post-fabrication electrical trimming of silicon bulk ... - Semantic Scholar
POST-FABRICATION ELECTRICAL TRIMMING OF SILICON BULK ACOUSTIC RESONATORS USING JOULE HEATING A.K Samarao and F. Ayazi Georgia Institute of Technology, Atlanta, Georgia, USA
for all possible inaccuracies that stem from the microfabrication processes.
ABSTRACT
This paper presents a new method to electrically trim the resonance frequency of a Silicon Bulk Acoustic Resonator (SiBAR) post fabrication. Width-extensional mode silicon resonators are heated by passing a current through their resonating elements. This causes a mass loading gold pattern to diffuse into the bulk of the resonator. Upon cooling, the gold diffusion increases the stiffness of the resonating structure slightly, which reflects as an upward shift in resonance frequency. Thus, silicon resonators can be permanently trimmed to a desired frequency value by an electrical calibration step. As a proof of concept, an upward frequency shift of 240 kHz is demonstrated for a 4000 mass loaded 100 MHz SiBAR after one hour of Joule heating with 30 mA of DC current.
Mass Loading
SuppoQ SiBAR
\ M.
r.
( Vp+ IV
11 Freq.
|I I
>iX re
Gold diffuses into Silicon
INTRODUCTION
Silicon micromechanical resonators have been gaining importance in recent years owing to their small form factor, ease of integration and high fQ products. High-frequency and high-Q width-extensional mode SiBARs fabricated using the HARPSS process have shown atmospheric Q factors in excess of 10'000 at or above 100 MHz, with moderate motional resistances (Q-1000 Q) [1,2]. The resonance frequency of silicon micromechanical resonators is dependent on the physical dimensions of the resonating structure. This causes the frequency of the micromachined resonator to deviate from a designed target value due to variations in photolithography, etching and film thickness. It can be shown that 2 ptm variations in the thickness of an optimized 100 MHz width-extensional-mode SiBAR can cause 0.50O variation in its center frequency [3], while lithographic variations of ±0.1 ptm in the width of the resonator can cause additional 0.500 frequency variations. Our group had previously reported on the tuning of SiBAR frequency using electrical signals [1, 4]. Electrostatic voltage tuning of high frequency SiBARs is inefficient due to the large stiffness of the device [1] and heat-induced continuous current tuning of the device consumes large power [4]. In addition, these tuning techniques are limited in their tuning range and cannot be used to adjust the resonance frequency in case of large offsets (-1 0 o), which are quite typical in microfabrication. It is also well known that the frequency of mechanical resonators can be shifted downwards by deposition of a mass loading layer such as a metal on the surface of the resonating structure [5]. However, the thickness of the mass loading layer cannot be accurately controlled, and are subjected to the limitations of the metal evaporation systems. Though laser trimming [6] has been shown to shift the resonance frequency of silicon resonators downwards or upwards, the trimming is not precise as it is difficult to control the amount of material deposited or removed by the laser. This calls for an efficient post-fabrication trimming technique which can adjust the resonance frequency precisely to compensate
978-1-4244-2978-3/09/$25.00 ©2009 IEEE
C) 'M
(VCI
d)
Figure 1: Schematic of electrical trimming of SiBAR using Joule heating; (a) Mass-loaded SiBAR; (b) Joule heating by passing a current through the body of the resonator; (c) Diffusion of gold into silicon; (d) Gold diffused SiBAR at room temperature shows an upward shift infrequency.
ELECTRICAL TRIMMING PRINCIPLE
In this work, a thin-film layer of gold is evaporated and patterned on the surface of the SiBAR during the fabrication process of the device. After the resonator is packaged, the SiBAR is heated up by passing a relatively large current through its resonating body during an electrical calibration step, as illustrated in Figure 1. High current densities due to the small cross-section area of the SiBAR create enough Joule heating to enable the diffusion of gold into the bulk of the silicon resonator. The advantage of gold over other metals is that gold diffuses into silicon at a much lower eutectic temperature of the silicon-gold binary system (360C), which is very low compared to the individual melting points of gold (1064°C) and silicon (1414°C). To calculate the temperature of a 100 MHz SiBAR for various durations of Joule heating with a given cross section area (41.5 ptm x 20 ptm) and resistivity (0.01 Qcm), the electro-thermal model based on the conservation of energy [7, 8] was used. As discussed later, a silicon beam of such dimensions can be heated to the eutectic temperature in less than five minutes by using currents of 600 mA or more. However, the maximum value of the current in the case of a SiBAR is limited by the small cross-section area of its two narrow supports (illustrated in Figure l(a)). These supports are designed to be as narrow as possible to reduce acoustic loss and achieve high-Q, which causes increased current densities at the support regions leading to higher temperatures that can melt the supports. For the proof of concept, an optimum
892
Authorized licensed use limited to: Georgia Institute of Technology. Downloaded on May 8, 2009 at 18:29 from IEEE Xplore. Restrictions apply.
