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A z-axis differential capacitive SOI accelerometer with vertical comb electrodes
Sensors and Actuators A 116 (2004) 378–383
A z-axis differential capacitive SOI accelerometer with vertical comb electrodes Toshiyuki Tsuchiya∗ , Hirofumi Funabashi Department of Mechanical Engineering, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan Received 20 February 2004; received in revised form 2 April 2004; accepted 6 May 2004 Available online 8 July 2004
Abstract This paper describes a differentially detecting capacitive z-axis SOI accelerometer using a set of vertical comb electrodes. The device structure has only one silicon layer and there are no lower or upper electrodes. z-axis acceleration was differentially detected by using a set of newly proposed vertical comb electrodes of different movable and fixed heights. The sensing area was 1.1 mm × 1.1 mm × 15 m. The performance of the accelerometer was calculated and measured experimentally to determine its linear capacitance change and voltage output against input acceleration. The measured capacitance sensitivity and its linearity were 1.1 fF/G and 0.21%, respectively. © 2004 Elsevier B.V. All rights reserved. Keywords: Accelerometer; Vertical; Comb electrode; SOI
1. Introduction Capacitive accelerometers using SOI wafers are highly reliable devices because they use single crystal silicon (SCS) as structural material [1]. Lateral accelerometers have been developed using comb electrodes and differentially detecting parallel electrodes to obtain linear output. Vertical (z-axis) accelerometers have been developed using either upper or lower electrodes as fixed electrodes [2]. However, it is difficult to use vertical accelerometers for differential detection because it requires both upper and lower electrodes. It is difficult to fabricate such a structure using a SOI wafer. It is also difficult to prevent stiction because of the flat and closely positioned electrode surfaces. Recently, vertical comb electrodes have been proposed for vertical displacement measurement as well as vertical actuation. These electrodes are used in vertical accelerometers using CMOS interconnections [3] and torsional micro-mirrors fabricated using deep RIE [4]. However, the fabrication process of these devices is complicated and requires precise alignment of the structures. To fabricate vertical (z-axis) differential SOI accelerometers we developed a different type of vertical comb electrode. All the sensing structures of accelerometers including the mass, beams, and electrodes are fabricated in the top device layer of a SOI wafer. The vertical electrode is fabricated us∗ Corresponding author. Tel.: +81 75-753-4753; fax: +81 75-753-5250. E-mail address: [email protected] (T. Tsuchiya).
0924-4247/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2004.05.008
ing two mask layers and a time-controlled RIE process. An accelerometer using vertical comb electrodes will have the following features: (1) simple sensor structure, (2) simple fabrication process, (3) linear capacitance change and voltage output, and (4) good cross-axis sensitivity. In this paper, we first describe the developed accelerometer and vertical electrodes. The capacitance and electrostatic force were calculated to predict the device performance and demonstrate its features. We then describe the performance of the vertical accelerometer.
2. Operational principle We fabricated a set of vertical comb electrodes. The cross-sections of the vertical comb electrodes are shown in Fig. 1. The thicknesses of the neighboring electrodes are different and the lower surfaces of the electrodes are placed on the same plane in order to make the change in capacitance different between the moving directions of movable fingers. If their thicknesses are same, the moving direction cannot be determined from the change in the capacitance. The change in capacitance of the vertical comb electrodes can be explained using the same principle of lateral comb electrodes. The capacitance is proportional to the overlapping area of parallel electrodes, if we neglect the edge effect. Capacitance C1 of the vertical electrode whose movable finger is thinner than the fixed finger decreases linearly when
T. Tsuchiya, H. Funabashi / Sensors and Actuators A 116 (2004) 378–383
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Fig. 1. Cross-section of vertical comb electrodes.
