Lead zirconate titanate MEMS accelerometer using interdigitated electrodes

Sensors and Actuators A 107 (2003) 26–35

Lead zirconate titanate MEMS accelerometer using interdigitated electrodes Han Geun Yu a , L. Zou b , K. Deng b , R. Wolf c , S. Tadigadapa a,∗ , S. Trolier-McKinstry c a

c

Department of Electrical Engineering, Pennsylvania State University, University Park, PA 16802, USA b Wilcoxon Research Inc., Gaithersburg, MD, USA Department of Material Science and Engineering, Pennsylvania State University, University Park, PA 16802, USA Received 6 April 2003; received in revised form 18 June 2003; accepted 19 June 2003

Abstract Piezoelectric bulk micromachined accelerometers have been designed and fabricated using silicon micromachining techniques. These devices use interdigitated (IDT) electrodes to exploit a combination of the d33 and d31 piezoelectric responses of lead zirconate titanate (PZT) thin films. A simple fabrication process involving only three photomasks and two deep-trench reactive ion-etching (DRIE) steps has been developed. Frequency response measurement has been used to measure the sensitivity of the devices as well as the bandwidth. Voltage sensitivities in the range of 1.3–7.86 mV/g with corresponding resonance frequencies in the range of 23–12 kHz have been obtained for these accelerometers. The voltage sensitivity mode of the interdigitated electrode accelerometer results in a higher acceleration sensitivity than that for a through-the-thickness poled PZT accelerometers with identical device structure. © 2003 Elsevier B.V. All rights reserved. Keywords: MEMS Accelerometer; Lead Zirconate Titanate (PZT); Interdigitated Electrode; Piezoelectric Accelerometer

1. Introduction Commercialization of high-performance, low cost, microelectromechanical (MEM) accelerometers for automotive applications has motivated the interest in utilizing similar devices in consumer products, biomedical devices, industrial monitoring, and military applications, which require large bandwidth and high-sensitivity [1]. Of the various types of accelerometers, piezoelectric accelerometers offer high-Q (80–100), high output impedance, and low damping [2–4]. ZnO [5], AlN [6] and lead zirconate titanate (PZT) [6,7] films have been employed in piezoelectric microaccelerometers and microsensors. Of these, PZT films exhibit the highest piezoelectric coefficients and therefore offer the opportunity for highest sensitivity. The piezoelectric coefficients of thin film PZT are an order of magnitude larger than those of ZnO and AlN [6]. In PZT, the magnitude of the piezoelectric coefficient varies with the angle between the applied stress and the poling direction. In a typical accelerometer, the small out-of-plane motion of the proof mass results in the development of an in-plane stress in the accelerometer sensing membrane. In the case where ∗ Corresponding author. Tel.: +1-814-865-2730; fax: +1-814-865-7065. E-mail address: [email protected] (S. Tadigadapa).

0924-4247/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0924-4247(03)00271-1

the PZT film is poled through-the-thickness of the film, the applied stress and poling directions are perpendicular and results in the d31 -mode response. However, if the PZT film is poled in the plane of the film, the in-plane stress and poling direction can be made to coincide resulting in the d33 -response. For PZT films, the typical d33 piezoelectric coefficient is two to three times larger than the d31 piezoelectric coefficient. In this work, bulk micromachined accelerometers were designed and fabricated using silicon microfabrication methods. The devices utilized interdigitated (IDT) electrodes to achieve in-plane poling of the PZT films for exploiting the d33 -mode of operation [8]. A simple fabrication process involving only three photomasks along with two deep-trench reactive ion-etching (DRIE) steps was developed to fabricate the accelerometers.

