Ab initio-Theory of Point Defects and Defect Complexes in SiC
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Abstract
The work investigates the intrinsic and extrinsic defects in SiC by means of an ab initio approach based on density functional theory. This includes the study of the migration of the defects as well as the impact of the intrinsic defects on the annealing of the implantation damage and on the dopant diffusion. The vibrational signatures of carbon-related defects and defect aggregates are obtained, allowing a comparison with the photoluminescence data. We show in this work that the silicon and the carbon interstitials play an important role in all diffusion-related processes in SiC. We find that silicon self-diffusion in p-type and intrinsic material is driven by interstitials, while in n-type material an interstitial mechanism and a vacancy mechanism compete. Carbon always migrates via an interstitial mechanism, regardless the Fermi level position and the stoichiometry. We find that the diffusivity of the carbon interstitial is much higher than that of the silicon interstitial due to significantly lower migration barriers. We deduce a hierarchy of the various annealing mechanisms, i.e. the vacancy-interstitial recombination, the transformation of the defects into other stable defect configurations and the migration to sinks. While for the carbon vacancy the recombination with interstitials always is the first annealing stage, we find that for a silicon vacancy the annealing behaviour depends on the Fermi level. While in p-type material the transformation into a vacancy-antisite complex dominates, in intrinsic and n-type materials the recombination with interstitials prevails. We find that the energetics of the recombination depends on the initial distance between the vacancy and the interstitial. For close pairs it is small and increases towards the value of the migration barrier for distant pairs. The last annealing stage is always the onset of the migration of the defect. This picture consistently explains the complex annealing behaviour of the T1 EPR center in 3C-SiC. The self-interstitials are also important for the dopant migration. Considering boron as an example, we find that it migrates via a kick-out mechanism where both silicon and carbon interstitials can initiate the diffusion. The effect of the interstitials is thereby restricted to the respective sublattice. We find that boron migrates in a positively charged state, which is in agreement with experimental results. In the hexagonal polytype we predict an anisotropic dopant diffusion due to the strong dependence of the formation energy of the dopant split-interstitials on the orientation relative to the hexagonal axis. A further important finding is that the mobile carbon interstitials can aggregate and form stable clusters. We find two different types of clusters. One type are the carbon interstitial clusters, the other type are the carbon clusters around carbon-antisite positions. The carbon aggregates can significantly affect the annealing of the implantation damage. They can trap the mobile carbon interstitials at a lower temperature and re-emit them again at a higher temperature. In addition, the carbon clusters are persistent defect centers. Due to the low carbon mass and the strong bonds they give rise to distinct vibrational modes above the SiC bulk phonon spectrum which should allow their observation in photoluminescence experiments. We analyse the localised vibrational modes and investigate the isotope shifts which result from the incorporation of ^{13}C. We find that the di-carbon antisite complex shows a LVM spectrum which is comparable to the universal lines of the D_{II} center. It cannot explain the whole D_{II} spectrum, but describes the important universal core features of the center. We propose that the origin of the D_{II} center is a larger carbon aggregate with the di-carbon antisite as the core structure. Both the di-carbon antisite and the carbon split-interstitial are discussed as models of the P-T centers. The defects possess LVMs at appropriate frequencies. However, we find that the isotope splitting of the di-carbon antisite is incompatible with the isotope splitting observed for the P-T centers. On the contrary, the isotope splitting of the carbon split-interstitial agrees with the experimentally observed results. The investigation of small antisite clusters like the tri-carbon antisite reveals that vibrational frequencies up to 250meV should be observed from the carbon-based defects. The highest LVM of this defect and its threefold isotope splitting are in excellent agreement with the high-frequency mode of the U-center. Yet, the additional modes of the tri-carbon antisite are not observed experimentally, so that an unambiguous identification of the center remains to be achieved.
Abstract
Die vorliegende Arbeit untersucht intrinsische und extrinsische Defekte in SiC mittels einer auf der Dichtefunktionaltheorie basierenden ab initio-Methode. Es wird die Migration der intrinsischen Defekte als auch deren Bedeutung für das Ausheilen von Implantationsschäden und für die Dotieratomdiffusion behandelt. Wir berechnen die Schwingungsspektren kohlenstoffbasierter Defekte und Defektaggregate, die wir mit experimentell gemessenen Photolumineszenzspektren vergleichen. Wir zeigen in dieser Arbeit, dass die Silizium- und Kohlenstoff-Zwischengitteratome bei allen Diffusionsprozessen in SiC eine wichtige Rolle spielen. In p-dotiertem und intrinsischem (bzw. kompensiertem) SiC wird die Silizium-Selbstdiffusion durch Silizium-Zwischengitteratome vermittelt, während in n-dotiertem SiC der Zwischengitter- und der Leerstellenmechanismus konkurrieren. Kohlenstoff diffundiert unabhängig vom Fermi-Niveau und der Kristall-Stöchiometrie immer über Zwischengitteratome. Die Diffusivität der Kohlenstoff-Zwischengitteratome ist durch die niedrigere Migrationsbarriere wesentlich höher ist als die der Silizium-Zwischengitteratome. Des weiteren erstellen wir in dieser Arbeit eine Hierarchie möglicher Ausheilmechanismen. Dies umfasst die Rekombination von Leerstellen mit Zwischengitteratomen, die Umwandlung der Defekte in andere stabile Defektkonfigurationen und die Diffusion der Defekte zu Senken. Während bei der Kohlenstoffleerstelle die Rekombination mit Zwischengitteratomen immer den ersten Ausheilschritt darstellt, hängt für die Silizium-Leerstelle das Ausheilverhalten vom Fermi-Niveau ab. In p-dotiertem SiC dominiert die Umwandlung in einen Leerstellen-Antisite-Komplex, in intrinsischem und