyzer are used. A Lakeshore high-frequency vacuum probe station with heated chuck is alternatively used for carrying out the measurements in vacuum. All reported Q values are measured in air unless otherwise stated. The motional impedance of the resonators is extracted from the minimum S21 loss considering 50-Ohm termination on both ports.
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Fig. 5. Optical viewgraphs of (a) a third-order and (b) 4-resonator coupled-array TPoS resonator.
Fig. 7. The frequency response plot of a 94-MHz 9th-order TPoS resonator.
Fig. 6. The frequency response plot of a 94-MHz third-order TPoS resonator.
A. High-Order Versus Arrayed Resonators Top-view optical viewgraphs of a third-order ZnO-onsilicon resonator and a 4-resonator arrayed counterpart are shown in Fig. 5. These devices are fabricated on a 5-μm-thick SOI substrate. The ZnO film is ~0.5 μm thick, and the BOX layer is removed from the backside on this wafer. The center-tocenter top electrode pitch size for these devices is 40 μm. The third-order device is 160 μm long, whereas the arrayed resonators are only 60 μm long. A typical measured frequency response plot of the thirdorder ZnO-on-silicon resonator under discussion is shown in Fig. 6. The frequency response of a 9th-order resonator designed to operate at the same frequency (same finger pitch) is demonstrated in Fig. 7. Although, the motional impedance of this device is significantly lower than the third-order device, the number of spurious modes and their vibration amplitudes are critically increased. For comparison, the wide-span (100 MHz) frequency response of a 12-resonator coupled-array is demonstrated in Fig. 8, along with a scanning electron micrograph (SEM) of the fabricated device. Unlike the third-order and the 9th-order devices, no strong spurious peak is detected in the 94-MHz vicinity
of the primary resonance peak. Measured frequency responses of arrayed devices located on the same die of the 5-μm-thick processed wafer with 4, 6, and 12 coupled resonators are shown in Fig. 9. The dimensions of the metal electrodes for the 4-resonator array are different than the other 2 resonators, causing the relatively large shift in the center frequency. The motional impedances are ~550 Ω for the 4-resonator, 210 Ω for the 6-resonator, and 110 Ω for the 12-resonator arrays. The predicted inverse proportionality of the motional impedance with the number of resonators in the array holds with good precision for the 2 larger devices. These results confirm that the motional impedance of the coupled-array device can be systematically decreased while avoiding spurious modes. B. Resonators With Oxide A 2-µm-thick SOI substrate with 2 µm BOX layer is used as the starting substrate for the fabrication of a temperature-stable resonator. For these resonators the BOX layers are etched in the ICP from the top. Therefore, the ~2 µm oxide layer is included in the stack of the resonant structure. To realize a near-zero TCF resonator the thickness of the oxide layer with the positive TCF has to be comparable with the thickness of the silicon, the AlN, and the metal layers (which all have negative TCF). Because the thickness of the BOX layer cannot be typically more than a few microns, the thickness of the silicon layer is reduced. A typical frequency response plot measured from a 12-resonator arrayed device fabricated on this substrate is shown in Fig.10. Even though the dimensions of this device are the same as the device measured in Fig. 6, the measured resonance frequency is decreased from ~95 MHz to less than 82 MHz, a direct result of including the oxide layer in the resonant structure. The elastic modulus of oxide (~75 GPa) [15] is
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Fig. 8. The wide-span (100 MHz) frequency response and the SEM of a 12-resonator coupled-array. Fig. 10. The frequency response of a temperature-compensated 12-resonator coupled array.
Fig. 9. Frequency response plots of 4-, 6-, and 12-resonator coupled arrays.
lower than the elastic modulus of silicon (~150 GPa) and therefore the resonance frequency is decreased. C. AlN-on-Silicon Resonators AlN-on-silicon resonators are fabricated on a 10 µm SOI wafer, and the thickness of the sputtered AlN layer is 1 µm. The frequency response of a third-order resonator with 40 µm finger pitch is shown in Fig. 11. For this device the resonance frequency is increased compared with the ZnO-on-silicon counterpart. This is mostly due to the fact that the acoustic velocity of AlN (11 400 m/s) is greater than the acoustic velocity of ZnO (6400 m/s) [16]. As explained, the same top electrode pattern can excite the fundamental extensional resonance mode of the rectangular plate. The frequency response plot is shown in Fig. 12. The resonance frequency (~35.5 MHz) is onethird of the third-order mode as expected, and the motional impedance is larger even though the quality factor is larger. The unloaded quality factor of the resonance peak shown above is increased to ~17 000 when measured in
vacuum (Fig. 13). The motional impedance of the device in vacuum is also reduced with the increase in Q as expected [5]. It was noted that the quality factors of devices fabricated on a thick (10 μm) silicon device layer were on average higher than the values measured from resonators fabricated on thinner SOI substrates (confirmed for ZnO devices as well). This observation is in agreement with the anticipated effect of the silicon layer on reducing the overall acoustic loss in TPoS resonators. The motional impedance of a high-frequency high-order TPoS resonator is further reduced by increasing the order number. The frequency response shown in Fig. 14 is measured from a 9th-order 208 MHz device with a 20 µm finger pitch. The impedance is only ~70 Ω and the unloaded Q is ~6100 in air. This resonator demonstrates the highest f·Q product measured in this work (~1.26 × 1012) which is a relatively large value compared with results reported at similar frequency ranges [7]. As shown in the next sections, use of this device will result in an excellent close-tocarrier phase noise for an oscillator that operates in air. V. Nonlinear Vibration Measurement The small size of micromechanical resonators, despite any advantages, creates an inevitable drawback when it comes to the maximum allowable stored energy—in other words, power handling, which measures the amount of power that can be applied to or delivered by the resonator. Power handling is mostly limited by the nonlinearity mechanisms in the resonator. In piezoelectric resonators with small piezoelectric coefficients, electric and electrostatic nonlinearities can be disregarded as they relate to the effect of nonlinear elastic constants [17]. This is different than the case for capacitive resonators, in which the transduction nonlinearity is significant [9].
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Since nonlinear vibration of the resonator will introduce noise and distortion in the output signal of the system, the level of applied power to the resonator should be kept less than the nonlinear limits at all times. In a linear massspring system, the spring coefficient is a constant whereas in a nonlinear system the coefficient can be written as
k = k 0(1 + k 1x + k 2x 2 + ¼),
(4)
where k1, k2, …, are nonlinear spring coefficients. A nonlinear spring coefficient will cause higher harmonics of the resonance frequency (ωn) to appear in the output. Therefore, the nonlinear resonance frequency (frequency at which the largest vibration amplitude occurs) is dependent on the vibration amplitude (A) [9]:
æ 5k 12 2 3k 2 2 ö÷ w nonlinear = w n ççè 1 A + A ÷÷ø . 12 8
Fig. 11. The frequency response and the SEM of a third-order AlN-onsilicon resonator.
