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14 MHz Micromechanical Oscillator
T. Mattila1, O. Jaakkola1, J. Kiihamäki2, J. Karttunen2, T. Lamminmäki3,
P. Rantakari3, A. Oja1, H. Seppä1, H. Kattelus2 and I. Tittonen3
1
VTT Automation, P. O. Box 1304, FIN-02044, Finland
2
3
VTT Electronics, P. O. Box 1101, FIN-02044, Finland
Helsinki University of Technology, Metrology Research Institute,
P. O. Box 3000, FIN-02015, Finland
SUMMARY
Operation of a 14 MHz micromechanical oscillator is demonstrated and analyzed.
Single-crystal silicon microbridge with submicron electrode gaps is utilized as the
resonator element. The oscillator shows a noise floor of -120 dBc/Hz and a nearcarrier noise of -105 dBc/Hz at 1 kHz offset. The oscillator noise is dominated by
amplifier noise. By comparing the oscillator performance with conventional quartz
oscillators, advantages and limitations of the micromechanical components in RFtechnology are discussed.
Keywords: micromechanical oscillator, oscillator noise
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INTRODUCTION
As the number of wireless communication devices increases, the small size and integration
possibilities of micromechanical rf-components become significant advantages. Since the
characteristic frequency scales roughly inversely proportional to the size of the component, recent
developments in fabrication technology have made possible the realization of microresonators
operating in the VHF-to-UHF range (10-100 MHz)
miniaturized components
[1-5]. However, the small size of the
brings numerous challenges to be overcome: in general, the gap
between vibrational and thermal energies becomes narrower [6] making a high signal-to-noise
ratio harder to obtain. Also, the impedance levels of rf-microcomponents are typically high,
making the noise-matching of electromechanical coupling interface problematic.
In the present paper we address the above issues by analysing a 14 MHz oscillator based on a
micromechanical Si resonator. Although showing significantly improved noise performance
compared with the existing work [1,2,4], the present oscillator is found to exhibit a modest
performance when compared with macroscopic quartz oscillators [6]. The central performance
limitations are discussed.
RESONATOR FABRICATION
Fig. 1 shows the silicon micromechanical clamped-clamped (bridge) resonator utilized in the
present study. The width (length) of the beam was 4 (44) µm, respectively. The component was
manufactured using deep reactive ion etching (DRIE) of silicon-on-insulator (SOI) wafer with 8
µm thick device layer. The resonating beam was released from the oxide layer by wet-etching
with HF. Coupling to the mechanical vibration of the bridge was made capacitively across the
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gap d = 0.5 µm using two electrodes with the length Le = 34 µm as shown in Fig. 1. Electrical
contacts to the structure were made using wire bonding to 100 µm x 100 µm contact pads. Each
pad resulted into a parasitic capacitance of Cpad ~ 0.3 pF to the subsrate through the 1 µm thick
SiO2 layer. The substrate was grounded to remove the feed-through via the pad capacitances.
RESONATOR MEASUREMENT
The bridge resonator was driven by one of the electrodes while the other was used for the
detection of vibration (Fig. 2). UDC=100 V bias voltage was applied for the capacitive coupling.
The resonator was placed in a vacuum chamber with pressure p < 10-2 mbar causing negligible air
damping.
The resonance current was detected with an amplifier block with a low-noise JFET (Philips
BF545B) as the first stage. The amplifier was run in a common-source configuration with drain
resistor Rd ~ 1 kΩ corresponding to a 12 dB voltage gain. The input capacitance was estimated as
Cin ~ 5 pF from measurements using known capacitor values in place on the resonator. Due to the
capacitive detection of the resonance currect, loading of the resonator Q remained insignificant.
The JFET was followed by additional amplifier stages forming the output buffer to
50
Ω impedance. The transmission data were recorded with a HP4396B network analyser.
Fig. 3 shows the measured resonator transmission data. The resonance was detected at fr ~ 14.3
MHz with a quality factor of Q ~ 1500. The rather low Q-value is set by the low aspect ratio (L/w
= 11) leading to energy leakage to the support structures [7]. The feedthrough
parasitic
capacitance (parallel with the resonator) estimated from the measured data was Cpthru ~ 17 fF.
