posic/talks/dpg_2008.tex

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  27 \graphicspath{{../img/}}
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  29 \usepackage[setpagesize=false]{hyperref}
  30
  31 \usepackage{semcolor}
  32 \usepackage{semlayer}           % Seminar overlays
  33 \usepackage{slidesec}           % Seminar sections and list of slides
  34
  35 \input{seminar.bug}             % Official bugs corrections
  36 \input{seminar.bg2}             % Unofficial bugs corrections
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  38 \articlemag{1}
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  40 \special{landscape}
  41
  42 \begin{document}
  43
  44 \extraslideheight{10in}
  45 \slideframe{none}
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  48
  49 % specify width and height
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  61
  62 % itemize level ii
  63 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
  64
  65 % topic
  66
  67 \begin{slide}
  68 \begin{center}
  69
  70  \vspace{16pt}
  71
  72  {\LARGE\bf
  73   Molecular dynamics simulation study\\
  74   of the silicon carbide precipitation process
  75  }
  76
  77  \vspace{24pt}
  78
  79  \textsc{\small \underline{F. Zirkelbach}$^1$, J. K. N. Lindner$^1$,
  80          K. Nordlund$^2$, B. Stritzker$^1$}\\
  81
  82  \vspace{32pt}
  83
  84  \begin{minipage}{2.0cm}
  85   \begin{center}
  86   \includegraphics[height=1.6cm]{uni-logo.eps}
  87   \end{center}
  88  \end{minipage}
  89  \begin{minipage}{8.0cm}
  90   \begin{center}
  91    {\footnotesize
  92     $^1$ Experimentalphysik IV, Institut f"ur Physik,\\
  93          Universit"at Augsburg, Universit"atsstr. 1,\\
  94          D-86135 Augsburg, Germany
  95    }
  96   \end{center}
  97  \end{minipage}
  98  \begin{minipage}{2.3cm}
  99   \begin{center}
 100   \includegraphics[height=1.5cm]{Lehrstuhl-Logo.eps}
 101   \end{center}
 102  \end{minipage}
 103
 104  \vspace{16pt}
 105
 106  \begin{minipage}{4.0cm}
 107   \begin{center}
 108   \includegraphics[height=1.6cm]{logo_eng.eps}
 109   \end{center}
 110  \end{minipage}
 111  \begin{minipage}{8.0cm}
 112   \begin{center}
 113   {\footnotesize
 114    $^2$ Accelerator Laboratory, Department of Physical Sciences,\\
 115    University of Helsinki, Pietari Kalmink. 2,\\
 116    00014 Helsinki, Finland
 117   }
 118   \end{center}
 119  \end{minipage}
 120 \end{center}
 121 \end{slide}
 122
 123 % contents
 124
 125 % no contents for such a short talk!
 126
 127 % start of contents
 128
 129 \begin{slide}
 130
 131  {\large\bf
 132   Motivation / Introduction
 133  }
 134
 135  \vspace{16pt}
 136
 137  Reasons for understanding the SiC precipitation process:
 138
 139  \begin{itemize}
 140   \item 3C-SiC wide band gap semiconductor formation
 141   \item Strained Si (no precipitation wanted!)
 142  \end{itemize}
 143
 144  \vspace{16pt}
 145
 146  Si / 3C-SiC facts:
 147
 148  \begin{minipage}{8cm}
 149  \begin{itemize}
 150   \item Unit cell:
 151         \begin{itemize}
 152          \item {\color{orange}fcc} $+$
 153          \item {\color{gray}fcc shifted $1/4$ of volume diagonal}
 154         \end{itemize}
 155   \item Lattice constants: $4a_{Si}\approx5a_{SiC}$
 156   \item Silicon density:
 157         \[
 158         \frac{n_{SiC}}{n_{Si}}=
 159         \frac{4/a_{SiC}^3}{8/a_{Si}^3}=
 160         \frac{5^3}{2\cdot4^3}={\color{cyan}97,66}\,\%
 161         \]
 162  \end{itemize}
 163  \end{minipage}
 164  \hspace{8pt}
 165  \begin{minipage}{4cm}
 166  \includegraphics[width=4cm]{sic_unit_cell.eps}
 167  \end{minipage}
 168
 169 \end{slide}
 170
 171  \small
 172 \begin{slide}
 173
 174  {\large\bf
 175   Motivation / Introduction
 176  }
 177
 178  \small
 179  \vspace{6pt}
 180
 181  Supposed conversion mechanism of heavily carbon doped Si into SiC:
 182
 183  \vspace{8pt}
 184
 185  \begin{minipage}{3.8cm}
 186  \includegraphics[width=3.7cm]{sic_prec_seq_01.eps}
 187  \end{minipage}
 188  \hspace{0.6cm}
 189  \begin{minipage}{3.8cm}
 190  \includegraphics[width=3.7cm]{sic_prec_seq_02.eps}
 191  \end{minipage}
 192  \hspace{0.6cm}
 193  \begin{minipage}{3.8cm}
 194  \includegraphics[width=3.7cm]{sic_prec_seq_03.eps}
 195  \end{minipage}
