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DESIGN AND SIMULATION OF A NOVEL OPERATION MODE OFINTEGRATED FERROELECTRIC MICRO-SENSORSChao Wang a; Zheyao Wang a; Tianling Ren a; Litian Liu a

a Institute of Microelectronics, Tsinghua University, Beijing, P. R. China

Online Publication Date: 01 November 2006

To cite this Article Wang, Chao, Wang, Zheyao, Ren, Tianling and Liu, Litian(2006)'DESIGN AND SIMULATION OF A NOVELOPERATION MODE OF INTEGRATED FERROELECTRIC MICRO-SENSORS',Integrated Ferroelectrics,78:1,59 — 67

To link to this Article: DOI: 10.1080/10584580600657294

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Integrated Ferroelectrics, 78: 59–67, 2006

Copyright © Taylor & Francis Group, LLC

ISSN 1058-4587 print / 1607-8489 online

DOI: 10.1080/10584580600657294

Design and Simulation of a Novel Operation Modeof Integrated Ferroelectric Micro-Sensors

Chao Wang, Zheyao Wang,∗ Tianling Ren, and Litian Liu

Institute of Microelectronics, Tsinghua University, Beijing 100084, P. R. China

ABSTRACT

This paper presents the design, modeling, and simulation of Lead Zirconate Titanate(PZT) based micro-sensors. The PZT thin film is polarized in-plane in stead of through-thickness, and thus utilizes d33 working mode other than d31 working mode. Micro-sensors using cantilever structures and InterDigital Electrodes (IDE) are numericallyanalyzed by Finite Element Analysis (FEA) method. The relation between the sen-sitivity and the IDE configurations is presented, and some results and conclusionscan be used as future design guidelines. The simulation results show that the volt-age sensitivity of micro-sensors utilizing d33 mode can be several times or even tenstimes higher than those utilizing conventional d31 mode. The high sensitivity togetherwith the ease of fabrication makes micro-sensors using d33 mode more competitive andattractive.

Keywords: Integrated ferroelectric micro-sensors; Lead Zirconate Titanate (PZT);finite element analysis; d33 working mode; in-plane polarization; interdigital electrodes

1. INTRODUCTION

Ferroelectric materials, such as Pb(Zrx,Ti1−x)O3 (PZT), have been comprehen-sively utilized in integrated ferroelectric micro-sensors and micro-actuators.Most of these micro-sensors use through-thickness polarized ferroelectric filmsand operate in d31 mode to convert mechanical loads into electrical signals [1, 2].Recently, in-plane polarized ferroelectric films have been proposed to developsmart devices [3–7], including micro-actuators [8], micro-switches [9, 10],micro-accelerometers [11], micro-transducers [12], and micro-transducer ar-rays [13]. The sensitivity of micro-sensors utilizing d33 mode can be several

Received April 17, 2005; in final form January 23, 2006.∗Corresponding author. E-mail: z.wang@tsinghua.edu.cn

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times or even tens times higher than that of conventional ones utilizing d31

mode [3, 5, 13]. There are two main reasons for the sensitivity improvement.First, higher piezoelectric coefficient can be utilized because d33 is at least twotimes of d31 for commonly used ferroelectric materials. Second, the sensitivityof micro-sensors utilizing d33 mode depends strongly on the configurations andthe sizes of the top electrodes, and thus it is possible to optimize sensitivity bychanging the top electrodes patterns other than the thickness of the ferroelectricfilms, making the design more flexible.

With the development of such kind of micro-sensors, it is necessary to an-alyze the behaviors of d33 mode based micro-sensors to obtain optimal designs.However, theoretical and numerical analyses have seldom been addressed dueto the complexity and novelty of the in-plane polarization. Bernstein et al. pro-posed a lumped element equivalent circuit for modeling d33 mode based trans-ducers [13], and Gross proposed a model to describe the electric field propertiesof such kind of PZT films [10]. Considering that Finite Element Method (FEM)is more convenient than theoretical method in analyzing complex structures andthat accurate FEM models for ferroelectric films using d33 mode are not avail-able yet, this paper presents the FEM simulations and analyses of ferroelectricmicro-sensors using d33 mode to design and optimize the performance.

