Composition modulation and nanophase separation in a binary epilayer

When a thin binary layer grows epitaxially on an elemental substrate, the c omposition often modulates in the plane of the layer. The layer may even de mix when the bulk of the same composition is miscible. Sometimes the layer separates into two phases, forming periodic stripes or other regular patter ns. The size of the separated phases may be in the range 1-100 nm, and stab le against coarsening on annealing. This paper develops a thermodynamic fra mework to study these remarkable phenomena. For an epilayer less than a few monolayers thick, the excess energy cannot be attributed to individual sou rces of superficial misfit. Instead, we lump the epilayer and adjacent mono layers of the substrate into a single superficial object, and specify the e xcess surface energy for the object. The variation of the surface energy de nsity with the variation of the strain defines surface stress. When the com position modulates in the epilayer, the surface stress is nonuniform, defor ms the substrate, and reduces the total energy. Consequently, the compositi on-dependent surface stress tends to refine phases, resisting coarsening. I n a stability analysis, we perturb a uniform concentration field into a sin usoidal field with a small amplitude and an arbitrary wavelength. The entro py of mixing stabilizes the uniform layer for long wavelengths. To stabiliz e the uniform layer for short wavelengths, we assume that the surface energ y density also depends on concentration-gradient. A stability condition sho ws the combined elastic, entropic, and gradient effects. We also outline a dynamical system, which can be used to study pattern emergence and evolutio n during annealing. (C) 2000 Elsevier Science Ltd. All rights reserved.