HIGH-FREQUENCY CAPACITIVE DISK ... - Semantic Scholar
HIGH-FREQUENCY CAPACITIVE DISK GYROSCOPES IN (100) AND (111) SILICON Houri Johari and Farrokh Ayazi School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta, GA 30332-0250 {houri,ayazi}@ece.gatech.edu; Tel: (404) 894-9496; Fax: (404) 385-6650
ABSTRACT This paper reports on the design and implementation of capacitive bulk acoustic wave (BAW) disk gyroscopes in single crystal silicon. The capacitive BAW disk gyroscopes are stationary devices operating in their degenerative MHzfrequency bulk acoustic modes with very small vibration amplitudes (100Hz) under very high-Q mode-matched condition. Since the BAW gyros are stationary devices with very large stiffness, they exhibit superior shock resistance.
2. BAW DISK GYOSCOPE DESIGN As schematically shown in Fig. 1, the coriolis-based BAW gyroscope consists of a center-supported disk structure with capacitively-coupled drive, sense and control electrodes. The capacitive BAW disk gyros are implemented in single crystal silicon (SCS) and designed to operate in either the primary or secondary degenerative elliptic bulk acoustic modes. z-axis
(1)
30°
where qdrive is the drive amplitude; ω0, M, and Qeffect-sense are the natural frequency, mass and effective quality factor at the sense mode, respectively; kB is the Boltzmann constant and T is the absolute temperature. It is desirable to reduce the noise floor of vibrating gyros without having to increase the mass and drive amplitude, which is difficult to achieve in low power and small size. This work is aimed at improving the noise floor in resonating gyros by: 1) increasing the resonant frequency by 2 to 3 orders of magnitude (to 2-8MHz), and 2) substantially increasing the Q by utilizing bulk acoustic modes that experience significantly less TED compared to flexural modes. The very high Q of the bulk acoustic modes will translate into superior bias stability in these gyros. In addition, the large stiffness of the device makes it less
1-4244-0951-9/07/$25.00 ©2007 IEEE.
susceptible to air damping, which simplifies the packaging and reduces the manufacturing cost.
47
Tuning electrodes Drive electrode
Sense electrode
Figure 1: Schematic diagram of the capacitive BAW disk Gyroscope in (100) silicon.
Due to the anisotropic nature of (100) SCS, only the secondary elliptical modes of (100) SCS disk that are spatially 30º apart have identical frequencies (Fig. 2a). In a (111) SCS [5] disk gyros, the primary elliptical modes of
MEMS 2007, Kobe, Japan, 21-25 January 2007.
disk (which are offset by 45º instead of 30°) have identical frequencies (Fig. 2b). As a result, electrodes should be placed at every 30º for (100) SCS or 45º for (111) SCS circumferentially around the disk to maximize the sense and drive transduction. In order to release the disk gyroscope from the front side, release holes are added to the disk structure. The release holes are carefully devised and repeated symmetrically every 30º in (100) Si disk (or 45° in (111) Si disk) to minimize any possible frequency split between the two degenerative elliptic modes.
substrate are removed using the Bosch process to define the electrodes. Finally, the device is released in HF. The buried oxide layer of the SOI can be used to support the disk at the bottom, which calls for careful timing of the HF release. The polysilicon trace on the surface is required to provide DC bias to the disk (Fig. 4). Also, each poly electrode partially extends out on the disk structure to provide an outof-plane shock stop for the device. The described process is compatible with Analog Device’s SOIMEMS process [4, 6] and can be integrated with CMOS electronics by adding some pre- and post-CMOS fabrication steps.
(a) Grow and pattern the initial oxide and etch the trenches
(b) Deposit SACOX, and LPCVD poly, pattern SACOX
(c) Deposit LPCVD poly, boron doped and anneal
(d) Pattern poly, etch poly and Si substrate, release in HF
(a)
Figure 3: The process flow of center-supported disk gyro on SOI wafer.
