Dislocation modelling in realistic Si-Ge nanostructures

SiGe heterostructures have gained a lot of interests in view of developing devices integrated into the main-stream Silicon technology and also from a scientific point of view as a prototypical system to understand the properties of more complex systems, such as III-V semiconductors. Si-Ge epitaxial structures, as well as other mismatched heteroepitaxial materials, have a high potential to improve the state-of-the-art of Si devices, thanks to the fact that the strain modifies the band structures of this material class, opening new possibility of band-gap engineering. Since the nineties, the development of devices having strained-SiGe layers as the active part occurred, in particular the heterojunction bipolar transistors, further developed to what is presently the fourth-generation of SiGe technology. Also the introduction of strained Si layers by using relaxed SiGe virtual substrates, is very important, for example, for the complementary metal–oxide–semiconductor (CMOS) technology. In order to effectively exploit SiGe or strained-Si layers in any application, it is fundamental to growth high quality single crystalline materials, reducing as much as possible the defect density in the active volume and the surface corrugation, and to obtain the desired strain state in the epitaxial layers. However the possibility of using such heterostructures for any application, is hindered by the nucleation of dislocation, which is often an unavoidable strain-relief mechanisms. Dislocation formation affects both the final material quality and the relaxation degree of mismatched layers. These defects are often charged and act as non-radiative recombination centers and it is generally accepted that they are detrimental for opto-electronic devices based on Si-Ge semiconductors. In the past years, a lot of effort has been devoted reduce the defect density or to segregate dislocations in non-active regions. However, dislocation engineering, intended as the precise control of dislocation position, has always been a goal out of reach, because of the nucleation of such defects at unpredictable sites at the surface or at other heterogeneities. It is clear that predicting the extent of the plastic relaxation process and governing dislocation nucleation and positioning would be of the utmost importance. Self-assembled nanoislands and nanowires, represent other novel heterostructures that can be exploited to obtain defect-free configurations with the desired strain state. Even in this case, very high stresses arise from the epitaxial integration of lattice mismatched materials and dislocation formation remains a competitive strain relief mechanism. Hence it is of fundamental importance to determine the coherency limits of such nanostructures and to elucidate the main strain relief mechanisms in the attempt to predict the final dislocation microstructure and strain state in heteroepitaxial systems. The main goal of this work, is the understanding of the fundamental mechanisms of dislocation nucleation and propagation in Si-Ge nanostructures (i.e. films, nanoislands and nanowires) through dislocation modelling. Even if dislocation formation and motion relies on a sequence of discrete atomic displacements, such defects induce in a crystal a smooth deformation field in the entire structure. The elastic theory of dislocations provides a good description of such stress field and of the elastic energy, as produced by dislocations in bulk materials or in finite size solids with simple geometries. In order to assess the stresses and the energetics of plastically relaxed multifaceted structures, characterized by an high surface to volume ratio and typical length scale in the order of tens or hundreds of nanometers, linear elasticity theory numerically solved by finite element methods is the most suitable tool, since in this approximation the dislocation-surface interaction can be correctly taken into account. Moreover, the motion of dislocations in nanostructures can be handled by using three-dimensional dislocation dynamics simulations. This simulation technique, originally developed to study plasticity in bulk materials, has been demonstrated to give accurate results also for nanometric systems, and is the tool of choice to study the motion and interactions of a large density of dislocation in thin films or three-dimensional nanocrystals. Important properties determined by the atomistic nature of dislocations moving in a discrete lattice, can be included, both in the finite element calculations and in dislocation dynamics simulations, by adopting simple rules that take into account such atomistic features. The first topic addressed in this work, is the investigation of plastic relaxation in SiGe epitaxial films aimed at governing dislocation nucleation and positioning. In particular, we show with the help of finite element calculations and dislocation dynamics simulations that a turning point to direct dislocation formation and propagation in predefined regions, is the introduction of preferential nucleation sites through substrate nanopatterning. Theoretical predictions indicating effective dislocation trapping along the features of trench- or pit-patterned substrates are discussed and compared with tailored experiments of SiGe deposition on nanopatterned substrate. The second issue investigated here concerns self-assembled SiGe nanoislands. In these epitaxial nanostructures an intriguing mechanism of dislocation ordering is observed. In this work we reproduced such behavior by using a simple analytical model based on energetics considerations. Furthermore, the plastic relaxation onset for dislocation formation has been determined in epitaxial islands grown on pit-patterned substrates and nucleated in pits. The key factors influencing dislocation formation in such structures have been identified, opening new possibility to grow large defect-free islands on nanopattered substrates. Finally, dislocation formation in core-shell nanowires has been considered. Elastic and plastic strain relaxaion has been investigated in such structures and a mechanism for dislocation nucleation and propagation in core-shell nanowires is presented. This allowed us to predict dislocation configurations that are more efficient in the strain relief process and the expected misfit dislocation pattern at the core-shell interface.