From: hackbard Date: Thu, 2 Sep 2010 23:31:40 +0000 (+0200) Subject: last evening checks, one more before released to joerg and eva X-Git-Url: https://hackdaworld.org/gitweb/?p=lectures%2Flatex.git;a=commitdiff_plain;h=cd28b4f3b75792bec8323e00a0516059874650b9 last evening checks, one more before released to joerg and eva --- diff --git a/posic/publications/defect_combos.tex b/posic/publications/defect_combos.tex index 947c86e..3f4a433 100644 --- a/posic/publications/defect_combos.tex +++ b/posic/publications/defect_combos.tex @@ -184,9 +184,9 @@ The obtained values are within the same order of magnitude than values derived f \subsection{Pairs of C$_{\text{i}}$} -C$_{\text{i}}$ pairs of the \hkl<1 0 0>-type have been considered in the first part. +First of all C$_{\text{i}}$ pairs of the \hkl<1 0 0>-type have been investigated. Fig.~\ref{fig:combos_ci} schematically displays the position of the initial C$_{\text{i}}$ \hkl[0 0 -1] DB and the various positions for the second defect (1-5) used for investigating the defect pairs. -Table~\ref{table:dc_c-c} summarizes the binding energies for the combination with a second C-Si \hkl<1 0 0> DB obtained for different orientations. +Table~\ref{table:dc_c-c} summarizes the binding energies for the combination with a second C-Si \hkl<1 0 0> DB obtained for different orientations at positions 1 to 5. \begin{figure} %\begin{minipage}{0.49\columnwidth} \subfigure[]{\label{fig:combos_ci}\includegraphics[width=0.45\columnwidth]{combos_ci.eps}} @@ -285,7 +285,7 @@ C-C distance [nm] & 0.14 & 0.46 & 0.65 & 0.86 & 1.05 & 1.08 \caption{Binding energies $E_{\text{b}}$ and C-C distance of energetically most favorable C$_{\text{i}}$ \hkl<1 0 0>-type defect pairs separated along bonds in the \hkl[1 1 0] direction.} \label{table:dc_110} \end{table} -The binding energy of these configurations with respect to the C-C distance is plotted in Fig.~\ref{fig:dc_110} +The binding energy of these configurations with respect to the C-C distance is plotted in Fig.~\ref{fig:dc_110}. \begin{figure} \includegraphics[width=\columnwidth]{db_along_110_cc_n.ps} \caption{Minimum binding energy of dumbbell combinations separated along \hkl[1 1 0] with respect to the C-C distance. The blue line is a guide for the eye and the green curve corresponds to the most suitable fit function consisting of all but the first data point.} @@ -383,7 +383,7 @@ Obviously agglomeration of C$_{\text{i}}$ and C$_{\text{s}}$ is energetically fa The eneregtically most favorable configuration (configuration b) forms a strong but compressively strained C-C bond with a separation distance of \unit[0.142]{nm} sharing a Si lattice site. Again, conclusions concerning the probability of formation are drawn by investigating migration paths. Since C$_{\text{s}}$ is unlikely to exhibit a low activation energy for migration the focus is on C$_{\text{i}}$. -Pathways starting from the two next most favored configurations were investigated, all of them showing activation energies above \unit[2.2-3.5]{eV}. +Pathways starting from the two next most favored configurations were investigated, which show activation energies above \unit[2.2]{eV} and \unit[3.5]{eV} respectively. Although lower than the barriers for obtaining the ground state of two C$_{\text{i}}$ defects the activation energies are yet considered too high. For the same reasons as in the last subsection, structures other than the ground state configuration are, thus, assumed to arise more likely due to much lower activation energies necessary for their formation and still comparatively low binding energies. @@ -493,7 +493,7 @@ For this reason C$_{\text{s}}$ without a nearby interacting Si$_{\text{i}}$ DB, As mentioned above, configurations of C$_{\text{s}}$ and Si$_{\text{i}}$ DBs might be especially important at higher temperatures due to the low activation energy necessary for its formation. At higher temperatures the contribution of entropy to structural formation increases, which might result in a spatial separation even for defects located within the capture radius. -Indeed an ab initio molecular dynamics run at \unit[900]{$^{\circ}$C} starting from configuration \RM{1}, which -- based on the above findings -- is assumed to recombine into the ground state configuration, results in a separation the C$_{\text{s}}$ and Si$_{\text{i}}$ DB by more than 4 next neighbor distances realized in a repeated migration mechnism of annihilating and arising Si DBs. +Indeed an ab initio molecular dynamics run at \unit[900]{$^{\circ}$C} starting from configuration \RM{1}, which -- based on the above findings -- is assumed to recombine into the ground state configuration, results in a separation of the C$_{\text{s}}$ and Si$_{\text{i}}$ DB by more than 4 next neighbor distances realized in a repeated migration mechnism of annihilating and arising Si DBs. The atomic configurations for two different points in time are shown in Fig.~\ref{fig:md}. Si atoms 1 and 2, which form the initial DB, occupy usual Si lattice sites in the final configuration while atom 3 occupies an interstitial site. \begin{figure} @@ -524,7 +524,7 @@ The ground state configurations of these defects, i.e. the Si$_{\text{i}}$ \hkl< A quantitatively improved activation energy of \unit[0.9]{eV} for a qualitatively equal migration path based on studies by Capaz et.~al.