(b)
Figure 2: ANSYS simulation of: (a) 800µm diameter (100) Si disk gyroscopes (two second order modes) both at 6MHz but 30º apart spatially; (b) 1200µm diameter (111) Si disk gyroscope (two primary modes) both at 2.90MHz but 45º apart spatially.
One of the critical parameters in designing a coriolis gyroscope is the angular gain. The angular gain (Ag) is defined as the ratio of the change in the vibration pattern angle to the applied angle of rotation. The angular gain depends on the sensor structure as well as the type of resonant modes in operation. The angular gain of a solid disk structure is derived to be 1.8× larger for primary elliptic modes than for the secondary elliptic modes. Since the sensitivity is linearly proportional to the angular gain, BAW disk gyros in (111) Si have higher sensitivity compared to the identical devices in (100) Si. Nevertheless, (100) silicon substrates have advantages in terms of CMOS compatibility and supply availability compared to (111) silicon substrates.
4. EXPERIMENTAL RESULTS A number of (100) Si and (111) Si disk gyroscopes were tested. A sinusoidal drive signal was applied to the drive electrode and the output signal was monitored at the sense electrode. The sense electrode is located 30° apart from the drive electrode in (100) silicon disk gyros and 45° apart in (111) silicon disk gyros. Measurement Results of (100) Silicon Disk Gyroscope Figure 4 shows SEM picture of an 800µm diameter (100) disk gyroscope (50µm thick).
3. FABRICATION The prototype gyroscopes were fabricated in thick SOI wafers (30-50µm thick) using the HARPSS process. A brief process flow is shown in Fig. 3. The process starts with patterning a 2µm thick oxide mask on the substrate. Deep trenches are etched through the device layer of the SOI to define the resonating SCS structures. A thin layer of sacrificial LPCVD oxide is deposited to form the capacitive gaps, and subsequently trenches are filled with LPCVD polysilicon. Next, the sacrificial oxide was patterned on the surface and the LPCVD polysilicon layer is deposited. After patterning the polysilicon on the surface to define the pads, polysilicon inside the trenches as well as parts of the silicon
48
Figure 4: SEM view of 800µm diameter (100) Si disk gyro with 250nm capacitive gap for 50µm thick disk.
The high-order elliptical modes of the 800µm diameter (100) disk gyroscope were observed at 5.9MHz with a frequency split of 300Hz. Figure 5 shows the measured Q
8 6 4
Vout (m V)
of 125,000 and 100,000 for the high order elliptical modes of this device in 1 mTorr vacuum. The corresponding Q values in 10Torr vacuum were still very high for this device (100,000 and 74,000).
-150
49dB
2 0 -100
-50
-2 -4
∆f=290Hz
0
50
100
150
Sensitivity of (100) SCS disk gyro: 70 µV/°/sec
-6 -8
Input Rotation rate (deg/sec)
Figure 7: The measured sensitivity results from 800µm diameter (100) SCS disk gyroscope with discrete electronics.
Measurement Results of (111) Silicon Disk Gyroscope Drive mode Freq = 5.8825 MHz Q= 100,000
Sense mode Freq = 5.8825 MHz Q= 125,000
(In 1 milli-Torr vacuum)
(In 1 milli-Torr vacuum)
Figure 8 shows SEM view of a 1200µm diameter (111) disk gyroscope (35µm thick).
Figure 5: The frequency response of high order elliptical modes of 800µm diameter (100) SCS disk gyroscope at 5.9MHz in 1mTorr vacuum with Vp=3V (∆f=300Hz).
The small initial frequency separation of 290 Hz between the drive and sense modes of this device can be matched by the application of proper tuning voltages to the tuning electrodes around the disk gyroscope. The matched-mode quality factor of the device was recorded to be 12,000, as shown in Fig. 6. Mode-matching was achieved by applying a tuning DC voltage of 10V. A large bandwidth of ~490Hz was measured for the BAW disk gyroscope at frequency of 5.88MHz, which is 100× larger than low frequency gyroscopes operating in mode-matched condition [1-3].