2. Accelerometer design In this work, an annular diaphragm design reported earlier was chosen (see Fig. 1) [7]. The annular structure has a proof mass of radius r1 (which was chosen to be 1 mm); this also corresponds to the inner radius of the diaphragm while the outer radius of the diaphragm is r2 . For small proof mass deflections, if E is the Young’s modulus of the diaphragm

H.G. Yu et al. / Sensors and Actuators A 107 (2003) 26–35

27

Fig. 1. Design of the interdigitated electrodes and the accelerometer: (a) shows the mask layout of the two capacitors located at the inner and outer edges of the annular diaphragm and the three electrodes that are utilized for collecting charge separately, and (b) schematic cross-sectional view of the accelerometer. r1 and r2 are outer and inner radii of the diaphragm, respectively.

material, ν is the Poisson’s ratio; the spring constant of the diaphragm structure can be written as [9–11]
    −1 r12 r12 F 8πD 1 r2 2 k= = 2 1− 2 −2 2 ln wmax 2 r1 r2 r2 r2 − r12 (1) where D is the flexural rigidity of the diaphragm and is defined as D=

Eh3 12(1 − ν2 )

(2)

Assuming the outer radius of the diaphragm to be 2 mm and a wafer thickness of 460 ␮m, the required thickness of the membrane for a 20 kHz fundamental resonance was determined to be 31.5 ␮m. Silicon’s Young’s modulus of 160 × 109 Pa, and Poisson’s ratio of 0.28 were used in the above calculation. Comparable calculations were made for several diaphragm radii. Since the basic accelerometer structure was optimized to result in a large bandwidth, the sensitivity is expected to be comparatively small. In order to obtain a high-sensitivity from the accelerometer, it is therefore necessary both to

use a high piezoelectric coefficient material, and to use the coefficients efficiently. Dense PbZr0.52 Ti0.48 O3 (PZT) films have d31 and d33 piezoelectric coefficients of about −45 and 120 pC/N [12,13]. As can be seen from these values, the d33 coefficient is desirable. For the annular design here, out-of-plane deflection of the proof mass in response to an acceleration will result in both radial and tangential stresses in the plane of the diaphragm. Thus, interdigitated electrodes enable use of both d33 and d31 coefficients. Use of interdigitated electrodes offers several other advantages in a sensor. Since the spacing of the electrodes rather than the thickness of the PZT film (for d31 -mode) determines the capacitance of the device, the impedance of the accelerometer can be easily optimized by varying the electrode spacing. The PZT film thickness can now be chosen to be as thin as is practical to get good, repeatable piezoelectric properties. Because the voltage sensitivity is the charge sensitivity divided by the capacitance of the device, the low capacitance of the interdigitated structure increases the voltage sensitivity of the accelerometer. Although the voltage noise of the accelerometer goes up as the inverse of the square root of the capacitance, the voltage signal-to-noise ratio (SNR) still increases as the inverse of

28

H.G. Yu et al. / Sensors and Actuators A 107 (2003) 26–35

10

Stress (kPa)

5

0 1

1.2

1.4

1.6

1.8

2

Radius (mm) -5

-10

-15 Fig. 2. Stress distribution along the radial direction of the diaphragm with a rigid center. The inner radius is 1 mm and outer radius is 2 mm, and a diaphragm thickness of 31.5 ␮m has been used in this calculation for a force of 1 g applied on the proof mass.

the square root of capacitance as the capacitance is decreased [14]. The radial stress (σ r ) in the annular diaphragm is plotted in Fig. 2. For a given annular diaphragm dimensions, it can be seen that the stress maximum occurs at the inner radius r = r1 and is 57% more than the stress at the outer radius. The tangential stress, σ t, where the electrodes lie, can be approximated as σt = νσr

(3)

near the edges of the diaphragm [7]. It can also be seen from Fig. 2 that the stress induced by the applied acceleration has opposite signs along the radial direction in the diaphragm near the proof mass and near the frame. Therefore, to maximize the sensor output, two separate interdigitated electrode capacitors must be located in the vicinity of the two clamped edges of the diaphragm where maximum stresses occur. These separately located capacitors collect charge independently. As described previously [7], due to the opposite sign of the stress at the location of the two capacitors, the PZT must be poled in opposite directions such that the charge accumulated in each capacitor has the same polarity. For efficient charge collection, several pairs of electrodes forming capacitors connected in parallel over an area of the diaphragm are more efficient than a single capacitor over the same area. This is mainly because smaller inter-electrode spacing allows for more efficient poling of the piezoelectric material while multiple capacitors increase the total charge collecting area.