current of 30 mA was found to create the required Joule heating for gold diffusion without affecting the performance of the SiBAR under test and within reasonable lengths of time. Figure 2 shows the calculated temperature of the SiBAR for various durations of Joule heating at 30 mA. The glow color due to Joule heating can be seen by placing the SiBAR under an optical microscope, as shown in Figure 3. It can be seen that the glow is maximum at the support regions indicating that they heat up the most as expected. The supports can be made wider to pass higher current to reduce the duration of Joule heating, but at the cost of reducing the Q factor. 1000
X
a
m a-)
.E V
800
Figure 3: Optical images of Joule heating of the SiBAR at 30 mA after (a) 1 hour (b) 2 hours (c) 3 hours (d) 4 hours.
-
700-
-
The trenches are refilled with doped LPCVD polysilicon and are etched back to the surface. The oxide on the surface is patterned (Figure 4(b)) to define the shape of the polarization voltage (Vp) pads. Input/Output pads are patterned through a second doped LPCVD polysilicon layer (Figure 4(c)), and the remaining silicon is etched
600 1-
500 400 300 1
1.5
2
2.5
3
3.5
back to the BOX layer of the SOI to isolate input/output and Vp pads. Gold is evaporated and patterned (Figure
4
Duration of Joule heating at 30 mA (in Hours) Figure
for var rous
4(d)) on the SiBAR surface using a lift-off process. Gold deposited on silicon without any adhesive layer as that will hinder the gold diffusion into the SiBAR. Finally, the device is released in hydrofluoric acid. ANSYS predicted a 1 MHz downshift in frequency for a blanket deposition of 150 nm thick gold layer on the entire surface of the SiBAR, referred to in this work as 100% mass loading. Every 10% mass loading results in a 100 kHz downward shift in frequency. The SEM images of the 4000 and 80% mass-loaded SiBARs are shown in Figures 5 and 6. The different pattern densities of gold can be clearly seen.
MHis durations
of Joule heating
at
30 mA.
Ab out one hour of Joule heating heats up the SiBAR to 363° C which will favor the formation of the silicon-
gold etutectic. The thin mass-loading gold layer will diffuse into the bulk of the silicon at this temperature to form a eutectic alloy which has 19% silicon by atomic weight [9]. As gold atoms diffuse into silicon, they initially form a metastable gold-silicide [10, 11], wherein gold gelts into the silicon interstitials, breaking Si-Si bonds and cre ating voids owing to its relatively larger atomic size. IJpon further heating, supersaturation occurs followe d by decomposition of the gold-silicide to a more stable Ipolysilicon with intermediate voids and Au-Si bonds. The Au-Si bonds are stronger than the Si-Si bonds they rer)lace [12]. As a result, the gold diffusion increases the stififness (E) of the resonating silicon structure upon cooling . However, the voids introduced in silicon due to gold di ffusion reduce its density (p). These collectively increase the acoustic velocity of the resonating structure which corresponds to a higher resonance frequency. Thus, the SiBAR can be permanently trimmed to a desired value with mass loading by gold followed by an electrical calibration step. With further Joule heating, the structure stabilizes
more
RESULTS Figure 7 shows the measured frequencies of various mass-loaded SiBARs before and after trimming via Joule heating. All devices were tested in vacuum and a DC current of 3OmA was used for post-fabrication trimming of the resonators. SiBAR
VpPd
Support I
until no metastable structure exists.
iviass
FABRICATION
The fabrication process of the SiBAR is similar to the reported in [1]. Trenches are etched into the device layer of a 20 ptm thick SOI using an oxide mask (Figure 4(a)). These trenches define the dimensions of the SiBAR and its supports. The 100 MHz SiBARs are 41.5 ptm wide and 415 pm long. The supports are 3 ptm wide and 6 ptm long. The capacitive gap of the SiBAR is defined by the thickness of the grown thermal oxide. In this work, a capacitive gap of 100 nm is achieved.
Loaaing
one
SILICON
POLYSILICON
Figure 4: Fabrication SiBAR.
