more properties of c in si

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

diff --git a/posic/thesis/sic.tex b/posic/thesis/sic.tex
index 9926ccd..a55b216 100644 (file)
--- a/posic/thesis/sic.tex
+++ b/posic/thesis/sic.tex
@@ -280,17 +280,40 @@ This enables the synthesis of large area SiC films.
 
 \section{Substoichiometric concentrations of carbon in crystalline silicon}
 
-The C solid solubility in bulk Si is quite low
-% carbon as an impurity / solubility / lattice distortion / diffusion
-% agglomeration phenomena
-% suppression of transient enhanced diffusion of dopant species
-% strained silicon / heterostructures
+In the following some basic properties of C in crystalline Si are reviewed.
+A lot of work has been done contributing to the understanding of C in Si either as an isovalent impurity as well as at concentrations exceeding the solid solubility limit.
+A comprehensive survey on C-mediated effects in Si has been published by Skorupa and Yankov \cite{skorupa96}.
+
+\subsection{Carbon as an impurity in silicon}
+
+Below the solid solubility, C mainly occupies substitutionally Si lattice sites in Si \cite{newman65}.
+Due to the much smaller covalent radius of C compared to Si every incorporated C atom leads to a decrease in the lattice constant corresponding to a lattice contraction of about one atomic volume \cite{baker68}.
+The induced strain is assumed to be responsible for the low solid solubility of C in Si, which was determined \cite{bean71} to be
+\begin{equation}
+c_{\text{s}}=\unit[4\times10^{24}]{cm^{-3}}
+\cdot\exp(\unit[-2.3]{eV/k_{\text{B}}T})
+\text{ .} \text{{\color{red}k recursive!}}
+\end{equation}
+The barrier of diffusion of substitutional C has been determined to be around \unit[3]{eV} \cite{newman61}.
+However, as suspected due to the substitutional position, the diffusion of C requires intrinsic point defects, i.e. Si self-interstitials and vacancies.
+Similar to phosphorous and boron, which exclusively use self-interstitials as a diffusion vehicle, the diffusion of C atoms is expected to obey the same mechanism.
+Indeed, enhanced C diffusion was observed in the presence of self-interstitial supersaturation \cite{kalejs84} indicating an appreciable diffusion component involving self-interstitials and only a negligible contribution by vacancies.
+Substitutional C and interstitial Si react into a C-Si complex forming a dumbbell structure oriented along a crystallographic \hkl<1 0 0> direction on a regular Si lattice site.
+This structure, the so called C-Si \hkl<1 0 0> dumbbell structure, was initially suspected by local vibrational mode absorption \cite{bean70} and finally verified by electron paramegnetic resonance \cite{watkins76} studies on irradiated Si substrates at low temperatures.
+Measuring the annealing rate of the defect as a function of temperature reveals barriers for migration ranging from \unit[0.73]{eV} \cite{song90} to \unit[0.87]{eV} \cite{tipping87}.
+% diffusion pathway?
+
+%\subsection{Agglomeration phenomena}
+% c-si agglomerattion as an alternative to sic precipitation (due to strain)
+% -> maybe this fits better in prec model in next chapter
+
+\subsection{Suppression of transient enhanced diffusion of dopant species}
+
+\subsection{Strained silicon and silicon heterostructures}
 %   -> skorupa 3.2: c sub vs sic prec  
 %   -> my own links: strane etc ...
 %   -> skorupa 3.5: heterostructures
 
-% hmm ... extra section needed?
-
 \section{Assumed cubic silicon carbide conversion mechanisms}
 \label{section:assumed_prec}