nlsop/poster/nlsop_ibmm2006_ver2.tex

   1 \documentclass[portrait,a0b,final]{a0poster}
   2 \usepackage{epsf,psfig,pstricks,multicol,pst-grad,color}
   3 \usepackage{graphicx,amsmath,amssymb}
   4 \graphicspath{{../img/}}
   5 \usepackage[german]{babel}
   6
   7 \begin{document}
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  18 % Groesse der einzelnen Spalten als Anteil der Gesamt-Textbreite
  19 \renewcommand{\columnfrac}{.31}
  20
  21 % header
  22 \vspace{-1cm}
  23 \begin{header}
  24   \begin{minipage} {.13\textwidth}
  25         \includegraphics[height=11cm]{uni-logo.eps}
  26   \end{minipage} \hfill
  27   \begin{minipage}   {.73\textwidth}
  28      \centerline{{\Huge \bfseries Monte Carlo simulation study of a selforganisation}}
  29      \centerline{{\Huge \bfseries process leading to ordered precipitate structures}}
  30      \vspace*{1cm}
  31      \centerline{\huge\textsc {\underline{F.~Zirkelbach}}, M.~H"aberlen,
  32                                J.~K.~N.~Lindner, B.~Stritzker}
  33      \vspace*{1cm}
  34      \centerline{\Large Institut f"ur Physik, Universit"at Augsburg,
  35                         D-86135 Augsburg, Germany}
  36   \end{minipage} \hfill
  37   \begin{minipage} {.13\textwidth}
  38       \includegraphics[height=10cm]{Lehrstuhl-Logo.eps}
  39   \end{minipage} \hfill
  40 \end{header}
  41
  42 \begin{poster}
  43
  44 \vspace{-1cm}
  45 \begin{pcolumn}
  46   \begin{pbox}
  47     \section*{Motivation}
  48         {\bf
  49         Experimentally observerd seflorganisation process at high-dose carbon
  50         implantations under certain implantation conditions.}
  51         \begin{itemize}
  52                 \item Spherical and lamellar amorphous inclusions at the upper
  53                       a/c interface
  54                 \begin{center}
  55                         \includegraphics[width=20cm]{k393abild1_e.eps}
  56                 \end{center}
  57                 Cross section TEM image:\\
  58                 $180 \, keV$ $C^+ \rightarrow Si$,
  59                 $T=150 \, ^{\circ} \mathrm{C}$,
  60                 Dose: $4.3 \times 10^{17} \, cm^{-2}$\\
  61                 black/white: crystalline/amorphous material\\
  62                 L: amorphous lamellae, S: spherical amorphous inclusions
  63                 \item Carbon accumulation in amorphous volumes
  64                 \begin{center}
  65                         \includegraphics[width=20cm]{eftem.eps}
  66                 \end{center}
  67                 Brightfield TEM and respective EFTEM image:\\
  68                 $180 \, keV$ $C^+ \rightarrow Si$,
  69                 $T=200 \, ^{\circ} \mathrm{C}$,
  70                 Dose: $4.3 \times 10^{17} \, cm^{-2}$\\
  71                 yellow/blue: high/low concentrations of carbon
  72         \end{itemize}
  73         {\bf
  74         Observed for a number of ion/target combinations for which the
  75         material undergoes drastic density change upon amorphisation.}\\
  76         {\scriptsize
  77         A. H. van Ommen, Nucl. Instr. and Meth. B 39 (1989) 194.\\
  78         E. D. Specht et al., Nucl. Instr. and Meth. B 84 (1994) 323.\\
  79         M. Ishimaru et al., Nucl. Instr. and Meth. B 166-167 (2000) 390.}
  80   \end{pbox}
  81   \vspace{-1cm}
  82   \begin{pbox}
  83     \section*{Model}
  84         {\bf
  85         Model schematically displaying the formation of ordered lamellae
  86         with increasing dose.}
  87         \vspace{1cm}
  88         \begin{center}
  89                 \includegraphics[width=20cm]{modell_ng_e.eps}
  90         \end{center}
  91         \begin{itemize}
  92 \item supersaturation of $C$ in $c-Si$\\
  93       $\rightarrow$ {\bf carbon induced} nucleation of spherical
  94       $SiC_x$-precipitates
  95 \item high interfacial energy between $3C-SiC$ and $c-Si$\\
  96       $\rightarrow$ {\bf amourphous} precipitates
  97 \item $20 - 30\,\%$ lower silicon density of $a-SiC_x$ compared to $c-Si$\\
  98       $\rightarrow$ {\bf lateral strain} (black arrows)
  99 \item implantation range near surface\\
 100       $\rightarrow$ {\bf ralaxation} of {\bf vertical strain component}
 101 \item reduction of the carbon supersaturation in $c-Si$\\
 102       $\rightarrow$ {\bf carbon diffusion} into amorphous volumina
 103       (white arrows)
 104 \item remaining lateral strain\\
 105       $\rightarrow$ {\bf strain induced} lateral amorphisation
 106         \end{itemize}
 107   \end{pbox}
 108   \vspace{-1cm}
 109   \begin{pbox}
 110     \section*{Simulation}
 111         \begin{minipage}[t]{0.5\textwidth}
 112                 {\bf Discretisation of the target}
 113                 \begin{center}
 114                         \includegraphics[width=12cm]{gitter_e.eps}
 115                 \end{center}
 116                 \vspace{2cm}
 117                 \begin{itemize}