BURIED OXIDE
process
893 Authorized licensed use limited to: Georgia Institute of Technology. Downloaded on May 8, 2009 at 18:29 from IEEE Xplore. Restrictions apply.
THERMAL OXIDE
GOLD
flow of mass-loaded
Joule heating when the eutectic temperature is reached. Subsequent heating leads to a more stable resonating structure which will correspond to smaller frequency shifts. Hence, four hours of Joule heating shifts up the 40% and 80% mass loaded SiBAR by only 430 kHz and 35 kHz respectively. A shift of 430 kHz over four hours corresponds to a trimming rate of approximately 2 kHz per minute, which makes very precise and controlled electrical trimming possible. The 40% mass loaded SiBAR is designed to give a resonance frequency of 99.6 MHz (i.e., a downshift of 400 kHz from 100 MHz). But it can be seen that variations in the SiBAR fabrication and also in the thickness of the deposited gold offsets the resonance frequency to 99.46 MHz. The electrical trimming time needed to shift up this frequency to the designed 99.6 MHz can be calculated to be 35 minutes from Figure 7. Thus, all variations of the SiBAR fabrication can be compensated successfully. From Figure 7, it can also be seen that the 40% mass loaded SiBAR exceeds the resonance frequency of unloaded SiBAR with longer hours of Joule heating. This suggests the formation of a structure with stronger Au-Si bonds and less dense packing with voids, to provide a higher acoustic velocity than crystalline silicon. After electrical trimming, these devices were taken through temperature cycling by heating them in an oven to 85°C for 6 hours and back to room temperature. No frequency hysteresis was observed, confirming the temperature stability of the trimmed resonator. Although the mass loading reduces the Q of a SiBAR from its unloaded pure-silicon value, Figure 8 shows that the Q increases slightly with longer hours of Joule heating.
Figure 5: A SEM image of a 40% mass-loaded SiBAR.
Figure 6: A SEM image of a 80% mass-loaded SiBAR. In Figure 7, the curve labeled as 'Pre-Joule-Heating', shows the downward shift in frequency due to the massloading with various pattern densities of 150 nm thick gold. The 100% mass-loading offers a downward shift of 996.2 kHz in resonance frequency which is in very good agreement with ANSYS simulations. At a polarization voltage of 15 V, the unloaded SiBAR has a Q of 48'000. The mass loading lowers the Q to 23'000 in 40% and to 18'000 in 100% mass-loaded devices. One hour of Joule heating at 30 mA shifts up the 40% mass loaded SiBAR with smaller islands of gold by 240 kHz and 80% mass loaded SiBAR with larger islands of gold by 17 kHz. This suggests that the localized heating of the SiBAR diffuses smaller islands of gold more readily than larger islands thereby showing larger frequency shifts than the later.
26U 200
U 1 00% Mass Loaded SiBAR
it! a-,
a
23000
A
22000 21000 A
Heating 19000
99.8
----- Heating at 30 mA for 1 hour before cooling to 25C
0
18000
before cooling to 25C
e
a)
99.2
IL 0 a)
99
c
98.8
a)
98.86
1L 0.5
1
1.5
2
2.5
3
3.5
4
Duration of heating the SiBAR at 30 mA (in hours)
-x- Heating at 30 mA for 3 hours
m994
-
0
Heating at 30 mA for 2 hours before cooling to 25C
99.6
°
660% Mass Loaded SiBAR
A80% Mass Loaded SiBAR
20000 -*- Pre-Joule
C
L
24000 0
100 I E
*
4*0% Mass Loaded SiBAR
Figure 8: Measured increase in the Q of the mass loaded SiBAR for increasing duration ofJoule heating.
Heating at3O mAfor4 hours before cooling to 25C
DISCUSSIONS
0
20
40
60
80
Incremental percentage of mass loaded area
100
12,0
Figure 7: Measured post-fabrication electrictal trimming of the SiBAR using Joule heating. It can also be seen that, for a given mass-loacled SiBAR, the percentage increase in resonance frequenc decreases with increasing durations of Joule heating. A .s explained ret llUUIl hwln r rf81 earlier, the diffusion mainly occurs at the fi13L
~y
In applications where the silicon resonators are designed with wider supports, the Joule heating can be performed with a higher current, and thereby reducing the frequency trimming time. If the silicon resonator is assumed to have to have a uniform cross section area (41.5 ptm x 20 ptm) and resistivity (0.01 Q-cm) as presented in this work, but without any narrow support regions, then the duration of Joule heating for such a
silicon resonator at various high currents and the of the silicon beam [7, 8] is shown in Figure 9.
corresponding temperature
894 Authorized licensed use limited to: Georgia Institute of Technology. Downloaded on May 8, 2009 at 18:29 from IEEE Xplore. Restrictions apply.
