posic/talks/mpi_app.tex

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  36
  37 % units
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  39
  40 \usepackage{semcolor}
  41 \usepackage{semlayer}           % Seminar overlays
  42 \usepackage{slidesec}           % Seminar sections and list of slides
  43
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  80 \begin{document}
  81
  82 \extraslideheight{10in}
  83 \slideframe{plain}
  84
  85 \pagestyle{empty}
  86
  87 % specify width and height
  88 \slidewidth 26.3cm
  89 \slideheight 19.9cm
  90
  91 % margin
  92 \def\slidetopmargin{-0.15cm}
  93
  94 \newcommand{\ham}{\mathcal{H}}
  95 \newcommand{\pot}{\mathcal{V}}
  96 \newcommand{\foo}{\mathcal{U}}
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  98
  99 % itemize level ii
 100 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
 101
 102 % nice phi
 103 \renewcommand{\phi}{\varphi}
 104
 105 % roman letters
 106 \newcommand{\RM}[1]{\MakeUppercase{\romannumeral #1{}}}
 107
 108 % colors
 109 \newrgbcolor{si-yellow}{.6 .6 0}
 110 \newrgbcolor{hb}{0.75 0.77 0.89}
 111 \newrgbcolor{lbb}{0.75 0.8 0.88}
 112 \newrgbcolor{hlbb}{0.825 0.88 0.968}
 113 \newrgbcolor{lachs}{1.0 .93 .81}
 114
 115 % shortcuts
 116 \newcommand{\si}{Si$_{\text{i}}${}}
 117 \newcommand{\ci}{C$_{\text{i}}${}}
 118 \newcommand{\cs}{C$_{\text{sub}}${}}
 119 \newcommand{\degc}[1]{\unit[#1]{$^{\circ}$C}{}}
 120 \newcommand{\distn}[1]{\unit[#1]{nm}{}}
 121 \newcommand{\dista}[1]{\unit[#1]{\AA}{}}
 122 \newcommand{\perc}[1]{\unit[#1]{\%}{}}
 123
 124 % no vertical centering
 125 %\centerslidesfalse
 126
 127 % layout check
 128 %\layout
 129 \begin{slide}
 130 \center
 131 {\Huge
 132 E\\
 133 F\\
 134 G\\
 135 A B C D E F G H G F E D C B A
 136 G\\
 137 F\\
 138 E\\
 139 }
 140 \end{slide}
 141
 142 % topic
 143
 144 \begin{slide}
 145 \begin{center}
 146
 147  \vspace{16pt}
 148
 149  {\LARGE\bf
 150   Atomistic simulation studies\\[0.2cm]
 151   in the C/Si system
 152  }
 153
 154  \vspace{48pt}
 155
 156  \textsc{Frank Zirkelbach}
 157
 158  \vspace{48pt}
 159
 160  Application talk at the Max Planck Institute for Solid State Research
 161
 162  \vspace{08pt}
 163
 164  Stuttgart, November 2011
 165
 166 \end{center}
 167 \end{slide}
 168
 169 % no vertical centering
 170 \centerslidesfalse
 171
 172 \ifnum1=0
 173
 174 % intro
 175
 176 \begin{slide}
 177
 178 %{\large\bf
 179 % Phase diagram of the C/Si system\\
 180 %}
 181
 182 \vspace*{0.2cm}
 183
 184 \begin{minipage}{6.5cm}
 185 \includegraphics[width=6.5cm]{si-c_phase.eps}
 186 \begin{center}
 187 {\tiny
 188 R. I. Scace and G. A. Slack, J. Chem. Phys. 30, 1551 (1959)
 189 }
 190 \end{center}
 191 \begin{pspicture}(0,0)(0,0)
 192 \psellipse[linecolor=blue,linewidth=0.1cm](3.55,4.0)(0.5,2.9)
 193 \end{pspicture}
 194 \end{minipage}
 195 \begin{minipage}{6cm}
 196 {\bf Phase diagram of the C/Si system}\\[0.2cm]
 197 {\color{blue}Stoichiometric composition}
 198 \begin{itemize}
 199 \item only chemical stable compound
 200 \item wide band gap semiconductor\\
 201       \underline{silicon carbide}, SiC
 202 \end{itemize}
 203 \end{minipage}
 204
 205 \end{slide}
 206
 207 % motivation / properties / applications of silicon carbide
 208
 209 \begin{slide}
 210
 211 \vspace*{1.8cm}
 212
 213 \small
 214
 215 \begin{pspicture}(0,0)(13.5,5)
 216
 217  \psframe*[linecolor=hb](-0.2,0)(12.9,5)
 218
 219  \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](5.2,1)(6.5,1)(6.5,3)(5.2,3)
 220  \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](6.4,0.5)(7.7,2)(7.7,2)(6.4,3.5)
 221
 222  \rput[lt](0,4.6){\color{gray}PROPERTIES}
 223
 224  \rput[lt](0.3,4){wide band gap}
 225  \rput[lt](0.3,3.5){high electric breakdown field}
 226  \rput[lt](0.3,3){good electron mobility}
 227  \rput[lt](0.3,2.5){high electron saturation drift velocity}
 228  \rput[lt](0.3,2){high thermal conductivity}
 229
 230  \rput[lt](0.3,1.5){hard and mechanically stable}
 231  \rput[lt](0.3,1){chemically inert}
 232
 233  \rput[lt](0.3,0.5){radiation hardness}
 234
 235  \rput[rt](12.7,4.6){\color{gray}APPLICATIONS}
 236
 237  \rput[rt](12.5,3.85){high-temperature, high power}
 238  \rput[rt](12.5,3.5){and high-frequency}
 239  \rput[rt](12.5,3.15){electronic and optoelectronic devices}
 240
 241  \rput[rt](12.5,2.35){material suitable for extreme conditions}
 242  \rput[rt](12.5,2){microelectromechanical systems}
 243  \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements}
 244
 245  \rput[rt](12.5,0.85){first wall reactor material, detectors}
 246  \rput[rt](12.5,0.5){and electronic devices for space}
 247
 248 \end{pspicture}
 249
 250 \begin{picture}(0,0)(5,-162)
 251 \includegraphics[height=2.2cm]{3C_SiC_bs.eps}
 252 \end{picture}
 253 \begin{picture}(0,0)(-120,-162)
 254 \includegraphics[height=2.2cm]{nasa_600c_led.eps}
 255 \end{picture}
 256 \begin{picture}(0,0)(-270,-162)
 257 \includegraphics[height=2.2cm]{6h-sic_3c-sic.eps}
 258 \end{picture}
 259 %%%%
 260 \begin{picture}(0,0)(10,65)
 261 \includegraphics[height=2.8cm]{sic_switch.eps}
 262 \end{picture}
 263 %\begin{picture}(0,0)(-243,65)
 264 \begin{picture}(0,0)(-110,65)
 265 \includegraphics[height=2.8cm]{ise_99.eps}
 266 \end{picture}
 267 %\begin{picture}(0,0)(-135,65)
 268 \begin{picture}(0,0)(-100,65)
 269 \includegraphics[height=1.2cm]{infineon_schottky.eps}
 270 \end{picture}
 271 \begin{picture}(0,0)(-233,65)
 272 \includegraphics[height=2.8cm]{solar_car.eps}
 273 \end{picture}
 274
 275 \end{slide}
 276
 277 % motivation
 278
 279 \begin{slide}
 280
 281  {\large\bf
 282   Polytypes of SiC\\[0.4cm]
 283  }
 284
 285 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
 286 \begin{minipage}{1.9cm}
 287 {\tiny cubic (twist)}
 288 \end{minipage}
 289 \begin{minipage}{2.9cm}
 290 {\tiny hexagonal (no twist)}
 291 \end{minipage}
 292
 293 \begin{picture}(0,0)(-150,0)
 294  \includegraphics[width=7cm]{polytypes.eps}
 295 \end{picture}
 296
 297 \vspace{0.6cm}
 298
 299 \footnotesize
 300
 301 \begin{tabular}{l c c c c c c}
 302 \hline
 303  & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
 304 \hline
 305 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
 306 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
 307 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
 308 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
 309 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
 310 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