 118                         \item divided into cells with a cube length of $3 \, nm$
 119                         \item periodic boundary conditions in $x$,$y$-direction
 120                 \end{itemize}
 121         \end{minipage}
 122         \begin{minipage}[t]{0.5\textwidth}
 123                 {\bf TRIM collision statstics}
 124                 \begin{center}
 125                         \includegraphics[width=12cm]{trim_coll_e.eps}
 126                 \end{center}
 127                 \begin{itemize}
 128                         \item[] $\Rightarrow$ identical depth profiles for
 129                                  number of
 130                                 collisions per depth and nuclear stopping power
 131                         \item[] $\Rightarrow$ mean constant energy loss per
 132                                  collision
 133                 \end{itemize}
 134         \end{minipage}
 135   \end{pbox}
 136
 137
 138 \end{pcolumn}
 139 \begin{pcolumn}
 140
 141   \begin{pbox}
 142     \section*{Simulation algorithm}
 143     {\bf
 144     The simulation algorithm consists of the following three parts looped
 145     $s$ times corresponding to a dose $D=s/(64\times64\times(3 \, nm)^2)$:}
 146         \subsection*{1. Amorphisation/Recrystallisation}
 147         \begin{itemize}
 148                 \item random numbers distributed according to
 149                       the nuclear energy loss to determine the
 150                       volume in which a collision occurs
 151                 \item compute local probability for amorphisation:\\
 152                       %\vspace{0.1cm}
 153
 154                       \centerline{\fcolorbox[rgb]{0.,0.,0.}{1.,1.,.8}{
 155                       \begin{minipage}{20cm}
 156 \[
 157  p_{c \rightarrow a}(\vec{r}) = {\color{green} p_b} + {\color{blue} p_c c_C(\vec{r})} + {\color{red} \sum_{\textrm{amorphous neighbours}} \frac{p_s c_C(\vec{r'})}{(r-r')^2}}
 158 \]
 159                       \end{minipage}
 160                       }}
 161                       \vspace{1cm}
 162                       and recrystallisation:\\
 163                       %\vspace{0.1cm}
 164
 165                       \centerline{\fcolorbox[rgb]{0.,0.,0.}{1.,1.,.8}{
 166                       \begin{minipage}{20cm}
 167 \[
 168 p_{a \rightarrow c}(\vec r) = (1 - p_{c \rightarrow a}(\vec r)) \Big(1 - \frac{\sum_{direct \, neighbours} \delta (\vec{r'})}{6} \Big) \, \textrm{,}
 169 \]
 170 \[
 171 \delta (\vec r) = \left\{
 172 \begin{array}{ll}
 173         1 & \textrm{if volume at position $\vec r$ is amorphous} \\
 174         0 & \textrm{otherwise} \\
 175 \end{array}
 176 \right.
 177 \]
 178                       \end{minipage}
 179                       }}
 180                       \vspace{1cm}
 181                 \item loop for the mean amount of hits by the ion
 182         \end{itemize}
 183         Three contributions to the amorphisation process controlled by:
 184         \begin{itemize}
 185                 \item {\color{green} $p_b$} normal 'ballistic' amorphisation
 186                 \item {\color{blue} $p_c$} carbon induced amorphisation
 187                 \item {\color{red} $p_s$} stress enhanced amorphisation
 188         \end{itemize}
 189         \subsection*{2. Carbon incorporation}
 190                 \begin{itemize}
 191                         \item random numbers distributed according to
 192                               the implantation profile to determine the
 193                               incorporation volume
 194                         \item increase the amount of carbon atoms in
 195                               that volume
 196                 \end{itemize}
 197         \subsection*{3. Diffusion/Sputtering}
 198                 \begin{itemize}
 199                         \item every $d_v$ steps transfer $d_r$ of the
 200                               carbon atoms of crystalline volumina to
 201                               an amorphous neighbour volume
 202                         \item do the sputter routine after $n$ steps
 203                               corresponding to $3 \, nm$ of substrat
 204                               removal
 205                 \end{itemize}
 206                 {\bf
 207                 Simulation parameters $d_v$, $d_r$ and $n$ control the
 208                 diffusion and sputtering process.}
 209   \end{pbox}
 210   \vspace{-1cm}
 211   \begin{pbox}
 212         \section*{Comparison of experiment and simulation}
 213          \begin{center}
 214                 \includegraphics[width=25cm]{dosis_entwicklung_ng_e_1-2.eps}
 215         \end{center}
 216         \begin{center}
 217                 \includegraphics[width=25cm]{dosis_entwicklung_ng_e_2-2.eps}
 218         \end{center}
 219         Simulation parameters:\\
 220         $p_b=0.01$, $p_c=0.001$, $p_s=0.0001$, $d_r=0.05$, $d_v=1 \times 10^6$.