Equivalent electrical circuit values [8] (see Fig. 4) reproducing the measured data were found to
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be Rm ~ 1 MΩ, Cm ~ 8 aF, Lm ~ 15 H. The coupling gap capacitance between the bridge and the
fixed electrodes was calculated as Cw ~ 4 fF.
OSCILLATOR CIRCUIT DESIGN AND MEASUREMENT
The resonator measurement setup was converted to an oscillator closed-loop configuration by
connecting the amplifier output to resonator input as shown in Fig. 4. The JFET was followed by
additional gain stages [represented by the amplifier block containing (G,φ)] to fulfill the selfoscillation condition: the amplifier gain was set to just compensate for the resonator dissipation
Rm at closed-loop phase shift set equal to zero. A high-impedance buffer amplifier connected to
the low-impedance (50 Ω) output of the sustaining amplifier allowed the measurement of the
oscillation signal without perturbing the oscillator operation. In the resonator output, the effect of
parasitic pad capacitance Cp ~ 0.3 pF was small due to the dominance of the amplifier input
capacitance Cin ~ 5 pF. In the resonator input, the role of the parasitic pad capacitance (Z(Cp) ~
45 kΩ) was mainly to increase the oscillator power consumption by drawing a major part of the
sustaining amplifier output current. For the oscillator measurement, the setup was further refined
by a careful shielding of the fringe fields, reducing the feedthrough capacitance to Cpthru ~ 3.5 fF,
and the bias voltage was raised to UDC ~ 130 V. HP4396B was used to measure the oscillator
output spectrum.
The sharp peak in Fig. 5 demonstrates the succesful oscillator operation. The output carrier level,
reduced to the amplifier input, was vs ~ 2.0 mV (rms). This corresponds to a mechanical vibration
amplitude of a few percent of the gap: xvib ~
vs Cin
η
~ 0.05 d = 0.025 µm , where η = U DC
∂C w
is the
∂x
electromechanical coupling constant. The oscillation amplitude was limited by the resonator nonlinearity [9]. Resonator transmission data measurements at high drive levels revealed that the
vibration was constrained by both mechanical (spring-hardening) and capacitive (spring-
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softening) non-linearities [10]. The cross-over from mechanical to capacitive non-linearity was
measured to occur at UDC ~ 105 V bias voltage.
The measured open-loop (UDC = 0 V, resonator switched off) noise level at the amplifier input
was vn ~ 2.0 nV/ Hz (rms). Thus combined with the signal level of vs ~ 2.0 mV (rms), the
expected N/S-ratio should approach -120 dBc/Hz. Direct measurement of such large N/S-ratios
using a spectrum analyser is not straightforward due their limited dynamic range. This problem is
further emphasized for measurement of noise at a small frequency offset from the carrier
(oscillator spectral purity), which is the central quantity of interest here.
To facilitate the
measurement of near-carrier noise, we have used the standard technique [11] depicted in Fig. 6: a
reference oscillator is phase-locked to the micromechanical oscillator. The feedback loop is
constructed to keep relative phase between the two oscillators at 90 degress, resulting in zero DCoutput level in the mixer output. By filtering away the up-mixed carrier at 2ωr , the carriers have
been removed and it is straighforward to measure the noise at audio frequencies, corresponding to
the phase noise (amplitude noise “removed” by the phase lock condition) of the oscillators.
Obviously, in order to determine the noise of the micromechanical oscillator, the reference
oscillator must have a better noise performance: we have a used a HP E4426B precision signal
source which was verified to give a single-side-band noise of Lf ~ -125 dBc/Hz at 1 kHz offset
from a 14 MHz carrier. The phase-lock loop was operated at ~20 Hz bandwidth.
The oscillator phase noise, measured using the outlined techique, is shown in Fig. 7. The phase
noise level at 1 kHz offset from the carrier is ~ -105 dBc/Hz. At 10 kHz frequency offset the N/Sratio approaches a noise floor of -120 dBc/Hz, expected from the open-loop amplifier noise level.
