An outstanding puzzle concerning strained-layer semiconductors is that metastable structures can be grown in which exact coherence with the lattice is apparently conserved in layers much thicker than the equilibrium critical thickness. Using standard descriptions of dislocation dynamics and relaxation via plastic flow, a model for the relaxation of an initially coherent metastable strained layer is developed. This model is applied to relief of mismatch strain in the SiGe/Si(100) system, and good agreement with experimental data is found. Furthermore, the combined effect of relaxation kinetics and finite instrumental resolution on the observed critical thickness was calculated. The results successfully reproduce experimental data on metastable critical thickness in the SiGe/Si(100) system.
We have measured the temperature-dependent onset of strain relief in metastable SijcGei-* strained layers grown on Ge substrates. On the basis of these measurements, and physical arguments, we propose that strained-layer breakdown is most directly determined not by thickness and lattice mismatch, but rather by (l) an "excess" stress (the difference between that due to misfit strain and that due to dislocation line tension) and (2) temperature. With use of these parameters, observed regimes of stability and metastability are shown to be described within a simple, unified framework. PACS numbers: 68.65.+g, 68.55.Bd, 81.40.Lm Strained epitaxial films, first studied theoretically nearly four decades ago, 1 have attracted much interest recently. Partly, this interest stems from observations of structural metastability in films grown by state-of-theart techniques. In this regard, an outstanding question has been how to correlate growth conditions with subsequent structural perfection of the film. The original equilibrium theories of Ball and van der Merwe, 2 Matthews and Blakeslee, 3 and co-workers predicted that, below a critical thickness, lattice mismatch between substrate and film would be accommodated entirely by film strain. Above this thickness, film strain would be partly relieved by misfit dislocations.The pioneering work of Kasper, 4 Bean, 5 and coworkers in the SiGe system showed, however, that under some growth conditions strain in films above the critical thickness is not measurably relieved. Only above a second critical thickness does measurable relief occur, and even then, the amount of relief is not in accord with equilibrium theory. Most recently, the work of Fritz 6 and of Dodson and Tsao 7 suggests that the observed metastability can be explained by sluggish plastic deformation rates accompanied by a finite experimental resolution. The second critical thickness is that for which strain relief is just sufficient to be observable.A full treatment of the kinetics of plastic deformation of thin epitaxial films, however, is nontrivial. Even deformation of bulk materials occurs by a number of complex mechanisms, and little is known about whether deformation in thin films occurs by the same mechanisms. Nevertheless, it is clear that any mechanism must be governed principally by the two parameters shear stress (the driving force for deformation) and temperature. Indeed, for bulk materials, deformation rates can be elegantly expressed with the stress-temperature diagrams (or "deformation mechanism maps") introduced by Frost and Ashby. 8 In this Letter, we argue that the stability and metastability of thin strained layers is determined mainly by the kinetics of plastic deformation and hence is governed by stress and temperature. However, we propose that the stress which actually drives dislocation motion is the difference between the usual stress due to misfit strain and an "effective" stress due to dislocation-line tension. Observable strain relief occurs only if this "excess" stress exceeds a critical value ...
Bonding in the near-surface region is strongly influenced by the truncation of the lattice at the surface. This many-body effect is examined quantitatively by use of the embedded-atom method on lowindex transition-metal surfaces. An unreconstructed metal surface is found to have a tensile strain of several percent. This many-body surface strain is an important factor in the energetics of surface structure, serving as a parameter combining surface stress and nonlinear elastic effects. In particular, it is demonstrated that the surface strain drives surface reconstruction, and also produces asymmetry in the stability properties of thin mismatched epitaxial overlayers.
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