+
+in addition, it is instructive to look at combinations of Cs and Si_i.
+the most favorable configuration is obtained for
+Cs located right next to the 110 Si db within the 110 chain.
+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.
+
+in total, these findings demonstrate 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 16
+
+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, which results in a spatial separation,
+even for defects located within the capture radius.
+
+!!!
+to conclude, the results of the investigations of defect combinations
+suggest an increased participation of Cs already in the initial stage
+of precipitation due to its high probability of incidence.
+
+slide 17
+
+as a last task, reproducing the SiC precipitation is attempted
+by successive insertion of 6000 C atoms,
+the number necessary to form a minimal precipitate,
+into a supercell consisting of 31 Si unit cells in each direction.
+insertion is realized at constant temperature.
+due to the high amount of particles,
+the classical potential must be used.
+since low carbon diffusion due to the overestimated barriers is expected,
+insertion volumes v2 and v3 next to the total volume v1 are considered.
+v2 corresponds to the minimal precipiatte size.
+v3 contains the amount of silicon atoms to form such a minimal precipitate.
+after insertion, the simulation is continued for 100 ps
+follwed by a cooling sequence downto 20 degrees celsius.
+
+slide 18
+
+the radial distribution function of simulations at 450 dc,
+an operative and efficient temperature in ibs, are shown.
+
+for the low C concentration simulation,
+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.
+the second peak is an artifact due to the cut-off.
+the C-C peak at 0.31 nm, as expected in cubic SiC,
+is generated by concatenated, differently oriented Ci dbs.
+the same distance is also expected for the Si atoms, and, indeed,
+the db structure stretches the Si-Si next neighbor distance,
+which is represented by nonzero values in the correlation function.
+
+so, the formation of Ci dumbbells indeed occurs.
+even the C atoms are already found in a separation as expected in cubic SiC.
+
+turning to the high C concentration simulations,
+a high amount of strongly bound C-C bonds
+as in graphite or diamond is observed.
+due to increased defect and damage densities
+defect arrangemnets are hard to categorize and trace.
+only short range order is observed.
+and, indeed, by comparing to other distribution data,
+an amorphous SiC-like phase is identified.
+
+slide 19
+
+to summarize, the formation of cubic SiC fails to appear.
+neither agglomeration of C interstitials
+nor a transition into SiC can be identified.
+
+slide 20
+
+having a closer look, there are two obvious reasons for this obstacle.
+
+first of all, there is the time scale problem inherent to md in general,
+which results in a slow phase space propagation due to
+a large amount of local minima separated by large energy barriers.
+accelerated methods, like temperature accelerated MD and so on, exist
+to bypass the time scale problem while retaining proper thermodynamic sampling.
+
+however, in addition, the overestimated diffusion barriers,
+due to the short range character of the potential,
+intensify this problem, which I termed:
+potential enhanced slow phase space propagation.
+
+the approach used in this study is to simply increase the temperature, however,
+without possible corrections.
+accelerated methods or higher time scales applied exclusively
+are assumed to be not sufficient.
+anyways, in this case,
+structural evolution instead of equilibrium properties are matter of interest.
+
+slide 21
+
+and indeed, promising changes are observed by comparing,
+again the radial distribution data for temperatures up to 2050 dc.
+first of all, the cut-off artifact disappears.
+more important, a transition into a clearly Cs dominated structure takes place,
+as can be seen by direct comparison with the respective reference peaks of Cs.
+
+the rising Si-Si peak is due to stretched Si-C-Si structures
+along a 110 direction.
+
+the C-C next neighbor pairs are reduced,
+which is mandatory for SiC formation.
+the peak at roughly 0.3 nm gets slightly shifted to higher distances,
+due to a decrease of interstitial carbon combinations accompanied by an
+increase in interstitial and substitutional as well as pure substitutional
+combinations.
+increasing values in this range
+correspond to bonds of Cs and another Cs with a nearby Si_i atom.
+
+slide 22
+
+to conclude, stretched coherent structures are directly observed.
+therefore, it is expected that Cs is extensively involved
+in the precipitation process for implantations at elevated temperatures.
+
+the emission of Si_i serves several needs:
+as a vehicle to rearrange stable Cs,
+as a building block for the surrounding Si host or further SiC formation.
