Structure Design and Fabrication of Silicon Resonant Micro-accelerometer Based on Electrostatic Rigidity

Transcription

1 Proceeings of the Worl Congress on Engineering 9 Vol I WCE 9, July 1 -, 9, Lonon, U.K. Structure Design an Fabrication of Silicon Resonant Micro-accelerometer Base on Electrostatic Rigiity ZHANG Feng-tian, HE Xiao-ping, SHI Zhi-gui, ZHOU Wu Abstract The structure characteristics an working principle of silicon resonant micro-accelerometer base on electrostatic rigiity are presente. Dynamic characteristics of ouble-ene tuning fork (DETF) in the sensor are analyze. Force equilibrium equations of mass an DETF are built respectively for with or without acceleration, through which the relationship between DETF resonant frequency an acceleration is obtaine. The influences of fole supporting beams linke with proof mass an gap between capacitive parallel plates on the sensor sensitivity are analyze, an finally a resonant micro accelerometer with sensitivity of 6Hz/g is esigne an fabricate with bulk-silicon issolve processes. Inex Terms Electrostatic rigiity; Resonance; Accelerometer; Bulk-silicon issolve processes. I. INTRODUCTION Resonant principle has been wiely use for measuring physical parameters such as mass, acceleration, force, flow or pressure. The main avantage of a resonant sensor over other sensing principles is its quasi-igital output, which implies goo resistance to noise or electrical interference an simple interface to a igital system. Resonant accelerometer has been prouce an wiely use for many years, for example, RBA5 of Honeywell Company. Most resonant accelerometers use quartz material for its excellent piezoelectric performance, but the quartz fabrication is expensive an not compatible with IC (integrate circuits) fabrication technology, which makes it impossible to integrate the sensor an its interface circuits on one chip. Resonant accelerometers base on the silicon micromachining technology become very attractive ue to low cost, small size, compatibility with IC fabrication processes, an potential application in the fiels where size an high precision are require. Most silicon resonant accelerometers etect resonant frequency of the vibrating beam subjecte to axial loaing which relates to inertial force Manuscript receive February 7, 9. Zhang Feng-tian is with the Institute of Electronic Engineering, China Acaemy of Engineering Physics, Mianyang, Sichuan, China. (Phone: , fax: , zftstuart@sohu.com). He Xiao-ping is with the Institute of Electronic Engineering, China Acaemy of Engineering Physics, Mianyang, Sichuan, China ( hxp@xlea.com). SHI Zhi-gui is with the Institute of Electronic Engineering, China Acaemy of Engineering Physics, Mianyang, Sichuan, China (szg@xlea.com).. Zhou Wu is with the Southwest Jiaotong University, Chengu, Sichuan, China( zhouwu916@yahoo.com.cn). on the proof mass. The vibrating beam is excite by alternating electrostatic or electrothermal force, an the frequency change is sense by capacitors or piezoresistive resistors respectively [1-6]. In a relatively new concept of resonant accelerometer, inertial force of the proof mass pushes or pulls one electroe as one part of the proof mass, an changes the gap istance of the parallel-plate capacitor, then the electrostatic force between parallel plate electroes changes with the gap istance, an equivalently changes the efficient mechanical rigiity of the vibrating beam [7-8]. In the previous work of other research groups, the accelerometer was fabricate an showe excellent performances. But the movement an ynamic characteristics of the vibrating beam were not presente, which is very important for unerstaning the working principle an the sensor structure esign. Therefore, in this stuy, the movement an ynamic characteristics are analyze with mechanical ynamic theory. The relationship between resonant frequency of the vibrating beam an acceleration is obtaine in theory. Finally, a resonant accelerometer with sensitivity of 6Hz/g is esigne an fabricate with bulk-silicon issolve processes. II. OPERATING PRINCIPLE The concept of the