Equilibrium Configuration of Epitaxially Strained Thin Film Surfaces
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CONFIGURATION
OF EPITAXIALLY STRAINED THIN FILM
K. JAGANNADHAM*, J. NARAYAN*, AND J.P. HIRTH** *Department of Materials Science and Engineering, North Carolina State University, Raleigh, NC 27695, [email protected]. "**Department of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164. ABSTRACT The formation of convex and concave regions on the surface of a strained thin epitaxial film on a thick substrate is analyzed by minimization of energy associated with the configuration. The strain energy change resulting from the formation of undulations is modelled with the strain in the film represented by a continuous distribution of dislocations along the perturbed surface and the interface. A discrete dislocation model is also used when periodic undulations are formed. Results of energy minimization for germanium or germanium-silicon alloy films on silicon substrate illustrate that convex regions tend to grow. On the other hand, convex regions formed to conserve mass in shape changes associated with concave regions become stable with minimum energy under quasi-equilibrium when the mobility of adatoms is low. We have determined the size and radius of curvature of the undulations at minimum energy and conclude that it is favorable to form atomic steps on the surfaces from which dislocation generation and strain relaxation takes place. INTRODUCTION Strained epitaxial thin films are known to develop convex and concave regions of surface to lower the energy associated with the heterostructure configuration [1-3]. The driving force for the development of the undulations and the associated atomic steps is identified with a larger decrease in strain energy than the resulting increase in surface energy. It is known that the activation energy for nucleation of misfit dislocations at the atomic steps is reduced and the strain in the film is relaxed at a lower critical thickness [4,5]. We have shown earlier that the build up of strain energy with the thickness of the film helps the activation energy for dislocation nucleation to be overcome by generation of atomic steps at the surface [4,5]. The radius of curvature of the surface should become small so that the formation of single or multiple atomic steps becomes necessary. The formation of sinusoidal perturbations on stressed solid surfaces has been analyzed to provide an estimation of wavelength of perturbation [2]. Observation of the formation of cusps on the surface of Ge 0 .5Si 0.5 epilayers grown on Si substrate is also reported [6]. In the present analysis, the formation of concave and convex regions at the surface of the epilayer is considered through a determination of the energy of the configuration. MODEL OF RELAXED SURFACE We have considered, as shown in Fig. 1, the initial stages of relaxation by invoking a perturbation of the surface in which a cylindrical convex region of radius R, and length 2L1 forms to conserve mass in shape change resulting from formation of a concave region of radius R2 and length 2L 2. In addition, we have
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