slide 1

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, i.e.
a controversy concerning the precipitation mechanism present in the literature.

slide 2

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
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
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(nowadays superceded by direct band gap materials like GaN).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.
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
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.

slide 6

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 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

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 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.
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

now ...

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