Continuum and Semi-discrete Simulations of Heteroepitaxial Semiconductor Relaxation by Dislocations

• Main Author: Andersen, Dustin
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01-01-2018
• Subjects: Materials science
• ISBN: 9780438516199; 0438516192

The goal of this thesis was to expand understanding of the energetics and kinetics of relaxation by dislocations in heteroepitaxial semiconductor layers through continuum and semi-discrete simulations of relaxation combined with existing data from experimentally analyzed heterolayers. The semiconductor crystal systems studied here are SiGe/Si(100), SiGe/Si(110), a-plane AlGaN/GaN, and c-plane AlGaN/GaN. The primary focus is on misfit-accommodating dislocations, however, the effects of inclined threading dislocations on relaxation are also briefly considered. There are four major thrusts to the work presented here. The first is on extending and exploring the capabilities of a previously developed continuum level simulator in describing variations in relaxation pathways in GeSi/Si(100) heterostructures due to changes in layer parameters such as composition, growth rate, growth temperature, and the balance of different sources of dislocation nucleation. Here we found that the simulator was able to attain reasonable matching to experimental data from the literature, and where it was not able to, we were able to propose and test variations in dislocation nucleation mechanisms as tentative explanations for these variances. We were also able to generate multi-parameter relaxation curves to highlight regions of highest sensitivity in the growth parameters that lead to significantly different final layer strain and total dislocation quantities. The second major thrust of the thesis was to understand how asymmetric strain conditions lead to changes in the relaxation rate and also the final strain in the layer. Such asymmetric strain arises both from differences in the interfacial in-plane lattice parameters and relaxation mechanisms in different in-plane directions. A reformulation of the isotropic linear elastic equation for applied dislocation stress was derived, leading to the conclusion that when one in-plane direction is not relaxed, the orthogonal direction over-relaxes in response. Simulation results for this mechanism are presented for both SiGe/Si(110) and a-plane AlGaN/GaN. The third major thrust of the thesis asked how extensible our continuum level simulations are to other crystal systems. This question was answered in part with our previous work developing the SiGe/Si(110) simulator from the SiGe/Si(100). This work describes an extension to a totally new crystal system (a-plane and c-plane III-Nitrides). The major considerations for this extension are changes to the dislocation slip systems and energetics, the dislocation kinetics, the dislocation array geometry, and differences in relaxation mechanisms (e.g. inclined threading dislocations). This work shows the necessary calculations for determining the most probable active slip systems (for a-plane III-Nitrides), and also shows the changes necessary to spacing, length, and strain calculations due to the new dislocation array geometry for both a-plane and c-plane III-Nitrides. Experimental values are drawn from the literature. Initial results from the converted simulator are presented. The final major thrust of this dissertation focuses on understanding the detailed distributions of the spacings and lengths of misfit dislocations in the interfacial array, and how they may be affected by nucleation and blocking mechanisms. Such distributions would dictate the probability of interaction between dislocations within an array and thus alter the rate of relaxation. This work was based on our development of an algorithm to convert the output of the continuum simulator into a discrete representation of the dislocation array. This led to the observation that the underlying distribution for the dislocation spacing is an exponential, and that the length distribution takes on unique shapes dependent upon the nucleation mechanisms and the evolution of strain in the layer. We show that deviations from the exponential spacing distribution should also contain information regarding the type of nucleation within the layer. Our initial experimental Electron Channeling Contrast Imaging in the Scanning Electron Microscope (ECCI-SEM) evidence shows that the dislocations do appear to follow the exponential. Our experimental work also shows an exponential for the length distribution, which is unexpected, but which we propose originates from the effect of dislocation blocking. In summary, we showcased ways of highlighting the regions of instability in final layer strain for simulated growth over large parameter spaces. We discovered that asymmetric relaxation of a heteroepitaxial layer can lead to an unexpected reversal of the sign of the strain in the relaxed direction, and illustrated how such conditions arise for both SiGe/Si(110) and the a-plane III-Nitrides. We have learned what changes are necessary to extend a continuum level misfit dislocation relaxation simulation to a new crystal system (specifically the c-plane and a-plane III-Nitrides) and have illustrated how alternative relaxation mechanisms can be integrated into the model. Finally, we found the unexpected result of an exponential distribution for the dislocation spacing distribution (corroborated by the literature), and further learned that different nucleation mechanisms can alter the shape of not only the dislocation spacing distribution, but also the length distribution.