Limitations of the critical thickness condition

The criterion refers to the conditions which prevail when it first becomes possible for any threading dislocation to advance. The ability to detect the onset of relaxation depends on the resolution of the technique used to observe dislocation motion (Fritz (1987), Gourley et al. (1988)). X-ray diffraction methods detect average strain over an area on the order of a square millimeter, and a detectable change in average strain occurs only after extensive dislocation activity at thicknesses well in excess of the true critical thickness. Consequently, such methods are ineffective in efforts to actually observe the onset of dislocation glide in strained layers. 

The model also presumes that the threading dislocation exists in a layer that is otherwise spatially uniform. However, the behavior of a dislocation can be strongly influenced by other dislocations present, either on parallel or intersecting glide planes. Dislocation interactions will be considered in Chapter 7. Behavior can also be influenced by geometrical features in the film. For example, patterning can result in an array of trenches with free surfaces within the film or small mesas on which the film material is deposited. The motion of a dislocation can also be influenced by fluctuations in surface topography of the film. 

At the level of the above discussion, the critical thickness condition G = 0 is based on elastic continuum concepts only. This overlooks a variety of effects that may bear on the process in some cases. Among these are the glide resistance due to the Peierls-Nabarro stress of the material (Matthews 1975), the role of surface or interface energy (Cammarata and 

Sieradzki 1989), the resistance due to creation or annihilation of a surface ledge in the wake of the threading dislocation (Matthews 1975), the presence of a deposition flux during dislocation motion, and the possibility of dissociation of the dislocations into Shockley partial dislocations (Alexander 1986). Thus, the critical thickness condition could be restated a G = 71. where 7Z is a resisting force representing any or all of these additional effects. 

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