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Molecular beam epitaxy of InAs on micro-and nano-scale patterned GaAs(001) substrates was studied. An InAs epilayer grown on the micro-scale patterned substrate exhibits islands with {1 1 3}-type facets, and is similar to that grown on the flat (unpatterned) substrate. In contrast, the preferred growth of InAs on the nano-scale patterned substrate is in the 001 direction and exhibits islands with {1 1 0}-type facets. The thickness of the dense dislocation networks at the interface due to strain relaxation is reduced by the micro-scale pattern in comparison with the flat substrate, while for growth on the nano-scale patterned substrate, the strain relaxes via the formation of stacking faults more than dislocations. X-ray diffraction reveals that the strains in the 300 nm InAs epilayers are nearly fully relaxed, and the patterns tend to decrease the lattice constants of the epilayer, implying mass transport of Ga atoms into the epilayer from the GaAs substrates.

An expression for the four-potential of an em field is derived as a path integral involving the fields, the formula being analogous to one given in elementary vector analysis.When the vector field F ( r ) is solenoidal in a region R (div F ( r ) = 0 in R ) , provided F ( r ) is continuously differentiable in R, a vector potential C ( r ) exists for F ( r )

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