SELF-BALANCED HIGH-RESOLUTION CAPACITIVE MICROACCELEROMETERS USING BRANCHED FINGER

ELECTRODES WITH HIGH-AMPLITUDE SENSE VOLTAGE

Ki-Ho Han and Young-Ho Cho

Digital Nanolocomotion Center Korea Advanced Institute of Science and Technology

373- 1 Kusong-dong, Y usong-kit, 'I'aejoii 305-70 1. Republic of Korea P h i : +82-42-869-869 1 / Fax: +82-42-869-8690 / E-mail: dnc$kaist.ac.kr

ABSTRtICT

This paper presents a high-resolution capacitive inicro- accelerometer. whose low-noise selt Ibrce-balancing et'fect has been achieved by using branched tinger electrodes with high-amplitude anti-phase sense voltage. We reduce the mechanical noise of the microaccelerometer to the level of 5.5pg/& by increasing the proof-mass based on tlie deep RIE process ofan SO1 wafer. We reduce the electrical noise as low as 0.6pg/& by using an anti-phase high-amplitude square-wave sense voltage of I9V. The nonlinearity problem arising from the h igh-vol tage capacitive detection has been solved b) a new electrode design of branched finger form. Combined use of the branched finger electrode and the high-amplitude sense voltage has generated self force-balancing effects, resulting in a good linearity of 0.044% with an 140% increase of the bandwidth from 726Hz to I .734Hz.

INTRODUCTION

High-resolution microaccelerometers have potentials to open up new market opportunities such as personal inforination systems, computer input devices, games, toys and personal navigation systems. .4lthough the high-resolution accelerometers require the resolution as low as 3- IOpgi & [ I ] , until now the reported microaccelerometers have shown the resolution of 25-SOOpg1 [2-61. The resolution of the microaccelerometers has been limited mainly by mechanical noise. Therefore, recent studies [4-6] have focused on the reduction of tlie mechanical noise by increasing the proot-mass. The methods of niult i wafer bonding (41. combined surface- and bulk-micromacliining [5]. or R I E o f SO1 wafers [6 l are used for reducing the mechanical noise. thereby making the mechanical noise lower than the electrical noise. No\vadays. the electrical noise 01' iiiicroiiccc'leroiiictcrs places major technical harrier to iicliie\ e a liigli-rcsolutic,n. In this papcr. \ve propose a tie\\ iiiicr(~;icceIcroiiieter design ti)r a IOU clectrical iioisc. 11 igti-resol u t ion per limnancc.

I n thc coti\ciitiotiiil straight linger electrodes (Fig. I a ) 12- 71. the lii~li-amplitu~le sense \ oltage causes nonlineai-it> and

0-7803-7185-2/02/$10.00 02002 IEEE 714

instability problems. Thus. we have devised a new type of sensing electrodes having branched tingers (Fig. 1 b). thereby introducing self-balancing effects for the enhanced linearity and stability of the high-voltage capacitive detection.

In this paper, we develop a high-resolution capacitive microaccelerometer with the electrical noise reduced using high-amplitude sense voltage. Using the microaccelerometer fabricated by the deep RIE process of an SO1 wafer. we measure noise levels, and compare the results with the predicted values. The self force-balancing effect is measured and compared with estimated result, and through the excitation test we measure the sensitikit! and linearity of the fabricated branched finger capacitive microaccelerometer.

(a> (b) Fig.1 Comparison of the electrodes of capacitive microacceleronieters: (a) conventional straight finger electrodes; (b) present branched finger electrodes

r-7

(.. .A(. ,,

Fig.2 I:qui\alent clectrical model 01' tlie branched linger capaciti\ e micl.oaccelcrometel..

DESIGN AND THEORETICAL ANALYSIS 2c 01' v 2

Y (7) c ~ F 2 ~ , t N , V,'

k =--= ax lodo

The microaccelerometer consists of a sense element for sensing external acceleration and a detection circuitry for As %(7) shows, the electrical stiffness of the branched electrical manipulation, Figure 2 shows an equivalent finger capacitive miCrOaCCelerOmeter Can be positive. electrical model of the proposed branched finger capacitive Hence, the branched finger capacitive microaccelerometer microaccelerometer. The capacitances between the achieves self force-balancing effect that induces electrical fixed and movable electrodes in Fig.2 are defined as stiffness increase effect without for electronic feedback loop.

