G. Ravichandran Aeronautics & Mechanical Engineering Graduate Aeronautical Laboratories California Institute of Technology

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1 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

2 An approach to large strain actuation PbTiO 3 Pb Ti c c a = 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 %

3 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

4 Frustration leads to domains minimize: W e,p on average Electrodes provide shielding

5 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

6 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)

7 Characterization: structure-properties link Apply constant stress, cyclic electric field: σ σ Burcsu, Ravichandran & Bhattacharya, V V σ σ Strain (%) , ,000 Electric field (V/cm) Supported by ARO

8 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.

9 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 domain wall Are domain walls mobile? Do they damage the material? In polycrystals? In thin films? , ,000 Electric field (V/cm)

10 Strain at Different Compressive Stress Bulk BaTiO3

11 Actuation Strain and Coercive Field Actuation Strain vs. Stress σ Actuation Strain (%) (001) Crystal (001) Crystal (100) Crystal Phase diagram for 001 BaTiO 3 V Compressive Stress (MPa)

12 In Situ Microscopy 1.0 MPa

13 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

14 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

5 mm (100) crystal after experiment (001)

15 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

16 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

17 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

Microelectromechanical systems (MEMS) have become an increasingly important area of

1 Chapter 1 Introduction 1.1 Background Microelectromechanical systems (MEMS) have become an increasingly important area of technology. This is due to the premise that the efficiencies of high volume production