Effective Direct Piezoelectric Constants in Epitaxial Ferroelectric Films as MEMS Sensors
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CC5.7.1
Effective direct piezoelectric constants in epitaxial ferroelectric films as MEMS sensors Jun Ouyang 1, R. Ramesh1, 2, and A. L. Roytburd 1 Materials Research and Science Engineering Center, Dept. of Materials Science and Engineering, University of Maryland, College Park, MD, 20742. 2 Current address: Dept. of Materials Science and Engineering, University of California, Berkeley, CA 94720-1760. 1
ABSTRACT Following our previous work on the converse piezoelectric constant- d33C , f in epitaxial ferroelectric films for MEMS actuator applications1, the orientation dependence of the direct D D piezoelectric constants d33D , f , d 31 , f and e31, f are generally formulated, which can help to predict and optimize the performance of piezoelectric MEMS sensor devices based on ferroelectric thin films. Numerical results are obtained and discussed for Pb(ZrxTi1-x)O3 thin films grow on Si substrates with various compositions and structures. INTRODUCTION Recently, there is an increasing number of research works on ferroelectric films as sensor components in micro-electric-mechanical system (MEMS), which aims at realizing direct piezoelectric functions by capacitive sensing in a reduced length scale2-5. In a general configuration for a piezoelectrically driven MEMS sensor, a ferroelectric thin film is grown on top of a thick substrate, a stress or a strain field from the surrounding environment is applied to the substrate and sensed by the ferroelectric film via the lateral constraint imposed by the substrate. The primary goal of this article is to calculate the effective direct piezoelectric D D constants d33D , f , d 31 , f and e31, f of a substrate-constrained single domain ferroelectric film as a function of its crystallographic structure and orientation (“D” denotes “direct piezoelectric effect”, “f” denotes “film”). This information will provide a framework of reference for evaluating direct piezoelectric properties of clamped ferroelectric films. As an example, we will apply the general results to films with different compositions in the Pb(ZrxTi1-x)O3 solid solutions (PZT), which is a typical ferroelectric system having a morphotropic phase boundary (MPB) separating two ferroelectric phases (tetragonal and rhombohedral). THEORY The widely used piezoelectric constants characterizing piezoelectric sensing processes D D are the longitudinal d33D , f constant and the transverse d 31 , f and e31, f constants. A piezoelectric sensor is said to be in a longitudinal sensing mode when a longitudinal force is applied along the normal of the device and a charge is generated on the surface of the ferroelectric film and then is collected and analyzed. On the other hand, a transverse sensing mode is when in-plane stresses or strains are applied to the device to induce the charge. For a (001) oriented tetragonal film, 6,7 D D d33D , f , d 31 , f and e31, f constants are expressed in Eq (1):
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d 33D , f = Q3E / σ 33 = d33 + 2( s13E , sub − s13E , f )d 31 /(s11E , f + s12E , f )
(1.1)
E, f E, f D E sub sub E , sub E
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