In the case of Is( << w,, , the sensing voltage generated by the external acceleration, uer, , mechanical noise, a,,,,, , and electrical noise, v,,, , are obtained as

C , = C,,,, +C, + AC ( 1 a)

C , = Co,,2 +Co - AC (Ib) I / ?

1 ;, = [ ( f , (4+c ) + [ $)2 pc 1 (8) where C,,,, and C,,,, are the parasitic capacitances between the fixed and movable electrodes, C , is sense capacitance, and AC is the sense capacitance change when the proof- mass displacement, x , generates. The sense capacitance, C,, is given by

where the resonant frequency, (*, , is defined by

k w 2 + 2

ni (9) r I ,

(2) N I I , c, = &,t ~

d, The Eq.(8) is utilized for the signal-to-noise ratio, SNR, of the branched finger capacitive microaccelerometer

where E,, is the permeability of air around the sense element and t is the structure thickness. N , is the number of comb

between the combs. From Eq.(2), we can induce the sense overlap, I , is the comb overlap length and d, is the gap

[;;3, +[io? y ; ) Z ] ' I 2

capacitance change XYR = (10) 'Lr,

E tN A C = O x ( 3 ) From Eq.( lo), the resolution of the microaccelerometer

do is obtained as

The sensing voltage, V, , caused by the proof-mass displacement is then obtained by

From Eq.( 1 I ) , we can know that the electrical noise and the resolution decrease according to the sense voltage increases. Also? the Proposed branched finger capacitive microaccelerometer generates the self force-balancing effect caused by the branched finger electrode in Eq.(7), and achieves both the increased bandwidth in Eq.(9) and the

(4) .s. . 1; = y - r \ 2AC = c, i c, + c,. 4

where C,, is the parasitic capacitance between preamplifier positive input node and signal ground. y is defined:

2~,rl , N , I Y=- ( 5 ) improved resolution in Eq.( 1 I ) . do C, +C2 +C,,

MICROFABRICATION PROCESS

The branched finger capacitive microaccelerometer is fabricated using a single-mask deep RIE process, as shown

2 ~ ~ t N , V( 2c,,.v( , in Fig.3. The microaccelerometer is defined by the deep RIE etching of the top silicon layer of SO1 wafer, whose top silicon layer of 40+1 pm thickness is heavily doped with phosphorus (0.1n.cm). In Fig.3b, PR (PhotoResist: AZ5214) is coated and patterned to obtain a mask for the deep RIE etching. In Fig.3c, the microaccelerometer is

From Eq.(4), the electrostatic force, F , between the fixed and movable electrodes is obtained by

F = - (2- y ) p +- y -x (6) I , d" 4;

where c',,, = C,,., = Co1,2 . electrical stiffness is given by

From the above equation, the

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Table 1. Measured dimension of the microaccelerometer.

SusDension width. w 3.7 rum1 Structure thickness, t I 40 [ W I

Finger gap, do Suspension stiffness, k,*

Suspension length, I I 580 [ F I 1.8 [ P I

1.06 Ir\r/m]

Proof-mass, m I 51 [PSI TOQI initial caDacitance. C, I 2.4 rDF1

Overall size I 2 0 x 2 2 rmmxmml * Based on the E=l30 [GPa]

Bulh-silicon (40 pm)

riAu (200Ai2000A)

(b) Deep RIE process Fig.3 Single-mask fabrication process.

(d) Cr/ Au evaporation

defined by the deep RIE etching of the 40 pm-thick single crystalline silicon, followed by the removal of the 2 pm- thick buried oxide layer using BOE (Buffered Oxide Etchant) solution. The wafer, rinsed in isopropyl alcohol, has been dried in an infrared lamp for solving the sticking problem (Fig.3d). In Fig.3d, 200&2000A-thick Cr/Au layers are evaporated without mask to form electrode pads for gold wire bonding. Figures 4 and Table 1 show scanning electron micrographs and measured dimension of the fabricated microaccelerometer, respectively.

EXPERIMENTAL RESULTS AND DISCUSSION

The fabricated microaccelerometer is measured by the readout technique using the 250kHz anti-phase high- amplitude sense voltage copping method, as shown in Fig.5. The motion of the movable electrode of Fig.5 generates an electrostatic force opposing the motion, providing more simple and automated force-balancing scheme compared to the conventional force-balancing scheme [7] requiring additional negative electromechanical feedback loop. Figures 6a and 6b show the output signal and its power spectrum measured from the fabricated microaccelerometer for a IOHz, lg sinusoidal acceleration at the sense voltage, Vs, of 19V, respectively. The signal-to-noise ratio of 105dB (Fig.6b) demonstrates the detection resolution of 5.5pg/&. Other peaks observed at harmonic frequencies in Fig.6b are the noises generated by the electromagnetic exciter.

