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}
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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: 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/sic_prec_temp.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
 484 \end{slide}
 485
 486 \begin{slide}
 487
 488  {\large\bf
 489   Summary / Outlook
 490  }
 491
 492 \vspace{24pt}
 493
 494 \begin{itemize}
 495  \item Importance of understanding C in Si
 496  \item Interstitial configurations in silicon using the Albe potential
 497  \item Indication of SiC precipitation
 498 \end{itemize}
 499
 500 \vspace{16pt}
 501
 502 \begin{itemize}
 503  \item Displacement and stress calculations
 504  \item Diffusion dependence of temperature and carbon concentration
 505  \item Analyzing results of the precipitation simulation runs
 506  \item Analyzing self-designed Si/SiC interface
 507 \end{itemize}
 508
 509 \end{slide}
 510
 511 \end{document}
 512