Mechanics of Advanced Functional Materials

1 Introduction
2 Basic Solutio of Elastic and Electric Fields of Piezoelectric Materials
with Inclusio and Defects
2.1 The Coupled Differential Equatio of Elastic and Electric Fields in Piezoelectric Solids
2.1.1 Thermodynamic Framework
2.1.2 Linear Co titutive Equatio 
2.1.3 The Equation of Equlibrium
2.1.4 The Basic Equatio of a Static Electric Field
2.1.5 Differential Equatio for Piezoelectric Materials
2.2 Boundary Conditio 
2.3 Solution Methods for Two-Dime ional Problems
2.3.1 The Stroh Formalism for Piezoelectric Materials
2.3.2 The Lekhnitskii Formalism for Piezoelectric Materials
2.3.3 Conformal Tra formation of the Core Function
2.4 Basic Solutio for Two-Dime ional Problems
2.4.1 Elliptical Cylindrical Inclusio in Piezoelectric Materials
2.4.2 Cracks
2.4.3 Dislocatio and Line Charges
2.5 Solution Methods for Three-Dime ional Problems
2.5.1 Eige trai and Equivalent Inclusion Method
2.5.2 Method of Fourier Integrals
2.5.3 Method of Green's Function
2.6 Basic Solution for Three-Dime ional Problems
2.6.1 Ellipsoidal Inhomogeneous Inclusio 
2.6.2 Flat Elliptical Cracks
2.6.3 Ellipsoidal Inhomogeneity Embedded in an Infinite Matrix when both Phases Undergo Eige trai 
2.6.4 Green's Function
2.7 Remarks
References

3 Micromechanics Models of Piezoelectric and Ferroelectrie Composites
3.1 Background
3.2 Some Definitio 
3.3 Effective Material Co tants of Piezoelectric Composites
3.3.1 The Dilute Model
3.3.2 The Self-Co istent Model
3.3.3 The Mori-Tanaka Mean Field Model
3.3.4 The Differential Model
3.4 Energy Formulation of Ferroelectric Composites
3.4.1 Elastic Strain Energy De ity for Ferroelectric Composites
3.4.2 Intri ic Free Energy De ity for Ferroelectric Composites
3.4.3 Total Free Energy for Ferroelectric Composites with Spherical Inclusio 
3.5 Phase Diagrams
3.5.1 Total Free Energy for Ferroelectric Composites with
Spherical Inclusio and Equiaxed Strai 
3.5.2 Phase Diagrams and Total Polarizatio 
3.6 Remarks
Appendix A： Radon Tra form
References

4 Determination of the Smallest Sizes of Ferroeleetric Nanodomai 
4.1 Introduction
4.2 Electric Fields in Ferroelectric Thin Film
4.2.1 General Expression of Electric Field of Ferroelectric Domain
4.2.2 AFM-Induced Electric Field in Ferroelectric Thin Films
4.3 Energy Expressio 
4.3.1 Energy Expression for 180~ Domain in a Ferroelectric
Film Covered with Top and Bottom Electrodes
4.3.2 Energy Expression for 180~ Domain in Ferroelectric
Film Induced by an AFM Tip without the Top Electrode
4.4 Driving Force and Evolution Equatio of Domain Growth
4.5 Stability Analysis
4.6 Remarks
Appendix B： Derivation of the Electric and Magnetic Field for a Growing 180&deg； Domain
References

