posic/talks/mpi_app.tex

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   2 %\documentclass[landscape,semhelv,draft]{seminar}
   3 \documentclass[landscape,semhelv]{seminar}
   4
   5 \usepackage{verbatim}
   6 \usepackage[greek,german]{babel}
   7 \usepackage[latin1]{inputenc}
   8 \usepackage[T1]{fontenc}
   9 \usepackage{amsmath}
  10 \usepackage{latexsym}
  11 \usepackage{ae}
  12
  13 \usepackage{calc}               % Simple computations with LaTeX variables
  14 \usepackage{caption}            % Improved captions
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  16
  17 \usepackage{fancyhdr}           % Headers and footers definitions
  18 \usepackage{fancyvrb}           % Fancy verbatim environments
  19 \usepackage{pstricks}           % PSTricks with the standard color package
  20
  21 \usepackage{pstricks}
  22 \usepackage{pst-node}
  23 \usepackage{pst-grad}
  24
  25 %\usepackage{epic}
  26 %\usepackage{eepic}
  27
  28 \usepackage{layout}
  29
  30 \usepackage{graphicx}
  31 \graphicspath{{../img/}}
  32
  33 \usepackage{miller}
  34
  35 \usepackage[setpagesize=false]{hyperref}
  36
  37 % units
  38 \usepackage{units}
  39
  40 \usepackage{semcolor}
  41 \usepackage{semlayer}           % Seminar overlays
  42 \usepackage{slidesec}           % Seminar sections and list of slides
  43
  44 \input{seminar.bug}             % Official bugs corrections
  45 \input{seminar.bg2}             % Unofficial bugs corrections
  46
  47 \articlemag{1}
  48
  49 \special{landscape}
  50
  51 % font
  52 %\usepackage{cmbright}
  53 %\renewcommand{\familydefault}{\sfdefault}
  54 %\usepackage{mathptmx}
  55
  56 \usepackage{upgreek}
  57
  58 \begin{document}
  59
  60 \extraslideheight{10in}
  61 \slideframe{plain}
  62
  63 \pagestyle{empty}
  64
  65 % specify width and height
  66 \slidewidth 26.3cm
  67 \slideheight 19.9cm
  68
  69 % margin
  70 \def\slidetopmargin{-0.15cm}
  71
  72 \newcommand{\ham}{\mathcal{H}}
  73 \newcommand{\pot}{\mathcal{V}}
  74 \newcommand{\foo}{\mathcal{U}}
  75 \newcommand{\vir}{\mathcal{W}}
  76
  77 % itemize level ii
  78 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
  79
  80 % nice phi
  81 \renewcommand{\phi}{\varphi}
  82
  83 % roman letters
  84 \newcommand{\RM}[1]{\MakeUppercase{\romannumeral #1{}}}
  85
  86 % colors
  87 \newrgbcolor{si-yellow}{.6 .6 0}
  88 \newrgbcolor{hb}{0.75 0.77 0.89}
  89 \newrgbcolor{lbb}{0.75 0.8 0.88}
  90 \newrgbcolor{hlbb}{0.825 0.88 0.968}
  91 \newrgbcolor{lachs}{1.0 .93 .81}
  92
  93 % shortcuts
  94 \newcommand{\si}{Si$_{\text{i}}${}}
  95 \newcommand{\ci}{C$_{\text{i}}${}}
  96 \newcommand{\cs}{C$_{\text{sub}}${}}
  97 \newcommand{\degc}[1]{\unit[#1]{$^{\circ}$C}{}}
  98 \newcommand{\distn}[1]{\unit[#1]{nm}{}}
  99 \newcommand{\dista}[1]{\unit[#1]{\AA}{}}
 100 \newcommand{\perc}[1]{\unit[#1]{\%}{}}
 101
 102 % no vertical centering
 103 %\centerslidesfalse
 104
 105 % layout check
 106 %\layout
 107 \begin{slide}
 108 \center
 109 {\Huge
 110 E\\
 111 F\\
 112 G\\
 113 A B C D E F G H G F E D C B A
 114 G\\
 115 F\\
 116 E\\
 117 }
 118 \end{slide}
 119
 120 % topic
 121
 122 \begin{slide}
 123 \begin{center}
 124
 125  \vspace{16pt}
 126
 127  {\LARGE\bf
 128   Atomistic simulation studies\\[0.2cm]
 129   in the C/Si system
 130  }
 131
 132  \vspace{48pt}
 133
 134  \textsc{Frank Zirkelbach}
 135
 136  \vspace{48pt}
 137
 138  Application talk at the Max Planck Institute for Solid State Research
 139
 140  \vspace{08pt}
 141
 142  Stuttgart, November 2011
 143
 144 \end{center}
 145 \end{slide}
 146
 147 % no vertical centering
 148 \centerslidesfalse
 149
 150 \ifnum1=0
 151
 152 % intro
 153
 154 \begin{slide}
 155
 156 %{\large\bf
 157 % Phase diagram of the C/Si system\\
 158 %}
 159
 160 \vspace*{0.2cm}
 161
 162 \begin{minipage}{6.5cm}
 163 \includegraphics[width=6.5cm]{si-c_phase.eps}
 164 \begin{center}
 165 {\tiny
 166 R. I. Scace and G. A. Slack, J. Chem. Phys. 30, 1551 (1959)
 167 }
 168 \end{center}
 169 \begin{pspicture}(0,0)(0,0)
 170 \psellipse[linecolor=blue,linewidth=0.1cm](3.55,4.0)(0.5,2.9)
 171 \end{pspicture}
 172 \end{minipage}
 173 \begin{minipage}{6cm}
 174 {\bf Phase diagram of the C/Si system}\\[0.2cm]
 175 {\color{blue}Stoichiometric composition}
 176 \begin{itemize}
 177 \item only chemical stable compound
 178 \item wide band gap semiconductor\\
 179       \underline{silicon carbide}, SiC
 180 \end{itemize}
 181 \end{minipage}
 182
 183 \end{slide}
 184
 185 % motivation / properties / applications of silicon carbide
 186
 187 \begin{slide}
 188
 189 \vspace*{1.8cm}
 190
 191 \small
 192
 193 \begin{pspicture}(0,0)(13.5,5)
 194
 195  \psframe*[linecolor=hb](-0.2,0)(12.9,5)
 196
 197  \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](5.2,1)(6.5,1)(6.5,3)(5.2,3)
 198  \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](6.4,0.5)(7.7,2)(7.7,2)(6.4,3.5)
 199
 200  \rput[lt](0,4.6){\color{gray}PROPERTIES}
 201
 202  \rput[lt](0.3,4){wide band gap}
 203  \rput[lt](0.3,3.5){high electric breakdown field}
 204  \rput[lt](0.3,3){good electron mobility}
 205  \rput[lt](0.3,2.5){high electron saturation drift velocity}
 206  \rput[lt](0.3,2){high thermal conductivity}
 207
 208  \rput[lt](0.3,1.5){hard and mechanically stable}
 209  \rput[lt](0.3,1){chemically inert}
 210
 211  \rput[lt](0.3,0.5){radiation hardness}
 212
 213  \rput[rt](12.7,4.6){\color{gray}APPLICATIONS}
 214
 215  \rput[rt](12.5,3.85){high-temperature, high power}
 216  \rput[rt](12.5,3.5){and high-frequency}
 217  \rput[rt](12.5,3.15){electronic and optoelectronic devices}
 218
 219  \rput[rt](12.5,2.35){material suitable for extreme conditions}
 220  \rput[rt](12.5,2){microelectromechanical systems}
 221  \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements}
 222
 223  \rput[rt](12.5,0.85){first wall reactor material, detectors}
 224  \rput[rt](12.5,0.5){and electronic devices for space}
 225
 226 \end{pspicture}
 227
 228 \begin{picture}(0,0)(5,-162)
 229 \includegraphics[height=2.2cm]{3C_SiC_bs.eps}
 230 \end{picture}
 231 \begin{picture}(0,0)(-120,-162)
 232 \includegraphics[height=2.2cm]{nasa_600c_led.eps}
 233 \end{picture}
 234 \begin{picture}(0,0)(-270,-162)
 235 \includegraphics[height=2.2cm]{6h-sic_3c-sic.eps}
 236 \end{picture}
 237 %%%%
 238 \begin{picture}(0,0)(10,65)
 239 \includegraphics[height=2.8cm]{sic_switch.eps}
 240 \end{picture}
 241 %\begin{picture}(0,0)(-243,65)
 242 \begin{picture}(0,0)(-110,65)
 243 \includegraphics[height=2.8cm]{ise_99.eps}
 244 \end{picture}
 245 %\begin{picture}(0,0)(-135,65)
 246 \begin{picture}(0,0)(-100,65)
 247 \includegraphics[height=1.2cm]{infineon_schottky.eps}
 248 \end{picture}
 249 \begin{picture}(0,0)(-233,65)
 250 \includegraphics[height=2.8cm]{solar_car.eps}
 251 \end{picture}
 252
 253 \end{slide}
 254
 255 % motivation
 256
 257 \begin{slide}
 258
 259  {\large\bf
 260   Polytypes of SiC\\[0.4cm]
 261  }
 262
 263 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
 264 \begin{minipage}{1.9cm}
 265 {\tiny cubic (twist)}
 266 \end{minipage}
 267 \begin{minipage}{2.9cm}
 268 {\tiny hexagonal (no twist)}
 269 \end{minipage}
 270
 271 \begin{picture}(0,0)(-150,0)
 272  \includegraphics[width=7cm]{polytypes.eps}
 273 \end{picture}
 274
 275 \vspace{0.6cm}
 276
 277 \footnotesize
 278
 279 \begin{tabular}{l c c c c c c}
 280 \hline
 281  & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
 282 \hline
 283 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
 284 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
 285 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
 286 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
 287 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
 288 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
 289 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
 290 \hline
 291 \end{tabular}
 292
 293 \begin{pspicture}(0,0)(0,0)
 294 \psellipse[linecolor=green](5.7,2.10)(0.4,0.5)
 295 \end{pspicture}
 296 \begin{pspicture}(0,0)(0,0)
 297 \psellipse[linecolor=green](5.6,0.92)(0.4,0.2)
 298 \end{pspicture}
 299 \begin{pspicture}(0,0)(0,0)
 300 \psellipse[linecolor=red](10.45,0.45)(0.4,0.2)
 301 \end{pspicture}
 302
 303 \end{slide}
 304
 305 % fabrication
 306
 307 \begin{slide}
 308
 309  {\large\bf
 310   Fabrication of silicon carbide
 311  }
 312
 313  \small
 314
 315  \vspace{2pt}
 316
 317 \begin{center}
 318  {\color{gray}
 319  \emph{Silicon carbide --- Born from the stars, perfected on earth.}
 320  }
 321 \end{center}
 322
 323 \vspace{2pt}
 324
 325 SiC thin films by MBE \& CVD
 326 \begin{itemize}
 327  \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
 328  \item \underline{Commercially available} semiconductor power devices based on
 329        \underline{\foreignlanguage{greek}{a}-SiC}
 330  \item Production of favored \underline{3C-SiC} material
 331        \underline{less advanced}
