Substrate Clamping Effects on Irreversible Domain Wall Dynamics in Lead Zirconate Titanate Thin Films

The role of long-range strain interactions on domain wall dynamics is explored through macroscopic and local measurements of nonlinear behavior in mechanically clamped and released polycrystalline lead zirconate-titanate (PZT) films. Released films show a dramatic change in the global dielectric nonlinearity and its frequency dependence as a function of mechanical clamping. Furthermore, we observe a transition from strong clustering of the nonlinear response for the clamped case to almost uniform nonlinearity for the released film. This behavior is ascribed to increased mobility of domain walls. These results suggest the dominant role of collective strain interactions mediated by the local and global mechanical boundary conditions on the domain wall dynamics. The work presented in this Letter demonstrates that measurements on clamped films may considerably underestimate the piezoelectric coefficients and coupling constants of released structures used in microelectromechanical systems, energy harvesting systems, and microrobots.

Figure 1

(a) Fabrication process of the diaphragm structures. Dry-etch steps define the top electrode features and openings down to Si and the bottom electrode. Isotropic etch using ${\mathrm{XeF}}_2$ releases the actuator. (b) SEM image of a cross section of the fabricated device. (c) Field dependence of the real dielectric permittivity for the fully clamped PZT capacitor, for the fully released PZT, and for the fully released and broken PZT capacitor. The orange (light gray) and violet (medium gray) data points were obtained by normalizing for the released region using a parallel capacitor model. (d) Calculated and measured minor hysteresis loops (uncorrected for the area fraction which was released).

Figure 2

Frequency dispersion of the Rayleigh parameters extrapolated from the ac field dependence of the dielectric constant for clamped capacitors and released but still intact electrodes. The square data points are normalized Rayleigh parameters from 14% released areas using a parallel capacitor model. The error bars take into account errors from the area and Rayleigh parameter fittings.

Figure 3

Deformation strains associated with the formation of domains could couple mechanically to the underlying substrate. (a) Local stresses develop at the PZT-bottom electrode interface which may differ from the average residual stress and influence the domain wall mobility. (b) Removal of mechanical constraints imposed by the Si substrate at the PZT-bottom electrode interface allows the domain walls to respond to the electric field more freely.

Figure 4

(a) Topography map, (b) resonance frequency ${\omega }_0$ map, (c) phase at ${\omega }_0$ averaged over $V_{\mathrm{ac}}$, and (d) standard deviation of ${\omega }_0(V_{\mathrm{ac}})$. The dotted line indicates the clamped-released boundary.

Figure 5

Dependence of nonlinearity on the mechanical boundary condition. (a) ${\alpha }_d/d_{33,\mathrm{init}}$ ratio map highlighting the released (blue [dark gray]) and clamped (orange [medium-light gray]) regions used for (b) the absolute frequency and (c) cumulative relative frequency histograms.