\end{slide}
-% motivation
-
-\begin{slide}
-
-\headphd
- {\large\bf
- Polytypes of SiC\\[0.6cm]
- }
-
-\vspace{0.6cm}
-
-\includegraphics[width=3.8cm]{cubic_hex.eps}\\
-\begin{minipage}{1.9cm}
-{\tiny cubic (twist)}
-\end{minipage}
-\begin{minipage}{2.9cm}
-{\tiny hexagonal (no twist)}
-\end{minipage}
-
-\begin{picture}(0,0)(-150,0)
- \includegraphics[width=7cm]{polytypes.eps}
-\end{picture}
-
-\vspace{0.6cm}
-
-\footnotesize
-
-\begin{tabular}{l c c c c c c}
-\hline
- & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
-\hline
-Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
-Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
-Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
-Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
-Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
-Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
-Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
-\hline
-\end{tabular}
-
-\begin{pspicture}(0,0)(0,0)
-\psellipse[linecolor=green](5.7,2.05)(0.4,0.50)
-\end{pspicture}
-\begin{pspicture}(0,0)(0,0)
-\psellipse[linecolor=green](5.6,0.89)(0.4,0.20)
-\end{pspicture}
-\begin{pspicture}(0,0)(0,0)
-\psellipse[linecolor=red](10.45,0.42)(0.4,0.20)
-\end{pspicture}
-
-\end{slide}
-
% fabrication
+\ifnum1=0
\begin{slide}
\headphd
%\end{minipage}
\end{slide}
+\fi
\begin{slide}
$\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
{\color{blue}precipitates}
\item \underline{Implantation step 2}\\[0.1cm]
- Little remaining dose | \unit[180]{keV} | \degc{250}\\
+ Low remaining amount of dose | \unit[180]{keV} | \degc{250}\\
$\Rightarrow$
Destruction/Amorphization of precipitates at layer interface
\item \underline{Annealing}\\[0.1cm]
\begin{itemize}
\item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
\begin{itemize}
- \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites
+ \item {\color{blue}Substitutionally} incorporated C on regular Si lattice sites
\item \si{} reacting with further C in cleared volume
\end{itemize}
\item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
\end{itemize}
$\Rightarrow$ mobile {\color{red}\ci} opposed to
stable {\color{blue}\cs{}} configurations
-\item Strained silicon \& Si/SiC heterostructures
+\item Strained silicon \& Si$_{1-y}$C$_y$ heterostructures
{\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
\begin{itemize}
- \item {\color{blue}Coherent} SiC precipitates (tensile strain)
+ \item Initial {\color{blue}coherent} SiC precipitates (tensile strain)
\item Incoherent SiC (strain relaxation)
\end{itemize}
\end{itemize}
\scriptsize
-\vspace{0.1cm}
+\vspace{0.2cm}
\begin{minipage}{6.8cm}
\framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
\end{minipage}
\begin{minipage}{5.4cm}
\includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
-\end{minipage}\\[0.2cm]
+%\end{minipage}\\[0.2cm]
+\end{minipage}\\[0.3cm]
%\hrule
%
\begin{minipage}{6.8cm}
\includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
\end{minipage}\\[0.1cm]
%
-\begin{center}
-Reorientation pathway composed of two consecutive processes of the above type
-\end{center}
+%\begin{center}
+%Reorientation pathway composed of two consecutive processes of the above type
+%\end{center}
\end{slide}
\underline{Augsburg}
\begin{itemize}
\item Prof. B. Stritzker
- \item Prof. F. Haider
\item Ralf Utermann
\end{itemize}
- \underline{Berlin/Brandenburg}
- \begin{itemize}
- \item PD V. Eyert
- \end{itemize}
-
\underline{Helsinki}
\begin{itemize}
\item Prof. K. Nordlund
\item Dr. E. Rauls
\end{itemize}
-\vspace{0.1cm}
+\vspace{ 0.2cm}
\begin{center}
\framebox{
-\bf Thank you for your attention!
+\normalsize\bf Thank you for your attention!