 332  \item Quality and size not yet sufficient
 333 \end{itemize}
 334 \begin{picture}(0,0)(-310,-20)
 335   \includegraphics[width=2.0cm]{cree.eps}
 336 \end{picture}
 337
 338 \vspace{-0.2cm}
 339
 340 Alternative approach:
 341 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
 342
 343 \vspace{0.2cm}
 344
 345 \scriptsize
 346
 347 \framebox{
 348 \begin{minipage}{3.15cm}
 349  \begin{center}
 350 \includegraphics[width=3cm]{imp.eps}\\
 351  {\tiny
 352   Carbon implantation
 353  }
 354  \end{center}
 355 \end{minipage}
 356 \begin{minipage}{3.15cm}
 357  \begin{center}
 358 \includegraphics[width=3cm]{annealing.eps}\\
 359  {\tiny
 360   \unit[12]{h} annealing at \degc{1200}
 361  }
 362  \end{center}
 363 \end{minipage}
 364 }
 365 \begin{minipage}{5.5cm}
 366  \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm]
 367  \begin{center}
 368  {\tiny
 369   XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
 370  }
 371  \end{center}
 372 \end{minipage}
 373
 374 \end{slide}
 375
 376 % contents
 377
 378 \begin{slide}
 379
 380 {\large\bf
 381  Systematic investigation of C implantations into Si
 382 }
 383
 384 \vspace{1.7cm}
 385 \begin{center}
 386 \hspace{-1.0cm}
 387 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
 388 \end{center}
 389
 390 \end{slide}
 391
 392 % outline
 393
 394 \fi
 395
 396 \begin{slide}
 397
 398 {\large\bf
 399  Outline
 400 }
 401
 402 \vspace{1.7cm}
 403 \begin{center}
 404 \hspace{-1.0cm}
 405 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
 406 \end{center}
 407
 408 \begin{pspicture}(0,0)(0,0)
 409 \rput(6.0,7.0){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=white,gradend=red,gradlines=1000,gradmidpoint=0.5,linestyle=none]{
 410 \begin{minipage}{11cm}
 411 {\color{black}Diploma thesis}\\
 412  \underline{Monte Carlo} simulation modeling the selforganization process\\
 413  leading to periodic arrays of nanometric amorphous SiC precipitates
 414 \end{minipage}
 415 }}}
 416 \end{pspicture}
 417 \begin{pspicture}(0,0)(0,0)
 418 \rput(6.0,-0.5){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=white,gradend=blue,gradmidpoint=0.5,gradlines=1000,linestyle=none]{
 419 \begin{minipage}{11cm}
 420 {\color{black}Doctoral studies}\\
 421  Classical potential \underline{molecular dynamics} simulations \ldots\\
 422  \underline{Density functional theory} calculations \ldots\\[0.2cm]
 423  \ldots on defect formation and SiC precipitation in Si
 424 \end{minipage}
 425 }}}
 426 \end{pspicture}
 427 \begin{pspicture}(0,0)(0,0)
 428 \psellipse[linecolor=red,linewidth=0.05cm](5,3.0)(0.8,1.0)
 429 \end{pspicture}
 430 \begin{pspicture}(0,0)(0,0)
 431 \psellipse[linecolor=blue,linewidth=0.05cm](8.2,3.2)(1.5,1.6)
 432 \end{pspicture}
 433
 434 \end{slide}
 435
 436 \begin{slide}
 437
 438 {\large\bf
 439  Selforganization of nanometric amorphous SiC lamellae
 440 }
 441
 442 \begin{pspicture}(0,0)(0,0)
 443 \psframebox[fillstyle=gradient,gradbegin=white,gradend=red,gradlines=1000,gradmidpoint=0.5,linestyle=none]{
 444 \begin{minipage}{14cm}
 445 \hfill
 446 \vspace*{0.5cm}
 447 \end{minipage}
 448 }
 449 \end{pspicture}
 450
 451 \small
 452
 453 \vspace{0.2cm}
 454
 455 \begin{itemize}
 456  \item Regularly spaced, nanometric spherical\\
 457        and lamellar amorphous inclusions\\
 458        at the upper a/c interface
 459  \item Carbon accumulation\\
 460        in amorphous volumes
 461 \end{itemize}
 462
 463 \vspace{0.4cm}
 464
 465 \begin{minipage}{12cm}
 466 \includegraphics[width=9cm]{../../nlsop/img/k393abild1_e_l.eps}\\
 467 {\scriptsize
 468 XTEM bright-field, \unit[180]{keV} C$^+ \rightarrow$ Si, \degc{150},
 469 Dose: \unit[4.3 $\times 10^{17}$]{cm$^{-2}$}
 470 }
 471 \end{minipage}
 472
 473 \begin{picture}(0,0)(-182,-215)
 474 \begin{minipage}{6.5cm}
 475 \begin{center}
 476 \includegraphics[width=6.5cm]{../../nlsop/img/eftem.eps}\\[-0.2cm]
 477 {\scriptsize
 478 XTEM bright-field and respective EFTEM C map
 479 }
 480 \end{center}
 481 \end{minipage}
 482 \end{picture}
 483
 484 \end{slide}
 485
 486 \end{document}
 487 \ifnum1=0
 488
 489 \begin{slide}
 490
 491 {\large\bf
 492  Model displaying the formation of ordered lamellae
 493 }
 494
 495 \vspace{0.1cm}
 496
 497 \begin{center}
 498  \includegraphics[width=8.0cm]{../../nlsop/img/modell_ng_e.eps}
 499 \end{center}
 500
 501 \footnotesize
 502
 503 \begin{itemize}
 504 \item Supersaturation of C in c-Si\\
 505       $\rightarrow$ {\bf Carbon induced} nucleation of spherical
 506       SiC$_x$-precipitates
 507 \item High interfacial energy between 3C-SiC and c-Si\\
 508       $\rightarrow$ {\bf Amorphous} precipitates
 509 \item \unit[20-- 30]{\%} lower silicon density of a-SiC$_x$ compared to c-Si\\
 510       $\rightarrow$ {\bf Lateral strain} (black arrows)
 511 \item Implantation range near surface\\
 512       $\rightarrow$ {\bf Relaxation} of {\bf vertical strain component}
 513 \item Reduction of the carbon supersaturation in c-Si\\
 514       $\rightarrow$ {\bf Carbon diffusion} into amorphous volumina
 515       (white arrows)
 516 \item Remaining lateral strain\\
 517       $\rightarrow$ {\bf Strain enhanced} lateral amorphisation
 518 \item Absence of crystalline neighbours (structural information)\\
 519       $\rightarrow$ {\bf Stabilization} of amorphous inclusions
 520       {\bf against recrystallization}
 521 \end{itemize}
 522
 523 \end{slide}
 524
 525 \begin{slide}
 526
 527 {\large\bf
 528  Implementation of the Monte Carlo code
 529 }
 530
 531 \small
 532
 533 \begin{enumerate}
 534  \item \underline{Amorphization / Recrystallization}\\
 535        Ion collision in discretized target determined by random numbers
 536        distributed according to nuclear energy loss.
 537        Amorphization/recrystallization probability:
 538 \[
 539 p_{c \rightarrow a}(\vec{r}) = {\color{green} p_b} + {\color{blue} p_c c_C(\vec{r})} + {\color{red} \sum_{\textrm{amorphous neighbours}} \frac{p_s c_C(\vec{r'})}{(r-r')^2}}
 540 \]
 541 \begin{itemize}
 542  \item {\color{green} $p_b$} normal `ballistic' amorphization
 543  \item {\color{blue} $p_c$} carbon induced amorphization
 544  \item {\color{red} $p_s$} stress enhanced amorphization
 545 \end{itemize}
 546 \[
 547 p_{a \rightarrow c}(\vec r) = (1 - p_{c \rightarrow a}(\vec r)) \Big(1 - \frac{\sum_{direct \, neighbours} \delta (\vec{r'})}{6} \Big) \, \textrm{,}
 548 \]
 549 \[
 550 \delta (\vec r) = \left\{
 551 \begin{array}{ll}
 552         1 & \textrm{if volume at position $\vec r$ is amorphous} \\
 553         0 & \textrm{otherwise} \\
 554 \end{array}
 555 \right.
 556 \]
 557  \item \underline{Carbon incorporation}\\
 558        Incorporation volume determined according to implantation profile
 559  \item \underline{Diffusion / Sputtering}
 560        \begin{itemize}
 561         \item Transfer fraction of C atoms
 562               of crystalline into neighbored amorphous volumes
 563         \item Remove surface layer
 564        \end{itemize}
 565 \end{enumerate}
 566
 567 \end{slide}
 568
 569 \begin{slide}
 570
 571 \begin{minipage}{3.7cm}
 572 {\large\bf
 573  Results
 574 }
 575
 576 \footnotesize
 577
 578 \vspace{1.0cm}
 579
 580 Evolution of the \ldots
 581 \begin{itemize}
 582  \item continuous\\
 583        amorphous layer
 584  \item a/c interface
 585  \item lamella precipitates
 586 \end{itemize}
 587 \ldots reproduced!\\[1.5cm]
 588
 589 {\color{blue}
 590 \begin{center}
 591 Experiment \& simulation\\
 592 in good agreement\\[1.0cm]
 593
 594 Simulation is able to model the whole depth region\\[1.0cm]
 595 \end{center}
 596 }
 597
 598 \end{minipage}
 599 \begin{minipage}{0.4cm}
 600 \vfill
 601 \end{minipage}
 602 \begin{minipage}{8.0cm}
 603  \vspace{-0.2cm}
 604  \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e_1-2.eps}\\
 605  \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e2_2-2.eps}
 606 \end{minipage}
 607
 608 \end{slide}
 609
 610 \begin{slide}
 611
 612 {\large\bf
 613  Structural \& compositional details
 614 }
 615
 616 \begin{minipage}[t]{7.5cm}
 617 \includegraphics[height=6.5cm]{../../nlsop/img/ac_cconc_ver2_e.eps}\\
 618 \end{minipage}
 619 \begin{minipage}[t]{5.0cm}
 620 \includegraphics[height=6.5cm]{../../nlsop/img/97_98_e.eps}
 621 \end{minipage}
 622
 623 \footnotesize
 624
 625 \vspace{-0.1cm}
 626
 627 \begin{itemize}
 628  \item Fluctuation of C concentration in lamellae region
 629  \item \unit[8--10]{at.\%} C saturation limit
 630        within the respective conditions
 631  \item Complementarily arranged and alternating sequence of layers\\
 632        with a high and low amount of amorphous regions
 633  \item C accumulation in the amorphous phase / Origin of stress
 634 \end{itemize}
 635
 636 \begin{picture}(0,0)(-265,-30)
 637 \framebox{
 638 \begin{minipage}{3cm}
 639 \begin{center}
 640 {\color{blue}
 641 Precipitation process\\
 642 gets traceable\\
 643 by simulation!
