Micromechanical analysis of surface defects

Many overlayer/substrate systems exhibit a form of thin-film growth, which involves a layer-by-layer mode, subsequently switching to a three-dimensional growth (Stranski-Krastanov [SK]). This phenomenon has serious material implications because the layer-by-layer growth mode is often preferred in a number of important engineering applications. Recent experimental evidence suggests that the SK mode and resulting morphologies are controlled by local interactions among defects on growing crystal surfaces and cannot be properly characterized on the basis of thermodynamics alone. Surface defects corresponding to adatoms, vacancies and steps, together with misfit dislocations interact with each other affecting and often dominating the kinetic processes. Little work has actually been done in this area and problems of fundamental importance such as the elastic interaction between an adatom and a step or a misfit dislocation have not been addressed. The theoretical modeling that will be discussed here is focused on the local elastic field in the vicinity of adatoms, vacancies and steps as well as on issues involving their interaction. To obtain the near-the-defect behavior, a modified lattice theory is employed; this approach was developed by extending the eigenstrain concept into the classical lattice theory. Green's functions for infinite and semi-infinite lattice spaces are derived and verified by comparing their asymptotic expressions with the corresponding continuum solutions. The analysis establishes the fact that differences between lattice and continuum solutions exist only in a small neighborhood of the defect. A Local Lattice Method (LLM) is subsequently proposed to study near defect deformation when a lattice level solution is required. It is shown through examples that the LLM is a simple and effective numerical scheme, regardless of the problem geometry.