(5)
It can be seen from (5) that a nonzero first-order nonlinear spring coefficient (k1) will shift down the resonance frequency and the second-order nonlinear coefficient (k2) will shift the frequency either up or down depending on its sign. It is usually assumed that the largest allowable vibration amplitude (xc) is the amplitude at the bifurcation (the critical point after which the amplitude versus frequency plot will demonstrate hysteresis). By using the maximum allowable vibration amplitude, the maximum stored energy in the resonator can be calculated from
E max =
1 k 0x c2. 2
(6)
Therefore, the maximum stored energy is proportional to the stiffness and the second power of critical vibration amplitude (xc). Small nonlinear spring coefficients will cause the critical vibration amplitude, and consequently, the power handling to increase. Nonlinear spring coefficients are dictated by material properties and are different for each material of choice. To compare the nonlinearity limitations for different materials a normalized parameter called energy density is defined as the maximum allowable energy divided by the volume of the resonant structure. Silicon exhibits larger energy density than piezoelectric materials such as quartz [9]. Considering the factors just noted, a TPoS resonator is expected to exhibit better power handling compared with devices made of a thin piezoelectric material only. The reason is two-fold—the higher stiffness of the resonant structure from the added thickness of the substrate to the stack along with the large energy density of the silicon substrate. In this paper, the experimental study of the resonator nonlinearity is carried out by analyzing the frequency response at variable input signal levels. The goal is not to characterize the nonlinearity but rather to compare the
Fig. 12. The frequency response of the third-order resonator in fundamental mode.
nonlinear behavior of the different resonators designed and fabricated for this study. Fig. 15 shows overlapped frequency responses of a thirdorder resonator (ZnO-on-silicon fabricated on a 5-μm-thick SOI) excited with a source power ranging from −5 dBm to 15 dBm. As seen the bifurcation occurs for input power of ~15 dBm. For a 12-resonator coupled-array, the power handling is significantly improved. As seen in Fig. 16, only a slight deformation of the resonance peak toward the left is observed at 15-dBm input. This improvement can be related to the increased actuation area for the coupled-array resonator (larger resonant structure). The next set of experiments clearly demonstrates the effect of the silicon layer included in the resonant structure on improving the power handling in a TPoS resonator. Fig. 17 shows overlapped frequency response plots of a third-order AlN-on-silicon resonator fabricated on the 10-μm-thick SOI substrate and excited in the fundamental
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Fig. 15. The nonlinearity measurement for a third-order TPoS resonator.
Fig. 13. The frequency response of the third-order AlN TPoS resonator in fundamental mode measured in vacuum.
Fig. 16. The nonlinearity measurement for a 12-resonator coupled array TPoS resonator.
VI. Oscillator Design and Implementation Fig. 14. The frequency response of a 9th-order AlN-on-silicon resonator with 20 µm finger pitch size.
mode. The network analyzer output power is varied from −15 dBm to 10 dBm. As shown, a very minute change is observed in the resonance peak. After completion of this measurement, the device layer silicon is etched away from the backside in an ICP tool. Frequency responses of the device measured for several applied input powers are overlapped in Fig. 18 (after silicon etching). Measured Q is reduced to ~740 (from ~5000 before etching silicon) and the resonance peak is deformed starting from –10 dBm of applied power. As expected, the resonance frequency after etching the silicon layer is slightly increased as the acoustic velocity in AlN is higher than acoustic velocity in silicon. The fact that after etching the silicon layer the resonator is highly nonlinear, and the measured quality factor of the resonator is reduced can confirm the advantages of including the silicon substrate in a lateral-extensional piezoelectric resonator.
The resonators fabricated in this work are utilized to make oscillators. The sustaining circuitry of the oscillators is designed to be very simple with a minimal number of active components. The low motional impedance of the resonator reduces the number of gain stages required to sustain oscillation. The excellent power handling of these devices improves the phase noise of the oscillator and eliminates the need for the automatic level control (ALC) circuit that is typically required in capacitive oscillators to ensure operation of the resonator in the linear region [2], [18]. By eliminating the ALC, the overall phase-noise performance of the oscillator is improved as noise from the ALC circuit would otherwise be directly injected into the oscillation loop, deteriorating performance. The power consumption of the oscillator is reduced as well. In addition, the coupled-array resonators are free of spurious modes, eliminating the possibility of locking to an undesired mode while the resonator actuation area is increased to enable lower motional impedance. To sustain the oscillation, the amplifier should create 180° phase shift because the output signal phase of both coupled-array and high-order resonators are shifted 180° relative to the input signal phase. Therefore, the discrete
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Fig. 17. The nonlinearity measurement for an AlN-on-silicon resonator fabricated on a 10-μm-thick SOI substrate.
Fig. 18. The nonlinearity measurement after etching silicon.
transimpedance amplifier (TIA) can be simplified to a single NPN transistor in a self-biased common-emitter configuration (Fig. 19). In this design, an emitter degeneration resistor (R3) is used to improve the linearity while maintaining sufficient voltage headroom for oscillation. The feedback resistor (R2) eliminates the need for a separate biasing network and improves the overall phase-noise performance of the oscillator. This is because in a closed-loop TIA the effect of the noise associated with the load of the amplifier on the input-referred noise current of the system is reduced by a factor proportional to R2−2, where R2 is the feedback resistor [19]. The transistor (T1) is chosen between BPF520 (fT ~45 GHz) or BPF620 (fT ~70 GHz) to ensure stability and high gain at high operation frequencies. It should be noted that this oscillator design is chosen mainly for its simplicity (single transistor) and does not necessarily represent an optimized circuit for demonstration of the best phase-noise performance. To further improve the phase noise, the TIA configuration needs to be modified to a more complex topology with more active components. A. AlN-on-Silicon Oscillators The first oscillator demonstrated in this section is assembled based on a third-order AlN-on-silicon resonator
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Fig. 19. The schematic circuit of a typical single-transistor TPoS oscillator.
similar to the one previously shown in Fig. 11. The oscillation circuit components are chosen as follows: R1 = 560 Ω, R2 = 10 kΩ, R3 = 10 Ω and T1 is a silicon germanium RF transistor (BFP620). The oscillation at 105.7 MHz starts with 0.98 supply voltage and 350 µA current (Pmin ~340 µW). The measured phase noise and wave form of the oscillator are shown in Fig. 20. The phase noise of the oscillator is measured using an Agilent E5500 phase noise measurement system, and the oscillator output is buffered (and amplified) before being connected to the 50 Ω-terminated input of the instrument. The oscillation power for this oscillator is 3 dBm. The farfrom-carrier phase-noise performance of this oscillator is less than −145 dBc/Hz, which is remarkably low considering the low power consumption of the TIA and relatively high impedance of the resonator. The close-to-carrier phase noise of the oscillator is −88 dBc/Hz at 1-kHz offset from the carrier frequency. The close-to-carrier phase noise density of an oscillator is inversely proportional to the square of the resonator Q [20]. Thus, higher-Q TPoS resonators produced through design optimization would enable TPoS-based oscillators with significantly improved close-to-carrier phase noise. The temperature shift of frequency for the 105.7 MHz oscillator is measured and plotted in Fig. 21. The extracted TCF from this plot is ~−29 ppm/°C. To demonstrate the effect of the resonator characteristic on the performance of the oscillator, the resonator of Fig. 14 is used in making a 208-MHz oscillator. The phase noise of the oscillator is measured and shown in Fig. 22. The close-to-carrier phase noise (−94 dBc/Hz at 1-kHz offset) is lower than that of the 105.7-MHz oscillator discussed earlier as a result of the higher quality factor and the lower motional impedance of the resonator. The oscillation power for this oscillator is increased to 5 dBm due to lower motional impedance and the higher power handling of the resonator (increased actuation area compared with the 106-MHz resonator). Therefore, the far-from-carrier phase noise (−152 dBc/Hz) is surprisingly low for a micromechanical oscillator at this frequency. Relative to state-of-the-art high-frequency capacitive os-
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Fig. 20. The measured phase noise and the wave form of the oscillator built based on the third-order AlN-on-silicon resonator.
Fig. 22. The measured phase noise of the 208 MHz oscillator.
Fig. 21. The measured TCF plot of the 105.7 MHz oscillator.
cillators reported in the literature, Table I shows that the close-to-carrier phase noise of the presented oscillator is comparable if down-converted to the same operation frequency and the phase-noise floor is ~30 dB lower. When the cost associated with vacuum packaging capacitive oscillators is also accounted for, this TPoS oscillator will be seen as advantageous.
Fig. 23. The measured phase noise of the coupled-array temperaturestable oscillator.
B. Temperature-Stable Oscillator The oscillator discussed in this section is based on a typical temperature-compensated 12-resonator coupledarray demonstrated in Section IV.B. The ~82 MHz oscillation starts with 1.1 V supply voltage and less than 2 mA of current, and the oscillation power is ~0.8 dBm. The buffered output signal is connected to the phase-noise measurement system and the result is shown in Fig. 23. As discussed previously, the resonator utilized here is fabricated on a relatively thin silicon device layer (2 μm) to enable near-zero TCF. Consequently, the power handling of this device is significantly less than the AlN-onsilicon resonators made on 10 μm SOI and utilized in the oscillators previously discussed. Since the oscillation power is not controlled by an ALC unit, the resonator can be driven to nonlinear operation regime. The dominant 1/f 3
Fig. 24. The measured TCF plot of the temperature-stable oscillator.