 311 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
 312 \hline
 313 \end{tabular}
 314
 315 \begin{pspicture}(0,0)(0,0)
 316 \psellipse[linecolor=green](5.7,2.10)(0.4,0.5)
 317 \end{pspicture}
 318 \begin{pspicture}(0,0)(0,0)
 319 \psellipse[linecolor=green](5.6,0.92)(0.4,0.2)
 320 \end{pspicture}
 321 \begin{pspicture}(0,0)(0,0)
 322 \psellipse[linecolor=red](10.45,0.45)(0.4,0.2)
 323 \end{pspicture}
 324
 325 \end{slide}
 326
 327 % fabrication
 328
 329 \begin{slide}
 330
 331  {\large\bf
 332   Fabrication of silicon carbide
 333  }
 334
 335  \small
 336
 337  \vspace{2pt}
 338
 339 \begin{center}
 340  {\color{gray}
 341  \emph{Silicon carbide --- Born from the stars, perfected on earth.}
 342  }
 343 \end{center}
 344
 345 \vspace{2pt}
 346
 347 SiC thin films by MBE \& CVD
 348 \begin{itemize}
 349  \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
 350  \item \underline{Commercially available} semiconductor power devices based on
 351        \underline{\foreignlanguage{greek}{a}-SiC}
 352  \item Production of favored \underline{3C-SiC} material
 353        \underline{less advanced}
 354  \item Quality and size not yet sufficient
 355 \end{itemize}
 356 \begin{picture}(0,0)(-310,-20)
 357   \includegraphics[width=2.0cm]{cree.eps}
 358 \end{picture}
 359
 360 \vspace{-0.2cm}
 361
 362 Alternative approach:
 363 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
 364
 365 \vspace{0.2cm}
 366
 367 \scriptsize
 368
 369 \framebox{
 370 \begin{minipage}{3.15cm}
 371  \begin{center}
 372 \includegraphics[width=3cm]{imp.eps}\\
 373  {\tiny
 374   Carbon implantation
 375  }
 376  \end{center}
 377 \end{minipage}
 378 \begin{minipage}{3.15cm}
 379  \begin{center}
 380 \includegraphics[width=3cm]{annealing.eps}\\
 381  {\tiny
 382   \unit[12]{h} annealing at \degc{1200}
 383  }
 384  \end{center}
 385 \end{minipage}
 386 }
 387 \begin{minipage}{5.5cm}
 388  \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm]
 389  \begin{center}
 390  {\tiny
 391   XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
 392  }
 393  \end{center}
 394 \end{minipage}
 395
 396 \end{slide}
 397
 398 % contents
 399
 400 \begin{slide}
 401
 402 {\large\bf
 403  Systematic investigation of C implantations into Si
 404 }
 405
 406 \vspace{1.7cm}
 407 \begin{center}
 408 \hspace{-1.0cm}
 409 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
 410 \end{center}
 411
 412 \end{slide}
 413
 414 % outline
 415
 416 \begin{slide}
 417
 418 {\large\bf
 419  Outline
 420 }
 421
 422 \vspace{1.7cm}
 423 \begin{center}
 424 \hspace{-1.0cm}
 425 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
 426 \end{center}
 427
 428 \begin{pspicture}(0,0)(0,0)
 429 \rput(6.0,7.0){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{
 430 \begin{minipage}{11cm}
 431 {\color{black}Diploma thesis}\\
 432  \underline{Monte Carlo} simulation modeling the selforganization process\\
 433  leading to periodic arrays of nanometric amorphous SiC precipitates
 434 \end{minipage}
 435 }}}
 436 \end{pspicture}
 437 \begin{pspicture}(0,0)(0,0)
 438 \rput(6.0,-0.5){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=blue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{
 439 \begin{minipage}{11cm}
 440 {\color{black}Doctoral studies}\\
 441  Classical potential \underline{molecular dynamics} simulations \ldots\\
 442  \underline{Density functional theory} calculations \ldots\\[0.2cm]
 443  \ldots on defect formation and SiC precipitation in Si
 444 \end{minipage}
 445 }}}
 446 \end{pspicture}
 447 \begin{pspicture}(0,0)(0,0)
 448 \psellipse[linecolor=red,linewidth=0.05cm](5,3.0)(0.8,1.0)
 449 \end{pspicture}
 450 \begin{pspicture}(0,0)(0,0)
 451 \psellipse[linecolor=blue,linewidth=0.05cm](8.2,3.2)(1.5,1.6)
 452 \end{pspicture}
 453
 454 \end{slide}
 455
 456 \begin{slide}
 457
 458 \headdiplom
 459 {\large\bf
 460  Selforganization of nanometric amorphous SiC lamellae
 461 }
 462
 463 \small
 464
 465 \vspace{0.2cm}
 466
 467 \begin{itemize}
 468  \item Regularly spaced, nanometric spherical\\
 469        and lamellar amorphous inclusions\\
 470        at the upper a/c interface
 471  \item Carbon accumulation\\
 472        in amorphous volumes
 473 \end{itemize}
 474
 475 \vspace{0.4cm}
 476
 477 \begin{minipage}{12cm}
 478 \includegraphics[width=9cm]{../../nlsop/img/k393abild1_e_l.eps}\\
 479 {\scriptsize
 480 XTEM bright-field, \unit[180]{keV} C$^+ \rightarrow$ Si, \degc{150},
 481 Dose: \unit[4.3 $\times 10^{17}$]{cm$^{-2}$}
 482 }
 483 \end{minipage}
 484
 485 \begin{picture}(0,0)(-182,-215)
 486 \begin{minipage}{6.5cm}
 487 \begin{center}
 488 \includegraphics[width=6.5cm]{../../nlsop/img/eftem.eps}\\[-0.2cm]
 489 {\scriptsize
 490 XTEM bright-field and respective EFTEM C map
 491 }
 492 \end{center}
 493 \end{minipage}
 494 \end{picture}
 495
 496 \end{slide}
 497
 498 \begin{slide}
 499
 500 \headdiplom
 501 {\large\bf
 502  Model displaying the formation of ordered lamellae
 503 }
 504
 505 \vspace{0.1cm}
 506
 507 \begin{center}
 508  \includegraphics[width=8.0cm]{../../nlsop/img/modell_ng_e.eps}
 509 \end{center}
 510
 511 \footnotesize
 512
 513 \begin{itemize}
 514 \item Supersaturation of C in c-Si\\
 515       $\rightarrow$ {\bf Carbon induced} nucleation of spherical
 516       SiC$_x$-precipitates
 517 \item High interfacial energy between 3C-SiC and c-Si\\
 518       $\rightarrow$ {\bf Amorphous} precipitates
 519 \item \unit[20-- 30]{\%} lower silicon density of a-SiC$_x$ compared to c-Si\\
 520       $\rightarrow$ {\bf Lateral strain} (black arrows)
 521 \item Implantation range near surface\\
 522       $\rightarrow$ {\bf Relaxation} of {\bf vertical strain component}
 523 \item Reduction of the carbon supersaturation in c-Si\\
 524       $\rightarrow$ {\bf Carbon diffusion} into amorphous volumina
 525       (white arrows)
 526 \item Remaining lateral strain\\
 527       $\rightarrow$ {\bf Strain enhanced} lateral amorphisation
 528 \item Absence of crystalline neighbours (structural information)\\
 529       $\rightarrow$ {\bf Stabilization} of amorphous inclusions
 530       {\bf against recrystallization}
 531 \end{itemize}
 532
 533 \end{slide}
 534
 535 \begin{slide}
 536
 537 \headdiplom
 538 {\large\bf
 539  Implementation of the Monte Carlo code
 540 }
 541
 542 \small
 543
 544 \begin{enumerate}
 545  \item \underline{Amorphization / Recrystallization}\\
 546        Ion collision in discretized target determined by random numbers
 547        distributed according to nuclear energy loss.
