Chang Liu MASS UIUC Micromachined Piezoelectric Devices Chang Liu Micro Actuators, Sensors, Systems Group University of Illinois at Urbana-Champaign

Chang Liu MASS UIUC Definition Direct Piezo Effect –a mechanical stress on a material produces an electrical polarization Inverse Piezo Effect –an applied electric field in a material produces dimensional changes and stresses within a material. In general, both piezoelectricity and inverse piezoelectricity are denoted piezoelectric effects.

Chang Liu MASS UIUC History First discovered in 1880 by Curies. Two important macro-scale applications that defined the growth of field –quartz resonator for timing standard The frequency of the quartz oscillator is determined by the cut and shape of the quartz crystal. miniature encapsulated tuning forks which vibrate 32,768 times per second –ultrasonic transceivers for marine warfare and medical imaging. Walter Cady ( ) Inventor of quartz resonator Tuning fork quartz resonator

Chang Liu MASS UIUC Submarine Applications Civil/military monitoring

Chang Liu MASS UIUC Asymmetric Crystal Produces Piezoelectric Effect Symmetric (centrosymmetric) lattice structure does not produce piezoelectricity when deformed. Asymmetic lattice structures do!

Chang Liu MASS UIUC The Coordinate System

Chang Liu MASS UIUC Direct D: Electrical Polarization T: Applied Mechanical Stress d: Piezoelectric Coefficient Matrix ε: Electrical Permittivity Matrix E: Electrical Field

Chang Liu MASS UIUC Inverse Piezoelectricity s: Strain Vector S: Compliance Matrix

Chang Liu MASS UIUC Unit of Piezoelectric Coefficient Unit of d 33 is the unit of electric displacement over the unit of the stress. Thus

Chang Liu MASS UIUC Reverse Piezoelectricity Strain as a function of applied field is governed by Verify the unit –charge multiplied by electric field is force.

Chang Liu MASS UIUC Which is Axis 3? If no poling is applied, the axis normal to the substrate of deposition is axis 3. If poling is applied, the axis of applied poling is axis 3.

Chang Liu MASS UIUC Semiconductors – Are they piezoelectric? Si is symmetric and does not exhibit piezoelectricity. –(Si: positive charge; bond electrons: negative change) GaAs lattice is not symmetric and exhibits piezoelectricity.

Chang Liu MASS UIUC Common Piezoelectric Materials ZnO –sputtered thin film –d 33 =246 pC/N Lead zirconate titanate (PZT) –ceramic bulk, or sputtering thin film –d 33 =110 pC/N Quartz –bulk single crystal –d 33 =2.33 pC/N Polyvinylidene fluoride (PVDF) –polymer –d 33 =1.59 pC/N. Diagram of a sputtering system.

Chang Liu MASS UIUC Issues for Materials Poling –establishment of preferred sensing direction –application of electric field for long period of time after material is formed Curie temperature –temperature above which the piezoelectric property will be lost. Material purity –the piezoelectric constant is sensitive to the composition of the material and can be damaged by defects. Frequency response –most materials have sufficient leakage and cannot “hold” a DC force. The DC response is therefore not superior but can be improved by materials deposition/preparation conditions. Bulk vs thin film –bulk materials are easy to form but can not integrate with MEMS or IC easily. Thin film materials are not as thick and overall displacement is limited.

Chang Liu MASS UIUC Table 2: Properties of selected piezoelectric materials. MaterialRelative permitivity (dielectric constant) Young’s modulus (GPa) Density (kg/m 3 ) Coupling factor (k) Curie temperature ( o C) ZnO ** PZT-4 (PbZrTiO 3 ) PZT-5A (PbZrTiO3) Quartz (SiO 2 ) ** Lithium tantalate (LiTaO 3 ) Lithium niobate (LiNbO 3 ) ** PVDF

Chang Liu MASS UIUC Quartz

Chang Liu MASS UIUC PZT lead zirconate titanate (Pb(Zr x,Ti 1-x )O 3, or PZT) Pb(Zr 0.40,Ti 0.60 )TiO 3

Chang Liu MASS UIUC ZnO

Chang Liu MASS UIUC Bilayer Bending A p and A e are the cross-section areas of the piezoelectric and the elastic layer, E p and E e are the Young’s modulus of the piezoelectric and the elastic layer, and t p and t e are the thickness of the piezoelectric and the elastic layer

