APPLIED PHYSICS
MODERN PHYSICS OF FERROELECTRICS ESSENTIAL BACKGROUND 1 THEORY OF POLARIZATION A MODERN APPROACH 30 A LANDAU PRIMER FOR FERROELECTRICS 67 FIRST PRINCIPLES STUDIES OF FERROELECTRIC OXIDES 114 ANALOGIES AND DIFFERENCES BETWEEN FERROELECTRICS AND FERROMAGNETS 171 GROWTH AND NOVEL APPLICATIONS OF EPITAXIAL OXIDE THIN FILMS 213 FERROELECTRIC SIZE EFFECTS 299 NANOSCALE STUDIES OF DOMAIN WALLS IN EPITAXIAL FERROELECTRIC THIN FILMS 331 CONTENTS MODERN PHYSICS OF FERROELECTRICS ESSENTIAL BACKGROUND ABSTRACT PRINCIPLES OF FERROELECTRICITY AND INFORMATION ABOUT FERROELECTRIC MATE RIALS AND THEIR APPLICATIONS ARE REVIEWED THE CHARACTERIZATION OF FERROELECTRIC BE HAVIOR THROUGH MEASUREMENT OF ELECTRICAL HYSTERESIS IS DISCUSSED IN DETAIL THE MAIN FAMILIES OF FERROELECTRIC OXIDES INCLUDING PEROVSKITE COMPOUNDS AND SOLID SOLUTIONS LITHIUM NIOBATE LAYERED OXIDES MAGNETIC FERROELECTRIC OXIDES AND ELECTRONIC FER ROELECTRICS ARE PRESENTED AND THEIR CRYSTAL STRUCTURES AND POLARIZATIONS GIVEN THE E ECTS OF PRESSURE AND EPITAXIAL STRAIN ON PEROVSKITES ARE DESCRIBED RECENT ADVANCES IN THE UNDERSTANDING OF FERROELECTRICITY IN THIN LMS SUPERLATTICES AND NANOSTRUC TURES ARE MENTIONED FINALLY AN OVERVIEW OF APPLICATIONS OF FEROELECTRIC MATERIALS BOTH ESTABLISHED APPLICATIONS AND THOSE UNDER DEVELOPMENT IS INCLUDED 1 INTRODUCTION A FERROELECTRIC IS AN INSULATING SYSTEM WITH TWO OR MORE DISCRETE STABLE OR METASTABLE STATES OF DI ERENT NONZERO ELECTRIC POLARIZATION IN ZERO APPLIED ELECTRIC ELD REFERRED TO AS SPONTANEOUS POLARIZATION FOR A SYSTEM TO BE CONSIDERED FERROELECTRIC IT MUST BE POSSIBLE TO SWITCH BETWEEN THESE STATES WITH AN APPLIED ELECTRIC ELD WHICH CHANGES THE RELATIVE ENERGY OF THE STATES THROUGH THE COUPLING OF THE ELD TO THE POLARIZATION E P THE CONCEPT OF ELECTRIC POLARIZATION IS THUS KEY TO AN UNDERSTANDING OF FERROELECTRICITY FOR A NITE SYSTEM ELECTRIC POLARIZATION IS STRAIGHTFORWARDLY DE NED AS THE DIPOLE MOMENT OBTAINED FROM THE CHARGE DENSITY DIVIDED BY THE SYSTEM VOLUME THOUGH IT SHOULD BE NOTED THAT FOR ULTRASMALL SYSTEMS THE BOUNDARIES OF THE SYSTEM ARE NOT SHARP FOR AN IN NITE CRYSTAL THE DE NITION OF POLARIZATION AS A BULK PROPERTY LONG PROVED CONSIDERABLY MORE DI CULT TO FORMULATE THE RESOLUTION SUGGESTED BY RESTA KING SMITH AND VANDERBILT AND NOW GENERALLY REFERRED TO AS THE MODERN THEORY OF POLARIZATION IS TO IDENTIFY THE POLARIZATION AS AN INTEGRATED CURRENT THROUGH A TRANSFORMATION 1 FROM ONE VARIANT TO ANOTHER THE RESULT BEING EXPRESSED AS A BERRY PHASE THIS FOCUS ON THE INDUCED CURRENT HAS THE ADDITIONAL ADVANTAGE OF MAKING A DIRECT CONNECTION TO THE ELECTRICAL