5 Size and Surface Effects of Phase Tra ition on Nanoferroelectrie Materials
5.1 Introduction and Overview of Ferroelectrics in Nanoscale Dime io 
5.1.1 Ferroelectric Thin Films in Nanoscale Dime io 
5.1.2 Ferroelectric Tunneling Junctio and Capacito in Nanoscale Dime io 
5.1.3 Ferroelectric Multilaye in Nanoscale
5.1.4 Ferroelectric Nanowires and Nanotubes
5.1.5 Ferroelectric Nanograi or Nanoislands on Substrates
5.2 Thermodynamic Modeling and Stability Analysis of Ferroelectric Systems
5.2.1 Background of the Thermodynamic Modeling for Ferroeleclrics
5.2.2 Electrostatics for Ferroelectrics
5.2.3 Thermodynamics of Ferroelectrics
5.2.4 Stability Analysis on Critical Properties of Ferroelectric Systems
5.3 Ferroelectric Thin Films in Nanoscale
5.3.1 Thermodynamic Model for a Thick Ferroelectric Film
5.3.2 Size and Surface Effects on Ferroelectric Thin Films
5.3.3 The Evolution Equation and Stability of the Stationary States ..
5.3.4 Curie Temperature and Critical Thickness
5.3.5 Curie-Weiss Law of Ferroelectric Thin Film in Nanoscale
5.4 Critical Properties of Ferroelectric Capacito or Tunnel Junctio ..
5.4.1 The Thermodynamic Potential of the Ferroelectric
Capacito or Tunnel Junctio 
5.4.2 The Evolution Equation and Stability of the Stationary States..
5.4.3 Curie Temperature of the Ferroelectric Capacito or
Tunnel Junctio 
5.4.4 Polarization as a Function of Thickness of the Ferroelectric
Capacito or Tunnel Junctio 
5.4.5 Critical Thickness of the Ferroelectric Capacito or
Tunnel Junctio 
5.4.6 Curie-Weiss Relation of the Ferroelectric Capacito or
Tunnel Junctio .
5.5 Ferroelectric Superlattices in Nanoscale
5.5.1 The Free Energy Functional ofFerroelectric Superlattices
5.5.2 The Phase Tra ition Temperature ofPTO/STO Superlattice.
5.5.3 Polarizafion and Critical Thickness ofPTO/STO Superlattice
5.5.4 The Curie-Weiss-Type Relation ofPTO/STO Superlattice
5.6 Ferroelectric Nanowires and Nanotubes
5.6.1 Surface Te ion ofFerroelectric Nanowires and Nanotubes.
5.6.2 Size and Surface Effects on Ferroelectric Nanowires
5.6.3 Ferroelectric Nanotubes
5.7 Ferroelectric Nanograi or Nanoislands
5.7.1 Free Energy of Ferroelectric Nanograi or Nanoislands
5.7.2 Stability of the Ferroelectric State and Tra ition
Characteristics
5.7.3 Critical Properties of Nanograi or Nanoislands
5.8 Remarks
References

6 Strain Engineering： Ferroeleetrie Films on Compliant Substrates
6.1 Background
6.2 Manipulation of Phase Tra ition Behavior of Ferroelectric Thin
Films on Compliant Substrates
6.2.1 Free Energy Expressio 
6.2.2 Evolution Equatio 
6.2.3 Manipulation of Ferroelectric Tra ition Temperature and Critical Thickness
6.2.4 Manipulation of the Order of Tra ition
6.3 Piezoelectric Bending Respo e and Switching Behavior of
Ferroelectric Thin Film with Compliant Paraelectric Substrate
6.3.1 Model of Ferroelectric Thin Film with Compliant
Paraelectric Substrate and the Energy Expressio 
6.3.2 Solution of the Evolution Equation
6.3.3 The Stationary and Relative Bending Displacements of the
Bilayer
6.3.4 Dynamic Piezoelectric and Bending Respo e of the
Bilayer Under a Cyclic Electric Field
6.3.5 Examples and Discussio 
6.4 Critical Thickness for Dislocation Generation in Piezoelectric Thin
Films on Substrate
6.4.1 Elastic and Electric Fields in a Piezoelectric Semi-Infinite
Space with a Dislocation
6.4.2 Critical Thickness for Dislocation Generation
6.4.3 Effect of Piezoelectric Behavior of the Materials on the
Critical Thickness for Dislocation Formation
6.5 Critical Thickness of Dislocation Generation in Ferroelectdc
Thin Film on a Compliant Substrate
6.5.1 Mechanical Properties of the Problem
6.5.2 The Formation Energy and the Critical Thickness of Spontaneous Formation of Misfit Dislocation
6.6 Remarks
References