\cite{capaz94} to experimental values\cite{song90,lindner06,tipping87} ranging from \unit[0.70-0.87]{eV} reinforce their derived mechanism of diffusion for C$_{\text{i}}$ in Si. The investigation of defect pairs indicates a general trend of defect agglomeration mainly driven by the potential of strain reduction. -Obtained results for the most part compare well with results gained in previous studies\cite{leary97,capaz98,mattoni2002,liu02} and show an astnishingly good agreement with experiment\cite{song90}. +Obtained results for the most part compare well with results gained in previous studies\cite{leary97,capaz98,mattoni2002,liu02} and show an astonishingly good agreement with experiment\cite{song90}. Configurations involving two C impurities indeed exhibit the ground state for structures consisting of C-C bonds, which are responsible for the vast gain in energy. However, based on investigations of possible migration pathways, these structures are less likely to arise than structures, in which both C atoms are interconnected by another Si atom, which is due to high activation energies of the respective pathways or alternative pathways with less high activation energies, which, however, involve intermediate unfavorable configurations. Thus, agglomeration of C$_{\text{i}}$ is expected while the formation of C-C bonds is assumed to fail to appear by thermally activated diffusion processes. @@ -547,8 +547,8 @@ These findings allow to draw conclusions on the mechanisms involved in the proce Agglomeration of C$_{\text{i}}$ is energetically favored and enabled by a low activation energy for migration. Although ion implantation is a process far from thermodynamic equlibrium, which might result in phases not described by the Si/C phase diagram, i.e. a C phase in Si, high activation energies are believed to be responsible for a low probability of the formation of C clusters. -Unrolling these findings on the initially stated controversy present in the precipitation model, an increased participation of C$_{\text{s}}$ already in the initial stage must be assumed. -Thermally activated C$_{\text{i}}$ might turn into C$_{\text{s}}$. +Unrolling these findings on the initially stated controversy present in the precipitation model, an increased participation of C$_{\text{s}}$ already in the initial stage must be assumed due to its high probability of incidence. +In addition, thermally activated, C$_{\text{i}}$ might turn into C$_{\text{s}}$. The associated emission of Si$_{\text{i}}$ serves two needs: as a vehicle for other C$_{\text{s}}$ and as a supply of Si atoms needed elsewhere to form the SiC structure. As for the vehicle, Si$_{\text{i}}$ is believed to react with C$_{\text{s}}$ turning it into a highly mobile C$_{\text{i}}$ again, allowing for the rearrangement of the C atom. The rearrangement is crucial to end up in a configuration of C atoms only occupying substitutionally the lattice sites of one of the fcc lattices that build up the diamond lattice as expected in 3C-SiC. @@ -563,7 +563,7 @@ Regions showing dark contrasts in an otherwise undisturbed Si lattice are attrib However, there is no particular reason for the C species to reside in the interstitial lattice. Contrasts are also assumed for Si$_{\text{i}}$. Once precipitation occurs regions of dark contrasts disappear in favor of Moir\'e patterns indicating 3C-SiC in c-Si due to the mismatch in the lattice constant. -Until then, however, these regions are either composed of stretched coherent SiC and interstitials or of yet contracted incoherent SiC surrounded by Si and interstitials too small to be detected in HREM. +Until then, however, these regions are either composed of stretched coherent SiC and interstitials or of already contracted incoherent SiC surrounded by Si and interstitials too small to be detected in HREM. In both cases Si$_{\text{i}}$ might be attributed a third role, which is the partial compensation of tensile strain either in the stretched SiC or at the interface of the contracted SiC and the Si host. In addition, the experimentally observed alignment of the \hkl(h k l) planes of the precipitate and the substrate is statisfied by the mechanism of successive positioning of C$_{\text{s}}$. @@ -574,7 +574,7 @@ In contrast, there is no obvious reason for the topotactic orientation of an agg In summary, C and Si point defects in Si, combinations of these defects and diffusion processes within such configurations have been investigated. It is shown that C interstitials in Si tend to agglomerate, which is mainly driven by a reduction of strain. Investigations of migration pathways, however, allow to conclude that C clustering fails to appear by thermally activated processes due to high activation energies of the the respective diffusion processes. -A highly attractive interaction and a large capture radius has been identified for the C$_{\text{i}}$ \hkl<1 0 0> DB and the vacancy indicating a high probability for the formation of C$_{\text{s}}$ +A highly attractive interaction and a large capture radius has been identified for the C$_{\text{i}}$ \hkl<1 0 0> DB and the vacancy indicating a high probability for the formation of C$_{\text{s}}$. In contrast, a rapidly decreasing interaction with respect to the separation distance has been identified for C$_{\text{s}}$ and a Si$_{\text{i}}$ \hkl<1 1 0> DB resulting in a low probability of defects exhibiting respective separations to transform into the C$_{\text{i}}$ \hkl<1 0 0> DB, which constitutes the ground state configuration for a C atom introduced into otherwise perfect Si. Based on these findings conclusions on basic processes involved in the SiC precipitation in bulk Si are drawn. It is concluded that the precipitation process is governed by the formation of C$_{\text{s}}$ already in the initial stages.