1400 a) *¢
1200
-
150 mA
-
250 mA
-
350 mA
ACKNOWLEDGEMENTS
Authors would like to thank the staff at the Georgia Tech Microelectronics Research Center (MiRC) for their assistance. This work was supported by DARPA under the Analog Spectral Processors (ASP) Program.
I-*
U) a) 1000
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800
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600
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CU
REFERENCES
E 400
[1] S. Pourkamali, G. K. Ho and F. Ayazi, "LowImpedance VHF and UHF Capacitive Silicon Bulk Acoustic Wave Resonators Part I: Concept and Fabrication", IEEE Trans. Electron Devices, pp. 2017-2023, 2007. [2] H. M. Lavasani, A. K. Samarao, G. Casinovi and F. Ayazi, "A 145 MHz Low Phase-Noise Capacitive Silicon Micromechanical Oscillator", IEEE Intl. Electron Devices Meeting 2008. [3] G. Casinovi, X. Gao and F. Ayazi, "Analytical Modeling and Numerical Simulation of Capacitive Silicon Bulk Acoustic Resonators", IEEE Intl. Conf on Microelectromech. Syst. 2009. [4] K. Sundaresan, G. K. Ho, S. Pourkamali and F. Ayazi, "Electronically Temperature Compensated Silicon Bulk Acoustic Resonator Reference Oscillators", J. Solid State Circuits, pp. 1425-1434, 2007. [5] C. G. Courcimault and M. G. Allen, "High-Q Mechanical Tuning of MEMS Resonators using a Metal Deposition - Annealing technique", Transducers 2005, pp. 875-878. [6] W- T. Hsu, A. R. Brown, "Frequency Trimming of MEMS Resonator Oscillators", IEEE Intl. Freq. Control Sym. 2007, pp 1088-1091 [7] L. Lin, "Selective encapsulations of MEMS: Micro channels, needles, resonators, and electromechanical filters", Ph.D. dissertation, Dept. Mech. Eng., Univ. California at Berkeley, Berkeley, CA, 1993. [8] Y. T. Cheng, L. Lin and K. Najafi, "Localized Silicon Fusion and Eutectic Bonding for MEMS Fabrication and Packaging", J. Microelectromech. Syst., vol. 9, pp. 3-8, 2000. [9] H. Okamoto and T. B. Massalski: Binary Phase Diagrams (1986), pp. 312. [10]B. Bokhonov and M. Korchagin, "In Situ Investigation of Stage of the Formation of Eutectic Alloys in Si-Au and Si-Al Systems", J. Alloys and Compounds, vol. 312, pp. 238-250, 2000. [11] S. Takeda, H. Fujii, Y. Kawakita, S. Tahara, S. Nakashima, S. Kohara and M. Itou, "Structure of eutectic alloys of Au with Si and Ge", J. Alloys and Compounds, vol. 452, pp. 149-153, 2008. [12]L. Lin, Y. T. Cheng and K. Najafi, "Formation of Silicon-Gold Eutectic Bond Using Localized Heating Method", Japanese J. Applied Physics, vol. 37, pp. 1412-1414, 1998.
0
C20 X 200
0
0
5 10 15 20 25 Duration of Joule heating (in minutes)
30
Figure 9: Calculated temperature of a 41.5 um wide and 20 um thick silicon resonator for various duration of Joule heating at different currents. Using such higher currents, the eutectic temperature can be reached within 5 to 15 minutes of Joule heating. It can be seen from Figure 10 that the glow color of such a silicon beam due to Joule heating at 600 mA can be seen within one minute. The beam glows bright red after 5 minutes of heating, after which it melts. These suggest the
possibility of performing electrical trimming of silicon micromechanical resonators within few minutes for resonators with wider support elements.
Figure 10: Optical images of Joule heating of a 41.5 um wide and 20 um thick silicon beam for various durations of Joule heating at 600 mA.
CONCLUSION
Post-fabrication electrical trimming of SiBARs has been demonstrated. The SiBARs were mass loaded with different pattern densities of gold to achieve different downward shift in the resonance frequency. Using Joule heating, the gold patterns were diffused into the resonating silicon structure, which upon cooling exhibits an increased stiffness. This reflects as an upward shift in the resonance frequency. An upward shift of up to 240 kHz at 99.45 MHz has been demonstrated with one hour of Joule heating at 30 mA. This electrical trimming technique offers the possibility to compensate for all the variations in the microfabrication processes without compromising on the performance of the resonator. The possibilities of reducing the electrical trimming durations down to few minutes have also been discussed.
