Dynamical simulation of the evolution of single dislocation configurations in MBE grown heterostructures

Submission note: A thesis submitted in total fulfilment of the requirements for the degree of Doctor of Philosophy to the School of Engineering and Mathematical Sciences, Faculty of Science, Technology and Engineering, La Trobe University, Bundoora.

The objective of this work was to study the evolution by simulation of a single threading dislocation in an arbitrarily complex, multilayered, semiconductor heterostructure containing materials such as InGaAsN, AlInAsN and InAlGaAs grown on GaAs substrates by Molecular Beam Epitaxy. The evolution follows the monolayer by monolayer MBE growth process and assumes linear elasticity theory as it applies to an isotropic material. The Peach-Koehler force is calculated at each Point of Interest (POI) along the dislocation line, which is a closed or infinite loop comprising of infinitesimal straight segments. The stresses at a POI arise from bi-layer stresses due to layer misfits, the self-stress of the dislocation itself and stresses arising from the necessity to cancel all stresses acting at the growth surface, which is constantly changing its position. The model calculates the dynamic evolution of the dislocation configuration during the semiconductor material growth process, calculating all stresses as layer upon layer is added and taking into account the effects of frictional stress as expressed by the Peierls force. Because of hysteresis effects the history of the evolution of the dislocation configuration as monolayers are added contributes to the final dislocation configuration. The model includes a velocity dependent Peierls friction force, consistent with experimentally observed dislocation glide. To the author’s knowledge there has to date been no work presenting an analysis of dislocation configuration evolution during the growth process which includes calculation of cancelling surface stresses and takes into account the effects of adding one mono-layer at a time. This work has also developed strategies for making the surface stress calculations accurate and efficient and for this purpose comparison with a set of analytically solvable dislocation configurations has been invaluable. The calculation of self-stresses was performed with strategies to manage the singularity at the core. The final result has been the creation of a working program capable of modelling dislocation configuration evolution in arbitrarily complex strained multi-layers.