}
\end{center}
\end{slide}
+\begin{slide}
+
+\headphd
+ {\large\bf
+ Polytypes of SiC\\[0.6cm]
+ }
+
+\vspace{0.6cm}
+
+\includegraphics[width=3.8cm]{cubic_hex.eps}\\
+\begin{minipage}{1.9cm}
+{\tiny cubic (twist)}
+\end{minipage}
+\begin{minipage}{2.9cm}
+{\tiny hexagonal (no twist)}
+\end{minipage}
+
+\begin{picture}(0,0)(-150,0)
+ \includegraphics[width=7cm]{polytypes.eps}
+\end{picture}
+
+\vspace{0.6cm}
+
+\footnotesize
+
+\begin{tabular}{l c c c c c c}
+\hline
+ & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
+\hline
+Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
+Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
+Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
+Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
+Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
+Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
+Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
+\hline
+\end{tabular}
+
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=green](5.7,2.05)(0.4,0.50)
+\end{pspicture}
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=green](5.6,0.89)(0.4,0.20)
+\end{pspicture}
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=red](10.45,0.42)(0.4,0.20)
+\end{pspicture}
+
+\end{slide}
+
\end{document}
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
+most important, 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 highly efficient
slide 3
-although the local order of the silicon and carbon atoms
-characterized by the tetrahedral bond is always the same,
-more than 250 different polytypes exist,
-which differ in the one-dimensional stacking sequence of
-identical, close-packed SiC bilayers,
-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.
-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 considered most effective for highly efficient
-high-performance electronic devices.
-
-slide [4] OR 5
-
-SiC is rarely found in nature and, thus, must be synthesized.
-
-nowadays, much progress has been achieved in SiC thin film growth
-by molecular beam epitaxy and chemical vapor deposition.
-indeed, commerically available semiconductor devices based on alpha SiC exist,
-however, production of the advantageous cubic type is less advanced,
-structural and electrical qualities 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.
-this was extensively investigated and optimized here in augsburg
-in the group of joerg lindner to obtain homogeneous SiC layers
-with sharp interfaces to the Si host, as can bee seen in the hrtem image.
-
-slide 4 or [5]
-
-one method to fabricate the adavntageous cubic polytiype is ibs,
+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.
-a two-step implantation process was suggested.
-the trick is to destroy stable precipitates that form 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,
+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
+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.
-slide 4/5
-
-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
+however, 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 6
+slide 4
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.
+in the case of SiC, one of the fcc lattice sites is occupied 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.
+in total, this results in a only slightly lower silicon density for SiC.
-the mechanism is schematically displayed here.
+the mechanism is schematically displayed.
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.
+sharing regular silicon lattice sites.
with increasing dose and time these dumbbells agglomerate into large clusters,
-indicated by dark contrasts and an otherwise undisturbed lattice in hrtem.
+indicated by dark contrasts in 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
+precipitation is accompanied by the emission of only 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.
+#it is worth to note that the hkl planes of substrate and SiC match.
-slide 7
+slide 5
however, controversial findings and conclusions exist in the literature.
instead of a carbon interstitial (Ci) based mechanism,
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
+at different temperatures show 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.
the task of the present study is to understand the precipitation mechanism
in the context of these controversial results.
-slide 8
+slide 6
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
+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,
-i would like to give a short summary and conclusion.
+a short summary and conclusion is given.
-slide 9
+slide 7
in md, a system of n particles is described on the microscopic level
by numerically integrating newtons equations of motion.
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.
-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.
+#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.
electron density, which minimizes the energy,
i.e. it has the variational property.
now, the kohn sham (ks) approach constitutes a hartree-like formulation
-of the hk minimal principle, which maps the system of interacting particles to
+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.
#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.
+the vasp code is 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 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
+slide 8
defect structures are obtained by creating a supercell of crystalline silicon
-with periodic boundary conditions and temperature and pressure set to zero.
+with 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.
+is taken to be the cohesive energy per atom of 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
+configurations whereas the binding energy for non-interacting isolated defects
approaches zero.
migration barriers from one stable configuration into another
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, all these discrepancies have to be taken into account
-in the following investigations of defect combinations.
-
-slide 12
+slide 9
-the situation is much better for carbon defects.
+the method 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 hexagonal defect is unstable relaxing into the ground state.
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
+slide 10
-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.
+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.
in number one, the carbon atom resides in the 110 plane
crossing the bc configuration.
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
+slide 11
the situation changes completely for the classical description.
path number one, from the 00-1 to bc configuration
nevertheless, diffusion barriers are drastically overestimated
by the classical potentials, a problem, which needs to be addressed later on.
-slide 16
+slide 12
implantation of highly energetic carbon atoms results in a multiplicity
of possible point defects and respective combinations.
finally, I would like to say thank you.
+
+
+
+
+slide X polytypes
+
+although the local order of the silicon and carbon atoms
+characterized by the tetrahedral bond is always the same,
+more than 250 different polytypes exist,
+which differ in the one-dimensional stacking sequence of
+identical, close-packed SiC bilayers,
+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.
+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 considered most effective for highly efficient
+high-performance electronic devices.
+
+slide X silicon self interstitials
+
+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, all these discrepancies have to be taken into account
+in the following investigations of defect combinations.
+
+slide X quantum mechanical details of 100 and bc
+
+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.
+
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