Table of Contents. Chapter 1. Dielectricity, Piezoelectricity, Pyroelectricity and Ferroelectricity... 1

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1 Preface... General Introduction... xiii xvii Chapter 1. Dielectricity, Piezoelectricity, Pyroelectricity and Ferroelectricity Crystal structure Crystal = lattice + pattern Seven primitive lattices 14 Bravais lattices Two-hundred and thirty space groups Thirty-two point groups (or crystal classes) Reticular planes X-rays see crystals Piezoelectricity, pyroelectricity and ferroelectricity definitions Simplified examples Dielectric effect Piezoelectric effect Pyroelectric effect Ferroelectric effect Electrostrictive effect Three typical structures: wurtzite, ilmenite and perovskite Wurtzite structure Ilmenite structure Perovskite structure Bibliography... 23

2 vi Integration of Ferroelectric and Piezoelectric Thin Films Chapter 2. Thermodynamic Study: a Structural Approach History Revisiting statistical thermodynamics Introduction Notion of equilibrium, statistical postulate Numbers of accessible states of a system Energy variation work and heat Heat transfer: entropy and absolute temperature Thermal energy: heat transfer Quasistatic transformation with work and heat transfer Example of a constant pressure and temperature experiment State functions Linear equations piezoelectricity Non linear equations electrostriction Bibliography Chapter 3. Ferroelectric-paraelectric Phase Transition Thermodynamic Modeling Hypothesis on Gibbs elastic energy Second-order transition Effects of stresses First-order transition Conclusion Bibliography Chapter 4. Mechanical Formalism Introduction Hooke s law Definitions of local strains Local strains in small strains hypothesis Meaning of matrix S Definition of local strains The strain tensor Physical meaning of T ij Equations of motion in a deformable solid Stress-strain relation Hooke s generalized law Dynamic relation Elastic energy density... 86

3 vii Expression of elastic energy density Symmetry of the elasticity tensor Expression of the elasticity tensor as a function of elements of symmetry Bibliography Chapter 5. Dielectric Formalism Introduction The dielectric effect seen by Faraday Electric polarization and displacement The dielectric constant The local field in dielectrics: polarization catastrophe Dielectric relaxation The various relaxations Kramers-Kronig relations Electric energy density Bibliography Chapter 6. Piezoelectric Formalism and Mathieu PIJOLAT 6.1. Thermodynamic equations Reducing coefficients using crystal symmetry Example of a calculation: point group 3m One-dimensional microscopic model Electromechanical coupling coefficient Piezoelectric coefficients of key materials Calculating coupling as a function of crystal orientation Piezoelectric coefficients in the case of ferroelectric materials Relation between piezoelectric formalism and matter Bibliography Chapter 7. Acoustic Formalism Alexandre REINHARDT 7.1. Propagation of bulk waves Propagation of bulk waves in an elastic medium Elastic wave propagation in a piezoelectric medium Bulk wave resonator Piezoelectric plate vibrations Plate delimited by arbitrary acoustic impedance media Bimorph plate

4 viii Integration of Ferroelectric and Piezoelectric Thin Films Piezoelectric plate between two electrodes Equivalent electric circuit Bulk acoustic waves filter Bibliography Chapter 8. Electrostrictive Formalism Foundations of electrostriction Thermodynamic model of electrostriction case of the resonator The electrostriction tensor Microscopic model of electrostriction One-dimensional model Origin of spontaneous polarization in perovskite crystals Electrostrictive resonator Bibliography Chapter 9. Electric Characterization , Gwenaël LE RHUN and Emilien BOUYSSOU 9.1. Static piezoelectric characterization of thin films Notion of effective coefficients Piezoelectric characterization of coefficient e 31eff Model Example of characterization: PZT films Piezoelectric and atomic force microscopy Atomic force microscope Piezoresponse force microscope Ferroelectric measurement Sawyer-Tower circuit Virtual ground circuit Dielectric measurement Leakage current in metal/insulator/metal structures Metal/insulator contact: definitions Conduction mechanisms limited by the interfaces Bulk-limited conduction mechanisms Bibliography Chapter 10. Piezoelectric Resonators and Filters Alexandre REINHARDT and Christophe BILLARD Acoustic resonators: principle and history Quartz resonators High-frequency operation of resonators

5 ix Perfecting FBAR and SMR resonators BAW technology Introduction BAW filter topology Parameters of the BAW resonator and their impact on filter response Examples of realizations CRF technology Introduction Operating principles of CRF filters Example of implementations Bibliography Chapter 11. High Overtone Bulk Acoustic Resonator (HBAR) Mathieu PIJOLAT, Chrystel DEGUET and Sylvain BALLANDRAS About HBAR Generalities Principle Description of the spectrum Technology Technological constraints Choice of materials Geometry of resonators Examples of implementations LNO on LNO Validation of parameter extractions: LNO on HBAR/FBAR Si Conclusions about HBAR Bibliography Chapter 12. Electrostrictive Resonators Alexandre VOLATIER, Brice IVIRA, Christophe ZINCK, Nizar BEN HASSINE and Introduction State of the art Introduction Formalism of the electrostrictive resonator Experimental implementations /30 BST resonator without acoustic insulation STO resonator on Bragg mirror BST resonator on an acoustic Bragg mirror BST resonator on a membrane

6 x Integration of Ferroelectric and Piezoelectric Thin Films Simulation of a filter with electrostrictive resonators Status of perovskite electrostrictive resonators PZT-based tunable frequency ferroelectric acoustic resonator Introduction Technology RF characterization and discussion Nonlinear effect in piezoelectric AlN Introduction Piezoelectric-electrostrictive phenomenological model Application: AlN resonator on a Bragg mirror Conclusion with nonlinear AlN Conclusion with electrostriction Bibliography Chapter 13. Thin Film Piezoelectric Transducers Matthieu CUEFF, Patrice REY, Fabien FILHOL and Introduction State of the art Resonant membranes Technology of PZT resonant membranes Frequency characterization of membranes A resonant pressure sensor Conclusion on the study of Si/PZT resonant membranes Resonant micromirror Introduction Technology and design of the resonant micromirror Characterization of the devices Conclusion about micromirrors Piezoelectric micro-switch Interest in piezoelectric films for micro-switches General description of the component Analytical development of the bimorph beam as actuator of the micro-switch Stack chosen for the piezoelectric actuator Multilayer analytical model Effect of temperature compensation The piezoelectric film Releasing the membrane Electrical characterizations

7 xi Sign of piezoelectric coefficients Bibliography List of Authors Index