\usepackage[dvips]{graphicx}
\graphicspath{{./img/}}
+\usepackage[lmargin=3cm,rmargin=2cm,tmargin=2cm,bmargin=2cm,noheadfoot]{geometry}
+
%\usepackage{./graphs}
\title{Modelling of a selforganization process leading to periodic arrays of nanometric amorphous precipitates by ion irradiation}
\begin{document}
+\hyphenation{TRIM}
+
\begin{center}
{\Large\bf
Modelling of a selforganization process leading to periodic arrays of nanometric amorphous precipitates by ion irradiation
\begin{center}
{\large
- F. Zirkelbach, M. Häberlen, J. K. N. Lindner and B. Stritzker
+ F. Zirkelbach, M. Häberlen\footnote{corresponding author:\\email: maik.haeberlen@physik.uni-augsburg.de\\phone: +49-821-5983498\\fax: +49-821-5983425}, J. K. N. Lindner, and B. Stritzker
\par
}
\end{center}
\begin{center}
{\scriptsize
- Institute of Physics, University of Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany
+ Institut für Physik, Universität Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany
\par
}
\end{center}
Abstract
}
-We developed a Monte-Carlo-Simulation code based on a simple model that tries to explain the selforganization process leading to periodic arrays of nanometric amorphous precipitates by ion irradiation. In the present work we focus on high-dose carbon implantation into silicon. Due to the compressive stress caused by amorphous $SiC_x$ on the $Si$ host lattice, which is relaxing in vertical direction as this process occurs near the target surface, preferential amorphization of the stressed regions between amorphous inclusions during continued implantation is taking place. This, together with the diffusion of carbon into the amorphous volumes, to reduce the carbon supersaturation in the crystalline volumes leads to a uniform configuration of amorphous, lamella preciptates with high carbon concentration. The simulation is able to reproduce results gained by cross-sectional TEM meassurements of high-dose carbon implanted silicon. Adjusting the simulation parameters we found a configuration matching the depth distribution and the average length of these amorphous arrays. Furthermore conditions can be specified as a necessity for the selforganization process and information about the configuration in the layers of the target, which is not easily measurable is obtained.
+Ion irradiation of materials which undergo a drastic density change upon amorphization have been shown to exhibit selforganized, nanometric structures of the amorphous phase in the crystalline host lattice. In order to better understand the process a Monte-Carlo-Simulation code based on a simple model is developed. In the present work we focus on high-dose carbon implantations into silicon. The simulation is able to reproduce results gained by cross-sectional TEM measurements of high-dose carbon implanted silicon. Necessary conditions can be specified for the selforganization process and information is gained about the compositional and structural state during the ordering process which is difficult to be obtained by experiment.
\newpage
\section{Introduction}
-Formation of nanometric selforganized ordered amorphous lamella precipitates is observed at certain conditions at high-dose implantation of impurity atoms. The present work focuses on high-dose carbon implantation into silicon. Typical doses are $1-10 \times 10^{17} cm^{-2}$ with an ion energy of $180 keV$. Temperatures below $400 \, ^{\circ} \mathrm{C}$ are needed. A model describing the selforganization process will be introduced, followed by a review of the implementation of the simulation code. Results of the Monte-Carlo-Simulation will be compared to cross-sectional TEM measurements. Necessary conditions for observing lamella precipitates are named and some additional, difficult to measure information like the carbon distribution and amorphous/crystalline structure in the layers of the target were obtained.
+The formation of nanometric, selforganized, amorphous, lamellar precipitates as a result of high-dose implantation of impurity ions is observed at certain implantation conditions for various ion/target combinations [1-3]. This is surprising since high-dose impurity implantations usually result in the formation of unordered ensembles of precipitates with a broad size distribution \cite{4}. The present work focuses on high-dose carbon implantations into silicon, with doses of $1-10 \times 10^{17} cm^{-2}$, an ion energy of $180 \, keV$ and substrate temperatures below $400 \, ^{\circ} \mathrm{C}$ [4,5]. An example of such a lamellar structure is given in the cross-sectional transmission electron microscopy (XTEM) image in Figure \ref{xtem}. A model describing the selforganization process is introduced in this article. This model is used to implement a Monte-Carlo simulation code which reproduces the amorphization and precipitation process. Simulation results will be compared with XTEM measurements. Necessary conditions for creating lamellar precipitates are identified and some additional, difficult-to-gain measure information like the carbon distribution and the influence of stress on the amorphous/crystalline structure in the layers is obtained.
