\subsection{Carbon as an impurity in silicon}
-Below the solid solubility, C mainly occupies substitutionally Si lattice sites in Si \cite{newman65}.
+Below the solid solubility, C impurities mainly occupy 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}
\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}.
+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}, which is highly mobile compared to substitutional C.
% diffusion pathway?
+% expansion of the lattice (positive strain)
%\subsection{Agglomeration phenomena}
% c-si agglomerattion as an alternative to sic precipitation (due to strain)
\subsection{Suppression of transient enhanced diffusion of dopant species}
+The predominant diffusion mechanism of most dopants in Si based on native self-interstitials \cite{fahey89} has a large impact on the diffusion behavior of dopants that have been implanted in Si.
+The excess population of Si self-interstitials created by low-energy implantations of dopants for shallow junction formation in submicron technologies may enhance the diffusion of the respective dopant during annealing by more than one order of magnitude compared to normal diffusion.
+This kind of diffusion, labeled transient enhanced diffusion (TED), which is driven by the presence of non-equilibrium concentrations of point defects, was first discovered for implantations of boron in Si \cite{hofker74} and is well understood today \cite{michel87,cowern90,stolk95,stolk97}.
+The TED of B was found to be inhibited in the presence of a sufficient amount of incorporated C \cite{cowern96}.
+This is due to the reduction of the excess Si self-interstitials with substitutional C atoms forming the C-Si interstitial complex \cite{stolk97,zhu98}.
+Therefore, incorporation of C provides a promising method for suppressing TED enabling an improved shallow junction formation in future Si devices.
+
+% in general: high c diffusion in areas of high damage, low diffusion for substitutional or even sic prec
+
\subsection{Strained silicon and silicon heterostructures}
-% -> skorupa 3.2: c sub vs sic prec
-% -> my own links: strane etc ...
-% -> skorupa 3.5: heterostructures
-\section{Assumed cubic silicon carbide conversion mechanisms}
+% lattice location of implanted carbon
+Radiation damage introduced during implantation and a high concentration of the implanted species, which results in the reduction of the topological constraint of the host lattice imposed on the implanted species, can affect the manner of impurity incorporation.
+The probability of finding C, which will be most stable at sites for which the number of neighbors equals the natural valence, i.e. substitutionally on a regular Si site of a perfect lattice, is, thus, reduced at substitutional lattice sites and likewise increased at interstitial sites.
+Indeed, x-ray rocking curves reveal a positive lattice strain, which is decreased but still remains with increasing annealing temeprature, indicating the location of the majority of implanted C atoms at interstitial sites \cite{isomae93}.
+Due to the absence of dislocations in the implanted region interstitial C is assumed to prevent clustering of implantation-induced Si self-interstitials by agglomeration of C-Si interstitials or the formation of SiC precipitates accompanied by a relaxation of the lattice strain.
+
+% link to strain engineering
+However, there is great interest to incorporate C onto substitutional lattice sites, which results in a contraction of the Si lattice due to the smaller covalent radius of C compared to Si \cite{baker68}, causing tensile strain, which is applied to the Si lattice.
+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.
+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}.
+Since high temperatures used in the solid-phase epitaxial regrowth method promotes SiC precipitation, other groups realized substitutional C incorporation for strained Si$_{1-y}$C$_y$/Si heterostructures \cite{iyer92,fischer95,powell93,osten96,osten99,laveant2002} or partially to fully strain-compensated (even inversely distorted \cite{osten94_2}) Si$_{1-x-y}$Ge$_x$C${_y}$ layers on Si \cite{eberl92,powell93_2,osten94,dietrich94} by \ac{MBE}.
+Investigations reveal a strong dependence of the growth temperature on the amount of substitutionally incorporated C, which is increased for decreasing temperature accompanied by deterioration of the crystal quality \cite{osten96,osten99}.
+While not being compatible to very-large-scale integration technology, C concentrations of \unit[2]{\%} and more have been realized \cite{laveant2002}.
+
+\section{Assumed silicon carbide conversion mechanisms}
\label{section:assumed_prec}
-Although much progress has been made in 3C-SiC thin film growth in the above-mentioned growth methods during the last decades, there is still potential
-.. compatible to the established and highly developed technology based on silicon.