3. Fabrication The interdigitated PZT MEMS accelerometers were fabricated using three masks. The process required one

front-to-back side alignment and two DRIE steps. The three mask levels consist of top electrode definition, backside accelerometer frame (die size) definition, and backside proof mass area definition. The fabrication process flow is shown in Fig. 3. Diameter 4 in., n-type 1 0 0 (1–10 cm), double-side-polished, silicon wafers having 0.5 ␮m SiO2 layers on them were used in this work. A 0.5 ␮m thick ZrO2 layer followed by a 0.6 ␮m thick PZT layer was deposited by a sol–gel process [15]. The top metal layers of Cr (20 nm) and Au (120 nm) were deposited via electron-beam and thermal evaporation, respectively on top of the PZT layer. All of the processes until this step are performed as blanket depositions. The first photolithography step is a front-to-backside alignment. After development, the top Au and Cr layers were etched using a RIE etch process to form the interdigitated capacitors on top of the PZT. In the fabrication of these devices the PZT and ZrO2 layers were not patterned. Instead, backside DRIE etch was used to define the accelerometer. AZ4620 photoresist was spun up to a thickness of ∼13 ␮m to define the die frames, diaphragms, and proof masses of the annular structures. The first DRIE step performed in the accelerometer frame areas determined the final thickness of the diaphragms. The etch was performed for 25 min and resulted in an etched depth of 30±1.5 ␮m. This was followed by a buffered oxide etch (BOE) to remove the patterned oxide on the diaphragm areas, after which a second DRIE step was used to etch through the wafer in the frame areas (Fig. 3). Visual end point detection was used. The deep reactive ion etch over a wafer is not uniform and tends to etch the edges of the wafer much faster than the center of the wafer in a radially symmetric pattern. The etch rate varied by as much as 5–7% for the process conditions used [7]. Therefore, for a through wafer-etch, the thickness of the diaphragms produced was found to vary by as much as

H.G. Yu et al. / Sensors and Actuators A 107 (2003) 26–35

29

Fig. 3. Schematic illustration of the fabrication process.

20–35 ␮m across the wafer. Fig. 4 shows optical images of the fabricated accelerometers.

4. Measurements Remanent polarization and coercive field of the PZT thin films were obtained from P–E hysteresis measurement. For the P–E hysteresis measurement, an RT66A standardized ferroelectric test system in the virtual ground testing mode was used. A remanent polarization of ∼16 ␮C/cm2 and coercive field of ∼35 kV/cm were obtained for the sol–gel deposited PZT thin films, suggesting some process damage to the piezoelectric.

Frequency response measurements were made using a calibrated reference sensor with a bandwidth of >25 kHz. A schematic of the setup is shown in Fig. 5. An electromagnetic shaker generated the mechanical acceleration. The accelerometer under test was glued with thick grease on top of the reference accelerometer, which in turn was mounted firmly on the shaker table. The test accelerometers were packaged on a ceramic substrate. During packaging of the sensor, a little space between the proof mass of the accelerometer and the ceramic package substrate was left to minimize the effect of squeeze damping effect arising from surrounding air. Therefore, small epoxy pedestals were made on the package using the glue before mounting the sensor on the substrate. The output signals from both

30

H.G. Yu et al. / Sensors and Actuators A 107 (2003) 26–35

mathematically, Vtest (ω) 10Htest (ω)P(ω) 10Htest (ω) R(ω) = = = Vref (ω) Href (ω)P(ω) Href (ω)

Fig. 4. Optical picture of the accelerometer: (a) the front side with the interdigitated electrodes (see inset), and (b) shows the proof mass and the accelerometer frame.

the test accelerometer and reference accelerometer were analyzed using a SR 785 dynamic signal analyzer. Before the signal was connected to the analyzer, the charge signals from the test accelerometer and the reference accelerometer were converted to voltage signals. The signal from the accelerometer under test was amplified by a factor of 10. Since the input force function from the shaker table was common to both the reference and test accelerometers, the measured voltage ratio is a direct measurement of the Sensitivity function H(ω) of the test accelerometer. Expressed

