posic/talks/mpi_app.tex

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