the movable finger moves downward. However, it does not change until the top of the movable finger reaches the top of the fixed finger, and then it decreases linearly until the bottom of the movable finger reaches the top of the fixed finger. The dashed line in Fig. 2 shows the change in capacitance against vertical displacement. The change in capacitance C2 is symmetric to the change in C1 with respect to the origin of the displacement. Therefore, difference C between the two electrodes changes linearly both in the upward and downward directions. Although the actual capacitance plotted in Fig. 2 as a solid line suffers from the edge effect, this differential capacitance will change linearly in a wide range. Comb fingers with such a shape can be easily fabricated from a single structural layer using time-controlled etching processes. This operating principle was examined using finite element analysis and a simple 2D FEM model whose analysis area was between the centers of the movable and fixed electrodes. The calculated capacitance, C1 , of this half model is plotted against the movable finger displacement in Fig. 3. The differential capacitance, C, was also calculated and plotted. The capacitance sensitivity was 2.74 aF/m per unit lateral length of the comb electrodes. The non-linearity was about 1% in the range of ±5 m in the vertical displacement. The actuation ability of the vertical comb electrode as a electrostatic actuator was determined by electrostatic force calculations. Vertical electrostatic force Fc at an applied voltage of 2.5 V is plotted in Fig. 3. The vertical force at the origin was 5.1 pN per unit lateral length (1 m), about 70% of the maximum force.
Fig. 2. Schematic explanation of the change in capacitance of a set of vertical comb electrodes.
Fig. 3. Capacitance and electrostatic force of vertical comb electrodes. Differential capacitance was calculated assuming a symmetry between the capacitances C1 and C2.
3. Device structure A z-axis capacitive SOI accelerometer was fabricated using vertical comb electrodes. The accelerometer is shown schematically in Fig. 4. The sensor has a central proof mass, a set of vertical comb electrodes, and four suspension beams. The beams have a spiral shape to restrict the mass movement in the z-direction. Two vertical comb electrodes (C1 and C2 ) are placed diagonally in the sensing area. Two accelerometers with beams of different lengths were fabricated, and their properties were calculated. The mass displacement was calculated using an analytical model, in which the mass was assumed rigid and the four suspending beams were deflected by the acceleration force at the center of the mass. The change in capacitance against the mass displacement was calculated using the predicted sensitivity in Table 1. The actuation force generated at one set
Fig. 4. Schematic structure of accelerometer.
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Table 1 Parameters of vertical accelerometers
Sensing area (mm) Beam length (m) Beam width (m) Electrode gap (m) Electrode height (m) Electrode length (m) No. of electrodes Mass (kg) Base capacitance (pF) Spring constant (N/m) Displacement (nm/G) Capacitance change (fF/G) Actuation force (N at 4 V)
Type A
Type B
1.1 × 1.1 768 4 3 15/7.5 200 140 1.40 × 10−8 0.95 20.1 6.8 1.1 0.36
1.1 × 1.1 565 4 3 15/7.5 200 148 1.27 × 10−8 1.0 50.6 2.5 0.42 0.38
of vertical comb electrodes by applying a voltage was also calculated. The force was about 0.3 N, and it was equal to an acceleration input of 2.5 G at an applied voltage of 4 V. This electrostatic force is capacitively detectable using other comb electrodes in a self-test function of sensor devices. The parameters of the two accelerometers are summarized in Table 1. The vibration mode was evaluated using FEM. The results for the first 10 modes are shown in Fig. 5. The first mode is vertical vibration, which is preferable for stable device operation. The second and third modes are torsional vibration around two different diagonal axes. The ninth and tenth modes are horizontal and their frequencies are more than 10 times the frequencies of the original mode, which results in high stiffness of the sensing structure along the horizontal axis and can provide good cross-axis sensitivity of the device. 4. Fabrication The fabrication process of the sensor using double-layer masks and trench RIE is shown in Fig. 6. Backside polished