(4)

where R(ω) is the relative response function. The calibrated sensitivity of the reference sensor was 0.43 pC/g. The absolute sensitivity was then calculated. Fig. 6 shows the ratio of the output of the test accelerometer to the output of the reference accelerometer in the frequency range of 1000–30,000 Hz. The sensitivity figure was extracted from the flat low frequency region. Results from the measurements showed a charge sensitivity in the range of 0.13–0.67 pC/g. The frequency response also shows the resonance frequency peak. For, linearity measurement, a lock-in-amplifier was used for measuring the output voltage of the reference and the MEMS accelerometers. With the input drive signal of the shaker table fixed at a frequency of 1 kHz, the input acceleration was gradually increased. Fig. 7 shows the output of the accelerometer is linear in the 0–1.5 g acceleration range and the slope of the straight line fit gives an average sensitivity of 5.11 mV/g which compares quite well with the sensitivity value of 5.3 mV/g calculated from the frequency response measurement. The frequency dependent impedance of the interdigitated capacitors was measured using an HP 4194A impedance analyzer at an excitation voltage of 0.5 V. Fig. 8 shows a typical impedance measurement result. The values of the resonance frequency measured using this technique were within 5% of the values measured from the frequency response measurements. The piezoelectric coefficients are temperature dependent in PZT films. Therefore, changes in temperature are expected to manifest as output signals. In order to experimentally measure the temperature dependence of the signal output on temperature, the frequency response measurement was performed inside a chamber, the temperature of which could be varied between 0 and 100 ◦ C. The frequency response measurement was performed at five different temperatures and the accelerometer along with the shaker table was allowed enough time at each temperature to reach temperature

Fig. 5. Schematic of the setup for the frequency response measurement, A and B are charge amplifiers. The reference accelerometer and the test accelerometer are mounted on top of each other.

H.G. Yu et al. / Sensors and Actuators A 107 (2003) 26–35

31

Fig. 6. Frequency response of an accelerometer with a resonance frequency of 24.1 kHz and sensitivity of 0.53 pC/g.

10

Output voltage (mV)

9

Output Voltage (mV)

8 Sensitivity (mV/g)

7

8 7

6

6

5

5

4

4

3

3

2

fresonance

Slope=5.11mV/g

Sensitivity (mV/g)

9

2

1

1

0

0 0

0.5

1

1.5

2

Acceleration(g)=x9.81m/s2

Fig. 7. Acceleration versus voltage output at 1 kHz. The plot shows the linearity of the MEMS accelerometer. Error is in the range of 8%.

equilibrium. The measurement performed on a single accelerometer showed ∼0.3%/◦ C sensitivity variation in the 0–100 ◦ C temperature range.

5. Discussion 5.1. Frequency response of the accelerometers Since the accelerometer can be represented as a simple spring mass system, the resonance frequency of the accelerometer can be given by



k M  (8πD/r22 )[(1/2)(1 − (r12 /r22 )) 1 −2(r12 /(r22 − r12 ))(ln(r2 /r1 ))2 ]−1 = 2π M 1 = 2π

(5) where M is the mass of the accelerometer proof mass. To compare the experimentally measured resonance frequencies with those predicted using Eq. (5), the devices with the same r1 /r2 ratios were separated. Fig. 8 shows the results of the measured and predicted resonance frequencies. A closer look at the two graphs shows that the measured resonance frequencies for all the devices are slightly higher than those predicted, even after accounting for a membrane thickness error of ±3 ␮m. It is known that when ZrO2 /PZT thin films are deposited on oxide coated silicon wafers using chemical solution deposition, a tensile stress is generated in these films. For 2 ␮m thick film-stacks the magnitude of this stress has been measured to be ∼100 MPa [16]. A tensile stress in the diaphragm arising from these tensile layers is expected to increase the resonance frequency of the accelerometer. To account for the net in-plane internal tensile stress σ, the superposition principle was used whereby an additional term to the bending resistance due to internal stress was added. It was found that this resulted in a very minor change (∼0.5%), implying that for a 20–35 ␮m thick silicon membrane, with 2 ␮m thick 100 MPa tensile ZrO2 /PZT layer, the overall

32

H.G. Yu et al. / Sensors and Actuators A 107 (2003) 26–35

Resonance Frequency (kHz)

26 Experimentally Measured Theoretically Predicted Resonance Frequency with residual stress Resonance Frequency with reduced diaphragm

24 22 20 18 16 14 12 10 17

22

32

37

Experimentally Measured Theoretically Predicted Resonance Frequency with residual stress Resonance Frequency with reduced diaphragm