+Although high-quality films of single-crystalline 3C-SiC can be produced by means of \ac{IBS} the precipitation mechanism in bulk Si is not yet fully understood.
+Indeed, closely investigating the large amount of literature reveals controversial ideas of SiC formation, which are reviewed in more detail in the following.
-Although tremendous progress has been achieved in the above-mentioned growth methods during the last decades, available wafer dimensions and crystal qualities are not yet statisfactory.
+\begin{figure}[ht]
+\begin{center}
+\subfigure[]{\label{fig:sic:hrem:c-si}\includegraphics[width=0.48\columnwidth]{tem_c-si-db.eps}}
+\subfigure[]{\label{fig:sic:hrem:sic}\includegraphics[width=0.48\columnwidth]{tem_3c-sic.eps}}
+\end{center}
+\caption{High resolution transmission electron microscopy (HREM) micrographs\cite{lindner99_2} of agglomerates of C-Si dimers showing dark contrasts and otherwise undisturbed Si lattice fringes (a) and equally sized Moir\'e patterns indicating 3C-SiC precipitates (b).}
+\label{fig:sic:hrem}
+\end{figure}
+
+\ac{HREM} investigations of C-implanted Si at room temperature followed by \ac{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 \ac{HREM}, as can be seen in Fig.~\ref{fig:sic:hrem:c-si}.
+A topotactic transformation into a 3C-SiC precipitate occurs once a critical radius of \unit[2]{nm} to \unit[4]{nm} is reached.
+The precipitation is manifested by the disappearance of the dark contrasts in favor of Moir\'e patterns (Fig.~\ref{fig:sic:hrem:sic}) due to the lattice mismatch of \unit[20]{\%} of the 3C-SiC precipitate and the Si host.
+The insignificantly lower Si density of SiC of approximately \unit[3]{\%} compared to c-Si results in the emission of only a few excess Si atoms.
+
+
+The formation of SiC by a preceeding agglomeration of C-Si dumbbells is supported by studies ... \cite{koegler03,eichhorn99}
+
+
+
+In contrast, investigations of strained Si$_{1-y}$C$_y$/Si heterostructures formed by MBE\cite{strane94,guedj98}, which incidentally involve the formation of SiC nanocrystallites, suggest an initial coherent precipitation by agglomeration of substitutional instead of interstitial C.
+
+Coherency is lost once the increasing strain energy of the stretched SiC structure surpasses the interfacial energy of the incoherent 3C-SiC precipitate and the Si substrate.
+
+These two different mechanisms of precipitation might be attributed to the respective method of fabrication.
+
+While in CVD and MBE surface effects need to be taken into account, SiC formation during IBS takes place in the bulk of the Si crystal.
+
+However, in another IBS study Nejim et~al.\cite{nejim95} propose a topotactic transformation that is likewise based on the formation of substitutional C.
+
+The formation of substitutional C, however, is accompanied by Si self-interstitial atoms that previously occupied the lattice sites and a concurrent reduction of volume due to the lower lattice constant of SiC compared to Si.
+
+Both processes are believed to compensate one another.
+
+
+%cites:
+
+% continue with strane94 and werner96
+
+%ibs, c-si agglom: werner96,werner97,eichhorn99,lindner99_2,koegler03
+%hetero, coherent sic by sub c: strane94,guedj98
+%ibs, c sub: nejim95
+%ibs, indicated c sub: martin90 + conclusions reeson8x, eichhorn02
+%more: taylor93, kitabatake contraction along 110, koegler03
+%taylor93: sic prec only/more_easy if self interstitials are present
+
+% -> skorupa 3.2: c sub vs sic prec
+
+% remember!
+% werner96/7: rt implants followed by rta < 800: C-Si db aggloms | > 800: 3C-SiC
+% taylor93: si_i reduces interfacial energy (explains metastability) of sic/si
+% eichhorn02: high imp temp more efficient than postimp treatment
+
+% todo
+% add sharp iface image!
-... \cite{lindner99_2} ...
on surface ... md contraction along 110 ... kitabatake ... and ref in lindner ... rheed from si to sic ...
projects / lectures / latex.git / blobdiff