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TABLE I: Comparisons of MEMS Oscillators. Cited in This Work Oscillator
Capacitive Disk [2]
Capacitive SiBAR [1]
*61 MHz
*103 MHz
208 MHz
−110 −128 −132 61 48 000 Yes
−108 −120 −136 103 80 000 Yes
−105 −133 −163
−100 −128 −158 208 6100 No
−94 −122 −152
PN@1 KHz (dBc/Hz) PN@10 KHz (dBc/Hz) PN floor (dBc/Hz) fosc (MHz) Resonator Q Vacuum * Down-converted for comparison
component of the phase noise between 100 Hz and 1 kHz, which differs from the dominant 1/f 2 component observed for AlN-on-silicon oscillators at the same frequency offset, can be related to this reduced power handling [18]. The measured close-to-carrier phase noise is higher (−72 dBc/ Hz at 1 kHz offset) compared with measurements presented earlier as a result of the discussed lower power handling of the resonator while also being affected by the lower Q. The loaded Q can be estimated from the phase-noise plot using the Leeson’s frequency [21] and is approximately 1100. On the other hand, the temperature characteristic of the oscillator (Fig. 24) shows the advantage of incorporating the oxide layer in the resonant structure. The extracted TCF for this oscillator is ~−2.4 ppm/°C which is more than 12 times lower than the value measured for uncompensated oscillators. VII. Conclusion In this paper, low-power reference oscillators based on thin-film piezoelectric-on-substrate (TPoS) resonators were presented at VHF frequencies. TPoS resonators fabricated on a relatively thick (10 μm) silicon-on-insulator (SOI) substrate exhibit high quality factors and very low motional impedances while operating in air. The power handling of these devices was shown to be high due to the added thickness of the high power density silicon layer in the resonant structure. These features suggest TPoS resonators as attractive candidates for implementation of lowpower, high-frequency oscillators with excellent phase-noise performance. A 208-MHz oscillator designed in accordance with this paper was shown to outperform previous oscillators based on capacitive devices. A temperature-stable oscillator at 82 MHz with a TCF of ~−2.4 ppm/°C was also demonstrated, in which the buried oxide layer of the SOI substrate was incorporated in the resonant structure of the TPoS resonator. References [1] K. Sundaresan, G. K. Ho, S. Pourkamali, and F. Ayazi, “A low phase noise 100MHz silicon BAW reference oscillator,” in Proc. IEEE Custom Integrated Circuits Conf., San Jose, CA, 2006, pp. 841–844A.
[2] Y. Lin, S. Lee, S.-S. Li, Y. Xie, Z. Ren, and C. T.-C. Nguyen, “Series-resonant VHF micromechanical resonator reference oscillators,” IEEE J. Solid-State Circuits, vol. 39, pp. 2477–2491, Dec. 2004. [3] W.-T. Hsu, and C. T.-C. Nguyen, “Stiffness-compensated temperature-insensitive micromechanical resonators,” in The 15th IEEE Int. Conf. on Micro Electro Mech. Syst., 2002, pp. 731–734. [4] S. Humad, R. Abdolvand, G. K. Ho, G. Piazza, and F. Ayazi, “High frequency micromechanical piezo-on-silicon block resonators,” in IEDM ‘03 Technical Digest, 8–10 Dec. 2003, pp. 39.3.1–39.3.4. [5] G. K. Ho, R. Abdolvand, A. Sivapurapu, S. Humad, and F. Ayazi, “Piezoelectric-on-silicon lateral bulk acoustic wave micromechanical resonators,” J. Microelectromech. Syst., vol. 17, no. 2, pp. 512–520, Apr. 2008. [6] V. Yantchev and I. Katardjiev, “Micromachined thin film plate acoustic resonators utilizing the lowest order symmetric lamb wave mode,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 54, no. 1, pp. 87–95, Jan. 2007. [7] G. Piazza, P. J. Stephanou, and A. P. Pisano, “Piezoelectric Aluminum Nitride Vibrating Contour-Mode MEMS Resonators,” J. Microelectromech. Syst., vol. 15, no. 6, pp. 1406–1418, Dec. 2006. [8] C. Zhang, C. G. Xu, and Q. Jiang, “Characterization of the squeeze film damping effect on the quality factor of a microbeam resonator,” J. Micromech. Microeng., vol. 14, no. 10, pp. 1302–1306, 2004. [9] V. Kaajakari, T. Mattila, A. Oja, and H. Seppä, “Nonlinear limits for single-crystal silicon microresonators,” J. Microelectromech. Syst., vol. 13, no. 5, pp. 715–724, Oct. 2004. [10] R. Abdolvand and F. Ayazi, “Enhanced power handling and quality factor in thin-film piezoelectric-on-substrate resonators,” in Proc. IEEE Ultrasonics Symp., 2007, pp. 608–611. [11] K. M. Lakin, K. T. McCarron, and J. F. McDonald, “Temperature compensated bulk acoustic thin film resonators,” in Proc. IEEE Ultrason. Symp., 2000, pp. 855–858. [12] R. Abdolvand, G. K. Ho, J. Butler, and F. Ayazi, “ZnO-onnanocrystalline-diamond lateral bulk acoustic resonators,” in Proc. 20th IEEE Int. Conf. Micro Electro Mech. Syst. (MEMS 2007), Kobe, Japan, 2007, pp. 795–798. [13] G. K. Ho, R. Abdolvand, and F. Ayazi, “High order composite bulk acoustic resonators,” Proc. 20th IEEE Int. Conf. Micro Electro Mech. Syst. (MEMS 2007), Kobe, Japan, 2007, pp. 791– 794. [14] R. Abdolvand, H. Mirilavasani, and F. Ayazi, “Single-resonator dual-frequency thin-film piezoelectric-on-substrate oscillator,” in Electron Devices Meeting. IEDM ’07. 2007, pp. 419– 422 [15] G. Carlotti, L. Doucet, and M. Dupeux, “Elastic properties of silicon dioxide films deposited by chemical vapor deposition from tetraethylorthosilicate,” Thin Solid Films, vol. 296, no. 1–2, pp. 102–105, Mar. 1997. [16] K. M. Lakin, “Fundamental properties of thin film resonators,” in Proc. 45th Annu. Symp. Freq. Contr., 1991, pp. 201–206. [17] H. F. Tiersten and and D. S. Stevens, “An analysis of nonlinear resonance in contoured-quartz crystal resonators,” J. Acoust. Soc. Am., vol. 80, no. 4, pp. 1122–1132, Oct. 1986. [18] S. Lee and C. T.-C. Nguyen, “Influence of automatic level control on micromechanical resonator oscillator phase noise,” in Proc. IEEE Int. Freq. Contr. Symp., 2003, pp. 341–349. [19] B. Razavi, Design of Integrated Circuits for Optical Communications. New York: McGraw-Hill Science, 2002.
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[20] A. Hajimiri and T. H. Lee, “A general theory of phase noise in electrical oscillators,” IEEE J, Solid-State Circuits, vol. 33, no. 2, pp. 179–194, Feb. 1998. [21] D. B. Leeson, “A simple model of feedback oscillator noise spectrum,” Proc. IEEE, vol. 54, pp. 329–330, Feb. 1966.
Reza Abdolvand (S’02) received the B.S. and M.S. degrees in electrical engineering from Sharif University of Technology, Tehran, Iran, in 1999 and 2001, respectively. He then joined the Georgia Institute of Technology, Atlanta, GA, in 2002, where he received the Ph.D. degree in the School of Electrical and Computer Engineering in 2008. Dr. Abdolvand has been with the School of Electrical and Computer Engineering at Oklahoma State University as an assistant professor since August 2007. His research interests lie in the area of micro/nano-electromechanical systems with a special focus on design, fabrication, and characterization of integrated microresonators with applications in RF circuits and resonant sensors. He holds five issued and pending patents in the field of micromachining techniques and resonant microdevices.
