CRITICAL THICKNESS CONDITION FOR GROWTH OF STRAINED QUANTUM WIRES IN SUBSTRATE V-GROOVES

The physical system under study is a quantum wire of roughly triangular cross section grown epitaxially in a V-shaped groove on a patterned (100) surface of a cubic substrate. The walls of the groove are {111} planes of the substrate material, so that the wire extends along a 〈110〉 direction. For a given thickness, or depth, of the wire, an analysis is presented which leads to an estimate of the smallest elastic mismatch strain for which the wire remains stable against formation of misfit dislocations, in the spirit of the Matthews-Bladeslee condition, taking into account both the free surface effect and the mismatch strain effect. Comparison is made with the experimental observations of T. Arakawa, S. Tsukamoto, Y. Nagamune, M. Nishioka, J.-H. Lee, and Y. Arakawa [Jpn. J. Appl. Phys. 32, L1377 (1993)].© 1995 American Institute of Physics.