1. Piezoelectric MEMS Resonator Measurement and Characterization
April 6, 2004
Joung-Mo Kang, David Carter, Doug White, and Amy Duwel
The Charles Stark Draper Laboratory

2. Presentation Overview
Background and device models
Filter design
L-Bar measurements
Parasitic investigations
Conclusion

3. Device Overview and Goals
18 x 5.5 mm bar with 3.5 mm tethers
Desired: a high performance RF channel-select filter bank on a chip
0.3-3 GHz frequencies
high selectivity  high Q
compatible with silicon IC technologies
small size  high density
low loss
device characteristics defined by lateral geometry
10 x 5 mm bar with 1 mm tethers

4. Device Structure
Circuit Model
resonator
Ctethers

5. Longitudinal Resonance
Longitudinal Mode Shape
tethers placed at displacement node
longitudinal displacement amplitude on the order of nm
other types of mechanical resonances cancel out in charge at lower frequencies

6. Butterworth Van-Dyke ModelC L C t p c r t r l 8 we 2 l e wl = R = L = C = C z 2 Q 8 we 8 we 2 tc p 2 t
MEMS
MTO
DARPA

7. BVD Impedance Function
l = 5.5 mm
w = 3.0 mm
t = 0.5 mm
Q = 10,000
L = 342 mH
C = fF
R = 189 W
C0 = 2.98 fF
860
865
870
875
880
885
890
895
900
905
910 10 2 4 6 8
Impedance Magnitude (W)
-90
-45 45 90
Impedance Phase (degrees)

8. Filter Design Primary Objectives:
Review existing crystal filter topologies and assess performance metrics.
Down-select a filter topology based on specifications set by RF group.
Define fabrication requirements and tolerances to achieve desired performance with each topology

9. Dual Resonator Ladder Zs RS Vout Vin Zp RL
Extremely robust (trying to minimize cap, needed to break wafer, at one point shattered wafers and still got resonances from devices)

10. Lattice Filter wa wb Vin Vout R Zb Za
Impedance of Za and Zb Za Zb
Full filter response wa wb
Extremely robust (trying to minimize cap, needed to break wafer, at one point shattered wafers and still got resonances from devices)

11. Lattice Filter
Extremely robust (trying to minimize cap, needed to break wafer, at one point shattered wafers and still got resonances from devices)

12. Simple Ladder Filter Vin C12 RL RS Z=sL+1/sC Vout
Wideband Response
-20
-40
-60
Magnitude (dB)
Extremely robust (trying to minimize cap, needed to break wafer, at one point shattered wafers and still got resonances from devices)
-80
-100
-120
-140
102
103
104
105
106
Frequency (MHz)

13. Simple Ladder Filter
Effect of bar length mismatch on filter characteristic
797.5
798
798.5
799
799.5
800
800.5
801
801.5
802
802.5
-30
-20
-10
Filter Transmission (dB)
data1
data2
data3
-270
-180
-90 90
Phase (degrees)
no mismatch
0.1 %
0.3 %
Nominal values:
l = 6.04 mm
w = 3.22 mm
t = 0.5 mm
RS, RL = 1758 W
C12 = fF
Extremely robust (trying to minimize cap, needed to break wafer, at one point shattered wafers and still got resonances from devices)

14. Mechanically Coupled Devices
Vin
Vout RS RL
C12

15. Device Measurement Primary Objectives:
Confirm successful operation of resonators and accuracy of the analytic model (f vs. l, spurious modes)
Fit measurements to a discrete circuit model, adjust model if necessary, and extract resonator parameters (ie, determine resonator Q)
Use resonator performance results and analysis of parasitics to guide process and design improvements

16. Device Measurement 5 mm 3 mm L C R Co RS RL
~800 MHz resonator structure
Device (GSG configuration) L C R
Extremely robust (trying to minimize cap, needed to break wafer, at one point shattered wafers and still got resonances from devices) Co RS RL

17. First Round Devices Longitudinal axis AlN contact C Co L R RL Rs Cthru
S21 (dB)
100 50
675
800 MHz
925
Cthru=0
Cthru=2pF
5 mm Bar, Q=104 C Co L R RL Rs
Cthru 30 20 10
140
160 MHz
180
Cthru=2pF
25 mm Bar, Q=103
S21 (dB)

18. First Round L-Bar Resonance
-16
-15.9
-15.8
-15.7
-15.6
-15.5 69 70 71 72 73
146
150
147
149
148
Frequency (MHz)
Phase (degrees)
S21 (dB)
Cthru ~ 2 pF

19. Measurement Results Fundamental Length Resonances Frequency (MHz)
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
200
400
600
800
1 / mm
Frequency (MHz)
~ 3.8 GHz - mm 1 2 E r × =
-21
-20
-19
-18
-17
-16
-15
120
130
140
150
160
Frequency (MHz)
S21 (dB)
30 mm bar
25 mm bar
Fundamental Length Resonances
Fundamental Width Resonances -9 -8 -7 -6
600
700
800
900
Frequency (MHz)