Hossein M. Lavasani was born in 1979 in Tehran. He received the B.S. degree in electrical engineering from Sharif University of Technology, Tehran, Iran in 2001, and the M.S. degree from Arizona State University, Tempe, in 2003. From 2003 to 2004, he was with Medtronics Microelectronics Center, Phoenix, as an IC design engineer where he was in charge of developing logic and mixed-signal circuits for microcontroller units used in pacemakers. Since then, he has been working toward the Ph.D. degree at the Georgia Institute of Technology, Atlanta. His research interests are in the area of interface circuit design and characterization for high-frequency micromechanical oscillators.
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Gavin K. Ho was born in Vancouver, Canada. He received the M.Eng. degree and B.A.Sc. degree with distinction in mechanical engineering from the University of British Columbia, Canada, in 2001. He then received the M.S.E.C.E. degree and Ph.D. degree in electrical and computer engineering in 2004 and 2008, respectively, from the Georgia Institute of Technology. He was a process development engineer at Analog Devices, Inc. in Cambridge, MA, from 2006 to 2008. He enjoyed teaching undergraduate courses at Georgia Tech in 2005 and 2006. His research interests include capacitive and piezoelectric micromechanical resonators for sensors, reference oscillators and bandpass filters. Dr. Ho was the recipient of the UBC Letson Prize in 2001. In 2002, he received the Col. Oscar P. Cleaver Award and N. Walter Cox Fellowship from the Georgia Institute of Technology.
Farrokh Ayazi received the B.S. degree in electrical engineering from the University of Tehran, Iran, in 1994, and the M.S. and Ph.D. degrees in electrical engineering from the University of Michigan, Ann Arbor, in 1997 and 2000, respectively. He joined the faculty of the Georgia Institute of Technology in December 1999, where he is now an associate professor in the School of Electrical and Computer Engineering. His research interests are in the areas of integrated micro- and nano-electromechanical resonators, IC design for MEMS and sensors, RF MEMS, inertial sensors, and microfabrication techniques. Prof. Ayazi is a 2004 recipient of the NSF CAREER Award, the 2004 Richard M. Bass Outstanding Teacher Award (determined by the vote of the ECE senior class), and the Georgia Tech College of Engineering Cutting Edge Research Award for 2001–2002. He received a Rackham Predoctoral Fellowship from the University of Michigan for 1998–1999. He is an editor for the IEEE/ASME Journal of Microelectromechanical Systems, and serves on the technical program committees of the IEEE International Solid State Circuits Conference (ISSCC), and the International Conference on Solid State Sensors, Actuators and Microsystems (Transducers).
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Thin-Film Piezoelectric-on-Silicon Resonators for High-Frequency Reference Oscillator Applications Reza Abdolvand, Hossein M. Lavasani, Gavin K. Ho, and Farrokh Ayazi Abstract—This paper studies the application of lateral bulk acoustic thin-film piezoelectric-on-substrate (TPoS) resonators in high-frequency reference oscillators. Low-motionalimpedance TPoS resonators are designed and fabricated in 2 classes—high-order and coupled-array. Devices of each class are used to assemble reference oscillators and the performance characteristics of the oscillators are measured and discussed. Since the motional impedance of these devices is small, the transimpedance amplifier (TIA) in the oscillator loop can be reduced to a single transistor and 3 resistors, a format that is very power-efficient. The lowest reported power consumption is ~350 µW for an oscillator operating at ~106 MHz. A passive temperature compensation method is also utilized by including the buried oxide layer of the silicon-on-insulator (SOI) substrate in the structural resonant body of the device, and a very small (−2.4 ppm/°C) temperature coefficient of frequency is obtained for an 82-MHz oscillator.
I. Introduction
M
icromachined high-Q frequency-selective components with small form-factor are in high demand to replace quartz crystal resonators in temperature-stable, low-phase-noise oscillator applications. Significant progress has been made in developing oscillators that utilize silicon-micromachined capacitive resonators with Q values comparable to that of a quartz resonator [1], [2]. However, high-frequency capacitive resonators require relatively high dc polarization voltages (5–20 V) for operation, which complicates the design of the oscillator in low-voltage CMOS circuits. Moreover, the motional impedance of capacitive resonators is much larger than for quartz resonators and their power handling is usually lower. These resonators are operated at low pressures (mTorr regime), which makes their packaging process costly and challenging. Also, the temperature compensation techniques demonstrated so far usually lose efficiency at high frequencies [3]. Thin-film piezoelectric-on-substrate (TPoS) resonators, which the authors have investigated in previous work [4], [5], are a class of lateral extensional resonators with the potential to address some of the issues just mentioned. These resonators, similar to other micromachined piezo-
Manuscript received February 4, 2008; accepted June 30, 2008. R. Abdolvand is with the School of Electrical and Computer Engineering at Oklahoma State University (e-mail: reza.abdolvand@ okstate.edu). H. Mirilavasani and F. Ayazi are with the Georgia Institute of Technology, Atlanta. Digital Object Identifier 10.1109/TUFFC.2008.976 0885–3010/$25.00
electric resonators [6], [7], benefit from the large coupling factor of piezoelectric transduction, which provides for very small motional impedance at relatively high frequencies. The realized lower motional impedance eliminates the need for multiple gain stages in oscillator applications. Moreover, the use of low-loss substrates in TPoS resonators (e.g., single crystal silicon) leads to improved structural integrity while requiring a very thin (less than 1 μm) layer of piezoelectric. Also, the residual stress in the film is more tolerable. The contribution of squeezefilm damping on the quality factor of TPoS resonators is also significantly less compared to capacitive resonators with ultra-narrow transduction gaps [8]. Therefore, vacuum packaging may not be necessary, which makes the technology more cost-competitive. Also notably, the power handling in TPoS resonators is high due to inclusion of high power-density material such as silicon in the resonant structure (compared with the same device solely made of a thin piezoelectric film) [9], [10]. Consequently, the far-from-carrier phase noise in TPoS-based oscillators can be further reduced by increasing the oscillation power. Another important advantage of TPoS resonators over capacitive devices is that no bias voltage is necessary for their operation, a very attractive feature considering the low operating voltage of modern integrated circuits. In this work, application of high-frequency TPoS resonators in frequency reference oscillators (at VHF band) is studied. An arraying technique for systematically reducing the motional impedance of high-frequency TPoS resonators is introduced and compared with the conventional high-order designs. Also, the benefit of including the silicon substrate in the resonant structure on reducing the phase noise of TPoS-based oscillators is experimentally demonstrated. Furthermore, the temperature coefficient of frequency (TCF) of TPoS resonators is shown to be reduced by incorporating the buried oxide (BOX) layer of the silicon-on-insulator (SOI) substrate in the resonator structure. The large positive TCF of the oxide layer [11] compensates for the negative TCF of the rest of the material in the resonant structure and enables near-zero-TCF devices, provided the thickness of the layers is controlled. II. Resonator Structure A TPoS resonator comprises a thin-film piezoelectric layer sandwiched between 2 metallic electrodes stacked on top of a relatively thick substrate layer. The substrate
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Fig. 2. The third-order lateral-extensional resonance mode-shape of a block resonator simulated in COMSOL.