\newpage
\section{Model}
-A model describing the formation of nanometric selforganized ordered amorphous $SiC_x$ inclusions was introduced in \cite{1}\cite{2}. Figure \ref{1} shows the evolution into ordered lamellae with increasing dose.
+A model describing the formation of nanometric, selforganized, regularly arranged, amorphous $SiC_x$ inclusions was introduced in \cite{5}. The basic idea is schematically displayed in Figure \ref{model}, giving the evolution into ordered lamellae with increasing dose.
%\begin{figure}[!h]
%\begin{center}
%\end{center}
%\end{figure}
-As a result of the supersaturation of carbon atoms in silicon there is a nucleation of spherical $SiC_x$-precipitates. The almost $20\%$ lattice misfit of the diamond lattice of crystalline silicon ($c-Si$, $a=0.543 \, nm$) to the cubic polytype of $SiC$ ($3C-SiC$, $a=0.436 \, nm$) causes a large interfacial energy, which could be reduced if one of the participants exists in the amorphous phase. It has been shown \cite{1} that $SiC$ turns into the amorphous phase. In fact, amorphous silicon ($a-Si$) would recrystallize under the granted conditions due to ion beam induced recrystallization. Stoichiometric $SiC$ has a smaller atomic density than $c-Si$. The same is assumed for substoichiometric $a-SiC_x$. Hence the amorphous $SiC_x$ tends to expand, and as a result compressive stress is applied on the $Si$ host lattice. As the process occurs near the targets surface, the stress is relaxing in vertical direction and there is just lateral stress remaining. Thus volumes between amorphous inclusions will more likely turn into amorphous phase, as the stress hampers the reassembly of the atoms on their lattice site, while amorphous volumes located in a crystalline neighbourhood will recrystallize in all probability. In addition carbon diffuses to the amorphous volumes in order to reduce the supersaturation of carbon in the crystalline volumes. As a consequence the amorphous volumes hold plenty of carbon.
+As a result of supersaturation of carbon atoms in silicon at high concentrations there is a nucleation of spherical $SiC_x$ precipitates. Carbon implantations at much higher implantation temperatures usually lead to the precipitation of cubic $SiC$ (3C-SiC, $a=0.436 \, nm$) \cite{4}. The lattice misfit of almost $20\%$ of 3C-SiC would cause a large interfacial energy with the crystalline $Si$ matrix \cite{6}. This energy could be reduced if one of the phases exists in the amorphous state. Energy filtered XTEM studies in \cite{7} have revealed that the amorphous phase is more carbon-rich than the crystalline surrounding. In addition, annealing experiments have shown that the amorphous phase is stable against crystallization at temperatures far above the recrystallization temperature of amorphous $Si$. Prolonged annealing at $900 \, ^{\circ} \mathrm{C}$ turns the lamellae into ordered chains of amrphous and crystalline 3C-SiC nanoprecipitates \cite{8} demonstrating again the carbon-rich nature of amorphous inclusions. Since at the implantation conditions chosen pure $a-Si$ would recrystallize by ion beam induced crystallization \cite{9}, it is understandable that it is the carbon-rich side of the two phases which occurs in the amorphous state in the present phase separation process.
+
+Stoichiometric $SiC$ has a smaller $Si$ atomic density than $c-Si$ [10,11]. A reduced density is also assumed for substoichiometric $a-SiC_x$. Hence the amorphous $SiC_x$ tends to expand and as a result compressive stress is applied on the $Si$ host lattice represented by arrows in Figure \ref{model}. As the process occurs near the target surface, stress is relaxing in the vertical direction and there is mainly lateral stress remaining ("R" in Figure \ref{model}). Thus volumes between amorphous inclusions will more likely turn into an amorphous phase as the stress hampers the rearrangement of atoms on regular lattice sites. In contrast, $a-Si$ volumes located in a crystalline neighbourhood will recrystallize in all probability at the present implantation conditions.