 548        Amorphization/recrystallization probability:
 549 \[
 550 p_{c \rightarrow a}(\vec{r}) = {\color{green} p_b} + {\color{blue} p_c c_C(\vec{r})} + {\color{red} \sum_{\textrm{amorphous neighbours}} \frac{p_s c_C(\vec{r'})}{(r-r')^2}}
 551 \]
 552 \begin{itemize}
 553  \item {\color{green} $p_b$} normal `ballistic' amorphization
 554  \item {\color{blue} $p_c$} carbon induced amorphization
 555  \item {\color{red} $p_s$} stress enhanced amorphization
 556 \end{itemize}
 557 \[
 558 p_{a \rightarrow c}(\vec r) = (1 - p_{c \rightarrow a}(\vec r)) \Big(1 - \frac{\sum_{direct \, neighbours} \delta (\vec{r'})}{6} \Big) \, \textrm{,}
 559 \]
 560 \[
 561 \delta (\vec r) = \left\{
 562 \begin{array}{ll}
 563         1 & \textrm{if volume at position $\vec r$ is amorphous} \\
 564         0 & \textrm{otherwise} \\
 565 \end{array}
 566 \right.
 567 \]
 568  \item \underline{Carbon incorporation}\\
 569        Incorporation volume determined according to implantation profile
 570  \item \underline{Diffusion / Sputtering}
 571        \begin{itemize}
 572         \item Transfer fraction of C atoms
 573               of crystalline into neighbored amorphous volumes
 574         \item Remove surface layer
 575        \end{itemize}
 576 \end{enumerate}
 577
 578 \end{slide}
 579
 580 \fi
 581
 582 \begin{slide}
 583
 584 \begin{minipage}{3.7cm}
 585 \headdiplom
 586 {\large\bf
 587  Results
 588 }
 589
 590 \footnotesize
 591
 592 \vspace{1.2cm}
 593
 594 Evolution of the \ldots
 595 \begin{itemize}
 596  \item continuous\\
 597        amorphous layer
 598  \item a/c interface
 599  \item lamella precipitates
 600 \end{itemize}
 601 \ldots reproduced!\\[1.4cm]
 602
 603 {\color{blue}
 604 \begin{center}
 605 Experiment \& simulation\\
 606 in good agreement\\[1.0cm]
 607
 608 Simulation is able to model the whole depth region\\[1.2cm]
 609 \end{center}
 610 }
 611
 612 \end{minipage}
 613 \begin{minipage}{0.5cm}
 614 \vfill
 615 \end{minipage}
 616 \begin{minipage}{8.0cm}
 617  \vspace{-0.3cm}
 618  \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e_1-2.eps}\\
 619  \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e2_2-2.eps}
 620 \end{minipage}
 621
 622 \end{slide}
 623
 624 \begin{slide}
 625
 626 \headdiplom
 627 {\large\bf
 628  Structural \& compositional details
 629 }
 630
 631 \begin{minipage}[t]{7.5cm}
 632 \includegraphics[height=6.5cm]{../../nlsop/img/ac_cconc_ver2_e.eps}\\
 633 \end{minipage}
 634 \begin{minipage}[t]{5.0cm}
 635 \includegraphics[height=6.5cm]{../../nlsop/img/97_98_e.eps}
 636 \end{minipage}
 637
 638 \footnotesize
 639
 640 \vspace{-0.1cm}
 641
 642 \begin{itemize}
 643  \item Fluctuation of C concentration in lamellae region
 644  \item \unit[8--10]{at.\%} C saturation limit
 645        within the respective conditions
 646  \item Complementarily arranged and alternating sequence of layers\\
 647        with a high and low amount of amorphous regions
 648  \item C accumulation in the amorphous phase / Origin of stress
 649 \end{itemize}
 650
 651 \begin{picture}(0,0)(-265,-30)
 652 \framebox{
 653 \begin{minipage}{3cm}
 654 \begin{center}
 655 {\color{blue}
 656 Precipitation process\\
 657 gets traceable\\
 658 by simulation!
 659 }
 660 \end{center}
 661 \end{minipage}
 662 }
 663 \end{picture}
 664
 665 \end{slide}
 666
 667
 668 \end{document}
 669
 670 \ifnum1=0
 671
 672 % continue here
 673 %\fi
 674
 675 \begin{slide}
 676
 677 {\large\bf
 678  Model displaying the formation of ordered lamellae
 679 }
 680
 681 \framebox{
 682  \begin{minipage}{6.3cm}
 683  \begin{center}
 684  {\color{blue}
 685   Precipitation mechanism not yet fully understood!
 686  }
 687  \renewcommand\labelitemi{$\Rightarrow$}
 688  \small
 689  \underline{Understanding the SiC precipitation}
 690  \begin{itemize}
 691   \item significant technological progress in SiC thin film formation
 692   \item perspectives for processes relying upon prevention of SiC precipitation
 693  \end{itemize}
 694  \end{center}
 695  \end{minipage}
 696 }
 697
 698 \end{slide}
 699
 700 \begin{slide}
 701
 702  {\large\bf
 703   Supposed precipitation mechanism of SiC in Si
 704  }
 705
 706  \scriptsize
 707
 708  \vspace{0.1cm}
 709
 710  \begin{minipage}{3.8cm}
 711  Si \& SiC lattice structure\\[0.2cm]
 712  \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
 713  \hrule
 714  \end{minipage}
 715  \hspace{0.6cm}
 716  \begin{minipage}{3.8cm}
 717  \begin{center}
 718  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 719  \end{center}
 720  \end{minipage}
 721  \hspace{0.6cm}
 722  \begin{minipage}{3.8cm}
 723  \begin{center}
 724  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 725  \end{center}
 726  \end{minipage}
 727
 728  \begin{minipage}{4cm}
 729  \begin{center}
 730  C-Si dimers (dumbbells)\\[-0.1cm]
 731  on Si interstitial sites
 732  \end{center}
 733  \end{minipage}
 734  \hspace{0.2cm}
 735  \begin{minipage}{4.2cm}
 736  \begin{center}
 737  Agglomeration of C-Si dumbbells\\[-0.1cm]
 738  $\Rightarrow$ dark contrasts
 739  \end{center}
 740  \end{minipage}
 741  \hspace{0.2cm}
 742  \begin{minipage}{4cm}
 743  \begin{center}
 744  Precipitation of 3C-SiC in Si\\[-0.1cm]
 745  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 746  \& release of Si self-interstitials
 747  \end{center}
 748  \end{minipage}
 749
 750  \begin{minipage}{3.8cm}
 751  \begin{center}
 752  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 753  \end{center}
 754  \end{minipage}
 755  \hspace{0.6cm}
 756  \begin{minipage}{3.8cm}
 757  \begin{center}
 758  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 759  \end{center}
 760  \end{minipage}
 761  \hspace{0.6cm}
 762  \begin{minipage}{3.8cm}
 763  \begin{center}
 764  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 765  \end{center}
 766  \end{minipage}
 767
 768 \begin{pspicture}(0,0)(0,0)
 769 \psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
 770 \psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
 771 \rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
 772 \psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
 773 \rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 774  $4a_{\text{Si}}=5a_{\text{SiC}}$
 775  }}}
 776 \rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 777 \hkl(h k l) planes match
 778  }}}
 779 \rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 780 r = 2 - 4 nm
 781  }}}
 782 \end{pspicture}
 783
 784 \end{slide}
 785
 786 \begin{slide}
 787
 788  {\large\bf
 789   Supposed precipitation mechanism of SiC in Si
 790  }
 791
 792  \scriptsize
 793
 794  \vspace{0.1cm}
 795
 796  \begin{minipage}{3.8cm}
 797  Si \& SiC lattice structure\\[0.2cm]
 798  \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
 799  \hrule
 800  \end{minipage}
 801  \hspace{0.6cm}
 802  \begin{minipage}{3.8cm}
 803  \begin{center}
 804  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 805  \end{center}
 806  \end{minipage}
 807  \hspace{0.6cm}
 808  \begin{minipage}{3.8cm}
 809  \begin{center}
 810  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 811  \end{center}
 812  \end{minipage}
 813
 814  \begin{minipage}{4cm}
 815  \begin{center}
 816  C-Si dimers (dumbbells)\\[-0.1cm]
 817  on Si interstitial sites
 818  \end{center}
 819  \end{minipage}
 820  \hspace{0.2cm}
 821  \begin{minipage}{4.2cm}
 822  \begin{center}
 823  Agglomeration of C-Si dumbbells\\[-0.1cm]
 824  $\Rightarrow$ dark contrasts
 825  \end{center}
 826  \end{minipage}
 827  \hspace{0.2cm}
 828  \begin{minipage}{4cm}
 829  \begin{center}
 830  Precipitation of 3C-SiC in Si\\[-0.1cm]
 831  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 832  \& release of Si self-interstitials
 833  \end{center}
 834  \end{minipage}
 835
 836  \begin{minipage}{3.8cm}
 837  \begin{center}
 838  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 839  \end{center}
 840  \end{minipage}
 841  \hspace{0.6cm}
 842  \begin{minipage}{3.8cm}
 843  \begin{center}
 844  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 845  \end{center}
 846  \end{minipage}
 847  \hspace{0.6cm}
 848  \begin{minipage}{3.8cm}
 849  \begin{center}
 850  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 851  \end{center}
 852  \end{minipage}
 853
 854 \begin{pspicture}(0,0)(0,0)
 855 \psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
 856 \psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
 857 \rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
 858 \psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
 859 \rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 860  $4a_{\text{Si}}=5a_{\text{SiC}}$
 861  }}}
 862 \rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 863 \hkl(h k l) planes match
 864  }}}
 865 \rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 866 r = 2 - 4 nm
 867  }}}
 868 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
 869 \begin{minipage}{10cm}
 870 \small
 871 {\color{red}\bf Controversial views}
 872 \begin{itemize}
 873 \item Implantations at high T (Nejim et al.)