 221         \\[0.7cm]{\bf Conclusion:}
 222         \begin{itemize}
 223                 \item Essentially conforming formation and growth of the
 224                       continuous amorphous layer
 225                 \item Lamellar precipitates and their evolution at the upper
 226                       a/c interface with increasing dose is reproduced
 227         \end{itemize}
 228         {\bf\color{red} Simulation is able to model the whole
 229                         depth region affected by the
 230                         irradiation process}
 231   \end{pbox}
 232 \end{pcolumn}
 233 \begin{pcolumn}
 234
 235   \begin{pbox}
 236         \section*{Structural/compositional information}
 237         \begin{minipage}[t]{0.57\textwidth}
 238                 \includegraphics[height=15cm=]{ac_cconc_ver2_e.eps}
 239                 \begin{itemize}
 240                         \item Fluctuation of the carbon concentration in the
 241                               region of the lamellae
 242                         \item Saturation limit of carbon in c-$Si$ under given
 243                               implantation conditions between $8$ and
 244                               $10 \, at. \%$
 245                 \end{itemize}
 246         \end{minipage}
 247         \begin{minipage}[t]{0.43\textwidth}
 248                 \includegraphics[height=15cm]{97_98_ng_e.eps}
 249                 \begin{itemize}
 250                         \item Complementarily arranged and alternating sequence
 251                               of layers with high and low amount of amorphous
 252                               regions
 253                         \item Carbon accumulation in the amorphous phase
 254                 \end{itemize}
 255         \end{minipage}
 256   \end{pbox}
 257   \vspace{-1cm}
 258   \begin{pbox}
 259         \section*{Recipe:\\
 260                   Thick films of ordered lamellar structure}
 261         \begin{minipage}{0.33\textwidth}
 262                 {\bf Prerequisites:}\\
 263                 Crystalline silicon target with a nearly constant carbon
 264                 concentration at $10 \, at. \%$ in a $500 \, nm$ thick
 265                 surface layer
 266         \end{minipage}
 267         \begin{minipage}{0.65\textwidth}
 268                 \begin{center}
 269                         \includegraphics[width=15cm]{multiple_impl_cp_e.eps}
 270                 \end{center}
 271         \end{minipage}
 272         {\bf Creation:}
 273         \begin{itemize}
 274                 \item multiple energy ($180$-$10 \, keV$) $C^+$ $\rightarrow$
 275                       $Si$ implantation
 276                 \item $T=500 \, ^{\circ} \mathrm{C}$, to prevent amorphisation
 277         \end{itemize}
 278         \vspace{1cm}
 279         {\bf Stiring up:}\\[0.5cm]
 280         2nd $2 \, MeV$ $C^+$ $\rightarrow$ $Si$ implantation step at
 281         $150 \, ^{\circ} \mathrm{C}$
 282         \begin{itemize}
 283                 \item This does not significantly change the carbon
 284                       concentration in the top $500 \, nm$
 285                 \item Nearly constant energy loss in the affected depth region
 286         \end{itemize}
 287         \vspace{1cm}
 288         {\bf Result:}
 289         \vspace{0.7cm}
 290         \begin{center}
 291                 \includegraphics[width=25cm]{multiple_impl_e.eps}
 292         \end{center}
 293         \begin{itemize}
 294                 \item Already ordered structures after $100 \times 10^6$ steps
 295                       corresponding to a dose of $D=2.7 \times 10^{17} cm^{-2}$
 296                 \item More defined structures with increasing dose
 297         \end{itemize}
 298         {\bf\color{blue} Starting point for materials showing strong\\
 299                         photoluminescence}\\
 300         {\scriptsize Dihu Chen et al. Opt. Mater. 23 (2003) 65.}
 301   \end{pbox}
 302   \vspace{-1cm}
 303   \begin{pbox}
 304         \section*{Conclusions}
 305                 \begin{itemize}
 306                         \item Observation of self-organised nanometric
 307                               precipitates by ion irradiation
 308                         \item Model proposed describing the seoforganisation
 309                               process
 310                         \item Model implemented to a Monte Carlo simulation code
 311                         \item Simulation is able to reproduce experimental
 312                               observations
 313                         \item Modelling of the complete depth region affected
 314                               by the irradiation process
 315                         \item Precipitation process gets traceable by simulation
 316                         \item Detailed structural/compositional information
 317                               available by simulation
 318                         \item Recipe proposed for the formation of broad
 319                               distributions of lamellar structure
 320                 \end{itemize}
 321   \end{pbox}
 322
 323 \end{pcolumn}
 324 \end{poster}
 325 \end{document}
 326