26 Resonance Frequency (kHz)

27 Membrane Thickness (um)

(a)

24 22 20 18 16 14 12 16

(b)

18

20

22 24 26 Membrane Thickness (µm)

28

30

Fig. 8. Resonance frequency vs. membrane thickness plot (a) for r1 /r2 = 1.8 and (b) r1 /r2 = 2.0 devices. As can be seen from Eq. (5), the resonance frequency varies as h1.5 . Resonance frequencies considering residual stress in the PZT film and non-uniform thickness are also plotted. The dashed line is a linear fit to the measured resonance frequency data.

stiffness of the structure is dominated by the flexural rigidity of the plate rather than by the stress in the film layers. Observation of the diaphragms from the etched side of the plate revealed that the thickness of the annular diaphragms was not uniform in the radial direction. A flattened arch shaped variation in the thickness of the diaphragm was observed in the radial direction as shown in the optical interferometer profile of the diaphragm in Fig. 9. The optical interferometer profile shows that thickness variation across the membrane is at least 20 ␮m. Also it was observed that at the edges of the diaphragm no thickness data could be measured. This normally indicates that the gradient of the slope in this edge region is increasing very rapidly and therefore has the effect of reducing the width of the annular diaphragm. From Fig. 9, this reduction in the width (r2 − r1 ; Fig. 1) of the annular diaphragm is ∼100 ␮m (50 ␮m from each edge). The resonance frequency was predicted using

the corrected values of r1 and r2 and ignoring the ∼20 ␮m of thickness variation over the width of the diaphragm. A comparison of the predicted resonance frequencies versus thickness using the corrected values of diaphragm radius is also plotted in Fig. 8. The reduced diaphragm radius model predicts the resonance frequency within experimental error. 5.2. Sensitivity of the accelerometers In order to predict the sensitivity, the average values of the radial stress and tangential stress at each capacitor location, arising from 1 g of force acting on the proof mass, were calculated. The total charge Q generated from 1 g of force is given by   Q= Qi = (d33 σr,i + d31 σt,i )Ai (6) i

i

H.G. Yu et al. / Sensors and Actuators A 107 (2003) 26–35

33

Fig. 9. Surface profile of the etched side of the accelerometer membrane. As can be seen the diaphragm has a flattened arch shaped in cross-section with (A) 20 ␮m thicker than the middle of the membrane (B). The thickness profile at the edges of the diaphragm could not be obtained and is estimated to be about 0.05 mm.

It should be noted that because the d33 and d31 coefficients have opposite signs, the two contributions partially cancel. In Fig. 10, the sensitivity calculated using the expression above is compared with the measured sensitivity as a function of 1.2 Measured sensitivity

1

Sensitivity (pC/g)

Predicted sensitivity in d33 model 0.8 0.6 0.4 0.2 0 18

23

28

33

Thickness (um)

(a) 1.2

Measured sensitivity

Sensitivity (pC/g)

Predicted sensitivity with d33 model

0.8

0.4

0 16

(b)

21

26

31

Thickness (um)

Fig. 10. Comparison between measured sensitivity and predicted sensitivity: (a) r1 /r2 = 1.8; (b) r1 /r2 = 2.0.

thickness for the two types of accelerometers. In general, the measured sensitivity is higher than the predicted values and is overall a surprising result since any imperfections in the PZT film and misalignments are expected to only lower these values. The remnant polarization of the PZT film in this work, which is much lower than that in similar PZT film, shows that there are problems in the processing of the electrode. Although the discrepancy between the observed sensitivity and the predicted sensitivity could not be exactly quantified, these differences are thought to arise due to three main reasons namely: (i) the assumption that the piezoelectric material under the electrode area was “dead” and does not contribute to the output signal, (ii) imperfect mounting of the accelerometer resulting in actuation of higher modes of vibration, and (iii) local imperfections. In this work, the areas under the electrode were treated as dead areas (not contributing to the output signal). Since the total area under the electrode is comparable to the total spacing area, some errors in the predicted sensitivities can be expected by ignoring the contributions from the “dead areas”, if these were at all piezoelectrically active. Additionally, cross-sensitivity measurement on the accelerometers showed ∼4 times bigger values than that of the d31 mode accelerometers with identical mechanical design and dimensions [7], which may imply that the accelerometers was not mounted properly. The effect of a tilted accelerometer is considered as one of the factors which causes high cross-sensitivity and variability in the overall sensitivity in the various accelerometers. When acceleration is imparted at some arbitrary angle with respect to the normal direction of the accelerometer, the movement of the proof mass results in a more complicated stress profile. Also, local non-uniformities (notches) were observed in the diaphragm. These irregularities were formed on the backside of the diaphragm during DRIE step. These non-uniformities are expected to cause concentrated local stresses, which can result in high-sensitivity.

