Fig. 1. Schematic of PZT ferroelectric structure: (a) Paraelectric cubic phase; (b) ferroelectric tetragonal phase; (c) ferroelectric orthorhombic phase; (d) ferroelectric rhombohedral phase.

Fig. 2. (a)−(f) Free energy surface of PZT with the decrease of Ti composition (x = 0.8–0.2) at room temperature. Blue and red color represents the minimum and maximum value respectively; (g)−(i) Schematic of double well potential of tetragonal phase (g), mixed phase (h) and rhombohedral phase (i).

Fig. 3. Domain structures of PZT (x = 0.8, x = 0.48, x = 0.2) thin film with different substrate biaxial misfit strain (ε_sub = 0, ε_sub = –0.5%, ε_sub = 0.5%): (a)−(c) Domain structures of PZT (x = 0.8) thin films at ε_sub = 0, ε_sub = –0.5%, ε_sub = 0.5%; (d)−(f) domain structures of PZT (x = 0.48) thin films at ε_sub = 0, ε_sub = –0.5%, ε_sub = 0.5%; (g)−(h) domain structures of PZT (x = 0.2) thin films at ε_sub = 0, ε_sub = –0.5%, ε_sub = 0.5%.

Fig. 4. Hysteresis loops of PZT thin films with three Ti components at different substrate biaxial misfit strains (ε_sub = ± 0.1%, ± 0.5%, ± 1.0%), and P^* and E^* are normalized polarization and electric field: (a)−(c) The case of compressive strains; (d)−(f) the case of tensile strains.

Fig. 5. Normalized coercive field (E_c^*), saturation polarization (P_r^*), and remnant polarization (P_s^*) as a function of substrate misfit strain (ε_sub), where three PZT ferroelectric thin films with x = 0.8, 0.48 and 0.2 Ti component are considered: (a) Coercive field vs. strain; (b) saturation polarization vs. strain; (c) remnant polarization vs. strain.

Fig. 6. (a) Schematic of P-E loop used for energy storage; (b) the energy storage efficiency as a function of substrate misfit strain.