Strain effects on domain structures in ferroelectric thin films from phase‐field simulations

Abstract

Strain and applied external electric fields are known to influence domain evolution and associated ferroelectric responses in ferroelectric thin films. Here, phase‐field simulations are used to predict equilibrium domain structures and polarization‐field (P‐E) hysteresis loops of lead zirconate titanate (PZT) thin films under a series of mismatch strains, ranging from strongly tensile to strongly compressive. In particular, the evolution of domains and the P‐E curves under different applied strains reveal the mesoscale mechanism, the appearance of in‐plane polarization during domain switching, that is responsible for a relatively small coercive field and remnant polarization. A Landau energy distribution is analyzed to better understand the domain evolution under various strain conditions. The results provide guidance for choice of mismatched strains to yield the desired P‐E hysteresis loops and the domain structures.

The role of lattice dynamics in ferroelectric switching

“…Finally, we performed time-resolved phase-field simulations (Methods 33 ) to further investigate the relevant energy scales and the effects of clamping during switching. We simulated the same applied voltage (13 V) for both the clamped and membrane cases, and the evolution of elastic, electric, and Landau energy during the switching process (2000 time steps) was computed 49 , 50 (Fig. 5 ).…”

“…The current phase-field model for ferroelectric freestanding film is an extension to our previous model for bulk and epitaxial thin-film simulations 32 , 33 , 50 , 53 , 54 in which we use the spontaneous polarization p = (p 1 , p 2 , p 3 ) and oxygen octahedral tilt as the order parameters. A temporal evolution of the order parameters can be obtained by solving the time-dependent Ginzburg–Landau equation 55 , 56 : in which and are the kinetic coefficients, t is time, is the total free energy of BFO membrane.…”

The role of lattice dynamics in ferroelectric switching

“…to further investigate the relevant energy scales and the effects of clamping during switching. We simulated the same applied voltage (13V) for both the clamped and membrane cases, and the evolution of elastic, electric, and Landau energy during the switching process (1000 time steps; where each time step is ~100 fs) were computed [50], [51] (Fig. 5).…”

“…Phase-field simulation. The current phase-field model for ferroelectric free standing film is an extension to our previous model for bulk and epitaxial thin film simulations [30], [32], [51], [53], in which we use the spontaneous where hf means the membrane thickness. Second, since overall freestanding film is in a stress-free state, the in-plane macroscopic strain is set to be the average eigenstrain calculated from the current order parameter distribution.…”