Evolution of morphology and composition in three-dimensional fully faceted strained alloy crystals

Alloy structures such as core-shell particles, heteroepitaxial multilayers and nanowires have received a lot of attention in recent years due to their applications in logic, energy storage and optoelectronics. In typical growth conditions, the surfaces of these structures are usually faceted i.e. they adopt low-energy singular crystalline orientations. For alloy systems, the growth law for a fully faceted structure requires the specification of the normal velocity of each facet, the incorporation rate of each alloy component on the surface, and the exchange of surface atoms with the bulk. The latter process requires consideration of both surface segregation and possibly bulk material transport. By using only fundamental concepts of thermodynamics, we derive the governing equations for the growth of strained and fully faceted two-component crystals in regimes where surface material transport may be governed by surface-attachment limited kinetics or surface diffusion limited kinetics. In both cases we derive a very compact form for the surface mass fluxes from chemical potentials that account for the constraint stemming from the fact that while the growth rate of each alloy component can vary along the surface (as governed by the individual chemical potentials), their sum should remain constant along the facet and should be equal to the growth velocity of the facet. Within our approach, the dynamics of surface segregation and other important features of faceted crystal growth that lead to compositional patterning such as a kinetic barrier for exchange of alloy components between different facets emerge in a very natural fashion.