According to the processes of nucleation and growth of nanocrystalline silicon (nc-Si) with shape changing from sphere-like to disc-like in the a-SiNx/a-Si:H/a-SiNx sandwich structure or a-Si :H/a-SiNx multilayer structure, we have proposed the theoretical model of constrained crystallinzation based on the classical thermodynamics, in which the increase of the interfacial energy between nc-Si and a-SiNx causes the growth of nc-Si to halt, and concludes the critical thickness of a-Si sublayer (34 nm) for constrained crystallization, The model of constrained growth has been validated in a-SiNx/nc-Si/a-SiNx sandwich and nc-Si/a-SiNx multilayer structures formed by laser annealing and thermal annealing.