Kinetic Pathways to Strain Relaxation in the Si-Ge System
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Kinetic Pathways to Strain Relaxation in the Si-Ge System D.E. Jesson, K.M. Chen, and S.J. Pennycook Introduction The strain-induced transition of a planar film to a three-dimensional island morphology is presently a significant issue in the growth of semiconductor thin films. Strain-induced roughening can be problematic in the fabrication of coherently strained device structures where it is important to understand the early stages of the transition to avoid or suppress three-dimensional (3D) growth. On the other hand, the strain-driven transition is beneficial for the selfassembly of quantum dots where it is necessary to control the size distribution and self-organizing behavior of the islands. In both cases, it is clearly important to identify and understand the kinetic pathways to island formation. From a more basic perspective, the strain-induced transition of epitaxial films allows us to study in detail the interplay between elastic stresses and surface energy in a carefully controlled experimental environment. One would therefore hope that the lessons learned from model semiconductor systems will be of relevance to understanding related phenomena in other areas of materials science and physical metallurgy. The strain-induced two-dimensional (2D)-to-3D transition in the Si-Ge system is manifested by a rich variety of observed surface morphologies. In the case of pure Ge on Si(OOl), the 4% misfit strain induces the formation of so-called hut clusters with curious elongated shapes.1 Such islands form almost immediately after the deposition of a wetting layer. In the case of lower misfit alloys, a more gentle ripple morphology can result that develops far from the interface.2 A general trend in all of the experiments is the decreasing size of typical morphological features with increasing misfit stress. In this article, largely guided by our experimental results, we adopt a nucleation and
MRS BULLETIN/APRIL 1996
growth description of the 2D-to-3D transition.34 This approach appears particularly well-suited to explaining the wide spectrum of morphological development present in the Si-Ge system. A Nucleation Description of 3D Islanding The striking nature of the stressdriven 2D-to-3D transition can be observed and studied during the following
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Figure 1. Cross-sectional representations of (a) a coherently strained two-dimensional (2D) film and (b) a three-dimensional pyramidal island situated on top of a planar wetting layer. The respective contact angle and surface energy of the inclined facet are 8 and yf, and ys is the surface energy of the wetting layer. The compressive misfit stress is a.
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Kinetic Pathways to Strain Relaxation in the Si-Ge System
the island formation energy as a function of island volume V is given by3 = 4rV 2 / 3 tan I / 3 0-3V
a\\-v) TTfX
tend. (1)
Here 6 is the contact angle (Figure lb), a is. the misfit stress, /JL is the shear modulus, v is Poisson's ratio, and T = ytcsc0 - yscot d where yt and 75 are the respective facet and surface e
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