self-balanced navigation-grade capacitive microaccelerometers using branched finger electrodes and...

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 12, NO. 1, FEBRUARY 2003 11

Self-Balanced Navigation-Grade CapacitiveMicroaccelerometers Using Branched Finger

Electrodes and Their Performance forVarying Sense Voltage and Pressure

Ki-Ho Han and Young-Ho Cho, Member, IEEE

Abstract—This paper presents a navigation-grade capacitivemicroaccelerometer, whose low-noise high-resolution detectioncapability is achieved by a new electrode design based on a high-amplitude anti-phase sense voltage. We reduce the mechanicalnoise of the microaccelerometer to the level of 5.5 g Hz byincreasing the proof-mass based on deep RIE process of an SOIwafer. We reduce the electrical noise as low as 0.6g Hz byusing an anti-phase high-amplitude square-wave sense voltageof 19 V. The nonlinearity problem caused by the high-amplitudesense voltage is solved by a new electrode design of branchedfinger type. Combined use of the branched finger electrodeand high-amplitude sense voltage generates self force-balancingeffects, resulting in an 140% increase of the bandwidth from726 Hz to 1734 Hz. For a fixed sense voltage of 10 V, the total noiseis measured as 2.6 g Hz at the air pressure of 3.9 torr, whichis the 51% of the total noise of 5.1 g Hz at the atmosphericpressure. From the excitation test using 1 g, 10 Hz sinusoidalacceleration, the signal-to-noise ratio of the fabricated microac-celerometer is measured as 105 dB, which is equivalent to thenoise level of 5.7 g Hz. The sensitivity and linearity of thebranched finger capacitive microaccelerometer are measured as0.638 V/g and 0.044%, respectively. [803]

Index Terms—Branched finger electrode, electrical noise, high-amplitude sense voltage, mechanical noise, navigation-grade mi-croaccelerometer, self force-balancing.

I. INTRODUCTION

H IGH-RESOLUTION microaccelerometers have po-tentials to open up new market opportunities such as

personal navigation systems, computer input devices, gamesand toys. The advanced navigation-grade accelerometers(Table I) require a resolution in the range of 3–10g Hz[1], while the conventional microaccelerometers have shown aresolution of 25–800 g Hz [2]–[6].

In the capacitive microaccelerometer, the resolution ismainly constrained by the noise level, including the mechanicalnoise [7] and the electrical noise [8], [9]. The mechanicalnoise, caused by the Brownian motion of air, can be reduced

Manuscript received January 15, 2002; revised May 15, 2002. This work wassupported by the Creative Research Initiative Program of the Ministry of Scienceand Technology (MOST) under the project title of “Realization of Bio-AnalogicDigital Nanolocomotion”. Subject Editor G. B. Hocker.

The authors are with the Digital Nanolocomotion Center, Korea AdvancedInstitute of Science and Technology, 373-1 Guseong-dong, Yuseong-gu, Dae-jeon 305-701, Republic of Korea (e-mail: [email protected]).

Digital Object Identifier 10.1109/JMEMS.2002.805043

TABLE ISPECIFICATION OF ANAVIGATION -GRADE ACCELEROMETER[1]

by increasing either the proof-mass or the quality factor. Inthe surface-micromachined conventional microaccelerometer,the mass has been in the range of several microgram. Theresolution of the surface micromachined microaccelerometershas been governed mainly by the mechanical noise. Recentstudies [4]–[6] have focused on the reduction of the mechanicalnoise by increasing the mass. The methods of multi waferbonding [4], the combined surface- and bulk-micromachining[5], or the RIE process of SOI wafers [6] have been used forreducing the mechanical noise, thereby making the mechanicalnoise lower than the electrical noise.

Nowadays, the electrical noise of the microaccelerometersis the major technical barrier to achieve a high-resolution. Theelectrical noise, caused by the noise of the signal detection cir-cuitry, can be reduced by decreasing the gap between the fixedand movable electrodes or by increasing the sense voltage. Thegap can be reduced to the size of 1–2m, which is the fabrica-tion process limitation.

In this paper, we try to reduce the electrical noise by in-creasing the sense voltage. In the conventional straight fingerelectrodes [see Fig. 1(a)] characteristics of the fabricated mi-croaccelerometers for varying sense voltage and air pressure.