resonant accelerometer is shown in Fig.1. It consists of ouble-ene tuning fork (DETF), riving capacitors, sensing capacitors, proof mass, an supporting springs. The fixe comb electroes of riving capacitors are excite by an AC voltage with DC bias, DETF is connecte to groun, an the proof mass incluing the electroe of sensing capacitor is connecte to a DC voltage. In the horizontal plane, each clampe-clampe beam of DETF vibrates 18 out of phase with its natural frequency to cancel reaction forces at the ens when there is no acceleration. The sensing capacitors can etect the vibrating frequency of DETF through interface circuits. When there is acceleration, the proof mass moves near or away from the electroe of DETF uner inertial force an changes the gap istance of sensing capacitor. The electrostatic force between sensing electroes inuces an aitional electrostatic rigiity, which results in the variation of DETF resonant frequency with acceleration. Therefore, etecting the resonant frequency of DETF can measure acceleration. ISBN: WCE 9

2 Proceeings of the Worl Congress on Engineering 9 Vol I WCE 9, July 1 -, 9, Lonon, U.K. Fig.1. Principle schematic of a resonant accelerometer III. THEORY ANALYSIS Due to the symmetry of sensor structure, one half of the structure shown as in Fig. is analyze. The supporting spring in Fig.1 is realize with four fole beams which not only support the proof mass but also make it capable of moving freely along x axis. The DC voltage of the proof mass is V, the clampe-clampe beam of DETF is connecte to GND, an the riving voltage is V c Sin (ωt) with DC bias voltage V 1. The forces applie to the clampe-clampe beam inclue inertial force, amping force, elastic force, riving an sensing electrostatic forces. The mechanical ynamic equation of the vibrating beam can be written as AV N1 h( V 1 V sin( t)) my ε ε + c ω + cy + κy ( g x Y ) g (1) Where m is the effective mass of the vibrating beam, c amping coefficient, κ the effective spring constant of vibrating beam, ε the permittivity of free space ( F/m), A the efficient area of the sensing capacitor, V the sensing voltage, g the gap istance of riving capacitor an sensing capacitor, x an Y are respectively the isplacement of proof mass or vibrating beam relative to initial position when no voltages are applie, an N 1 is number of riving comb finger pairs, h is the structure thickness, ω is the frequency of AC voltage. The first part on the right in (1) is sensing electrostatic forces, while the secon part is riving electrostatic forces. In (1), it assumes that the amping force is proportional to velocity. Fig.. Schematic of the half structure From (1), we can see that electrostatic forces of the vibrating beam inclue fixe an alternate parts. We can think that the vibrating beam moves to some position by one fixe electrostatic force an vibrates harmonically about this equilibrium position. So Y in (1) can be expresse as y 1 +y, an yy sin(ωt+φ), where y 1 is the isplacement of vibrating beam by the fixe electrostatic force an y is the isplacement amplitue by harmonic force. If V 1 >>V c, with Taylor expansion, (1) can be rewritten as my + cy + κ( y1 + y) ( g () Vc sin( ωt) + y ( g g g Equivalently, we can obtain κy1 + ( g g () V c sin( ωt) m y + cy + ( κ ) y ( g g (4) Equation () escribes the isplacement of vibrating beam by fixe force. We can see that y 1 is etermine by the riving or sensing DC voltage in aition to the sensor structure an size. Equation (4) is the harmonic oscillation equation. It shows that there is an aitional force proportional to the vibrating amplitue in (4), equivalently an aitional rigiity cause by electrostatic force between parallel plates of sensing capacitor. The rigiity name electrostatic rigiity κ e can be written as εav κ e ( g (5) Then, the resonant frequency of vibrating beam is as follows 1 κ κ e f n π m (6) When there is acceleration which irection shown as in Fig., the isplacement of proof mass cause by inertial force is x. The electrostatic force between parallel plates of sensing capacitor will change an result in isplacement