895 Authorized licensed use limited to: Georgia Institute of Technology. Downloaded on May 8, 2009 at 18:29 from IEEE Xplore. Restrictions apply.
for all possible inaccuracies that stem from the microfabrication processes.
ABSTRACT
This paper presents a new method to electrically trim the resonance frequency of a Silicon Bulk Acoustic Resonator (SiBAR) post fabrication. Width-extensional mode silicon resonators are heated by passing a current through their resonating elements. This causes a mass loading gold pattern to diffuse into the bulk of the resonator. Upon cooling, the gold diffusion increases the stiffness of the resonating structure slightly, which reflects as an upward shift in resonance frequency. Thus, silicon resonators can be permanently trimmed to a desired frequency value by an electrical calibration step. As a proof of concept, an upward frequency shift of 240 kHz is demonstrated for a 4000 mass loaded 100 MHz SiBAR after one hour of Joule heating with 30 mA of DC current.
Mass Loading
SuppoQ SiBAR
\ M.
r.
( Vp+ IV
11 Freq.
|I I
>iX re
Gold diffuses into Silicon
INTRODUCTION
Silicon micromechanical resonators have been gaining importance in recent years owing to their small form factor, ease of integration and high fQ products. High-frequency and high-Q width-extensional mode SiBARs fabricated using the HARPSS process have shown atmospheric Q factors in excess of 10'000 at or above 100 MHz, with moderate motional resistances (Q-1000 Q) [1,2]. The resonance frequency of silicon micromechanical resonators is dependent on the physical dimensions of the resonating structure. This causes the frequency of the micromachined resonator to deviate from a designed target value due to variations in photolithography, etching and film thickness. It can be shown that 2 ptm variations in the thickness of an optimized 100 MHz width-extensional-mode SiBAR can cause 0.50O variation in its center frequency [3], while lithographic variations of ±0.1 ptm in the width of the resonator can cause additional 0.500 frequency variations. Our group had previously reported on the tuning of SiBAR frequency using electrical signals [1, 4]. Electrostatic voltage tuning of high frequency SiBARs is inefficient due to the large stiffness of the device [1] and heat-induced continuous current tuning of the device consumes large power [4]. In addition, these tuning techniques are limited in their tuning range and cannot be used to adjust the resonance frequency in case of large offsets (-1 0 o), which are quite typical in microfabrication. It is also well known that the frequency of mechanical resonators can be shifted downwards by deposition of a mass loading layer such as a metal on the surface of the resonating structure [5]. However, the thickness of the mass loading layer cannot be accurately controlled, and are subjected to the limitations of the metal evaporation systems. Though laser trimming [6] has been shown to shift the resonance frequency of silicon resonators downwards or upwards, the trimming is not precise as it is difficult to control the amount of material deposited or removed by the laser. This calls for an efficient post-fabrication trimming technique which can adjust the resonance frequency precisely to compensate
978-1-4244-2978-3/09/$25.00 ©2009 IEEE
C) 'M
(VCI
d)
Figure 1: Schematic of electrical trimming of SiBAR using Joule heating; (a) Mass-loaded SiBAR; (b) Joule heating by passing a current through the body of the resonator; (c) Diffusion of gold into silicon; (d) Gold diffused SiBAR at room temperature shows an upward shift infrequency.
ELECTRICAL TRIMMING PRINCIPLE
In this work, a thin-film layer of gold is evaporated and patterned on the surface of the SiBAR during the fabrication process of the device. After the resonator is packaged, the SiBAR is heated up by passing a relatively large current through its resonating body during an electrical calibration step, as illustrated in Figure 1. High current densities due to the small cross-section area of the SiBAR create enough Joule heating to enable the diffusion of gold into the bulk of the silicon resonator. The advantage of gold over other metals is that gold diffuses into silicon at a much lower eutectic temperature of the silicon-gold binary system (360C), which is very low compared to the individual melting points of gold (1064°C) and silicon (1414°C). To calculate the temperature of a 100 MHz SiBAR for various durations of Joule heating with a given cross section area (41.5 ptm x 20 ptm) and resistivity (0.01 Qcm), the electro-thermal model based on the conservation of energy [7, 8] was used. As discussed later, a silicon beam of such dimensions can be heated to the eutectic temperature in less than five minutes by using currents of 600 mA or more. However, the maximum value of the current in the case of a SiBAR is limited by the small cross-section area of its two narrow supports (illustrated in Figure l(a)). These supports are designed to be as narrow as possible to reduce acoustic loss and achieve high-Q, which causes increased current densities at the support regions leading to higher temperatures that can melt the supports. For the proof of concept, an optimum
892
Authorized licensed use limited to: Georgia Institute of Technology. Downloaded on May 8, 2009 at 18:29 from IEEE Xplore. Restrictions apply.
