X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Ftalks%2Fdefense.txt;h=325510dbfa80b8599743885fb1b70e9a8a0126bb;hp=ab47a0abe4fdf9117f5ac24563ad817a5d3c868e;hb=b72d5fabe9b016843d069c4478310ea67e76fc47;hpb=e08a97849ebaf34c088eef126bf83fa8a4267119 diff --git a/posic/talks/defense.txt b/posic/talks/defense.txt index ab47a0a..325510d 100644 --- a/posic/talks/defense.txt +++ b/posic/talks/defense.txt @@ -4,7 +4,8 @@ dear examiners, dear colleagues. welcome everybody to the the defense of my doctor's thesis entitled ... as usual, i would like to start with a small motivation, which in this case focuses on the materials system, SiC. -and, thereby, approach the problem to be investigated within this study. +and, thereby, approach the problem to be investigated within this study, i.e. +a controversy concerning the precipitation mechanism present in the literature. slide 2 @@ -35,8 +36,7 @@ towards an extensive development and use of regenerative energies and emobility. moreover, due to the large bonding energy, SiC is a hard and chemical inert material -suitable for applications under extreme conditions -and for microelectromechanical systems. +suitable for applications under extreme conditions. its radiation hardness allows the operation as a first wall reactor material and as electronic devices in space. @@ -47,7 +47,7 @@ is the only stable compound in the C/Si system. SiC is a mainly covalent material in which both, the Si and C atom are sp3 hybridized. the local order of the silicon and carbon atoms -characterized by the tetrahedral bond is the same for all polytypes. +characterized by the tetrahedral bond is always the same. however, more than 250 different polytypes exist, which differ in the one-dimensional stacking sequence of identical, close-packed SiC bilayers, @@ -58,12 +58,12 @@ 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. -Despite the lower charge carrier mobilities for low electric fields, -SiC clearly outperforms Si. +despite the lower charge carrier mobilities for low electric fields, +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 most effective for highly efficient +thus, the cubic polytype is considered most effective for highly efficient high-performance electronic devices. slide 4 @@ -74,13 +74,16 @@ the fact that natural SiC is almost only observed as individual presolar SiC stardust grains near craters of meteorite impacts already indicates the complexity involved in the synthesis process. -however, nowadays, much progress has been achieved in SiC thin film growth. +however, nowadays, much progress has been achieved in thin film growth +by molecular beam epitaxy and chemical vapor deposition. indeed, commerically available semiconductor devices based on alpha SiC exist, although these are still extremely expensive. -however, production of the advantageous cubic polytype material is less advanced. +however, production of the advantageous cubic type is less advanced, +mainly due to the mismatches in the thermal expansion coefficient and the lattice parameter -(with respect to the substrate) cause a considerable amount of defects, -which is responsible for structural and electrical qualities +(with respect to the substrate) +which cause a considerable amount of defects, +that is responsible for structural and electrical qualities that are not yet satisfactory. next to CVD and MBE, the ion beam synthesis technique, which consists of @@ -95,27 +98,495 @@ this enables the synthesis of large are SiC films. slide 5 -the ibs synthesis of ... +the ibs synthesis of SiC was extensively investigated and optimized +here in augsburg in the group of joerg lindner. +a two-step implantation process was suggested. +the trick is to destroy stable precipitates at the layer interface +by implanting a remaining low amount of the dose at lower temperatures +to enable redistribution of the C profile during annealing, +which results in a homogeneous SiC layers with a sharp interface +as you can see in this cross section tem image. -and the task of this work is to gain insight into SiC precipitation in silicon. +however, the precipitation itself is not yet fully understood. +understanding the effective underlying processes of precipitation +will enable significant progress in thin film formation of cubic SiC +and likewise offer perspectives for processes that rely upon prevention +of SiC precipitation, for example the fabrication of strained silicon. slide 6 -supposed conv mech +there is an assumed mechanism of precipitation based on the formation and +agglomeration of interstitial carbon. +first note, however, that silicon as well as SiC consists of two fcc lattices +displaced by one quater of the volume diagonal. +in the case of SiC one of the fcc lattice atoms is replaced by carbon atoms. +4 lattice constants of silicon correspond to 5 lattice constants of SiC. +thus, in total, the silicon density is only slightly lower in SiC. +the mechanism is schematically displayed