 196
 197  \vspace{8pt}
 198
 199  \begin{minipage}{3.8cm}
 200  Formation of C-Si dumbbells on regular c-Si lattice sites
 201  \end{minipage}
 202  \hspace{0.6cm}
 203  \begin{minipage}{3.8cm}
 204  Agglomeration into large clusters (embryos)\\
 205  \end{minipage}
 206  \hspace{0.6cm}
 207  \begin{minipage}{3.8cm}
 208  Precipitation of 3C-SiC + Creation of interstitials\\
 209  \end{minipage}
 210
 211  \vspace{12pt}
 212
 213  Experimentally observed:
 214  \begin{itemize}
 215   \item Minimal diameter of precipitation: 4 - 5 nm
 216   \item (hkl)-planes identical for Si and SiC
 217  \end{itemize}
 218
 219 \end{slide}
 220
 221 \begin{slide}
 222
 223  {\large\bf
 224   Simulation details
 225  }
 226
 227  \vspace{12pt}
 228
 229  MD basics:
 230  \begin{itemize}
 231   \item Microscopic description of N particle system
 232   \item Analytical interaction potential
 233   \item Hamilton's equations of motion as propagation rule\\
 234         in 6N-dimensional phase space
 235   \item Observables obtained by time average
 236  \end{itemize}
 237
 238  \vspace{12pt}
 239
 240  Application details:
 241  \begin{itemize}
 242   \item Integrator: Velocity Verlet, timestep: $1\, fs$
 243   \item Ensemble control: NVT, Berendsen thermostat, $\tau=100.0$
 244   \item Potential: Tersoff-like bond order potential\\
 245         \[
 246         E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
 247         \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
 248         \]
 249         \begin{center}
 250         {\scriptsize P. Erhart and K. Albe. Phys. Rev. B 71 (2005) 035211}
 251         \end{center}
 252  \end{itemize}
 253
 254  \begin{picture}(0,0)(-240,-70)
 255   \includegraphics[width=5cm]{tersoff_angle.eps}
 256  \end{picture}
 257
 258 \end{slide}
 259
 260 \begin{slide}
 261
 262  {\large\bf
 263   Simulation details
 264  }
 265
 266  \vspace{20pt}
 267
 268  Interstitial experiments:
 269
 270  \vspace{12pt}
 271
 272  \begin{itemize}
 273   \item Initial configuration: $9\times9\times9$ unit cells Si
 274   \item Periodic boundary conditions
 275   \item $T=0 \, K$
 276   \item Insertion of Si / C atom at
 277         \begin{itemize}
 278          \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
 279          \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
 280          \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
 281                $\rightarrow$ {\color{magenta}110 dumbbell}
 282          \item random positions (critical distance check)
 283         \end{itemize}
 284   \item Relaxation time: $2\, ps$
 285   \item Optional heating-up
 286  \end{itemize}
 287
 288  \begin{picture}(0,0)(-210,-45)
 289   \includegraphics[width=6cm]{unit_cell.eps}
 290  \end{picture}
 291
 292 \end{slide}
 293
 294 \begin{slide}
 295
 296  {\large\bf
 297   Results
 298  } - Si self-interstitial experiments
 299
 300  \small
 301
 302  \begin{minipage}[t]{4.3cm}
 303  \underline{Tetrahedral}\\
 304  $E_f=3.41\, eV$\\
 305  \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
 306  \end{minipage}
 307  \begin{minipage}[t]{4.3cm}
 308  \underline{110 dumbbell}\\
 309  $E_f=4.39\, eV$\\
 310  \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
 311  \end{minipage}
 312  \begin{minipage}[t]{4.3cm}
 313  \underline{Hexagonal} \hspace{4pt}
 314  \href{../video/si_self_int_hexa.avi}{$\rhd$}\\
 315  $E_f^{\star}\approx4.48\, eV$ (unstable!)\\
 316  \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
 317  \end{minipage}
 318
 319  \underline{Random insertion}
 320
 321  \begin{minipage}{4.3cm}
 322  $E_f=3.97\, eV$\\
 323  \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
 324  \end{minipage}
 325  \begin{minipage}{4.3cm}
 326  $E_f=3.75\, eV$\\
 327  \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
 328  \end{minipage}
 329  \begin{minipage}{4.3cm}
 330  $E_f=3.56\, eV$\\
 331  \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
 332  \end{minipage}
 333
 334 \end{slide}
 335
 336 \begin{slide}
 337
 338  {\large\bf
 339   Results
 340  } - Carbon interstitial experiments
 341
 342  \small
 343
 344  \begin{minipage}[t]{4.3cm}
 345  \underline{Tetrahedral}\\
 346  $E_f=2.67\, eV$\\
