X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Ftalks%2Femrs2012.txt;h=efd8304b85f34c0b2ec996aecadca8483f7e8d6a;hp=676db777a18c05efb99c7be9e6d6f6235163c2e6;hb=147329059cdda2ebf293426b7fdbcd13b0c783f9;hpb=f0ac0a8402afa79a6a06b9841db95bcfaf670303 diff --git a/posic/talks/emrs2012.txt b/posic/talks/emrs2012.txt index 676db77..efd8304 100644 --- a/posic/talks/emrs2012.txt +++ b/posic/talks/emrs2012.txt @@ -2,12 +2,12 @@ slide 1 thank you very much and welcome everybody. as the title suggests / as already mentioned ... -... i am going to present theoretical results of investigations -of defect structures and mobilities in silicon. +... i am going to present results of theoretical investigations +of defects and defect mobilities in silicon. slide 2 -of course there is an experimental / practical motivation, +there is of course an experimental / practical motivation, which is the ion beam synthesis (IBS) of thin films of epitaxial 3C-SiC in Si. IBS consists of high-dose C implantation in Si followed by an annealing step, which, if properly done, results in buried homogeneous thin films of SiC @@ -53,170 +53,87 @@ accompanied by strain relaxation. these findings suggest a mechanism based on the agglomeration of substitutional instead of interstitial carbon. -slide 6 +slide 5 to understand the precipitation mechanism in the context of these controversial results atomistic simulations are performed. -HIER WEITER - -in md, a system of n particles is described -by numerically integrating newtons equations of motion. -the particle interaction is given by an analytical interaction potential. -observables are obtained by taking time or ensemble averages. - -roughly 6000 atoms were used to investigate defect structures -and nearly a quater of a million for the precipitation simulations. -the equations of motion are integrated by the velocity verlet algorithm -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 to zero inbetween the first and next neighbor atom. -simulations are performed in the isothermal-isobaric ensemble -realized by the berendsen thermostat and barostat. - -the basic concept of dft is the hohenberg kohn (hk) theorem, which states that -the ground-state wavefunction is a unique functional of the ground-state -electron density, which minimizes the energy, -i.e. it has the variational property. -now, the kohn sham (ks) approach constitutes a hartree-like formulation -of the hk minimal principle, which maps the system of interacting electrons to -an auxillary system of non-interacting electrons in an effective potential. -however formally exact by introducing an energy functional, -which accounts for exchange and correlation. -the kohn sham equations need to be solved in a self consistency loop. - -the vasp code is used for this purpose. -it utilizes plane waves to expand the ks wavefunctions. -an energy cut-off of 300 eV is employed. -the electron-ion interaction is described by ultrasoft pseudopotentials. -the generalized gradient approximation is used to solve the ks equations. -sampling in k space is restricted to the gamma point. -the supercell consists of 216 atoms. +namely, molecular dynamics simulations, +employing an empirical Tersoff-like short range bond order potential +developed by Erhart and Albe. +a large amount of atoms can be simulated. -slide 8 +moreover, the investigations are extended by first-principles calculations +based on dft using the plane wave pseudopotgential vasp code. +of course limited to smaller systems. -defect structures are obtained by creating a supercell of crystalline silicon. -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. +slide 6 -next to the structure, defects can be characterized by the formation energy, -which is defined by this formula. +using these methods we can now investigate single defect structures, +which can be characterized by the formation energy. -combinations of defects can be characterized by the binding energy, -the difference of the formation energy of the defect combination and -the isolated defects. -this way, binding energies below zero correspond to energetically favorable -configurations whereas the binding energy for non-interacting isolated defects -approaches zero. +Defect combinations can be described by the binding energy, +the difference of the formation energy of the defect combination +and the isoltaed defects. -migration barriers from one stable configuration into another -are obtained by the constrained relaxation technique. -the diffusing atom is displaced stepwise from the starting -to the final position and relaxation is only allowed -perpendicular to the displacement direction. -each step the configurational energy is recorded. +to acquire the mobilities migration barriers +are obtained by a constrained relaxation technique. -slide 9 +slide 7 + +now let's turn to the results ... +... of carbon interstitial defects in silicon. -this has been used to investigate, amongst others, -carbon interstitial defects in silicon. 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. + +it is worth to note that the bond centered configuration +is unstable only within the empirical description, relaxing into the 110 DB. +however, the formation energy is quite high +so this does not pose 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. +has the lowest formation energy and is drastically underestimated within EA. regarding the problem addressed in this study, this might constitute a problem. 