high-temperature, high-power and high-frequency electronic
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-#(nowadays superceded by direct band gap materials like GaN).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.
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 only a few excess silicon atoms
-into the silicon host, since there is more space.
+the excess silicon atoms are released in the silicon host,
+since there is more space.
#it is worth to note that the hkl planes of substrate and SiC match.
slide 5
-however, controversial findings and conclusions exist in the literature.
+however, controversial findings 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,
slide 7
-in md, a system of n particles is described on the microscopic level
+in md, a system of n particles is described
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.
roughly 6000 atoms were used to investigate defect structures
-and nearly a quater of a million atoms for the precipitation simulations.
+and nearly a quater of a million 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 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.
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.
+which accounts for exchange and correlation.
the kohn sham equations need to be solved in a self consistency loop.
the vasp code is used for this purpose.
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.
+each step the configurational energy is recorded.
slide 9
slide 10
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.
+two of the intuitively guessed migration pathways of a carbon 00-1 db 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.
+due to symmetry it is sufficient to consider only the first half
+of the transition path.
an activation energy of 1.2 eV is obtained.
actually another barrier exists to reach a ground-state configuration.
slide 11
the situation changes completely for the classical description.
-path number one, from the db to the bc configuration
-shows the lowermost migration barrier of 2.2 eV.
+path number one, 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 ab inito result.
+the barrier is overestimated by a factor of 2.4.
moreover, the ea description predicts the bc configuration to be unstable
relaxing into the 110 db configuration.
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
+however, a 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 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
+however, 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.
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.
+in contrast, 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.
+in addition, it is instructive to look at combinations of Cs and Si_i.
+the most favorable configuration is obtained for
+Cs located right next to the 110 Si db within the 110 chain.
+this configuration 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.
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,
+the number necessary to form a minimal precipitate,
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.
+the classical potential must be 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.
to summarize, the formation of cubic SiC fails to appear.
neither agglomeration of C interstitials
-nor a transition into crystalline SiC can be identified.
+nor a transition into SiC can be identified.
slide 20
however, in addition, the overestimated diffusion barriers,
due to the short range character of the potential,
-intensify this problem, which I called:
+intensify this problem, which I termed:
potential enhanced slow phase space propagation.
the approach used in this study is to simply increase the temperature, however,
anyways, in this case,
structural evolution instead of equilibrium properties are matter of interest.
-slide 25
+slide 21
and indeed, promising changes are observed by comparing,
again the radial distribution data for temperatures up to 2050 dc.
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,
+which is mandatory for SiC formation.
+the peak at roughly 0.3 nm gets slightly shifted 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.
+correspond to bonds of Cs and another Cs with a nearby Si_i atom.
-slide 26
+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
+to conclude, stretched coherent structures are directly observed.
+therefore, it is expected 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
+as a building block for the surrounding Si host or further SiC formation.
+and for strain compensation either 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.
+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
+thus, 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 27
+slide 23
to summarize and conclude ...
-defect structures were described by both methods.
+point defects were investigated by both methods.
the interstitial carbon mmigration path was identified.
-it turned out that the the diffusion barrier is drastically overestimated
+it turned out that the diffusion barrier is drastically overestimated
within the ea description.
combinations of defects were investigated by first principles methods.
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.
+concerning the precipitation simulations, the problem of
+potential enhanced slow phase space propagation was discussed.
+high temperatures are assumed necessary to simulate ibs conditions.
+at low temperatures a dumbbell dominated structure is obatined
+whereas
+it is expected that
+Stretched structures of SiC were observed at elevated temperatures.
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.
+the role of the Si_i was outlined.
-in total, it is my feeling, that cubic SiC precipitation occurs by successive
-agglomeration of substitutional C.
+in total, these results suggest,
+that cubic SiC precipitation occurs by successive agglomeration of Cs.
-slide 28
+slide 24
finally, I would like to thank all of the people listed on this slide,
categorized by location.
projects / lectures / latex.git / blobdiff