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Piezoelectricity Lecture 8-1 Piezoelectricity Department of Mechanical Engineering Piezoelectricity Piezoelectricity – Discovered by Pierre Curie and Paul Jacques in 1880 – Generating an electric charge in a material when subjecting it to applied stress, and conversely, generating a mechanical strain in response to an applied electrical field Induced force or strain Force or strain V Induced ∆Q, ∆V Piezoelectric mat’l Piezoelectric mat’l Department of Mechanical Engineering Department of Mechanical Engineering Piezoelectric Effect Department of Mechanical Engineering Dielectrics without center symmetry Piezoelectricity For isotropic dielectric materials, [ε ] matrix reduced to scalar ε, Gauss’s Representation of total, free, and bound charge densities by field vector law may be rewritten as ∫ D ⋅ da = q S This explain why D is often called the charge density For dielectric materials, electric dipoles, i.e., closely coupled pairs of charges, will result in electric polarization, P, which is equal to the bound charge density. D = ε o E + P Department of Mechanical Engineering Piezoelectric Effect In some dielectric materials (crystals, ceramics, polymers) without center symmetry, an electric polarization can be generated by the application of mechanical stresses.----Piezo-electricity – P = d σ, direct effect – ε = d E , converse effect P: polarization (pC/m2) σ : stress (N/m2) ε :strain d: piezoelectric coefficient (pC/N or m/V) Department of Mechanical Engineering Piezoelectric constant & coupling coefficient Piezoelectric constants – d [C/N] = (charge developed)/(applied stress) – g [V-m/N] = (Electric field developed)/(applied stress) – h [m/V]=(Strain developed)/(applied E-field) – e [N/V-m] = (Stress developed)/(applied E-field) Electromechanical coupling coefficient (k) – Parameter used to compare different piezoelectric materials – A measure of the interchange of electrical & mechanical energy Department of Mechanical Engineering 3-D expression General expression – Piezoelectric effect is orientation dependant – 1-D 3-D i 3 ~ (σ=0, no stress) ε k = dik Ei 6 ∑ (E=0, no E-field) i=1 Pi = ∑ dikσ k k =1 1,2,3 axial stress, 4,5,6 shear stress ε1 d11 d21 d31 σ σ 1 = x, ….. ε d d d 2 12 22 32 E 1 σ1 ε3 d13 d23 d33 = E2 σ ε d d d 2 4 14 24 34 P1 d11 d12 d13 d14 d15 d16 E3 σ ε d d d = 3 5 15 25 35 P2 d21 d22 d23 d24 d25 d26 σ 4 ε6 d16 d26 d36 P d d d d d d 3 31 32 33 34 35 36 σ 5 Field σ 6 strain polarization stress Department of Mechanical Engineering Piezoelectric Coefficients For Piezoelectric PZT, BaTiO3, PbTiO3 (E=0, no E-field) (σ=0, no stress) 3 ~ 6 ε k = ∑ dik Ei = Pi = ∑ dikσ k i 1 k =1 ε1 0 0 d31 σ1 ε σ 2 0 0 d31 2 E1 P1 0 0 0 0 d15 0 ε 3 0 0 d33 σ 3 = E2 P2 = 0 0 0 d15 0 0 ε 4 0 d15 0 σ 4 E3 P3 d31 d31 d33 0 0 0 σ ε 5 d15 0 0 5 ε 0 0 0 σ 6 6 Department of Mechanical Engineering Piezoelectric Effect - When a voltage is applied across the thickness of the piezoelectric materials ∆L=d31 ·V3 · L/t, ∆w=d31 ·V3 · w/t , ∆t=d33 ·V3 - When a force F, is applied, in the length, width or thickness direction V3=d31 ·F1/(ε11 ·L), V3=d31 · F2/(ε11 ·w), V3=d33 · F3 · t/(ε33 ·L ·w) Department of Mechanical Engineering P=d σ Open circuit voltage Department of Mechanical Engineering Department of Mechanical Engineering Change in length per unit applied voltage ε 3 = d33E3 ∆l V = d 3 l 33 l −12 ∆l = d33V3 = 370×10 (m /V )×1(V ) 0.37nm Stacked actuator Note: ∆l is independent of l! It only depends on the voltage V3, and piezoelectric coefficient Department of Mechanical Engineering Piezoelectric Effect Here T: thickness F: applied force Department of Mechanical Engineering Piezoelectric Effect Department of Mechanical Engineering Piezoelectricity Piezoelectric Materials Important parameters for piezo- materials – Ceramics – piezoelectric strain coefficient d (m/V) Pb(ZrTi)O3 (PZT), PbTiO3 (PT), etc. – piezoelectric voltage coefficient g(Vm/N) – Single crystals – electromechanical coupling k33, k 31, k t Quartz, LiTaO3, LiNbO3, PZN-PT,etc – dielectric constant K – Polymers – dielectric loss tangent tanδ PVDF and copolymers, nylon, etc. – mechanical quality factor Q – Composites – acoustic impedance ρc PZT-polymer 0-3, 2-2, 1-3 composites, etc. – Thin/thick films PZT, PT, ZnO and AlN films Property Unit PZT PVDF ZnO PZT film Typical ceramic film (4 µm on Si) -12 properties of PZT, d33 (10 )C/N 220 -33 12 246 -12 PVDF, ZnO d31 (10 )C/N -93 23 -4.7 -105 -12 d15 (10 )C/N 694 -12 ? Crystalline quartz Κ3 ε33/εo 730 12 8.2 1400 tanδ 0.004 0.02 0.03 d11 d12 0 d14 0 0 k31 0.31 0.12 0 0 0 0 d25 d26 Q 400 6 2 ρc (10 )kg/m - 30 2.7 0 0 0 0 0 0 sec d = -d = -d /2 = 2.31 pC/N, d = -d = 0.73 pC/N 11 12 26 