Physical mechanism of surface roughening of the radial Ge-core/Si-shell nanowire heterostructure and thermodynamic prediction of surface stability of the InAs-core/GaAs-shell nanowire structure.

As a promising and typical semiconductor heterostructure at the nanoscale, the radial Ge/Si NW heterostructure, that is, the Ge-core/Si-shell NW structure, has been widely investigated and used in various nanodevices such as solar cells, lasers, and sensors because of the strong changes in the band structure and increased charge carrier mobility. Therefore, to attain high quality radial semiconductor NW heterostructures, controllable and stable epitaxial growth of core-shell NW structures has become a major challenge for both experimental and theoretical evaluation. Surface roughening is usually undesirable for the epitaxial growth of high quality radial semiconductor NW heterostructures, because it would destroy the core-shell NW structures. For example, the surface of the Ge-core/Si-shell NWs always exhibits a periodic modulation with island-like morphologies, that is, surface roughening, during epitaxial growth. Therefore, the physical understanding of the surface roughening behavior during the epitaxial growth of core-shell NW structures is essential and urgent for theoretical design and experimentally controlling the growth of high quality radial semiconductor NW heterostructures. Here, we proposed a quantitative thermodynamic theory to address the physical process of epitaxial growth of core-shell NW structures and surface roughening. We showed that the transformation from the Frank-van der Merwe mode to the Stranski-Krastanow mode during the epitaxial growth of radial semiconductor NW heterostructures is the physical origin of surface roughening. We deduced the thermodynamic criterion for the formation of the surface roughening and the phase diagram of growth and showed that the radius of the NWs and the thickness of the shell layer can not only determine the formation of the surface roughening in a core-shell NW structure, but also control the periodicity and amplitude of the surface roughness. The agreement between the theoretical results and the experimental data of the Ge-core/Si-shell NW structure implied that the established approach could be applicable to the understanding and design of various semiconductor core-shell NW structures. Consequentially, we used the established theoretical model to study the epitaxial growth of the InAs-core/GaAs-shell NW structure and predict the surface roughening formation, as well as the periodicity and amplitude of the surface roughness, which provided useful information to theoretically design and experimentally control the epitaxial growth of the radial InAs-core/GaAs-shell NW structure.