slide 1
-dear examiners, dear colleagues.
+dear referees, 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.
the semiconductor material SiC has remarkable physical and chemical properties,
which make it a promising new material in various fields of applications.
-the wide band gap and high breakdown field
+most important, the wide band gap and high breakdown field
as well as the high electron mobility and saturation drift velocity
in conjunction with its unique thermal stability and conductivity
-unveil SiC as the ideal candidate for
+unveil SiC as the ideal candidate for highly efficient
high-temperature, high-power and high-frequency electronic
-and opto-electronic devices.
-
-in fact light emission from SiC crystal rectifiers was observed
-already in the very beginning of the 20th century
-constituting the brirth of solid state optoelectronics.
-and indeed, the first blue light emitting diodes in 1990 were based on SiC.
-(nowadays superceded by direct band gap materials like GaN).
-
-the focus of SiC based applications, however,
-is in the area of solid state electronic devices
-experiencing revolutionary performance improvements enabled by its capabilities.
-devices can be designed much thinner with increased dopant concentrations
-resulting in highly efficient rectifier diodes and switching transistors.
-one example is displayed: a SiC based inverter with an efficiency of 98.5%
-designed by the frauenhofer institute for solar energy systems.
+and opto-electronic devices, which can operate in harsh environments.
+
+#in fact light emission from SiC crystal rectifiers was observed
+#already in the very beginning of the 20th century
+#constituting the brirth of solid state optoelectronics.
+#and indeed, the first blue light emitting diodes in 1990 were based on SiC.
+#(nowadays superceded by direct band gap materials like GaN).
+
+a SiC based inverter with an efficiency of almost 99% has been realized.
therefore, SiC constitutes a promising candidate to become the key technology
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.
-its radiation hardness allows the operation as a first wall reactor material
-and as electronic devices in space.
-
slide 3
-the stoichiometric composition of silicon and carbon
-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 always the same.
-however, more than 250 different polytypes exist,
-which differ in the one-dimensional stacking sequence of
-identical, close-packed SiC bilayers,
-which can be situated on one of three possible positions (abbreviated a,b,c).
-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.
-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 considered most effective for highly efficient
-high-performance electronic devices.
-
-slide 4
-
-SiC is rarely found in nature and, thus, must be synthesized.
-it was first observed by moissan from a meteor crater in arizona.
-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 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 type is less advanced,
-mainly due to the
-mismatches in the thermal expansion coefficient and the lattice parameter
-(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
-high dose ion implantation followed by a high-temperature annealing step
-turned out to constitute a promising method to form buried layers of SiC in Si
-as indicated in this sketch.
-due to the high areal homogenity achieved in ibs
-the size is only limited by the beam scanning equipment
-and sythesized films do not exhibit surface bending effects
-in contrast these formed by cvd and mbe.
-this enables the synthesis of large are SiC films.
-
-slide 5
-
-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
+one method to fabricate 3C-SiC, the cubic phase of SiC, is ibs,
+i.e. high dose ion implantation followed by a high-temperature annealing step,
+this was extensively investigated here in augsburg in the group of j lindner.
+an optimized two-step implantation process was suggested.
+the trick is to destroy stable precipitates
+that formed at the layer interface during the first implantation step
+by implanting a low remaining amount of the regular dose at lower temperatures.
+this enables redistribution of the C atoms during annealing,
+which results in a homogeneous SiC layer with a sharp interface
as you can see in this cross section tem image.
-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.
+however, already the precipitation, at elevated temperatures,
+is not yet fully understood.
-slide 6
+slide 4
-there is an assumed mechanism of precipitation based on the formation and
+there is an assumed mechanism, however, which is 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.
+in the case of SiC, one of the fcc lattice sites is occupied 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.
+in total, this results in a only slightly lower silicon density for SiC.
-the mechanism is schematically displayed here.
-a pair of black dots represent two atoms of the two fcc lattices.
+the mechanism is schematically displayed.
+a pair of black dots represents 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.