+
+Carbon is assumed to diffuse from the crystalline to the amorphous volumes in order to reduce the supersaturation of carbon in the crystalline interstices. As a consequence the amorphous volumes accumulate carbon.
\newpage
\section{Simulation}
-Before discussing the implementation some assumptions and approximations have to be made. Figure \ref{2} shows the stopping powers and carbon concentration profile calculated by TRIM. The depth region we are interested in is between $0-300 \, nm$, the region between the surface of the target and the beginning of the continuous amorphous $SiC_x$ layer (from now on called simulation window), where the nuclear stopping power and the implantation profile can be approximated by a linear function of depth. Furthermore the probability of amorphization is assumed to be proportional to the nuclear stopping power. A local probability of amorphization somewhere in the target is composed of three parts, the ballistic, carbon-induced and stress-induced amorphization. The ballistic amorphization is proportional to the nuclear stopping power, as mentioned before. The carbon-induced amorphization is a linear function of the local carbon concentration. The stress-induced amorphization is proportional to the compressive stress applied by the amorphous neighbours. Thus the probability of a crystalline volume getting amorphous can be calculated as follows,
-\[
- p_{c \rightarrow a} = b_{ap} + a_{cp} \times c^{local}_{carbon} + \sum_{amorphous \, neighbours} \frac{a_{ap} \times c_{carbon}}{distance^2}
-\]
-with $b_{ap}$, $a_{cp}$ and $a_{ap}$ being parameters of the simulation to weight the three different ways of amorphization. The probability of an amorphous volume turning crystalline should behave contrary to $p_{c \rightarrow a}$ and thus is assumed to $p_{a \rightarrow c} = 1 - p_{c \rightarrow a}$.
+Before discussing the simulation algorithm some assumptions and approximations have to be made. Figure \ref{trim} shows the stopping powers and carbon concentration profiles calculated by TRIM \cite{12}. The depth region we are interested in is between $0-300 \, nm$ (furtheron called simulation window), the region between the target surface and the beginning of the continuous amorphous $SiC_x$ layer at the implantation conditions of Figure \ref{xtem}. The nuclear stopping power and the implantation profile can be approximated by a linear function of depth within the simulation window.
-Figure \ref{3} shows the target devided into $64 \times 64 \times 100$ volumes with a side length of $3 \, nm$. Each of it has a state (crystalline/amorphous) and keeps the local carbon concentration. The simulation algorithm consists of three parts, the amorphization/recrystallization process, the carbon-implanting process and finally the diffusion process.
+The target is devided into $64 \times 64 \times 100$ cells with a side length of $3 \, nm$. Each of it has a crystalline or amorphous state and keeps the local carbon concentration. The cell is addressed by a position vector $\vec r = (k,l,m)$, where $k$, $l$, $m$ are integers.
-For the amorphization/recrystallization process, random coordinates are computed to specify the volume which is hit by an implanted carbon ion. The two random numbers corresponding to the $x$ and $y$ coordinates are generated with a uniform probability distribution, $p(x)dx=dx \textrm{, } p(y)dy=dy$. The random number corresponding to the $z$ coordinate is distributed according to the linear approximated nuclear stopping power, $p(z)dz=(a_{el} \times z+b_{el})dz$, where $a_{el}$ and $b_{el}$ are simulation parameters describing the nuclear energy loss. After calculating the local probability of amorphization of that volume $p_{c \rightarrow a}$, another random number decides, depending on the current state, whether the volume gets amorphous or recrystallized. This step is looped for the average hit per ion in the simulation window, counted by TRIM collision data.
