revealing “butterfly loops” [32]
. These loops are a clear signature for a piezoelectric hysteresis in the thin film.
The piezoelectric effect is a factor of ~2 stronger for grains oriented with [100] out-of-plane direction than for grains oriented with [110] out-of-plane direction,
evidencing piezoelectric anisotropy.
Considering a linear voltage drop over the entire film thickness of 710 nm, the piezoelectric coefficient in the lab reference frame dperp at U = 9 V for the PZT (100)
and PZT (110) yields ~230 and ~110 pm/V,
respectively. These values are in good agreement with theoretical piezoelectric coefficients found in literature for these two crystalline orientations [33,34].