We propose that large heteroepitaxial stress causes InAs to melt when deposited on GaAs(001) at approximately 770 K. This leads to mixing with the substrate in order to realize a local minimum in the Gibbs free energy of the liquid phase, producing an approximate liquid composition of In0.8Ga0.2As.The liquid phase facilitates mass transport, leading to quantum dot formation. Dot formation occurs after 2.0 monolayers of liquid material accumulate in order to minimize the surface tension but without reducing the net coordination of the liquid phase atoms. Ge quantum dots on Si(001) are also discussed, and the influence of viscosity effects is inferred.
We examine two derivations of the Shuttleworth equation ͑which is a relation between surface stress g, surface tension ␥, and surface strain͒, and identify the flaws we perceive. Rectifying the perceived flaws leads not to the Shuttleworth equation but to g-␥ equivalence. We conclude that surface stress is merely the generalization of the concept of surface tension to an elastically anisotropic system; the surface free-energy density is one-half of the trace of the surface stress tensor, to lowest order. In our opinion, our conclusions lead to a more coherent and elegant form of surface thermodynamics which should prove useful in controlling and in understanding nanometer-scale fabrication.
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