current of 30 mA was found to create the required Joule heating for gold diffusion without affecting the performance of the SiBAR under test and within reasonable lengths of time. Figure 2 shows the calculated temperature of the SiBAR for various durations of Joule heating at 30 mA. The glow color due to Joule heating can be seen by placing the SiBAR under an optical microscope, as shown in Figure 3. It can be seen that the glow is maximum at the support regions indicating that they heat up the most as expected. The supports can be made wider to pass higher current to reduce the duration of Joule heating, but at the cost of reducing the Q factor. 1000
X
a
m a-)
.E V
800
Figure 3: Optical images of Joule heating of the SiBAR at 30 mA after (a) 1 hour (b) 2 hours (c) 3 hours (d) 4 hours.
-
700-
-
The trenches are refilled with doped LPCVD polysilicon and are etched back to the surface. The oxide on the surface is patterned (Figure 4(b)) to define the shape of the polarization voltage (Vp) pads. Input/Output pads are patterned through a second doped LPCVD polysilicon layer (Figure 4(c)), and the remaining silicon is etched
600 1-
500 400 300 1
1.5
2
2.5
3
3.5
back to the BOX layer of the SOI to isolate input/output and Vp pads. Gold is evaporated and patterned (Figure
4
Duration of Joule heating at 30 mA (in Hours) Figure
for var rous
4(d)) on the SiBAR surface using a lift-off process. Gold deposited on silicon without any adhesive layer as that will hinder the gold diffusion into the SiBAR. Finally, the device is released in hydrofluoric acid. ANSYS predicted a 1 MHz downshift in frequency for a blanket deposition of 150 nm thick gold layer on the entire surface of the SiBAR, referred to in this work as 100% mass loading. Every 10% mass loading results in a 100 kHz downward shift in frequency. The SEM images of the 4000 and 80% mass-loaded SiBARs are shown in Figures 5 and 6. The different pattern densities of gold can be clearly seen.
MHis durations
of Joule heating
at
30 mA.
Ab out one hour of Joule heating heats up the SiBAR to 363° C which will favor the formation of the silicon-
gold etutectic. The thin mass-loading gold layer will diffuse into the bulk of the silicon at this temperature to form a eutectic alloy which has 19% silicon by atomic weight [9]. As gold atoms diffuse into silicon, they initially form a metastable gold-silicide [10, 11], wherein gold gelts into the silicon interstitials, breaking Si-Si bonds and cre ating voids owing to its relatively larger atomic size. IJpon further heating, supersaturation occurs followe d by decomposition of the gold-silicide to a more stable Ipolysilicon with intermediate voids and Au-Si bonds. The Au-Si bonds are stronger than the Si-Si bonds they rer)lace [12]. As a result, the gold diffusion increases the stififness (E) of the resonating silicon structure upon cooling . However, the voids introduced in silicon due to gold di ffusion reduce its density (p). These collectively increase the acoustic velocity of the resonating structure which corresponds to a higher resonance frequency. Thus, the SiBAR can be permanently trimmed to a desired value with mass loading by gold followed by an electrical calibration step. With further Joule heating, the structure stabilizes
more
RESULTS Figure 7 shows the measured frequencies of various mass-loaded SiBARs before and after trimming via Joule heating. All devices were tested in vacuum and a DC current of 3OmA was used for post-fabrication trimming of the resonators. SiBAR
VpPd
Support I
until no metastable structure exists.
iviass
FABRICATION
The fabrication process of the SiBAR is similar to the reported in [1]. Trenches are etched into the device layer of a 20 ptm thick SOI using an oxide mask (Figure 4(a)). These trenches define the dimensions of the SiBAR and its supports. The 100 MHz SiBARs are 41.5 ptm wide and 415 pm long. The supports are 3 ptm wide and 6 ptm long. The capacitive gap of the SiBAR is defined by the thickness of the grown thermal oxide. In this work, a capacitive gap of 100 nm is achieved.
Loaaing
one
SILICON
POLYSILICON
Figure 4: Fabrication SiBAR.
