Analytic solutions for strain distributions in quantum-wire structures

Abstract

Analytic expressions are derived for the strain field due to a lattice-mismatched quantum wire buried in an infinite medium whose cross-section is composed of any combination of line elements and circular arcs. Expressions for the strain field for rectangular, triangular and circular quantum wires are found confirming published results. For the rectangular wire, useful limiting relations are obtained for the stress components close to the edge of the wire. Good agreement is demonstrated with measurements of lattice spacing reported by Chen et al. [Appl. Phys. Lett. 65, 2202 (1994)] for an In0.2Ga0.8As/GaAs rectangular wire if the indium concentration is assumed to be 24%. The strain field of a single AlGaAs/GaAs crescent-shaped wire, with and without lateral wells, is presented. The lateral wells introduce only minor modifications to the strain distribution when compared to a wire of the same thickness but without lateral wells. For a crescent-shaped quantum-wire stack, it is found that the strain field of each wire is almost independent of other wires in the stack when the wire separation is five times the thickness or more.