(a) (b) Figure 7 compares the measured and estimated noise Fig-4 Fabricated microacc~krometer: (a) top view; (b) components of the fabricated microaccelerometer for enlarged view of the branched finger electrodes. varying sense voltage. In Fig.7a, the total noise of

5.5pg/& has been measured at Vs=19V, resulting in a 220% noise reduction compared to that of 12.2pgl& measured at Vs=IV. The electrical noise has been reduced to 0.6pg/& at Vs=19V, showing an order of magnitude improvement compared to the electrical noise of 6pg/ & at Vs=l V. For the sense voltage higher than 1 V (Fig.7a and

Fig.5 Schematic of the readout technique for the 7b), the electrical noise of the microaccelerometer becomes microaccelerometer on an electromagnetic exciter. smaller than the constant mechanical noise level of

----_7-- 5.5pgi & . Figure 8 illustrates the self force-balancing effect of the branched finger electrodes for varying sense voltage. The electrostatic stiffness caused by the electrostatic balancing force has been increased to 6.09Nlm at Vs=19V from that of 1.06N/m at Vs=OV, thus producing additional stiffness at the rate of 0.014N/m/V' for the enhanced linearity and bandwidth of the microaccelerometer at the higher sense voltage. Figure 9 shows the measured

(a) (b) sensitivity and linearity of 0.638V/g and 0.044%, Fig.6 Output of the fabricated microaccelerometer measured respectively. Other measured performance of the at the sense voltage of I9V for a IOHz, Ig sinusoidal acceleration: (a) output signal; (b) power spectrum.

(0.

0 - 0 4

-0 6

Time [sec] Frequency [Hz]

microaccelerometer has been sumlnarized in Table 2.

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Detection range Resonant frequency

Resolution

Sensitivity I 0.638 [V/g] Linearity 0.044 [Yo]

f 2 [SI 1.73 [kHz]

5.5 [pg/JHz 3

0.019 [nm] Minimum detectable proof-mass displacement

I 10

d_-.-_-..___lA 2 ;o,L I 1 Sense voltage, Vs M

10 Sense voltage, Vs [VI

(a) (b) Fig.7 Measured and estimated noise levels of the microaccelerometer for varying sense voltage, Vs: (a) electrical and total noise; (b) mechanical noise.

mass based on deep RIE process of an SO1 wafer, and the electrical noise as low as 0 . 6 p g / G by using the high- amplitude sense voltage of 19V. In order to improve the nonlinearity caused from the high-amplitude sense voltage, we modified the conventional straight finger electrode into the branched finger electrode. We obtained the self force- balancing effect, which produce stiffness increase rate of 0.014N/m/V2 for enhanced linearity and bandwidth of the microaccelerometer. We also measured the sensitivity and linearity of 0.638V/g and 0.044%, respectively. Consequently, by the branched finger electrode with the high-amplitude sense voltage, we could be maintains proper bandwidth by induction of the self force-balancing effect, though the heavy proof-mass is used for reducing the mechanical noise, and also obtained good linearity.

ACKNOW LEDG EM ENTS

This work has been supported by the National Creative Research Initiative Program of the Ministry of Science and Technology (MOST) under the project title of “Realization of Bio-Analogic Digital Nanolocomotion.”

REFERENCES

Frequency [Hz]

o Measured fr ~~~ Eslimated fr

-_..-.- ._ 0 5 10 15

Sense voltage, Vs [V] (a) (b)

Fig.8 Frequency response of the microaccelerometer varying sense voltage, Vs: (a) amplitude response; resonant frequency response.

S e n s i M y = 0.638V/g] Lineanty = 0 044%

F 1 0 ,

! p j

for (b)

00 0 5 I O I 5 20

Acceleration [g] Fig.9 Microaccelerometer output for varying acceleration measured for 1 OHz acceleration at the sense voltage of 19V.

CONCLAJSIONS

We developed a high-resolution capacitive micro- accelerometer using the branched finger electrodes with the high-amplitude sense voltage. We reduced the mechanical noise to the level of .5..5pg/& by increasing the proof-

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[7] W. tiuehnel, S. Sherman, “A Surface Micromachined Silicon Accelerometer with On-chip Detection Circuitry,” Sensors and Actuators, A 45, pp.7-16, 1994.

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