% fabrication
-\ifnum1=0
-\begin{slide}
-
-\headphd
- {\large\bf
- Fabrication of silicon carbide
- }
-
- \small
-
- \vspace{2pt}
-
-\begin{center}
- {\color{gray}
- \emph{Silicon carbide --- Born from the stars, perfected on earth.}
- }
-\end{center}
-
-\vspace{2pt}
-
-SiC thin films by MBE \& CVD
-\begin{itemize}
- \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
- \item \underline{Commercially available} semiconductor power devices based on
- \underline{\foreignlanguage{greek}{a}-SiC}
- \item Production of favored \underline{3C-SiC} material
- \underline{less advanced}
- \item Quality and size not yet sufficient
-\end{itemize}
-\begin{picture}(0,0)(-310,-20)
- \includegraphics[width=2.0cm]{cree.eps}
-\end{picture}
-
-\vspace{-0.5cm}
-
-%\begin{center}
-%\color{red}
-%\framebox{
-%{\footnotesize\color{black}
-% Mismatch in \underline{thermal expansion coeefficient}
-% and \underline{lattice parameter} w.r.t. substrate
-%}
-%}
-%\end{center}
-
-\vspace{0.1cm}
-
-{\bf Alternative approach}\\
-Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
-
-\vspace{0.1cm}
-
-\scriptsize
-
-\framebox{
-\begin{minipage}{3.15cm}
- \begin{center}
-\includegraphics[width=3cm]{imp.eps}\\
- {\tiny
- Carbon implantation
- }
- \end{center}
-\end{minipage}
-\begin{minipage}{3.15cm}
- \begin{center}
-\includegraphics[width=3cm]{annealing.eps}\\
- {\tiny
- Postannealing at $>$ \degc{1200}
- }
- \end{center}
-\end{minipage}
-}
-\begin{minipage}{5.5cm}
- \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm]
- \begin{center}
- {\tiny
- XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
- }
- \end{center}
-\end{minipage}
-
-%\begin{minipage}{5.5cm}
-%\begin{center}
-%{\footnotesize
-%No surface bending effects\\
-%High areal homogenity\\[0.1cm]
-%$\Downarrow$\\[0.1cm]
-%Synthesis of large area SiC films possible
-%}
-%\end{center}
-%\end{minipage}
-
-\end{slide}
-\fi
-
\begin{slide}
\headphd
not yet fully understood
}
\end{center}
- \vspace*{0.1cm}
- \renewcommand\labelitemi{$\Rightarrow$}
- Details of the SiC precipitation
- \begin{itemize}
- \item significant technological progress\\
- in SiC thin film formation
- \item perspectives for processes relying\\
- upon prevention of SiC precipitation
- \end{itemize}
+% \vspace*{0.1cm}
+% \renewcommand\labelitemi{$\Rightarrow$}
+% Details of the SiC precipitation
+% \begin{itemize}
+% \item significant technological progress\\
+% in SiC thin film formation
+% \item perspectives for processes relying\\
+% upon prevention of SiC precipitation
+% \end{itemize}
\end{minipage}
}}
\rput(-6.8,5.5){\pnode{h0}}
{\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
\begin{itemize}
\item Initial {\color{blue}coherent} SiC structures (tensile strain)
- \item Incoherent SiC (strain relaxation)
+ \item Incoherent SiC nanocrystals (strain relaxation)
\end{itemize}
\end{itemize}
\vspace{0.1cm}
\end{minipage}
\end{minipage}
-\vspace{0.2cm}
+\vspace{0.3cm}
-\begin{minipage}[b]{6cm}
+\begin{minipage}[t]{6cm}
{\bf Defect formation energy}\\
\framebox{
-$E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm]
-Particle reservoir: Si \& SiC\\[0.2cm]
+$E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.5cm]
+%Particle reservoir: Si \& SiC\\[0.2cm]
{\bf Binding energy}\\
\framebox{
$
$E_{\text{b}}<0$: energetically favorable configuration\\
$E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
\end{minipage}
-\begin{minipage}[b]{6cm}
+\begin{minipage}[t]{6cm}
+\vspace{1.4cm}
{\bf Migration barrier}
\footnotesize
\begin{itemize}
\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]
\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]
+ $\nearrow$ \ci{} pure \cs{} combinations ($\Downarrow$)\\[0.05cm]
Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si}
\end{itemize}
\end{minipage}
\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]
+ $\nearrow$ \ci{} pure \cs{} combinations ($\Downarrow$)\\[0.05cm]
Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si}
\end{itemize}
\end{minipage}
{\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\
\end{center}
\begin{itemize}
-\item Stretched coherent SiC structures\\
-$\Rightarrow$ Precipitation process involves {\color{blue}\cs}
-\item Role of \si{}
+\item Stretched coherent SiC structures directly observed
+\begin{center}
+\psframebox[linecolor=blue,linewidth=0.05cm]{
+\begin{minipage}{7cm}
+\centering
+\cs{} extensively involved in the precipitation mechanism\\
+\end{minipage}
+}
+\end{center}
+\item Emission of \si{} serves several needs:
\begin{itemize}
\item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
\item Building block for surrounding Si host \& further SiC
\psframebox[linecolor=blue,linewidth=0.05cm]{
\begin{minipage}{7cm}
\centering
-Precipitation mechanism involving \cs\\
High T $\leftrightarrow$ IBS conditions far from equilibrium\\
\end{minipage}
}
% skip high c conc
\fi
-% for preparation
-%\fi
-
\begin{slide}
\headphd
\item Identified \ci{} migration path
\item EA drastically overestimates the diffusion barrier
\end{itemize}
- \item Combinations of defects
+ \item Combinations of defects (DFT)
\begin{itemize}
\item Agglomeration of point defects energetically favorable
\item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
\begin{itemize}
\item Prof. B. Stritzker
\item Ralf Utermann
+ \item EP \RM{4}
\end{itemize}
\underline{Helsinki}
\item Dr. E. Rauls
\end{itemize}
-\vspace{ 0.2cm}
+\vspace{0.2cm}
\begin{center}
\framebox{
\normalsize\bf Thank you for your attention!