 644 }
 645 \end{center}
 646 \end{minipage}
 647 }
 648 \end{picture}
 649
 650 \end{slide}
 651
 652
 653 \end{document}
 654
 655 % continue here
 656 \fi
 657
 658 \ifnum1=0
 659
 660 \begin{slide}
 661
 662 {\large\bf
 663  Model displaying the formation of ordered lamellae
 664 }
 665
 666 \framebox{
 667  \begin{minipage}{6.3cm}
 668  \begin{center}
 669  {\color{blue}
 670   Precipitation mechanism not yet fully understood!
 671  }
 672  \renewcommand\labelitemi{$\Rightarrow$}
 673  \small
 674  \underline{Understanding the SiC precipitation}
 675  \begin{itemize}
 676   \item significant technological progress in SiC thin film formation
 677   \item perspectives for processes relying upon prevention of SiC precipitation
 678  \end{itemize}
 679  \end{center}
 680  \end{minipage}
 681 }
 682
 683 \end{slide}
 684
 685 \begin{slide}
 686
 687  {\large\bf
 688   Supposed precipitation mechanism of SiC in Si
 689  }
 690
 691  \scriptsize
 692
 693  \vspace{0.1cm}
 694
 695  \begin{minipage}{3.8cm}
 696  Si \& SiC lattice structure\\[0.2cm]
 697  \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
 698  \hrule
 699  \end{minipage}
 700  \hspace{0.6cm}
 701  \begin{minipage}{3.8cm}
 702  \begin{center}
 703  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 704  \end{center}
 705  \end{minipage}
 706  \hspace{0.6cm}
 707  \begin{minipage}{3.8cm}
 708  \begin{center}
 709  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 710  \end{center}
 711  \end{minipage}
 712
 713  \begin{minipage}{4cm}
 714  \begin{center}
 715  C-Si dimers (dumbbells)\\[-0.1cm]
 716  on Si interstitial sites
 717  \end{center}
 718  \end{minipage}
 719  \hspace{0.2cm}
 720  \begin{minipage}{4.2cm}
 721  \begin{center}
 722  Agglomeration of C-Si dumbbells\\[-0.1cm]
 723  $\Rightarrow$ dark contrasts
 724  \end{center}
 725  \end{minipage}
 726  \hspace{0.2cm}
 727  \begin{minipage}{4cm}
 728  \begin{center}
 729  Precipitation of 3C-SiC in Si\\[-0.1cm]
 730  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 731  \& release of Si self-interstitials
 732  \end{center}
 733  \end{minipage}
 734
 735  \begin{minipage}{3.8cm}
 736  \begin{center}
 737  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 738  \end{center}
 739  \end{minipage}
 740  \hspace{0.6cm}
 741  \begin{minipage}{3.8cm}
 742  \begin{center}
 743  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 744  \end{center}
 745  \end{minipage}
 746  \hspace{0.6cm}
 747  \begin{minipage}{3.8cm}
 748  \begin{center}
 749  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 750  \end{center}
 751  \end{minipage}
 752
 753 \begin{pspicture}(0,0)(0,0)
 754 \psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
 755 \psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
 756 \rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
 757 \psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
 758 \rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 759  $4a_{\text{Si}}=5a_{\text{SiC}}$
 760  }}}
 761 \rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 762 \hkl(h k l) planes match
 763  }}}
 764 \rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 765 r = 2 - 4 nm
 766  }}}
 767 \end{pspicture}
 768
 769 \end{slide}
 770
 771 \begin{slide}
 772
 773  {\large\bf
 774   Supposed precipitation mechanism of SiC in Si
 775  }
 776
 777  \scriptsize
 778
 779  \vspace{0.1cm}
 780
 781  \begin{minipage}{3.8cm}
 782  Si \& SiC lattice structure\\[0.2cm]
 783  \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
 784  \hrule
 785  \end{minipage}
 786  \hspace{0.6cm}
 787  \begin{minipage}{3.8cm}
 788  \begin{center}
 789  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 790  \end{center}
 791  \end{minipage}
 792  \hspace{0.6cm}
 793  \begin{minipage}{3.8cm}
 794  \begin{center}
 795  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 796  \end{center}
 797  \end{minipage}
 798
 799  \begin{minipage}{4cm}
 800  \begin{center}
 801  C-Si dimers (dumbbells)\\[-0.1cm]
 802  on Si interstitial sites
 803  \end{center}
 804  \end{minipage}
 805  \hspace{0.2cm}
 806  \begin{minipage}{4.2cm}
 807  \begin{center}
 808  Agglomeration of C-Si dumbbells\\[-0.1cm]
 809  $\Rightarrow$ dark contrasts
 810  \end{center}
 811  \end{minipage}
 812  \hspace{0.2cm}
 813  \begin{minipage}{4cm}
 814  \begin{center}
 815  Precipitation of 3C-SiC in Si\\[-0.1cm]
 816  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 817  \& release of Si self-interstitials
 818  \end{center}
 819  \end{minipage}
 820
 821  \begin{minipage}{3.8cm}
 822  \begin{center}
 823  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 824  \end{center}
 825  \end{minipage}
 826  \hspace{0.6cm}
 827  \begin{minipage}{3.8cm}
 828  \begin{center}
 829  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 830  \end{center}
 831  \end{minipage}
 832  \hspace{0.6cm}
 833  \begin{minipage}{3.8cm}
 834  \begin{center}
 835  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 836  \end{center}
 837  \end{minipage}
 838
 839 \begin{pspicture}(0,0)(0,0)
 840 \psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
 841 \psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
 842 \rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
 843 \psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
 844 \rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 845  $4a_{\text{Si}}=5a_{\text{SiC}}$
 846  }}}
 847 \rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 848 \hkl(h k l) planes match
 849  }}}
 850 \rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 851 r = 2 - 4 nm
 852  }}}
 853 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
 854 \begin{minipage}{10cm}
 855 \small
 856 {\color{red}\bf Controversial views}
 857 \begin{itemize}
 858 \item Implantations at high T (Nejim et al.)
 859  \begin{itemize}
 860   \item Topotactic transformation based on \cs
 861   \item \si{} as supply reacting with further C in cleared volume
 862  \end{itemize}
 863 \item Annealing behavior (Serre et al.)
 864  \begin{itemize}
 865   \item Room temperature implants $\rightarrow$ highly mobile C
 866   \item Elevated T implants $\rightarrow$ no/low C redistribution/migration\\
 867         (indicate stable \cs{} configurations)
 868  \end{itemize}
 869 \item Strained silicon \& Si/SiC heterostructures
 870  \begin{itemize}
 871   \item Coherent SiC precipitates (tensile strain)
 872   \item Incoherent SiC (strain relaxation)
 873  \end{itemize}
 874 \end{itemize}
 875 \end{minipage}
 876  }}}
 877 \end{pspicture}
 878
 879 \end{slide}
 880
 881 \begin{slide}
 882
 883  {\large\bf
 884   Molecular dynamics (MD) simulations
 885  }
 886
 887  \vspace{12pt}
 888
 889  \small
 890
 891  {\bf MD basics:}
 892  \begin{itemize}
 893   \item Microscopic description of N particle system
 894   \item Analytical interaction potential
 895   \item Numerical integration using Newtons equation of motion\\
 896         as a propagation rule in 6N-dimensional phase space
 897   \item Observables obtained by time and/or ensemble averages
 898  \end{itemize}
 899  {\bf Details of the simulation:}
 900  \begin{itemize}
 901   \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
 902   \item Ensemble: NpT (isothermal-isobaric)
 903         \begin{itemize}
 904          \item Berendsen thermostat:
 905                $\tau_{\text{T}}=100\text{ fs}$
 906          \item Berendsen barostat:\\
 907                $\tau_{\text{P}}=100\text{ fs}$,
 908                $\beta^{-1}=100\text{ GPa}$
 909         \end{itemize}
 910   \item Erhart/Albe potential: Tersoff-like bond order potential
 911   \vspace*{12pt}
 912         \[
 913         E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
 914         \pot_{ij} = {\color{red}f_C(r_{ij})}
 915         \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
 916         \]
 917  \end{itemize}
 918
 919  \begin{picture}(0,0)(-230,-30)
 920   \includegraphics[width=5cm]{tersoff_angle.eps}
 921  \end{picture}
 922
 923 \end{slide}
 924
 925 \begin{slide}
 926
 927  {\large\bf
 928   Density functional theory (DFT) calculations
 929  }
 930
 931  \small
 932
 933  Basic ingredients necessary for DFT
 934
 935  \begin{itemize}
 936   \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
 937         \begin{itemize}
 938          \item ... uniquely determines the ground state potential
 939                / wavefunctions
 940          \item ... minimizes the systems total energy
 941         \end{itemize}
 942   \item \underline{Born-Oppenheimer}
 943         - $N$ moving electrons in an external potential of static nuclei
 944 \[
 945 H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
 946               +\sum_i^N V_{\text{ext}}(r_i)
 947               +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
 948 \]
 949   \item \underline{Effective potential}
 950         - averaged electrostatic potential \& exchange and correlation
 951 \[
 952 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
 953                  +V_{\text{XC}}[n(r)]
 954 \]
 955   \item \underline{Kohn-Sham system}
 956         - Schr\"odinger equation of N non-interacting particles
 957 \[
 958 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
 959 =\epsilon_i\Phi_i(r)
 960 \quad
 961 \Rightarrow
 962 \quad
 963 n(r)=\sum_i^N|\Phi_i(r)|^2
 964 \]
 965   \item \underline{Self-consistent solution}\\
 966 $n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
 967 which in turn depends on $n(r)$
 968   \item \underline{Variational principle}