II. DEIGN AND ANALYSIS

A. Structure and Motion Analysis

The microaccelerometer consists of a sense element and a de-tection circuitry. The sense element converts the external accel-eration into proof-mass displacement, and then the displacementis detected and transformed into an electrical output signal bythe detection circuitry.

1057-7157/03$17.00 © 2003 IEEE

12 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 12, NO. 1, FEBRUARY 2003

Fig. 1. Comparison of the sensing electrodes of capacitive motion detectors:(a) straight finger electrodes and (b) branched finger electrodes.

The second-order differential equation for the proof-mass dis-placement, , is expressed as

(1)

where , and are the mass of the proof-mass, the dampingcoefficient and the mechanical stiffness, respectively. The terms,

and , represent the external force and the external ac-celeration, respectively. From the solution of (1) for the dis-placement using the Laplace transform, we obtain the second-order transfer function, expressed in terms of natural frequency

and damping ratio , as follows:

(2)

where and are the Laplace transforms of thedisplacement and the external acceleration, respectively. Forthe external acceleration frequency well below the naturalfrequency, the displacement reduces to , which isproportional to the external acceleration.

Fig. 2. The branched finger capacitive microaccelerometer: (a) simplifiedschematic model and (b) equivalent electrical model.

B. Noise Analysis

The noise of the microaccelerometer is divided into the me-chanical and the electrical noise components. The mechanicalnoise [7], , is generated by the Brownian motion of the airaround the sense element, and is expressed as

(3)

where , , and are the Boltzmann’s constant,the absolute temperature, the natural frequency and the qualityfactor, respectively. Equation (3) shows that a heavy proof-massand/or a high quality factor are required for a low mechanicalnoise of the microaccelerometer.

The electrical noise [8] caused by the electrical componentsin the detection circuitry is determined mainly by the noise [9] inthe frond-end preamplifier, as shown in Fig. 2(a). The electricalnoise, , is given by

(4)

wheretheterms, , , and ,denote theresonant frequency,the gap between the fixed and movable electrodes, the sensevoltage and the input noise voltage, respectively. The lowerelectrical noise in (4) is achieved either by the narrower gap

HAN AND CHO: SELF-BALANCED NAVIGATION-GRADE CAPACITIVE MICROACCELEROMETERS 13

Fig. 3. Functional block diagram of the branched finger capacitive microaccelerometer.

between the fixed and movable electrodes or by the higher sensevoltage.Usually, theminimumelectrodegapis in therangeof1–2

m depending on the line width of MEMS fabrication process.Therefore, we propose high-amplitude sense voltage for reduc-ing the electrical noise of the capacitive microaccelerometer.

The high-amplitude sense voltage reduces the electricalnoise, but generates a problem degrading the linearity of thestraight finger capacitive microaccelerometer, as shown inFig. 1(a). In the case of the straight finger electrode with high-amplitude sense voltage, the nonlinearity is mainly caused bythe nonlinear electrostatic force between the fixed and movableelectrodes. The electrostatic force,, between the fixed andmovable electrodes and the nonlinearity of the straight fingerelectrode are expressed, as follows:

(5)

Nonlinearity (6)

Equation (6) shows that the nonlinearity of the straight fingerelectrode is proportional to the square of the sense voltage.

To solve the nonlinearity problem at high-amplitude sensevoltage,wemodify the straight fingerelectrode into the branchedfinger electrode, as shown in Fig. 1(b). In the branched fingerelectrodes, the electrostatic force is independent of the displace-ment; therefore the linearity is maintained at the high-amplitudesense voltage. In Section II-C, we analyze the performance ofthe branched finger capacitive microaccelerometer.