+and for strain compensation either at the Si/SiC interface
+or in the stretched SiC structure, which, again,
+was diretly observed in simulation.
+
+this perfectly explains the results of the annealing experiments
+stated in the beginning of this talk.
+at low temperatures highly mobile Ci
+whereas at high temperatures stable Cs configurations are formed.
+
+thus, it is further concluded that high temperatures are necessary to model
+ibs conditions, which are far from equilibrium.
+the high temperatures deviate the system from thermodynamic equilibrium
+enabling Ci to turn into Cs.
+
+slide 23
+
+to summarize and conclude ...
+point defects were investigated by both methods.
+the interstitial carbon mmigration path was identified.
+it turned out that the diffusion barrier is drastically overestimated
+within the ea description.
+
+combinations of defects were investigated by first principles methods.
+the agglomeration of point defects is energetically favorable.
+however, substitutional carbon arises in all probability.
+even transitions from the ground state are very likely to occur.
+
+concerning the precipitation simulations, the problem of
+potential enhanced slow phase space propagation was discussed.
+high temperatures are assumed necessary to simulate ibs conditions.
+at low temperatures a dumbbell dominated structure is obatined
+whereas
+it is expected that
+Stretched structures of SiC were observed at elevated temperatures.
+it is thus concluded that
+substitutional carbon is heavily involved in the precipitation process.
+the role of the Si_i was outlined.
+
+in total, these results suggest,
+that cubic SiC precipitation occurs by successive agglomeration of Cs.
+
+slide 24
+
+finally, I would like to thank all of the people listed on this slide,
+categorized by location.
+
+thank you for your attention!
+
+
+
+
+
+slide X polytypes
+
+although the local order of the silicon and carbon atoms
+characterized by the tetrahedral bond is always the same,
+more than 250 different polytypes exist,
+which differ in the one-dimensional stacking sequence of
+identical, close-packed SiC bilayers,
+the stacking sequence of the most important polytypes is displayed here.
+the 3c polytype is the only cubic polytype.
+
+different polytypes exhibit different properties,
+which are listed in the table
+and compared to other technologically relevant semiconductor materials.
+SiC clearly outperforms silicon.
+among the different polytypes, the cubic phase shows the highest
+break down field and saturation drift velocity.
+additionally, these properties are isotropic.
+thus, the cubic polytype is considered most effective for highly efficient
+high-performance electronic devices.
+
+slide X silicon self interstitials
+
+in the following, structures and formation energies
+of silicon self-interstitial defects are shown.
+the classical potential and ab initio method predicts formation energies,
+which are within the same order of magnitude.
+however, discrepancies exist.
+quantum-mechanical results reveal the silicon 110 interstitial dumbbell (db)
+as the ground state closely followed by the hexagonal and tetrahedral
+configuration, which is the consensus view for silicon interstitials.
+in contrast, the ea potential favors the tetrahedral configuration,
+a known problem, which arises due to the cut-off
+underestimating the closely located second next neighbors.
+the hexagonal defect is not stable
+opposed to results of the authors of the potential.
+first, it seems to condense at the hexagonal site but suddenly
+begins to move towards a more favoarble position,
+close to the tetrahedral one but slightly displaced along all 3 coordinate axes.
+this energy is equal to the formation energy given in the original work.
+this artificial configuration, however, turns out to have negligible influence
+in finite temperature simulations due to a low migration barrier into the
+tetrahedral configuration.
+nevertheless, all these discrepancies have to be taken into account
+in the following investigations of defect combinations.
+
+slide X quantum mechanical details of 100 and bc
+
+it is worth to note that there are differences in the 100 defect geometries
+obtained by both methods.
+while the carbon-silicon distance of the db is equal,
+the db position inside the tetrahedron differs significantly.
+of course, the classical potential is not able to reproduce
+the clearly quantum mechanically dominated character of bonding.
+
+more important, the bc configuration is found to constitute
+a local minimum configuration and not a saddle point as found in another study.
+this is due to the neglection of spin in these calculations, which,
+however, is necessary as can already be seen from simple molecular orbital
+considerations, assuming a sp hybridized carbon atom due to the linear bond.
+this assumption turns to be right as indicated by the charge density isosurface
+which shows a net spin up density located in a torus around the C atom.
+