Critical Stresses forSixGe1−xStrained-Layer Plasticity

Abstract

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 ...

Minimum energy paths for dislocation nucleation in strained epitaxial layers

“…1 The predicted critical value from this equilibrium consideration however, both from continuous elastic models 2,3 and from models incorporating layer discreteness, 4 is much smaller than the observed experimental value for the breakdown of the epitaxial state. This suggests that the defect-free ͑coher-ent͒ state above the equilibrium critical thickness is metastable 5 and the rate of dislocation generation is actually controlled by kinetic considerations. The idea of strain relaxation as an activated process is supported by experimental results for the temperature dependence of the critical thickness.…”

“…The idea of strain relaxation as an activated process is supported by experimental results for the temperature dependence of the critical thickness. 5,6 It is also the fundamental assumption in kinetic semiempirical models. 7 Physically, it is expected that the lowest energy barrier for the nucleation of dislocations would correspond to a path that initiates from the free surface ͑with or without defects͒.…”

Design and characterization of high optical quality InGaAs/GaAs/AlGaAs-based polariton microcavities

“…The limit we identify in this study therefore corresponds to the edge of a metastable region where grownin defects are insufficiently mobile to result in observable strain relaxation within the growth time (see Ref. 16). …”

Low-Dimensional Group III-V Compound Semiconductor Structures

“…27,28,29 For group III-V compound semiconductors characterized by fairly strong covalent chemical bonds, however substantial discrepancies between outcomes of equilibrium approaches and those obtained from experiments were often noticed due partly to relatively high Peierls barriers. The important role of thermal fluctuations and the influence of free energy gradients were suggested 30 and the dynamics of misfit dislocations relieved by continuous plastic deformation was described. 31 The model, referred to as configuration-dependent reactive incorporation (CDRI) model, 32.33.34 with an atomistic view for the epitaxial growth of group III-V compound semiconductor thin films was developed 37 through kinetic Monte-Carlo simulations and introduced with inspiration of several pioneering experimental works 35,36 on the nature of the adsorption, dissociative reaction, and incorporation of arsenic molecules in homoepitaxial growth of gallium arsenide and related alloys.…”