slide 1 thank you very much and welcome everybody. as the title suggests / as already mentioned ... ... i am going to present results of theoretical investigations of defects and defect mobilities in silicon. slide 2 there is of course an experimental / practical motivation, which is the ion beam synthesis (IBS) of thin films of epitaxial 3C-SiC in Si. IBS consists of high-dose C implantation in Si followed by an annealing step, which, if properly done, results in buried homogeneous thin films of SiC as can bee seen in the XTEM image. however, the precipitation in the first step is not yet fully understood. this will be adressed in this study. after sketching controversial ideas of the mechanism of precipitation, the utilized simulation techniques are explained followed by a summary of the most important results of these calculations. slide 3 one assumed mechanism is schematically displayed here. incorporated carbon atoms form C-Si dumbbells on regular Si lattice sites. with increasing dose and time these dumbbells agglomerate into large clusters, indicated by dark contrasts in the otherwise undisturbed lattice in hrtem. once a critical radius of 2-4 nm is reached, the interfacial energy due to the lattice mismatch is overcome and precipitation occurs. this is manifested by the disappearance of the dark contrasts in favor of moire patterns, again due to the lattice mismatch of SiC and silicon. the excess silicon atoms are released in the silicon host, since there is more space. #it is worth to note that the hkl planes of substrate and SiC match. slide 4 however, controversial findings exist in the literature. instead of a carbon interstitial (Ci) based mechanism, nejim et al propose a transformation based on substitutionally incorporated carbon (Cs) and the generation of interstitial silicon, which reacts with further impanted carbon in the cleared volume. investigations of the annealing behavior of implantations at low and high temperatures show high and almost zero carbon diffusion respectively. this suggests the formation of mobile Ci at low temperatures opposed to much more stable Cs configurations at elevated temperatures. furthermore, investigations of strained SiC/Si heterostructures, find initial coherent SiC structures, which, in this case, incidentally transform into incoherent SiC nanocrystals accompanied by strain relaxation. these findings suggest a mechanism based on the agglomeration of substitutional instead of interstitial carbon. slide 5 to understand the precipitation mechanism in the context of these controversial results atomistic simulations are performed. namely, molecular dynamics simulations, employing an empirical Tersoff-like short range bond order potential developed by Erhart and Albe. a large amount of atoms can be simulated. moreover, the investigations are extended by first-principles calculations based on dft using the plane wave pseudopotgential vasp code. of course limited to smaller systems. slide 6 using these methods we can now investigate single defect structures, which can be characterized by the formation energy. Defect combinations can be described by the binding energy, the difference of the formation energy of the defect combination and the isoltaed defects. to acquire the mobilities migration barriers are obtained by a constrained relaxation technique. slide 7 now let's turn to the results ... ... of carbon interstitial defects in silicon. both methods provide the correct order of the formation energies and find the 100 db to be the ground state. the hexagonal defect is unstable relaxing into the ground state. it is worth to note that the bond centered configuration is unstable only within the empirical description, relaxing into the 110 DB. however, the formation energy is quite high so this does not pose a serious limitation. the substitutional defect, which is not an interstitial defect, has the lowest formation energy and is drastically underestimated within EA. regarding the problem addressed in this study, this might constitute a problem. however, it turns out, that combination of Cs and Si_i are very well described by the ea potential, with formation energies higher than the ground state. slide 8 concerning the defect mobility, by first-principles methods, a migration path is found, the 00-1 to 0-10 transition, with a barrier that excellently matches experimental values. the migration path is identified, it involves a change in orientation of the DB. related to the just mentioned instability of the BC configuration, the most probable transition for the empirical potential involves an intermediate 110 DB configuration. this results in a barrier, which is up to 3.4 times higher than the ab initio or experimental value. At least, there is the same change in orientation, a qualitative agreement. slide 9 implantation of carbon atoms results in a multiplicity of possible point defects and respective combinations. thus, in the following, defect combinations of an initial carbon interstitial and further types of defects created in the vicinity are inestigated by dft. concerning combinations of 100-type interstitials, there are lots of negative values for the binding energy, so the agglomeration of C_i is indeed energetically favorable, mainly due to a reduction of strain. a capture radius clearly exceeding 1 nm is observed for the interaction of DBs along the 110 direction. however, the interpolated graph suggests the disappearance of attractive forces between the two lowest separation distances. so this suggests agglomeration of C but the absence of C clustering. slide 10 if a vacancy is created next to the Ci defect, a situation absolutely conceivable in ibs, structures are obtained, which exhibit low migration barriers for the transition into the Cs configuration. in contrast, high barriers are necessary for the reverse process. based on this, a high probability of stable Cs configurations must be concluded. slide 11 in addition, it is instructive to look at combinations of Cs and Si_i. this configuration is still less favorable than the Ci 100 ground state. however, the interaction of C_s and Si_i drops quickly to zero indicating a low capture radius. in ibs, configurations exceedinig this separation distance are easily produced. moreover, a low transition barrier is found from the ground state into the configuration of separated defects. the barrier is even smaller than migration barrier for carbon. in addition, the low migration barrier of interstitial silicon, enables configurations of further separated Cs and Si_i defects. these findings suggest that configurations of Cs and Si_i, instead of the thermodynamic ground state, play an important role in ibs, which indeed constitutes a process far from equilibrium. slide 12 this is supported by results of an ab inito md simulation at 900 dc. the initial configuration of Cs and Si_i does not recombine into the gs, instead, the defects are separated by more than 4 neighbor distances realized in a repeated migration mechanism of annihilating and arising Si_i dbs. clearly, at higher temperatures, the contribution of entropy to structural formation increases, resulting in configurations of C_s and Si_i. slide 13 these findings are supported by results of empirical potential MD simulations employed to directly simulate precipitation. 6000 C atoms are inserted at constant temperature into a Si volume consisting of 31 Si unit cells in each direction. smaller insertion volumes were also considered due to an expected low diffusion. however - here - we only consider the total volume. after insertion, the simulation is continued for 100 ps follwed by a cooling sequence downto 20 degrees celsius. slide 14 the radial distribution function of Si-C bonds of simulations at 450 dc, an operative and efficient temperature in ibs, are shown. a clearly 100 C-Si db dominated structure is obtained, which is obvious by comparing it to the reference distribution generated by a single Ci defect. so, the formation of Ci dumbbells indeed occurs but no agglomeration is observed. one reason is the drastically overestimated dissufion barrier within the empirical potential description as outlined earlier. due to this, simulations are performed at increased temperatures. agglomeration and precipitation is still not observed, however, a phase transition into a clearly Cs dominated structure can be observed with increasing temperature by comparing with the reference peak. stretched coherent structures of SiC are directly observed and the Si_i could be attributed the role of strain reduction. slide 15 i would like to conclude. based on both, ...