Fig. 1. The schematic viewgraph of a two-port third-order TPoS resonator.
layer, which usually comprises a large portion of the resonant structure, is chosen from low-acoustic-loss material such as single crystal silicon or nano-crystalline diamond (NCD) [12]. The metal electrodes are patterned to match the strain field in a targeted resonance mode-shape. The resonator can be configured in 1- or 2-port configurations. All the resonators discussed in this work are 2-port designs. By applying an alternating signal to the input electrode, a vertical alternating electric field is induced in the piezoelectric film and consequently a corresponding lateral stress is introduced in the structure due to the nonzero d31 coefficient of the piezoelectric film. This stress field is responsible for excitation of the lateral extensional resonance modes of the structure and the resulting vibration is converted back to electrical signal on the output electrodes [5]. With a careful electrode design, the coupling factor is optimized and the motional impedance of the resonator is minimized. The resonators used in this paper had bottom electrodes covering the entire resonant structure (e.g., a ground plane), although the bottom electrode can optionally be patterned to match the shape of the top electrode. A. High-Order Design The designed top electrode pattern for excitation of high-order lateral-extensional resonance modes of a rectangular plate resembles an interdigitated transducer (Fig. 1) [13]. The resonant frequency of the device can be approximated using
f =
1 2(W /n)
E eff 1 = v a,eff, r eff 2L p
(1)
where W is the total width of the block, Eeff is the effective Young’s modulus of the stack along the width direction, ρeff is the effective density of the stack, and n is the number of fingers. Alternatively, the equation can be written
as a function of Lp (finger pitch) and va,eff (effective acoustic velocity along the width of the block). The resonator is suspended by 2 beams attached to the middle of the structure on both sides. The resonator can be modeled as a simple series RLC circuit [5]. The motional impedance of a fundamental mode resonator with two electrodes covering the entire top surface [5] is
R1 »
pt tot E eff r eff 2 2d 31 E f2WQ
,
(2)
where ttot is the total thickness of the block, d31 is the transverse piezoelectric coefficient, Ef is the Young’s modulus of the piezoelectric film, and Q is the quality factor of the resonator. For a high-order device, it can be shown that the impedance is:
R 1,n »
R1 , N
(3)
where N = n for even n, and N = (n2 − 1)/n for odd n. Intuitively, this is very simple. As the number of regions or multiple of resonators is increased, the impedance decreases by N. The top electrode design matches the periodic strain field pattern of the block structure excited in the highorder lateral-extensional resonance modes. As an example, the third-order mode shape of a rectangular plate simulated in COMSOL is shown in Fig. 2. The color code in this picture demonstrates the strain field. Bluish colors present areas under compressive strain and reddish colors are representative of the tensile strain. At resonance, opposite charges are accumulated on the 2 electrodes because the strain polarity alternates from one finger to the other. Therefore, the output signal phase is 180° shifted relative to the input signal phase. It is worth mentioning that using the same electrode pattern, the fundamental resonance mode of the structure can also be excited, where strain field is uniform across the whole structure. However, we have shown that the sustained oscillation frequency can be selected between the 2 frequencies without the need for any mode-suppression circuitry
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Fig. 3. The schematic viewgraph of a two-resonator coupled-array TPoS resonator.
[14]. This is achievable by exploiting the dissimilar phase shift of the output signal, which is 0° for the fundamental mode and 180° for the third harmonic. Therefore, an inverting amplifier in the oscillation loop would only sustain the frequency of the third harmonic mode. B. Arrayed Design The motional impedance of the high-order TPoS resonators is reduced by increasing the resonance order (number of fingers) due to the proportional increase in the transduction area [13]. However, the small suspension beams located at 2 nodal points of a wide freestanding resonant structure are not constraining enough to prevent excitation of unwanted resonance modes. Therefore, an increase of spurious modes in the frequency response of a TPoS resonator is predicted to be observed as the resonance order is increased. The validity of this prediction will be proved experimentally in Section IV.A. A solution to this problem is suggested in Fig. 3, which shows a design for a coupled array of individual resonators in which each section of the resonant plate is supported with a separate set of support beams (corresponding to an individual resonator). This design improves the rigidity of the resonant structure and consequently suppresses the vibration amplitude of the spurious modes. The excited resonant mode in this design is the second harmonic lateral mode-shape of the plate, in which the input and the output signals are out-of-phase (area covered by one electrode is expanding while the other portion is contracting and vice versa). The motional impedance of a coupled-array resonator is ideally inversely proportional to the number of resonators in the array (combination of individual impedances in parallel). III. Fabrication Process The process flow for TPoS resonators fabricated on SOI is briefly described in Fig. 4. The important modifica-
Fig. 4. The schematic diagram of the process flow.
tion compared with the prior process described in [5] is in the release step. The buried oxide (BOX) layer in the SOI substrate is optionally etched from the top side in an inductively coupled plasma (ICP) etcher using the same mask layer that defines the device structure (mask 4), by which the BOX layer attached to the resonant structure is kept intact, thus improving the temperature stability of the resonator. The bottom metal electrode is chosen based on the piezoelectric film utilized. Sputtered ZnO and AlN are used for the resonators studied in this paper. Despite ZnO’s deposition simplicity, the resistivity of the film is hard to control. On the other hand AlN, which was deposited by an outside foundry, provides for an excellent insulation layer. Gold is the bottom electrode metal of choice for resonators fabricated with sputtered ZnO, both because the vertical alignment of the c-plane ZnO grains on gold was enhanced and also because gold does not react with the chemical etchant used for patterning the ZnO layer. Molybdenum is chosen for the AlN films because it is a high Q metal. The top electrode is made of Al for both ZnO and AlN devices. IV. Frequency Response Measurement To measure frequency response of the fabricated resonators, a Karl-Suss high-frequency probe station, Cascade GSG probes, and an E8364 Agilent network analyzer are used. A Lakeshore high-frequency vacuum probe station with heated chuck is alternatively used for carrying out the measurements in vacuum. All reported Q values are measured in air unless otherwise stated. The motional impedance of the resonators is extracted from the minimum S21 loss considering 50-Ohm termination on both ports.
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Fig. 5. Optical viewgraphs of (a) a third-order and (b) 4-resonator coupled-array TPoS resonator.
Fig. 7. The frequency response plot of a 94-MHz 9th-order TPoS resonator.
Fig. 6. The frequency response plot of a 94-MHz third-order TPoS resonator.
A. High-Order Versus Arrayed Resonators Top-view optical viewgraphs of a third-order ZnO-onsilicon resonator and a 4-resonator arrayed counterpart are shown in Fig. 5. These devices are fabricated on a 5-μm-thick SOI substrate. The ZnO film is ~0.5 μm thick, and the BOX layer is removed from the backside on this wafer. The center-tocenter top electrode pitch size for these devices is 40 μm. The third-order device is 160 μm long, whereas the arrayed resonators are only 60 μm long. A typical measured frequency response plot of the thirdorder ZnO-on-silicon resonator under discussion is shown in Fig. 6. The frequency response of a 9th-order resonator designed to operate at the same frequency (same finger pitch) is demonstrated in Fig. 7. Although, the motional impedance of this device is significantly lower than the third-order device, the number of spurious modes and their vibration amplitudes are critically increased. For comparison, the wide-span (100 MHz) frequency response of a 12-resonator coupled-array is demonstrated in Fig. 8, along with a scanning electron micrograph (SEM) of the fabricated device. Unlike the third-order and the 9th-order devices, no strong spurious peak is detected in the 94-MHz vicinity
of the primary resonance peak. Measured frequency responses of arrayed devices located on the same die of the 5-μm-thick processed wafer with 4, 6, and 12 coupled resonators are shown in Fig. 9. The dimensions of the metal electrodes for the 4-resonator array are different than the other 2 resonators, causing the relatively large shift in the center frequency. The motional impedances are ~550 Ω for the 4-resonator, 210 Ω for the 6-resonator, and 110 Ω for the 12-resonator arrays. The predicted inverse proportionality of the motional impedance with the number of resonators in the array holds with good precision for the 2 larger devices. These results confirm that the motional impedance of the coupled-array device can be systematically decreased while avoiding spurious modes. B. Resonators With Oxide A 2-µm-thick SOI substrate with 2 µm BOX layer is used as the starting substrate for the fabrication of a temperature-stable resonator. For these resonators the BOX layers are etched in the ICP from the top. Therefore, the ~2 µm oxide layer is included in the stack of the resonant structure. To realize a near-zero TCF resonator the thickness of the oxide layer with the positive TCF has to be comparable with the thickness of the silicon, the AlN, and the metal layers (which all have negative TCF). Because the thickness of the BOX layer cannot be typically more than a few microns, the thickness of the silicon layer is reduced. A typical frequency response plot measured from a 12-resonator arrayed device fabricated on this substrate is shown in Fig.10. Even though the dimensions of this device are the same as the device measured in Fig. 6, the measured resonance frequency is decreased from ~95 MHz to less than 82 MHz, a direct result of including the oxide layer in the resonant structure. The elastic modulus of oxide (~75 GPa) [15] is
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Fig. 8. The wide-span (100 MHz) frequency response and the SEM of a 12-resonator coupled-array. Fig. 10. The frequency response of a temperature-compensated 12-resonator coupled array.