 969         - minimize total energy with respect to $n(r)$
 970  \end{itemize}
 971
 972 \end{slide}
 973
 974 \begin{slide}
 975
 976  {\large\bf
 977   Density functional theory (DFT) calculations
 978  }
 979
 980  \small
 981
 982  \vspace*{0.2cm}
 983
 984  Details of applied DFT calculations in this work
 985
 986  \begin{itemize}
 987   \item \underline{Exchange correlation functional}
 988         - approximations for the inhomogeneous electron gas
 989         \begin{itemize}
 990          \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
 991          \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
 992         \end{itemize}
 993   \item \underline{Plane wave basis set}
 994         - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
 995 \[
 996 \rightarrow
 997 \text{Fourier series: } \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r), \quad E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}
 998 \qquad ({\color{blue}300\text{ eV}})
 999 \]
1000   \item \underline{Brillouin zone sampling} -
1001         {\color{blue}$\Gamma$-point only} calculations
1002   \item \underline{Pseudo potential}
1003         - consider only the valence electrons
1004   \item \underline{Code} - VASP 4.6
1005  \end{itemize}
1006
1007  \vspace*{0.2cm}
1008
1009  MD and structural optimization
1010
1011  \begin{itemize}
1012   \item MD integration: Gear predictor corrector algorithm
1013   \item Pressure control: Parrinello-Rahman pressure control
1014   \item Structural optimization: Conjugate gradient method
1015  \end{itemize}
1016
1017 \begin{pspicture}(0,0)(0,0)
1018 \psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
1019 \end{pspicture}
1020
1021 \end{slide}
1022
1023 \begin{slide}
1024
1025  {\large\bf
1026   C and Si self-interstitial point defects in silicon
1027  }
1028
1029  \small
1030
1031  \vspace*{0.3cm}
1032
1033 \begin{minipage}{8cm}
1034 Procedure:\\[0.3cm]
1035   \begin{pspicture}(0,0)(7,5)
1036   \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1037    \parbox{7cm}{
1038    \begin{itemize}
1039     \item Creation of c-Si simulation volume
1040     \item Periodic boundary conditions
1041     \item $T=0\text{ K}$, $p=0\text{ bar}$
1042    \end{itemize}
1043   }}}}
1044 \rput(3.5,2.1){\rnode{insert}{\psframebox{
1045  \parbox{7cm}{
1046   \begin{center}
1047   Insertion of interstitial C/Si atoms
1048   \end{center}
1049   }}}}
1050   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1051    \parbox{7cm}{
1052    \begin{center}
1053    Relaxation / structural energy minimization
1054    \end{center}
1055   }}}}
1056   \ncline[]{->}{init}{insert}
1057   \ncline[]{->}{insert}{cool}
1058  \end{pspicture}
1059 \end{minipage}
1060 \begin{minipage}{5cm}
1061   \includegraphics[width=5cm]{unit_cell_e.eps}\\
1062 \end{minipage}
1063
1064 \begin{minipage}{9cm}
1065  \begin{tabular}{l c c}
1066  \hline
1067  & size [unit cells] & \# atoms\\
1068 \hline
1069 VASP & $3\times 3\times 3$ & $216\pm 1$ \\
1070 Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
1071 \hline
1072  \end{tabular}
1073 \end{minipage}
1074 \begin{minipage}{4cm}
1075 {\color{red}$\bullet$} Tetrahedral\\
1076 {\color{green}$\bullet$} Hexagonal\\
1077 {\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
1078 {\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
1079 {\color{cyan}$\bullet$} Bond-centered\\
1080 {\color{black}$\bullet$} Vacancy / Substitutional
1081 \end{minipage}
1082
1083 \end{slide}
1084
1085 \begin{slide}
1086
1087  \footnotesize
1088
1089 \begin{minipage}{9.5cm}
1090
1091  {\large\bf
1092   Si self-interstitial point defects in silicon\\
1093  }
1094
1095 \begin{tabular}{l c c c c c}
1096 \hline
1097  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
1098 \hline
1099  VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
1100  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
1101 \hline
1102 \end{tabular}\\[0.2cm]
1103
1104 \begin{minipage}{4.7cm}
1105 \includegraphics[width=4.7cm]{e_kin_si_hex.ps}
1106 \end{minipage}
1107 \begin{minipage}{4.7cm}
1108 \begin{center}
1109 {\tiny nearly T $\rightarrow$ T}\\
1110 \end{center}
1111 \includegraphics[width=4.7cm]{nhex_tet.ps}
1112 \end{minipage}\\
1113
1114 \underline{Hexagonal} \hspace{2pt}
1115 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
1116 \framebox{
1117 \begin{minipage}{2.7cm}
1118 $E_{\text{f}}^*=4.48\text{ eV}$\\
1119 \includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
1120 \end{minipage}
1121 \begin{minipage}{0.4cm}
1122 \begin{center}
1123 $\Rightarrow$
1124 \end{center}
1125 \end{minipage}
1126 \begin{minipage}{2.7cm}
1127 $E_{\text{f}}=3.96\text{ eV}$\\
1128 \includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
1129 \end{minipage}
1130 }
1131 \begin{minipage}{2.9cm}
1132 \begin{flushright}
1133 \underline{Vacancy}\\
1134 \includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
1135 \end{flushright}
1136 \end{minipage}
1137
1138 \end{minipage}
1139 \begin{minipage}{3.5cm}
1140
1141 \begin{flushright}
1142 \underline{\hkl<1 1 0> dumbbell}\\
1143 \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
1144 \underline{Tetrahedral}\\
1145 \includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
1146 \underline{\hkl<1 0 0> dumbbell}\\
1147 \includegraphics[width=3.0cm]{si_pd_albe/100.eps}
1148 \end{flushright}
1149
1150 \end{minipage}
1151
1152 \end{slide}
1153
1154 \begin{slide}
1155
1156 \footnotesize
1157
1158  {\large\bf
1159   C interstitial point defects in silicon\\[-0.1cm]
1160  }
1161
1162 \begin{tabular}{l c c c c c c r}
1163 \hline
1164  $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\
1165 \hline
1166  VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1167  Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1168 \hline
1169 \end{tabular}\\[0.1cm]
1170
1171 \framebox{
1172 \begin{minipage}{2.7cm}
1173 \underline{Hexagonal} \hspace{2pt}
1174 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1175 $E_{\text{f}}^*=9.05\text{ eV}$\\
1176 \includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
1177 \end{minipage}
1178 \begin{minipage}{0.4cm}
1179 \begin{center}
1180 $\Rightarrow$
1181 \end{center}
1182 \end{minipage}
1183 \begin{minipage}{2.7cm}
1184 \underline{\hkl<1 0 0>}\\
1185 $E_{\text{f}}=3.88\text{ eV}$\\
1186 \includegraphics[width=2.7cm]{c_pd_albe/100.eps}
1187 \end{minipage}
1188 }
1189 \begin{minipage}{2cm}
1190 \hfill
1191 \end{minipage}
1192 \begin{minipage}{3cm}
1193 \begin{flushright}
1194 \underline{Tetrahedral}\\
1195 \includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
1196 \end{flushright}
1197 \end{minipage}
1198
1199 \framebox{
1200 \begin{minipage}{2.7cm}
1201 \underline{Bond-centered}\\
1202 $E_{\text{f}}^*=5.59\text{ eV}$\\
1203 \includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
1204 \end{minipage}
1205 \begin{minipage}{0.4cm}
1206 \begin{center}
1207 $\Rightarrow$
1208 \end{center}
1209 \end{minipage}
1210 \begin{minipage}{2.7cm}
1211 \underline{\hkl<1 1 0> dumbbell}\\
1212 $E_{\text{f}}=5.18\text{ eV}$\\
1213 \includegraphics[width=2.7cm]{c_pd_albe/110.eps}
1214 \end{minipage}
1215 }
1216 \begin{minipage}{2cm}
1217 \hfill
1218 \end{minipage}
1219 \begin{minipage}{3cm}
1220 \begin{flushright}
1221 \underline{Substitutional}\\
1222 \includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
1223 \end{flushright}
1224 \end{minipage}
1225
1226 \end{slide}
1227
1228 \begin{slide}
1229
1230 \footnotesize
1231
1232  {\large\bf\boldmath
1233   C \hkl<1 0 0> dumbbell interstitial configuration\\
1234  }
1235
1236 {\tiny
1237 \begin{tabular}{l c c c c c c c c}
1238 \hline
1239  Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
1240 \hline
1241 Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
1242 VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
1243 \hline
1244 \end{tabular}\\[0.2cm]
1245 \begin{tabular}{l c c c c }
1246 \hline
1247  Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
1248 \hline
1249 Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
1250 VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
1251 \hline
1252 \end{tabular}\\[0.2cm]
1253 \begin{tabular}{l c c c}
1254 \hline
1255  Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
1256 \hline
1257 Erhart/Albe & 0.084 & -0.091 & 0.175 \\
1258 VASP & 0.109 & -0.065 & 0.174 \\
1259 \hline
1260 \end{tabular}\\[0.6cm]
1261 }
1262
1263 \begin{minipage}{3.0cm}
1264 \begin{center}
1265 \underline{Erhart/Albe}
1266 \includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
1267 \end{center}
1268 \end{minipage}
1269 \begin{minipage}{3.0cm}
1270 \begin{center}
1271 \underline{VASP}
1272 \includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
1273 \end{center}
1274 \end{minipage}\\
1275
1276 \begin{picture}(0,0)(-185,10)
1277 \includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
1278 \end{picture}
1279 \begin{picture}(0,0)(-280,-150)
1280 \includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
1281 \end{picture}
1282
1283 \begin{pspicture}(0,0)(0,0)
1284 \psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
1285 \psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
1286 \psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
1287 \psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
1288 \end{pspicture}
1289
1290 \end{slide}
1291
1292 \begin{slide}
1293
1294 \small
1295
1296 \begin{minipage}{8.5cm}
1297
1298  {\large\bf
1299   Bond-centered interstitial configuration\\[-0.1cm]
1300  }
1301
1302 \begin{minipage}{3.0cm}
1303 \includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1304 \end{minipage}