}
\end{center}
+Referees: PD V. Eyert \& Prof. Haider
\end{slide}
#and indeed, the first blue light emitting diodes in 1990 were based on SiC.
#(nowadays superceded by direct band gap materials like GaN).
-as an example a SiC based inverter with an efficiency of 98.5%
-designed by the frauenhofer institute for solar energy systems is displayed.
+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.
slide 3
-one method to fabricate the 3C-SiC, the cubic phase of SiC, is ibs,
+one method to fabricate 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 here in augsburg in the group of joerg lindner.
-even an optimized two-step implantation process was suggested.
+this was extensively investigated here in augsburg in the group of j lindner.
+an optimized two-step implantation process was suggested.
the trick is to destroy stable precipitates
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,
+by implanting a low remaining amount of the regular dose at lower temperatures.
+this enables 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, 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
-and likewise offer perspectives for processes that rely upon prevention
-of SiC precipitation, for example the fabrication of strained silicon.
slide 4
-there is an assumed mechanism of precipitation based on the formation and
+there is an assumed mechanism, however, which is 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.
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 show high and zero carbon diffusion
-for the room temperature and elevated temperature implantations respectively.
+investigations of the annealing behavior of implantations at low and high
+temperatures show high and almost zero carbon diffusion 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,
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
+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.
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.
+sampling in k space is restricted to the gamma point.
+the supercell consists of 216 atoms.
slide 8
-defect structures are obtained by creating a supercell of crystalline silicon
-with temperature and pressure set to zero.
+defect structures are obtained by creating a supercell of crystalline silicon.
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 of the fully relaxed structure.
+next to the structure, defects can be characterized by the formation energy,
+which is defined by this formula.
combinations of defects can be characterized by the binding energy,
the difference of the formation energy of the defect combination and
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
+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.
slide 9
-the method has been used to investigate, amongst others,
+this has been used to investigate, amongst others,
carbon interstitial defects in silicon.
both methods provide the correct order of the formation energies
and find the 100 db to be the ground state.
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.
+regarding the problem addressed in this study, this might constitute a problem.
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.
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.
+the barrier is 2.4 times higher than ab inito result.
-however, the ea description predicts the bc configuration to be unstable
+moreover, 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,
likewise relaxes into the 110 db structure without constraints.
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.
+and 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.
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 barriers or energetically unfavorable
-intermediate configurations to obtain this configuration are found.
+however, 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.
-in contrast, for the second most favorable configuration,
-a migration path with a low barrier exists.
-moreover, this type of defect is represented two times more often
-than the ground state.
+this suggests that agglomeration of Ci indeed is expected, but no C clustering.
-this suggests that agglomeration of Ci indeed is expected.
-
-slide 17
+slide 13
this is reinforced by the plot of the binding energy of Ci dbs
-separated along the 110 direction with respect to the C-C distance.
+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.
this supports the assumption of C agglomeration and the absence of C clustering.
-slide 18
+slide 14
if a vacancy is created next to the Ci defect,
a situation absolutely conceivable in ibs,
-the obtained structure will most likely turn into the Cs configuration.
-if the vacancy is created at position 1, the Cs configuration is directly
-obtained in the relaxation process.
-if it is created at other positions, e.g. 2 and 3,
-only low barriers are necessary for a transition into the Cs configuration
-whereas high barriers are necessary for the reverse process.
+structures are obtained, which exhibit low migration barriers
+for the transition into the Cs configuration.
+high barriers are necessary for the reverse process.
-based on this, a high probability for the formation of Cs,
-which is found to be extremely stable, must be concluded.
+based on this, a high probability of stable Cs configurations must be concluded.
-slide 19
+slide 15
-in addition, it is instructive to look at combinations of Cs and Si_i,
-again, a situation which is very likely to arise due to implantation.
+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.
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 transition barrier from the ground state Ci 100 db
-into the configuration of Cs and Si_i.
+moreover, a low transition barrier is found from the ground state
+into the configuration of separated defects.
the barrier is even smaller than migration barrier for carbon.
