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.
defect structures are obtained by creating a supercell of crystalline silicon
with periodic boundary conditions and temperature and pressure set to zero.
-the interstitial carbon or silicon atom is inserted followed by
-structural relaxation into a local minimum configuration.
+the interstitial carbon or silicon atom is inserted,
+for example at the tetrahedral or heexagonal site,
+followed by structural relaxation into a local minimum configuration.
next to the structure, defects can be characterized by formation energies,
which is defined by this formula, where the chemical potential
slide 11
-
+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, 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
+
+
+
+slide 17
+slide 18
+slide 19
+slide 20
+slide 21
+slide 22
+slide 23
+slide 24
+slide 25
+slide 26
+slide 27
+
projects / lectures / latex.git / blobdiff