1305 \begin{minipage}{5.2cm}
1306 \begin{itemize}
1307  \item Linear Si-C-Si bond
1308  \item Si: one C \& 3 Si neighbours
1309  \item Spin polarized calculations
1310  \item No saddle point!\\
1311        Real local minimum!
1312 \end{itemize}
1313 \end{minipage}
1314
1315 \framebox{
1316  \tiny
1317  \begin{minipage}[t]{6.5cm}
1318   \begin{minipage}[t]{1.2cm}
1319   {\color{red}Si}\\
1320   {\tiny sp$^3$}\\[0.8cm]
1321   \underline{${\color{black}\uparrow}$}
1322   \underline{${\color{black}\uparrow}$}
1323   \underline{${\color{black}\uparrow}$}
1324   \underline{${\color{red}\uparrow}$}\\
1325   sp$^3$
1326   \end{minipage}
1327   \begin{minipage}[t]{1.4cm}
1328   \begin{center}
1329   {\color{red}M}{\color{blue}O}\\[0.8cm]
1330   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1331   $\sigma_{\text{ab}}$\\[0.5cm]
1332   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1333   $\sigma_{\text{b}}$
1334   \end{center}
1335   \end{minipage}
1336   \begin{minipage}[t]{1.0cm}
1337   \begin{center}
1338   {\color{blue}C}\\
1339   {\tiny sp}\\[0.2cm]
1340   \underline{${\color{white}\uparrow\uparrow}$}
1341   \underline{${\color{white}\uparrow\uparrow}$}\\
1342   2p\\[0.4cm]
1343   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1344   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1345   sp
1346   \end{center}
1347   \end{minipage}
1348   \begin{minipage}[t]{1.4cm}
1349   \begin{center}
1350   {\color{blue}M}{\color{green}O}\\[0.8cm]
1351   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1352   $\sigma_{\text{ab}}$\\[0.5cm]
1353   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1354   $\sigma_{\text{b}}$
1355   \end{center}
1356   \end{minipage}
1357   \begin{minipage}[t]{1.2cm}
1358   \begin{flushright}
1359   {\color{green}Si}\\
1360   {\tiny sp$^3$}\\[0.8cm]
1361   \underline{${\color{green}\uparrow}$}
1362   \underline{${\color{black}\uparrow}$}
1363   \underline{${\color{black}\uparrow}$}
1364   \underline{${\color{black}\uparrow}$}\\
1365   sp$^3$
1366   \end{flushright}
1367   \end{minipage}
1368  \end{minipage}
1369 }\\[0.1cm]
1370
1371 \framebox{
1372 \begin{minipage}{4.5cm}
1373 \includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
1374 \end{minipage}
1375 \begin{minipage}{3.5cm}
1376 {\color{gray}$\bullet$} Spin up\\
1377 {\color{green}$\bullet$} Spin down\\
1378 {\color{blue}$\bullet$} Resulting spin up\\
1379 {\color{yellow}$\bullet$} Si atoms\\
1380 {\color{red}$\bullet$} C atom
1381 \end{minipage}
1382 }
1383
1384 \end{minipage}
1385 \begin{minipage}{4.2cm}
1386 \begin{flushright}
1387 \includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
1388 {\color{green}$\Box$} {\tiny unoccupied}\\
1389 {\color{red}$\bullet$} {\tiny occupied}
1390 \end{flushright}
1391 \end{minipage}
1392
1393 \end{slide}
1394
1395 \begin{slide}
1396
1397  {\large\bf\boldmath
1398   Migration of the C \hkl<1 0 0> dumbbell interstitial
1399  }
1400
1401 \scriptsize
1402
1403  {\small Investigated pathways}
1404
1405 \begin{minipage}{8.5cm}
1406 \begin{minipage}{8.3cm}
1407 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
1408 \begin{minipage}{2.4cm}
1409 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1410 \end{minipage}
1411 \begin{minipage}{0.4cm}
1412 $\rightarrow$
1413 \end{minipage}
1414 \begin{minipage}{2.4cm}
1415 \includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
1416 \end{minipage}
1417 \begin{minipage}{0.4cm}
1418 $\rightarrow$
1419 \end{minipage}
1420 \begin{minipage}{2.4cm}
1421 \includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
1422 \end{minipage}
1423 \end{minipage}\\
1424 \begin{minipage}{8.3cm}
1425 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
1426 \begin{minipage}{2.4cm}
1427 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1428 \end{minipage}
1429 \begin{minipage}{0.4cm}
1430 $\rightarrow$
1431 \end{minipage}
1432 \begin{minipage}{2.4cm}
1433 \includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
1434 \end{minipage}
1435 \begin{minipage}{0.4cm}
1436 $\rightarrow$
1437 \end{minipage}
1438 \begin{minipage}{2.4cm}
1439 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
1440 \end{minipage}
1441 \end{minipage}\\
1442 \begin{minipage}{8.3cm}
1443 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
1444 \begin{minipage}{2.4cm}
1445 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1446 \end{minipage}
1447 \begin{minipage}{0.4cm}
1448 $\rightarrow$
1449 \end{minipage}
1450 \begin{minipage}{2.4cm}
1451 \includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
1452 \end{minipage}
1453 \begin{minipage}{0.4cm}
1454 $\rightarrow$
1455 \end{minipage}
1456 \begin{minipage}{2.4cm}
1457 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
1458 \end{minipage}
1459 \end{minipage}
1460 \end{minipage}
1461 \framebox{
1462 \begin{minipage}{4.2cm}
1463  {\small Constrained relaxation\\
1464          technique (CRT) method}\\
1465 \includegraphics[width=4cm]{crt_orig.eps}
1466 \begin{itemize}
1467  \item Constrain diffusing atom
1468  \item Static constraints
1469 \end{itemize}
1470 \vspace*{0.3cm}
1471  {\small Modifications}\\
1472 \includegraphics[width=4cm]{crt_mod.eps}
1473 \begin{itemize}
1474  \item Constrain all atoms
1475  \item Update individual\\
1476        constraints
1477 \end{itemize}
1478 \end{minipage}
1479 }
1480
1481 \end{slide}
1482
1483 \begin{slide}
1484
1485  {\large\bf\boldmath
1486   Migration of the C \hkl<1 0 0> dumbbell interstitial
1487  }
1488
1489 \scriptsize
1490
1491 \framebox{
1492 \begin{minipage}{5.9cm}
1493 \begin{flushleft}
1494 \includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
1495 \end{flushleft}
1496 \begin{center}
1497 \begin{picture}(0,0)(60,0)
1498 \includegraphics[width=1cm]{vasp_mig/00-1.eps}
1499 \end{picture}
1500 \begin{picture}(0,0)(-5,0)
1501 \includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
1502 \end{picture}
1503 \begin{picture}(0,0)(-55,0)
1504 \includegraphics[width=1cm]{vasp_mig/bc.eps}
1505 \end{picture}
1506 \begin{picture}(0,0)(12.5,10)
1507 \includegraphics[width=1cm]{110_arrow.eps}
1508 \end{picture}
1509 \begin{picture}(0,0)(90,0)
1510 \includegraphics[height=0.9cm]{001_arrow.eps}
1511 \end{picture}
1512 \end{center}
1513 \vspace*{0.35cm}
1514 \end{minipage}
1515 }
1516 \begin{minipage}{0.3cm}
1517 \hfill
1518 \end{minipage}
1519 \framebox{
1520 \begin{minipage}{5.9cm}
1521 \begin{flushright}
1522 \includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
1523 \end{flushright}
1524 \begin{center}
1525 \begin{picture}(0,0)(60,0)
1526 \includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
1527 \end{picture}
1528 \begin{picture}(0,0)(5,0)
1529 \includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
1530 \end{picture}
1531 \begin{picture}(0,0)(-55,0)
1532 \includegraphics[width=1cm]{vasp_mig/0-10.eps}
1533 \end{picture}
1534 \begin{picture}(0,0)(12.5,10)
1535 \includegraphics[width=1cm]{100_arrow.eps}
1536 \end{picture}
1537 \begin{picture}(0,0)(90,0)
1538 \includegraphics[height=0.9cm]{001_arrow.eps}
1539 \end{picture}
1540 \end{center}
1541 \vspace*{0.3cm}
1542 \end{minipage}\\
1543 }
1544
1545 \vspace*{0.05cm}
1546
1547 \framebox{
1548 \begin{minipage}{5.9cm}
1549 \begin{flushleft}
1550 \includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
1551 \end{flushleft}
1552 \begin{center}
1553 \begin{picture}(0,0)(60,0)
1554 \includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps}
1555 \end{picture}
1556 \begin{picture}(0,0)(10,0)
1557 \includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
1558 \end{picture}
1559 \begin{picture}(0,0)(-60,0)
1560 \includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps}
1561 \end{picture}
1562 \begin{picture}(0,0)(12.5,10)
1563 \includegraphics[width=1cm]{100_arrow.eps}
1564 \end{picture}
1565 \begin{picture}(0,0)(90,0)
1566 \includegraphics[height=0.9cm]{001_arrow.eps}
1567 \end{picture}
1568 \end{center}
1569 \vspace*{0.3cm}
1570 \end{minipage}
1571 }
1572 \begin{minipage}{0.3cm}
1573 \hfill
1574 \end{minipage}
1575 \begin{minipage}{6.5cm}
1576 VASP results
1577 \begin{itemize}
1578  \item Energetically most favorable path
1579        \begin{itemize}
1580         \item Path 2
1581         \item Activation energy: $\approx$ 0.9 eV
1582         \item Experimental values: 0.73 ... 0.87 eV
1583        \end{itemize}
1584        $\Rightarrow$ {\color{blue}Diffusion} path identified!
1585  \item Reorientation (path 3)
1586        \begin{itemize}
1587         \item More likely composed of two consecutive steps of type 2
1588         \item Experimental values: 0.77 ... 0.88 eV
1589        \end{itemize}
1590        $\Rightarrow$ {\color{blue}Reorientation} transition identified!