C. Sensing Performance Analysis

Fig. 2(a) shows a simplified geometric model of the branchedfinger capacitive microaccelerometer. From Fig. 2(a), we inducethe equivalent electrical model, Fig. 2(b), of the branched fingercapacitive microaccelerometer. The capacitance,, betweenthe fixed electrode 1 and the movable electrode, and the capac-itance, , between the fixed electrode 2 and the movable elec-trode are defined as follows

(7a)

(7b)

where , and are the sense capacitance, the changeof the sense capacitance due to the displacement and the par-asitic capacitances between the fixed and movable electrodes,respectively. The sense capacitance,, is given by

(8)

where , , and are the permeability of air, the thicknessof the structure, the number of comb overlap, and the overlappedlength of the combs, respectively. In (8), the terms,, ,and , denote the gap between the finger and the comb, the gapbetween the fingers, the total overlapped length of the fingersand the total overlapped length between the finger and the comb,respectively. From (8), the change of the sense capacitance,,is expressed by

(9)

The sense voltage, , caused by the displacement,, is ob-tained by

(10)

where is the parasitic capacitance between the preamplifierinput port and signal ground. The term,, of (10) is defined asfollows:

(11)

On the other hand, the branched finger capacitive microac-celerometer generates the self force-balancing effect by thebranched finger electrode structure, as shown in Fig. 2(a). Ifthe displacement,, is generated by the external acceleration,the sensing voltage shown in (10) becomes proportional to thesense voltage applied to the near fixed electrode. Then, the elec-trostatic force between the near fixed electrode and the movableelectrode becomes smaller than the electrostatic force betweenthe far fixed electrode and the movable electrode. Therefore,the movable electrode is forced in the opposite direction to thedisplacement by the unbalance of the electrostatic forces. It isthe self force-balancing effect in the branched finger capacitiveaccelerometer.

Now, we derive theoretical equations of the self force-bal-ancing effect. In Fig. 3(a), is the electrostatic force betweenthe fixed electrode 1 and the movable electrode, andis theelectrostatic force between the fixed electrode 2 and the mov-able electrode. They are expressed as

(12a)

(12b)


Fig. 4. Single-mask fabrication process.

Fig. 5. Fabricated branched finger capacitive microaccelerometer: (a) top viewand (b) enlarged view of the branched finger electrodes.

TABLE IIGEOMETRICCHARACTERISTICS OF THECAPACITIVE MICROACCELEROMETER

For the sensing voltage , the unbalance of the electrostaticforces at the proof-mass is generated. The electrostatic forcefrom the unbalance is obtained as

(13)


Fig. 6. Instrument setup for dynamic characteristic measurement of the branched finger capacitive microaccelerometer.

From (13), the electrical stiffness generated by the electro-static force is given by

(14)

Equation (14) shows that the branched finger capacitivemicroaccelerometer produces the positive electrical stiff-ness, which is equivalent to the force-balancing effect in aclosed-loop accelerometer. In the conventional capacitive mi-croaccelerometers [2]–[4], the force-balancing scheme requiresadditional circuitry for the electronic feedback loop. In thebranched finger capacitive microaccelerometer, however, theforce-balancing effect is induced inherently by the branchedfinger electrode structure, generating self force-balancingeffect.

Fig. 3 shows the functional block diagram of the branchedfinger capacitive microaccelerometer. From Fig. 3, we obtainthe sensing voltage, , including the mechanical and electricalnoises as follows:

(15)

where is the natural frequency and is the resonant fre-quency, respectively. The resonant frequency,, is expressedin terms of the natural frequency, , the electrical stiffness, ,and the mass, as shown as follows:

(16)

Fig. 7. Frequency response curve of the branched finger capacitive micro-accelerometer.

The signal-to-noise ratio (SNR) of the microaccelerometer isobtained as:

SNR (17)

From (17), the resolution of the branched finger capacitive mi-croaccelerometer is expressed as follows

Resolution (18)

Equation (18) shows that the electrical noise and the resolu-tion is reduced by the increase of the sense voltage. Equations(16) and (18) illustrate that the branched finger capacitive mi-croaccelerometer achieves the increased bandwidth and the im-proved resolution.

III. M ICROFABRICATION PROCESS

The branched finger capacitive microaccelerometer is fabri-cated using a single-mask deep RIE process, as shown in Fig. 4.The microaccelerometer is defined by the deep RIE etchingof the top silicon layer of the SOI wafer [see Fig. 4(a)]. Thislayer, which has the thickness of 401 m, is heavily dopedwith phosphorus (0.1 cm). In Fig. 4(b), PR (PhotoResist:AZ5214) is coated and patterned to obtain a mask for the deepRIE etching. In Fig. 4(c), the microaccelerometer is defined bythe deep RIE etching of the 40-m-thick single crystal silicon,


Fig. 8. Instrument setup for the noise measurement of the branched finger capacitive microaccelerometer.