BURIED OXIDE
process
893 Authorized licensed use limited to: Georgia Institute of Technology. Downloaded on May 8, 2009 at 18:29 from IEEE Xplore. Restrictions apply.
THERMAL OXIDE
GOLD
flow of mass-loaded
Joule heating when the eutectic temperature is reached. Subsequent heating leads to a more stable resonating structure which will correspond to smaller frequency shifts. Hence, four hours of Joule heating shifts up the 40% and 80% mass loaded SiBAR by only 430 kHz and 35 kHz respectively. A shift of 430 kHz over four hours corresponds to a trimming rate of approximately 2 kHz per minute, which makes very precise and controlled electrical trimming possible. The 40% mass loaded SiBAR is designed to give a resonance frequency of 99.6 MHz (i.e., a downshift of 400 kHz from 100 MHz). But it can be seen that variations in the SiBAR fabrication and also in the thickness of the deposited gold offsets the resonance frequency to 99.46 MHz. The electrical trimming time needed to shift up this frequency to the designed 99.6 MHz can be calculated to be 35 minutes from Figure 7. Thus, all variations of the SiBAR fabrication can be compensated successfully. From Figure 7, it can also be seen that the 40% mass loaded SiBAR exceeds the resonance frequency of unloaded SiBAR with longer hours of Joule heating. This suggests the formation of a structure with stronger Au-Si bonds and less dense packing with voids, to provide a higher acoustic velocity than crystalline silicon. After electrical trimming, these devices were taken through temperature cycling by heating them in an oven to 85°C for 6 hours and back to room temperature. No frequency hysteresis was observed, confirming the temperature stability of the trimmed resonator. Although the mass loading reduces the Q of a SiBAR from its unloaded pure-silicon value, Figure 8 shows that the Q increases slightly with longer hours of Joule heating.
Figure 5: A SEM image of a 40% mass-loaded SiBAR.
Figure 6: A SEM image of a 80% mass-loaded SiBAR. In Figure 7, the curve labeled as 'Pre-Joule-Heating', shows the downward shift in frequency due to the massloading with various pattern densities of 150 nm thick gold. The 100% mass-loading offers a downward shift of 996.2 kHz in resonance frequency which is in very good agreement with ANSYS simulations. At a polarization voltage of 15 V, the unloaded SiBAR has a Q of 48'000. The mass loading lowers the Q to 23'000 in 40% and to 18'000 in 100% mass-loaded devices. One hour of Joule heating at 30 mA shifts up the 40% mass loaded SiBAR with smaller islands of gold by 240 kHz and 80% mass loaded SiBAR with larger islands of gold by 17 kHz. This suggests that the localized heating of the SiBAR diffuses smaller islands of gold more readily than larger islands thereby showing larger frequency shifts than the later.
26U 200
U 1 00% Mass Loaded SiBAR
it! a-,
a
23000
A
22000 21000 A
Heating 19000
99.8
----- Heating at 30 mA for 1 hour before cooling to 25C
0
18000
before cooling to 25C
e
a)
99.2
IL 0 a)
99
c
98.8
a)
98.86
1L 0.5
1
1.5
2
2.5
3
3.5
4
Duration of heating the SiBAR at 30 mA (in hours)
-x- Heating at 30 mA for 3 hours
m994
-
0
Heating at 30 mA for 2 hours before cooling to 25C
99.6
°
660% Mass Loaded SiBAR
A80% Mass Loaded SiBAR
20000 -*- Pre-Joule
C
L
24000 0
100 I E
*
4*0% Mass Loaded SiBAR
Figure 8: Measured increase in the Q of the mass loaded SiBAR for increasing duration ofJoule heating.
Heating at3O mAfor4 hours before cooling to 25C
DISCUSSIONS
0
20
40
60
80
Incremental percentage of mass loaded area
100
12,0
Figure 7: Measured post-fabrication electrictal trimming of the SiBAR using Joule heating. It can also be seen that, for a given mass-loacled SiBAR, the percentage increase in resonance frequenc decreases with increasing durations of Joule heating. A .s explained ret llUUIl hwln r rf81 earlier, the diffusion mainly occurs at the fi13L
~y
In applications where the silicon resonators are designed with wider supports, the Joule heating can be performed with a higher current, and thereby reducing the frequency trimming time. If the silicon resonator is assumed to have to have a uniform cross section area (41.5 ptm x 20 ptm) and resistivity (0.01 Q-cm) as presented in this work, but without any narrow support regions, then the duration of Joule heating for such a
silicon resonator at various high currents and the of the silicon beam [7, 8] is shown in Figure 9.
corresponding temperature
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1400 a) *¢
1200
-
150 mA
-
250 mA
-
350 mA
ACKNOWLEDGEMENTS
Authors would like to thank the staff at the Georgia Tech Microelectronics Research Center (MiRC) for their assistance. This work was supported by DARPA under the Analog Spectral Processors (ASP) Program.