 874  \begin{itemize}
 875   \item Topotactic transformation based on \cs
 876   \item \si{} as supply reacting with further C in cleared volume
 877  \end{itemize}
 878 \item Annealing behavior (Serre et al.)
 879  \begin{itemize}
 880   \item Room temperature implants $\rightarrow$ highly mobile C
 881   \item Elevated T implants $\rightarrow$ no/low C redistribution/migration\\
 882         (indicate stable \cs{} configurations)
 883  \end{itemize}
 884 \item Strained silicon \& Si/SiC heterostructures
 885  \begin{itemize}
 886   \item Coherent SiC precipitates (tensile strain)
 887   \item Incoherent SiC (strain relaxation)
 888  \end{itemize}
 889 \end{itemize}
 890 \end{minipage}
 891  }}}
 892 \end{pspicture}
 893
 894 \end{slide}
 895
 896 \begin{slide}
 897
 898  {\large\bf
 899   Molecular dynamics (MD) simulations
 900  }
 901
 902  \vspace{12pt}
 903
 904  \small
 905
 906  {\bf MD basics:}
 907  \begin{itemize}
 908   \item Microscopic description of N particle system
 909   \item Analytical interaction potential
 910   \item Numerical integration using Newtons equation of motion\\
 911         as a propagation rule in 6N-dimensional phase space
 912   \item Observables obtained by time and/or ensemble averages
 913  \end{itemize}
 914  {\bf Details of the simulation:}
 915  \begin{itemize}
 916   \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
 917   \item Ensemble: NpT (isothermal-isobaric)
 918         \begin{itemize}
 919          \item Berendsen thermostat:
 920                $\tau_{\text{T}}=100\text{ fs}$
 921          \item Berendsen barostat:\\
 922                $\tau_{\text{P}}=100\text{ fs}$,
 923                $\beta^{-1}=100\text{ GPa}$
 924         \end{itemize}
 925   \item Erhart/Albe potential: Tersoff-like bond order potential
 926   \vspace*{12pt}
 927         \[
 928         E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
 929         \pot_{ij} = {\color{red}f_C(r_{ij})}
 930         \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
 931         \]
 932  \end{itemize}
 933
 934  \begin{picture}(0,0)(-230,-30)
 935   \includegraphics[width=5cm]{tersoff_angle.eps}
 936  \end{picture}
 937
 938 \end{slide}
 939
 940 \begin{slide}
 941
 942  {\large\bf
 943   Density functional theory (DFT) calculations
 944  }
 945
 946  \small
 947
 948  Basic ingredients necessary for DFT
 949
 950  \begin{itemize}
 951   \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
 952         \begin{itemize}
 953          \item ... uniquely determines the ground state potential
 954                / wavefunctions
 955          \item ... minimizes the systems total energy
 956         \end{itemize}
 957   \item \underline{Born-Oppenheimer}
 958         - $N$ moving electrons in an external potential of static nuclei
 959 \[
 960 H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
 961               +\sum_i^N V_{\text{ext}}(r_i)
 962               +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
 963 \]
 964   \item \underline{Effective potential}
 965         - averaged electrostatic potential \& exchange and correlation
 966 \[
 967 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
 968                  +V_{\text{XC}}[n(r)]
 969 \]
 970   \item \underline{Kohn-Sham system}
 971         - Schr\"odinger equation of N non-interacting particles
 972 \[
 973 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
 974 =\epsilon_i\Phi_i(r)
 975 \quad
 976 \Rightarrow
 977 \quad
 978 n(r)=\sum_i^N|\Phi_i(r)|^2
 979 \]
 980   \item \underline{Self-consistent solution}\\
 981 $n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
 982 which in turn depends on $n(r)$
 983   \item \underline{Variational principle}
 984         - minimize total energy with respect to $n(r)$
 985  \end{itemize}
 986
 987 \end{slide}
 988
 989 \begin{slide}
 990
 991  {\large\bf
 992   Density functional theory (DFT) calculations
 993  }
 994
 995  \small
 996
 997  \vspace*{0.2cm}
 998
 999  Details of applied DFT calculations in this work
1000
1001  \begin{itemize}
1002   \item \underline{Exchange correlation functional}
1003         - approximations for the inhomogeneous electron gas
1004         \begin{itemize}
1005          \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
1006          \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
1007         \end{itemize}
1008   \item \underline{Plane wave basis set}
1009         - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
1010 \[
1011 \rightarrow
1012 \text{Fourier series: } \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r), \quad E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}
1013 \qquad ({\color{blue}300\text{ eV}})
1014 \]
1015   \item \underline{Brillouin zone sampling} -
1016         {\color{blue}$\Gamma$-point only} calculations
1017   \item \underline{Pseudo potential}
1018         - consider only the valence electrons
1019   \item \underline{Code} - VASP 4.6
1020  \end{itemize}
1021
1022  \vspace*{0.2cm}
1023
1024  MD and structural optimization
1025
1026  \begin{itemize}
1027   \item MD integration: Gear predictor corrector algorithm
1028   \item Pressure control: Parrinello-Rahman pressure control
1029   \item Structural optimization: Conjugate gradient method
1030  \end{itemize}
1031
1032 \begin{pspicture}(0,0)(0,0)
1033 \psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
1034 \end{pspicture}
1035
1036 \end{slide}
1037
1038 \begin{slide}
1039
1040  {\large\bf
1041   C and Si self-interstitial point defects in silicon
1042  }
1043
1044  \small
1045
1046  \vspace*{0.3cm}
1047
1048 \begin{minipage}{8cm}
1049 Procedure:\\[0.3cm]
1050   \begin{pspicture}(0,0)(7,5)
1051   \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1052    \parbox{7cm}{
1053    \begin{itemize}
1054     \item Creation of c-Si simulation volume
1055     \item Periodic boundary conditions
1056     \item $T=0\text{ K}$, $p=0\text{ bar}$
1057    \end{itemize}
1058   }}}}
1059 \rput(3.5,2.1){\rnode{insert}{\psframebox{
1060  \parbox{7cm}{
1061   \begin{center}
1062   Insertion of interstitial C/Si atoms
1063   \end{center}
1064   }}}}
1065   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1066    \parbox{7cm}{
1067    \begin{center}
1068    Relaxation / structural energy minimization
1069    \end{center}
1070   }}}}
1071   \ncline[]{->}{init}{insert}
1072   \ncline[]{->}{insert}{cool}
1073  \end{pspicture}
1074 \end{minipage}
1075 \begin{minipage}{5cm}
1076   \includegraphics[width=5cm]{unit_cell_e.eps}\\
1077 \end{minipage}
1078
1079 \begin{minipage}{9cm}
1080  \begin{tabular}{l c c}
1081  \hline
1082  & size [unit cells] & \# atoms\\