Figure 8: SEM view of 1200µm diameter (111) Si disk gyro with 180nm capacitive gap for 35µm thick disk.
The primary elliptic modes of this device were observed less than 100Hz apart without applying any tuning voltage. The Qeffective-sense of (111) disk gyroscopes was 66,000 and 58,000, in 1mTorr and 1Torr vacuum, respectively (Fig. 9).
Freq=2.9 MHz Qsense-effective= 66,000 BW=45Hz In 1 milli-Torr vacuum Freq = 5.8831 MHz Qmatch-mode= 12,000, BW ~ 490Hz In 1mTorr vacuum
(a)
Figure 6: The matched-mode frequency response of high order elliptical modes of 800µm diameter SCS disk gyroscope at Vp=10V, and BW of 494Hz (In 1mTorr vacuum).
The sensor output voltage was measured at different angular speeds. As shown in Fig. 7, the measured rate sensitivity of 800µm diameter (100) SCS disk gyroscope is 70µV/°/sec, which is 6× higher than that of the low frequency polysilicon star gyroscope reported in [3].
49
Freq=2.9 MHz Qsense-effective= 58,000 In 1 Torr vacuum (b)
Figure 9: The frequency response of primary elliptical modes of 1200µm diameter (111) SCS disk gyroscope at 2.9MHz: (a) In 1mTorr vacuum with Vp=5V; (b) In 1Torr with Vp=7V.
The rate sensitivity response of 1200µm diameter (111) SCS disk is presented in Fig. 10. The measured rate sensitivity of 1200µm diameter (111) BAW disk gyroscope with discrete electronics is 0.32mV/°/sec, which demonstrates higher rate sensitivity compared to the (100) disk (0.07mV/°/sec). This is expected due to the larger angular gain and smaller frequency separation of the two elliptic modes in the (111) disk.
designs, the minimum detectable rotation rate is limited by the electronic noise which is mainly due to the high operating frequency. This problem can be solved by further increasing the gap aspect-ratio (AR>250) and use of low noise amplifiers (Vn
ABSTRACT This paper reports on the design and implementation of capacitive bulk acoustic wave (BAW) disk gyroscopes in single crystal silicon. The capacitive BAW disk gyroscopes are stationary devices operating in their degenerative MHzfrequency bulk acoustic modes with very small vibration amplitudes (100Hz) under very high-Q mode-matched condition. Since the BAW gyros are stationary devices with very large stiffness, they exhibit superior shock resistance.
2. BAW DISK GYOSCOPE DESIGN As schematically shown in Fig. 1, the coriolis-based BAW gyroscope consists of a center-supported disk structure with capacitively-coupled drive, sense and control electrodes. The capacitive BAW disk gyros are implemented in single crystal silicon (SCS) and designed to operate in either the primary or secondary degenerative elliptic bulk acoustic modes. z-axis
(1)
30°
where qdrive is the drive amplitude; ω0, M, and Qeffect-sense are the natural frequency, mass and effective quality factor at the sense mode, respectively; kB is the Boltzmann constant and T is the absolute temperature. It is desirable to reduce the noise floor of vibrating gyros without having to increase the mass and drive amplitude, which is difficult to achieve in low power and small size. This work is aimed at improving the noise floor in resonating gyros by: 1) increasing the resonant frequency by 2 to 3 orders of magnitude (to 2-8MHz), and 2) substantially increasing the Q by utilizing bulk acoustic modes that experience significantly less TED compared to flexural modes. The very high Q of the bulk acoustic modes will translate into superior bias stability in these gyros. In addition, the large stiffness of the device makes it less
1-4244-0951-9/07/$25.00 ©2007 IEEE.
susceptible to air damping, which simplifies the packaging and reduces the manufacturing cost.
