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Dislocation-interaction-based model of strained-layer relaxation
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View: Figures


Image of FIG. 1.
FIG. 1.

Top: slip systems of the fcc crystal. The triangular faces of the pyramid lie parallel to the allowed glide planes; their edges show the respective directions of the Burgers vectors that can glide on each plane. Only the four Burgers vectors with a component in the [001] direction are active in relieving biaxial strain. Bottom: same-perspective sequential snapshots of a threading segment propagating on a (111) glide plane in a strained layer of height . As the thread propagates, it leaves behind a misfit pair . The analogous free-surface problem is obtained by slicing off the top half of the strained layer.

Image of FIG. 2.
FIG. 2.

The four categories of localized dislocation-dislocation encounters which can occur in the relaxing layer.

Image of FIG. 3.
FIG. 3.

Basic thread-trapping functions, obtained by summing over all possible dislocation-dislocation interactions. governs thread-misfit collisions and describes thread-thread collisions. The driving force is the force driving the motion of any particular thread. In the calculation of individual interactions, this is the available applied force . In situ, it becomes .

Image of FIG. 4.
FIG. 4.

Distribution of local misfit forces exerted on a test thread by a random misfit array: (a) distribution sampled by an arbitrarily placed thread; (b) distribution filtered so as to approximate sampling by a free thread, where the structure near the cutoff arises from the structure in Fig. 3. As shown by the arrow, the value assumed for here is . The curves show distributions for values of increasing (from left to right) from 0 to , in steps of . Several sets of distributions, more refined and extending to higher values of than the set shown in the figure, were used in the computations.

Image of FIG. 5.
FIG. 5.

The functions plotted against . The curves (from left to right) are for of 2, 3, 4, 6, and 10, respectively.

Image of FIG. 6.
FIG. 6.

Residual strain divided by critical strain observed in helium-implanted and annealed free-surface layers as a function of layer thickness. Solid circles refer to layers grown by ultrahigh vacuum chemical vapor deposition and solid triangles to layers grown by rapid thermal vapor deposition. The × marks show the numerical simulations reported in Ref. 26. The lines show the predictions of the analytical model for different values of (in units of ).

Image of FIG. 7.
FIG. 7.

Model predictions (solid lines) and numerical simulations (dotted lines) for relaxation starting at twice the critical strain. The initial dislocation densities , from top to bottom, are 2, 8, and 32 (in units of ). The error bars denote scatter in the individual simulation runs. The horizontal dashed line indicates the critical strain.

Image of FIG. 8.
FIG. 8.

Model predictions (solid lines) and numerical simulations (dotted lines) for relaxation starting at four times the critical strain. The initial dislocation densities are the same as in Fig. 7.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Dislocation-interaction-based model of strained-layer relaxation