-in addition, a low migration barrier of the interstitial silicon,
+in addition, the low migration barrier of interstitial silicon,
enables configurations of further separated Cs and Si_i defects.
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.
-slide 20
+slide 16
-once more, this is supported by results of an ab inito md simulation at 900 dc.
+this is supported by results of an ab inito md simulation at 900 dc.
the initial configuration of Cs and Si_i does not recombine into the gs,
instead, the defects are separated by more than 4 neighbor distances
realized in a repeated migration mechanism of annihilating and arising Si_i dbs.
clearly, at higher temperatures, the contribution of entropy
-to structural formation increases, which might result in a spatial separation,
+to structural formation increases, which results in a spatial separation,
even for defects located within the capture radius.
+!!!
to conclude, the results of the investigations of defect combinations
suggest an increased participation of Cs already in the initial stage
of precipitation due to its high probability of incidence.
-slide 21
+slide 17
as a last task, reproducing the SiC precipitation is attempted
by successive insertion of 6000 C atoms,
after insertion, the simulation is continued for 100 ps
follwed by a cooling sequence downto 20 degrees celsius.
-slide 22
+slide 18
-the radial distribution of Si-C, C-C and Si-Si bonds of simulations at 450 dc,
+the radial distribution function 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,
+for the low C concentration 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 an artifact due to the cut-off,
-correpsonding to the Si-C cut-off distance of 0.26 nm.
+the second peak is an artifact due to the cut-off.
the C-C peak at 0.31 nm, as expected in cubic SiC,
is generated by concatenated, differently oriented Ci dbs.
the same distance is also expected for the Si atoms, and, indeed,
so, the formation of Ci dumbbells indeed occurs.
even the C atoms are already found in a separation as expected in cubic SiC.
-turning to the high C concentration simulations, i.e. the v1 and v2 simulation,
+turning to the high C concentration simulations,
a high amount of strongly bound C-C bonds
as in graphite or diamond is observed.
due to increased defect and damage densities
and, indeed, by comparing to other distribution data,
an amorphous SiC-like phase is identified.
-slide 23
+slide 19
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 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.
+neither agglomeration of C interstitials
+nor a transition into crystalline SiC can be identified.
-slide 24
+slide 20
having a closer look, there are two obvious reasons for this obstacle.
-first of all, there is the time scale problem inherent to md in general.
-to minimize the integration error, the time step must be chosen smaller
-than the reciprocal of the fastes vibrational mode.
-several local minima exist, which are separated by large energy barriers.
-due to the low probability for escaping such a local minimum,
-a transition event correpsonds to a multiple of vibrational periods.
-a phase transition, in turn, consists of many such infrequent transition events.
-new accelerated methods, like temperature accelerated MD and so on,
-have been developed to bypass the time scale problem while retaining proper
-thermodynamic sampling.
-
-in addition, the overestimated diffusion barriers,
+first of all, there is the time scale problem inherent to md in general,
+which results in a slow phase space propagation due to
+a large amount of local minima separated by large energy barriers.
+accelerated methods, like temperature accelerated MD and so on, exist
+to bypass the time scale problem while retaining proper thermodynamic sampling.
+
+however, in addition, the overestimated diffusion barriers,
due to the short range character of the potential,
intensify this problem, which I called:
potential enhanced slow phase space propagation.
without possible corrections.
accelerated methods or higher time scales applied exclusively
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,
+anyways, in this case,
structural evolution instead of equilibrium properties are matter of interest.
slide 25
and indeed, promising changes are observed by comparing,
again the radial distribution data for temperatures up to 2050 dc.
first of all, the cut-off artifact disappears.
-more important, a transition from a 100 db into a Cs dominated structure
-takes place,
+more important, a transition into a clearly Cs dominated structure takes place,
as can be seen by direct comparison with the respective reference peaks of Cs.
-the rising Si-Si peak at 0.325 nm is due to two Si atoms next to a Cs atom.
+the rising Si-Si peak is due to stretched Si-C-Si structures
+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.
-the amount of bonds due to Ci combinations, represented by dashed arrows,
-decreases accompanied by an increase of bonds due to combinations of
-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.
+the peak at roughly 0.3 nm gets slightly shifter 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.
slide 26
in the precipitation process for implantations at elevated temperatures.
the emission of Si_i serves several needs:
-as a vehicle to rearrange Cs,
-realized by recombination into the highly mobile Ci configuration.
+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
at low temperatures highly mobile Ci whereas at high temperatures stable Cs
configurations are formed.
-to summarize, the results suggest that Cs plays an important role
-in the precipitation process.
-moreover, high temperatures are necessary to model ibs conditions,
-which are far from equilibrium.
+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.
the role of the Si_i was outlined and in one case also directly observed
in simulation.
+in total, it is my feeling, that cubic SiC precipitation occurs by successive
+agglomeration of substitutional C.
+
slide 28
-finally, I would like to thank all of the people listed on this slide.
+finally, I would like to thank all of the people listed on this slide,
+categorized by location.
thank you for your attention!
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