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.
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