SOI wafers were used. Two-layer masks of plasma CVD SiO2 films were fabricated after aluminum-pad fabrication. A time-controlled trench RIE was processed twice. The etching depth of each RIE process was half the thickness of the SOI layer. The first mask layer was removed between the two trench RIE processes. After the front-side passivation by plasma CVD SiO2 , the substrate under the device structure was anisotropically etched from the backside by using TMAH solution. Finally, the SiO2 films for the trench mask and the passivation and sacrificial layers were removed by BHF. The fabricated device is shown in Fig. 7. The proof mass, four suspension beams, and vertical comb electrodes were successfully fabricated. In the vertical comb electrodes, the lower height electrodes were shown as the gray line, because the electrodes were smaller than the other structures and the top surface of the electrodes was roughened by RIE. Fig. 8 shows a close-up of the vertical comb fingers. The height of the lower height electrodes became a half of the thickness of the SOI layer. The vertical comb fingers that have two different height fingers were successfully fabricated. However, the fabricated cross section shows two inadequate shapes that might cause the deviations and the errors in capacitance change. One was the residue at the edges of the lower height electrodes. The residue that looks like a needle may have been caused by the positive taper angle of the trench RIE. The fabrication of the vertical comb electrodes are follows: at the first trench RIE, the half height trenches that became electrode gaps were formed. Then, at the second trench RIE, the rest of the gap trenches and the lower height electrodes were simultaneously formed. The sidewall formed by the first RIE was quickly passivated at the beginning of the second RIE. These passivation reagents may act as the mask for second RIE, which causes the formation of the needle-shaped residue. The needle-like residue can be reduced by optimizing the RIE conditions. If the taper angle of the sidewall becomes more than 90◦ , the residue will disappear. We can also remove this residue using an etching
Fig. 5. Vibration mode of accelerometer. Each deformation plot shows the vibration mode at the underlined frequency.
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Fig. 6. Fabrication process.
process, such as HF + HNO3 solutions and chemical dry etch (CDE) process without degrading the electrode shape, because the residue was very thin. The other inadequate shape was the width of the lower part of the electrodes. The lower part of the thicker electrodes became wider than the other parts. This may be caused by the two layer SiO2 films for the trench mask. Though the “loading effect” in RIE process is one of the reasons for such a tapered shape, it was not the reason because the electrode gap was not symmetric at the respect of the electrode gap. The formation was schematically explained in Fig. 9. Because the SiO2 film for the second trench mask was deposited and patterned first, the SiO2 film for the first trench mask was thickened at the step of the second trench mask. Due to the insufficient etching time for the patterning the first trench mask, small amount of SiO2 film at the step may be remained. We can reduce the residue by expanding the RIE etch time for SiO2 films.
5. Device performance
Fig. 7. Fabricated z-axis accelerometer.
A switched capacitor circuit was used to measure the change in capacitance. The voltage applied to the electrodes was 5 V. The output voltage was measured by applying ac-
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Fig. 9. Details of the vertical combs fabrication. Substrate was omitted in this figure. (a) Second trench mask formation (plasma CVD SiO2 ). (b) First mask film deposition (plasma CVD SiO2 ). The film was thicken at the edge of the second mask. (c) First mask formation. The residue was formed at the thickend part. (d) First trench RIE. The residue shape is transffered to the SOI layer. (e) First mask removal. (f) second RIE.
Fig. 8. Close-up view of vertical comb electrodes: (a) bird’s view and (b) cross-section.
celeration using a shaker table. A reference accelerometer (Ono Sokki NP-2110) was attached to the table with the fabricated sensors. The applied acceleration was ±200 m/s2 (20 G) and its frequency was 5–200 Hz. The output voltages of the two accelerometers with different beam lengths against the output of the reference accelerometer are shown in Fig. 10. The nonlinearity of accelerometers A and B was 0.21 and 1.1%, respectively. The displacement range was about ±200 nm, as shown in Fig. 10, which is less than 5% of the calculated range where the differential capacitance changes linearly. Therefore, this device has a measurement range of ±500 G. The calculated and measured properties of the accelerometer with 768 m-long support beams are listed in Table 2. The differential capacitance sensitivity was 1.3 fF/G, slightly higher than the calculated value. This may have been caused by the approximation of the stiffness of the accelerometers. Although the mass was assumed rigid in this analysis, it was also deformed by the input acceleration. From the FEM analysis, the displacement sensitivity at the center of the
Fig. 10. Sensitivity of accelerometers.