here. +a pair of black dots represent two atoms of the two fcc lattices. +the incorporated carbon atoms form C-Si dumbbells +situated on regular silicon lattice sites. +with increasing doese these dumbbells agglomerate into large clusters, +indicated by dark contrasts and an otherwise undisturbed lattice in hrtem. +once a critical radius of 2-4 nm is reached, +the interfacial energy due to the lattice mismatch is overcome +and precipitation occurs. +this is manifested by the disappearance of the dark contrasts in favor of +moire patterns, again due to the lattice mismatch of SiC and silicon. +due to the slightly lower silicon density of SiC, +precipitation is accompanied by the emission of a few excess silicon atoms +into the silicon host, since there is more space. +it is worth to note that the hkl planes of substrate and SiC match. slide 7 -however, controversial ... exists in literature +however, controversial findings and conclusions exist in the literature. +instead of a carbon interstitial (Ci) based mechanism, +nejim et al propose a transformation based on substitutionally incorporated +carbon (Cs) and the generation of interstitial silicon, +which reacts with further impanted carbon in the cleared volume. +investigations of the annealing behavior of implantations +at different temperatures showed high and zero carbon diffusion +for the room temperature and elevated temperature implantations respectively. +this suggests the formation of mobile Ci at low temperatures +opposed to much more stable Cs configurations at elevated temperatures. +furthermore, investigations of strained SiC/Si heterostructures, +find initial coherent SiC structures, which, in this case, +incidentally transform into incoherent SiC nanocrystals +accompanied by strain relaxation. + +these findings suggest a mechanism based on the agglomeration of substitutional +instead of interstitial carbon atoms. +the task of the present study is to understand the precipitation mechanism +in the context of these controversial results. slide 8 -this (insight) is achieved by atomistic simulations, which are explained after the assumed precipitation mechnisms present in literature are presented ... +therefore, atomistic simulations are utilized, +to gain insight on a microscopic level not accessible by experiment. +namely, molecular dynamics (md) simulations and density functional theory (dft) +calculations, which are explained in the following, are used +to investigate carbon and silicon defect configurations as well as to +directly model SiC precipitation. +finally, after these results are presented, +i would like to give a short summary and conclusion. slide 9 + +in md, a system of n particles is described on the microscopic level +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. + +in this case roughly 6000 atoms were used to investigate defect structures +and nearly a quater of a million atoms 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 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. +simulations are performed in the isothermal-isobaric ensemble +realized by the berendsen thermostat and barostat. + +furthermore, highly accurate quantum mechanical calculations +based on dft are used. +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. +in that way, the many body problem can be described by the electron density, +which depends only on the 3 spatial coordinates. +now, the kohn sham (ks) approach constitutes a hartree-like formulation +of the hk minimal principle, which maps the system of interacting particles to +an auxillary system of non-interacting electrons in an effective potential. +however formally exact by introducing an energy functional, +which accounts for the exchange and correlation energy. +the effective potential yields a ground-state density +for non-interacting electrons, which is equal to that for interacting electrons +in the external potential. +the kohn sham equations need to be solved in a self consistency loop. + +the vasp code was 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. +brillouin zone sampling is restricted to the gamma point. +the supercell consists of 216 atoms, 3 silicon unit cells in each direction, +of course much less atoms compared to the highly efficient md technique. + 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, +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 +is taken to be the cohesive energy per atom for the fully relaxed structure. + +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 while the binding energy for non-interacting isolated defects +approaches zero. + +migration barriers from one stable configuration into another +are obtained by the constrained relaxation technique. +atoms involving great structural changes are displaced stepwise +from the starting to the final position and relaxation is only allowed +perpendicular to the displacement direction. +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. +