In this paper, we adapted the Stranski-Krastanow (SK) mode to the heteroepitaxial growth of NWs and suggested three general growth modes (SK, island SK, and coherent SK) covering all phenomena observed from nanostructures epitaxially grown on single crystal substrates. A strain versus dislocation (SVD) model was also established to define these three modes. The SVD model analyzes the competition between strain energy and dislocation energy at the NW-substrate interface. Experimental data acquired from ZnO NWs grown on GaN substrates via the three modes exhibited a good match to our theoretical prediction. NWs could be grown coherently on the substrate only when their sizes are smaller than the critical size. A defective intermediate structure was found to be necessary for growing nanostructures larger than the critical sizes. The SVD model has also been successfully applied to ZnO nanofins grown on GaN and ZnO NWs grown on sapphire, which demonstrated the generality of the SVD model for understanding the heteroepitaxial growth behaviors of various nanostructures. This work provided a necessary quantitative complement to the thermodynamics and diffusion kinetics in predicting the nanostructure growth phenomena.
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