Multi-Disciplinary University Initiative Army Research Office Engineering Microstructural Complexity in Ferroelectric Devices Mechanical Characterization G. Ravichandran Aeronautics & Mechanical Engineering Graduate Aeronautical Laboratories California Institute of Technology Kick-off Meeting May 30, 2001
An approach to large strain actuation PbTiO 3 Pb Ti c c a = 1.065 O a High temperature (non-polar cubic) Room temperature (<001> polarized tetragonal) Six equivalent <001> cubic directions give six equivalent states at room temperature Switching between variants gives large strain BaTiO 3 : 1% PbTiO 3 : 6.5 %
Potential Energy of Ferroelectric minimize exchange stored applied field electrostatic W encodes information about crystallography and texture: it has a multi-well structure. ϕ electric potential for a given polarization C 1 C 2 Q V Ω Exchange energy is negligible in large specimens Shu and Bhattacharya, 2000
Frustration leads to domains minimize: W e,p + + + + + ++ + - - - - - - - - - - on average Electrodes provide shielding
Low energy domain walls minimize n Domain wall requires (Mechanical compatibility) (Electrostatic compatibility) simultaneously. Overdetermined? Magic of symmetry: Simultaneous solution if for a 180 rotation R Tetragonal 90 Rhombohedral 107 Orthorhombic 60,90,100 DeSimone and James, 1997 Shu and Bhattacharya, 2000
Phases of Barium Titanate Cubic to tetragonal phase transition results in a spontaneous strain and polarization BaTiO 3 Ba 2+ Ti 4+ O 2- c c a = 1.01 a Cubic (high temp) Tetragonal (room temp)
Characterization: structure-properties link Apply constant stress, cyclic electric field: σ σ Burcsu, Ravichandran & Bhattacharya, 2000 0 V V σ σ 1.0 2 Strain (%) 0 1-10,000 0 10,000 Electric field (V/cm) Supported by ARO
Domain Visualization Birefringence Birefringence generates contrast between 90 domains when viewed through crossed polarizers I ( πd λ) = I sin (2θ)sin n o 2 2 Linear Polarizer d Linear Polarizer
Domain walls mediate switching Switching gives large strain, E but energy barrier is extremely high! Domain walls lower the energy barrier by enabling nucleation and growth 1.0 Strain (%) Experiments in BaTiO 3 2 90 domain wall Are domain walls mobile? Do they damage the material? In polycrystals? In thin films? 0 1-10,000 0 10,000 Electric field (V/cm)
Strain at Different Compressive Stress Bulk BaTiO3
Actuation Strain and Coercive Field Actuation Strain vs. Stress 1 0.9 σ Actuation Strain (%) 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 (001) Crystal (001) Crystal (100) Crystal 0 1 2 3 4 5 Phase diagram for 001 BaTiO 3 V Compressive Stress (MPa)
In Situ Microscopy 1.0 MPa
Domains in Single Crystal Thin Films Free-standing film with electrodes Electrostatic field energy is negligible Out-of-plane mechanical mismatch costs negligible energy Low energy domain walls only requires t (in-plane mechanical compatibility) Many more domain walls compared to bulk! Suggest strategies for microactuation
Electromechanical Characterization BaTiO3-PbTiO3 (BT-PT) Pseudo-single crystals (Biaxially textured thin films) Test Bed Programmable applied field (E) Constant force (f) applied to structure (compliant system) Deformed shape & polarized video microscopy
Damage & Failure: Bulk Crystals Cracks develop over the course of the experiments For polydomain crystals are parallel to the initial domain structure 5 mm (100) crystal after experiment (001) crystal after experiment Spark path along crack face 1 mm
Fatigue and Failure Characterization Electro-mechanical loading Mechanical loading through wafer bending Evolution of domain wall nucleation and motion Assess mechanical integrity with cycling (e.g., Hinges ) Measure charge and polarization degradation In-situ visualization of nucleation of cracks Validation of models for reliability
Mechanics Bulk response of PT Thin films of BT-PT Mechanical performance: strain, work output Frequency response Reilability (Fatigue and Fracture) Mechanisms Outlook Kinetics of domain motion under applied field and stress Hysteresis-Dissipation Domains: bulk versus thin films Processing Theory Characterization