polytypes substituted

[lectures/latex.git] / posic / thesis / sic.tex

diff --git a/posic/thesis/sic.tex b/posic/thesis/sic.tex
index 0379687..5629f6f 100644 (file)
--- a/posic/thesis/sic.tex
+++ b/posic/thesis/sic.tex
@@ -26,13 +26,21 @@ The polytypes differ in the one-dimensional stacking sequence of identical, clos
 Each SiC bilayer can be situated in one of three possible positions (abbreviated a, b or c) with respect to the lattice while maintaining the tetrahedral bonding scheme of the crystal.
 \begin{figure}[t]
 \begin{center}
 Each SiC bilayer can be situated in one of three possible positions (abbreviated a, b or c) with respect to the lattice while maintaining the tetrahedral bonding scheme of the crystal.
 \begin{figure}[t]
 \begin{center}

-\includegraphics[width=10cm]{polytypes.eps}
+\includegraphics[height=5.5cm]{polytypes_own.eps}\\[0.1cm]
+\begin{minipage}{0.45\textwidth}
+{\small
+\hspace*{0.05cm} a \hspace*{0.09cm} b \hspace*{0.09cm} c \hspace*{0.44cm} a \hspace*{0.09cm} b \hspace*{0.44cm} a \hspace*{0.09cm} b \hspace*{0.09cm} c \hspace*{0.44cm} a \hspace*{0.09cm} b \hspace*{0.09cm} c \hspace*{0.09cm} a\\
+\hspace*{0.5cm} 3C \hspace*{0.9cm} 2H \hspace*{1.0cm} 4H \hspace*{1.3cm} 6H
+}
+\end{minipage}
+%\includegraphics[width=10cm]{polytypes.eps}

 \end{center}
 \caption{Stacking sequence of SiC bilayers of the most common polytypes of SiC (from left to right): 3C, 2H, 4H and 6H.}
 \label{fig:sic:polytypes}
 \end{figure}
 Fig.~\ref{fig:sic:polytypes} shows the stacking sequence of the most common and technologically most important SiC polytypes, which are the cubic (3C) and hexagonal (2H, 4H and 6H) polytypes.
 
 \end{center}
 \caption{Stacking sequence of SiC bilayers of the most common polytypes of SiC (from left to right): 3C, 2H, 4H and 6H.}
 \label{fig:sic:polytypes}
 \end{figure}
 Fig.~\ref{fig:sic:polytypes} shows the stacking sequence of the most common and technologically most important SiC polytypes, which are the cubic (3C) and hexagonal (2H, 4H and 6H) polytypes.
 

+\bibpunct{}{}{,}{n}{}{}

 \begin{table}[t]
 \begin{center}
 \begin{tabular}{l c c c c c c}
 \begin{table}[t]
 \begin{center}
 \begin{tabular}{l c c c c c c}


@@ -51,9 +59,11 @@ Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
 \hline
 \end{tabular}
 \end{center}
 \hline
 \end{tabular}
 \end{center}

-\caption[Properties of SiC polytypes and other semiconductor materials.]{Properties of SiC polytypes and other semiconductor materials. Doping concentrations are $10^{16}\text{ cm}^{-3}$ (A) and $10^{17}\text{ cm}^{-3}$ (B) respectively. References: \cite{wesch96,casady96,park98}. {\color{red}Todo: add more refs + check all values!}}
+\caption[Properties of SiC polytypes and other semiconductor materials.]{Properties of SiC polytypes and other semiconductor materials. Doping concentrations are $10^{16}\text{ cm}^{-3}$ (A) and $10^{17}\text{ cm}^{-3}$ (B) respectively. References: \cite[]{wesch96,casady96,park98}.}

 \label{table:sic:properties}
 \end{table}
 \label{table:sic:properties}
 \end{table}

+\bibpunct{[}{]}{,}{n}{}{}
+% todo add more refs + check all values!

 Different polytypes of SiC exhibit different properties.
 Some of the key properties are listed in Table~\ref{table:sic:properties} and compared to other technologically relevant semiconductor materials.
 Despite the lower charge carrier mobilities for low electric fields SiC outperforms Si concerning all other properties.
 Different polytypes of SiC exhibit different properties.
 Some of the key properties are listed in Table~\ref{table:sic:properties} and compared to other technologically relevant semiconductor materials.
 Despite the lower charge carrier mobilities for low electric fields SiC outperforms Si concerning all other properties.


@@ -342,7 +352,7 @@ However, there is great interest to incorporate C onto substitutional lattice si
 Thus, substitutional C enables strain engineering of Si and Si/Si$_{1-x}$Ge$_x$ heterostructures \cite{yagi02,chang05,kissinger94,osten97}, which is used to increase charge carrier mobilities in Si as well as to adjust its band structure \cite{soref91,kasper91}.
 % increase of C at substitutional sites
 Epitaxial layers with \unit[1.4]{at.\%} of substitutional C have been successfully synthesized in preamorphized Si$_{0.86}$Ge$_{0.14}$ layers, which were grown by CVD on Si substrates, using multiple-energy C implantation followed by solid-physe epitaxial regrowth at \unit[700]{$^{\circ}$C} \cite{strane93}.
 Thus, substitutional C enables strain engineering of Si and Si/Si$_{1-x}$Ge$_x$ heterostructures \cite{yagi02,chang05,kissinger94,osten97}, which is used to increase charge carrier mobilities in Si as well as to adjust its band structure \cite{soref91,kasper91}.
 % increase of C at substitutional sites
 Epitaxial layers with \unit[1.4]{at.\%} of substitutional C have been successfully synthesized in preamorphized Si$_{0.86}$Ge$_{0.14}$ layers, which were grown by CVD on Si substrates, using multiple-energy C implantation followed by solid-physe epitaxial regrowth at \unit[700]{$^{\circ}$C} \cite{strane93}.