14 25 Department of Mechanical Engineering Piezoelectricity Piezoelectric Composites for transducer applications Department of Mechanical Engineering Piezoelectric actuators and sensors Piezoelectric longitudinal and Piezoelectric multilayer and Piezoelectric Shear mode actuator transverse effect bimorph actuators Longitudinal multilayer actuator Large output force, low displacement Shear mode actuator Medium force and displacement Bending mode actuator Low force, large displacement Department of Mechanical Engineering Piezoelectric actuators and sensors Department of Mechanical Engineering PZT film deposition - Sol-gel method Well Studied and widely used for PZT films Organometallic compounds (such as metal alkoxide) as precursors All chemicals dissolved in solvent to form a solution (sol) Polymerization to produce a gel with a continuous network Advantages Homogeneity, mixing in molecular level Low processing temperature Precise control of stoichiometric Department of Mechanical Engineering PZT film deposition by sol-gel processing -----Solution preparation Lead acetate trihydrate Acetic acid Pb(CH3COO)23H2O CH3COOH Refluxed/dehydrated Zirconium 150oC Titanium n-propoxide isopropoxide Zr[OC3H7]4 Ti[OCH(CH ) ] Mixed in N2 atm. 3 2 4 PZT composition Pb-excess Ethylene glycol De-ionized CH2OHCH2OH Mixed/refluxed H2O 80oC 0.9 M solution Stable in air For film spin-on coatingDepartment of Mechanical Engineering PZT film deposition by sol-gel Processing - Thin/thick film deposition O.9 M solution Pt/Ti/SiO2/Si Spin-on coating substrate 7500 rpm, 30 sec. o Hot plate Dried at 105 C Multilayer coating 400oC to remove residual organics To densify Pre-annealing the layer 600oC Film with Annealing Formation of desired PZT films thickness 700oC Department of Mechanical Engineering P-E Hysteresis Loop • Sol-gel PZT • 5.0 µm • High P Department of Mechanical Engineering Piezoelectric Accelerometer Department of Mechanical Engineering Piezoelectric Accelerometer Piezo Micro-accelerometer: (a) the front side with the interdigitated electrodes (see inset), and (b) shows the proof mass and the accelerometer frame. Department of Mechanical Engineering Piezoelectric Accelerometer 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. Frequency response of an accelerometer with a resonance frequency of 24.1 kHz and sensitivity of 0.53 pC/g Department of Mechanical Engineering Piezoelectric Accelerometer Schematic view of the mass deflection of a DRIE (a) and KOH (b) etched mass for perpendicular (a) and parallel (b) acceleration, respectively. Department of Mechanical Engineering Piezoelectric Accelerometer Fabrication process of the triaxial accelerometer. (a) Depositing all layers, silicon dioxide, platinum bottom electrode, PZT, platinum top electrode and gold bond pads; (b) patterning of top electrode, PZT and bottom electrode; (c) silicon (DRIE) and silicon dioxide (RIE) dry etching of the front using the bottom electrode as a mask; (d) DRIE of the back. Department of Mechanical Engineering Piezoelectric Accelerometer Schematic of fabrication process. Typical accelerometer impact response Department of Mechanical Engineering Piezoelectric actuators and sensors Microactuators – ink droplet ejectors (printhead) – piezoelectric transformers – piezoelectric scanning tunneling microscope tip Microsensors – accelerometers – micro-resonators – surface acoustic wave (SAW) devices – underwater acoustic imaging sensors Performance Criteria – Actuators generative force/momentum displacement frequency response – Sensors sensitivity frequency response stability or repeatability Department of Mechanical Engineering Piezoelectric MEMS Devices Cantilever Connection pads Electrodes Passivation layer PZT Silicon Nitride Silicon Piezoelectric PZT-on-Si cantilever resonantor Department of Mechanical Engineering Piezoelectric Micropumps Pump Department of Mechanical Engineering Acoustic Imaging Sensors n-Si (100) wafer Oxdi ze d Photoresist pattern Oxide etching Boron-diffused layer 5-10 µ m, as etch stop oxide removal LTO deposition EDP or KOH etching to form cavity Pt/Ti metal layer sputtering PZT layer deposition by sol-gel spin-on coating PZT patterning by wet chemical etching Top Pt/Ti metal layer sputtering & patterning Department of Mechanical Engineering Piezoelectric Printhead Department of Mechanical Engineering Example: Piezo Ink Jet Piezo- actuator deforms Xerox when electrical pulse Lexmark... applied Department of Mechanical Engineering Example: Piezo Ink Jet Printheads Three Types: – Rod type. Using multilayer piezoelectric (PZT) ceramic actuator arrays Department of Mechanical Engineering Example:
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