34

H.G. Yu et al. / Sensors and Actuators A 107 (2003) 26–35

Table 1 Comparison of the capacitance, charge sensitivity, voltage sensitivity of the d33 - and d31 -mode accelerometers with similar resonance frequencies r1 /r2 ratio

d31 -mode of operationa

IDT electrodes Resonance frequency (kHz)

Capacitance (pF)

Sensitivity (pC/g or mV/g)

Resonance frequency (kHz)

Capacitance (nF)

Sensitivity (pC/g or mV/g)

0.55

15.8 17.1

102 91.5

0.514 (5.3) 0.486 (4.8)

12.3 17.8

2.5 2.5

1.53 (0.61) 0.5 (0.20)

0.5

15.5 23.1

78 78

0.613 (6.5) 0.53 (6.0)

21.1 22.0

2 2

0.53 (0.21) 0.47 (0.19)

a

Calculated from [16].

6. Comparison between d 31 - and IDT-accelerometers In order to compare the performance of d31 - and interdigitated-mode accelerometers, devices with identical proof mass and diaphragm shape and dimensions with parallel plate capacitor configuration (d31 -mode) and interdigitated capacitor configuration were fabricated. Table 1 compares the capacitance, charge and voltage sensitivity of interdigitated and d31 -mode accelerometers with similar resonance frequencies. As can be seen from Table 1, the capacitance of the d33 -mode accelerometers was about 20 times smaller than the capacitance of the d31 -mode accelerometers. This difference was achieved by using 10 ␮m interdigitated electrode spacing in the interdigitated-mode accelerometers and ∼10 concentric ring capacitors connected in parallel. The results on the d31 -mode accelerometers used here for comparison are from the earlier reported results by Wang et al. [7,17]. The charge sensitivity of the interdigitated-mode accelerometers is similar to d31 -mode accelerometers. It can also be seen from Table 1 that for devices with similar resonance frequencies (implying accelerometers with similar membrane thickness) those operating in the interdigitated-mode show ∼20 times higher voltage sensitivities. The high voltage sensitivity is due to the ∼20 times smaller capacitance of the interdigitated-mode accelerometers (since voltage sensitivity = charge sensitivity/device capacitance) as compared to the d31 -mode accelerometers. In terms of signal-to-noise ratio (SNR) the performance of the interdigitated-accelerometers is therefore superior to that of the d31 -accelerometers. This is because the voltage noise of the accelerometer goes up as the inverse of the square root of the capacitance, while the voltage signal increases as the inverse of the capacitance resulting in a net increase in SNR as the inverse square root of the capacitance. Therefore the SNR of the interdigitated-mode accelerometer is ∼4.5 times greater than the d31 -mode accelerometer. 7. Conclusions In this paper, a novel PZT microelectromechanical accelerometer using interdigitated electrodes was fabricated and presented. Compared with d31 -mode accelerometer

with the same structure, the interdigitated electrode accelerometer was ∼10 times better in voltage sensitivity. The resonance frequency of the accelerometers was explained by using the bending stiffness model for a circular plate with a rigid center. Correction to the size of the annular diaphragm size arising due to etch non-uniformity accounted for the observed difference between the observed and measured resonance frequencies. Contributions from these two modes were considered to predict the sensitivity of the accelerometer assuming the proof mass was deflected perfectly out-of-plane. However, this model underestimated the overall sensitivity. The discrepancy between the observed sensitivity and the predicted sensitivity could not be exactly quantified and was thought to arise due to three main reasons namely: (i) the assumption that the piezoelectric material under the electrode area was “dead” and does not contribute to the output signal, (ii) imperfect mounting of the accelerometer resulting in actuation of higher modes of vibration, and (iii) local imperfections. An improved fabrication process resulting in a more uniform membrane thickness and understanding of the poling efficiency and direction throughout the PZT film in the electroded area is required for further investigation into the performance of these devices and will be continued as part of future work in this area.