Fig. 9. Measured and estimated noise levels of the branched finger capacitivemicroaccelerometer for varying sense voltage,V s: (a) electrical and total noiselevels and (b) mechanical noise level.

TABLE IIIMEASUREDPERFORMANCE OF THECAPACITIVE MICROACCELEROMETER

Fig. 10. Dynamic response of the branched finger capacitive microacceler-ometer for varying sense voltage,V s: (a) amplitude response and (b) resonantfrequency response.

followed by the removal of a 2-m-thick buried oxide layerusing buffered oxide etchant (BOE) solution. The wafer, rinsedin isopropyl alcohol, is dried in an infrared lamp for solvingthe sticking problem. In Fig. 4(d), 200/2000 -thick Cr/Aulayers are evaporated without mask to form electrode pads forgold wire bonding.

Fig. 5 shows a scanning electron micrograph of the fabri-cated branched finger capacitive microaccelerometer, and thegeometric characteristics are listed in Table II.


Fig. 11. Dynamic response of the branched finger capacitive microacceler-ometer for varying air pressure at the sense voltage of 10 V: (a) amplituderesponse and (b) quality factor response.

IV. EXPERIMENTAL RESULTS AND DISCUSSION

A. Noise Levels for Varying Sense Voltage

Fig. 6 shows the instrument set-up for the measurement ofdynamic characteristics of the fabricated branched finger capac-itive microaccelerometer. Fig. 7 shows the frequency responsecurve of the microaccelerometer. The curve shows that the nat-ural frequency and the quality factor of the microaccelerometerare measured 726 Hz and 1, respectively.

The electrical and total noise levels of the microaccelerom-eter are measured by using a low noise amplifier and a spectrumanalyzer, as shown in Fig. 8. The measured electrical and totalnoise levels are plotted with the estimated values in Fig. 9(a)for varying sense voltage. The measured mechanical noise isobtained by subtracting the measured electrical noise from themeasured total noise. Fig. 9(b) compares the measured and esti-mated values of mechanical noise. Fig. 9(a) shows that the elec-trical noise of the fabricated microaccelerometer is in the levelof 0.6 g Hz at the sense voltage of 19 V, which is an order ofmagnitude reduction of the electrical noise level of 6g Hzat 1 V. At lower sense voltage, the measured electrical noise is ingood agreement with the estimated value. At the sense voltagehigher than 12 V, the measured electrical noise shows satura-tion, resulting in the electrical noise of 0.60.08 g Hz at

Fig. 12. Measured and estimated noise levels of the branched finger capacitivemicroaccelerometer for varying air pressure at the sense voltage of 10 V: (a)electrical and total noise levels and (b) mechanical noise level.

19 V, which is 66% larger than the estimated electrical noise of0.36 g Hz.

Total noise level, including the electrical and mechanicalnoises, is measured as 5.5g Hz at the sense voltage of 19V, which is 45% of the total noise of 12g Hz at the sensevoltage of 1 V. Fig. 9(b) shows that the measured and estimatedmechanical noises are independent of the sense voltage. InFig. 9(b), the measured mechanical noise of 5.50.72 g Hzis 28% larger than the estimated value of 4.30.2 g Hz.The measured mechanical noise level, obtained by subtractingthe measured electrical noise from the measured total noise,places the upper bounds of the mechanical noise.

The measured noises, the minimum detectable displacementand acceleration levels are summarized in Table III. The min-imum detectable displacement and acceleration levels of the mi-croaccelerometer are 0.19and 148 g, respectively.

B. Stiffness Increase Effect

The frequency response curves in Fig. 10 show that the res-onant frequency increases as the sense voltage increases. It im-plies that the effective stiffness of the branched finger capaci-tive microaccelerometer increases with the sense voltage by theself force-balancing effect, as shown in (13). The self force-bal-ancing effect results in an increased stiffness of 5.07 N/m at


TABLE IVSTIFFNESSVARYING RATE FOR THEDIFFERENTTYPES OF THEBRANCHED FINGER ELECTRODES

the sense voltage of 19 V, compared to the stiffness of 0.88N/m at 0 V. It means that the additional stiffness at the rate of0.0116 0.0017 N/m/V is generated as the sense voltage in-creases.

