From 73f99861c74346c7df7abd2009e768483feb937c Mon Sep 17 00:00:00 2001 From: hackbard Date: Tue, 27 Sep 2011 15:23:41 +0200 Subject: [PATCH] more commas and fixed a sentence --- posic/thesis/md.tex | 38 +++++++++++++++++++------------------- 1 file changed, 19 insertions(+), 19 deletions(-) diff --git a/posic/thesis/md.tex b/posic/thesis/md.tex index 71123ea..d09373b 100644 --- a/posic/thesis/md.tex +++ b/posic/thesis/md.tex @@ -27,11 +27,11 @@ with $a_{\text{SiC}}$ being the lattice constant of 3C-SiC. In IBS experiments, the smallest precipitates observed have radii starting from \unit[2]{nm} up to \unit[4]{nm}. For the initial simulations, a total amount of 6000 C atoms corresponding to a radius of approximately \unit[3.1]{nm} is chosen. In separated simulations, the 6000 C atoms are inserted in three regions of different volume ($V_1$, $V_2$, $V_3$) within the simulation cell. -For reasons of simplification these regions are rectangularly shaped. +For reasons of simplification, these regions are rectangularly shaped. $V_1$ is chosen to be the total simulation volume. $V_2$ approximately corresponds to the volume of a minimal 3C-SiC precipitate. $V_3$ is approximately the volume containing the amount of Si atoms necessary to form such a precipitate, which is slightly smaller than $V_2$ due to the slightly lower Si density of 3C-SiC compared to c-Si. -The two latter insertion volumes are considered since no diffusion of C atoms is expected within the simulated period of time at prevalent temperatures. +The two latter insertion volumes are considered since no long-range diffusion of C atoms is expected within the simulated period of time at prevalent temperatures. This is due to the overestimated activation energy for the diffusion of a \ci \hkl<1 0 0> DB, as pointed out in section~\ref{subsection:defects:mig_classical}. For rectangularly shaped precipitates with side length $L$ the amount of C atoms in 3C-SiC and Si atoms in c-Si is given by \begin{equation} @@ -144,20 +144,20 @@ Fig.~\ref{fig:md:prec_fc} displays a flow chart of the applied steps involved in \end{figure} The radial distribution function $g(r)$ for C-C and Si-Si distances is shown in Fig.~\ref{fig:md:pc_si-si_c-c}. -\begin{figure}[tp] -\begin{center} - \includegraphics[width=0.7\textwidth]{sic_prec_450_si-si_c-c.ps} -\end{center} -\caption[Radial distribution function of the C-C and Si-Si distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of {\unit[450]{$^{\circ}$C}} and cooled down to room temperature.]{Radial distribution function of the C-C and Si-Si distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of \unit[450]{$^{\circ}$C} and cooled down to room temperature. The bright blue graph shows the Si-Si radial distribution for pure c-Si. The insets show magnified regions of the respective type of bond.} -\label{fig:md:pc_si-si_c-c} -\end{figure} -\begin{figure}[tp] -\begin{center} - \includegraphics[width=0.7\textwidth]{sic_prec_450_energy.ps} -\end{center} -\caption[Total energy per atom as a function of time for the whole simulation sequence and for all three types of insertion volumes.]{Total energy per atom as a function of time for the whole simulation sequence and for all three types of insertion volumes. Arrows mark the end of C insertion and the start of the cooling process respectively.} -\label{fig:md:energy_450} -\end{figure} +\begin{figure}[tp]% +\begin{center}% + \includegraphics[width=0.7\textwidth]{sic_prec_450_si-si_c-c.ps}% +\end{center}% +\caption[Radial distribution function of the C-C and Si-Si distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of {\unit[450]{$^{\circ}$C}} and cooled down to room temperature.]{Radial distribution function of the C-C and Si-Si distances for 6000 C atoms inserted into the three different volumes $V_1$, $V_2$ and $V_3$ at a temperature of \unit[450]{$^{\circ}$C} and cooled down to room temperature. The bright blue graph shows the Si-Si radial distribution for pure c-Si. The insets show magnified regions of the respective type of bond.}% +\label{fig:md:pc_si-si_c-c}% +\end{figure}% +\begin{figure}[tp]% +\begin{center}% + \includegraphics[width=0.7\textwidth]{sic_prec_450_energy.ps}% +\end{center}% +\caption[Total energy per atom as a function of time for the whole simulation sequence and for all three types of insertion volumes.]