variation y 1 of the electroe on the vibrating beam. Thus, the gap istance of sensing parallel-plate capacitor change x+ y 1. The electrostatic rigiity inuce by sensing parallel-plate capacitor will vary an alter resonant frequency of the vibrating beam shown as κ 1 ( g ( x Δx) Δy1)) fn π m (7) Due to that the natural frequency of vibrating beam is greatly higher than that of proof mass-spring system, the electrostatic force frequency applie to the proof mass by beam vibrating is also largely higher than that of proof mass-string system. So the isplacement of proof mass cause by beam vibrating can be neglecte. When there is no acceleration, the elastic force an electrostatic force applie to the proof mass are equal. We can obtain the force ISBN: WCE 9

3 Proceeings of the Worl Congress on Engineering 9 Vol I WCE 9, July 1 -, 9, Lonon, U.K. equilibrium equation of proof mass as follow κ sx ( g (8) Where κ s is spring constant of the fole supporting beams linke with proof mass. When there is acceleration shown as in Fig., the gap of sensing capacitor will change, an the elastic force plus inertial force is equal to electrostatic force by sensing capacitor, the force equilibrium equation can be written as κ ( x Δx) Ma ( g ( x Δx) Δy1)) s (9) Here M refers to the mass of the proof mass. As for the vibrating beam, from (), we can obtain ( g ( x Δx) Δy1)) g (1) + ma κ ( y1 Δy1) When the sensor structure size, riving an sensing voltage are etermine, from () (8) (9) (1), we can calculate the value of x, y 1, x, y 1, an substitute them into (7), the relationship between the beam vibrating frequency an acceleration can be obtaine, which is important for sensor structure esign. cause by inertial force of the proof mass is larger when the fole beam is narrow an long, an electrostatic rigiity varies greatly. Also, too narrow or long fole beams will affect the strength an resistance to impact, even maybe result in absorption of capacitor plates an estroy the structure stability. Sensitivity(Hz/g) Sensitivity (Hz/g) Sensing voltage(v) (a) IV. STRUCTURE DEIGN The accelerometer sensitivity irectly affects its precision. The important aspect of sensor structure esign is to etermine proper structure size to improve the sensor sensitivity when the structure stability is guarantee. The sensor sensitivity will be calculate at ifferent structure size, riving or sensing voltage, with the above establishe equations. The vibrating beam is 5μm long an 5μm wie. The sensor structure is 5μm in thickness. The riving AC amplitue is 1V with 15V DC bias. The fole supporting beams are U-shape. Fig.a shows the relationship between the sensor sensitivity an sensing voltage when the capacitor gap is μm, the fole beam is 45μm long an 6μm with. Fig.b presents the variation of sensitivity with the capacitor gap istance when the fole beam is 45μm long an 6μm wie an sensing voltage is 16V. We can see that sensor sensitivity is 7Hz/g or 5Hz/g when sensing voltage is 17V or 18V respectively. Larger sensing voltage an small capacitor gap mean higher sensitivity. The reason is that the sensing capacitor electrostatic force increases when sensing voltage increases an capacitor gap gets narrow, then the variation of electrostatic rigiity at same acceleration become larger an prouce larger eviation of vibrating beam resonant frequency. But too large sensing voltage an small capacitor gap may lea to absorption of capacitor plates an structure stability will be ruine. Fig.c is the relationship of sensor sensitivity an fole supporting beam with, an Fig. shows that of sensor sensitivity an supporting beam length. We can see that narrower an longer supporting beams can improve sensor sensitivity. This is ue to that the capacitor gap variation Sensitivity(Hz/g) Sensitivity (Hz/g) Gap istance of capacitor (μm) (b) Length of fole beam(μm) (c) With of fole beam (μm) () Fig.. Sensor sensitivity versus voltage an structure size From above analysis, smaller capacitor gap, longer an narrower supporting beam, an larger sensing voltage are expecte to improve the sensor sensitivity. But in the respect ISBN: WCE 9

