X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=blobdiff_plain;f=posic%2Ftalks%2Fdefense.txt;h=79243cc7594edb4529e5db19482cb217afb34dab;hp=83f618d904254d2bfd05b76c71e1c21347c44735;hb=348f10f39655e4efc37eb22f88ac02c75ec60c23;hpb=3f65cf44692d94497ff4a2ac366cb91b97ac3012 diff --git a/posic/talks/defense.txt b/posic/talks/defense.txt index 83f618d..79243cc 100644 --- a/posic/talks/defense.txt +++ b/posic/talks/defense.txt @@ -3,21 +3,262 @@ 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 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 +(nowadays superceded by direct band gap materials like GaN).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 ... + slide 12 slide 13 slide 14