Stable configurations in strained epitaxial layers

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Abstract
Two guiding principles for the determination of stable configurations in strained epitaxial layers (epilayers) are considered. One states that dislocations will be introduced so that the epilayer attains the lowest-energy configuration. The other considers the force acting on a threading dislocation, tending to drive it across the epilayer, depositing a misfit dislocation as it moves: the Matthews-Blakeslee force balance model states that strain relaxation will occur via threading motion until the force due to the relaxed strain is insufficient to drive a dislocation across the epilayer. It is demonstrated in this work that previously neither of these principles has been correctly applied. An exact solution for the energy of a period array of misfit dislocations has recently become available, which makes a precise analysis possible. The correct application of the energy minimization and force balance principles is discussed and the relationship between the two approaches is clarified. An exact expression for the driving force acting on a threading dislocation between two misfit dislocations in a periodic array is derived and used to demonstrate that, if a mechanistic approach is taken to the problem of strain relaxation, then the concept of a unique stable configuration no longer exists. This fact can be used to help to explain the observed metastability in partially relaxed strained epilayers.