Morphological instability of heteroepitaxial growth on vicinal substrates: A phase-field crystal study

We investigate morphological instability of heteroepitaxially grown thin films on vicinal substrates with the phase-field-crystal (PFC) model. The PFC model is tuned to have a sharp transition between solid and liquid. Thus, steps, terraces and kinks can be clearly identified. The substrate is modeled by an external pining potential. Varying vicinal angle and misfit between substrate and film a phase-diagram for morphological instability of the strained thin film near equilibrium is constructed. The morphology of the growing strained thin film follows the equilibrium morphological phase-diagram, but indicates less critical mismatch strain for dislocation formation. For small mismatch strains, the step-flow and the step-bunching modes contribute to the coherent film growth on the vicinal substrate, whereas for large mismatch strains, the strong non-coherent film growth tendency is caused due to the increased possibility of the mismatch dislocation formation, as companied by the island growth on the hill-and-valley facetted structures. Our simulation results demonstrate interconnection of the steps, the islands, and the mismatch dislocations during the heteroepitaxial growth on the vicinal substrate.