\end{itemize}
$\Rightarrow$ mobile {\color{red}\ci} opposed to
stable {\color{blue}\cs{}} configurations
-\item Strained silicon \& Si$_{1-y}$C$_y$ heterostructures
+\item Strained Si$_{1-y}$C$_y$/Si heterostructures
{\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
\begin{itemize}
- \item Initial {\color{blue}coherent} SiC precipitates (tensile strain)
+ \item Initial {\color{blue}coherent} SiC structures (tensile strain)
\item Incoherent SiC (strain relaxation)
\end{itemize}
\end{itemize}
\begin{itemize}
\item Bond-centered configuration unstable\\
$\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
- \item Minima of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
+ \item Minimum of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
$\rightarrow$ \ci{} \hkl<1 1 0> DB
\end{itemize}
\vspace{0.1cm}
\begin{minipage}{6.1cm}
\scriptsize
\underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
-\hkl<1 0 0> C-Si dumbbell dominated structure
+\ci{} \hkl<1 0 0> dumbbell dominated structure
\begin{itemize}
\item Si-C bumbs around \unit[0.19]{nm}
\item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
\begin{minipage}{6cm}
\centering
Formation of \ci{} dumbbells\\
-C atoms in proper 3C-SiC distance first
+C atoms separated as expected in 3C-SiC
\end{minipage}
}}
\end{pspicture}\\[0.1cm]
\begin{minipage}{6.1cm}
\scriptsize
\underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
-\hkl<1 0 0> C-Si dumbbell dominated structure
+\ci{} \hkl<1 0 0> dumbbell dominated structure
\begin{itemize}
\item Si-C bumbs around \unit[0.19]{nm}
\item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
\vspace{0.2cm}
{\bf Time scale problem of MD}\\[0.2cm]
-Precise integration \& thermodynamic sampling\\
+Minimize integration error \& precise thermodynamic sampling\\
$\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
$\omega$: vibrational mode\\
$\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
\underline{Si-C bonds:}
\begin{itemize}
\item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
- \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
+ \item Structural change: \ci{} \hkl<1 0 0> DB $\rightarrow$
+ {\color{blue}\cs{}}
\end{itemize}
\underline{Si-Si bonds:}
{\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
\underline{C-C bonds:}
\begin{itemize}
\item C-C next neighbour pairs reduced (mandatory)
- \item Peak at 0.3 nm slightly shifted
- \begin{itemize}
- \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
- $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
- combinations (|)\\
- $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
- ($\downarrow$)
- \item Range [|-$\downarrow$]:
- {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
- with nearby Si$_{\text{I}}$}
- \end{itemize}
+ \item Peak at 0.3 nm slightly shifted\\[0.05cm]
+ $\searrow$ \ci{} combinations (dashed arrows)\\
+ $\nearrow$ \ci{} \hkl<1 0 0> \& {\color{blue}\cs{} combinations} (|)\\
+ $\nearrow$ \ci{} \hkl<1 0 0> \& \cs{} combinations (|)\\[0.05cm]
+ Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si}
\end{itemize}
\end{minipage}
\begin{itemize}
\item C-C next neighbour pairs reduced (mandatory)
\item Peak at 0.3 nm slightly shifted
- \begin{itemize}
- \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
- $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
- combinations (|)\\
- $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
- ($\downarrow$)
- \item Range [|-$\downarrow$]:
- {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
- with nearby Si$_{\text{I}}$}
- \end{itemize}
+ \item Peak at 0.3 nm slightly shifted\\[0.05cm]
+ $\searrow$ \ci{} combinations (dashed arrows)\\
+ $\nearrow$ \ci{} \hkl<1 0 0> \& {\color{blue}\cs{} combinations} (|)\\
+ $\nearrow$ \ci{} \hkl<1 0 0> \& \cs{} combinations (|)\\[0.05cm]
+ Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si}
\end{itemize}
\end{minipage}
slide 1
-dear examiners, dear colleagues.