1083 \hline
1084 VASP & $3\times 3\times 3$ & $216\pm 1$ \\
1085 Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
1086 \hline
1087  \end{tabular}
1088 \end{minipage}
1089 \begin{minipage}{4cm}
1090 {\color{red}$\bullet$} Tetrahedral\\
1091 {\color{green}$\bullet$} Hexagonal\\
1092 {\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
1093 {\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
1094 {\color{cyan}$\bullet$} Bond-centered\\
1095 {\color{black}$\bullet$} Vacancy / Substitutional
1096 \end{minipage}
1097
1098 \end{slide}
1099
1100 \begin{slide}
1101
1102  \footnotesize
1103
1104 \begin{minipage}{9.5cm}
1105
1106  {\large\bf
1107   Si self-interstitial point defects in silicon\\
1108  }
1109
1110 \begin{tabular}{l c c c c c}
1111 \hline
1112  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
1113 \hline
1114  VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
1115  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
1116 \hline
1117 \end{tabular}\\[0.2cm]
1118
1119 \begin{minipage}{4.7cm}
1120 \includegraphics[width=4.7cm]{e_kin_si_hex.ps}
1121 \end{minipage}
1122 \begin{minipage}{4.7cm}
1123 \begin{center}
1124 {\tiny nearly T $\rightarrow$ T}\\
1125 \end{center}
1126 \includegraphics[width=4.7cm]{nhex_tet.ps}
1127 \end{minipage}\\
1128
1129 \underline{Hexagonal} \hspace{2pt}
1130 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
1131 \framebox{
1132 \begin{minipage}{2.7cm}
1133 $E_{\text{f}}^*=4.48\text{ eV}$\\
1134 \includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
1135 \end{minipage}
1136 \begin{minipage}{0.4cm}
1137 \begin{center}
1138 $\Rightarrow$
1139 \end{center}
1140 \end{minipage}
1141 \begin{minipage}{2.7cm}
1142 $E_{\text{f}}=3.96\text{ eV}$\\
1143 \includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
1144 \end{minipage}
1145 }
1146 \begin{minipage}{2.9cm}
1147 \begin{flushright}
1148 \underline{Vacancy}\\
1149 \includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
1150 \end{flushright}
1151 \end{minipage}
1152
1153 \end{minipage}
1154 \begin{minipage}{3.5cm}
1155
1156 \begin{flushright}
1157 \underline{\hkl<1 1 0> dumbbell}\\
1158 \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
1159 \underline{Tetrahedral}\\
1160 \includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
1161 \underline{\hkl<1 0 0> dumbbell}\\
1162 \includegraphics[width=3.0cm]{si_pd_albe/100.eps}
1163 \end{flushright}
1164
1165 \end{minipage}
1166
1167 \end{slide}
1168
1169 \begin{slide}
1170
1171 \footnotesize
1172
1173  {\large\bf
1174   C interstitial point defects in silicon\\[-0.1cm]
1175  }
1176
1177 \begin{tabular}{l c c c c c c r}
1178 \hline
1179  $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\
1180 \hline
1181  VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1182  Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1183 \hline
1184 \end{tabular}\\[0.1cm]
1185
1186 \framebox{
1187 \begin{minipage}{2.7cm}
1188 \underline{Hexagonal} \hspace{2pt}
1189 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1190 $E_{\text{f}}^*=9.05\text{ eV}$\\
1191 \includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
1192 \end{minipage}
1193 \begin{minipage}{0.4cm}
1194 \begin{center}
1195 $\Rightarrow$
1196 \end{center}
1197 \end{minipage}
1198 \begin{minipage}{2.7cm}
1199 \underline{\hkl<1 0 0>}\\
1200 $E_{\text{f}}=3.88\text{ eV}$\\
1201 \includegraphics[width=2.7cm]{c_pd_albe/100.eps}
1202 \end{minipage}
1203 }
1204 \begin{minipage}{2cm}
1205 \hfill
1206 \end{minipage}
1207 \begin{minipage}{3cm}
1208 \begin{flushright}
1209 \underline{Tetrahedral}\\
1210 \includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
1211 \end{flushright}
1212 \end{minipage}
1213
1214 \framebox{
1215 \begin{minipage}{2.7cm}
1216 \underline{Bond-centered}\\
1217 $E_{\text{f}}^*=5.59\text{ eV}$\\
1218 \includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
1219 \end{minipage}
1220 \begin{minipage}{0.4cm}
1221 \begin{center}
1222 $\Rightarrow$
1223 \end{center}
1224 \end{minipage}
1225 \begin{minipage}{2.7cm}
1226 \underline{\hkl<1 1 0> dumbbell}\\
1227 $E_{\text{f}}=5.18\text{ eV}$\\
1228 \includegraphics[width=2.7cm]{c_pd_albe/110.eps}
1229 \end{minipage}
1230 }
1231 \begin{minipage}{2cm}
1232 \hfill
1233 \end{minipage}
1234 \begin{minipage}{3cm}
1235 \begin{flushright}
1236 \underline{Substitutional}\\
1237 \includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
1238 \end{flushright}
1239 \end{minipage}
1240
1241 \end{slide}
1242
1243 \begin{slide}
1244
1245 \footnotesize
1246
1247  {\large\bf\boldmath
1248   C \hkl<1 0 0> dumbbell interstitial configuration\\
1249  }
1250
1251 {\tiny
1252 \begin{tabular}{l c c c c c c c c}
1253 \hline
1254  Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
1255 \hline
1256 Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
1257 VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
1258 \hline
1259 \end{tabular}\\[0.2cm]
1260 \begin{tabular}{l c c c c }
1261 \hline
1262  Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
1263 \hline
1264 Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
1265 VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
1266 \hline
1267 \end{tabular}\\[0.2cm]
1268 \begin{tabular}{l c c c}
1269 \hline
1270  Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
1271 \hline
1272 Erhart/Albe & 0.084 & -0.091 & 0.175 \\
1273 VASP & 0.109 & -0.065 & 0.174 \\
1274 \hline
1275 \end{tabular}\\[0.6cm]
1276 }
1277
1278 \begin{minipage}{3.0cm}
1279 \begin{center}
1280 \underline{Erhart/Albe}
1281 \includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
1282 \end{center}
1283 \end{minipage}
1284 \begin{minipage}{3.0cm}
1285 \begin{center}
1286 \underline{VASP}
1287 \includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
1288 \end{center}
1289 \end{minipage}\\
1290
1291 \begin{picture}(0,0)(-185,10)
1292 \includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
1293 \end{picture}
1294 \begin{picture}(0,0)(-280,-150)
1295 \includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
1296 \end{picture}
1297
1298 \begin{pspicture}(0,0)(0,0)
1299 \psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
1300 \psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
1301 \psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
1302 \psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
1303 \end{pspicture}
1304
1305 \end{slide}
1306
1307 \begin{slide}
1308
1309 \small
1310
1311 \begin{minipage}{8.5cm}
1312
1313  {\large\bf
1314   Bond-centered interstitial configuration\\[-0.1cm]
1315  }
1316
1317 \begin{minipage}{3.0cm}
1318 \includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1319 \end{minipage}