1591 \end{itemize}
1592 \end{minipage}
1593
1594 \end{slide}
1595
1596 \begin{slide}
1597
1598  {\large\bf\boldmath
1599   Migration of the C \hkl<1 0 0> dumbbell interstitial
1600  }
1601
1602 \scriptsize
1603
1604  \vspace{0.1cm}
1605
1606 \begin{minipage}{6.5cm}
1607
1608 \framebox{
1609 \begin{minipage}[t]{5.9cm}
1610 \begin{flushleft}
1611 \includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
1612 \end{flushleft}
1613 \begin{center}
1614 \begin{pspicture}(0,0)(0,0)
1615 \psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
1616 \end{pspicture}
1617 \begin{picture}(0,0)(60,-50)
1618 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
1619 \end{picture}
1620 \begin{picture}(0,0)(5,-50)
1621 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
1622 \end{picture}
1623 \begin{picture}(0,0)(-55,-50)
1624 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
1625 \end{picture}
1626 \begin{picture}(0,0)(12.5,-40)
1627 \includegraphics[width=1cm]{110_arrow.eps}
1628 \end{picture}
1629 \begin{picture}(0,0)(90,-45)
1630 \includegraphics[height=0.9cm]{001_arrow.eps}
1631 \end{picture}\\
1632 \begin{pspicture}(0,0)(0,0)
1633 \psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
1634 \end{pspicture}
1635 \begin{picture}(0,0)(60,-15)
1636 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
1637 \end{picture}
1638 \begin{picture}(0,0)(35,-15)
1639 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
1640 \end{picture}
1641 \begin{picture}(0,0)(-5,-15)
1642 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
1643 \end{picture}
1644 \begin{picture}(0,0)(-55,-15)
1645 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
1646 \end{picture}
1647 \begin{picture}(0,0)(12.5,-5)
1648 \includegraphics[width=1cm]{100_arrow.eps}
1649 \end{picture}
1650 \begin{picture}(0,0)(90,-15)
1651 \includegraphics[height=0.9cm]{010_arrow.eps}
1652 \end{picture}
1653 \end{center}
1654 \end{minipage}
1655 }\\[0.1cm]
1656
1657 \begin{minipage}{5.9cm}
1658 Erhart/Albe results
1659 \begin{itemize}
1660  \item Lowest activation energy: $\approx$ 2.2 eV
1661  \item 2.4 times higher than VASP
1662  \item Different pathway
1663 \end{itemize}
1664 \end{minipage}
1665
1666 \end{minipage}
1667 \begin{minipage}{6.5cm}
1668
1669 \framebox{
1670 \begin{minipage}{5.9cm}
1671 %\begin{flushright}
1672 %\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
1673 %\end{flushright}
1674 %\begin{center}
1675 %\begin{pspicture}(0,0)(0,0)
1676 %\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
1677 %\end{pspicture}
1678 %\begin{picture}(0,0)(60,-5)
1679 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
1680 %\end{picture}
1681 %\begin{picture}(0,0)(0,-5)
1682 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
1683 %\end{picture}
1684 %\begin{picture}(0,0)(-55,-5)
1685 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
1686 %\end{picture}
1687 %\begin{picture}(0,0)(12.5,5)
1688 %\includegraphics[width=1cm]{100_arrow.eps}
1689 %\end{picture}
1690 %\begin{picture}(0,0)(90,0)
1691 %\includegraphics[height=0.9cm]{001_arrow.eps}
1692 %\end{picture}
1693 %\end{center}
1694 %\vspace{0.2cm}
1695 %\end{minipage}
1696 %}\\[0.2cm]
1697 %
1698 %\framebox{
1699 %\begin{minipage}{5.9cm}
1700 \includegraphics[width=5.9cm]{00-1_110_0-10_mig_albe.ps}
1701 \end{minipage}
1702 }\\[0.1cm]
1703
1704 \begin{minipage}{5.9cm}
1705 Transition involving \ci{} \hkl<1 1 0>
1706 \begin{itemize}
1707  \item Bond-centered configuration unstable\\
1708        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1709  \item Transition minima of path 2 \& 3\\
1710        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1711  \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV
1712  \item 2.4 - 3.4 times higher than VASP
1713  \item Rotation of dumbbell orientation
1714 \end{itemize}
1715 \vspace{0.1cm}
1716 \begin{center}
1717 {\color{blue}Overestimated diffusion barrier}
1718 \end{center}
1719 \end{minipage}
1720
1721 \end{minipage}
1722
1723 \end{slide}
1724
1725 \begin{slide}
1726
1727  {\large\bf\boldmath
1728   Combinations with a C-Si \hkl<1 0 0>-type interstitial
1729  }
1730
1731 \small
1732
1733 \vspace*{0.1cm}
1734
1735 Binding energy:
1736 $
1737 E_{\text{b}}=
1738 E_{\text{f}}^{\text{defect combination}}-
1739 E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
1740 E_{\text{f}}^{\text{2nd defect}}
1741 $
1742
1743 \vspace*{0.1cm}
1744
1745 {\scriptsize
1746 \begin{tabular}{l c c c c c c}
1747 \hline
1748  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1749  \hline
1750  \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1751  \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1752  \hkl<0 -1 0> & {\color{orange}-2.39} & -0.17 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
1753  \hkl<0 1 0> & {\color{cyan}-2.25} & -1.90 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
1754  \hkl<-1 0 0> & {\color{orange}-2.39} & -0.36 & {\color{cyan}-2.25} & {\color{purple}-0.12} & {\color{magenta}-1.88} & {\color{gray}-0.05}\\
1755  \hkl<1 0 0> & {\color{cyan}-2.25} & -2.16 & {\color{green}-0.10} & {\color{blue}-0.27} & {\color{violet}-1.38} & {\color{yellow}-0.06}\\
1756  \hline
1757  C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1758  Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1759 \hline
1760 \end{tabular}
1761 }
1762
1763 \vspace*{0.3cm}
1764
1765 \footnotesize
1766
1767 \begin{minipage}[t]{3.8cm}
1768 \underline{\hkl<1 0 0> at position 1}\\[0.1cm]
1769 \includegraphics[width=3.5cm]{00-1dc/2-25.eps}
1770 \end{minipage}
1771 \begin{minipage}[t]{3.5cm}
1772 \underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
1773 \includegraphics[width=3.2cm]{00-1dc/2-39.eps}
1774 \end{minipage}
1775 \begin{minipage}[t]{5.5cm}
1776 \begin{itemize}
1777  \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\
1778        $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
1779  \item Stress compensation / increase
1780  \item Unfavored: antiparallel orientations
1781  \item Indication of energetically favored\\
1782        agglomeration
1783  \item Most favorable: C clustering
1784  \item However: High barrier ($>4\,\text{eV}$)
1785  \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$
1786        (Entropy)
1787 \end{itemize}
1788 \end{minipage}
1789
1790 \begin{picture}(0,0)(-295,-130)
1791 \includegraphics[width=3.5cm]{comb_pos.eps}
1792 \end{picture}
1793
1794 \end{slide}
1795
1796 \begin{slide}
1797
1798  {\large\bf\boldmath
1799   Combinations of C-Si \hkl<1 0 0>-type interstitials
1800  }
1801
1802 \small
1803
1804 \vspace*{0.1cm}
1805
1806 Energetically most favorable combinations along \hkl<1 1 0>
1807
1808 \vspace*{0.1cm}
1809
1810 {\scriptsize
1811 \begin{tabular}{l c c c c c c}
1812 \hline
1813  & 1 & 2 & 3 & 4 & 5 & 6\\
1814 \hline
1815 $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
1816 C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
1817 Type & \hkl<-1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0> & \hkl<1 0 0>, \hkl<0 -1 0>\\
1818 \hline
1819 \end{tabular}
1820 }
1821
1822 \vspace*{0.3cm}
1823
1824 \begin{minipage}{7.0cm}
1825 \includegraphics[width=7cm]{db_along_110_cc.ps}
1826 \end{minipage}
1827 \begin{minipage}{6.0cm}
1828 \begin{itemize}
1829  \item Interaction proportional to reciprocal cube of C-C distance
1830  \item Saturation in the immediate vicinity
1831  \renewcommand\labelitemi{$\Rightarrow$}
1832  \item Agglomeration of \ci{} expected
1833  \item Absence of C clustering
1834 \end{itemize}
1835 \begin{center}
1836 {\color{blue}
1837  Consisten with initial precipitation model
1838 }
1839 \end{center}
1840 \end{minipage}
1841
1842 \vspace{0.2cm}
1843
1844 \end{slide}
1845
1846 \begin{slide}
1847
1848  {\large\bf\boldmath
1849   Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
1850  }
1851
1852  \scriptsize
1853
1854 %\begin{center}
1855 %\begin{minipage}{3.2cm}
1856 %\includegraphics[width=3cm]{sub_110_combo.eps}
1857 %\end{minipage}
1858 %\begin{minipage}{7.8cm}
1859 %\begin{tabular}{l c c c c c c}
1860 %\hline
1861 %C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
1862 %                   \hkl<1 0 1> & \hkl<-1 0 1> \\
1863 %\hline
1864 %1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
1865 %2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
1866 %3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
1867 %4 & \RM{4} & B & D & E & E & D \\
1868 %5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
1869 %\hline
1870 %\end{tabular}
1871 %\end{minipage}
1872 %\end{center}
1873
1874 %\begin{center}
1875 %\begin{tabular}{l c c c c c c c c c c}
1876 %\hline
1877 %Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
1878 %\hline
1879 %$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
1880 %$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
1881 %$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
1882 %\hline
1883 %\end{tabular}
1884 %\end{center}
1885
1886 \begin{minipage}{6.0cm}
1887 \includegraphics[width=5.8cm]{c_sub_si110.ps}
1888 \end{minipage}
1889 \begin{minipage}{7cm}
1890 \scriptsize
1891 \begin{itemize}
1892  \item IBS: C may displace Si\\
1893        $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
1894  \item Assumption:\\
1895        \hkl<1 1 0>-type $\rightarrow$ favored combination
1896  \renewcommand\labelitemi{$\Rightarrow$}
1897  \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
1898  \item Less favorable than C-Si \hkl<1 0 0> dumbbell
1899  \item Interaction drops quickly to zero\\
1900        $\rightarrow$ low capture radius
1901 \end{itemize}
1902 \begin{center}
1903  {\color{blue}
1904  IBS process far from equilibrium\\
1905  \cs{} \& \si{} instead of thermodynamic ground state
1906  }
1907 \end{center}
1908 \end{minipage}
1909
1910 \begin{minipage}{6.5cm}
1911 \includegraphics[width=6.0cm]{162-097.ps}
1912 \begin{itemize}
1913  \item Low migration barrier
1914 \end{itemize}
1915 \end{minipage}
1916 \begin{minipage}{6.5cm}
1917 \begin{center}
1918 Ab initio MD at \degc{900}\\
1919 \includegraphics[width=3.3cm]{md_vasp_01.eps}
1920 $t=\unit[2230]{fs}$\\
1921 \includegraphics[width=3.3cm]{md_vasp_02.eps}
1922 $t=\unit[2900]{fs}$
1923 \end{center}
1924 {\color{blue}
1925 Contribution of entropy to structural formation
1926 }
1927 \end{minipage}
1928
1929 \end{slide}
1930
1931 \begin{slide}
1932
1933  {\large\bf\boldmath
1934   Migration in C-Si \hkl<1 0 0> and vacancy combinations
1935  }
1936
1937  \footnotesize
1938
1939 \vspace{0.1cm}
