Three Dimensional Surface Waviness of an Epitaxial Layer Due to Surface Diffusion Induced by Interface Misfit Dislocatio

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ABSTRACT It has been observed that, for some strained epitaxial layer systems, the surface of the layer develops roughness or waviness which correlates spatially with the positions of underlying interface misfit dislocations which partially relax the elastic mismatch strain. A model based on redistribution of mass by surface diffusion is analyzed to estimate the waviness of the three dimensional thermodynamic equilibrium surface due to intersecting arrays of interface misfit dislocations.

INTRODUCTION Several investigators have reported direct observations of ridges on the surfaces of strained layers which correlate in position with misfit dislocations at the interface between the strained layer and its substrate. By means of electron microscopy, Fitzgerald et al. [1] noted the appearance of long, parallel ridges on the free surface of a InGaAs/GaAs system following partial strain relaxation. It was suggested that, due to the strain of the misfit dislocations, the nearby surface offered a preferred site for adatom attachment during deposition. The presence of such ridges in the same material system was also observed by Harvey et al. [2] by means of atomic force microscopy, but in this case they were apparently formed during a high temperature anneal of a metastable strained layer rather than during growth.

For partially relaxed compositionally graded Sil_,Ge. layers, Fitzgerald et al. [3] and Hsu et al. [4] observed surface roughness, referred to as a cross-hatch pattern.

They found the degree of surface cross-hatch to be related to the inhomogeneous strain fields in the layer due to the underlying misfit dislocations. Similar surface features in

compositionally graded Sii-=Gex layers have also been observed by Shiryaev et al. [5]. There is evidence that some strained semiconductor systems will develop surface waviness during film growth before the formation of interface misfit dislocations, if substrate temperatures are sufficiently high. By means of transmission electron microscopy and atomic force microscopy, Cullis et al. [6,7] found surface waviness to form during growth of strained Sil-,Ge. epitaxial layers on Si, preceding misfit dislocation generation, under conditions when the flat shape is known to be unstable. A proposed idea is that the surface of a strained layer will roughen, prior to misfit dislocation nucleation, and that the nonuniform strain along the surface will lead to formation of dislocations at the highest stress concentration sites. It is well known that the high stress concentration in the troughs of a wavy surface will decrease the barrier for dislocation formation [8]. However, if the dislocations grow out of the surface troughs then the spacing of the dislocations would be equal to the instability wavelength. Experimental observations have shown the dislocation spacing to be much smaller than the instability wavelength [2,6,7]. Thus, it is likely that the misfit dislocations are 45 Mat. Res. Soc. Symp. Proc. Vol. 356 0 1995 Materials Research Society

Figure 1. Schematic of an epit