AND OPTICAL MEANS OF MEASURING POLARIZATION ANOTHER NOVEL ASPECT OF THIS FORMALISM IS THAT POLARIZATION IS NOT A VECTOR PROPERTY BUT RATHER A LATTICE P 0 2ER WHERE R IS A VECTOR OF THE CRYSTAL BRAVAIS LATTICE AND IS THE VOLUME OF THE UNIT CELL AN INTUITIVE STRUCTURE BASED PICTURE IS PROVIDED BY A REFORMULATION OF THE BERRY PHASE EXPRESSION IN TERMS OF THE CENTERS OF CRYSTALLINE WANNIER FUNCTIONS THESE IDEAS AND THEIR APPLICATION TO FERROELECTRICS ARE MORE FULLY EXPLAINED IN THE CONTRIBUTION BY RESTA AND VANDERBILT IN THIS OVERVIEW WE PRESENT AN INTRODUCTION TO FERROELECTRIC MATERIALS WITH THE INFORMATION NEEDED AS BACKGROUND FOR READING THE SUBSEQUENT CHAPTERS OF THIS BOOK WE ONLY INCLUDE THE MOST ESSENTIAL POINTS WITH SPECIAL ATTENTION TO THOSE NOT AVAILABLE ELSEWHERE FOR MORE COMPREHENSIVE BACKGROUND WE RE FER THE READER TO THE CLASSIC BOOK BY LINES AND GLASS 1 WHICH IS STILL VERY USEFUL DESPITE ITS COPYRIGHT DATE OF 1977 AND TO THE INVALUABLE COMPILATIONS OF DATA FROM THE LITERATURE IN THE SERIES OF VOLUMES OF LANDOLT B ORNSTEIN 2 3 WE START BY DISCUSSING THE CHARACTERIZATION OF FERROELECTRIC BEHAVIOR THROUGH MEASUREMENT OF POLARIZATION SWITCHING HYSTERESIS LOOPS THIS IS FOLLOWED BY A DISCUSSION OF THE RELATION BETWEEN FERROELECTRICITY AND CRYSTAL STRUCTURE MORE GENERALLY ATOMIC ARRANGEMENT AND THEN A DESCRIPTION OF THE CRYSTAL STRUC TURES ELECTRIC POLARIZATIONS AND PHASE DIAGRAMS OF THE MOST COMMONLY STUD IED FERROELECTRIC OXIDES THIS INFORMATION WILL BE A HANDY REFERENCE AS THESE MATERIALS ARE DISCUSSED IN THE VARIOUS CHAPTERS OF THIS BOOK FINALLY WE GIVE UP TO DATE PERSPECTIVES ON TWO AREAS IN WHICH THERE HAS BEEN RAPID DEVELOP MENTS IN RECENT YEARS 1 NITE SIZE E ECTS IN FERROELECTRIC THIN LMS SUPER LATTICES AND NANOSTRUCTURES AND 2 TECHNOLOGICAL APPLICATIONS OF FERROELECTRIC OXIDES 2 SWITCHING AND HYSTERESIS LOOPS AS MENTIONED ABOVE A DE NING PROPERTY OF FERROELECTRICITY IS THE SWITCHING BETWEEN DI ERENT METASTABLE STATES BY THE APPLICATION AND REMOVAL OF AN ELECTRIC ELD THE MECHANISM OF SWITCHING IS UNDERSTOOD TO TAKE PLACE ON SCALES LONGER THAN THE UNIT CELL SCALE AND GENERALLY TO REQUIRE THE GROWTH AND SHRINKING OF DOMAINS THROUGH THE MOTION OF DOMAIN WALLS AS WILL BE DISCUSSED IN MORE DETAIL IN THE CONTRIBUTION BY LICHTENSTEIGER DAWBER AND TRISCONE AND THE CONTRIBUTION BY PARUCH GIAMARCHI AND TRISCONE WHILE THE SMALL DISTORTION CRYSTALLOGRAPHIC CRITERION DISCUSSED IN THE NEXT SECTION SHOULD GENERALLY ALLOW SWITCHING THE OBSERVATION OF AN ELECTRIC HYSTERESIS LOOP FIG 1 IS CONSIDERED NECESSARY TO ESTABLISH FERROELECTRICITY IN ITS CANONICAL FORM THE FERROELECTRIC P E