1320 \begin{minipage}{5.2cm}
1321 \begin{itemize}
1322  \item Linear Si-C-Si bond
1323  \item Si: one C \& 3 Si neighbours
1324  \item Spin polarized calculations
1325  \item No saddle point!\\
1326        Real local minimum!
1327 \end{itemize}
1328 \end{minipage}
1329
1330 \framebox{
1331  \tiny
1332  \begin{minipage}[t]{6.5cm}
1333   \begin{minipage}[t]{1.2cm}
1334   {\color{red}Si}\\
1335   {\tiny sp$^3$}\\[0.8cm]
1336   \underline{${\color{black}\uparrow}$}
1337   \underline{${\color{black}\uparrow}$}
1338   \underline{${\color{black}\uparrow}$}
1339   \underline{${\color{red}\uparrow}$}\\
1340   sp$^3$
1341   \end{minipage}
1342   \begin{minipage}[t]{1.4cm}
1343   \begin{center}
1344   {\color{red}M}{\color{blue}O}\\[0.8cm]
1345   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1346   $\sigma_{\text{ab}}$\\[0.5cm]
1347   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1348   $\sigma_{\text{b}}$
1349   \end{center}
1350   \end{minipage}
1351   \begin{minipage}[t]{1.0cm}
1352   \begin{center}
1353   {\color{blue}C}\\
1354   {\tiny sp}\\[0.2cm]
1355   \underline{${\color{white}\uparrow\uparrow}$}
1356   \underline{${\color{white}\uparrow\uparrow}$}\\
1357   2p\\[0.4cm]
1358   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1359   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1360   sp
1361   \end{center}
1362   \end{minipage}
1363   \begin{minipage}[t]{1.4cm}
1364   \begin{center}
1365   {\color{blue}M}{\color{green}O}\\[0.8cm]
1366   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1367   $\sigma_{\text{ab}}$\\[0.5cm]
1368   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1369   $\sigma_{\text{b}}$
1370   \end{center}
1371   \end{minipage}
1372   \begin{minipage}[t]{1.2cm}
1373   \begin{flushright}
1374   {\color{green}Si}\\
1375   {\tiny sp$^3$}\\[0.8cm]
1376   \underline{${\color{green}\uparrow}$}
1377   \underline{${\color{black}\uparrow}$}
1378   \underline{${\color{black}\uparrow}$}
1379   \underline{${\color{black}\uparrow}$}\\
1380   sp$^3$
1381   \end{flushright}
1382   \end{minipage}
1383  \end{minipage}
1384 }\\[0.1cm]
1385
1386 \framebox{
1387 \begin{minipage}{4.5cm}
1388 \includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
1389 \end{minipage}
1390 \begin{minipage}{3.5cm}
1391 {\color{gray}$\bullet$} Spin up\\
1392 {\color{green}$\bullet$} Spin down\\
1393 {\color{blue}$\bullet$} Resulting spin up\\
1394 {\color{yellow}$\bullet$} Si atoms\\
1395 {\color{red}$\bullet$} C atom
1396 \end{minipage}
1397 }
1398
1399 \end{minipage}
1400 \begin{minipage}{4.2cm}
1401 \begin{flushright}
1402 \includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
1403 {\color{green}$\Box$} {\tiny unoccupied}\\
1404 {\color{red}$\bullet$} {\tiny occupied}
1405 \end{flushright}
1406 \end{minipage}
1407
1408 \end{slide}
1409
1410 \begin{slide}
1411
1412  {\large\bf\boldmath
1413   Migration of the C \hkl<1 0 0> dumbbell interstitial
1414  }
1415
1416 \scriptsize
1417
1418  {\small Investigated pathways}
1419
1420 \begin{minipage}{8.5cm}
1421 \begin{minipage}{8.3cm}
1422 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
1423 \begin{minipage}{2.4cm}
1424 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1425 \end{minipage}
1426 \begin{minipage}{0.4cm}
1427 $\rightarrow$
1428 \end{minipage}
1429 \begin{minipage}{2.4cm}
1430 \includegraphics[width=2.4cm]{c_pd_vasp/bc_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/100_next_2333.eps}
1437 \end{minipage}
1438 \end{minipage}\\
1439 \begin{minipage}{8.3cm}
1440 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
1441 \begin{minipage}{2.4cm}
1442 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1443 \end{minipage}
1444 \begin{minipage}{0.4cm}
1445 $\rightarrow$
1446 \end{minipage}
1447 \begin{minipage}{2.4cm}
1448 \includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
1449 \end{minipage}
1450 \begin{minipage}{0.4cm}
1451 $\rightarrow$
1452 \end{minipage}
1453 \begin{minipage}{2.4cm}
1454 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
1455 \end{minipage}
1456 \end{minipage}\\
1457 \begin{minipage}{8.3cm}
1458 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
1459 \begin{minipage}{2.4cm}
1460 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1461 \end{minipage}
1462 \begin{minipage}{0.4cm}
1463 $\rightarrow$
1464 \end{minipage}
1465 \begin{minipage}{2.4cm}
1466 \includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
1467 \end{minipage}
1468 \begin{minipage}{0.4cm}
1469 $\rightarrow$
1470 \end{minipage}
1471 \begin{minipage}{2.4cm}
1472 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
1473 \end{minipage}
1474 \end{minipage}
1475 \end{minipage}
1476 \framebox{
1477 \begin{minipage}{4.2cm}
1478  {\small Constrained relaxation\\
1479          technique (CRT) method}\\
1480 \includegraphics[width=4cm]{crt_orig.eps}
1481 \begin{itemize}
1482  \item Constrain diffusing atom
1483  \item Static constraints
1484 \end{itemize}
1485 \vspace*{0.3cm}
1486  {\small Modifications}\\
1487 \includegraphics[width=4cm]{crt_mod.eps}
1488 \begin{itemize}
1489  \item Constrain all atoms
1490  \item Update individual\\
1491        constraints
1492 \end{itemize}
1493 \end{minipage}
1494 }
1495
1496 \end{slide}
1497
1498 \begin{slide}
1499
1500  {\large\bf\boldmath
1501   Migration of the C \hkl<1 0 0> dumbbell interstitial
1502  }
1503
1504 \scriptsize
1505
1506 \framebox{
1507 \begin{minipage}{5.9cm}
1508 \begin{flushleft}
1509 \includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
1510 \end{flushleft}
1511 \begin{center}
1512 \begin{picture}(0,0)(60,0)
1513 \includegraphics[width=1cm]{vasp_mig/00-1.eps}
1514 \end{picture}
1515 \begin{picture}(0,0)(-5,0)
1516 \includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
1517 \end{picture}
1518 \begin{picture}(0,0)(-55,0)
1519 \includegraphics[width=1cm]{vasp_mig/bc.eps}
1520 \end{picture}
1521 \begin{picture}(0,0)(12.5,10)
1522 \includegraphics[width=1cm]{110_arrow.eps}
1523 \end{picture}
1524 \begin{picture}(0,0)(90,0)
1525 \includegraphics[height=0.9cm]{001_arrow.eps}
1526 \end{picture}
1527 \end{center}
1528 \vspace*{0.35cm}
1529 \end{minipage}
1530 }
1531 \begin{minipage}{0.3cm}
1532 \hfill
1533 \end{minipage}
1534 \framebox{
1535 \begin{minipage}{5.9cm}
1536 \begin{flushright}
1537 \includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
1538 \end{flushright}
1539 \begin{center}
1540 \begin{picture}(0,0)(60,0)
1541 \includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
1542 \end{picture}
1543 \begin{picture}(0,0)(5,0)
1544 \includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
1545 \end{picture}
1546 \begin{picture}(0,0)(-55,0)
1547 \includegraphics[width=1cm]{vasp_mig/0-10.eps}
1548 \end{picture}
1549 \begin{picture}(0,0)(12.5,10)
1550 \includegraphics[width=1cm]{100_arrow.eps}
1551 \end{picture}
1552 \begin{picture}(0,0)(90,0)
1553 \includegraphics[height=0.9cm]{001_arrow.eps}
1554 \end{picture}
1555 \end{center}
1556 \vspace*{0.3cm}
1557 \end{minipage}\\
1558 }
1559
1560 \vspace*{0.05cm}
1561
1562 \framebox{
1563 \begin{minipage}{5.9cm}
1564 \begin{flushleft}
1565 \includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
1566 \end{flushleft}
1567 \begin{center}
1568 \begin{picture}(0,0)(60,0)
1569 \includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps}
1570 \end{picture}
1571 \begin{picture}(0,0)(10,0)
1572 \includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
1573 \end{picture}
1574 \begin{picture}(0,0)(-60,0)
1575 \includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps}
1576 \end{picture}
1577 \begin{picture}(0,0)(12.5,10)
1578 \includegraphics[width=1cm]{100_arrow.eps}
1579 \end{picture}
1580 \begin{picture}(0,0)(90,0)
1581 \includegraphics[height=0.9cm]{001_arrow.eps}
1582 \end{picture}
1583 \end{center}
1584 \vspace*{0.3cm}
1585 \end{minipage}
1586 }
1587 \begin{minipage}{0.3cm}
1588 \hfill
1589 \end{minipage}
1590 \begin{minipage}{6.5cm}
1591 VASP results
1592 \begin{itemize}
1593  \item Energetically most favorable path
1594        \begin{itemize}
1595         \item Path 2
1596         \item Activation energy: $\approx$ 0.9 eV
1597         \item Experimental values: 0.73 ... 0.87 eV
1598        \end{itemize}
1599        $\Rightarrow$ {\color{blue}Diffusion} path identified!
