Deformation Behavior of Strained Layer Heterostructures
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at the surface. The condition is fulfilled if the self-stress of an image misfit dislocation of equal strength and opposite sign at a position 2h along --L- - - -----the strained interface normal is superposed on the self-stress of the real primary dislocation. In general, the complete stress distribution for a h mixed dislocation is given by the superposition of the stress fields of the FreSrae real dislocation, the image dislocation, and a stress term derived from the IRI strained Uyer Airy stress function that makes the surface traction free. In our case of a It •mixed dislocation in a coaxial cylinder with its line parallel to the surface, the image construction gives the dominant part of the shear stress component. Since the corresponding Airy stress function term exerts no a RealPnmary Real ecodory force component along the strained interface normal, the shear stress of Dislocation Subsltrate Dislocation the dislocation construction is approximately obtained from the shear p ] stress of the image dislocation alone. Notice that only shear stresses in the slip system produce glide forces on a dislocation. In the continuum FIG. 1. Configuration of real and picture the presence of dislocations causes strains around the line and, as strained heteroepitaxial structure, a response to these, stresses as known from conventional elasticity theory. In linear approximation, the Volterra expression for the shear selfstress or, of a mixed straight dislocation due to its line tension in a region bounded by a cylinder of radius R is 2 G b (1- vcos G)(ln _ _ 1) b 4 r(I- V)R Cos 0 Image Dislocation
where G is the anisotropic shear modulus in the direction of the (001) plane of the epilayer material, v its Poisson's ratio, b is the magnitude of the Burgers vector, 0 is the angle between the dislocation Burgers vector and its line direction, 0 is the angle between the slip plane and the strained interface normal, and a is a factor which accounts for the energy in the dislocation core where linear elasticity does not apply. a is generally taken to be in the range from 1to 4 for covalently bonded semiconductor materials [101. Because of the logarithmic dependence and the R >> b Volterra regime, the elastic self-stress is insensitive to the precision of choice of a value of a . We set a 12.7 = 1. Here as is considered to act on the plane containing the dislocation line direction and the interface normal. So, referred to the slip plane surface, the shear component of the selfstress of a straight dislocation T, is given by Ts = coso (7, In the present case, then, an interfacial 60°-type misfit dislocation on the slip plane causes resolved shear stress, to wit: G b (1 - V) T.= 4 ;r (l - v) R cos
(2)
In R Tb
The ratio G/coso is the isotropic shear modulus in the I111 slip planes. Thus in this case the quantity brs is an image force given by the simple image construction. Under these conditions the attraction of the real primary dislocation toward the surface is obtained from the stress of the image dislocation alone. So far we have
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