mass was 20% larger than the calculated sensitivity. Based on this displacement sensitivity, we found that the calculated properties agreed with the measured properties. The vibration properties were measured using one set of vertical electrodes for electrostatic actuation, and the other set of vertical electrodes for capacitive detection. The measurements were carried out in vacuum (1.5 Torr). The frequency response of accelerometer A is plotted in Fig. 11. The Table 2 Calculated and measured properties of accelerometer A
Spring constant (N/m) Mass displacement (nm/G) Capacitance change (fF/G) Sensitivity (mV/G) Resonant frequency (kHz)
Calculated
FEM
Measured
20.1 6.8 1.1 54.6 6.03
16.3 8.4 1.3 64.6 5.46
– – 1.3 65.0 5.43
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ation. The device properties were calculated analytically and measured experimentally. The capacitance sensitivity of the accelerometer was 1.3 fF/G, which agreed with the calculated results.
References
Fig. 11. Resonant frequency of accelerometer.
first three modes agreed with the result of the finite element analysis in Fig. 5. The first mode was vertical vibration and the second and third modes were torsional vibrations. The fourth mode did not agree with the result of the FEM analysis. Some coupling between the sensor structure and the fixed electrode whose fundamental resonant frequency was about 40 kHz may have occurred. These vibration property measurements also confirmed the electrostatic actuation of the vertical combs. The measured actuation force was 80 nN at 4 V actuation, which is 20% of the calculated force.
6. Conclusion A z-axis capacitive accelerometer was fabricated using vertical comb electrodes. The vertical comb electrodes were made using only one silicon layer made from a SOI wafer. The electrodes were fabricated by a time-controlled trench RIE process to make one side of the comb electrodes thinner than the other. Differential detection allowed us to measure linear capacitance change against input acceler-
[1] B. Diem, P. Rey, S. Renard, S.V. Bosson, H. Bono, F. Michel, M.T. Delaye, G. Delapierre, SOI ‘SIMOX’ from bulk to surface micromachining, a new age for silicon sensors and actuators, Sens. Actuators A46–47 (1995) 8–16. [2] Y. Matsumoto, M. Iwakiri, H. Tanaka, M. Ishida, T. Nakamura, A capacitive accelerometer using SDB-SOI structure, Sens. Actuators A53 (1996) 267–272. [3] H. Xie, G.K. Fedder, in: Proceedings of the MEMS 2000 of A CMOS z-Axis Capacitive Accelerometer with Comb-Finger Sensing, pp. 496–501. [4] V. Milanovic, M. Last, K.S.J. Pister, Torsional Micromirrors with Lateral Actuators, in: Proceedings of the Transducers 2001, pp. 1298–1301.
Biographies Toshiyuki Tsuchiya received the MS degree from the University of Tokyo and the PhD degree from Nagoya University in 1993 and 2004, respectively. Since 1993, he has been with Toyota Central Research and Development Laboratories, Nagakute, Aichi, Japan. In 2004, he joined the Department of Mechanical Engineering, Kyoto University, Japan. He is currently engaged in the research of silicon surface micromachining, its sensor application, and thin film mechanical property evaluation. He was honored with R&D 100 Award for research in “Thin film tensile tester” in 1998. He is a member of the IEEE and the Institute of Electrical Engineers of Japan. Hirofumi Funabashi received the BS degree (Electronics Engineering) from Nagoya Institute of Technology in 1982. In 1982, he joined Toyota Central Research and Development Laboratories, Inc., Nagakute, Aichi. He is currently engaged in the research of silicon surface micromachining, its sensor application, and LSI Process Technology. Mr. Funabashi is a member of the Japan Society of Applied Physics.