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 10 - -as a next step, the Ci mobility is determined by the quantum mechanical method. -two of the intuitively guessed migration pathways of a carbon 00-1 db are shown. - -in number one, the carbon atom resides in the 110 plane -crossing the bc configuration. -due to symmetry it is sufficient to consider only the first half -of the transition path. -an activation energy of 1.2 eV is obtained. -actually another barrier exists to reach a ground-state configuration. - -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. +slide 8 -slide 11 +concerning the defect mobility, by first-principles methods, +a migration path is found, the 00-1 to 0-10 transition, +with a barrier that excellently matches experimental values. +the migration path is identified, it involves a change in orientation of the DB. -the situation changes completely for the classical description. -path number one, shows the lowermost migration barrier of 2.2 eV. -next to the fact, that this is a different pathway, -the barrier is overestimated by a factor of 2.4. - -moreover, the ea description predicts the bc configuration to be unstable -relaxing into the 110 db configuration. -additionally, the observed minimum in the classical 00-1 to 0-10 transition, -likewise relaxes into the 110 db structure without constraints. - -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. -and 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. +related to the just mentioned instability of the BC configuration, +the most probable transition for the empirical potential +involves an intermediate 110 DB configuration. +this results in a barrier, which is up to 3.4 times higher than the ab initio +or experimental value. +At least, there is the same change in orientation, a qualitative agreement. -slide 12 +slide 9 -implantation of highly energetic carbon atoms results in a multiplicity +implantation of 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. -the most favorable configuration shows a strong C-C bond. -however, a high migration barrier is necessary to obtain this configuration -in contrast to the second most favorable configuration, -which additionally is represented 2 times more often in the systematically -investigated configuration space. - -this suggests that agglomeration of Ci indeed is expected, but no C clustering. +and further types of defects created in the vicinity are inestigated by dft. -slide 13 +concerning combinations of 100-type interstitials, +there are lots of negative values for the binding energy, +so the agglomeration of C_i is indeed energetically favorable, +mainly due to a reduction of strain. -this is reinforced by the plot of the binding energy of dumbbells -separated along the 110 direction. -a capture radius clearly exceeding 1 nm is observed. +a capture radius clearly exceeding 1 nm is observed +for the interaction of DBs along the 110 direction. however, the interpolated graph suggests the disappearance of attractive forces between the two lowest separation distances. +so this suggests agglomeration of C but the absence of C clustering. -this supports the assumption of C agglomeration and the absence of C clustering. - -slide 14 +slide 10 if a vacancy is created next to the Ci defect, a situation absolutely conceivable in ibs, @@ -226,11 +143,9 @@ in contrast, high barriers are necessary for the reverse process. based on this, a high probability of stable Cs configurations must be concluded. -slide 15 +slide 11 in addition, it is instructive to look at combinations of Cs and Si_i. -the most favorable configuration is obtained for -Cs located right next to the 110 Si db within the 110 chain. this configuration is still less favorable than the Ci 100 ground state. however, the interaction of C_s and Si_i drops quickly to zero indicating a low capture radius. @@ -242,11 +157,11 @@ the barrier is even smaller than migration barrier for carbon. in addition, the low migration barrier of interstitial silicon, enables configurations of further separated Cs and Si_i defects. -in total, these findings demonstrate that configurations of Cs and Si_i, +these findings suggest that configurations of Cs and Si_i, instead of the thermodynamic ground state, play an important role in ibs, which indeed constitutes a process far from equilibrium. -slide 16 +slide 12 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, @@ -254,226 +169,46 @@ 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 results 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 already in the initial stage -of precipitation due to its high probability of incidence. - -slide 17 - -as a last task, reproducing the SiC precipitation is attempted -by successive insertion of 6000 C atoms, -the number necessary to form a minimal precipitate, -into a supercell consisting of 31 Si unit cells in each direction. -insertion is realized at constant temperature. -due to the high amount of particles, -the classical potential must be 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. +to structural formation increases, resulting in configurations of C_s and Si_i. + +slide 13 + +these findings are supported by results of empirical potential MD simulations +employed to directly simulate precipitation. + +6000 C atoms are inserted at constant temperature into a Si volume +consisting of 31 Si unit cells in each direction. + +smaller insertion volumes were also considered due to an expected low diffusion. +however - here - we only consider the total volume. + after insertion, the simulation is continued for 100 ps follwed by a cooling sequence downto 20 degrees celsius. -slide 18 +slide 14 -the radial distribution function of simulations at 450 dc, +the radial distribution function of Si-C bonds of simulations at 450 dc, an operative and efficient temperature in ibs, are shown. -for the low C concentration 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 an artifact due to the