1600  \item Reorientation (path 3)
1601        \begin{itemize}
1602         \item More likely composed of two consecutive steps of type 2
1603         \item Experimental values: 0.77 ... 0.88 eV
1604        \end{itemize}
1605        $\Rightarrow$ {\color{blue}Reorientation} transition identified!
1606 \end{itemize}
1607 \end{minipage}
1608
1609 \end{slide}
1610
1611 \begin{slide}
1612
1613  {\large\bf\boldmath
1614   Migration of the C \hkl<1 0 0> dumbbell interstitial
1615  }
1616
1617 \scriptsize
1618
1619  \vspace{0.1cm}
1620
1621 \begin{minipage}{6.5cm}
1622
1623 \framebox{
1624 \begin{minipage}[t]{5.9cm}
1625 \begin{flushleft}
1626 \includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
1627 \end{flushleft}
1628 \begin{center}
1629 \begin{pspicture}(0,0)(0,0)
1630 \psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
1631 \end{pspicture}
1632 \begin{picture}(0,0)(60,-50)
1633 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
1634 \end{picture}
1635 \begin{picture}(0,0)(5,-50)
1636 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
1637 \end{picture}
1638 \begin{picture}(0,0)(-55,-50)
1639 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
1640 \end{picture}
1641 \begin{picture}(0,0)(12.5,-40)
1642 \includegraphics[width=1cm]{110_arrow.eps}
1643 \end{picture}
1644 \begin{picture}(0,0)(90,-45)
1645 \includegraphics[height=0.9cm]{001_arrow.eps}
1646 \end{picture}\\
1647 \begin{pspicture}(0,0)(0,0)
1648 \psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
1649 \end{pspicture}
1650 \begin{picture}(0,0)(60,-15)
1651 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
1652 \end{picture}
1653 \begin{picture}(0,0)(35,-15)
1654 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
1655 \end{picture}
1656 \begin{picture}(0,0)(-5,-15)
1657 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
1658 \end{picture}
1659 \begin{picture}(0,0)(-55,-15)
1660 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
1661 \end{picture}
1662 \begin{picture}(0,0)(12.5,-5)
1663 \includegraphics[width=1cm]{100_arrow.eps}
1664 \end{picture}
1665 \begin{picture}(0,0)(90,-15)
1666 \includegraphics[height=0.9cm]{010_arrow.eps}
1667 \end{picture}
1668 \end{center}
1669 \end{minipage}
1670 }\\[0.1cm]
1671
1672 \begin{minipage}{5.9cm}
1673 Erhart/Albe results
1674 \begin{itemize}
1675  \item Lowest activation energy: $\approx$ 2.2 eV
1676  \item 2.4 times higher than VASP
1677  \item Different pathway
1678 \end{itemize}
1679 \end{minipage}
1680
1681 \end{minipage}
1682 \begin{minipage}{6.5cm}
1683
1684 \framebox{
1685 \begin{minipage}{5.9cm}
1686 %\begin{flushright}
1687 %\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
1688 %\end{flushright}
1689 %\begin{center}
1690 %\begin{pspicture}(0,0)(0,0)
1691 %\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
1692 %\end{pspicture}
1693 %\begin{picture}(0,0)(60,-5)
1694 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
1695 %\end{picture}
1696 %\begin{picture}(0,0)(0,-5)
1697 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
1698 %\end{picture}
1699 %\begin{picture}(0,0)(-55,-5)
1700 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
1701 %\end{picture}
1702 %\begin{picture}(0,0)(12.5,5)
1703 %\includegraphics[width=1cm]{100_arrow.eps}
1704 %\end{picture}
1705 %\begin{picture}(0,0)(90,0)
1706 %\includegraphics[height=0.9cm]{001_arrow.eps}
1707 %\end{picture}
1708 %\end{center}
1709 %\vspace{0.2cm}
1710 %\end{minipage}
1711 %}\\[0.2cm]
1712 %
1713 %\framebox{
1714 %\begin{minipage}{5.9cm}
1715 \includegraphics[width=5.9cm]{00-1_110_0-10_mig_albe.ps}
1716 \end{minipage}
1717 }\\[0.1cm]
1718
1719 \begin{minipage}{5.9cm}
1720 Transition involving \ci{} \hkl<1 1 0>
1721 \begin{itemize}
1722  \item Bond-centered configuration unstable\\
1723        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1724  \item Transition minima of path 2 \& 3\\
1725        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1726  \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV
1727  \item 2.4 - 3.4 times higher than VASP
1728  \item Rotation of dumbbell orientation
1729 \end{itemize}
1730 \vspace{0.1cm}
1731 \begin{center}
1732 {\color{blue}Overestimated diffusion barrier}
1733 \end{center}
1734 \end{minipage}
1735
1736 \end{minipage}
1737
1738 \end{slide}
1739
1740 \begin{slide}
1741
1742  {\large\bf\boldmath
1743   Combinations with a C-Si \hkl<1 0 0>-type interstitial
1744  }
1745
1746 \small
1747
1748 \vspace*{0.1cm}
1749
1750 Binding energy:
1751 $
1752 E_{\text{b}}=
1753 E_{\text{f}}^{\text{defect combination}}-
1754 E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
1755 E_{\text{f}}^{\text{2nd defect}}
1756 $
1757
1758 \vspace*{0.1cm}
1759
1760 {\scriptsize
1761 \begin{tabular}{l c c c c c c}
1762 \hline
1763  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1764  \hline
1765  \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1766  \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1767  \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}\\
1768  \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}\\
1769  \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}\\
1770  \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}\\
1771  \hline
1772  C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1773  Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1774 \hline
1775 \end{tabular}
1776 }
1777
1778 \vspace*{0.3cm}
1779
1780 \footnotesize
1781
1782 \begin{minipage}[t]{3.8cm}
1783 \underline{\hkl<1 0 0> at position 1}\\[0.1cm]
1784 \includegraphics[width=3.5cm]{00-1dc/2-25.eps}
1785 \end{minipage}
1786 \begin{minipage}[t]{3.5cm}
1787 \underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
1788 \includegraphics[width=3.2cm]{00-1dc/2-39.eps}
1789 \end{minipage}
1790 \begin{minipage}[t]{5.5cm}
1791 \begin{itemize}
1792  \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\
1793        $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
1794  \item Stress compensation / increase
1795  \item Unfavored: antiparallel orientations
1796  \item Indication of energetically favored\\
1797        agglomeration
1798  \item Most favorable: C clustering
1799  \item However: High barrier ($>4\,\text{eV}$)
1800  \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$
1801        (Entropy)
1802 \end{itemize}
1803 \end{minipage}
1804
1805 \begin{picture}(0,0)(-295,-130)
1806 \includegraphics[width=3.5cm]{comb_pos.eps}
1807 \end{picture}
1808
1809 \end{slide}
1810
1811 \begin{slide}
1812
1813  {\large\bf\boldmath
1814   Combinations of C-Si \hkl<1 0 0>-type interstitials
1815  }
1816
1817 \small
1818
1819 \vspace*{0.1cm}
1820
1821 Energetically most favorable combinations along \hkl<1 1 0>
1822
1823 \vspace*{0.1cm}
1824
1825 {\scriptsize
1826 \begin{tabular}{l c c c c c c}
1827 \hline
1828  & 1 & 2 & 3 & 4 & 5 & 6\\
1829 \hline
1830 $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
1831 C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
1832 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>\\
1833 \hline
