Figure 2: Domain patterns and domain width in PZT films grown on DSO substrate.
(a) 50 nm thick film: out-of-plane PFM amplitude map with yellow areas showing the piezoelectric activity of the c-domains and dark lines showing piezoelectrically inactive strips. The scale bar is 1 μm. (b) TEM and (c) HRSTEM cross-section of the film shown in a confirming that the inactive strips of a are a-domains. The scale bars are 50 and 5 nm, respectively. (d) 60 nm thick film: large-scale PFM scan showing a continuous parallel domain pattern throughout the whole scan range. Scan on different positions on the sample also show a purely parallel a-domain pattern parallel to the [
]S direction. The scale bar is 10 μm. (e) Magnification of the framed area in d, the scale bar is 1 μm. (f) Geometric phase analysis of HRSTEM images similar to c visualizing the evolution of the a-domain width with the film thickness. The scale bar is 10 nm for the 163nm thick film and 20 nm for the others. (g) Measured width of a-domains in stripe domain patterns as a function of film thickness (data points). Theoretical prediction for the thickness dependence of the a-domain width in sparse a-domain patterns, equation (11), calculated using the lattice parameters of free standing PZT, obtained by analysis of the actual lattice parameters of our films (solid line). The minimum domain width predicted by the theory and evaluated using the material parameters of a PZT film taken from ref. 1 (dashed line). The crossing point marked with hcr corresponds to the critical thickness for the domain formation given by equation (4).
