Topographic effect of the misfit dislocation dissociation in threefold symmetry epitaxial systems

Abstract

Epitaxial systems with semicoherent heterointerfaces contain sometimes complex biperiodic networks of misfit dislocations (MDs). Analytical solutions for the elastic fields of threefold symmetry structures can in fact be derived in the form of Fourier series, in which explicit constants takes account of the detailed geometry of the MD pattern. In principle, any complex planar pattern can be treated. The material is considered as elastically heterogeneous, each medium having its own isotropic elastic constants. As an application of the theory, the In As GaAs(111)A system is treated in detail as observed by Yamaguchi et al. (1997. Phys. Rev. B, 55, 1337), for which the InAs epitaxial layer has a thickness of 1.3nm. The dislocation network consists of edge MDs arranged in a regular hexagonal-based pattern, each alternate node being dissociated into a faulted triangle. Three different networks can be produced according to the dissociation extent:

1. a honeycomb network (no dissociation) formed by MDs with Burgers vectors b = ½(110)

2. a partially dissociated network with b = ½(110) and b = ⅙(112)

3. a faulted triangular network with only b = ⅙(112)

For each of these networks, a computer-generated topograph of the free surface is presented with a suggestive grey scale. In particular, it is shown that directly above each dissociated node the elevation increase is 0.122 nm when the network passes from configuration (i) to contiguration (iii).