A serious issue for the reliability and performance of heterostructure devices is the deteriorating influence of dislocations, which originate during the crystal growth of the epitaxial layers composing the heterostructure. For a film grown by the Volmer-Weber mechanism (island growth mode), dislocations may result from surface half-loop generation or from island coalescence. These dislocations are called threading dislocations. The dislocation line can either be straight and perpendicular or inclined to the interface. As a consequence, heterostructures have lines which propagate through their thickness, reaching the active part of the device and degrading its performance. It is important to note that the threading dislocation density is not constant along the film thickness. Growth techniques and dislocation configuration can reduce the density of threading dislocations. In particular, the density is reduced by reactions among dislocations when they, by some process, come in contact with each other. The driving force for this process is the minimization of the internal energy of the system. Reactions among inclined threading dislocations in bulk GaN were modeled by Mathis et al. [49]. The model supposes the inclination of threading dislocations as the only possible source for their reactions. An application of this model to semipolar GaN is given in Paragraph 5.2.1. The limit of Mathis’ model is that reactions among dislocations happen only if they are inclined with respect to the growth direction.
Real devices are based on heterostructures composed of many lattice mismatched layers. For such structures, regardless of the growth mechanisms – such as those by Frank-van der Merwe (layer-by-layer), Stranski-Krastanov (initial wetting followed by islanding), or Volmer-Weber (incoherent islanding) – increasing film thickness ultimately leads to the glide of the threading dislocations with the concomitant generation of so called misfit dislocations. In particular, below a certain layer thickness, called the critical thickness (CT), each film is grown pseudomorphically on the lower one, i.e., the film is grown with the same lattice parameter as the substrate. Consequently, the layer is strained, leading to large strain energy. When the critical thickness is reached, a relaxation of the strain occurs via plastic flow. The most common mechanism of plastic relaxation is the glide of the threading dislocations with the introduction of misfit dislocations along the interface between the two materials [17,28,82]. Gliding dislocations are called glissile dislocations, instead they are defined sessile when they can not glide below the critical thickness. Misfit dislocations change the stress gradient in the structure, causing its relaxation. The threading dislocation glide along the interface increases the probability of contact among dislocations. As a consequence, the probability of reactions increases in the presence of a glide, i.e., in presence of an interface between two mismatched materials. threading dislocation reactions and their density decrease due to dislocation glide along a bilayer interface, as modeled by Romanov et al. [66]. Romanov calculated the threading dislocation density in multilayered structures but his model differs from Mathis’ because threading dislocation glide is the only possible source for threading dislocation reactions. Threading dislocation inclination with respect to the growth direction, which is the source of reactions in Mathis model, is not considered. In addition, the different threading dislocation types present in hexagonal symmetry are neglected in Romanov’s work. Mathis and Romanov’s models can be considered complementary to each other, since each is based on a hypothesis not consider by the other.
In 2014 Ward and co-authors [79] evaluated the threading dislocation density reduction as a function of the misfit stress associated with two mismatched layers and the threading dislocation inclination together, using simple numerical modeling. Their result was that the key to significantly reduce threading dislocation density is the movement of threading dislocations resulting from misfit stress. The most important parameter affecting threading dislocation reduction is the amount of strain relaxed by misfit dislocations in the structure. The simple numerical model developed by Ward and coauthors can roughy describe the behavior of dislocations on average, since the different threading dislocation types and their specific reactions are not considered.
Real heterostructures are instead composed of many lattice mismatched film materials, where the reactions of the several threading dislocation types are simultaneously affected by their inclination and their glide along the interfaces. All these phenomena are not evaluated together by any of the above mentioned models. In this chapter, this gap is closed by proposing a new description of threading dislocation density in GaN-based multilayers considering the different threading dislocation types with their specific reactions and inclinations. Further, to go beyond Mathis’ efforts, the effect of the dislocation glide on the threading dislocation density is also evaluated. The new formulation also considers the impact of the hexagonal symmetry on threading dislocation glide, using the treatments proposed by Steeds [72] and Holec [24] (see Section 5.3). After the description of Mathis’ model in Section 5.2, the new treatment is described in Section 5.4. It is then applied to a simple case, the AlN/GaN bilayer, in order to separately evaluate the impact of the model parameters (see Paragraph 5.4.5). After that, the model is used to calculate the threading dislocation density in an Al1-xGaxN step-graded layer and in an (AlN/GaN)10 superlattice. The results are compared with experimental data from literature in Paragraph 5.4.6. General rules to decrease threading dislocation density in heterostructures are deduced and listed at the end of this chapter, including a proposal for further improvement of the model.