A buried strained quantum wire

A necessary condition on h, w, and Burgers vector 6 for formation of a strain relieving dislocation is considered next. 

An elegant general framework exists for the description of elastic fields in solids with misfitting inclusions (Eshelby 1957). However, the configuration under consideration here is sufficiently simple so that the stress distribution can be determined directly in a relatively straightforward way. 

The orientation of the glide plane on which the dislocation dipole is formed and the location of the dislocations depends on the geometrical configuration and crystallographic orientation of the material. To make the discussion more concrete, consider the case when the material has cubic crystallographic structure and the preferred shp planes are the 111 planes. 

The remaining task is to locate the position of the dislocations, represented symbolically by and in (6.56) and (6.57), for which it first becomes possible to have = 0. 

If em 0, then the sign of the Burgers vector must also be reversed but the calculation is otherwise unaffected. 

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Fig. 6.23. The two-dimensional configuration of a buried strained quantum wire (upper figure), where a long slender elastic inclusion of the quantum wire is embedded in an otherwise unperturbed matrix of an elastic material. In the lower left figure, the inclusion is subject to an imaginary uniform normal traction at its surface in such a manner that it fits perfectly into the rectangular cavity of the surrounding matrix without inducing any stress in the matrix material. The lower right figure represents the situation where the artificial normal traction on the inclusion surface is removed, whereby the strain in the inclusion is partially relaxed and the surrounding elastic matrix becomes stressed.

Fig. 6.24. A buried strained quantum wire with a slip plane oriented at an angle a to the x—axis. The glide of a threading dislocation leaves behind a dislocation dipole pair with 4 and lb denoting the positions of the dislocations. I denotes distance along the slip plane.

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