+The probability of amorphization is assumed to be proportional to the nuclear stopping power. A local probability of amorphization at any point in the target is composed of three contributions, the ballistic amorphization, a carbon-induced and a stress-induced amorphization. The ballistic amorphization probability $p_b$ is proportional to the nuclear stopping power as mentioned before. The carbon-induced contribution is a linear function of the local carbon concentration. The stress-induced portion is proportional to the compressive stress originating from the amorphous volumes in the vicinity, the stress amplitude decreasing with the square of distance $d=|\vec r - \vec{r'}|$. Thus the probability of a crystalline volume getting amorphous can be calculated as
+\begin{equation}
+ p_{c \rightarrow a}(\vec r) = p_{b} + p_{c} \, c_{carbon}(\vec r) + \sum_{amorphous \, neighbours} \frac{p_{s} \, c_{carbon}(\vec{r'})}{d^2} \quad ,
+\end{equation}
+with $p_{b}$, $p_{c}$ and $p_{s}$ being simulation parameters to weight the three different mechanisms of amorphization. The probability $p_{a \rightarrow c}$ of an amorphous volume to turn crystalline should behave contrary to $p_{c \rightarrow a}$ and is thus assumed as:
+\begin{equation}
+ p_{a \rightarrow c} = 1 - p_{c \rightarrow a} \quad .
+\end{equation}
-In an analogous manner random coordinates (expect the $z$ coordinate being distributed according the linear approximated implantation profile) are obtained to acquire the volume where the carbon ion gets stock and the local carbon concentration increases.
+The simulation algorithm consists of three parts, the amorphization/recrystallization process, the carbon incorporation and finally the carbon diffusion.
-Finally a standard diffusion algorithm is started, so the supersaturation of carbon in the crystalline volumes can be reduced. This process adds a few simulation parameters, the diffusion velocity, the diffusion rate and a switch whether to do diffusion in $z$-direction or not.
+For the amorphization/recrystallization process random values are computed to specify the volume which is hit by an impinging carbon ion. Two random numbers $x,y \in [0,1]$ are generated and mapped to the coordinates $k,l$ using a uniform probability distribution, $p(x)dx=dx \textrm{, } p(y)dy=dy$. A random number $z$ corresponding to the $m$ coordinate is distributed according to the linear approximated nuclear stopping power, $p(z)dz=(s z+s_0)dz$, where $s$ and $s_0$ are simulation parameters describing the nuclear energy loss. After calculating the local probability of amorphization $p_{c \rightarrow a}(k,l,m)$ of the selected volume another random number determines - depending on the current status - whether the volume turns amorphous, recrystallizes or remains unchanged. This step is looped for the average hits per ion in the simulation window as extracted from TRIM \cite{12} collision data.
+
+In the same manner random coordinates are determined to select the cell where the carbon ion gets incorporated. In this step the probability distribution describing the stopping power profile is replaced by a distribution for the linearly approximated concentration profile. The local carbon concentration in the selected cell is increased.
+
+Following carbon incorporation carbon diffusion is considered in order to allow a reduction of the supersaturation of carbon in the crystalline volumes. This is done by a simple diffusion algorithm in which the concentration difference for each two neighbouring cells is considered and partially balanced according to a given diffusion rate $d_r$ (simulation parameter). This time consuming diffusion process is repeated after each $d_v$ (simulation parameter) impinging ions. A switch is implemented to exclude diffusion in $z$-direction. As in experimental studies diffusional broadening of carbon concentration profiles has not been observed even at significantly higher implantation temperatures where no amorphous phase is formed \cite{13}, diffusion among crystalline volumes is assumed to be zero in the following simulations.
\newpage
\section{Results}
-Figure \ref{4} shows a comparison of a simulation result and a cross-sectional TEM snapshot of $180 \, keV$ implanted carbon in silicon at $150 \,^{\circ} \mathrm{C}$ with $4.3 \times 10^{17} cm^{-2}$. The depth the lamella structure is starting in ($300 \, nm$) and also the average length of these precipitates complies to that one of the experimental data. The arrays are ordered in uniform intervals. It can be seen that lamella selforganized structures can be reproduced by the simulation.
+Figure \ref{c-xtem} shows a comparison of a simulation result and a XTEM bright-field image of silicon implanted at $150 \,^{\circ} \mathrm{C}$ with $180 \, keV$ $C^+$ ions at a dose of $4.3 \times 10^{17} \, cm^{-2}$. Significant lamellar structure formation is observed in the depth interval between $200$ and $300 \, nm$ (Figure 4(b)). This is nicely reproduced by the simulation result shown in Figure 4(a). Even the average length of the precipitates complies to the experimental data. The lamellae are arranged in uniform intervals. Obviously the simulation is able to reproduce lamellar, selforganized structures.