A z-axis differential capacitive SOI accelerometer with vertical comb electrodes Toshiyuki Tsuchiya∗ , Hirofumi Funabashi Department of Mechanical Engineering, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan Received 20 February 2004; received in revised form 2 April 2004; accepted 6 May 2004 Available online 8 July 2004
Abstract This paper describes a differentially detecting capacitive z-axis SOI accelerometer using a set of vertical comb electrodes. The device structure has only one silicon layer and there are no lower or upper electrodes. z-axis acceleration was differentially detected by using a set of newly proposed vertical comb electrodes of different movable and fixed heights. The sensing area was 1.1 mm × 1.1 mm × 15 m. The performance of the accelerometer was calculated and measured experimentally to determine its linear capacitance change and voltage output against input acceleration. The measured capacitance sensitivity and its linearity were 1.1 fF/G and 0.21%, respectively. © 2004 Elsevier B.V. All rights reserved. Keywords: Accelerometer; Vertical; Comb electrode; SOI
1. Introduction Capacitive accelerometers using SOI wafers are highly reliable devices because they use single crystal silicon (SCS) as structural material [1]. Lateral accelerometers have been developed using comb electrodes and differentially detecting parallel electrodes to obtain linear output. Vertical (z-axis) accelerometers have been developed using either upper or lower electrodes as fixed electrodes [2]. However, it is difficult to use vertical accelerometers for differential detection because it requires both upper and lower electrodes. It is difficult to fabricate such a structure using a SOI wafer. It is also difficult to prevent stiction because of the flat and closely positioned electrode surfaces. Recently, vertical comb electrodes have been proposed for vertical displacement measurement as well as vertical actuation. These electrodes are used in vertical accelerometers using CMOS interconnections [3] and torsional micro-mirrors fabricated using deep RIE [4]. However, the fabrication process of these devices is complicated and requires precise alignment of the structures. To fabricate vertical (z-axis) differential SOI accelerometers we developed a different type of vertical comb electrode. All the sensing structures of accelerometers including the mass, beams, and electrodes are fabricated in the top device layer of a SOI wafer. The vertical electrode is fabricated us∗ Corresponding author. Tel.: +81 75-753-4753; fax: +81 75-753-5250. E-mail address: [email protected] (T. Tsuchiya).
0924-4247/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2004.05.008
ing two mask layers and a time-controlled RIE process. An accelerometer using vertical comb electrodes will have the following features: (1) simple sensor structure, (2) simple fabrication process, (3) linear capacitance change and voltage output, and (4) good cross-axis sensitivity. In this paper, we first describe the developed accelerometer and vertical electrodes. The capacitance and electrostatic force were calculated to predict the device performance and demonstrate its features. We then describe the performance of the vertical accelerometer.
2. Operational principle We fabricated a set of vertical comb electrodes. The cross-sections of the vertical comb electrodes are shown in Fig. 1. The thicknesses of the neighboring electrodes are different and the lower surfaces of the electrodes are placed on the same plane in order to make the change in capacitance different between the moving directions of movable fingers. If their thicknesses are same, the moving direction cannot be determined from the change in the capacitance. The change in capacitance of the vertical comb electrodes can be explained using the same principle of lateral comb electrodes. The capacitance is proportional to the overlapping area of parallel electrodes, if we neglect the edge effect. Capacitance C1 of the vertical electrode whose movable finger is thinner than the fixed finger decreases linearly when
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Fig. 1. Cross-section of vertical comb electrodes.
