Analysis of Nucleation of Dislocation Loops from Stressed Surfaces Based on the Peierls-Nabarro Dislocation Model
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Analysis of Nucleation of Dislocation Loops from Stressed Surfaces Based on the Peierls-Nabarro Dislocation Model Guanshui Xu Department of Mechanical Engineering University of California at Riverside Riverside, CA 92521 Phone: (909) 787-2497; Fax: (909) 787-2899; Email: [email protected] ABSTRACT Nucleation of dislocation loops from stressed crystal surfaces is analyzed based on a variational boundary integral method in the Peierls-Nabarro framework. The stress dependent activation energies required to activate dislocation loops from their stable to unstable saddle point configurations are determined. Compared to previous analyses of this problem based on continuum elastic dislocation theory, the presented analysis provides more definitive solutions because it eliminates the uncertain core cutoff parameter by allowing for the existence of an extended dislocation core as the embryonic dislocation evolves. Moreover, the shape of the dislocation loop is solved by the variational principle instead of assumed to be semicircular as in previous analyses based on continuum elastic dislocation theory. It is noteworthy that the presented methodology can be readily used to study effects of surface inhomogeneities such as cracks and steps on dislocation nucleation.
INTRODUCTION The fundamental mechanisms of dislocation nucleation from the stressed surface have been of considerable interest in a wide variety of scientific and engineering problems. One example is the growth of high-quality heteroepitaxial thin layer structures for fabrication of high-speed electronics and optoelectronics [1,2]. Since materials of layers are selected primarily on the basis of their electronic characteristics, it is unavoidable to have a mismatch in lattice parameter between the layer and substrate. This mismatch gives rise to mechanical stress, which in turn could induce nucleation of misfit dislocations from the surface [3-10] These dislocations in electronically active regions within devices are either detrimental by degrading the electrical and optoelectrical performance of materials or beneficial by generating self-organized quantum structures relevant to the next generation of devices [11]. Understanding the formation of dislocations in strained semiconductor layer materials, with an aim toward controlling them, is therefore of central interest in the semiconductor industry. Two conditions are of particular interest in understanding nucleation of a dislocation from a stressed surface. One is the critical stress under which dislocation nucleation occurs instantaneously from the surface at absolute zero. The other is the activation energy required to thermally activate dislocation nucleation at the stress level below this critical value at the finite temperature. In principle this problem needs to be solved at the atomistic level. The atomistic simulations with appropriate empirical potentials may be used to determine the first condition. It is, however, not effective in determining the activation energy because of its serious limitation to L1
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