C. Noise Levels for Varying Air Pressure

Equation (3) has shown that the mechanical noise of themicroaccelerometer is reduced by decreasing the air pressure.Fig. 11(a) shows the dynamic response of the branched fingercapacitive microaccelerometer for varying air pressure at thesense voltage of 10 V. The dynamic response shows that thequality factor increases as the air pressure decreases, as shownin Fig. 11(b). The quality factor is measured as 22 in the airpressure of 3.9 torr, which is an order of magnitude increaseof the quality factor compared to the quality factor of 1.7,measured in the atmospheric pressure.

Fig. 12(a) compares the measured electrical and total noiselevels with the estimated values for varying air pressure. Mea-sured mechanical noise is obtained by subtracting the measuredelectrical noise from the measured total noise, as shown inFig. 12(b), with the estimated values. Fig. 12(a) shows that thetotal noise level, including the electrical and mechanical noises,is measured as 2.6g Hz in the air pressure of 3.9 torr, whichis the 51% of the total noise of 5.1g Hz in the atmosphericpressure at the sense voltage of 10 V. Fig. 12(a) shows that themeasured electrical noise agrees well with the estimated value,which is independent of the air pressure. Fig. 12(b) shows thatthe measured and the estimated mechanical noises decreasewith the air pressure. The measured mechanical noise level ison the average 1g Hz larger than the estimated value. Theuncertainty of the measured mechanical noise is in the range of

0.7 g Hz. In the estimated mechanical noise, the qualityfactor uncertainty and the mass uncertainty are in the range of

0.19 g Hz and 0.27 g Hz, respectively. The discrep-ancy of 1 g Hz between the measured mechanical noise andthe estimated value is in the order of the uncertainty range.

Fig. 13. Measured and estimated stiffness varying rate for different branchedfinger electrode length.

D. Stiffness Varying Effect Depending on Branched FingerElectrode Length

In the branched finger electrode, the equation of the electricalstiffness, (14), includes a positive term and three negative terms.From (14), we obtain the stiffness varying rate, SVR, given by

(19)


Fig. 14. Instrument setup for the performance measurement of the branched finger capacitive microaccelerometer using an electromagnetic exciter.

Fig. 15. Output of the fabricated microaccelerometer measured at the sensevoltage of 19 V for a 10 Hz 1 g sinusoidal acceleration: (a) voltage output and(b) power spectrum output.

Equation (19) shows that the stiffness varying rate dependson the dimension of the branched finger electrode. Especially,the stiffness varying rate is a function of the branched fingerelectrode length. In order to measure variation of the stiffnessvarying rate depending on the change of the branched fingerelectrode length, we designed and fabricated a set capacitivemicroaccelerometers with eight different electrode lengths.Table IV summarizes the geometric characteristics of the eightdifferent branched finger capacitive microaccelerometers andthe measured stiffness varying rates.

Fig. 16. Microaccelerometer output for varying acceleration measured for a10 Hz acceleration at the sense voltage of 19 V.

Fig. 13 shows the measured and estimated stiffness varyingrate for different branched finger electrode lengths. FromFig. 13, we find that the three negative terms in (19) becomedominant when the branched finger electrode length is shorterthan 0.5 cm. Alternatively, when the branched finger electrodelength is longer than 0.5 cm, the positive term becomesdominant. Fig. 13 also shows that the electrical stiffness ofthe branched finger capacitive microaccelerometer becomespositive when the total branched finger electrode length islonger than 1 cm. From the measured results, we obtain adesign rule for the minimum total branched finger electrodelength to attain the positive electrical stiffness.

