posic/talks/dpg_2008.tex

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  27 \graphicspath{{../img/}}
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  29 \usepackage[setpagesize=false]{hyperref}
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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
  37
  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
  50 \slidewidth 27.7cm
  51 \slideheight 19.1cm
  52
  53 % shift it into visual area properly
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  57 \newcommand{\ham}{\mathcal{H}}
  58 \newcommand{\pot}{\mathcal{V}}
  59 \newcommand{\foo}{\mathcal{U}}
  60 \newcommand{\vir}{\mathcal{W}}
  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:
 156         \[
 157         4a_{Si}\approx5a_{SiC}
 158         \]
 159   \item Silicon density:
 160         \[
 161         \frac{n_{SiC}}{n_{Si}}=97,66\,\%
 162         \]
 163  \end{itemize}
 164  \end{minipage}
 165  \hspace{8pt}
 166  \begin{minipage}{4cm}
 167  \includegraphics[width=4cm]{sic_unit_cell.eps}
 168  \end{minipage}
 169
 170 \end{slide}
 171
 172  \small
 173 \begin{slide}
 174
 175  {\large\bf
 176   Motivation / Introduction
 177  }
 178
 179  \small
 180  \vspace{6pt}
 181
 182  Supposed conversion mechanism of heavily carbon doped Si into SiC:
 183
 184  \vspace{8pt}
 185
 186  \begin{minipage}{3.8cm}
 187  \includegraphics[width=3.7cm]{sic_prec_seq_01.eps}
 188  \end{minipage}
 189  \hspace{0.6cm}
 190  \begin{minipage}{3.8cm}
 191  \includegraphics[width=3.7cm]{sic_prec_seq_02.eps}
 192  \end{minipage}
 193  \hspace{0.6cm}
 194  \begin{minipage}{3.8cm}
 195  \includegraphics[width=3.7cm]{sic_prec_seq_03.eps}
 196  \end{minipage}
 197
 198  \vspace{8pt}
 199
 200  \begin{minipage}{3.8cm}
 201  Formation of C-Si dumbbells on regular c-Si lattice sites
 202  \end{minipage}
 203  \hspace{0.6cm}
 204  \begin{minipage}{3.8cm}
 205  Agglomeration into large clusters (embryos)\\
 206  \end{minipage}
 207  \hspace{0.6cm}
 208  \begin{minipage}{3.8cm}
 209  Precipitation of 3C-SiC + Creation of interstitials\\
 210  \end{minipage}
 211
 212  \vspace{12pt}
 213
 214  Experimentally observed:
 215  \begin{itemize}
 216   \item Minimal diameter of precipitation: 4 - 5 nm
 217   \item Equal orientation of Si and SiC (hkl)-planes
 218  \end{itemize}
 219
 220 \end{slide}
 221
 222 \begin{slide}
 223
 224  {\large\bf
 225   Simulation details
 226  }
 227
 228  \vspace{12pt}
 229
 230  MD basics:
 231  \begin{itemize}
 232   \item Microscopic description of N particle system
 233   \item Analytical interaction potential
 234   \item Hamilton's equations of motion as propagation rule\\
 235         in 6N-dimensional phase space
 236   \item Observables obtained by time average
 237  \end{itemize}
 238
 239  \vspace{12pt}
 240
 241  Application details:
 242  \begin{itemize}
 243   \item Integrator: Velocity Verlet, timestep: $1\, fs$
 244   \item Ensemble: NVT, Berendsen thermostat, $\tau=100.0$
 245   \item Potential: Tersoff-like bond order potential\\
 246         \[
 247         E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
 248         \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
 249         \]
 250         \begin{center}
 251         {\scriptsize P. Erhart and K. Albe. Phys. Rev. B 71 (2005) 035211}
 252         \end{center}
 253  \end{itemize}
 254
 255  \begin{picture}(0,0)(-240,-70)
 256   \includegraphics[width=5cm]{tersoff_angle.eps}
 257  \end{picture}
 258
 259 \end{slide}
 260
 261 \begin{slide}
 262
 263  {\large\bf
 264   Simulation details
 265  }
 266
 267  \vspace{8pt}
 268
 269  Interstitial simulations:
 270
