THE ENERGETICS OF DISLOCATION ARRAY STABILITY IN STRAINED EPITAXIAL LAYERS

Two aspects of the energetics of dislocation array stability in lattice-mismatched strained layers are addressed. The first concerns criteria for determining equilibrium dislocation distributions in strained layers; the second concerns the difference between the energies of arrays of dislocations in which the Burgers vectors of all dislocations are identical, and those in which the screw components of the Burgers vectors alternate. The conclusions reached are at variance with those of recent work by Feng and Hirth on periodic arrays of dipoles in an infinite body [X. Feng and J. P. Hirth, J. Appl. Phys. 72, 1386 (1992); J. P. Hirth and X. Feng, J. Appl. Phys. 67, 3343 (1990)]. In particular, it is emphasized that if layers remain in equilibrium then there is always a residual mean strain; in other words, the mismatch strain is never completely relaxed. Also it is shown, via a direct calculation, that although alternating the screw components of the Burgers vectors of dislocations within a single array is energetically favorable, it is preferable to have all screw components of the same sign within an array if two orthogonal arrays are considered. Although for comparison with the work of Feng and Hirth arrays of dipoles in an infinite body are considered in more detail, the stated conclusions are also shown to hold for arrays of unpaired dislocations near a free surface.