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.
the interaction is decribed by a Tersoff-like short-range bond order potential,
developed by erhart and albe.
the short range character is achieved by a cutoff function,
-which drops the interaction inbetween the first and second next neighbor atom.
+which drops the interaction inbetween the first and next neighbor atom.
the potential consists of a repulsive and an attractive part associated with
the bonding, which is limited by the bond order term, which takes
into consideration all atoms k influencing the bond of atoms i and j.
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
+
+as a last task, reproducing the SiC precipitation is attempted
+by successive insertion of 6000 C atoms,
+the number necessary to form a precipitate with a radius of approximately 3 nm,
+into a supercell consisting of 31 Si unit cells in each direction.
+insertion is realized at constant temperature.
+after insertion, the simulation is continued for 100 ps
+follwed by a cooling sequence downto 20 degrees celsius.
+due to the high amount of particles,
+the classical potential is exclusively 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.
+
+slide 22
+
+the radial distribution Si-C, C-C and Si-Si bonds of simulations,
+in which C was inserted at 450 dc,
+an operative and efficient temperature in ibs, are shown.
+
+for the low C concentration simulation, i.e. the v1 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 a cut-off artifact,
+correpsonding to the Si-C cut-off distance of 0.26 nm.
+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, i.e. the v1 and v2 simulation,
+a high amount of strongly bound C-C bonds
+as in graphite or diamond are observed.
+an increased defect and damage density is obtained,
+which makes it hard to categorize and trace defect arrangements.
+only short range orde is observed.
+and, indeed, comparing to other distribution data, an amorphous SiC-like
+phase is obtained.
+
+slide 23
+
+to summarize, the formation of cubic SiC fails to appear.
+in the v1 simulation, formation of Ci indeed occurs, however,
+agglomeration is missing.
+in the high concentration simulation, an amorphous SiC-like structure,
+which is not expected at 450 dc, is obtained.
+no rearrangemnt into crystalline cubic SiC is indicated.
+
+slide 24
+
+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.
+to minimize the integration error, the time step must be chosen smaller
+than the reciprocal of the fastes vibrational mode.
+several local minima exist, which are separated by large energy barriers.
+due to the low probability for escaping such a local minimum,
+a transition event correpsonds to a multiple of vibrational periods.
+a phase transition, in turn, consists of many such infrequent transition events.
+new accelerated methods, like temperature accelerated MD and so on,
+have been developed to bypass the time scale problem while retaining proper
+thermodynamic sampling.
+
+in addition, the overestimated diffusion barriers,
+due to the short range character of the potential,
+intensify this problem, which I called:
+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 oto be not sufficient.
+moreover, to legitimate the usage of increased temperatures:
+cubic SiC is also observed for higher temperatures,
+there is definitely a higher temperature inside the sample, and, anyways,
+structural evolution instead of equilibrium properties are matter of interest.
+
+slide 25
+
+and indeed, promising changes are observed by comparing,
+again the radial distribution data of Si-C, Si-Si and C-C bonds
+for temperatures up to 2050 dc.
+first of all, the cut-off artifact disappears.
+more important, a transition a 100 db into a Cs dominated structure takes place,
+as can be seen by direct comparison with the respective reference peaks.
+
+the Si-Si rising peak at 0.325 nm is due to two Si atoms next to a Cs atom.
+
+the C-C next neighbor pairs are reduced,
+which is mandatory for cubic SiC formation.
+the peak at roughly 0.3 nm gets slightly shifter to higher distances.
+the amount of bonds due to Ci 100 combinations, represented by dashed arrows,
+decreases accompanied by an increase of bonds due to combinations of
+Ci 100 and Cs and pure Cs combinations, represented by the dashed line and
+solid arrows respectively.
+increasing values in the range between the dashed line and first solid arrow
+correpsond to bonds of a Cs and another Cs with a nearby Si_i atom.
+
+slide 26
+
+to conclude, stretched coherent structures of SiC embedded in the Si host
+are directly observed.
+therefore, an increased participation of Cs is suggested
+for implantations at elevated temperatures,
+which simulate the conditions prevalent in ibs that deviate the system
+from thermodynamic equilibrium enabling Ci to turn into Cs.
+
+the emission of Si_i serves several needs:
+as a vehicle to rearrange the Cs,
+realized by recombination into the highly mobile Ci configuration.
+furthermore, it serves as a building block for the surrounding Si host
+or further SiC formation.
+finally, it may compensate stress 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.
+
+to summarize, the results suggest that Cs plays an important role
+in the precipitation process.
+moreover, high temperatures are necessary to model ibs conditions,
+which are far from equilibrium.
+
+slide 27
+
+to summarize and conclude
+
+slide 28
+
+in the end, I would like to say thank you.
+
projects / lectures / latex.git / blobdiff