X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Fthesis%2Fsic.tex;h=e51d3d6b4cc2913b32a46df7f74295e25549fe4d;hb=d5b0e9ca41375ef9492fdb0c79d4b7d19fe818e3;hp=5fe0564e02555ebb07b76603a205e893167c1c4f;hpb=deb1c40d072e9bbb20e69d6365233dceeb9f2bb9;p=lectures%2Flatex.git

diff --git a/posic/thesis/sic.tex b/posic/thesis/sic.tex
index 5fe0564..e51d3d6 100644
--- a/posic/thesis/sic.tex
+++ b/posic/thesis/sic.tex
@@ -330,27 +330,97 @@ Due to the absence of dislocations in the implanted region interstitial C is ass
 
 % 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,osten97}, which is used to increase charge carrier mobilities in Si as well as to adjust its band structure \cite{soref91,kasper91}.
+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 a rapid thermal annealing process \cite{strane96}.
-By MBE ... \cite{powell93,osten99}
+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.
-
-... \cite{lindner99_2} ...
+\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}.
+\begin{figure}[ht]
+\begin{center}
+\subfigure[]{\label{fig:sic:hrem:c-si}\includegraphics[width=0.25\columnwidth]{tem_c-si-db.eps}}
+\subfigure[]{\label{fig:sic:hrem:sic}\includegraphics[width=0.25\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}
+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 same mechanism was identified by high resolution x-ray diffraction \cite{eichhorn99}.
+For implantation temperatures of \unit[500]{$^{\circ}$C} C-Si dumbbells agglomerate in an initial stage followed by the additional appearance of aligned SiC precipitates in a slightly expanded Si region with increasing dose.
+The precipitation mechanism based on a preceeding dumbbell agglomeration as indicated by the above-mentioned experiemnts is schematically displayed in Fig.~\ref{fig:sic:db_agglom}.
+\begin{figure}[ht]
+\begin{center}
+\subfigure[]{\label{fig:sic:db_agglom:seq01}\includegraphics[width=0.30\columnwidth]{sic_prec_seq_01.eps}}
+%C-Si dumbbell formation
+\hspace*{0.2cm}
+\subfigure[]{\label{fig:sic:db_agglom:seq02}\includegraphics[width=0.30\columnwidth]{sic_prec_seq_02.eps}}
+%Dumbbell agglomeration
+\hspace*{0.2cm}
+\subfigure[]{\label{fig:sic:db_agglom:seq03}\includegraphics[width=0.30\columnwidth]{sic_prec_seq_03.eps}}
+%SiC formation and release of excess Si atoms
+\end{center}
+\caption[Two dimensional schematic of the assumed SiC precipitation mechanism based on an initial C-Si dumbbell agglomeration.]{Two dimensional schematic of the assumed SiC precipitation mechanism based on an initial C-Si dumbbell agglomeration. C atoms (red dots) incorporated into the Si (black dots) host form C-Si dumbbells (a), which agglomerate into clusters (b) followed by the precipitation of SiC and the emission of a few excess Si atoms (black circles), which are located in the interstitial Si lattice (c). The dotted lines mark the atomic spacing of c-Si in \hkl[1 0 0] direction indicating the $4/5$ ratio of the lattice constants of c-Si and 3C-SiC.}
+\label{fig:sic:db_agglom}
+\end{figure}
+The incorporated C atoms form C-Si dumbbells on regular Si lattice sites.
+With increasing dose and proceeding time the highly mobile dumbbells agglomerate into large clusters.
+Finally, when the cluster size reaches a critical radius, the high interfacial energy due to the 3C-SiC/c-Si lattice misfit is overcome and precipitation occurs.
+Due to the slightly lower silicon density of 3C-SiC excessive silicon atoms exist, which will most probably end up as self-interstitials in the c-Si matrix since there is more space than in 3C-SiC.
+
+In contrast, investigations of strained Si$_{1-y}$C$_y$/Si heterostructures formed by \ac{SPE} \cite{strane94} and \ac{MBE} \cite{guedj98}, which incidentally involve the formation of SiC nanocrystallites, suggest a coherent initiation of precipitation by agglomeration of substitutional instead of interstitial C.
+todo: more strane94 ...
+C incorporated as substitutional C.
+Increased temperatures enable diffusion by forming a C-Si interstitial dumbbell followed by the formation of small coherent precipitates.
+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.
+
+This different mechanism 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.
+Additionally IBS studies on \cite{martin90,...} ...
+The fact that the cubic phase instead of the thermodynamically favorable $\alpha$-SiC structure is formed supports the latter mechanism ...
+
+%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
+% eichhorn99: same as 02 + c-si agglomerates at low concentrations
+
+% todo
+% add sharp iface image!
+
+
 on surface ... md contraction along 110 ... kitabatake ... and ref in lindner ... rheed from si to sic ...
 
 in ibs ... lindner and skorupa ...