Below 1 kHz offset the phase noise increases rapidly (roughly as 1/f3, dashed line in Fig. 7); we
tentatively associate this effect to the mixing of low-frequency noise to near-carrier frequencies
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due to the non-linear operation point of the microresonator (the oscillation amplitude was limited
by the resonator non-linearity).
In general, we find that the oscillator noise is dominantly set by amplifier noise: this can be seen
in detail by calculating the intrinsic resonator noise. The resonator mechanical dissipations are
conveniently described by the equivalent circuit resistance Rm (Fig. 4). The associated noise
voltage is obtained as v n , Rm = 4kTRm . Since the amplifier input impedance Zin = 1/ωrCin ~ 3 kΩ
is much smaller than Rm ~1 MΩ and Cin >> Cpad, the resonator induced noise voltage in the
amplifier input (at ωr) can be approximately obtained as
v nin, Rm =
Z (C in )
v n , Rm ~ 0.4 nV/ Hz . This is
Rm
thus much smaller than the measured open-loop effective amplifier noise of vn ~ 2.0 nV/ Hz .
The domination of amplifier noise demostrates the noise-matching challenge with highimpedance levels in micromechanics. The noise-temperature TA for a typical amplifier seeing the
noise-optimum impedance is negligible compared with room temperature; in the present case, an
estimate for the optimum source impedance in the case of JFETs is Ropt ~ 1.63 Z(Cg), where Cg is
the gate capacitance [12]. Noise matching of the impedance levels, i.e. Rm ~ Ropt, would mean
that the resonator, being at T = 300 K, could be read with a negligible contribution of amplifier
noise. In the present case, however, the resonator series resistance Rm ~ 1 MΩ is much larger than
Ropt of a few kΩ's indicating that the system is far from noise-matched optimum. This is indeed
reflected by the dominance of amplifier noise. However, it should be emphasized that the above
analysis applies to near-carrier frequencies where the resonator impedance remains nearly
constant at Rm; at larger frequency offsets reaching a noise optimum requires additional
impedance matching techniques.
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CONCLUSIONS
The noise performance of a commercial 10 MHz quartz oscillator is typically better than -150
dBc/Hz at 1kHz offset from the carrier [6]. From the present study it is clear that, athough
showing improvement over previous published work [1,2,4], the measured micromechanical
oscillator short-term noise performance is currently clearly inferior to quartz oscillators. This is
principally due to two facts: 1) The energy reservoir (resonator mechanical vibration energy) is
unavoidably reduced as the size of the component is reduced. 2) Optimal electrical coupling
(noise-matching) to the mechanical energy reservoir is difficult to accomplish, since the resonator
is typically characterized by a high impedance.
Several methods to improve the noise performance can be considered: The small size of
microcomponents could allow the use of parallel resonators to increase the vibrational energy and
lower the impedance. A lower resonator impedance level could be obtained also by a more
optimized capacitive coupling (UDC close to pull-in voltage). Also, scaling down of the amplifier
in size would improve the noise-matching. This would be feasible using a fabrication process
that allows the integration of the resonator and amplifier on the same silicon chip. Using an
integrated amplifier would also assist in reducing the parasitic capacitances, leading to a
reduction in energy consumption to maintain the oscillations.
ACKOWLEDGMENT
We thank V. Ermolov, H. Kuisma, and T. Ryhänen for useful discussions. The financial support
from Nokia Research Center, VTI Hamlin and Finnish National Technology Agency is
acknowledged.
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REFERENCES
[1] T. A Roessig, R. T. Howe, A. P. Pisano and J. H. Smith, "Surface-Micromachined 1 MHz
Oscillator with Low-Noise Pierce Configuration", Solid-State Sensor and Actuator Workshop,
Transducer Res. Found., Cleveland, USA, (1998).
[2] C. T.-C. Nguyen abd R. T. Howe, "An Integrated CMOS Micromechanical Resonator High-Q
Oscillator", IEEE J. of Solid-State Circuits 34, 440 (1999).
[3] K. Wang, A.-C. Wong, and C. T.-C. Nguyen, "VHF Free-Free Beam High-Q
Micromechanical Resonators", J. Microelectromech. Syst. 9, 347 (2000).
