which are listed in the table
and compared to other technologically relevant semiconductor materials.
despite the lower charge carrier mobilities for low electric fields,
-SiC clearly outperforms Si.
+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.
in the following, structures and formation energies
of silicon self-interstitial defects are shown.
-the classical potential and ab initio method predict formation energies,
+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 ...
+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, these artificats have to be taken into account
+in the following investigations of defect combinations.
slide 12
+
+the situation is much better for carbon defects.
+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.
+the tetrahedral configuration is found to be unstable
+in contrast to the prediction of the classical potential, which, however,
+shows a high energy of formation making this defect very unlikely to occur.
+the opposite is found for the bond-centered configuration, which constitutes
+a stable configuration but is found unstable in the classical description,
+relaxing into the 110 db configuration.
+however, again, the formation energy is quite high and, thus,
+the wrong description is not posing a serious limitation.
+the substitutional defect, which is not an interstitial defect,
+has the lowest formation energy for both methods, although,
+it is drastically underestimated in the empirical approach.
+this might be a problem concerning the clarification of the controversial views
+of participation of Cs in the precipitation mechanism.
+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 13
+
+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.
+
slide 14
+
+here, two of the intuitively obvious migration pathways of a carbon 00-1 db,
+and the corresponding activation energies
+for the highly accurate quantum mechnaical calculations are shown.
+
+in number one, the carbon atom resides in the 110 plane
+crossing the bc configuration.
+due to symmetry it is sufficient to merely consider the migration into the bc
+configuration.
+an activation energy of 1.2 eV is obtained.
+
+in path two, the carbon atom moves towards the same silicon atom, however,
+it escapes the 110 plane and forms a 0-10 oriented db.
+the obtained actiavtion energy of 0.9 eV excellently matches experiment.
+thus, there is no doubt, the migration mechanism is identified.
+
+a simple reorientation process was also calculated.
+however, an energy of 1.2 eV was obtained.
+thus, reorientation is most probably composed of two consecutive processes of
+the above type.
+
slide 15
+
+the situation changes completely for the classical description.
+path number one, from the 00-1 to bc configuration
+shows the lowermost migration barrier of 2.2 eV.
+next to the fact, that this is a different pathway,
+the barrier is 2.4 times higher than the experimental and ab inito results.
+
+moreover, the ea description predicts the bc configuration to be unstable
+relaxing into the 110 db configuration.
+indeed, the observed minima in the 00-1 to 0-10 transition,
+is close to the 110 db structure.
+
+this suggests to investigate the transition involving the 110 configuration.
+this migration is displayed here,
+the 00-1 db turns into a 110 type followed by a final rotation into the 0-10 db
+configuration.
+barriers of 2.2 eV and 0.9 eV are obtained.
+these activation energies are 2.4 to 3.4 times higher than the ab initio ones.
+however, due to the above reasons, this is considered the most probable
+migration path in the ea description.
+after all, the expected change of the db orientation is fullfilled.
+
+nevertheless, diffusion barriers are drastically overestimated
+by the classical potentials, a problem, which needs to be addressed later on.
+
+slide 16
+
+implantation of highly energetic 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 at certain neighbor positions, numbered 1-5, are investigated.
+the investigations are restricted to dft calculations.
+energetically favorable and unfavorable configurations,
+determined by the binding energies,
+can be explained by stress compensation and increase respetively.
+
+as can be seen, the agglomeration of interstitial carbon is energetically
+favorable.
+indeed, the most favorable configuration shows a strong C-C bond.
+however, due to high migration barriers or energetically unfavorable
+intermediate configurations to obtain this configuration,
+only a low probability is assumed for C-C clustering.
+
+in contrast, for the second most favorable configuration,
+a migration path with a low barrier exists.
+moreover, within the systematically investigated configuration space,
+this type of defect pair is represented two times more often
+than the ground state.
+
+the results suggest that agglomeration of Ci indeed is expected.
+
+slide 17
+
+this is reinforced by the plot of the binding energy of Ci dbs
+separated along the 110 direction with respect to the C-C distance.
+the interaction is found to be proportional to the reciprocal cube
+of the distance for extended separations and saturates for the smallest
+possible distance, i.e. the ground state.
+a capture radius clearly extending 1 nm is observed.
+the interpolated graph suggests the disappearance of attractive forces
+between the two lowest separation distances of the defects.
+
+this supports the assumption of C agglomeration and the absence of C clustering.
+
+slide 18
+
+if a vacancy is created next to the Ci defect,
+a situation absolutely conceivable in ibs,
+the obtained structure will most likely turn into the Cs configuration.
+if the vacancy is created at position 1, the Cs configuration is directly
+obtained in the relaxation process.
+if it is created at other positions, e.g. 2 and 3,
+only low barriers into the Cs configuration exist
+and high barriers are necessary for the reverse process.
+
+based on this, a high probability for the formation of Cs,
+which is found to be extremely stable, must be concluded.
+
+slide 19
+
+in addition, it is instructive to look at combinations of Cs and Si_i,
+again, a situation which is very likely to arise due to implantation.
+Cs located right next to the 110 Si db within the 110 chain
+constitutes the energetically most favirable configuration,
+which, however, is still less favorable than the Ci 100 db,
+in which the silicon and carbon atom share a single lattice site.
+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.
+thus, Cs and Si_i, which do not react into the ground state,
+constitute most likely configurations to be found in ibs.
+
+this is supported by a low migration barrier necessary for the transition
+from the ground state Ci 100 db into the configuration of Cs and Si_i.
+in addition, a low migration barrier of the interstitial silicon,
+enables configurations of further separated Cs and Si_i defects.
+
+in total, these findings demonstrate that configurations of Cs and a Si_i db,
+instead of the thermodynamic ground state, play an important role in ibs,
+which indeed constitutes a process far from equilibrium.
+
+slide 20
+
+once more, 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 might result 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 in the precipitation process.
+
+slide 21
+
+now ...
+
+slide 22
+slide 23
+slide 24
+slide 25
+slide 26
+slide 27
+
projects / lectures / latex.git / blobdiff