+dear referees, 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.
one method to fabricate the 3C-SiC, the cubic phase of SiC, is ibs,
i.e. high dose ion implantation followed by a high-temperature annealing step,
-as extensively investigated and optimzed here in augsburg
-in the group of joerg lindner.
-an optimized two-step implantation process was suggested.
+as extensively investigated and here in augsburg in the group of joerg lindner.
+even an optimized two-step implantation process was suggested.
the trick is to destroy stable precipitates
-formed at the layer interface during the first implantation step
+that formed at the layer interface during the first implantation step
by implanting the low remaining amount of the regular dose at lower temperatures
to enable redistribution of the C atoms during annealing,
which results in a homogeneous SiC layer with a sharp interface
as you can see in this cross section tem image.
-however, the precipitation, at elevated temperatures,
+however, already the precipitation, at elevated temperatures,
is not yet fully understood.
detailed understanding of the effective underlying processes of precipitation
might enable significant progress in thin film formation of cubic SiC
in total, this results in a only slightly lower silicon density for SiC.
the mechanism is schematically displayed.
-a pair of black dots represent two atoms of the two fcc lattices.
+a pair of black dots represents two atoms of the two fcc lattices.
the incorporated carbon atoms form C-Si dumbbells
sharing regular silicon lattice sites.
with increasing dose and time these dumbbells agglomerate into large clusters,
accompanied by strain relaxation.
these findings suggest a mechanism based on the agglomeration of substitutional
-instead of interstitial carbon atoms.
+instead of interstitial carbon.
the task of the present study is to understand the precipitation mechanism
in the context of these controversial results.
calculations, which are explained on the following slides, are used
to investigate carbon and silicon defect configurations as well as to
directly model SiC precipitation.
-finally, after these results are presented,
+finally, after some selected results are presented,
a short summary and conclusion is given.
slide 7
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 next neighbor atom.
+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.
due to symmetry it is sufficient to merely consider the migration into the bc
configuration.
an activation energy of 1.2 eV is obtained.
-actually another barrier exists to reach a 100 type configuration.
+actually another barrier exists to reach a ground-state configuration.
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.
slide 11
the situation changes completely for the classical description.
-path number one, from the 00-1 to bc configuration
+path number one, from the db to the 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.
however, the ea description predicts the bc configuration to be unstable
relaxing into the 110 db configuration.
additionally, the observed minimum in the classical 00-1 to 0-10 transition,
-is close to the 110 db structure.
+likewise relaxes into the 110 db structure without constraints.
this suggests to investigate the transition involving the 110 configuration.
this migration is displayed here,
as can be seen, the agglomeration of interstitial carbon is energetically
favorable.
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.
+however, high migration barriers or energetically unfavorable
+intermediate configurations to obtain this configuration are found.
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
+moreover, this type of defect is represented two times more often
than the ground state.
-the results suggest that agglomeration of Ci indeed is expected.
+this suggests that agglomeration of Ci indeed is expected.
slide 17
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.
+which, however, 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.
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.
+this is supported by a low transition barrier from the ground state Ci 100 db
+into the configuration of Cs and Si_i.
+the barrier is even smaller than migration barrier for carbon.
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,
+in total, these findings demonstrate that configurations of Cs and Si_i,
instead of the thermodynamic ground state, play an important role in ibs,
which indeed constitutes a process far from equilibrium.
the number necessary to form a precipitate with a radius of approximately 3 nm,
into a supercell consisting of 31 Si unit cells in each direction.
insertion is realized at constant temperature.
-after insertion, the simulation is continued for 100 ps
-follwed by a cooling sequence downto 20 degrees celsius.
due to the high amount of particles,
the classical potential is exclusively 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.
v3 contains the amount of silicon atoms to form such a minimal precipitate.
