posic/talks/mpi_app.tex

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