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The subindices indicate that the field E is in the 3-direction (z-direction), i.e., normal to the film, while the strain is in the 1-And 2-direction (x-And y-direction) in the plane of the film.
However, in the above axis definition, it should be, strictly speaking, the d 11mode. For cubic symmetry, the piezoelectric parameters d 33and d 11are equal. However, for clamped films, this is not necessarily and even likely to be the case.
Since one is not interested in thickness changes, the indentation effect is not so relevant for the determination of d 31. In addition, the domain structure does not play a role in the effective value of d 31, although hard clamping and domain wall motion are taken into account.75
The tabulated samples from Refs. 52 and 54 are for very comparable samples with a 50 nm nucleation layer, 100 nm electrodes, and a 1 μ m PZT. All devices were made by the same researcher using the same deposition and patterning technologies (PLD for oxide layers and sputtering for the Pt layers).
Note that there is a significantly lower saturation polarization of the films on Pt compared to those on oxide nucleation layers (not shown in table), although all films are subject to the same in-plane tensile stress. This suggests increased polarization rotation into the plane for the first group of films. We speculate that it might be due to charged grain boundaries. However, this polarization difference is not reflected in very different values of the piezoelectric parameters for comparable films.
Although the monolithic integration of silicon compatible light sources is a field of intense research-e.g., using Si-Ge-Sn alloys-well-established packaging solutions can be used to integrate III-V laser diodes.
