posic/talks/dpg_2008.tex

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  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}
  46
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  48
  49 % specify width and height
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  51 \slideheight 19.1cm
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  53 % shift it into visual area properly
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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: 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{8pt}
 267
 268  Interstitial experiments:
 269
 270  \vspace{8pt}
 271
 272  \begin{pspicture}(0,0)(7,8)
 273   \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
 274    \parbox{7cm}{
 275    \begin{itemize}
 276     \item Initial configuration: $9\times9\times9$ unit cells Si
 277     \item Periodic boundary conditions
 278     \item $T=0 \, K$
 279    \end{itemize}
 280   }}}}
 281 \rput(3.5,3.5){\rnode{insert}{\psframebox{
 282  \parbox{7cm}{
 283   Insertion of C / Si atom:
 284   \begin{itemize}
 285    \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
 286    \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
 287    \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
 288          $\rightarrow$ {\color{magenta}110 dumbbell}
 289    \item random positions (critical distance check)
 290   \end{itemize}
 291   }}}}
 292   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
 293    \parbox{3.5cm}{
 294    Relaxation time: $2\, ps$
 295   }}}}
 296   \ncline[]{->}{init}{insert}
 297   \ncline[]{->}{insert}{cool}
 298  \end{pspicture}
 299
 300  \begin{picture}(0,0)(-210,-45)
 301   \includegraphics[width=6cm]{unit_cell.eps}
 302  \end{picture}
 303
 304 \end{slide}
 305
 306 \begin{slide}
 307
 308  {\large\bf
 309   Results
 310  } - Si self-interstitial experiments
 311
 312  \small
 313
 314  \begin{minipage}[t]{4.3cm}
 315  \underline{Tetrahedral}\\
 316  $E_f=3.41\, eV$\\
 317  \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
 318  \end{minipage}
 319  \begin{minipage}[t]{4.3cm}
 320  \underline{110 dumbbell}\\
 321  $E_f=4.39\, eV$\\
 322  \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
 323  \end{minipage}
 324  \begin{minipage}[t]{4.3cm}
 325  \underline{Hexagonal} \hspace{4pt}
 326  \href{../video/si_self_int_hexa.avi}{$\rhd$}\\
 327  $E_f^{\star}\approx4.48\, eV$ (unstable!)\\
 328  \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
 329  \end{minipage}
 330
 331  \underline{Random insertion}
 332
 333  \begin{minipage}{4.3cm}
 334  $E_f=3.97\, eV$\\
 335  \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
 336  \end{minipage}
 337  \begin{minipage}{4.3cm}
 338  $E_f=3.75\, eV$\\
 339  \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
 340  \end{minipage}
 341  \begin{minipage}{4.3cm}
 342  $E_f=3.56\, eV$\\
 343  \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
 344  \end{minipage}
 345
 346 \end{slide}
 347
 348 \begin{slide}
 349
 350  {\large\bf
 351   Results
 352  } - Carbon interstitial experiments
 353
 354  \small
 355
 356  \begin{minipage}[t]{4.3cm}
 357  \underline{Tetrahedral}\\
 358  $E_f=2.67\, eV$\\
 359  \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
 360  \end{minipage}
 361  \begin{minipage}[t]{4.3cm}
 362  \underline{110 dumbbell}\\
 363  $E_f=1.76\, eV$\\
 364  \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
 365  \end{minipage}
 366  \begin{minipage}[t]{4.3cm}
 367  \underline{Hexagonal} \hspace{4pt}
 368  \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
 369  $E_f^{\star}\approx5.6\, eV$ (unstable!)\\
 370  \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
 371  \end{minipage}
 372
 373  \underline{Random insertion}
 374
 375  \footnotesize
 376
 377 \begin{minipage}[t]{3.3cm}
 378    $E_f=0.47\, eV$\\
 379    \includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps}
 380    \begin{picture}(0,0)(-15,-3)
 381     001 dumbbell
 382    \end{picture}
 383 \end{minipage}
 384 \begin{minipage}[t]{3.3cm}