+
+Simulations with different model parameters allow to specify conditions for observing lamellar structures. First runs with a simplified version of the program have shown that it is essential to assume low amorphization probabilities to avoid early complete amorphization of the whole cell ensemble. Instead small amorphization parameters $p_b$, $p_c$, $p_s$ and a large number of simulation steps are required to observe lamellar structures. This finding is in agreement to the fact that due to the low nuclear energy deposition of the light carbon ions in silicon, amorphization would not be expected at all at these elevated target temperatures \cite{4} and thus carbon mediated amorphization has to be taken into account to explain the amorphization process.
-Furthermore conditions for observing lamella structures can be specified. Figure \ref{5} shows two identical simulation cycles with diffusion in $z$-direction switched off and on. The lamella structures only appear when diffusion in $z$-direction \ldots
+Figure \ref{zdiff} shows the results of two identical simulation runs with diffusion in $z$-direction switched off and on. The lamellar structures only appear if diffusion in $z$-direction is enabled. Amorphous volumes denude the neighbouring crystalline layers of carbon. In consequence the stability of such cells against recrystallization is enhanced, the probability to amorphize crystalline cells in the same depth is increased due to the stress term and the amorphization in the carbon denuded cells and their lateral vicinity is decreased. This fortifies the formation of lamellar precipitates. The result highlights the importance of the diffusion in $z$-direction for the selforganization process.
-TODO:\\
-- diffusion rate -> depth of lamella structures\\
-- complementary arrays of c/a precipitates for z and z+1\\
-- evt FFT bilder\\
-- summary\\
+In Figure \ref{diffrate} two simulation results with different diffusion rates are compared. Higher diffusion rates cause a larger depth domain of lamellar structure. This can be understood since higher diffusion rates result in amorphous volumes holding more carbon which consequently stabilizes the amorphous state. In case of slower diffusion rates (Figure 6(b)) the redistribution of carbon is too slow to allow for an effective agglomeration of carbon atoms in amorphous cells to stabilize the amorphous state against recrystallization. This results in a smaller total amount of amorphous material in Figure 6(a) compared to Figure 6(b). The stabilization occurs only at a depth larger than approximately $240 \, nm$ where the total concentration of carbon is high enough. The sufficient stabilization of amorphous volumes in this deeper depth zone enables also the more effective contribution of the stress mediated amorphization.
+
+The influence of the stress term $p_s$ is considered in Figure \ref{stress}. For otherwise the same conditions as in Figure 6(b) calculations with decreased $p_s$ in Figure 7(c),(b),(a) show a systematically reduced extension of the lamellae zone. The mean diameter of amorphous lamellae decreases with decreasing $p_s$. Both observations support the assumption of stress mediated amorphization as a mechanism contributing to lamella formation.
+
+Figure \ref{compl-str} shows the extension of amorphous lamellae in plane view for two consecutive slices $m$ and $m+1$ of the ensemble. It is obvious that amorphous and crystalline lamellae have a complementary arrangement in neighbouring slices (Figure 8(a),(b)) which again is a result of the carbon accumulation in the amorphous lamellae. This can be clearly seen by comparison with the corresponding carbon maps in Figure 8(c),(d).
\newpage
-\section{Conclusion}
+\section{Summary and conclusion}
+A simple model explaining the selforganization process of lamellar, amorphous precipitates during high-dose ion implantation is introduced. The implementation of the model in a simulation code is described. The simulation is able to reproduce the experimentally observed formation of lamellae. The evolution of these lamellar structures gets traceable by the simulation. The weight of different mechanisms which contribute to the selforganization process is explored by variation of simulation parameters. It is found that diffusion in $z$-direction and stress mediated amorphization are necessary to create ordered arrays of amorphous, lamellar precipitates. Thus by simulation, information is gained about the selforganization process which is not easily accessible by experimental techniques.