2. STRUCTURES AND PROPERTIES OF INTEGRATEDFERROELECTRIC FILMS

According to the “IEEE Standard on Piezoelectricity” [14], the Z coordinateaxis in modeling is chosen to be parallel to crystallographic c axis of PZTcrystal, i.e. the polarization direction, to make the piezoelectric coefficient d33

a positive value, which means that tension in the Z axis will generate a potentialdifference with its positive terminal on the +Z face. The X axis and Y axisfollow the right-handed coordinate rule.

2.1 d31 Mode Based Ferroelectric Films

The schematic view of a d31 mode based micro-sensor is given in Fig. 1(a). ThePZT film is sandwiched between top and bottom electrodes, and the electric fieldis constrained in PZT film because of the large permittivity of PZT comparedwith surrounding materials. The electric field is parallel to the polarization, andnormal to the surface of the PZT film. Accordingly, the Z axis is along thepolarization to ensure d33 a positive value.

2.2 d33 Mode Based Ferroelectric Films

The schematic view of d33 mode based micro-sensor is given in Fig. 1(b). Theelectric filed is also constrained in the PZT film, but the field distribution, as

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Figure 1. Schematic view of a micro-sensor utilizing (a) d31 mode (b) d33 mode.

shown in Fig. 2, is quite different from that of d31 mode based structures [3,6, 13, 15]. The accurate model for the piezoelectric properties of PZT filmis difficult to obtain since the electric field distribution and the polarizationdistribution of PZT are very complex. In Gross’s model [10], as shown inFig. 3(a), the electric fields beneath the top electrodes are neglected and thePZT films in these regions are simplified to pure elastic materials, while thefields in other regions are assumed to be parallel to the surface of PZT. However,when a polarization voltage is applied on the electrodes, the regions beneaththe electrodes are polarized mainly vertically due to the coupling effects ofparasitical capacitances. Considering this effect, the authors propose a novelmodel as shown in Fig. 3(b).

3. FEA MODEL CHARACTERIZATION

A three-layer cantilever structure is modeled, as shown in Fig. 4. The structureconsists of a supporting layer of SiO2, a layer of ferroelectric Pb(Zr0.52, Ti0.48) O3

film, and a layer of platinum top electrodes (silicon substrate and buffer layerare neglected for simplification). The Z axis is chosen in-plane to make d33

positive, and the X axis is perpendicular to the PZT film surface. The plateis clamped at the end where Z = 0, and the electrode at the clamped end isused as output to obtain large sensitivity because of the stress concentrationthere. One pair of electrodes or interdigital electrodes are positioned from the

Figure 2. Schematic view of electric field distribution of d33 mode based PZT film.

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Figure 3. Electric field distribution model of d33 mode based PZT film proposed by:(a) S. J. Gross (b) the authors.

clamped end to the free end. A 1000-Pa pressure is applied on the surface whereX = 0, and the electric potential of the electrode near the free end is fixed aszero.

ANSYS is used for simulation, and the material constants used in simula-tion are from published literature [16, 17]. The plate length and beam width areboth 250 µm; and the thickness of PZT, SiO2, and Pt are 0.5, 1, and 0.2 µm,respectively. The electrode gap g, electrode width d, and the interdigital elec-trode number N are variables in the simulation. In the following analysis, theboundary conditions and plate dimensions are kept unchanged.

According to [15], PZT film can be divided into several different re-gions as shown in Fig. 4, and this is confirmed by our simulation resultsshown in Fig. 5. Therefore, different material properties and element typesare used to model PZT in these regions, and the element types are listed inTable 1.

Regions A and E are active regions that contribute to charge accumulationand hence dominate the sensitivity; region B is basically inactive; and regionsC and D are transitional regions that do not affect the sensitivity much.

(1) Region A: the material is polarized along +Z axis; and the material prop-erties are the same as that of d31 model.

Figure 4. Micro-sensor model for FEA with: (a) one pair of electrodes (b) interdigitalelectrodes.

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Figure 5. Electric field distribution calculated by FEA (g = 50 µm and d = 30 µm).

(2) Region B: the material is un-polarized and thus non-ferroelectric; and henceonly mechanical properties are considered.

(3) Region C: the material is polarized along +X axis; and the material prop-erties can be derived from transforming material matrixes of region A by90 degrees.

(4) Region D: the material is polarized along −X axis; and the material prop-erties can be derived from transforming material matrixes of region A by270 degrees.

(5) Region E: this region is for IDE structures only; the material is polarizedalong −Z axis, and the material properties can be derived from transformingmaterial matrixes of region A by 180 degrees.

