Mechanics of Elastic Dislocations in Strained Layer Structures
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MECHANICS OF ELASTIC DISLOCATIONS IN STRAINED LAYER STRUCTURES L. B. FREUND, A. BOWER and J. C. RAMIREZ Division of Engineering, Brown University, Providence, RI 02912 ABSTRACT Application of the elastic continuum theory of dislocations to modeling of phenomena associated with elastic strain relaxation in strained layer epitaxial heterostructures is discussed. The concept of critical thickness for onset of strain relaxation in a strained epitaxial layer is first reviewed, and some extensions to periodic arrays of dislocations and to multiple layers are described. Then, two issues are addressed that arise when the assumptions underlying the critical thickness concept are not met. One issue concerns the nucleation of dislocations at the growth surface of an epitaxial film, particularly the influence of surface irregularities on the activation energy for surface nucleation. A second issue concerns the kinetics of glide of a threading dislocation as it lays down an interface misfit dislocation when the layer thickness exceeds the critical thickness. A generalized driving force for the glide process is defined, and a relationship between this force and the glide speed is proposed. INTRODUCTION It is generally accepted that the elastic continuum theory of dislocations provides a useful framework for the study of strain relaxation in strained layer heterostructures of interest in microelectronics and micro-optics. The situation is somewhat paradoxical, in the sense that the existence of a dislocation derives directly from the discrete nature of a crystalline lattice and that the physical processes of strain relaxation to be modeled are inherently non-elastic. Fortunately, systems of scientific interest and of practical importance -have a number of features that permit a convergence of the two views. For one thing, the dislocation densities in the systems of interest are sufficiently low so that the development of models involving isolated dislocations, or interactions of small numbers of dislocations, is justifiable. In addition, the deformation fields of lattice dislocations decay quite slowly with distance from a dislocation line on the scale of lattice dimensions. Finally, the mechanical forces acting on dislocations, and thus controlling their configurations, are representable in terms of global energy variations that are not particularly sensitive to the character of the lattice. While the case for use of continuum theories of dislocations is quite strong, a major shortcoming is that the details of the structure of the dislocation core are completely overlooked in the continuum approach. The unbounded elastic energy associated with the core of an ideal elastic dislocation is an awkward feature of the continuum models. It is addressed, typically, by assuming the existence of a cutoff radius. Roughly, this radial distance from the dislocation line is determined either as the smallest dimension for which the linear theory of elasticity makes sense or as a radial dimension outside of which the energy of the dislocation b
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