47
Tuning electrodes Drive electrode
Sense electrode
Figure 1: Schematic diagram of the capacitive BAW disk Gyroscope in (100) silicon.
Due to the anisotropic nature of (100) SCS, only the secondary elliptical modes of (100) SCS disk that are spatially 30º apart have identical frequencies (Fig. 2a). In a (111) SCS [5] disk gyros, the primary elliptical modes of
MEMS 2007, Kobe, Japan, 21-25 January 2007.
disk (which are offset by 45º instead of 30°) have identical frequencies (Fig. 2b). As a result, electrodes should be placed at every 30º for (100) SCS or 45º for (111) SCS circumferentially around the disk to maximize the sense and drive transduction. In order to release the disk gyroscope from the front side, release holes are added to the disk structure. The release holes are carefully devised and repeated symmetrically every 30º in (100) Si disk (or 45° in (111) Si disk) to minimize any possible frequency split between the two degenerative elliptic modes.
substrate are removed using the Bosch process to define the electrodes. Finally, the device is released in HF. The buried oxide layer of the SOI can be used to support the disk at the bottom, which calls for careful timing of the HF release. The polysilicon trace on the surface is required to provide DC bias to the disk (Fig. 4). Also, each poly electrode partially extends out on the disk structure to provide an outof-plane shock stop for the device. The described process is compatible with Analog Device’s SOIMEMS process [4, 6] and can be integrated with CMOS electronics by adding some pre- and post-CMOS fabrication steps.
(a) Grow and pattern the initial oxide and etch the trenches
(b) Deposit SACOX, and LPCVD poly, pattern SACOX
(c) Deposit LPCVD poly, boron doped and anneal
(d) Pattern poly, etch poly and Si substrate, release in HF
(a)
Figure 3: The process flow of center-supported disk gyro on SOI wafer.
(b)
Figure 2: ANSYS simulation of: (a) 800µm diameter (100) Si disk gyroscopes (two second order modes) both at 6MHz but 30º apart spatially; (b) 1200µm diameter (111) Si disk gyroscope (two primary modes) both at 2.90MHz but 45º apart spatially.
One of the critical parameters in designing a coriolis gyroscope is the angular gain. The angular gain (Ag) is defined as the ratio of the change in the vibration pattern angle to the applied angle of rotation. The angular gain depends on the sensor structure as well as the type of resonant modes in operation. The angular gain of a solid disk structure is derived to be 1.8× larger for primary elliptic modes than for the secondary elliptic modes. Since the sensitivity is linearly proportional to the angular gain, BAW disk gyros in (111) Si have higher sensitivity compared to the identical devices in (100) Si. Nevertheless, (100) silicon substrates have advantages in terms of CMOS compatibility and supply availability compared to (111) silicon substrates.
4. EXPERIMENTAL RESULTS A number of (100) Si and (111) Si disk gyroscopes were tested. A sinusoidal drive signal was applied to the drive electrode and the output signal was monitored at the sense electrode. The sense electrode is located 30° apart from the drive electrode in (100) silicon disk gyros and 45° apart in (111) silicon disk gyros. Measurement Results of (100) Silicon Disk Gyroscope Figure 4 shows SEM picture of an 800µm diameter (100) disk gyroscope (50µm thick).
3. FABRICATION The prototype gyroscopes were fabricated in thick SOI wafers (30-50µm thick) using the HARPSS process. A brief process flow is shown in Fig. 3. The process starts with patterning a 2µm thick oxide mask on the substrate. Deep trenches are etched through the device layer of the SOI to define the resonating SCS structures. A thin layer of sacrificial LPCVD oxide is deposited to form the capacitive gaps, and subsequently trenches are filled with LPCVD polysilicon. Next, the sacrificial oxide was patterned on the surface and the LPCVD polysilicon layer is deposited. After patterning the polysilicon on the surface to define the pads, polysilicon inside the trenches as well as parts of the silicon
48
Figure 4: SEM view of 800µm diameter (100) Si disk gyro with 250nm capacitive gap for 50µm thick disk.