Table 1Element types for FEA model

Material SiO2 Pt PZT (Regions A, C, D, and E) PZT (Region B)

Element type 45 41 5 64

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4. DESIGN AND OPTIMIZATION

4.1 Sensitivity Dependence of Micro-Sensor with Only One Pairof Electrodes

Since the polarization voltage increases linearly with electrode gap g, over-highpolarization voltage would be required when g is too large, and the air may evenbe broken down. Therefore, the electrode gap calculated here is no more than50 µm.

From Fig. 6(a), it is seen that the voltage sensitivity increases almost lin-early with g. This result is just as expected. Since the induced stress dependsmainly on the boundary conditions but not the electrode pattern, the electricdisplacement does not vary much from equation D3 = d3q Tq , and hence thevoltage sensitivity is linear with g as plotted from equation V3 = E3 · g =D3/ε3 · g.

From Fig. 6(b), it is clear that the voltage sensitivity decreases with elec-trode width d. This tendency is still in accordance with our model. Stress reachesthe maximum at the clamped end, and thus the PZT films near this end are mosteffective in improving the sensitivity. Since the films beneath the electrodesare not very effective, the increase of electrode width unavoidably reduces theeffectiveness of active regions and hence the sensitivity.

4.2 Sensitivity Dependence of Micro-Sensor with Interdigital Electrodes

A model using interdigital electrodes is established with d = 10 µm andg = 10 µm, as shown in Fig. 4(b). From Fig. 7, it is found that the voltagesensitivity decreases violently with the increase of the interdigital number N.

Figure 6. Voltage sensitivity versus: (a) electrode gap g (d = 10 µm) (b) electrodewidth d (g = 50 µm).

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Figure 7. Voltage sensitivity versus interdigital electrode number N (d = 10 µm, andg = 10 µm).

There are several possibilities for this result. First, as N increases, active re-gions occupy smaller percentage of PZT films and hence contribute less tothe sensitivity. Second, since the electrodes near the free end contribute lessin charge accumulation compared with those near the clamped end, the out-put charge increases more and more slowly with N whereas the capacitanceincreases linearly, resulting in the decrease of total output voltage.

4.3 Discussion

Table 2 listed the sensitivity of micro-sensors with different working modes.The model for d31 mode in the simulation is just as shown in Fig. 2 (a), and theplate dimensions and boundary conditions are the same as those of the modelfor d33 mode, and the polarization is vertical to PZT surface. It is clear thatd33 mode based micro-sensors have great advantage in voltage sensitivity andhence would be promising in future designs.

Table 2Comparison of sensitivity of micro-sensors with different working modes

d31 mode d33 mode d33 mode IDE

Electrode parameters / d = 10 µm d = 10 µm, d = 10 µm,g = 50 µm g = 10 µm g = 10 µm,

N = 12Voltage sensitivity (mv/Pa) 0.253 52.229 10.274 0.504Sensitivity improvement

compared with d31 mode1.000 206.090 40.540 1.990

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However, it should be noticed that the capacitances of d33 mode basedmicro-sensors are much smaller than conventional d31 mode based ones, andhence the charge sensitivity of such kind of micro-sensors would not be muchlarger, if not smaller, than d31 mode based ones. In another word, there is atrade-off between the voltage sensitivity and the capacitance.

5. CONCLUSION

In this paper, novel d33 mode based PZT micro-sensors have been analyzednumerically. The d33 mode based films have been divided into active, inactiveand transitional regions, which have different polarizations and hence distinctcontributions to the sensitivity. Based on the analysis, a simple model for d33

mode based integrated ferroelectric micro-sensors has been proposed. Usingthis model, further analysis is carried out by FEA software ANSYS. It is foundfrom the analysis that the sensitivity of such kind of micro-sensors dependsstrongly on the electrode width d and electrode gap g, hence it would be conve-nient for designers to design and optimize the sensitivity of the micro-sensorssince the electrode parameters d and g can be easily changed in fabrication. Be-sides, micro-sensors utilizing interdigital electrodes have also been simulated,and the function of sensitivity versus electrode number has been plotted.

ACKNOWLEDGMENT

The authors greatly appreciate Ningxin Zhang, Xiaoming Wu, Yi Yang andYiping Zhu for their valuable suggestions. This work is supported by NationalNatural Science Foundation of China (90407023), and “863” Program of China(2004AA404240).

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