Strain Relaxation by Dislocation Arrays in Thin Films
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STRAIN RELAXATION BY DISLOCATION ARRAYS IN THIN FILMS Prita Pant and Shefford P. Baker Dept. of Materials Science and Engineering, Cornell University, Ithaca, NY 14853 ABSTRACT An analytical model for strain relaxation by misfit dislocation arrays in thin films is presented that takes into account all components of the strain tensor, including shear strains. The model is developed for (001) films and applied to strain relaxation in (011) oriented FCC metal films. Our results show that shear strains strongly influence the total strain energy of the film. Since both the critical strain for dislocation formation, and the equilibrium spacing of dislocations in arrays depend on the minimum energy values, these quantities are found to be different from those predicted by previous models. This model is useful for understanding both critical strain data and strain relaxation in films. INTRODUCTION Thin film materials are being increasingly used in electronic and optoelectronic devices. Besides exhibiting suitable electronic and magnetic properties, these films must also maintain structural integrity in order to be useful. Thin films are often subjected to high stresses during manufacturing and/or use. For instance, a mismatch between the lattice parameters of an epitaxial film and its substrate causes the film to grow with uniform elastic strain. Plastic relaxation of strains by dislocations may be desirable if the goal is to reduce stresses, or undesirable, for instance, in devices where dislocations adversely affect electronic properties. Hence the conditions favoring the accommodation of misfit strain by dislocation arrays have been the focus of several studies1-5. A well-known concept in strain relaxation of epitaxial thin films is that of critical thickness. For a given lattice mismatch, a film initially grows pseudomorphically with a uniform elastic strain. The total strain energy in the film increases with increasing thickness, until at a certain thickness (critical thickness) it becomes energetically favorable to partially reduce the elastic strain by introducing dislocations into the film. This concept was first proposed by Frank and van der Merwe1 and further developed by Matthews and Blakeslee6,7, Freund8 and Willis and Jain4,9. Nix3 applied these models to strain relaxation in FCC metal films on substrates. While polycrystalline metal films do not usually grow with a strain due to lattice mismatch, the film could be strained, for example, due to thermal expansion mismatch between the film and substrate as the film substrate package is heated or cooled. In this case, the strain in a film of given thickness could be increased till a certain critical strain for dislocation propagation is reached. Critical thickness and critical strain represent the same criterion since the total strain energy can be varied by changing either the film thickness or the applied strain. Whether applied to epitaxial semiconductor, or to polycrystalline metal films, a common simplifying assumption is made in all of the dislocati
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