Modeling crosshatch surface morphology in growing mismatched layers. Part II: Periodic boundary conditions and dislocation groups
We present further developments and understanding of the commonly observed crosshatch surface morphology in strain-relaxed heteroepitaxial films. We have previously proposed that the crosshatch morphology is directly related with strain relaxation via threading dislocation glide which results in both surface step and misfit dislocation (MD) formation [see Andrews , J. Appl. Phys. 91, 1933 (2002)-now referred to as Part I]. In this article, we have used solutions for the stress fields and displacement fields for periodic MD arrays which include the effects of the free surface. These solutions avoid truncation errors associated with finite dislocation arrays that were used in Part I. We have calculated the surface height profile for relaxed films where the misfit dislocations were introduced randomly or the misfit dislocations were placed in groups with alternating sign of the normal component of their Burgers vector. We have calculated the surface height profiles where the slip step remains at the surface ["slip step only" (SSO)] and where the slip step is eliminated ["slip step eliminated" (SSE)] due to annihilation of opposite sense steps, such as could happen during growth or lateral mass transport. For relaxed films, we find that the surface height undulations, characteristic of crosshatch, increase with increasing film thickness for the SSO case, whereas the surface becomes flatter for the SSE case. Experiments on relaxed In0.25Ga0.75As films on (001) GaAs show that the surface height undulations in the  direction increase with increasing film thickness. Thus, we conclude that with increasing film thickness the crosshatch in the slow diffusion  direction is best described by the SSO case. (C) 2004 American Institute of Physics.