You can use Focused Ion Beam milling to make a cross sectional TEM specimen. You can find out the crystal structure, composition and grain size of oxide layer in addition to film thickness.

Probably you can see how uniform is your coated layer in cross-section.

There is a specialized focused ion beam milling equipment. They are used to prepare highly uniform cross section sample for TEM Analysis. You can find out the domain structure, diffraction plane to confirm the XRD analysis, thin film thickness, precise composition of the sample, crystal structure, grain structure and its size. Moreover, with varying electric field assisted TEM you can also see the domain structure with varying electric field. Further, the change in the domain structure with varying field can also suggest the phase transition with electric field. In short, you might get enough information for understanding the in-depth knowledge of your thin film.