Are you depositing your films by sputtering technique.
If not, then by which technique are you depositing the films.
As you might already know there are intrinsic and extrinsic stresses.
1) In sputtering techniques, depending upon the sputtering gas combination, sputtering power and Ar/O2 gas ratio, the residual stress in the deposited films varies. It can be either compressive or tensile. These stresses depending on the growth conditions are contributing to the intrinsic stresses, and large depend on the deposition condition and techniques.
2) The extrinsic stresses could arise due to the differences between the substrate and
and film properties.
3) In order to analyse the situation with annealing where stresses are changing, these could be linked re-transformation due to annealing in the internal crystal and microstructure in the films.
there is a wealth of literature on ZnO films deposited by different conditions on different substrates.
To start with, grain growth during annealing can induce tensile stress. The magnitude of the tensile stress depends on change in the grain size which in-turn depends on temperature . If high enough, the tensile stress generated can compensate/overcome the compressive growth stress.
the stress sign change may be due to Si uptake (a corrosion like mechanisms) from the substrate into ZnO, so you have a tensile stress at a critical temperature Tc (can you give a rough value about Tc?). Check for Si in ZnO with one of the techniques :X-ray refl. mode, Tem, Sem etc. .