 385    $E_f=1.62\, eV$\\
 386    \includegraphics[width=3.2cm]{c_in_si_int_rand_162_0.eps}
 387 \end{minipage}
 388 \begin{minipage}[t]{3.3cm}
 389    $E_f=2.39\, eV$ \hspace{2pt}
 390    \href{../video/c_in_si_int_rand_239.avi}{$\rhd$}\\
 391    \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps}
 392 \end{minipage}
 393 \begin{minipage}[t]{3.0cm}
 394    $E_f=3.41\, eV$ \hspace{2pt}
 395    \href{../video/c_in_si_int_rand_341.avi}{$\rhd$}\\
 396    \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps}
 397 \end{minipage}
 398
 399 \end{slide}
 400
 401 \begin{slide}
 402
 403  {\large\bf
 404   Simulation details
 405  }
 406
 407  \small
 408
 409  \vspace{8pt}
 410
 411  SiC precipitation experiments:
 412
 413  \vspace{8pt}
 414
 415  \begin{pspicture}(0,0)(12,8)
 416   % nodes
 417   \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
 418    \parbox{7cm}{
 419    \begin{itemize}
 420     \item Initial configuration: $31\times31\times31$ unit cells Si
 421     \item Periodic boundary conditions
 422     \item $T=450\, ^{\circ}C$
 423     \item Equilibration of $E_{kin}$ and $E_{pot}$ for $600\, fs$
 424    \end{itemize}
 425   }}}}
 426   \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{
 427    \parbox{7cm}{
 428    Insertion of $6000$ carbon atoms at constant\\
 429    temperature into:
 430    \begin{itemize}
 431     \item Total simulation volume {\pnode{in1}}
 432     \item Volume of minimal SiC precipitation {\pnode{in2}}
 433     \item Volume of necessary amount of Si {\pnode{in3}}
 434    \end{itemize}
 435   }}}}
 436   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
 437    \parbox{3.5cm}{
 438    Cooling down to $20\, ^{\circ}C$
 439   }}}}
 440   \ncline[]{->}{init}{insert}
 441   \ncline[]{->}{insert}{cool}
 442   \psframe[fillstyle=solid,fillcolor=white](7.5,1.8)(13.5,7.8)
 443   \psframe[fillstyle=solid,fillcolor=lightgray](9,3.3)(12,6.3)
 444   \psframe[fillstyle=solid,fillcolor=gray](9.25,3.55)(11.75,6.05)
 445   \rput(7.9,4.8){\pnode{ins1}}
 446   \rput(9.22,4.4){\pnode{ins2}}
 447   \rput(10.5,4.8){\pnode{ins3}}
 448   \ncline[]{->}{in1}{ins1}
 449   \ncline[]{->}{in2}{ins2}
 450   \ncline[]{->}{in3}{ins3}
 451  \end{pspicture}
 452
 453 \end{slide}
 454
 455 \begin{slide}
 456
 457  {\large\bf
 458   Very first results of the SiC precipitation experiments
 459  }
 460
 461  \begin{minipage}[t]{6.3cm}
 462   \includegraphics[width=6.0cm]{../plot/sic_prec_energy.ps}
 463   \includegraphics[width=6.0cm]{../plot/sic_prec_temp.ps}
 464  \end{minipage}
 465  \begin{minipage}[t]{6.3cm}
 466   \includegraphics[width=6.0cm]{../plot/sic_prec_energy_zoom.ps}
 467   \includegraphics[width=6.0cm]{../plot/foo150.ps}
 468  \end{minipage}
 469
 470 \end{slide}
 471
 472 \begin{slide}
 473
 474  {\large\bf
 475   Very first results of the SiC precipitation experiments
 476  }
 477
 478  \begin{minipage}[c]{12cm}
 479   \includegraphics[width=6.0cm]{../plot/sic_pc.ps}
 480   \hspace{4pt}
 481   \includegraphics[width=5.0cm]{sic_si-c-n.eps}
 482  \end{minipage}
 483  \begin{minipage}[c]{12cm}
 484   \includegraphics[width=6.0cm]{../plot/foo_end.ps}
 485   \hspace{4pt}
 486   \includegraphics[width=5.0cm]{foo_end.eps}
 487  \end{minipage}
 488
 489 \end{slide}
 490
 491 \begin{slide}
 492
 493  {\large\bf
 494   Summary / Outlook
 495  }
 496
 497 \vspace{24pt}
 498
 499 \begin{itemize}
 500  \item Importance of understanding the SiC precipitation mechanism
 501  \item Interstitial configurations in silicon using the Albe potential
 502  \item Indication of SiC precipitation
 503 \end{itemize}
 504
 505 \vspace{16pt}
 506
 507 \begin{itemize}
 508  \item Displacement and stress calculations
 509  \item Diffusion dependence of temperature and carbon concentration
 510  \item Analyzing results of the precipitation simulation runs
 511  \item Refinement of simulation sequence to create 3C-SiC
 512  \item Analyzing self-designed Si/SiC interface
 513 \end{itemize}
 514
 515 \end{slide}
 516
 517 \end{document}
 518