Critical Thickness for Three-Dimensional Epitaxial Island Growth
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CRITICAL THICKNESS FOR THREE-DIMENSIONAL ISLAND GROWTH
EPITAXIAL
K. JAGANNADHAM AND J. NARAYAN Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695 ABSTRACT loops in threeThe generation of misfit dislocation dimensional epitaxial islands grown on thick substrates is analyzed. The coherent strain in the island is described by virtual interfacial dislocation loops situated in the interface. The traction free surface boundary conditions are satisfied by the surface dislocation loops situated on the surface of the island. A misfit dislocation loop is formed and the changes in the energy of the configuration used to determine if the total energy is lowered. The numerical analysis is carried out for hemispherical islands of GaAs grown on (100) silicon with a misfit dislocation of Burgers vector 3.84 A. It has been found energetically favorable to nucleate a misfit dislocation loop at a distance of 3 A from the interface when the radius of the hemispherical island is equal to or greater than 40 A. In addition, a misfit dislocation loop could be nucleated at a larger distance from the interface when the size of the island is larger. INTRODUCTION The transformation of an island from a coherent pseudomorphic state to an incoherent equilibrium state has been analyzed quite extensively, both experimentally [1-3] and using analytical modelling [4-71. The growth of an epilayer has been classified into three categories [8]. In the first, a two-dimensional island on a substrate is attributed to low interfacial energy associated with the epilayer/substrate interface. The second category (Volmer-Weber) of growth of epitaxial layers consists of the islands grown on a substrate as a result of high interfacial energy. Finally, a combined planar and island growth (StranskiKrastanov) is also observed in certain systems with an initial two-dimensional growth. In this paper, growth of epitaxial islands is considered in order to determine the critical size for nucleation of lattice misfit dislocations. Specifically, the analysis is applied to GaAs growth on (100) silicon surfaces which tend to form as hemispherical islands. A HEMISPHERICAL ISLAND A hemispherical island grown on an infinitely thick substrate is considered. Therefore, we assume the strain in the substrate to be vanishing. The lattice mismatch with respect to the (100) silicon in the GaAs island in the x and y directions is described by virtual interface dislocation loops with mutually orthogonal Burgers vectors and located in the interface (x-y plane). Figure 1 is a schematic illustration of the virtual interfacial
Mat. Res. Soc. Symp. Proc. Vol. 130. 11989 Materials Research Society
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(100) Misfit Dislocation Loop "5" In the Epilayer Silicon Substrate
Figure 1. A schematic illustration of the h
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