To sustain crystal structure is it necessary to have some minimum mechanical stress, formed due to the annealing, below which it may go back to the initial amorphous nature?
This depends on a lot of different parameters - first of all, which material are you working with? How and on which substrate did you grow it, and to which temperature are you planning to anneal it?
UHMW-PE (ultra-high-molecular-weight polyester), e.g., gets a crystal-like structure by stretching during the production process. Similarly, fine stainless steel wires change their phase during the stretching process (possibly leading to ferromagnetism in originally nonmagnetic wires), which can be reversed by annealing. So - it depends on the experimental conditions, if there is any possibility to create / change a crystal-like structure by stress.
Besides, the question was related to "sustained crystal structure" - which sounds for me as if there was a crystal structure before and the material was nearly molten in the after-treatment under mechanical stress.
Can you give us a little bit more Information? Which high-k dielectric are you growing? To my knowledge, in the CVD process the lattice mismatch between the substrate and the high-k film decides whether a material grows amorphous or epicatically; I have no experience myself with RF sputtering. However, I know that heating may result in enhanced crystallinity (see, e.g., http://www.elmi.uni-bonn.de/en/sub/forschung/filme_e.html) - although I don't see anything about pressure or stress being reported there.