Influence of strain relaxation on the electronic properties of buried quantum wells and wires

Most analyses of strained quantum-well structures assume the quantum well to be effectively of infinite extent within the growth plane. There are, however, several situations where one of the lateral dimensions is of comparable magnitude to the layer thickness. These include (i) quantum wires where the ratio of wire width to thickness can be of the order of 10:1 or lower and (ii) buried heterostructure lasers where the ratio of the active-region width to thickness can be of the order of 100:1. A simple method for calculating cross-sectional strain distributions in such structures is presented. The quantum wells are assumed to be buried in an infinite isotropic medium (which neglects the effect of free surfaces). First a cylindrical wire is considered and it is shown that the radial strain component is significantly reduced compared with the lattice misfit. The analysis is extended to the quantum wire and buried heterostructure. The zone-centre band gap is calculated as a function of position in the cross-section. The results provide a broad indication of the likely effect of strain relaxation on the electronic properties.