Strain-Induced Modulations in the Surface Morphology of Heteroepitaxial Layers
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MRS BULLETIN/APRIL 1996
can be realized, the presence of strain in a heteroepitaxial system can severely affect the observed layer morphology. Theoretical Considerations of Morphology-Related Strain Relief The first theoretical treatment of morphological instability driven by stress in solids was presented by Asaro and Tiller3 and related to stress-corrosion cracking. Description of the stressdriven instability relevant to a range of other circumstances appeared subsequently4"9 and in particular, formulation in the context of epitaxially strained solid films was provided.10"17 At a phenomenological level, the driving force for the formation of nonplanar
surfaces is as follows. Figure 1 shows in diagrammatic form a film compressively strained upon a substrate where surface distortions are present as undulations with relatively rounded peaks and groove- or cusplike troughs. As will be seen in the following, this type of morphology can be formed in many experimental situations. The vertically aligned lattice planes are also shown, and it is immediately clear that the unconstrained lateral edges of the surface mounds allow these planes to dilate by lateral expansion. There is then partial elastic stress relief of the epitaxial material within each mound, and this can be quantitatively modeled using finite-element analysis.18 However a consequence of this relaxation is that there is a complementary additional compression of the lattice planes at the locations of the surface grooves. Nevertheless this latter compression is very localized so that the volume of material subjected to additional stress is much less than the volume experiencing partial stress relief. Overall there can be a reduction in the free energy of the system due to the formation of these morphological distortions. One very important additional parameter, which must be taken into account before it is possible to assess the stability of a strained layer, is the surface energy. As mentioned previously, a flat layer might be expected to represent the minimum energy condition. When a surface distortion is introduced, steps are created so that the area and energy of the surface increases. Indeed the larger the distortion, the larger the surface area and potentially, the larger the number density of steps. Therefore this factor inhibits surface roughening until the free-energy reduction in the system by stress relief outweighs the free-energy increase due to surface-area increase and step forma-
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Figure 1. Diagram showing elastic distortion of vertical lattice planes in a morphologically undulating heteroepitaxial layer under compressive stress upon its substrate.
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Strain-Induced Modulations in the Surface Morphology of Heteroepitaxial Layers
tion. Within this model, the surface undulations would actually form by migration of surface-deposited atoms under the influence of strain-induced chemical potential gradients. Based upon the scenario just outlined and assuming on an a priori basis correlated sinusoidal fluctuations in total layer thickness
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