Threading dislocation under nonequilibrium conditions

Early observations of elastic strain relaxation during growth of epitaxial layers led to paradoxical results. An attempt to interpret the observations on the basis of the critical thickness theory in its most elementary form suggested that, once the thickness of a film exceeded the critical thickness, the final elastic strain of the film should be determined by the thickness of the film alone, independent of the original, or fuUy coherent, mismatch strain. This is implied by the result in (6.27), which states that that the mean elastic strain predicted by the equilibrium condition G(/if) = 0 is completely determined by hf beyond critical thickness, no matter what the value of Cni- However, it was found that the post-growth elastic strain as measured by x-ray diffraction methods did indeed vary with the initial elastic mismatch strain, and it did so in different ways for different film thicknesses (Bean et al. 1984). As a consequence, the critical thickness theory came under question, and various alternate models were proposed to replace it. However, further study of the problem has revealed the relaxation process to be much richer in physical phenomena than anticipated, with the critical thickness theory revealing only part of the story. 

Virtually all observations of dislocation glide in bulk covalent crystals at stress levels above some modest threshold level on the order of 10 N/m reveal that the normal glide velocity on a particular slip system of a given material varies with resolved shear stress on the glide plane r es = o ijTi bi/b and absolute temperature T according to an Arrhenius relationship of the form 

The stress measure and closed within parentheses is defined so that (6.29) reduces to (6.28) in the limit as the film becomes very thick. It is likely that glide is accomplished by the thermally activated motion of kinks along the threading segment (Tuppen and Gibbings (1990) Hull et al. (1991)). A free surface or bimaterial interface may offer a better site for kink formation than interior points along the dislocation line, and this is an influence on relaxation that cannot be addressed directly by approaches based on continuum mechanics. 

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