20. Second Round L-Bar 10 mm x 5 mm device showing length and width modes
-40
-50
S21 Magnitude (dB)
-60
-70
-80
110
100 90
Extremely robust (trying to minimize cap, needed to break wafer, at one point shattered wafers and still got resonances from devices)
Phase (degrees) 80 70 60
100
200
300
400
500
600
700
800
900
1000
Frequency (MHz)

21. Fit to Model S21 data from 10mm x 5mm device Parasitics modeled as
port capacitance and
resistance
BVD circuit parameters
R= 35 kW
L= 1 mH
C=0.047 fF
C0=12.7 fF
Q of ~125

22. Metal-Oxide-Silicon Structures
100
200
300
400
500
600
700
800
900
1000
-100
-80
-60
-40
-20
S21 Magnitude (dB)
-200
Phase (degrees)
Frequency (MHz)
Extremely robust (trying to minimize cap, needed to break wafer, at one point shattered wafers and still got resonances from devices)

23. Glass Substrate OP6 fit parameters: pure open to ground
OP6 on Glass
OP6 fit parameters:
pure open to ground
1.43fF thru capacitance
-60
S21 Magnitude (dB)
-80
data
-100
simulation
500
1000
1500
2000
2500
3000
150
100
Phase (degrees)
Extremely robust (trying to minimize cap, needed to break wafer, at one point shattered wafers and still got resonances from devices) 50
500
1000
1500
2000
2500
3000
Frequency (MHz)

24. Glass Substrate OP1 fit parameters: pure open to ground
OP1 on Glass
OP1 fit parameters:
pure open to ground
2.6fF thru capacitance
-60
S21 Magnitude (dB)
-80
data
-100
simulation
500
1000
1500
2000
2500
3000
150
100
Phase (degrees)
Extremely robust (trying to minimize cap, needed to break wafer, at one point shattered wafers and still got resonances from devices) 50
500
1000
1500
2000
2500
3000
Frequency (MHz)

25. Conclusions
Filter designs will be implemented on upcoming mask layout. Mechanically coupled device will be used.
An accurate model of parasitics is vital for obtaining useful device measurements.
Ongoing work to define explanation for the 100 MHz resonance on silicon substrate, and the wideband phase noise

26. Draper Program Manager
Acknowledgements
Draper Engineering
Amy Duwel, David Carter, Doug White
Draper Fellows
Paul Calhoun, Luke Hohreiter
Draper Program Manager
James Sitomer
Acknowledgements:
Draper: Connie Cardoso, Mert Prince, Mark April,
Mark Mescher and Mathew Varghese
MIT: Prof. Charles Sodini
DARPA: Contract # DAAH01-01-C-R204

27. S-parameters j k V ¹ = , S - i i j +S
Extremely robust (trying to minimize cap, needed to break wafer, at one point shattered wafers and still got resonances from devices)

28. Z-parameters V1 = Z11I1 + Z12I2 V2 = Z21I1 + Z22I2
Extremely robust (trying to minimize cap, needed to break wafer, at one point shattered wafers and still got resonances from devices)

29. Two-port p model ( ) ( ) Z + = Z + = Z + = Z Z Z Z = Z = Z =c b a 11 Z + = ( ) c b a 22 Z + = c b a 12 Z + =
Extremely robust (trying to minimize cap, needed to break wafer, at one point shattered wafers and still got resonances from devices) Z Z Z Z = Z = Z =
Z = Z11Z22-Z122 a Z - Z b Z c Z - Z 22 12 12 11 12

30. Transformed Zb Impedance Data
1.5 2
2.5 3 10 1
Zb Magnitude and Phase
Impedance Magnitude (W) -2 -1
Impedance Phase (radians)
Frequency (GHz)
fs fp
|Zs|
|Zp| 1 w = 2 π f = s s LC C w = 2 π f = w 1 + p p s C R Z = R s 1 + j w RC s
Extremely robust (trying to minimize cap, needed to break wafer, at one point shattered wafers and still got resonances from devices) 1 - j w RC 1 Z = p p w 2 RC 2 w 2 RC 2 p p

31. BVD Model Fitting R = 2.76 W, L = 91.6 nH, C = 0.061 pF, C0 = 1.54 pF10 20 30 40 50 60 Zb
Magnitude and Phase
Impedance Magnitude (dB)
1.5 2
2.5 3 - 1
Impedance Phase (radians)
Frequency (GHz)
data
model
Extremely robust (trying to minimize cap, needed to break wafer, at one point shattered wafers and still got resonances from devices)
R = 2.76 W, L = 91.6 nH, C = pF, C0 = 1.54 pF

32. Filter Design Constraints
Constraints placed on equivalent circuit parameters by
bar geometry:
Q assumed to be a function of the process and static
Two degrees of freedom, l and w/t
Resonant frequency fixes l uniquely
For a given frequency, the other degree of freedom controls the “impedance level”
C/C0 fixed by piezoelectric materials parameters