 347  \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
 348  \end{minipage}
 349  \begin{minipage}[t]{4.3cm}
 350  \underline{110 dumbbell}\\
 351  $E_f=1.76\, eV$\\
 352  \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
 353  \end{minipage}
 354  \begin{minipage}[t]{4.3cm}
 355  \underline{Hexagonal} \hspace{4pt}
 356  \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
 357  $E_f^{\star}\approx5.6\, eV$ (unstable!)\\
 358  \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
 359  \end{minipage}
 360
 361  \underline{Random insertion}
 362
 363  \footnotesize
 364
 365 \begin{minipage}[t]{3.3cm}
 366    $E_f=0.47\, eV$\\
 367    \includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps}
 368    \begin{picture}(0,0)(-15,-3)
 369     001 dumbbell
 370    \end{picture}
 371 \end{minipage}
 372 \begin{minipage}[t]{3.3cm}
 373    $E_f=1.62\, eV$\\
 374    \includegraphics[width=3.2cm]{c_in_si_int_rand_162_0.eps}
 375 \end{minipage}
 376 \begin{minipage}[t]{3.3cm}
 377    $E_f=2.39\, eV$ \hspace{2pt}
 378    \href{../video/c_in_si_int_rand_239.avi}{$\rhd$}\\
 379    \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps}
 380 \end{minipage}
 381 \begin{minipage}[t]{3.0cm}
 382    $E_f=3.41\, eV$ \hspace{2pt}
 383    \href{../video/c_in_si_int_rand_341.avi}{$\rhd$}\\
 384    \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps}
 385 \end{minipage}
 386
 387 \end{slide}
 388
 389 \begin{slide}
 390
 391  {\large\bf
 392   Simulation details
 393  }
 394
 395  \small
 396
 397  \vspace{8pt}
 398
 399  SiC precipitation experiments:
 400
 401  \vspace{8pt}
 402
 403  \begin{pspicture}(0,0)(12,8)
 404   % nodes
 405   \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
 406    \parbox{7cm}{
 407    \begin{itemize}
 408     \item Initial configuration: $31\times31\times31$ unit cells Si
 409     \item Periodic boundary conditions
 410     \item $T=450\, ^{\circ}C$
 411     \item Equilibration of $E_{kin}$ and $E_{pot}$ for $600\, fs$
 412    \end{itemize}
 413   }}}}
 414   \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{
 415    \parbox{7cm}{
 416    Insertion of $6000$ carbon atoms at constant\\
 417    temperature into:
 418    \begin{itemize}
 419     \item Total simulation volume {\pnode{in1}}
 420     \item Volume of minimal SiC precipitation {\pnode{in2}}
 421     \item Volume of necessary amount of Si {\pnode{in3}}
 422    \end{itemize}
 423   }}}}
 424   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
 425    \parbox{3.5cm}{
 426    Cooling down to $20\, ^{\circ}C$
 427   }}}}
 428   \ncline[]{->}{init}{insert}
 429   \ncline[]{->}{insert}{cool}
 430   \psframe[fillstyle=solid,fillcolor=white](7.5,1.8)(13.5,7.8)
 431   \psframe[fillstyle=solid,fillcolor=lightgray](9,3.3)(12,6.3)
 432   \psframe[fillstyle=solid,fillcolor=gray](9.25,3.55)(11.75,6.05)
 433   \rput(7.9,4.8){\pnode{ins1}}
 434   \rput(9.22,4.4){\pnode{ins2}}
 435   \rput(10.5,4.8){\pnode{ins3}}
 436   \ncline[]{->}{in1}{ins1}
 437   \ncline[]{->}{in2}{ins2}
 438   \ncline[]{->}{in3}{ins3}
 439  \end{pspicture}
 440
 441 \end{slide}
 442
 443 \begin{slide}
 444
 445  {\large\bf
 446   Results
 447  }
 448
 449  SiC-precipitation experiments:
 450
 451  \begin{minipage}[t]{6.3cm}
 452   \includegraphics[width=6.0cm]{../plot/sic_prec_energy.ps}
 453   \includegraphics[width=6.0cm]{../plot/sic_prec_temp.ps}
 454  \end{minipage}
 455  \begin{minipage}[t]{6cm}
 456   \includegraphics[width=6.0cm]{../plot/sic_pc.ps}
 457   \includegraphics[width=6.0cm]{../plot/sic_prec_pc.ps}
 458  \end{minipage}
 459
 460 \end{slide}
 461
 462 \begin{slide}
 463
 464  {\large\bf
 465   Summary / Outlook
 466  }
 467
 468 \vspace{24pt}
 469
 470 \begin{itemize}
 471  \item Importance of understanding C in Si
 472  \item Interstitial configurations in silicon using the Albe potential
 473  \item Indication of SiC precipitation
 474 \end{itemize}
 475
 476 \vspace{16pt}
 477
 478 \begin{itemize}
 479  \item Displacement and stress calculations
 480  \item Diffusion dependence of temperature and carbon concentration
 481  \item Analyzing results of the precipitation simulation runs
 482  \item Analyzing self-designed Si/SiC interface
 483 \end{itemize}
 484
 485 \end{slide}
 486
 487 \end{document}
 488