{Total energy per atom as a function of time for the whole simulation sequence and for all three types of insertion volumes. Arrows mark the end of C insertion and the start of the cooling process respectively.}% +\label{fig:md:energy_450}% +\end{figure}% It is easily and instantly visible that there is no significant difference among the two simulations of high C concentration. Thus, in the following, the focus can indeed be directed to low ($V_1$) and high ($V_2$, $V_3$) C concentration simulations. The first C-C peak appears at about \unit[0.15]{nm}, which is comparable to the nearest neighbor distance of graphite or diamond. @@ -197,7 +197,7 @@ Fig.~\ref{fig:md:pc_si-c} displays the Si-C radial distribution function for all The first peak observed for all insertion volumes is at approximately \unit[0.186]{nm}. This corresponds quite well to the expected next neighbor distance of \unit[0.189]{nm} for Si and C atoms in 3C-SiC. By comparing the resulting Si-C bonds of a \ci{} \hkl<1 0 0> DB with the C-Si distances of the low concentration simulation, it is evident that the resulting structure of the $V_1$ simulation is clearly dominated by this type of defect. -This is not surprising, since the \ci{} \hkl<1 0 0> DB is found to be the ground-state defect of a C interstitial in c-Si and, for the low concentration simulations, a C interstitial is expected in every fifth Si unit cell only, thus, excluding defect superposition phenomena. +This is not surprising since the \ci{} \hkl<1 0 0> DB is found to be the ground-state defect of a C interstitial in c-Si and, for the low concentration simulations, a C interstitial is expected in every fifth Si unit cell only, thus, excluding defect superposition phenomena. The peak distance at \unit[0.186]{nm} and the bump at \unit[0.175]{nm} corresponds to the distance $r(3C)$ and $r(1C)$ as listed in Table~\ref{tab:defects:100db_cmp} and visualized in Fig.~\ref{fig:defects:100db_cmp}. In addition, it can be easily identified that the \ci{} \hkl<1 0 0> DB configuration contributes to the peaks at about \unit[0.335]{nm}, \unit[0.386]{nm}, \unit[0.434]{nm}, \unit[0.469]{nm} and \unit[0.546]{nm} observed in the $V_1$ simulation. Not only the peak locations but also the peak widths and heights become comprehensible. @@ -220,7 +220,7 @@ For high C concentrations, a rearrangement of the amorphous SiC structure, which Results of the last section indicate possible limitations of the MD method regarding the task addressed in this study. Low C concentration simulations do not reproduce the agglomeration of C$_{\text{i}}$ \hkl<1 0 0> DBs. High concentration simulations result in the formation of an amorphous SiC-like phase, which is unexpected since IBS experiments show crystalline 3C-SiC precipitates at prevailing temperatures. -Keeping in mind the results +%Keeping in mind the results On closer inspection, however, two reasons for describing this obstacle become evident, which are discussed in the following. The first reason is a general problem of MD simulations in conjunction with limitations in computer power, which results in a slow and restricted propagation in phase space. @@ -257,7 +257,7 @@ Since merely increasing the temperature leads to different equilibrium kinetics The TAD corrections are not applied in coming up simulations. This is justified by two reasons. First of all, a compensation of the overestimated bond strengths due to the short range potential is expected. -Secondly, there is no conflict applying higher temperatures without the TAD corrections, since crystalline 3C-SiC is also observed for higher temperatures than \unit[450]{$^{\circ}$C} in IBS~\cite{nejim95,lindner01}. +Secondly, there is no conflict applying higher temperatures without the TAD corrections since crystalline 3C-SiC is also observed for higher temperatures than \unit[450]{$^{\circ}$C} in IBS~\cite{nejim95,lindner01}. It is therefore expected that the kinetics affecting the 3C-SiC precipitation are not much different at higher temperatures aside from the fact that it is occurring much more faster. Moreover, the interest of this study is focused on structural evolution of a system far from equilibrium instead of equilibrium properties which rely upon proper phase space sampling. On the other hand, during implantation, the actual temperature inside the implantation volume is definitely higher than the experimentally determined temperature tapped from the surface of the sample. -- 2.39.2