X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fdefense.txt;h=9162a00b2489966ddf5e4a72438f17607bf6eb9d;hb=76d6eccdd362ad31cb4b701bfa7c78e43e30cd78;hp=94350c3151a512abbb00e703fdc975a55b477c6d;hpb=8a67bb480a220eaef92cce471d4cabcd71e66e40;p=lectures%2Flatex.git diff --git a/posic/talks/defense.txt b/posic/talks/defense.txt index 94350c3..9162a00 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. @@ -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 +248,129 @@ 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 + + + +slide 17 +slide 18 +slide 19 +slide 20 +slide 21 +slide 22 +slide 23 +slide 24 +slide 25 +slide 26 +slide 27 +