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Two kinds of ZnO polar step surface(0001)-Zn and(000-1)-O are systematically studied via density function theory(DFT)calculations.When an adatom(Zn/O)migrates from the upper surface to the descending step,they go through a sequence of states whose energy levels can be computed and arranged in to a step-by-step map.Analysis begins with the structures and energetics of different step edges.Then different diffusion processes of adatom on the steps are described.The results clearly show us how the adatom is trapped at the edge and how steps cause an Ehrich-Schwoebel barrier.The ES barrier affects ZnO island nucleation and developed morphology and gives us some explanations of experimental facts.