Steady-State Structures in Composition-Modulated Alloys: Kinetic Phase Transition Between 1D and 2D Patterns

A non-linear continuum theory of self-organized growth of composition-modulated structures in alloys is developed. It is shown that, for a lattice-matched alloy, where compositional and morphological instabilities are uncoupled in the linear regime, the two instabilities are coupled due to non-linear effects. Due to non-linear coupling, composition-induced stresses may lead to an instability of the advancing surface against undulations. A non-planar surface profile favors kinetic phase transition from the growth of a 1D modulated structure to the growth of a 2D one. A steady-state phase diagram in variables “temperature — growth velocity” is constructed which contains regions of homogeneous alloy growth, of 1D steady-state structures, of 2D steady-state structures, and the region where both 1D and 2D structures are possible. For zinc-blend semiconductors, the interplay between the anisotropic elasticity and anisotropic surface diffusion may lead to the kinetic phase transition between the growth of a 2D structure modulated in the elastically soft directions [100] and [010] to the growth of a 1D structure modulated in the direction of the fast diffusion [110]. Our theory explains this type of transition observed in the growth of InAlAs/InP.