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 is a motivation with respect to the materials system, SiC.
+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 ...
+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+(nowadays superceded by direct band gap materials like GaN).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 Si.
+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 predict 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 ...
+
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