The high-order elliptical modes of the 800µm diameter (100) disk gyroscope were observed at 5.9MHz with a frequency split of 300Hz. Figure 5 shows the measured Q
8 6 4
Vout (m V)
of 125,000 and 100,000 for the high order elliptical modes of this device in 1 mTorr vacuum. The corresponding Q values in 10Torr vacuum were still very high for this device (100,000 and 74,000).
-150
49dB
2 0 -100
-50
-2 -4
∆f=290Hz
0
50
100
150
Sensitivity of (100) SCS disk gyro: 70 µV/°/sec
-6 -8
Input Rotation rate (deg/sec)
Figure 7: The measured sensitivity results from 800µm diameter (100) SCS disk gyroscope with discrete electronics.
Measurement Results of (111) Silicon Disk Gyroscope Drive mode Freq = 5.8825 MHz Q= 100,000
Sense mode Freq = 5.8825 MHz Q= 125,000
(In 1 milli-Torr vacuum)
(In 1 milli-Torr vacuum)
Figure 8 shows SEM view of a 1200µm diameter (111) disk gyroscope (35µm thick).
Figure 5: The frequency response of high order elliptical modes of 800µm diameter (100) SCS disk gyroscope at 5.9MHz in 1mTorr vacuum with Vp=3V (∆f=300Hz).
The small initial frequency separation of 290 Hz between the drive and sense modes of this device can be matched by the application of proper tuning voltages to the tuning electrodes around the disk gyroscope. The matched-mode quality factor of the device was recorded to be 12,000, as shown in Fig. 6. Mode-matching was achieved by applying a tuning DC voltage of 10V. A large bandwidth of ~490Hz was measured for the BAW disk gyroscope at frequency of 5.88MHz, which is 100× larger than low frequency gyroscopes operating in mode-matched condition [1-3].
Figure 8: SEM view of 1200µm diameter (111) Si disk gyro with 180nm capacitive gap for 35µm thick disk.
The primary elliptic modes of this device were observed less than 100Hz apart without applying any tuning voltage. The Qeffective-sense of (111) disk gyroscopes was 66,000 and 58,000, in 1mTorr and 1Torr vacuum, respectively (Fig. 9).
Freq=2.9 MHz Qsense-effective= 66,000 BW=45Hz In 1 milli-Torr vacuum Freq = 5.8831 MHz Qmatch-mode= 12,000, BW ~ 490Hz In 1mTorr vacuum
(a)
Figure 6: The matched-mode frequency response of high order elliptical modes of 800µm diameter SCS disk gyroscope at Vp=10V, and BW of 494Hz (In 1mTorr vacuum).
The sensor output voltage was measured at different angular speeds. As shown in Fig. 7, the measured rate sensitivity of 800µm diameter (100) SCS disk gyroscope is 70µV/°/sec, which is 6× higher than that of the low frequency polysilicon star gyroscope reported in [3].
49
Freq=2.9 MHz Qsense-effective= 58,000 In 1 Torr vacuum (b)
Figure 9: The frequency response of primary elliptical modes of 1200µm diameter (111) SCS disk gyroscope at 2.9MHz: (a) In 1mTorr vacuum with Vp=5V; (b) In 1Torr with Vp=7V.
The rate sensitivity response of 1200µm diameter (111) SCS disk is presented in Fig. 10. The measured rate sensitivity of 1200µm diameter (111) BAW disk gyroscope with discrete electronics is 0.32mV/°/sec, which demonstrates higher rate sensitivity compared to the (100) disk (0.07mV/°/sec). This is expected due to the larger angular gain and smaller frequency separation of the two elliptic modes in the (111) disk.
designs, the minimum detectable rotation rate is limited by the electronic noise which is mainly due to the high operating frequency. This problem can be solved by further increasing the gap aspect-ratio (AR>250) and use of low noise amplifiers (Vn
