5.5  Summary

In this chapter Mathis’ model [49] is improved with regard to the dislocation glide along interfaces and its effect on the dislocation density. The new treatment assumes a simplified bidimensional geometry of the dislocation. Several kinetic factors affecting the dislocation movement, like temperature and speed of growth, are neglected. The results of the calculations show the following

1.

The glide of the dislocations alone one interface happen in a short range on tens of nanometer after the critical thickness. The glide increases the probability of reactions among dislocations, reducing their density. The reduction is generally small for a bilayer structure but can be magnified in multilayer structures;

2.

The effect of the inclination angle on the dislocation density is evident at a thickness much higher (on the order of hundreds of nanometers) than the critical thickness. The higher the inclination angle, the lower the final dislocation density. In particular, the island-growth mode seems to favor the inclination of the dislocations (see Chapter 3 and  [25]);

3.

Superlattice structures reduce the dislocation density more efficiently than the step-graded layer. In the last case, the glide of the dislocations can be neglected;

4.

Superlattice structures reduce the dislocation density by nearly one order of magnitude when the thickness of the structure is half μm, hence yielding good agreement with experimental data. This also demonstrates that the improved model better predicts the final density with respect to Mathis’ model. The efficiency of the superlattice is due to the high lattice mismatch between layers. The higher the lattice mismatch, the more intense the dislocation glide.

The model presented in this chapter can be improved by the following:

1.

Consideration of the real 3D geometry of the dislocation;

2.

Consideration of the actual dislocation-dislocation interactions. This would involve calculation of dislocation stress fields and, in fact, the employment of some methods of dislocation dynamics;

3.

Evaluation of the impact of the growth mode. Considering the island-growth mode would mean considering the different facets of each island and the different growth rates of the facets;

4.

Choosing of the inclination angle in relation to the growth mode (see Chapter 3 and  [25]). This would involve the calculation of the stochastic distribution of the angles – which dislocations assume during the layer growth – and in fact, the use of some statistical methods.