\newpage
-\begin{thebibliography}{20}
- \bibitem{1} J.K.N. Lindner, Appl. Phys. A 77 (2003) 27-38.
- \bibitem{2} M. Häberlen, J.K.N. Lindner, B. Stritzker, Nucl. Instr. and Meth. B 216 (2004) 36-40.
+\begin{thebibliography}{10}
+ \bibitem{1} L.L. Snead, S.J. Zinkle, J.C. Hay, M.C. Osborne, Nucl. Instr. and Meth. B 141 (1998) 123.
+ \bibitem{2} A.H. van Ommen, Nucl. Instr. and Meth. B 39 (1989) 194.
+ \bibitem{3} M. Ishimaru, R.M. Dickerson, K.E. Sickafus, Nucl. Instr. and Meth. B 166-167 (2000) 390.
+ \bibitem{4} J.K.N. Lindner, Appl. Phys. A 77 (2003) 27-38.
+ \bibitem{5} J.K.N. Lindner, M. Häberlen, M. Schmidt, W. Attenberger, B. Stritzker, Nucl. Instr. and Meth. B 186 (2000) 206-211.
+ \bibitem{6} W.J. Taylor, T.Y. Tan, U.Gösele, Appl. Phys. Lett. 62 (1993) 3336.
+ \bibitem{7} M. Häberlen, J.K.N. Lindner, B. Stritzker, to be published.
+ \bibitem{8} M. Häberlen, J.K.N. Lindner, B. Stritzker, Nucl. Instr. and Meth. B 206 (2003) 916-921.
+ \bibitem{9} J. Linnross, R.G. Elliman, W.L. Brown, J. Mater, Res. 3 (1988) 1208.
+ \bibitem{10} L. L. Horton, J. Bentley, L. Romana, A. Perez, C.J. McHargue, J.C. McCallum, Nucl. Intr. and Meth. B 65 (1992) 345.
+ \bibitem{11} W. Skorupa, V. Heera, Y. Pacaud, H. Weishart, in: F. Priolo, J.K.N. Lindner, A. Nylandsted Larsen, J.M. Poate (Eds.), New Trends in Ion Beam Processing of Materials, Europ. Mater. Res. Soc. Symp. Proc. 65, Part 1, Elsevier, Amsterdam, 1997, p. 114.
+ \bibitem{12} SRIM2000 Version of the TRIM program described by J.F. Ziegler, J.P. Biersack, U. Littmark in: The Stopping and Range of Ions in Matter, vol. 1, Pergamon Press, New York, 1985.
+ \bibitem{13} J.K.N. Lindner, W. Reiber, B. Stritzker, Mater. Sci. Forum Vols. 264-268 (1998) 215-218.
\end{thebibliography}
\newpage
-\listoffigures
+%\listoffigures
+
+\section*{Figure Captions}
+
+\begin{enumerate}
+ \item XTEM image of a $Si$ sample implanted with $180 \, keV \, C^+$ ions at a dose of $4.3 \times 10^{17} \, cm^{-2}$ and a substrate temperature of $150 \,^{\circ} \mathrm{C}$. Lamellar and spherical amorphous inclusions are marked by $L$ and $S$.
+ \item Schematic explaining the selforganization of amorphous $SiC_x$ precipitates and the evolution into ordered lamellae with increasing dose (see text).
+ \item Nuclear and electronic stopping powers and concentration profile of $180 \, keV \, C^+$ ions implanted in $Si$ calculated by TRIM.
+ \item Comparison of a simulation result and a XTEM image ($180 \, keV$ $C^+$ implantation into silicon at $150 \,^{\circ} \mathrm{C}$ and a dose of $4.3 \times 10^{17} cm^{-2}$). Amorphous cells are white.
+ \item Two identical simulation runs with diffusion switched off (left) and on (right).
+ \item Two identical simulation runs with different diffusion rates $d_r$. All other parameters are as in Figure 5(b).
+ \item Four simulation runs with different simulation parameter $p_s$. All other parameters are as in Figure 5(b).