+after insertion, the simulation is continued for 100 ps
+follwed by a cooling sequence downto 20 degrees celsius.
slide 22
-the radial distribution Si-C, C-C and Si-Si bonds of simulations,
-in which C was inserted at 450 dc,
+the radial distribution of Si-C, C-C and Si-Si bonds of simulations at 450 dc,
an operative and efficient temperature in ibs, are shown.
for the low C concentration simulation, i.e. the v1 simulation,
a clearly 100 C-Si db dominated structure is obtained,
which is obvious by comparing it to the
reference distribution generated by a single Ci defect.
-the second peak is a cut-off artifact,
+the second peak is an artifact due to the cut-off,
correpsonding to the Si-C cut-off distance of 0.26 nm.
the C-C peak at 0.31 nm, as expected in cubic SiC,
is generated by concatenated, differently oriented Ci dbs.
due to increased defect and damage densities
defect arrangemnets are hard to categorize and trace.
only short range order is observed.
-and, indeed, comparing to other distribution data, an amorphous SiC-like
-phase is obtained.
+and, indeed, by comparing to other distribution data,
+an amorphous SiC-like phase is identified.
slide 23
to summarize, the formation of cubic SiC fails to appear.
in the v1 simulation, formation of Ci indeed occurs, however,
agglomeration is missing.
-in the high concentration simulation, an amorphous SiC-like structure,
+in the v2/3 simulations, an amorphous SiC-like structure,
which is not expected at 450 dc, is obtained.
no rearrangemnt into crystalline cubic SiC is indicated.
the approach used in this study is to simply increase the temperature, however,
without possible corrections.
accelerated methods or higher time scales applied exclusively
-are assumed oto be not sufficient.
+are assumed to be not sufficient.
moreover, to legitimate the usage of increased temperatures:
cubic SiC is also observed for higher temperatures,
there is definitely a higher temperature inside the sample, and, anyways,
slide 25
and indeed, promising changes are observed by comparing,
-again the radial distribution data of Si-C, Si-Si and C-C bonds
-for temperatures up to 2050 dc.
+again the radial distribution data for temperatures up to 2050 dc.
first of all, the cut-off artifact disappears.
-more important, a transition a 100 db into a Cs dominated structure takes place,
-as can be seen by direct comparison with the respective reference peaks.
+more important, a transition from a 100 db into a Cs dominated structure
+takes place,
+as can be seen by direct comparison with the respective reference peaks of Cs.
-the Si-Si rising peak at 0.325 nm is due to two Si atoms next to a Cs atom.
+the rising Si-Si peak at 0.325 nm is due to two Si atoms next to a Cs atom.
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.
-the amount of bonds due to Ci 100 combinations, represented by dashed arrows,
+the amount of bonds due to Ci combinations, represented by dashed arrows,
decreases accompanied by an increase of bonds due to combinations of
-Ci 100 and Cs and pure Cs combinations, represented by the dashed line and
+Ci and Cs and pure Cs combinations, represented by the dashed line and
solid arrows respectively.
increasing values in the range between the dashed line and first solid arrow
correpsond to bonds of a Cs and another Cs with a nearby Si_i atom.
in the precipitation process for implantations at elevated temperatures.
the emission of Si_i serves several needs:
-as a vehicle to rearrange the Cs,
+as a vehicle to rearrange Cs,
realized by recombination into the highly mobile Ci configuration.
furthermore, it serves as a building block for the surrounding Si host
or further SiC formation.
concerning the precipitation simulations, the problem of the potential
enhanced slow phase space propagation was discussed.
-it was found that low and high temperatures result in structures
-dominated by interstitial and substitutional defects respectively.
-comparing with experiment, it is concluded,
-that high temperatures are necessary to model ibs conditions.
-it was concluded that Cs is involved in the precipitation process
-at elevated temperatures.
-the role of the Si_i was outlined and in one case directly observed
+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.
+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.
slide 28
-finally, I would like to say thank you.
+finally, I would like to thank all of the people listed on this slide.
+
+thank you for your attention!
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