the movable finger moves downward. However, it does not change until the top of the movable finger reaches the top of the fixed finger, and then it decreases linearly until the bottom of the movable finger reaches the top of the fixed finger. The dashed line in Fig. 2 shows the change in capacitance against vertical displacement. The change in capacitance C2 is symmetric to the change in C1 with respect to the origin of the displacement. Therefore, difference C between the two electrodes changes linearly both in the upward and downward directions. Although the actual capacitance plotted in Fig. 2 as a solid line suffers from the edge effect, this differential capacitance will change linearly in a wide range. Comb fingers with such a shape can be easily fabricated from a single structural layer using time-controlled etching processes. This operating principle was examined using finite element analysis and a simple 2D FEM model whose analysis area was between the centers of the movable and fixed electrodes. The calculated capacitance, C1 , of this half model is plotted against the movable finger displacement in Fig. 3. The differential capacitance, C, was also calculated and plotted. The capacitance sensitivity was 2.74 aF/m per unit lateral length of the comb electrodes. The non-linearity was about 1% in the range of ±5 m in the vertical displacement. The actuation ability of the vertical comb electrode as a electrostatic actuator was determined by electrostatic force calculations. Vertical electrostatic force Fc at an applied voltage of 2.5 V is plotted in Fig. 3. The vertical force at the origin was 5.1 pN per unit lateral length (1 m), about 70% of the maximum force.
Fig. 2. Schematic explanation of the change in capacitance of a set of vertical comb electrodes.
Fig. 3. Capacitance and electrostatic force of vertical comb electrodes. Differential capacitance was calculated assuming a symmetry between the capacitances C1 and C2.
3. Device structure A z-axis capacitive SOI accelerometer was fabricated using vertical comb electrodes. The accelerometer is shown schematically in Fig. 4. The sensor has a central proof mass, a set of vertical comb electrodes, and four suspension beams. The beams have a spiral shape to restrict the mass movement in the z-direction. Two vertical comb electrodes (C1 and C2 ) are placed diagonally in the sensing area. Two accelerometers with beams of different lengths were fabricated, and their properties were calculated. The mass displacement was calculated using an analytical model, in which the mass was assumed rigid and the four suspending beams were deflected by the acceleration force at the center of the mass. The change in capacitance against the mass displacement was calculated using the predicted sensitivity in Table 1. The actuation force generated at one set
Fig. 4. Schematic structure of accelerometer.
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Table 1 Parameters of vertical accelerometers
Sensing area (mm) Beam length (m) Beam width (m) Electrode gap (m) Electrode height (m) Electrode length (m) No. of electrodes Mass (kg) Base capacitance (pF) Spring constant (N/m) Displacement (nm/G) Capacitance change (fF/G) Actuation force (N at 4 V)
Type A
Type B
1.1 × 1.1 768 4 3 15/7.5 200 140 1.40 × 10−8 0.95 20.1 6.8 1.1 0.36
1.1 × 1.1 565 4 3 15/7.5 200 148 1.27 × 10−8 1.0 50.6 2.5 0.42 0.38
of vertical comb electrodes by applying a voltage was also calculated. The force was about 0.3 N, and it was equal to an acceleration input of 2.5 G at an applied voltage of 4 V. This electrostatic force is capacitively detectable using other comb electrodes in a self-test function of sensor devices. The parameters of the two accelerometers are summarized in Table 1. The vibration mode was evaluated using FEM. The results for the first 10 modes are shown in Fig. 5. The first mode is vertical vibration, which is preferable for stable device operation. The second and third modes are torsional vibration around two different diagonal axes. The ninth and tenth modes are horizontal and their frequencies are more than 10 times the frequencies of the original mode, which results in high stiffness of the sensing structure along the horizontal axis and can provide good cross-axis sensitivity of the device. 4. Fabrication The fabrication process of the sensor using double-layer masks and trench RIE is shown in Fig. 6. Backside polished