Acknowledgements The project was funded by grants from the National Institute of Standards and Technology WR-ATP-0001 and the National Science Foundation DMR-0102808.

References [1] N. Yazdi, F. Ayazi, K. Najafi, Micromachined Inertial Sensors, Proc. IEEE 86 (8) (1998) 1640–1659. [2] A. Partridge, J.K. Reynolds, B.W. Chui, E.M. Chow, A.M. Fitzgerald, L. Zhang, N.I. Maluf, T.W. Kenny, A high-performance planar piezoresistive accelerometer, J. Microelectromech. Syst. 9 (1) (2000) 58–66. [3] N. Yazdi, K. Najafi, An all-silicon single-wafer micro-g accelerometer with a combined surface and bulk micromachining process, J. Microelectromech. Syst. 9 (4) (2000) 544–550.

H.G. Yu et al. / Sensors and Actuators A 107 (2003) 26–35 [4] A. Iula, N. Lamberti, M. Pappalardo, Analysis and experimental evaluation of a new planar piezoelectric accelerometer, IEEE/ASME Trans. Mechatron. 4 (2) (1999) 207–212. [5] D. DeVoe, A.P. Pisano, Surface micromachined piezoelectric accelerometers (PiXLs), J. Microelectromech. Syst. 10 (2001) 180–186. [6] P. Muralt, PZT thin films for microsensors and actuators: where do we stand? IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 47 (4) (2000) 903–915. [7] L.-P. Wang, K. Deng, L. Zou, R. Wolf, R.J. Davis, S. TrolierMcKinstry, Microelectromechanical systems (MEMS) accelerometers using lead zirconate titanate thick films, IEEE Electron Device Lett. 23 (4) (2002) 182–184. [8] B. Xu, Y. Ye, J.J. Bernstein, R. Miller, L.E. Cross, Dielectric hysteresis from transverse electric fields in lead zirconate titanate thin films, Appl. Phys. Lett. 74 (23) (1999) 3549–3551. [9] W. Griffel, Plate Formulas, Frederick Ungar Publishing Co., Inc. New York, 1968. [10] S. Senturia, Microsystem Design, Kluwer Academic Publishers, Dordrecht, 2000. [11] H. Yu, Interdigitated electrode MEMS PZT accelerometer, M.Sc. thesis, The Pennsylvania State University, University Park, PA, 2002. [12] J.F. Shepard Jr., F. Chu, I. Kanno, S. Trolier-McKinstry, Characterization and aging response of the d31 piezoelectric coefficient of

[13]

[14] [15]

[16]

[17]

35

lead zirconate titanate thin films, J. Appl. Phys. 85 (9) (1999) 6711– 6716. F. Chu, F. Xu, J. Shepard Jr., S. Trolier-McKinstry, Thickness dependence of the electrical properties of sol–gel derived lead zirconate titanate thin films with (1 1 1) and (1 0 0) texture, in: MRS Proceedings on Ferroelectric Thin Films V, vol. 493, 1998, pp. 409– 414. A. Van der Ziel, Noise in Measurements, Wiley, New York, 1976, pp. 160–174. R.A. Wolf, Temperature dependence of the piezoelectric response of lead zirconate titanate films for MEMS applications, M.Sc. thesis, The Pennsylvania State University, University Park, PA, 2001. E. Hong, S.V. Krishnaswamy, C.B. Freidhoff, S. Trolier-McKinstry, Fabrication of piezoelectric diaphragm using lead zirconate titanate (PZT) films, in: A.A. Ayon S.M. Spearing, T. Buchheit, H. Kahn (Eds.), Materials Science of Microelectromechanical Systems (MEMS) Devices IV, Material Research Society Proceedings, vol. 687, Warrendale, PA, 2002. L.-P. Wang, R. Wolf, Y. Wang, K. Deng, L. Zou, R.J. Davis, S. Trolier-McKinstry, Design, fabrication, and measurement of high-sensitivity piezoelectric microelectromechanical systems accelerometers, J. Microelectromech. Syst., in press.