Fig. 9. Frequency response plots of 4-, 6-, and 12-resonator coupled arrays.
lower than the elastic modulus of silicon (~150 GPa) and therefore the resonance frequency is decreased. C. AlN-on-Silicon Resonators AlN-on-silicon resonators are fabricated on a 10 µm SOI wafer, and the thickness of the sputtered AlN layer is 1 µm. The frequency response of a third-order resonator with 40 µm finger pitch is shown in Fig. 11. For this device the resonance frequency is increased compared with the ZnO-on-silicon counterpart. This is mostly due to the fact that the acoustic velocity of AlN (11 400 m/s) is greater than the acoustic velocity of ZnO (6400 m/s) [16]. As explained, the same top electrode pattern can excite the fundamental extensional resonance mode of the rectangular plate. The frequency response plot is shown in Fig. 12. The resonance frequency (~35.5 MHz) is onethird of the third-order mode as expected, and the motional impedance is larger even though the quality factor is larger. The unloaded quality factor of the resonance peak shown above is increased to ~17 000 when measured in
vacuum (Fig. 13). The motional impedance of the device in vacuum is also reduced with the increase in Q as expected [5]. It was noted that the quality factors of devices fabricated on a thick (10 μm) silicon device layer were on average higher than the values measured from resonators fabricated on thinner SOI substrates (confirmed for ZnO devices as well). This observation is in agreement with the anticipated effect of the silicon layer on reducing the overall acoustic loss in TPoS resonators. The motional impedance of a high-frequency high-order TPoS resonator is further reduced by increasing the order number. The frequency response shown in Fig. 14 is measured from a 9th-order 208 MHz device with a 20 µm finger pitch. The impedance is only ~70 Ω and the unloaded Q is ~6100 in air. This resonator demonstrates the highest f·Q product measured in this work (~1.26 × 1012) which is a relatively large value compared with results reported at similar frequency ranges [7]. As shown in the next sections, use of this device will result in an excellent close-tocarrier phase noise for an oscillator that operates in air. V. Nonlinear Vibration Measurement The small size of micromechanical resonators, despite any advantages, creates an inevitable drawback when it comes to the maximum allowable stored energy—in other words, power handling, which measures the amount of power that can be applied to or delivered by the resonator. Power handling is mostly limited by the nonlinearity mechanisms in the resonator. In piezoelectric resonators with small piezoelectric coefficients, electric and electrostatic nonlinearities can be disregarded as they relate to the effect of nonlinear elastic constants [17]. This is different than the case for capacitive resonators, in which the transduction nonlinearity is significant [9].
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Since nonlinear vibration of the resonator will introduce noise and distortion in the output signal of the system, the level of applied power to the resonator should be kept less than the nonlinear limits at all times. In a linear massspring system, the spring coefficient is a constant whereas in a nonlinear system the coefficient can be written as
k = k 0(1 + k 1x + k 2x 2 + ¼),
(4)
where k1, k2, …, are nonlinear spring coefficients. A nonlinear spring coefficient will cause higher harmonics of the resonance frequency (ωn) to appear in the output. Therefore, the nonlinear resonance frequency (frequency at which the largest vibration amplitude occurs) is dependent on the vibration amplitude (A) [9]:
æ 5k 12 2 3k 2 2 ö÷ w nonlinear = w n ççè 1 A + A ÷÷ø . 12 8
Fig. 11. The frequency response and the SEM of a third-order AlN-onsilicon resonator.
(5)
It can be seen from (5) that a nonzero first-order nonlinear spring coefficient (k1) will shift down the resonance frequency and the second-order nonlinear coefficient (k2) will shift the frequency either up or down depending on its sign. It is usually assumed that the largest allowable vibration amplitude (xc) is the amplitude at the bifurcation (the critical point after which the amplitude versus frequency plot will demonstrate hysteresis). By using the maximum allowable vibration amplitude, the maximum stored energy in the resonator can be calculated from
E max =
1 k 0x c2. 2
(6)
Therefore, the maximum stored energy is proportional to the stiffness and the second power of critical vibration amplitude (xc). Small nonlinear spring coefficients will cause the critical vibration amplitude, and consequently, the power handling to increase. Nonlinear spring coefficients are dictated by material properties and are different for each material of choice. To compare the nonlinearity limitations for different materials a normalized parameter called energy density is defined as the maximum allowable energy divided by the volume of the resonant structure. Silicon exhibits larger energy density than piezoelectric materials such as quartz [9]. Considering the factors just noted, a TPoS resonator is expected to exhibit better power handling compared with devices made of a thin piezoelectric material only. The reason is two-fold—the higher stiffness of the resonant structure from the added thickness of the substrate to the stack along with the large energy density of the silicon substrate. In this paper, the experimental study of the resonator nonlinearity is carried out by analyzing the frequency response at variable input signal levels. The goal is not to characterize the nonlinearity but rather to compare the
Fig. 12. The frequency response of the third-order resonator in fundamental mode.
nonlinear behavior of the different resonators designed and fabricated for this study. Fig. 15 shows overlapped frequency responses of a thirdorder resonator (ZnO-on-silicon fabricated on a 5-μm-thick SOI) excited with a source power ranging from −5 dBm to 15 dBm. As seen the bifurcation occurs for input power of ~15 dBm. For a 12-resonator coupled-array, the power handling is significantly improved. As seen in Fig. 16, only a slight deformation of the resonance peak toward the left is observed at 15-dBm input. This improvement can be related to the increased actuation area for the coupled-array resonator (larger resonant structure). The next set of experiments clearly demonstrates the effect of the silicon layer included in the resonant structure on improving the power handling in a TPoS resonator. Fig. 17 shows overlapped frequency response plots of a third-order AlN-on-silicon resonator fabricated on the 10-μm-thick SOI substrate and excited in the fundamental
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Fig. 15. The nonlinearity measurement for a third-order TPoS resonator.
Fig. 13. The frequency response of the third-order AlN TPoS resonator in fundamental mode measured in vacuum.
Fig. 16. The nonlinearity measurement for a 12-resonator coupled array TPoS resonator.
VI. Oscillator Design and Implementation Fig. 14. The frequency response of a 9th-order AlN-on-silicon resonator with 20 µm finger pitch size.
mode. The network analyzer output power is varied from −15 dBm to 10 dBm. As shown, a very minute change is observed in the resonance peak. After completion of this measurement, the device layer silicon is etched away from the backside in an ICP tool. Frequency responses of the device measured for several applied input powers are overlapped in Fig. 18 (after silicon etching). Measured Q is reduced to ~740 (from ~5000 before etching silicon) and the resonance peak is deformed starting from –10 dBm of applied power. As expected, the resonance frequency after etching the silicon layer is slightly increased as the acoustic velocity in AlN is higher than acoustic velocity in silicon. The fact that after etching the silicon layer the resonator is highly nonlinear, and the measured quality factor of the resonator is reduced can confirm the advantages of including the silicon substrate in a lateral-extensional piezoelectric resonator.
