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Atomic force microscopy images, X-ray diffraction patterns, transmission electron microscopy (TEM) images, and selected-area electron-diffraction patterns showed that the surface roughness and the crystallinity of ZnO thin films with a (0001) hexagonal structure grown on n-Si (001) substrates by using plasma-assisted molecular beam epitaxy were enhanced by increasing the annealing temperature up to 600 $^\circ$C due mainly to the surface and interface energy effect for the ZnO thin films, and the corresponding results showed that the surface roughness and the crystallinity of the ZnO thin films annealed at 900 $^\circ$C deteriorated due to thermal diffusion in the sample. The TEM image for the ZnO/Si heterostructure annealed at 900 $^\circ$C showed that the interfacial layer was formed due to interdiffusion between the ZnO thin film and the n-Si (001) substrate.