-The tensile strain induced by the C atoms is found to compensates the compressive strain present due to the Ge atoms.
+The tensile strain induced by the C atoms is found to compensate the compressive strain present due to the Ge atoms.

 Studies on the thermal stability of Si$_{1-y}$C$_y$/Si heterostructures formed in the same way and equal C concentrations showed a loss of substitutional C accompanied by strain relaxation for temperatures ranging from \unit[810-925]{$^{\circ}$C} and the formation of spherical 3C-SiC precipitates with diameters of \unit[2-4]{nm}, which are incoherent but aligned to the Si host \cite{strane94}.
 During the initial stages of precipitation C-rich clusters are assumed, which maintain coherency with the Si matrix and the associated biaxial strain.
 Using this technique a metastable solubility limit was achieved, which corresponds to a C concentration exceeding the solid solubility limit at the Si melting point by nearly three orders of magnitude and, furthermore, a reduction of the defect denisty near the metastable solubility limit is assumed if the regrowth temperature is increased by rapid thermal annealing \cite{strane96}.
 Studies on the thermal stability of Si$_{1-y}$C$_y$/Si heterostructures formed in the same way and equal C concentrations showed a loss of substitutional C accompanied by strain relaxation for temperatures ranging from \unit[810-925]{$^{\circ}$C} and the formation of spherical 3C-SiC precipitates with diameters of \unit[2-4]{nm}, which are incoherent but aligned to the Si host \cite{strane94}.
 During the initial stages of precipitation C-rich clusters are assumed, which maintain coherency with the Si matrix and the associated biaxial strain.
 Using this technique a metastable solubility limit was achieved, which corresponds to a C concentration exceeding the solid solubility limit at the Si melting point by nearly three orders of magnitude and, furthermore, a reduction of the defect denisty near the metastable solubility limit is assumed if the regrowth temperature is increased by rapid thermal annealing \cite{strane96}.


@@ -359,7 +369,7 @@ Indeed, closely investigating the large amount of literature pulled up in the la
 High resolution transmission electron microscopy (HREM) investigations of C-implanted Si at room temperature followed by rapid thermal annealing (RTA) show the formation of C-Si dumbbell agglomerates, which are stable up to annealing temperatures of about \unit[700-800]{$^{\circ}$C}, and a transformation into 3C-SiC precipitates at higher temperatures \cite{werner96,werner97}.
 The precipitates with diamateres between \unit[2]{nm} and \unit[5]{nm} are incorporated in the Si matrix without any remarkable strain fields, which is explained by the nearly equal atomic density of C-Si agglomerates and the SiC unit cell.
 Implantations at \unit[500]{$^{\circ}$C} likewise suggest an initial formation of C-Si dumbbells on regular Si lattice sites, which agglomerate into large clusters \cite{lindner99_2}.
 High resolution transmission electron microscopy (HREM) investigations of C-implanted Si at room temperature followed by rapid thermal annealing (RTA) show the formation of C-Si dumbbell agglomerates, which are stable up to annealing temperatures of about \unit[700-800]{$^{\circ}$C}, and a transformation into 3C-SiC precipitates at higher temperatures \cite{werner96,werner97}.
 The precipitates with diamateres between \unit[2]{nm} and \unit[5]{nm} are incorporated in the Si matrix without any remarkable strain fields, which is explained by the nearly equal atomic density of C-Si agglomerates and the SiC unit cell.
 Implantations at \unit[500]{$^{\circ}$C} likewise suggest an initial formation of C-Si dumbbells on regular Si lattice sites, which agglomerate into large clusters \cite{lindner99_2}.

-The agglomerates of such dimers, which do not generate lattice strain but lead to a local increase of the lattice potential \cite{werner96}, are indicated by dark contrasts and otherwise undisturbed Si lattice fringes in HREM, as can be seen in Fig.~\ref{fig:sic:hrem:c-si}.
+The agglomerates of such dimers, which do not generate lattice strain but lead to a local increase of the lattice potential \cite{werner96,werner97}, are indicated by dark contrasts and otherwise undisturbed Si lattice fringes in HREM, as can be seen in Fig.~\ref{fig:sic:hrem:c-si}.

 \begin{figure}[t]
 \begin{center}
 \subfigure[]{\label{fig:sic:hrem:c-si}\includegraphics[width=0.25\columnwidth]{tem_c-si-db.eps}}
 \begin{figure}[t]
 \begin{center}
 \subfigure[]{\label{fig:sic:hrem:c-si}\includegraphics[width=0.25\columnwidth]{tem_c-si-db.eps}}


@@ -418,7 +428,5 @@ On the other hand, processes relying upon prevention of precipitation in order t
 % eichhorn02: high imp temp more efficient than postimp treatment
 % eichhorn99: same as 02 + c-si agglomerates at low concentrations
 % strane94/guedj98: my model - c redist by si int (spe) and surface diff (mbe)
 % eichhorn02: high imp temp more efficient than postimp treatment
 % eichhorn99: same as 02 + c-si agglomerates at low concentrations
 % strane94/guedj98: my model - c redist by si int (spe) and surface diff (mbe)

-
-% todo
-% own polytype stacking sequence image
+% serre95: low/high t implants -> mobile c_i / non-mobile sic precipitates