7 Derivation of the Landau-Ginzburg Expa ion Coefficients
7.1 Introduction
7.2 Fundamental of the Landau-Devo hire Theory
7.2.1 The History of the Landau Free Energy Theory
7.2.2 The Thermodynamic Functio of the Dielectrics and Phase Tra ition
7.2.3 The Expa ion of the Free Energy and Phase Tra ition
7.3 Determination of Landau Free Energy Expa ion Coefficients Based on Experimental Methods
7.3.1 The Experimental Observation of the Phase Tra ition Characteristics in Ferroelectrics
7.3.2 The Phenomenological Treatment of Devo hire Theory
7.3.3 The Elastic Gibbs Free Energy of PbTiO3 and Its Coefficients
7.3.4 The Determination of the Expa ion Coefficients from
the Fi t-Principle Calculation Based on the Effective
Hamiltonian Method
7.4 Gradient Terms in the Landau-Devo hire-Ginzburg Free Energy Expa ion
7.4.1 The Co ideration of Spatial Non-uniform Distribution
of the Order Paramete in the Landau Theory
7.4.2 The Critical Region and the Applicability of Landau
Mean Field Theory
7.4.3 Determination of the Gradient Terms from the Lattice
Dynamic Theory
7.4.4 The Extrapolation Length and the Gradient Coefficient
7.5 The Tra ve e Ising Model and Statistical Mechanics Approaches
7.5.1 Phase Tra ition from the Tra ve e Ising Model
7.5.2 Relatio hip of the Paramete Between Landau Theory
and the Tra ve e Ising Model
7.5.3 Determination of Landau-Ginzburg Free Energy Expa ion
Coefficients from Statistical Mechanics
7.6 Remarks
References

8 Multiferroie Materials
8.1 Background
8.2 Coupling Mechanism of Multiferroic Materials
8.2.1 Single Phase Multiferroic Materials
8.2.2 Magnetoelectric Composites
8.3 Theories of Magnetoeleclric Coupling Effect at Low Frequency
8.3.1 Energy Formulation for Multiferroic Composites
8.3.2 Phase Tra ition Behavio in Layered Structures
8.3.3 Magnetoelectfic Coupling Coefficients in Layered Structures
8.4 Magnetoelectric Coupling at Resonance Frequency
8.4.1 Magnetoelectric Coupling at Bending Modes
8.4.2 Magnetoelectfic Coupling at Electromechanical Resonance
8.4.3 Magnetoelectric Coupling at Ferromagnetic Resonance
8.5 Remarks
References

9 Dielectric Breakdown of Mieroeleetronie and Nanoeleetronie Devices.
9.1 Introduction
9.2 Basic Concepts
9.2.1 MOS Structure
9.2.2 Different Tunneling Modes
9.2.3 Dielectric Breakdown Modes
9.2.4 Defect Generation
9.2.5 Basic Statistical Concepts of Dielectric Breakdown
9.2.6 Stress Induced Leakage Current
9.2.7 Holes Generation
9.2.8 Energetics of Defects
9.3 Mechanism Analysis of Tunneling Phenomena in Thin Oxide Film.
9.3.1 Self-co istent SchrSdinger's and Poisson's Equatio 
9.3.2 Tra mission Coefficient
9.3.3 Tunneling Current Components
9.3.4 Microscopic Investigation of Defects from Fi t-Principles Calculation
9.3.5 Manipulating Tunneling by Applied Strai 
9.4 Degradation Models in Gate Oxide Films
9.4.1 Anode Hole Injection Model
9.4.2 Thermochemical Model
9.4.3 Anode Hydrogen Release Model
9.4.4 Thermal Breakdown Model
9.4.5 Mechanical-Stress-Induced Breakdown Model
9.4.6 Remarks
9.5 Statistical Models of Dielectric Breakdown
9.5.1 A Basic Statistical Model
9.5.2 A Three-Dime ional Statistical Model
9.5.3 Sphere and Cube Based Percolation Models
9.5.4 Combination of Percolation Model and Degradation Model
9.6 Damage of Dielectric Breakdown in MOSFET
9.6.1 Lateral Propagation of Breakdown Spot
9.6.2 Dielectric Breakdown-Induced Epitaxy
9.6.3 Dielectric Breakdown-Induced Migration
9.6.4 Meltdown and Regrowth of Silicided Poly-Si Gate
9.6.5 Damage in Substrate
9.7 Remarks
References
Index