SOI wafers were used. Two-layer masks of plasma CVD SiO2 films were fabricated after aluminum-pad fabrication. A time-controlled trench RIE was processed twice. The etching depth of each RIE process was half the thickness of the SOI layer. The first mask layer was removed between the two trench RIE processes. After the front-side passivation by plasma CVD SiO2 , the substrate under the device structure was anisotropically etched from the backside by using TMAH solution. Finally, the SiO2 films for the trench mask and the passivation and sacrificial layers were removed by BHF. The fabricated device is shown in Fig. 7. The proof mass, four suspension beams, and vertical comb electrodes were successfully fabricated. In the vertical comb electrodes, the lower height electrodes were shown as the gray line, because the electrodes were smaller than the other structures and the top surface of the electrodes was roughened by RIE. Fig. 8 shows a close-up of the vertical comb fingers. The height of the lower height electrodes became a half of the thickness of the SOI layer. The vertical comb fingers that have two different height fingers were successfully fabricated. However, the fabricated cross section shows two inadequate shapes that might cause the deviations and the errors in capacitance change. One was the residue at the edges of the lower height electrodes. The residue that looks like a needle may have been caused by the positive taper angle of the trench RIE. The fabrication of the vertical comb electrodes are follows: at the first trench RIE, the half height trenches that became electrode gaps were formed. Then, at the second trench RIE, the rest of the gap trenches and the lower height electrodes were simultaneously formed. The sidewall formed by the first RIE was quickly passivated at the beginning of the second RIE. These passivation reagents may act as the mask for second RIE, which causes the formation of the needle-shaped residue. The needle-like residue can be reduced by optimizing the RIE conditions. If the taper angle of the sidewall becomes more than 90◦ , the residue will disappear. We can also remove this residue using an etching
Fig. 5. Vibration mode of accelerometer. Each deformation plot shows the vibration mode at the underlined frequency.
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Fig. 6. Fabrication process.
process, such as HF + HNO3 solutions and chemical dry etch (CDE) process without degrading the electrode shape, because the residue was very thin. The other inadequate shape was the width of the lower part of the electrodes. The lower part of the thicker electrodes became wider than the other parts. This may be caused by the two layer SiO2 films for the trench mask. Though the “loading effect” in RIE process is one of the reasons for such a tapered shape, it was not the reason because the electrode gap was not symmetric at the respect of the electrode gap. The formation was schematically explained in Fig. 9. Because the SiO2 film for the second trench mask was deposited and patterned first, the SiO2 film for the first trench mask was thickened at the step of the second trench mask. Due to the insufficient etching time for the patterning the first trench mask, small amount of SiO2 film at the step may be remained. We can reduce the residue by expanding the RIE etch time for SiO2 films.
5. Device performance
Fig. 7. Fabricated z-axis accelerometer.
A switched capacitor circuit was used to measure the change in capacitance. The voltage applied to the electrodes was 5 V. The output voltage was measured by applying ac-
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Fig. 9. Details of the vertical combs fabrication. Substrate was omitted in this figure. (a) Second trench mask formation (plasma CVD SiO2 ). (b) First mask film deposition (plasma CVD SiO2 ). The film was thicken at the edge of the second mask. (c) First mask formation. The residue was formed at the thickend part. (d) First trench RIE. The residue shape is transffered to the SOI layer. (e) First mask removal. (f) second RIE.
Fig. 8. Close-up view of vertical comb electrodes: (a) bird’s view and (b) cross-section.
celeration using a shaker table. A reference accelerometer (Ono Sokki NP-2110) was attached to the table with the fabricated sensors. The applied acceleration was ±200 m/s2 (20 G) and its frequency was 5–200 Hz. The output voltages of the two accelerometers with different beam lengths against the output of the reference accelerometer are shown in Fig. 10. The nonlinearity of accelerometers A and B was 0.21 and 1.1%, respectively. The displacement range was about ±200 nm, as shown in Fig. 10, which is less than 5% of the calculated range where the differential capacitance changes linearly. Therefore, this device has a measurement range of ±500 G. The calculated and measured properties of the accelerometer with 768 m-long support beams are listed in Table 2. The differential capacitance sensitivity was 1.3 fF/G, slightly higher than the calculated value. This may have been caused by the approximation of the stiffness of the accelerometers. Although the mass was assumed rigid in this analysis, it was also deformed by the input acceleration. From the FEM analysis, the displacement sensitivity at the center of the
Fig. 10. Sensitivity of accelerometers.