1940
1941 \begin{minipage}[t]{3cm}
1942 \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
1943 \includegraphics[width=2.8cm]{00-1dc/0-59.eps}
1944 \end{minipage}
1945 \begin{minipage}[t]{7cm}
1946 \vspace{0.2cm}
1947 \begin{center}
1948  Low activation energies\\
1949  High activation energies for reverse processes\\
1950  $\Downarrow$\\
1951  {\color{blue}C$_{\text{sub}}$ very stable}\\
1952 \vspace*{0.1cm}
1953  \hrule
1954 \vspace*{0.1cm}
1955  Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
1956  $\Downarrow$\\
1957  {\color{blue}Formation of SiC by successive substitution by C}
1958
1959 \end{center}
1960 \end{minipage}
1961 \begin{minipage}[t]{3cm}
1962 \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
1963 \includegraphics[width=2.8cm]{00-1dc/3-14.eps}
1964 \end{minipage}
1965
1966
1967 \framebox{
1968 \begin{minipage}{5.9cm}
1969 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
1970 \begin{center}
1971 \begin{picture}(0,0)(70,0)
1972 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
1973 \end{picture}
1974 \begin{picture}(0,0)(30,0)
1975 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
1976 \end{picture}
1977 \begin{picture}(0,0)(-10,0)
1978 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
1979 \end{picture}
1980 \begin{picture}(0,0)(-48,0)
1981 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
1982 \end{picture}
1983 \begin{picture}(0,0)(12.5,5)
1984 \includegraphics[width=1cm]{100_arrow.eps}
1985 \end{picture}
1986 \begin{picture}(0,0)(97,-10)
1987 \includegraphics[height=0.9cm]{001_arrow.eps}
1988 \end{picture}
1989 \end{center}
1990 \vspace{0.1cm}
1991 \end{minipage}
1992 }
1993 \begin{minipage}{0.3cm}
1994 \hfill
1995 \end{minipage}
1996 \framebox{
1997 \begin{minipage}{5.9cm}
1998 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
1999 \begin{center}
2000 \begin{picture}(0,0)(60,0)
2001 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
2002 \end{picture}
2003 \begin{picture}(0,0)(25,0)
2004 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
2005 \end{picture}
2006 \begin{picture}(0,0)(-20,0)
2007 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
2008 \end{picture}
2009 \begin{picture}(0,0)(-55,0)
2010 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
2011 \end{picture}
2012 \begin{picture}(0,0)(12.5,5)
2013 \includegraphics[width=1cm]{100_arrow.eps}
2014 \end{picture}
2015 \begin{picture}(0,0)(95,0)
2016 \includegraphics[height=0.9cm]{001_arrow.eps}
2017 \end{picture}
2018 \end{center}
2019 \vspace{0.1cm}
2020 \end{minipage}
2021 }
2022
2023 \end{slide}
2024
2025 \begin{slide}
2026
2027  {\large\bf
2028   Conclusion of defect / migration / combined defect simulations
2029  }
2030
2031  \footnotesize
2032
2033 \vspace*{0.1cm}
2034
2035 Defect structures
2036 \begin{itemize}
2037  \item Accurately described by quantum-mechanical simulations
2038  \item Less accurate description by classical potential simulations
2039  \item Underestimated formation energy of \cs{} by classical approach
2040  \item Both methods predict same ground state: \ci{} \hkl<1 0 0> dumbbell
2041 \end{itemize}
2042
2043 Migration
2044 \begin{itemize}
2045  \item C migration pathway in Si identified
2046  \item Consistent with reorientation and diffusion experiments
2047 \end{itemize}
2048 \begin{itemize}
2049  \item Different path and ...
2050  \item overestimated barrier by classical potential calculations
2051 \end{itemize}
2052
2053 Concerning the precipitation mechanism
2054 \begin{itemize}
2055  \item Agglomeration of C-Si dumbbells energetically favorable
2056        (stress compensation)
2057  \item C-Si indeed favored compared to
2058        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2059  \item Possible low interaction capture radius of
2060        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2061  \item Low barrier for
2062        \ci{} \hkl<1 0 0> $\rightarrow$ \cs{} \& \si{} \hkl<1 1 0>
2063  \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
2064        C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
2065 \end{itemize}
2066 \begin{center}
2067 {\color{blue}Results suggest increased participation of \cs}
2068 \end{center}
2069
2070 \end{slide}
2071
2072 \begin{slide}
2073
2074  {\large\bf
2075   Silicon carbide precipitation simulations
2076  }
2077
2078  \small
2079
2080 {\scriptsize
2081  \begin{pspicture}(0,0)(12,6.5)
2082   % nodes
2083   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
2084    \parbox{7cm}{
2085    \begin{itemize}
2086     \item Create c-Si volume
2087     \item Periodc boundary conditions
2088     \item Set requested $T$ and $p=0\text{ bar}$
2089     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
2090    \end{itemize}
2091   }}}}
2092   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
2093    \parbox{7cm}{
2094    Insertion of C atoms at constant T
2095    \begin{itemize}
2096     \item total simulation volume {\pnode{in1}}
2097     \item volume of minimal SiC precipitate {\pnode{in2}}
2098     \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
2099           precipitate
2100    \end{itemize}
2101   }}}}
2102   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
2103    \parbox{7.0cm}{
2104    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
2105   }}}}
2106   \ncline[]{->}{init}{insert}
2107   \ncline[]{->}{insert}{cool}
2108   \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
2109   \rput(7.8,6){\footnotesize $V_1$}
2110   \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
2111   \rput(9.2,4.85){\tiny $V_2$}
2112   \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
2113   \rput(9.55,4.45){\footnotesize $V_3$}
2114   \rput(7.9,3.2){\pnode{ins1}}
2115   \rput(9.22,2.8){\pnode{ins2}}
2116   \rput(11.0,2.4){\pnode{ins3}}
2117   \ncline[]{->}{in1}{ins1}
2118   \ncline[]{->}{in2}{ins2}
2119   \ncline[]{->}{in3}{ins3}
2120  \end{pspicture}
2121 }
2122
2123 \begin{itemize}
2124  \item Restricted to classical potential simulations
2125  \item $V_2$ and $V_3$ considered due to low diffusion
2126  \item Amount of C atoms: 6000
2127        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
2128  \item Simulation volume: $31\times 31\times 31$ unit cells
2129        (238328 Si atoms)
2130 \end{itemize}
2131
2132 \end{slide}
2133
2134 \begin{slide}
2135
2136  {\large\bf\boldmath
2137   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2138  }
2139
2140  \small
2141
2142 \begin{minipage}{6.5cm}
2143 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2144 \end{minipage}
2145 \begin{minipage}{6.5cm}
2146 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2147 \end{minipage}
2148
2149 \begin{minipage}{6.5cm}
2150 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2151 \end{minipage}
2152 \begin{minipage}{6.5cm}
2153 \scriptsize
2154 \underline{Low C concentration ($V_1$)}\\
2155 \hkl<1 0 0> C-Si dumbbell dominated structure
2156 \begin{itemize}
2157  \item Si-C bumbs around 0.19 nm
2158  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2159        concatenated dumbbells of various orientation
2160  \item Si-Si NN distance stretched to 0.3 nm
2161 \end{itemize}
2162 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2163 \underline{High C concentration ($V_2$, $V_3$)}\\
2164 High amount of strongly bound C-C bonds\\
2165 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2166 Only short range order observable\\
2167 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2168 \end{minipage}
2169
2170 \end{slide}
2171
2172 \begin{slide}
2173
2174  {\large\bf\boldmath
2175   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2176  }
2177
2178  \small
2179
2180 \begin{minipage}{6.5cm}
2181 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2182 \end{minipage}
2183 \begin{minipage}{6.5cm}
2184 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2185 \end{minipage}
2186
2187 \begin{minipage}{6.5cm}
2188 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2189 \end{minipage}
2190 \begin{minipage}{6.5cm}
2191 \scriptsize
2192 \underline{Low C concentration ($V_1$)}\\
2193 \hkl<1 0 0> C-Si dumbbell dominated structure
2194 \begin{itemize}
2195  \item Si-C bumbs around 0.19 nm
2196  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2197        concatenated dumbbells of various orientation
2198  \item Si-Si NN distance stretched to 0.3 nm
2199 \end{itemize}
2200 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2201 \underline{High C concentration ($V_2$, $V_3$)}\\
2202 High amount of strongly bound C-C bonds\\
2203 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2204 Only short range order observable\\
2205 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2206 \end{minipage}
2207
2208 \begin{pspicture}(0,0)(0,0)
2209 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2210 \begin{minipage}{10cm}
2211 \small
2212 {\color{red}\bf 3C-SiC formation fails to appear}
2213 \begin{itemize}
2214 \item Low C concentration simulations
2215  \begin{itemize}
2216   \item Formation of \ci{} indeed occurs
2217   \item Agllomeration not observed
2218  \end{itemize}
2219 \item High C concentration simulations
2220  \begin{itemize}
2221   \item Amorphous SiC-like structure\\
2222         (not expected at prevailing temperatures)
2223   \item Rearrangement and transition into 3C-SiC structure missing
2224  \end{itemize}
2225 \end{itemize}
2226 \end{minipage}
2227  }}}
2228 \end{pspicture}
2229
2230 \end{slide}
2231
2232 \begin{slide}
2233
2234  {\large\bf
2235   Limitations of molecular dynamics and short range potentials
2236  }
2237
2238 \footnotesize
2239
2240 \vspace{0.2cm}
2241
2242 \underline{Time scale problem of MD}\\[0.2cm]
2243 Minimize integration error\\
2244 $\Rightarrow$ discretization considerably smaller than
2245               reciprocal of fastest vibrational mode\\[0.1cm]
2246 Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
2247 $\Rightarrow$ suitable choice of time step:
2248               $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
2249 $\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
2250 Several local minima in energy surface separated by large energy barriers\\
2251 $\Rightarrow$ transition event corresponds to a multiple
2252               of vibrational periods\\
2253 $\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
2254               infrequent transition events\\[0.1cm]
2255 {\color{blue}Accelerated methods:}
2256 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