HYSTERESIS LOOP IS SYMMETRIC AND THE REMNANT POLARIZATION AND COERCIVE ELDS ARE EASILY DE NED AND EX TRACTED THERE ARE HOWEVER A NUMBER OF POTENTIAL PITFALLS IN THE ACCURATE APPLIED PHYSICS 2 FIG 1 A HYSTERESIS LOOPS FOR A NUMBER OF PBTIO3 SRTIO3 SUPERLATTICE SAMPLES WITH DI ERENT POLARIZATIONS B THE CORRESPONDING CURRENT VOLTAGE LOOPS OBTAINED DURING VOLTAGE SWEEPS IN WHICH THE VOLTAGE IS CYCLED IN CONTRAST TO LEAKAGE CURRENT I V CURVES THAT MEASURE CURRENT WHEN THE VOLTAGE IS HELD CONSTANT FOR A PERIOD OF TIME FROM WHICH THE POLARIZATION VOLTAGE HYSTERESIS LOOPS ARE OBTAINED SHOWING CLEAR SWITCHING PEAKS AT THE COERCIVE VOLTAGE OF THE SAMPLE PERFORMANCE OF THIS MEASUREMENT THE STARTING POINT FOR ANY MEASUREMENT OF THIS KIND IS TO REALIZE THAT THE ELECTRICAL PROPERTIES OF A FERROELECTRIC LM CAN ONLY BE MEASURED WHEN IT IS FABRICATED AS A DEVICE MOST TYPICALLY A CAPACITOR THUS ANY MEASUREMENT ACTUALLY INVOLVES A WHOLE SYSTEM WITH ELECTRODES WIRES AND INTERFACES AND SOMETIMES IT IS THESE OTHER COMPONENTS OF THE SYSTEM THAT DOMINATE THE ELECTRICAL RESPONSE RATHER THAN THE INTRINSIC PROPERTIES OF THE MATERIAL OF INTEREST IN THIS SECTION WE BRIE Y COVER THE KEY WAYS IN WHICH FERROELECTRIC HYSTERESIS MEASUREMENTS ARE MADE WITH SPECIAL ATTENTION TO THE POTENTIAL ERRORS THAT CAN BE MADE AND THE METHODS THAT CAN BE USED TO AVOID THEM THE SAWYER TOWER CIRCUIT 4 THE ORIGINAL METHOD FOR MEASURING FERRO ELECTRIC HYSTERESIS IS SIMPLE IN CONCEPT IT IS ESSENTIALLY JUST A CAPACITANCE BRIDGE RELYING ON THE FACT THAT TWO CAPACITORS IN SERIES SHOULD HAVE THE SAME CHARGE ONE OF THESE CAPACITORS IS COMPRISED OF THE FERROELECTRIC AND THE OTHER IS A STANDARD CAPACITOR WITH A WELL DE NED CAPACITANCE THE POTENTIAL ACROSS THE STANDARD CAPACITOR IS PLOTTED ON THE Y AXIS AND THE AC VOLTAGE APPLIED TO THE FERROELECTRIC SAMPLE IS PLOTTED ON THE X AXIS IN THE X Y MODE OF AN OSCILLOSCOPE THE STANDARD CAPACITOR SHOULD BE CHOSEN TO HAVE A LARGE CAPACITANCE SO THAT THE POTENTIAL ACROSS IT IS SMALL ENOUGH NOT TO A ECT THE POTENTIAL ACROSS THE FERROELECTRIC SAMPLE IN THE IDEAL CASE WHERE THE CURRENT OWING DURING THIS MEASUREMENT IS PURELY DISPLACIVE THIS MEASUREMENT WILL GIVE ACCURATE VALUES OF THE FERROELECTRIC POLARIZATION A SIMPLE IMPLEMENTA TION OF THIS CIRCUIT ALONG WITH A DESCRIPTION OF A SIMPLE CLASSROOM EXPERIMENT TO OBSERVE FERROELECTRIC HYSTERESIS IN KNO3 IS DESCRIBED IN 5 UNFORTUNATELY ESPECIALLY WHEN THEY ARE GROWN AS THIN LMS FERROELECTRICS ARE SELDOM PERFECTLY RESISTIVE AND A HOST OF FACTORS SUCH AS GRAIN BOUNDARIES DEFECTS CONDUCTION PROCESSES SUCH AS SCHOTTKY INJECTION OR FOWLER NORDHEIM APPLIED PHYSICS 3