4 Proceeings of the Worl Congress on Engineering 9 Vol I WCE 9, July 1 -, 9, Lonon, U.K. of stability an strength, they shoul be controlle properly. So sensitivity an structure stability shoul be consiere at the same time when esigning the sensor structure size. The sensor structure size in this stuy is finally esigne as follows: fole supporting beam 45μm long an 6μm wie, capacitor gap μm wie, an sensing voltage 17V. The relationship between sensor resonant frequency an applie acceleration is shown in Fig.4. We can see that the esigne sensor sensitivity is at least 6Hz/g for one clampe-clampe beam of DETF. Resonant frequency (Hz) Acceleration (m/s ) Fig.4. Resonant frequency versus applie acceleration V. FABRICATION PROCESS The aopte fabrication process in this stuy is calle bulk-silicon issolve process. The process sequences are as follows: First, boron is heavily ope into the silicon wafer front sie to make the P++ etch-stop layer which is use as the structure layer an about 5μm thick; anchors for wafer-glass boning are patterne an etche on the wafer front sie with ICP eep etch technology(fig.5a); then, the sensor structure is patterne an etche with the secon ICP eep etching (Fig.5b); aluminum is sputtere on the glass wafer to form electroes through which ifferent voltage can be subjecte to ifferent parts of the sensor (Fig.5c);Finally, boning silicon wafer an glass wafer together using anoic boning (Fig.5)an etch the silicon wafer from backsie in KOH etch solution until arriving the etch-stop layer an obtaining the sensor structure(fig.5e). (a) Resonant accelerometer (b) Resonator Fig.6 The SEM pictures of the fabricate sensor VI. CONCLUSION In the silicon resonant accelerometer base on electrostatic rigiity, the proof mass will not vibrate when DETF beams vibrate without acceleration. Meanwhile, the proof mass will move away the initial equilibrium position with acceleration, an apply an aitional rigiity to the vibrating beam for change the resonant frequency. Accoring to the ynamic equations of proof mass an DETF, the accelerometer resonant frequency can be etermine at any acceleration. By analyzing effects of the structure size, sensing voltage on the sensor sensitivity, a sensor structure suitable for actual fabrication conition is esigne an fabricate. Future research work will focus on the measurement of the sensor performance. Fig.5. Fabrication processes The SEM pictures of the fabricate sensor structure are shown in Fig.6. REFERENCES [1] Chr. Burrer, J.Esteve. A novel resonant silicon accelerometer in bulk-micromachining technology. Sensors an Actuators A 46-47, 1995: [] Susan X. P. Su, Henry S. Yang, an Alice M. Agogino. A Resonant Accelerometer With Two-Stage Microleverage Mechanisms Fabricate by SOI-MEMS Technology. IEEE Sensors Journal, VOL. 5, NO. 6, 5:114-1 [] Ashwin A. Seshia,, Moorthi Palaniapan, Trey A. Roessig, Roger T. Howe, Rolan W. Gooch, Thomas R. Schimert, an Stephen Montague. A Vacuum Package Surface Micromachine Resonant Accelerometer. Journal of microelectromechnical Systems, vol.11, no.6, : [4] Mark Helsel, Gene Gassner, Mike Robinson an Jim Wooruff. A Navigation Grae Micro-Machine Silicon Accelerometer. IEEE 94: [5] Jia Yubin, Hao Yilong, an Zhang Rong. Bulk Silicon Resonant Accelerometer. Chinese Journal of Semiconuctors, Vol. 6, No., 5: [6] W. Burns, R. D. Horning, W. R. Herb, J. D. Zook, an H. Guckel. Resonant microbeam accelerometers. The 8th international Conference ISBN: WCE 9

5 Proceeings of the Worl Congress on Engineering 9 Vol I WCE 9, July 1 -, 9, Lonon, U.K. on Soli-State Sensors an Actuators, an Eurosensors IX. Stockholm, Sween, June 5-9, 1995: [7] B. L. Lee, C. H. Oh, Y. S. Oh, an K. Chun, A Novel Resonant Accelerometer: Electrostatic Stiffness Type, The 1th International Conference on Soli State Sensors an Actuators (Transucer 99), Senai, Japan, June 7-1, 1999, pp [8] Seonho Seok, Hak Kim, an Kukjin Chun. An Inertial-grae laterally-riven MEMS Differential Resonant Accelerometer.IEEE 4: M. Young, The Techincal Writers Hanbook. Mill Valley, CA: University Science, ISBN: WCE 9