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Three-Dimensional Epitaxy: Thermodynamic Stability Range of Coherent Germanium Nanocrystallites in Silicon Host

  • S. Balasubramanian (a1), G. Ceder (a1) and K. D. Kolenbrander (a1)

Abstract

We study the stability range for a coherent interface between Ge quantum dots and an epitaxial Si shell. The critical radius at which coherency is lost is evaluated as a function of Si shell thickness and Ge nanocrystallite radius by comparing the energy of the system in the coherent and incoherent state. We find that the system is coherent up to a Ge nanocrystallite radius of about 100 Å, irrespective of the Si shell thickness. Nanocrystallites of radii larger than 270 Å lose coherency by the generation of perfect dislocation loops. In nanocrystallites of intermediate radii ( between 100 Å and 270 Å), the coherency is lost by the introduction of partial dislocation loops enclosing a stacking fault. As the shell thickness decreases, the critical radius increases.

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