mass was 20% larger than the calculated sensitivity. Based on this displacement sensitivity, we found that the calculated properties agreed with the measured properties. The vibration properties were measured using one set of vertical electrodes for electrostatic actuation, and the other set of vertical electrodes for capacitive detection. The measurements were carried out in vacuum (1.5 Torr). The frequency response of accelerometer A is plotted in Fig. 11. The Table 2 Calculated and measured properties of accelerometer A
Spring constant (N/m) Mass displacement (nm/G) Capacitance change (fF/G) Sensitivity (mV/G) Resonant frequency (kHz)
Calculated
FEM
Measured
20.1 6.8 1.1 54.6 6.03
16.3 8.4 1.3 64.6 5.46
– – 1.3 65.0 5.43
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ation. The device properties were calculated analytically and measured experimentally. The capacitance sensitivity of the accelerometer was 1.3 fF/G, which agreed with the calculated results.
References
Fig. 11. Resonant frequency of accelerometer.
first three modes agreed with the result of the finite element analysis in Fig. 5. The first mode was vertical vibration and the second and third modes were torsional vibrations. The fourth mode did not agree with the result of the FEM analysis. Some coupling between the sensor structure and the fixed electrode whose fundamental resonant frequency was about 40 kHz may have occurred. These vibration property measurements also confirmed the electrostatic actuation of the vertical combs. The measured actuation force was 80 nN at 4 V actuation, which is 20% of the calculated force.
6. Conclusion A z-axis capacitive accelerometer was fabricated using vertical comb electrodes. The vertical comb electrodes were made using only one silicon layer made from a SOI wafer. The electrodes were fabricated by a time-controlled trench RIE process to make one side of the comb electrodes thinner than the other. Differential detection allowed us to measure linear capacitance change against input acceler-
[1] B. Diem, P. Rey, S. Renard, S.V. Bosson, H. Bono, F. Michel, M.T. Delaye, G. Delapierre, SOI ‘SIMOX’ from bulk to surface micromachining, a new age for silicon sensors and actuators, Sens. Actuators A46–47 (1995) 8–16. [2] Y. Matsumoto, M. Iwakiri, H. Tanaka, M. Ishida, T. Nakamura, A capacitive accelerometer using SDB-SOI structure, Sens. Actuators A53 (1996) 267–272. [3] H. Xie, G.K. Fedder, in: Proceedings of the MEMS 2000 of A CMOS z-Axis Capacitive Accelerometer with Comb-Finger Sensing, pp. 496–501. [4] V. Milanovic, M. Last, K.S.J. Pister, Torsional Micromirrors with Lateral Actuators, in: Proceedings of the Transducers 2001, pp. 1298–1301.
Biographies Toshiyuki Tsuchiya received the MS degree from the University of Tokyo and the PhD degree from Nagoya University in 1993 and 2004, respectively. Since 1993, he has been with Toyota Central Research and Development Laboratories, Nagakute, Aichi, Japan. In 2004, he joined the Department of Mechanical Engineering, Kyoto University, Japan. He is currently engaged in the research of silicon surface micromachining, its sensor application, and thin film mechanical property evaluation. He was honored with R&D 100 Award for research in “Thin film tensile tester” in 1998. He is a member of the IEEE and the Institute of Electrical Engineers of Japan. Hirofumi Funabashi received the BS degree (Electronics Engineering) from Nagoya Institute of Technology in 1982. In 1982, he joined Toyota Central Research and Development Laboratories, Inc., Nagakute, Aichi. He is currently engaged in the research of silicon surface micromachining, its sensor application, and LSI Process Technology. Mr. Funabashi is a member of the Japan Society of Applied Physics.