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600
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REFERENCES
E 400
[1] S. Pourkamali, G. K. Ho and F. Ayazi, "LowImpedance VHF and UHF Capacitive Silicon Bulk Acoustic Wave Resonators Part I: Concept and Fabrication", IEEE Trans. Electron Devices, pp. 2017-2023, 2007. [2] H. M. Lavasani, A. K. Samarao, G. Casinovi and F. Ayazi, "A 145 MHz Low Phase-Noise Capacitive Silicon Micromechanical Oscillator", IEEE Intl. Electron Devices Meeting 2008. [3] G. Casinovi, X. Gao and F. Ayazi, "Analytical Modeling and Numerical Simulation of Capacitive Silicon Bulk Acoustic Resonators", IEEE Intl. Conf on Microelectromech. Syst. 2009. [4] K. Sundaresan, G. K. Ho, S. Pourkamali and F. Ayazi, "Electronically Temperature Compensated Silicon Bulk Acoustic Resonator Reference Oscillators", J. Solid State Circuits, pp. 1425-1434, 2007. [5] C. G. Courcimault and M. G. Allen, "High-Q Mechanical Tuning of MEMS Resonators using a Metal Deposition - Annealing technique", Transducers 2005, pp. 875-878. [6] W- T. Hsu, A. R. Brown, "Frequency Trimming of MEMS Resonator Oscillators", IEEE Intl. Freq. Control Sym. 2007, pp 1088-1091 [7] L. Lin, "Selective encapsulations of MEMS: Micro channels, needles, resonators, and electromechanical filters", Ph.D. dissertation, Dept. Mech. Eng., Univ. California at Berkeley, Berkeley, CA, 1993. [8] Y. T. Cheng, L. Lin and K. Najafi, "Localized Silicon Fusion and Eutectic Bonding for MEMS Fabrication and Packaging", J. Microelectromech. Syst., vol. 9, pp. 3-8, 2000. [9] H. Okamoto and T. B. Massalski: Binary Phase Diagrams (1986), pp. 312. [10]B. Bokhonov and M. Korchagin, "In Situ Investigation of Stage of the Formation of Eutectic Alloys in Si-Au and Si-Al Systems", J. Alloys and Compounds, vol. 312, pp. 238-250, 2000. [11] S. Takeda, H. Fujii, Y. Kawakita, S. Tahara, S. Nakashima, S. Kohara and M. Itou, "Structure of eutectic alloys of Au with Si and Ge", J. Alloys and Compounds, vol. 452, pp. 149-153, 2008. [12]L. Lin, Y. T. Cheng and K. Najafi, "Formation of Silicon-Gold Eutectic Bond Using Localized Heating Method", Japanese J. Applied Physics, vol. 37, pp. 1412-1414, 1998.
0
C20 X 200
0
0
5 10 15 20 25 Duration of Joule heating (in minutes)
30
Figure 9: Calculated temperature of a 41.5 um wide and 20 um thick silicon resonator for various duration of Joule heating at different currents. Using such higher currents, the eutectic temperature can be reached within 5 to 15 minutes of Joule heating. It can be seen from Figure 10 that the glow color of such a silicon beam due to Joule heating at 600 mA can be seen within one minute. The beam glows bright red after 5 minutes of heating, after which it melts. These suggest the
possibility of performing electrical trimming of silicon micromechanical resonators within few minutes for resonators with wider support elements.
Figure 10: Optical images of Joule heating of a 41.5 um wide and 20 um thick silicon beam for various durations of Joule heating at 600 mA.
CONCLUSION
Post-fabrication electrical trimming of SiBARs has been demonstrated. The SiBARs were mass loaded with different pattern densities of gold to achieve different downward shift in the resonance frequency. Using Joule heating, the gold patterns were diffused into the resonating silicon structure, which upon cooling exhibits an increased stiffness. This reflects as an upward shift in the resonance frequency. An upward shift of up to 240 kHz at 99.45 MHz has been demonstrated with one hour of Joule heating at 30 mA. This electrical trimming technique offers the possibility to compensate for all the variations in the microfabrication processes without compromising on the performance of the resonator. The possibilities of reducing the electrical trimming durations down to few minutes have also been discussed.
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