2257
2258 \vspace{0.3cm}
2259
2260 \underline{Limitations related to the short range potential}\\[0.2cm]
2261 Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
2262 and 2$^{\text{nd}}$ next neighbours\\
2263 $\Rightarrow$ overestimated unphysical high forces of next neighbours
2264
2265 \vspace{0.3cm}
2266
2267 \framebox{
2268 \color{red}
2269 Potential enhanced problem of slow phase space propagation
2270 }
2271
2272 \vspace{0.3cm}
2273
2274 \underline{Approach to the (twofold) problem}\\[0.2cm]
2275 Increased temperature simulations without TAD corrections\\
2276 (accelerated methods or higher time scales exclusively not sufficient)
2277
2278 \begin{picture}(0,0)(-260,-30)
2279 \framebox{
2280 \begin{minipage}{4.2cm}
2281 \tiny
2282 \begin{center}
2283 \vspace{0.03cm}
2284 \underline{IBS}
2285 \end{center}
2286 \begin{itemize}
2287 \item 3C-SiC also observed for higher T
2288 \item higher T inside sample
2289 \item structural evolution vs.\\
2290       equilibrium properties
2291 \end{itemize}
2292 \end{minipage}
2293 }
2294 \end{picture}
2295
2296 \begin{picture}(0,0)(-305,-155)
2297 \framebox{
2298 \begin{minipage}{2.5cm}
2299 \tiny
2300 \begin{center}
2301 retain proper\\
2302 thermodynmic sampling
2303 \end{center}
2304 \end{minipage}
2305 }
2306 \end{picture}
2307
2308 \end{slide}
2309
2310 \begin{slide}
2311
2312  {\large\bf
2313   Increased temperature simulations at low C concentration
2314  }
2315
2316 \small
2317
2318 \begin{minipage}{6.5cm}
2319 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2320 \end{minipage}
2321 \begin{minipage}{6.5cm}
2322 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2323 \end{minipage}
2324
2325 \begin{minipage}{6.5cm}
2326 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2327 \end{minipage}
2328 \begin{minipage}{6.5cm}
2329 \scriptsize
2330  \underline{Si-C bonds:}
2331  \begin{itemize}
2332   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2333   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2334  \end{itemize}
2335  \underline{Si-Si bonds:}
2336  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2337  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2338  \underline{C-C bonds:}
2339  \begin{itemize}
2340   \item C-C next neighbour pairs reduced (mandatory)
2341   \item Peak at 0.3 nm slightly shifted
2342         \begin{itemize}
2343          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2344                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2345                combinations (|)\\
2346                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2347                ($\downarrow$)
2348          \item Range [|-$\downarrow$]:
2349                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2350                with nearby Si$_{\text{I}}$}
2351         \end{itemize}
2352  \end{itemize}
2353 \end{minipage}
2354
2355 \begin{picture}(0,0)(-330,-74)
2356 \color{blue}
2357 \framebox{
2358 \begin{minipage}{1.6cm}
2359 \tiny
2360 \begin{center}
2361 stretched SiC\\[-0.1cm]
2362 in c-Si
2363 \end{center}
2364 \end{minipage}
2365 }
2366 \end{picture}
2367
2368 \end{slide}
2369
2370 \begin{slide}
2371
2372  {\large\bf
2373   Increased temperature simulations at low C concentration
2374  }
2375
2376 \small
2377
2378 \begin{minipage}{6.5cm}
2379 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2380 \end{minipage}
2381 \begin{minipage}{6.5cm}
2382 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2383 \end{minipage}
2384
2385 \begin{minipage}{6.5cm}
2386 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2387 \end{minipage}
2388 \begin{minipage}{6.5cm}
2389 \scriptsize
2390  \underline{Si-C bonds:}
2391  \begin{itemize}
2392   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2393   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2394  \end{itemize}
2395  \underline{Si-Si bonds:}
2396  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2397  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2398  \underline{C-C bonds:}
2399  \begin{itemize}
2400   \item C-C next neighbour pairs reduced (mandatory)
2401   \item Peak at 0.3 nm slightly shifted
2402         \begin{itemize}
2403          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2404                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2405                combinations (|)\\
2406                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2407                ($\downarrow$)
2408          \item Range [|-$\downarrow$]:
2409                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2410                with nearby Si$_{\text{I}}$}
2411         \end{itemize}
2412  \end{itemize}
2413 \end{minipage}
2414
2415 %\begin{picture}(0,0)(-330,-74)
2416 %\color{blue}
2417 %\framebox{
2418 %\begin{minipage}{1.6cm}
2419 %\tiny
2420 %\begin{center}
2421 %stretched SiC\\[-0.1cm]
2422 %in c-Si
2423 %\end{center}
2424 %\end{minipage}
2425 %}
2426 %\end{picture}
2427
2428 \begin{pspicture}(0,0)(0,0)
2429 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2430 \begin{minipage}{10cm}
2431 \small
2432 {\color{blue}\bf Stretched SiC in c-Si}
2433 \begin{itemize}
2434 \item Consistent to precipitation model involving \cs{}
2435 \item Explains annealing behavior of high/low T C implants
2436       \begin{itemize}
2437        \item Low T: highly mobiel \ci{}
2438        \item High T: stable configurations of \cs{}
2439       \end{itemize}
2440 \end{itemize}
2441 $\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2442 $\Rightarrow$ Precipitation mechanism involving \cs{}
2443 \end{minipage}
2444  }}}
2445 \end{pspicture}
2446
2447 \end{slide}
2448
2449 \begin{slide}
2450
2451  {\large\bf
2452   Increased temperature simulations at high C concentration
2453  }
2454
2455 \footnotesize
2456
2457 \begin{minipage}{6.5cm}
2458 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2459 \end{minipage}
2460 \begin{minipage}{6.5cm}
2461 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2462 \end{minipage}
2463
2464 \vspace{0.1cm}
2465
2466 \scriptsize
2467
2468 \framebox{
2469 \begin{minipage}[t]{6.0cm}
2470 0.186 nm: Si-C pairs $\uparrow$\\
2471 (as expected in 3C-SiC)\\[0.2cm]
2472 0.282 nm: Si-C-C\\[0.2cm]
2473 $\approx$0.35 nm: C-Si-Si
2474 \end{minipage}
2475 }
2476 \begin{minipage}{0.2cm}
2477 \hfill
2478 \end{minipage}
2479 \framebox{
2480 \begin{minipage}[t]{6.0cm}
2481 0.15 nm: C-C pairs $\uparrow$\\
2482 (as expected in graphite/diamond)\\[0.2cm]
2483 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2484 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2485 \end{minipage}
2486 }
2487
2488 \begin{itemize}
2489 \item Decreasing cut-off artifact
2490 \item {\color{red}Amorphous} SiC-like phase remains
2491 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2492 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2493 \end{itemize}
2494
2495 \vspace{-0.1cm}
2496
2497 \begin{center}
2498 {\color{blue}
2499 \framebox{
2500 {\color{black}
2501 High C \& small $V$ \& short $t$
2502 $\Rightarrow$
2503 }
2504 Slow restructuring due to strong C-C bonds
2505 {\color{black}
2506 $\Leftarrow$
2507 High C \& low T implants
2508 }
2509 }
2510 }
2511 \end{center}
2512
2513 \end{slide}
2514
2515 \begin{slide}
2516
2517  {\large\bf
2518   Summary and Conclusions
2519  }
2520
2521  \scriptsize
2522
2523 %\vspace{0.1cm}
2524
2525 \framebox{
2526 \begin{minipage}[t]{12.9cm}
2527  \underline{Pecipitation simulations}
2528  \begin{itemize}
2529   \item High C concentration $\rightarrow$ amorphous SiC like phase
2530   \item Problem of potential enhanced slow phase space propagation
2531   \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2532   \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2533   \item High T necessary to simulate IBS conditions (far from equilibrium)
2534   \item Precipitation by successive agglomeration of \cs (epitaxy)
2535   \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2536         (stretched SiC, interface)
2537  \end{itemize}
2538 \end{minipage}
2539 }
2540
2541 %\vspace{0.1cm}
2542
2543 \framebox{
2544 \begin{minipage}{12.9cm}
2545  \underline{Defects}
2546  \begin{itemize}
2547    \item DFT / EA
2548         \begin{itemize}
2549          \item Point defects excellently / fairly well described
2550                by DFT / EA
2551          \item C$_{\text{sub}}$ drastically underestimated by EA
2552          \item EA predicts correct ground state:
2553                C$_{\text{sub}}$ \& \si{} $>$ \ci{}
2554          \item Identified migration path explaining
2555                diffusion and reorientation experiments by DFT
2556          \item EA fails to describe \ci{} migration:
2557                Wrong path \& overestimated barrier
2558         \end{itemize}
2559    \item Combinations of defects
2560          \begin{itemize}
2561           \item Agglomeration of point defects energetically favorable
2562                 by compensation of stress
2563           \item Formation of C-C unlikely
2564           \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2565           \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2566                 Low barrier (\unit[0.77]{eV}) \& low capture radius
2567         \end{itemize}
2568  \end{itemize}
2569 \end{minipage}
2570 }
2571
2572 \begin{center}
2573 {\color{blue}
2574 \framebox{Precipitation by successive agglomeration of \cs{}}
2575 }
2576 \end{center}
2577
2578 \end{slide}
2579
2580 \begin{slide}
2581
2582  {\large\bf
2583   Acknowledgements
2584  }
2585
2586  \vspace{0.1cm}
2587
2588  \small
2589
2590  Thanks to \ldots
2591
2592  \underline{Augsburg}
2593  \begin{itemize}
2594   \item Prof. B. Stritzker (accomodation at EP \RM{4})
2595   \item Ralf Utermann (EDV)
2596  \end{itemize}
2597
2598  \underline{Helsinki}
2599  \begin{itemize}
2600   \item Prof. K. Nordlund (MD)
2601  \end{itemize}
2602
2603  \underline{Munich}
2604  \begin{itemize}
2605   \item Bayerische Forschungsstiftung (financial support)
2606  \end{itemize}
2607
2608  \underline{Paderborn}
2609  \begin{itemize}
2610   \item Prof. J. Lindner (SiC)
2611   \item Prof. G. Schmidt (DFT + financial support)
2612   \item Dr. E. Rauls (DFT + SiC)
2613   \item Dr. S. Sanna (VASP)
2614  \end{itemize}
2615
2616 \vspace{0.2cm}
2617
2618 \begin{center}
2619 \framebox{
2620 \bf Thank you for your attention!
2621 }
2622 \end{center}
2623
2624 \end{slide}
2625
2626 \end{document}
2627
2628 \fi