 271  \vspace{8pt}
 272
 273  \begin{pspicture}(0,0)(7,8)
 274   \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
 275    \parbox{7cm}{
 276    \begin{itemize}
 277     \item Initial configuration: $9\times9\times9$ unit cells Si
 278     \item Periodic boundary conditions
 279     \item $T=0 \, K$
 280    \end{itemize}
 281   }}}}
 282 \rput(3.5,3.5){\rnode{insert}{\psframebox{
 283  \parbox{7cm}{
 284   Insertion of C / Si atom:
 285   \begin{itemize}
 286    \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
 287    \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
 288    \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
 289          $\rightarrow$ {\color{magenta}110 dumbbell}
 290    \item random positions (critical distance check)
 291   \end{itemize}
 292   }}}}
 293   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
 294    \parbox{3.5cm}{
 295    Relaxation time: $2\, ps$
 296   }}}}
 297   \ncline[]{->}{init}{insert}
 298   \ncline[]{->}{insert}{cool}
 299  \end{pspicture}
 300
 301  \begin{picture}(0,0)(-210,-45)
 302   \includegraphics[width=6cm]{unit_cell.eps}
 303  \end{picture}
 304
 305 \end{slide}
 306
 307 \begin{slide}
 308
 309  {\large\bf
 310   Results
 311  } - Si self-interstitial runs
 312
 313  \small
 314
 315  \begin{minipage}[t]{4.3cm}
 316  \underline{Tetrahedral}\\
 317  $E_f=3.41\, eV$\\
 318  \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
 319  \end{minipage}
 320  \begin{minipage}[t]{4.3cm}
 321  \underline{110 dumbbell}\\
 322  $E_f=4.39\, eV$\\
 323  \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
 324  \end{minipage}
 325  \begin{minipage}[t]{4.3cm}
 326  \underline{Hexagonal} \hspace{4pt}
 327  \href{../video/si_self_int_hexa.avi}{$\rhd$}\\
 328  $E_f^{\star}\approx4.48\, eV$ (unstable!)\\
 329  \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
 330  \end{minipage}
 331
 332  \underline{Random insertion}
 333
 334  \begin{minipage}{4.3cm}
 335  $E_f=3.97\, eV$\\
 336  \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
 337  \end{minipage}
 338  \begin{minipage}{4.3cm}
 339  $E_f=3.75\, eV$\\
 340  \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
 341  \end{minipage}
 342  \begin{minipage}{4.3cm}
 343  $E_f=3.56\, eV$\\
 344  \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
 345  \end{minipage}
 346
 347 \end{slide}
 348
 349 \begin{slide}
 350
 351  {\large\bf
 352   Results
 353  } - Carbon interstitial runs
 354
 355  \small
 356
 357  \begin{minipage}[t]{4.3cm}
 358  \underline{Tetrahedral}\\
 359  $E_f=2.67\, eV$\\
 360  \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
 361  \end{minipage}
 362  \begin{minipage}[t]{4.3cm}
 363  \underline{110 dumbbell}\\
 364  $E_f=1.76\, eV$\\
 365  \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
 366  \end{minipage}
 367  \begin{minipage}[t]{4.3cm}
 368  \underline{Hexagonal} \hspace{4pt}
 369  \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
 370  $E_f^{\star}\approx5.6\, eV$ (unstable!)\\
 371  \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
 372  \end{minipage}
 373
 374  \underline{Random insertion}
 375
 376  \footnotesize
 377
 378 \begin{minipage}[t]{3.3cm}
 379    $E_f=0.47\, eV$\\
 380    \includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps}
 381    \begin{picture}(0,0)(-15,-3)
 382     001 dumbbell
 383    \end{picture}
 384 \end{minipage}
 385 \begin{minipage}[t]{3.3cm}
 386    $E_f=1.62\, eV$\\
 387    \includegraphics[width=3.2cm]{c_in_si_int_rand_162_0.eps}
 388 \end{minipage}
 389 \begin{minipage}[t]{3.3cm}
 390    $E_f=2.39\, eV$\\
 391    \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps}