+sharing regular silicon lattice sites.
+with increasing dose and time these dumbbells agglomerate into large clusters,
+indicated by dark contrasts in 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
+precipitation is accompanied by the emission of only 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.
+#it is worth to note that the hkl planes of substrate and SiC match.
-slide 7
+slide 5
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.
+investigations of the annealing behavior of implantations at low and high
+temperatures show high and almost zero carbon diffusion 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,
accompanied by strain relaxation.
these findings suggest a mechanism based on the agglomeration of substitutional
-instead of interstitial carbon atoms.
+instead of interstitial carbon.
the task of the present study is to understand the precipitation mechanism
in the context of these controversial results.
-slide 8
+slide 6
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
+calculations, which are explained on the following slides, 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.
+finally, after some selected results are presented,
+a short summary and conclusion is given.
-slide 9
+slide 7
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
+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 second 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.
+which drops the interaction to zero 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
+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 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 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.
+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.
-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.
+sampling in k space is restricted to the gamma point.
+the supercell consists of 216 atoms.
-slide 10
+slide 8
-defect structures are obtained by creating a supercell of crystalline silicon
-with periodic boundary conditions and temperature and pressure set to zero.
+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.
-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.
+next to the structure, defects can be characterized by the formation energy,
+which is defined by this formula.
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
+configurations whereas 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
+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 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
+slide 9
-the situation is much better for carbon defects.
+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 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.
+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 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
+slide 10
-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.
+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,
+and the corresponding activation energies 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.
+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.
-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
+slide 11
the situation changes completely for the classical description.
-path number one, from the 00-1 to bc configuration
+path number one, from the db to the 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.
+the barrier is 2.4 times higher than ab inito result.
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.
+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,
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.
+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.
+slide 12
+
+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.
+the most favorable configuration shows a strong C-C bond.
+however, 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.
+
+slide 13
+
+this is reinforced by the plot of the binding energy of Ci dbs
+separated along the 110 direction.
+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 exceeding 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 14
+
+if a vacancy is created next to the Ci defect,
+a situation absolutely conceivable in ibs,
+structures are obtained, which exhibit low migration barriers
+for the transition into the Cs configuration.
+high barriers are necessary for the reverse process.
+
+based on this, a high probability of stable Cs configurations must be concluded.
+
+slide 15
+
+additionally, it is instructive to look at combinations of Cs and Si_i,
+again, a situation which is very likely to arise in ibs.
+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 ground state.
+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.
+
+moreover, a low transition barrier is found from the ground state
+into the configuration of separated defects.
+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,
+instead of the thermodynamic ground state, play an important role in ibs,
+which indeed constitutes a process far from equilibrium.
+
slide 16
+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 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 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.
+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.
+after insertion, the simulation is continued for 100 ps
+follwed by a cooling sequence downto 20 degrees celsius.
+
slide 18
+
+the radial distribution function 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 crystalline 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 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 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 cubic SiC formation.
+the peak at roughly 0.3 nm gets slightly shifter 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
+correpsond to bonds of Cs and another Cs with a nearby Si_i atom.
+
slide 22
+
+to conclude, stretched coherent structures of SiC embedded in the Si host
+are directly observed.
+therefore, it is concluded 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,
+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.
+
+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 ...
+defect structures were described by both methods.
+the interstitial carbon mmigration path was identified.
+it turned out that the 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 the potential
+enhanced slow phase space propagation was discussed.
+by comparing with experiment it is concluded
+that high temperatures are necessary to model simultae ibs conditions.
+at elevated temperatures stretched structures of SiC were directly observed
+in simulation.
+it is thus concluded that
+substitutional carbon is heavily involved in the precipitation process.
+the role of the Si_i was outlined and in one case also directly observed
+in simulation.
+
+in total, it is my feeling, that cubic SiC precipitation occurs by successive
+agglomeration of substitutional C.
+
slide 24
-slide 25
-slide 26
-slide 27
+
+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.
projects / lectures / latex.git / blobdiff