The resonators fabricated in this work are utilized to make oscillators. The sustaining circuitry of the oscillators is designed to be very simple with a minimal number of active components. The low motional impedance of the resonator reduces the number of gain stages required to sustain oscillation. The excellent power handling of these devices improves the phase noise of the oscillator and eliminates the need for the automatic level control (ALC) circuit that is typically required in capacitive oscillators to ensure operation of the resonator in the linear region [2], [18]. By eliminating the ALC, the overall phase-noise performance of the oscillator is improved as noise from the ALC circuit would otherwise be directly injected into the oscillation loop, deteriorating performance. The power consumption of the oscillator is reduced as well. In addition, the coupled-array resonators are free of spurious modes, eliminating the possibility of locking to an undesired mode while the resonator actuation area is increased to enable lower motional impedance. To sustain the oscillation, the amplifier should create 180° phase shift because the output signal phase of both coupled-array and high-order resonators are shifted 180° relative to the input signal phase. Therefore, the discrete
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Fig. 17. The nonlinearity measurement for an AlN-on-silicon resonator fabricated on a 10-μm-thick SOI substrate.
Fig. 18. The nonlinearity measurement after etching silicon.
transimpedance amplifier (TIA) can be simplified to a single NPN transistor in a self-biased common-emitter configuration (Fig. 19). In this design, an emitter degeneration resistor (R3) is used to improve the linearity while maintaining sufficient voltage headroom for oscillation. The feedback resistor (R2) eliminates the need for a separate biasing network and improves the overall phase-noise performance of the oscillator. This is because in a closed-loop TIA the effect of the noise associated with the load of the amplifier on the input-referred noise current of the system is reduced by a factor proportional to R2−2, where R2 is the feedback resistor [19]. The transistor (T1) is chosen between BPF520 (fT ~45 GHz) or BPF620 (fT ~70 GHz) to ensure stability and high gain at high operation frequencies. It should be noted that this oscillator design is chosen mainly for its simplicity (single transistor) and does not necessarily represent an optimized circuit for demonstration of the best phase-noise performance. To further improve the phase noise, the TIA configuration needs to be modified to a more complex topology with more active components. A. AlN-on-Silicon Oscillators The first oscillator demonstrated in this section is assembled based on a third-order AlN-on-silicon resonator
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Fig. 19. The schematic circuit of a typical single-transistor TPoS oscillator.
similar to the one previously shown in Fig. 11. The oscillation circuit components are chosen as follows: R1 = 560 Ω, R2 = 10 kΩ, R3 = 10 Ω and T1 is a silicon germanium RF transistor (BFP620). The oscillation at 105.7 MHz starts with 0.98 supply voltage and 350 µA current (Pmin ~340 µW). The measured phase noise and wave form of the oscillator are shown in Fig. 20. The phase noise of the oscillator is measured using an Agilent E5500 phase noise measurement system, and the oscillator output is buffered (and amplified) before being connected to the 50 Ω-terminated input of the instrument. The oscillation power for this oscillator is 3 dBm. The farfrom-carrier phase-noise performance of this oscillator is less than −145 dBc/Hz, which is remarkably low considering the low power consumption of the TIA and relatively high impedance of the resonator. The close-to-carrier phase noise of the oscillator is −88 dBc/Hz at 1-kHz offset from the carrier frequency. The close-to-carrier phase noise density of an oscillator is inversely proportional to the square of the resonator Q [20]. Thus, higher-Q TPoS resonators produced through design optimization would enable TPoS-based oscillators with significantly improved close-to-carrier phase noise. The temperature shift of frequency for the 105.7 MHz oscillator is measured and plotted in Fig. 21. The extracted TCF from this plot is ~−29 ppm/°C. To demonstrate the effect of the resonator characteristic on the performance of the oscillator, the resonator of Fig. 14 is used in making a 208-MHz oscillator. The phase noise of the oscillator is measured and shown in Fig. 22. The close-to-carrier phase noise (−94 dBc/Hz at 1-kHz offset) is lower than that of the 105.7-MHz oscillator discussed earlier as a result of the higher quality factor and the lower motional impedance of the resonator. The oscillation power for this oscillator is increased to 5 dBm due to lower motional impedance and the higher power handling of the resonator (increased actuation area compared with the 106-MHz resonator). Therefore, the far-from-carrier phase noise (−152 dBc/Hz) is surprisingly low for a micromechanical oscillator at this frequency. Relative to state-of-the-art high-frequency capacitive os-
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Fig. 20. The measured phase noise and the wave form of the oscillator built based on the third-order AlN-on-silicon resonator.
Fig. 22. The measured phase noise of the 208 MHz oscillator.
Fig. 21. The measured TCF plot of the 105.7 MHz oscillator.
cillators reported in the literature, Table I shows that the close-to-carrier phase noise of the presented oscillator is comparable if down-converted to the same operation frequency and the phase-noise floor is ~30 dB lower. When the cost associated with vacuum packaging capacitive oscillators is also accounted for, this TPoS oscillator will be seen as advantageous.
Fig. 23. The measured phase noise of the coupled-array temperaturestable oscillator.
B. Temperature-Stable Oscillator The oscillator discussed in this section is based on a typical temperature-compensated 12-resonator coupledarray demonstrated in Section IV.B. The ~82 MHz oscillation starts with 1.1 V supply voltage and less than 2 mA of current, and the oscillation power is ~0.8 dBm. The buffered output signal is connected to the phase-noise measurement system and the result is shown in Fig. 23. As discussed previously, the resonator utilized here is fabricated on a relatively thin silicon device layer (2 μm) to enable near-zero TCF. Consequently, the power handling of this device is significantly less than the AlN-onsilicon resonators made on 10 μm SOI and utilized in the oscillators previously discussed. Since the oscillation power is not controlled by an ALC unit, the resonator can be driven to nonlinear operation regime. The dominant 1/f 3
Fig. 24. The measured TCF plot of the temperature-stable oscillator.
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TABLE I: Comparisons of MEMS Oscillators. Cited in This Work Oscillator
Capacitive Disk [2]
Capacitive SiBAR [1]
*61 MHz
*103 MHz
208 MHz
−110 −128 −132 61 48 000 Yes
−108 −120 −136 103 80 000 Yes
−105 −133 −163
−100 −128 −158 208 6100 No
−94 −122 −152
PN@1 KHz (dBc/Hz) PN@10 KHz (dBc/Hz) PN floor (dBc/Hz) fosc (MHz) Resonator Q Vacuum * Down-converted for comparison
component of the phase noise between 100 Hz and 1 kHz, which differs from the dominant 1/f 2 component observed for AlN-on-silicon oscillators at the same frequency offset, can be related to this reduced power handling [18]. The measured close-to-carrier phase noise is higher (−72 dBc/ Hz at 1 kHz offset) compared with measurements presented earlier as a result of the discussed lower power handling of the resonator while also being affected by the lower Q. The loaded Q can be estimated from the phase-noise plot using the Leeson’s frequency [21] and is approximately 1100. On the other hand, the temperature characteristic of the oscillator (Fig. 24) shows the advantage of incorporating the oxide layer in the resonant structure. The extracted TCF for this oscillator is ~−2.4 ppm/°C which is more than 12 times lower than the value measured for uncompensated oscillators. VII. Conclusion In this paper, low-power reference oscillators based on thin-film piezoelectric-on-substrate (TPoS) resonators were presented at VHF frequencies. TPoS resonators fabricated on a relatively thick (10 μm) silicon-on-insulator (SOI) substrate exhibit high quality factors and very low motional impedances while operating in air. The power handling of these devices was shown to be high due to the added thickness of the high power density silicon layer in the resonant structure. These features suggest TPoS resonators as attractive candidates for implementation of lowpower, high-frequency oscillators with excellent phase-noise performance. A 208-MHz oscillator designed in accordance with this paper was shown to outperform previous oscillators based on capacitive devices. A temperature-stable oscillator at 82 MHz with a TCF of ~−2.4 ppm/°C was also demonstrated, in which the buried oxide layer of the SOI substrate was incorporated in the resonant structure of the TPoS resonator. References [1] K. Sundaresan, G. K. Ho, S. Pourkamali, and F. Ayazi, “A low phase noise 100MHz silicon BAW reference oscillator,” in Proc. IEEE Custom Integrated Circuits Conf., San Jose, CA, 2006, pp. 841–844A.