 392 \end{minipage}
 393 \begin{minipage}[t]{3.0cm}
 394    $E_f=3.41\, eV$\\
 395    \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps}
 396 \end{minipage}
 397
 398 \end{slide}
 399
 400 \begin{slide}
 401
 402  {\large\bf
 403   Simulation details
 404  }
 405
 406  \small
 407
 408  \vspace{8pt}
 409
 410  SiC precipitation simulations:
 411
 412  \vspace{8pt}
 413
 414  \begin{pspicture}(0,0)(12,8)
 415   % nodes
 416   \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
 417    \parbox{7cm}{
 418    \begin{itemize}
 419     \item Initial configuration: $31\times31\times31$ unit cells Si
 420     \item Periodic boundary conditions
 421     \item $T=450\, ^{\circ}C$
 422     \item Equilibration of $E_{kin}$ and $E_{pot}$ for $600\, fs$
 423    \end{itemize}
 424   }}}}
 425   \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{
 426    \parbox{7cm}{
 427    Insertion of $6000$ carbon atoms at constant\\
 428    temperature into:
 429    \begin{itemize}
 430     \item Total simulation volume {\pnode{in1}}
 431     \item Volume of minimal SiC precipitation {\pnode{in2}}
 432     \item Volume of necessary amount of Si {\pnode{in3}}
 433    \end{itemize}
 434   }}}}
 435   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
 436    \parbox{3.5cm}{
 437    Cooling down to $20\, ^{\circ}C$
 438   }}}}
 439   \ncline[]{->}{init}{insert}
 440   \ncline[]{->}{insert}{cool}
 441   \psframe[fillstyle=solid,fillcolor=white](7.5,1.8)(13.5,7.8)
 442   \psframe[fillstyle=solid,fillcolor=lightgray](9,3.3)(12,6.3)
 443   \psframe[fillstyle=solid,fillcolor=gray](9.25,3.55)(11.75,6.05)
 444   \rput(7.9,4.8){\pnode{ins1}}
 445   \rput(9.22,4.4){\pnode{ins2}}
 446   \rput(10.5,4.8){\pnode{ins3}}
 447   \ncline[]{->}{in1}{ins1}
 448   \ncline[]{->}{in2}{ins2}
 449   \ncline[]{->}{in3}{ins3}
 450  \end{pspicture}
 451
 452 \end{slide}
 453
 454 \begin{slide}
 455
 456  {\large\bf
 457   Very first results of the SiC precipitation runs
 458  }
 459
 460  \footnotesize
 461
 462  \begin{minipage}[b]{6.9cm}
 463   \includegraphics[width=6.3cm]{../plot/sic_prec_energy.ps}
 464   \includegraphics[width=6.3cm]{../plot/sic_prec_temp.ps}
 465  \end{minipage}
 466  \begin{minipage}[b]{5.5cm}
 467   \begin{itemize}
 468    \item {\color{red} Total simulation volume}
 469    \item {\color{green} Volume of minimal SiC precipitation}
 470    \item {\color{blue} Volume of necessary amount of Si}
 471   \end{itemize}
 472   \vspace{40pt}
 473   \includegraphics[width=6.3cm]{../plot/foo150.ps}
 474  \end{minipage}
 475
 476 \end{slide}
 477
 478 \begin{slide}
 479
 480  {\large\bf
 481   Very first results of the SiC precipitation runs
 482  }
 483
 484  \begin{minipage}[t]{6.9cm}
 485   \includegraphics[width=6.3cm]{../plot/sic_pc.ps}
 486   \includegraphics[width=6.3cm]{../plot/foo_end.ps}
 487   \hspace{12pt}
 488  \end{minipage}
 489  \begin{minipage}[c]{5.5cm}
 490   \includegraphics[width=6.0cm]{sic_si-c-n.eps}
 491  \end{minipage}
 492
 493 \end{slide}
 494
 495 \begin{slide}
 496
 497  {\large\bf
 498   Summary / Outlook
 499  }
 500
 501 \vspace{24pt}
 502
 503 \begin{itemize}
 504  \item Importance of understanding the SiC precipitation mechanism
 505  \item Interstitial configurations in silicon using the Albe potential
 506  \item Indication of SiC precipitation
 507 \end{itemize}
 508
 509 \vspace{24pt}
 510
 511 \begin{itemize}
 512  \item Displacement and stress calculations
 513  \item Refinement of simulation sequence to create 3C-SiC
 514  \item Analyzing self-designed Si/SiC interface
 515 \end{itemize}
 516
 517 \end{slide}
 518
 519 \end{document}
 520