[4] S. Lee, M. U. Demirci, C. T.-C. Nguyen, "A 10-MHz Micromechanical Resonator Pierce
Reference Oscillator for Communications", Digest of Technical Papers, Transducers '01
(Munich, Germany, 2001), p. 1094.
[5] D. W. Carr, S. Evoy, L. Sekaric, H. G. Craighead and J.M. Parpia, "Measurement of
mechanical resonance and losses in nanometer scale silicon wires", Appl. Phys. Lett. 75, 920
(1999).
[6] J. R. Vig and Y. Kim, "Noise in Microelectromechanical System Resonators", IEEE Trans.
Ultrason. Ferroelect. Freq. Contr. 46, 1558 (1999).
[7] K. Y. Yasumura, T. D. Stowe, E. M. Chow, T. Pfafman, T. W. Kenny, B. C. Stipe and D.
Rugar, "Quality Factors in Micron- and Submicron-Thick Cantilevers", J. Microelectromech.
Syst. 9, 117 (2000).
[8] T. Mattila, P. Häkkinen, O. Jaakkola, J. Kiihamäki, J. Kyynäräinen, A. Oja, H. Seppä, P.
Seppälä and T. Sillanpää, "Air damping in resonant micromechanical capacitive sensors", in
Proc. of 14th European Conference on Solid-State Transducers, Eurosensors XIV,
(Copenhagen, Denmark, 2000) p. 221.
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[9] C. Gui, R. Legtenberg, H. A. C. Tilmans, J. H. J. Fluitman, and M. Elwenspoek,
"Nonlinearity and Hysteresis of Resonant Strain Gauges", J. Microelectromech. Systems 7,
122 (1998).
[10] T. Veijola and T. Mattila, "Modeling of Nonlinear Micromechanical Resonators and Their
Simulation with Harmonic-Balance Method", accepted for publication in RF and Microwave
Computer-Aided Engineering.
[11] see e.g. D. Allan, in ”Time and Frequency: Theory and Fundamentals”, National Bureau of
Standards, USA, 1974, p.171.
[12] M. J. Buckingham, Noise in Electronic Devices and Systems, Halsted, New York, 1983.
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Figure captions:
Fig. 1: SEM (scanning electron microscope) picture of the 14 MHz micromechanical bridge
resonator. Bridge supports and outer parts of the electrodes are metallized.
Fig. 2: Resonator measurement setup.
Fig. 3: Amplitude g = Uout/Uin and phase of the resonator transmission response.
Fig. 4: Oscillator setup.
Fig. 5: Oscillator output spectrum in a 100 kHz range around the 14.3 MHz carrier. The
spectrum analyser resolution bandwidth was 300 Hz
Fig. 6: Oscillator phase noise measurement setup.
Fig. 7: Oscillator single-sideband phase noise. The noise decay slope for 1/f3 is illustrated by
dashed line.
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VTT
re
so
na
to
r
el
ec
tro
de
el
ec
tro
d
e
L = 44 um
d = 0.5 um
w = 4 um
Mattila et al: Figure 1.
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UDC
G
Uin
~
Mattila et al: Figure 2.
network
analyzer
Uout
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-44
100
|g| (dB)
80
-48
-50
60
-52
-54
14.24
10 kHz
14.26
14.28
14.30
Frequency (MHz)
Mattila et al: Figure 3.
14.32
40
14.34
Phase (deg)
-46
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Rd = 1 kΩ
Ω
Rm
Cm
Lm
Cthru
Cpad
JFET
BF545B
Cpad
Cin
0.3 pF
5 pF
G,φ
oscillator
output
Mattila et al.: Figure 4.
buffer
amplifier
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Output spectrum (dBV)
0
-20
-40
-60
-80
-100
-50000
-25000
0
Frequency offset (Hz)
Mattila et al.: Figure 5.
25000
50000
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SA
~
MEMS OSC
LPF
+
~
REF VCO
Mattila et al.: Figure 6
PLL
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SSB phase noise (dBc/Hz)
-60
-70
-80
3
1/f
-90
-100
-110
-120
-130
100
1000
Frequency offset (Hz)
Mattila et al.: Figure 7.
10000