[2] Y. Lin, S. Lee, S.-S. Li, Y. Xie, Z. Ren, and C. T.-C. Nguyen, “Series-resonant VHF micromechanical resonator reference oscillators,” IEEE J. Solid-State Circuits, vol. 39, pp. 2477–2491, Dec. 2004. [3] W.-T. Hsu, and C. T.-C. Nguyen, “Stiffness-compensated temperature-insensitive micromechanical resonators,” in The 15th IEEE Int. Conf. on Micro Electro Mech. Syst., 2002, pp. 731–734. [4] S. Humad, R. Abdolvand, G. K. Ho, G. Piazza, and F. Ayazi, “High frequency micromechanical piezo-on-silicon block resonators,” in IEDM ‘03 Technical Digest, 8–10 Dec. 2003, pp. 39.3.1–39.3.4. [5] G. K. Ho, R. Abdolvand, A. Sivapurapu, S. Humad, and F. Ayazi, “Piezoelectric-on-silicon lateral bulk acoustic wave micromechanical resonators,” J. Microelectromech. Syst., vol. 17, no. 2, pp. 512–520, Apr. 2008. [6] V. Yantchev and I. Katardjiev, “Micromachined thin film plate acoustic resonators utilizing the lowest order symmetric lamb wave mode,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 54, no. 1, pp. 87–95, Jan. 2007. [7] G. Piazza, P. J. Stephanou, and A. P. Pisano, “Piezoelectric Aluminum Nitride Vibrating Contour-Mode MEMS Resonators,” J. Microelectromech. Syst., vol. 15, no. 6, pp. 1406–1418, Dec. 2006. [8] C. Zhang, C. G. Xu, and Q. Jiang, “Characterization of the squeeze film damping effect on the quality factor of a microbeam resonator,” J. Micromech. Microeng., vol. 14, no. 10, pp. 1302–1306, 2004. [9] V. Kaajakari, T. Mattila, A. Oja, and H. Seppä, “Nonlinear limits for single-crystal silicon microresonators,” J. Microelectromech. Syst., vol. 13, no. 5, pp. 715–724, Oct. 2004. [10] R. Abdolvand and F. Ayazi, “Enhanced power handling and quality factor in thin-film piezoelectric-on-substrate resonators,” in Proc. IEEE Ultrasonics Symp., 2007, pp. 608–611. [11] K. M. Lakin, K. T. McCarron, and J. F. McDonald, “Temperature compensated bulk acoustic thin film resonators,” in Proc. IEEE Ultrason. Symp., 2000, pp. 855–858. [12] R. Abdolvand, G. K. Ho, J. Butler, and F. Ayazi, “ZnO-onnanocrystalline-diamond lateral bulk acoustic resonators,” in Proc. 20th IEEE Int. Conf. Micro Electro Mech. Syst. (MEMS 2007), Kobe, Japan, 2007, pp. 795–798. [13] G. K. Ho, R. Abdolvand, and F. Ayazi, “High order composite bulk acoustic resonators,” Proc. 20th IEEE Int. Conf. Micro Electro Mech. Syst. (MEMS 2007), Kobe, Japan, 2007, pp. 791– 794. [14] R. Abdolvand, H. Mirilavasani, and F. Ayazi, “Single-resonator dual-frequency thin-film piezoelectric-on-substrate oscillator,” in Electron Devices Meeting. IEDM ’07. 2007, pp. 419– 422 [15] G. Carlotti, L. Doucet, and M. Dupeux, “Elastic properties of silicon dioxide films deposited by chemical vapor deposition from tetraethylorthosilicate,” Thin Solid Films, vol. 296, no. 1–2, pp. 102–105, Mar. 1997. [16] K. M. Lakin, “Fundamental properties of thin film resonators,” in Proc. 45th Annu. Symp. Freq. Contr., 1991, pp. 201–206. [17] H. F. Tiersten and and D. S. Stevens, “An analysis of nonlinear resonance in contoured-quartz crystal resonators,” J. Acoust. Soc. Am., vol. 80, no. 4, pp. 1122–1132, Oct. 1986. [18] S. Lee and C. T.-C. Nguyen, “Influence of automatic level control on micromechanical resonator oscillator phase noise,” in Proc. IEEE Int. Freq. Contr. Symp., 2003, pp. 341–349. [19] B. Razavi, Design of Integrated Circuits for Optical Communications. New York: McGraw-Hill Science, 2002.
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[20] A. Hajimiri and T. H. Lee, “A general theory of phase noise in electrical oscillators,” IEEE J, Solid-State Circuits, vol. 33, no. 2, pp. 179–194, Feb. 1998. [21] D. B. Leeson, “A simple model of feedback oscillator noise spectrum,” Proc. IEEE, vol. 54, pp. 329–330, Feb. 1966.
Reza Abdolvand (S’02) received the B.S. and M.S. degrees in electrical engineering from Sharif University of Technology, Tehran, Iran, in 1999 and 2001, respectively. He then joined the Georgia Institute of Technology, Atlanta, GA, in 2002, where he received the Ph.D. degree in the School of Electrical and Computer Engineering in 2008. Dr. Abdolvand has been with the School of Electrical and Computer Engineering at Oklahoma State University as an assistant professor since August 2007. His research interests lie in the area of micro/nano-electromechanical systems with a special focus on design, fabrication, and characterization of integrated microresonators with applications in RF circuits and resonant sensors. He holds five issued and pending patents in the field of micromachining techniques and resonant microdevices.
Hossein M. Lavasani was born in 1979 in Tehran. He received the B.S. degree in electrical engineering from Sharif University of Technology, Tehran, Iran in 2001, and the M.S. degree from Arizona State University, Tempe, in 2003. From 2003 to 2004, he was with Medtronics Microelectronics Center, Phoenix, as an IC design engineer where he was in charge of developing logic and mixed-signal circuits for microcontroller units used in pacemakers. Since then, he has been working toward the Ph.D. degree at the Georgia Institute of Technology, Atlanta. His research interests are in the area of interface circuit design and characterization for high-frequency micromechanical oscillators.
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Gavin K. Ho was born in Vancouver, Canada. He received the M.Eng. degree and B.A.Sc. degree with distinction in mechanical engineering from the University of British Columbia, Canada, in 2001. He then received the M.S.E.C.E. degree and Ph.D. degree in electrical and computer engineering in 2004 and 2008, respectively, from the Georgia Institute of Technology. He was a process development engineer at Analog Devices, Inc. in Cambridge, MA, from 2006 to 2008. He enjoyed teaching undergraduate courses at Georgia Tech in 2005 and 2006. His research interests include capacitive and piezoelectric micromechanical resonators for sensors, reference oscillators and bandpass filters. Dr. Ho was the recipient of the UBC Letson Prize in 2001. In 2002, he received the Col. Oscar P. Cleaver Award and N. Walter Cox Fellowship from the Georgia Institute of Technology.
Farrokh Ayazi received the B.S. degree in electrical engineering from the University of Tehran, Iran, in 1994, and the M.S. and Ph.D. degrees in electrical engineering from the University of Michigan, Ann Arbor, in 1997 and 2000, respectively. He joined the faculty of the Georgia Institute of Technology in December 1999, where he is now an associate professor in the School of Electrical and Computer Engineering. His research interests are in the areas of integrated micro- and nano-electromechanical resonators, IC design for MEMS and sensors, RF MEMS, inertial sensors, and microfabrication techniques. Prof. Ayazi is a 2004 recipient of the NSF CAREER Award, the 2004 Richard M. Bass Outstanding Teacher Award (determined by the vote of the ECE senior class), and the Georgia Tech College of Engineering Cutting Edge Research Award for 2001–2002. He received a Rackham Predoctoral Fellowship from the University of Michigan for 1998–1999. He is an editor for the IEEE/ASME Journal of Microelectromechanical Systems, and serves on the technical program committees of the IEEE International Solid State Circuits Conference (ISSCC), and the International Conference on Solid State Sensors, Actuators and Microsystems (Transducers).
