X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Ftalks%2Fdefense.txt;h=325510dbfa80b8599743885fb1b70e9a8a0126bb;hp=94350c3151a512abbb00e703fdc975a55b477c6d;hb=b72d5fabe9b016843d069c4478310ea67e76fc47;hpb=8a67bb480a220eaef92cce471d4cabcd71e66e40 diff --git a/posic/talks/defense.txt b/posic/talks/defense.txt index 94350c3..325510d 100644 --- a/posic/talks/defense.txt +++ b/posic/talks/defense.txt @@ -59,7 +59,7 @@ different polytypes exhibit different properties, 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. @@ -186,7 +186,7 @@ with a time step of 1 fs. 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. @@ -224,8 +224,9 @@ slide 10 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 @@ -247,9 +248,345 @@ each step the configurational energy of the relaxed structure is recorded. 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 + +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. +