cut-off. -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, -a high amount of strongly bound C-C bonds -as in graphite or diamond is observed. -due to increased defect and damage densities -defect arrangemnets are hard to categorize and trace. -only short range order is observed. -and, indeed, by comparing to other distribution data, -an amorphous SiC-like phase is identified. - -slide 19 - -to summarize, the formation of cubic SiC fails to appear. -neither agglomeration of C interstitials -nor a transition into SiC can be identified. - -slide 20 - -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, -which results in a slow phase space propagation due to -a large amount of local minima separated by large energy barriers. -accelerated methods, like temperature accelerated MD and so on, exist -to bypass the time scale problem while retaining proper thermodynamic sampling. - -however, in addition, the overestimated diffusion barriers, -due to the short range character of the potential, -intensify this problem, which I termed: -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 to be not sufficient. -anyways, in this case, -structural evolution instead of equilibrium properties are matter of interest. - -slide 21 - -and indeed, promising changes are observed by comparing, -again the radial distribution data for temperatures up to 2050 dc. -first of all, the cut-off artifact disappears. -more important, a transition into a clearly Cs dominated structure takes place, -as can be seen by direct comparison with the respective reference peaks of Cs. - -the rising Si-Si peak is due to stretched Si-C-Si structures -along a 110 direction. - -the C-C next neighbor pairs are reduced, -which is mandatory for SiC formation. -the peak at roughly 0.3 nm gets slightly shifted to higher distances, -due to a decrease of interstitial carbon combinations accompanied by an -increase in interstitial and substitutional as well as pure substitutional -combinations. -increasing values in this range -correspond to bonds of Cs and another Cs with a nearby Si_i atom. - -slide 22 - -to conclude, stretched coherent structures are directly observed. -therefore, it is expected that Cs is extensively involved -in the precipitation process for implantations at elevated temperatures. - -the emission of Si_i serves several needs: -as a vehicle to rearrange stable Cs, -as a building block for the surrounding Si host or further SiC formation. -and for strain compensation either 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. - -thus, it is further concluded that high temperatures are necessary to model -ibs conditions, which are far from equilibrium. -the high temperatures deviate the system from thermodynamic equilibrium -enabling Ci to turn into Cs. - -slide 23 - -to summarize and conclude ... -point defects were investigated by both methods. -the interstitial carbon mmigration path was identified. -it turned out that the diffusion barrier is drastically overestimated -within the ea description. - -combinations of defects were investigated by first principles methods. -the agglomeration of point defects is energetically favorable. -however, substitutional carbon arises in all probability. -even transitions from the ground state are very likely to occur. - -concerning the precipitation simulations, the problem of -potential enhanced slow phase space propagation was discussed. -high temperatures are assumed necessary to simulate ibs conditions. -at low temperatures a dumbbell dominated structure is obatined -whereas -it is expected that -Stretched structures of SiC were observed at elevated temperatures. -it is thus concluded that -substitutional carbon is heavily involved in the precipitation process. -the role of the Si_i was outlined. - -in total, these results suggest, -that cubic SiC precipitation occurs by successive agglomeration of Cs. - -slide 24 - -finally, I would like to thank all of the people listed on this slide, -categorized by location. - -thank you for your attention! - - - - - -slide X polytypes - -although the local order of the silicon and carbon atoms -characterized by the tetrahedral bond is always the same, -more than 250 different polytypes exist, -which differ in the one-dimensional stacking sequence of -identical, close-packed SiC bilayers, -the stacking sequence of the most important polytypes is displayed here. -the 3c polytype is the only cubic polytype. - -different polytypes exhibit different properties, -which are listed in the table -and compared to other technologically relevant semiconductor materials. -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. -thus, the cubic polytype is considered most effective for highly efficient -high-performance electronic devices. - -slide X silicon self interstitials - -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, all these discrepancies have to be taken into account -in the following investigations of defect combinations. - -slide X quantum mechanical details of 100 and bc - -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. + +so, the formation of Ci dumbbells indeed occurs +but no agglomeration is observed. + +one reason is the drastically overestimated dissufion barrier +within the empirical potential description as outlined earlier. +due to this, simulations are performed at increased temperatures. +agglomeration and precipitation is still not observed, however, +a phase transition into a clearly Cs dominated structure +can be observed with increasing temperature +by comparing with the reference peak. +stretched coherent structures of SiC are directly observed +and the Si_i could be attributed the role of strain reduction. + +slide 15 + +i would like to conclude. +based on both, ...