+ \item Plane view display of amorphous (white) and crystalline (black) cells in two consecutive slices $m$ and $m+1$ (a,b) and corresponding carbon map (c,d). Higher carbon concentrations are given by higher brightness in (c,d).
+\end{enumerate}
\newpage
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=17cm]{k393abild1_e.eps}
+%\caption[XTEM image of a $Si$ sample implanted with $180 \, keV \, C^+$ ions at a dose of $4.3 \times 10^{17} \, cm^{-2}$ and a substrate temperature of $150 \,^{\circ} \mathrm{C}$. Lamellar and spherical amorphous inclusions are marked by $L$ and $S$.]{}
+\label{xtem}
+\\1
+\end{center}
+\end{figure}
+
\begin{figure}[!h]
\begin{center}
\includegraphics[width=17cm]{model1_e.eps}
-\caption[Rough model explaining the selforganization of amorphous $SiC_x$ precipitates and the evolution into ordered lamellae with increasing dose]{} \label{1}
+%\caption[Schematic explaining the selforganization of amorphous $SiC_x$ precipitates and the evolution into ordered lamellae with increasing dose (see text).]{}
+\label{model}
+\\2
\end{center}
\end{figure}
\begin{figure}[!h]
\begin{center}
\includegraphics[width=14cm]{2pTRIM180C.eps}
-\caption[Stopping powers and concentration profile calculated by TRIM]{} \label{2}
+%\caption[Nuclear and electronic stopping powers and concentration profile of $180 \, keV \, C^+$ ions implanted in $Si$ calculated by TRIM.]{}
+\label{trim}
+\\3
\end{center}
\end{figure}
\begin{figure}[!h]
\begin{center}
-\includegraphics[width=15cm]{gitter_e.eps}
-\caption[Target devided into $64 \times 64 \times 100$ volumes with a side length of $3 \, nm$ holding state and carbon concentration]{} \label{3}
+\includegraphics[width=15cm]{if_cmp2_e.eps}
+%\caption[Comparison of a simulation result and a XTEM image ($180 \, keV$ $C^+$ implantation into silicon at $150 \,^{\circ} \mathrm{C}$ and a dose of $4.3 \times 10^{17} cm^{-2}$). Amorphous cells are white.]{}
+\label{c-xtem}
+\\4
\end{center}
\end{figure}
\begin{figure}[!h]
\begin{center}
-\includegraphics[width=15cm]{if_cmp2_e.eps}
-\caption[Comparison of a simulation result and a cross-sectional TEM snapshot of $180 \, keV$ implanted carbon in silicon at $150 \,^{\circ} \mathrm{C}$ with $4.3 \times 10^{17} cm^{-2}$]{} \label{4}
+\includegraphics[width=8cm]{mit_ohne_diff_big_e.eps}
+%\caption[Two identical simulation runs with diffusion switched off (left) and on (right).]{}
+\label{zdiff}
+\\5
+\end{center}
+\end{figure}
+
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=8cm]{high_low_ac-diff_big_e.eps}
+%\caption[Two identical simulation runs with different diffusion rates $d_r$. All other parameters are as in Figure 5(b).]{}
+\label{diffrate}
+\\6
+\end{center}
+\end{figure}
+
+\begin{figure}[!h]
+\begin{center}
+\includegraphics[width=12cm]{high_to_low_a_e.eps}
+%\caption[Four simulation runs with different simulation parameter $p_s$. All other parameters are as in Figure 5(b).]{}
+\label{stress}
+\\7
\end{center}
\end{figure}
\begin{figure}[!h]
\begin{center}
-\includegraphics[width=15cm]{mit_ohne_diff.eps}
-\caption[Identical simulation cycles, with diffusion switched off (left) and on (right)]{} \label{5}
+\includegraphics[width=10cm]{all_z-z_plus_1_big.eps}
+%\caption[Plane view display of amorphous (white) and crystalline (black) cells in two consecutive slices $m$ and $m+1$ (a,b) and corresponding carbon map (c,d). Higher carbon concentrations are given by higher brightness in (c,d).]{}
+\label{compl-str}
+\\8
\end{center}
\end{figure}
projects / lectures / latex.git / blobdiff