Chang Liu MASS UIUC Example 1

Chang Liu MASS UIUC Actuator Example Cr/Au Si 3 N 4 ZnO Si 3 N 4 Cr 3 1

Chang Liu MASS UIUC Example 2 A patch of ZnO thin film is located near the base of a cantilever beam, as shown in the diagram below. The ZnO film is vertically sandwiched between two conducting films. The length of the entire beam is l. It consists of two segments – A and B. Segment A is overlapped with the piezoelectric material while segment B is not. The length of segments A and B are l A and l B, respectively. If the device is used as a force sensor, find the relationship between applied force F and the induced voltage.

Chang Liu MASS UIUC

Chang Liu MASS UIUC Solution The c-axis (axis 3) of deposited ZnO is generally normal to the front surface of the substrate it is deposited on, in this case the beam. A transverse force would produce a longitudinal tensile stress in the piezoelectric element (along axis 1), which in turn produces an electric field and output voltage along the c-axis. The shear stress components due to the force is ignored. The stress along the length of the piezoresistor is actually not uniform and changes with position. For simplicity, we assume the longitudinal stress is constant and equals the maximum stress value at the base. The maximum stress induced along the longitudinal direction of the cantilever is given by. The stress component is parallel to axis 1. According to Equation 2, the output electric polarization in the direction of axis 3 is. The overall output voltage is then. with Tpiezo being the thickness of the piezoelectric stack.

Chang Liu MASS UIUC Example 3 For the same cantilever as in Example 2, derive the vertical displacement at the end of the beam if it was used as an actuator. The applied voltage is V 3.

Chang Liu MASS UIUC Under the applied voltage, the electrical field in axis 3 is The applied electric field creates a longitudinal strain along axis 1, with the magnitude given by Equation 5 as Segment A is curved into an arc. The radius of the curvature r due to applied voltage can be found from Equation 13. The displacement at the end of segment A,, can be found by following similar procedure used in Example 1. The angular displacement at the end of the piezoelectric patch is The segment B does not curl and remains straight. The vertical displacement at the end of the beam is

Chang Liu MASS UIUC Example 4 A ZnO thin film actuator on a cantilever is biased by co-planar electrodes. The geometry of beams and piezoelectric patches is identical as in Example 2. Find the output voltage under the applied force. If the structure is used as an actuator, what are the stress components when a voltage is applied across the electrodes?

Chang Liu MASS UIUC The applied force generates two stress components – normal stress T 1 and shear stress T 5. The output electric field is related to the stresses according to the formula for direct effect of piezoelectricity Because no external field is applied, the terms E 1, E 2, and E 3 on the righthand side of the above equation are zero. The formula can be simplified to the form Therefore, The output voltage is related to the polarization in axis-1,

Chang Liu MASS UIUC Let’s find the output stress when the device is used as an actuator. Suppose a voltage V is applied across the longitudinal direction. Here we assume the spacing between the two electrode is l A, hence the magnitude of the electric field is The applied electric field creates a longitudinal strain along axis 1. The strain is found by Since no external stresses are applied, we set T 1 through T 6 zero. The simplified formula for strain is No longitudinal strain components are generated in this manner.

Chang Liu MASS UIUC Example 5 Derive the expression for the end displacement of piezoelectric transducer configured similarly as Example 4, with the difference that the electrodes are used to pole the ZnO material. In other words, axis-3 is now forced to lie in the longitudinal direction of the beam length. A voltage V is applied across two electrodes.

Chang Liu MASS UIUC The electric field in the longitudinal axis is The applied field induced a longitudinal strain (S 3 ) according to or We should use s 3 to replace s long in Equation 8. The subsequent analysis is similar to the one performed for Example 3.

Chang Liu MASS UIUC Case 7.1: Acceleration Sensor

Chang Liu MASS UIUC Case 7.2: Membrane Piezoelectric Accelerometer

Chang Liu MASS UIUC Case 7.3: Piezoelectric Acoustic Sensor (Pressure Sensor)

Chang Liu MASS UIUC Case 7.4: Piezoelectric Microphone

Chang Liu MASS UIUC Surface Elastic Waves