E. Excitation Test

The fabricated microaccelerometer is measured by thereadout technique using the 250 kHz complimentary high-am-plitude sense voltages chopping method, as shown in Fig. 14.Fig. 15(a) and (b) show the output signal and the powerspectrum, respectively, measured from the fabricated branchedfinger capacitive microaccelerometer for a 1 g, 10 Hz sinusoidalacceleration at the sense voltage of 19 V. From Fig. 15(b), thesignal-to-noise ratio of the microaccelerometer is measured as105 dB, which is equivalent to the noise level of 5.7g Hz.The dynamic noise level of 5.7g Hz agrees well with thestatic noise level of 5.5 g Hz measured in Section IV-A.Fig. 16 shows the output amplitude of fabricated microac-celerometer for varying input acceleration. From Fig. 16,


TABLE VPERFORMANCE COMPARISON OF THENAVIGATION -GRADE

MICROACCELEROMETERS

sensitivity and linearity of the fabricated microaccelerometerare measured as 0.638 V/g and 0.044%, respectively.

Table V compares the measured performance of the branchedfinger capacitive microaccelerometer with the specification ofa navigation grade accelerometer. From Table V, we know thatthe performance of the branched finger capacitive microac-celerometer satisfies the specification of a navigation gradeaccelerometer.

V. CONCLUSION

We have developed a navigation grade capacitive accelerom-eter using the branched finger electrode with high-amplitudesense voltage. From the branched finger capacitive microac-celerometer fabricated by the deep RIE on an SOI wafer, weachieved the total noise level of 5.5g Hz at the sense voltageof 19 V, and the stiffness varying rate of 0.01160.0017 N/m/Vis generated by the stiffness increase effect. In the air pres-sure test, the total noise is measured as 2.6g Hz at theair pressure of 3.9 torr, which is the 51% of the total noise of5.1 g Hz at the atmospheric pressure for an identical sensevoltage of 10 V. Using a set of the microaccelerometers havingeight different electrode lengths, we have measured the stiffnessvarying rates depending on the total branched finger electrodelength. We obtained the design rule for the minimum branchedfinger electrode length generating positive electrical stiffness.From the excitation test for a 1 g, 10 Hz sinusoidal accelera-tion, the SNR is measured as 105 dB, which is equivalent to thenoise level of 5.7 g Hz. The sensitivity and linearity of thebranched finger capacitive microaccelerometer are measured as0.638 V/g and 0.044%, respectively. From the measured perfor-mance, we have verified that the performance of the branchedfinger capacitive microaccelerometer satisfies the specificationof a navigation-grade accelerometer.

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Ki-Ho Han was born in Busan, Korea, in 1970.He received the B.S. and M.S. degrees in electricalengineering from the Korea Advanced Institute ofScience and Technology (KAIST), Daejeon, Korea,in 1993 and 1996, respectively, and the Ph.D. degreein mechanical engineering from KAIST for hishigh-resolution capacitive subnanometric motiondetectors using branched finger electrodes withhigh-amplitude sense voltage in 2002.

He is currently working as a Postdoctoral Asso-ciate in the Micro Instrumentation Research labora-

tory at the Georgia Institute of Technology, Atlanta. His research interests in-clude BioMEMS transducers, inertial microdevices, small signal detection cir-cuitry, and ASIC development for fully integrated microdevices and microsys-tems.

Young-Ho Cho (M’01) received the B.S. degreesumma cum laudefrom Yeungnam University,Taegu, Korea, in 1980, the M.S. degree from theKorea Advanced Institute of Science and Technology(KAIST), Seoul, Korea, in 1982, and the Ph.D.degree from the University of California at Berkeleyfor his electrostatic actuator and microflexuresuspension research completed in December 1990.

From 1982 to 1986, he was a Research Scientistof CAD/CAM Research Laboratory, Korea Instituteof Science and Technology (KIST), Seoul, Korea.

During 1987–1991, he worked as a Graduate Student Researcher (1987–1990)and a post-doctoral Researcher (1991) of the Berkeley Sensor and ActuatorCenter (BSAC) at the University of California at Berkeley. In August 1991, hemoved to KAIST, where he is currently an Associate Professor in the Depart-ments of BioSystems and Mechanical Engineering as well as the Director ofDigital Nanolocomotion Center. His research interests are focused on photonicand biofluidic microsystems with micro/nano-actuators and detectors. In Koreahe has pioneered MEMS research and has been active on the development ofelectromechanical, optomechanical and thermofluidic micro/nano-devices forautomotive, electronics, information and biomedical applications.

self-balanced navigation-grade capacitive microaccelerometers using branched finger electrodes and...

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