X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fdefense.txt;h=9162a00b2489966ddf5e4a72438f17607bf6eb9d;hb=76d6eccdd362ad31cb4b701bfa7c78e43e30cd78;hp=25514aaac7458fcfe0ee31a397828be38eb81d19;hpb=a08cd67251d6433ee23653e567601260436c923a;p=lectures%2Flatex.git diff --git a/posic/talks/defense.txt b/posic/talks/defense.txt index 25514aa..9162a00 100644 --- a/posic/talks/defense.txt +++ b/posic/talks/defense.txt @@ -4,6 +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, i.e. +a controversy concerning the precipitation mechanism present in the literature. slide 2 @@ -34,8 +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. @@ -46,7 +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, @@ -57,12 +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 @@ -73,36 +74,303 @@ 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 3c 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 -high dose ion implantation foolowed by a high-temperature annealing step -turned out to constitute a promising method to form buried layers of SiC in Si. -... +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. -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 -this (insight) is achieved by atomistic simulations, which are explained after the assumed precipitation mechnisms present in literature are presented ... +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 + + + +slide 17 +slide 18 +slide 19 +slide 20 +slide 21 +slide 22 +slide 23 +slide 24 +slide 25 +slide 26 +slide 27 +