1834 \end{tabular}
1835 }
1836
1837 \vspace*{0.3cm}
1838
1839 \begin{minipage}{7.0cm}
1840 \includegraphics[width=7cm]{db_along_110_cc.ps}
1841 \end{minipage}
1842 \begin{minipage}{6.0cm}
1843 \begin{itemize}
1844  \item Interaction proportional to reciprocal cube of C-C distance
1845  \item Saturation in the immediate vicinity
1846  \renewcommand\labelitemi{$\Rightarrow$}
1847  \item Agglomeration of \ci{} expected
1848  \item Absence of C clustering
1849 \end{itemize}
1850 \begin{center}
1851 {\color{blue}
1852  Consisten with initial precipitation model
1853 }
1854 \end{center}
1855 \end{minipage}
1856
1857 \vspace{0.2cm}
1858
1859 \end{slide}
1860
1861 \begin{slide}
1862
1863  {\large\bf\boldmath
1864   Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
1865  }
1866
1867  \scriptsize
1868
1869 %\begin{center}
1870 %\begin{minipage}{3.2cm}
1871 %\includegraphics[width=3cm]{sub_110_combo.eps}
1872 %\end{minipage}
1873 %\begin{minipage}{7.8cm}
1874 %\begin{tabular}{l c c c c c c}
1875 %\hline
1876 %C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
1877 %                   \hkl<1 0 1> & \hkl<-1 0 1> \\
1878 %\hline
1879 %1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
1880 %2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
1881 %3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
1882 %4 & \RM{4} & B & D & E & E & D \\
1883 %5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
1884 %\hline
1885 %\end{tabular}
1886 %\end{minipage}
1887 %\end{center}
1888
1889 %\begin{center}
1890 %\begin{tabular}{l c c c c c c c c c c}
1891 %\hline
1892 %Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
1893 %\hline
1894 %$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
1895 %$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
1896 %$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
1897 %\hline
1898 %\end{tabular}
1899 %\end{center}
1900
1901 \begin{minipage}{6.0cm}
1902 \includegraphics[width=5.8cm]{c_sub_si110.ps}
1903 \end{minipage}
1904 \begin{minipage}{7cm}
1905 \scriptsize
1906 \begin{itemize}
1907  \item IBS: C may displace Si\\
1908        $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
1909  \item Assumption:\\
1910        \hkl<1 1 0>-type $\rightarrow$ favored combination
1911  \renewcommand\labelitemi{$\Rightarrow$}
1912  \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
1913  \item Less favorable than C-Si \hkl<1 0 0> dumbbell
1914  \item Interaction drops quickly to zero\\
1915        $\rightarrow$ low capture radius
1916 \end{itemize}
1917 \begin{center}
1918  {\color{blue}
1919  IBS process far from equilibrium\\
1920  \cs{} \& \si{} instead of thermodynamic ground state
1921  }
1922 \end{center}
1923 \end{minipage}
1924
1925 \begin{minipage}{6.5cm}
1926 \includegraphics[width=6.0cm]{162-097.ps}
1927 \begin{itemize}
1928  \item Low migration barrier
1929 \end{itemize}
1930 \end{minipage}
1931 \begin{minipage}{6.5cm}
1932 \begin{center}
1933 Ab initio MD at \degc{900}\\
1934 \includegraphics[width=3.3cm]{md_vasp_01.eps}
1935 $t=\unit[2230]{fs}$\\
1936 \includegraphics[width=3.3cm]{md_vasp_02.eps}
1937 $t=\unit[2900]{fs}$
1938 \end{center}
1939 {\color{blue}
1940 Contribution of entropy to structural formation
1941 }
1942 \end{minipage}
1943
1944 \end{slide}
1945
1946 \begin{slide}
1947
1948  {\large\bf\boldmath
1949   Migration in C-Si \hkl<1 0 0> and vacancy combinations
1950  }
1951
1952  \footnotesize
1953
1954 \vspace{0.1cm}
1955
1956 \begin{minipage}[t]{3cm}
1957 \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
1958 \includegraphics[width=2.8cm]{00-1dc/0-59.eps}
1959 \end{minipage}
1960 \begin{minipage}[t]{7cm}
1961 \vspace{0.2cm}
1962 \begin{center}
1963  Low activation energies\\
1964  High activation energies for reverse processes\\
1965  $\Downarrow$\\
1966  {\color{blue}C$_{\text{sub}}$ very stable}\\
1967 \vspace*{0.1cm}
1968  \hrule
1969 \vspace*{0.1cm}
1970  Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
1971  $\Downarrow$\\
1972  {\color{blue}Formation of SiC by successive substitution by C}
1973
1974 \end{center}
1975 \end{minipage}
1976 \begin{minipage}[t]{3cm}
1977 \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
1978 \includegraphics[width=2.8cm]{00-1dc/3-14.eps}
1979 \end{minipage}
1980
1981
1982 \framebox{
1983 \begin{minipage}{5.9cm}
1984 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
1985 \begin{center}
1986 \begin{picture}(0,0)(70,0)
1987 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
1988 \end{picture}
1989 \begin{picture}(0,0)(30,0)
1990 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
1991 \end{picture}
1992 \begin{picture}(0,0)(-10,0)
1993 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
1994 \end{picture}
1995 \begin{picture}(0,0)(-48,0)
1996 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
1997 \end{picture}
1998 \begin{picture}(0,0)(12.5,5)
1999 \includegraphics[width=1cm]{100_arrow.eps}
2000 \end{picture}
2001 \begin{picture}(0,0)(97,-10)
2002 \includegraphics[height=0.9cm]{001_arrow.eps}
2003 \end{picture}
2004 \end{center}
2005 \vspace{0.1cm}
2006 \end{minipage}
2007 }
2008 \begin{minipage}{0.3cm}
2009 \hfill
2010 \end{minipage}
2011 \framebox{
2012 \begin{minipage}{5.9cm}
2013 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
2014 \begin{center}
2015 \begin{picture}(0,0)(60,0)
2016 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
2017 \end{picture}
2018 \begin{picture}(0,0)(25,0)
2019 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
2020 \end{picture}
2021 \begin{picture}(0,0)(-20,0)
2022 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
2023 \end{picture}
2024 \begin{picture}(0,0)(-55,0)
2025 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
2026 \end{picture}
2027 \begin{picture}(0,0)(12.5,5)
2028 \includegraphics[width=1cm]{100_arrow.eps}
2029 \end{picture}
2030 \begin{picture}(0,0)(95,0)
2031 \includegraphics[height=0.9cm]{001_arrow.eps}
2032 \end{picture}
2033 \end{center}
2034 \vspace{0.1cm}
2035 \end{minipage}
2036 }
2037
2038 \end{slide}
2039
2040 \begin{slide}
2041
2042  {\large\bf
2043   Conclusion of defect / migration / combined defect simulations
2044  }
2045
2046  \footnotesize
2047
2048 \vspace*{0.1cm}
2049
2050 Defect structures
2051 \begin{itemize}
2052  \item Accurately described by quantum-mechanical simulations
2053  \item Less accurate description by classical potential simulations
2054  \item Underestimated formation energy of \cs{} by classical approach
2055  \item Both methods predict same ground state: \ci{} \hkl<1 0 0> dumbbell
2056 \end{itemize}
2057
2058 Migration
2059 \begin{itemize}
2060  \item C migration pathway in Si identified
2061  \item Consistent with reorientation and diffusion experiments
2062 \end{itemize}
2063 \begin{itemize}
2064  \item Different path and ...
2065  \item overestimated barrier by classical potential calculations
2066 \end{itemize}
2067
2068 Concerning the precipitation mechanism
2069 \begin{itemize}
2070  \item Agglomeration of C-Si dumbbells energetically favorable
2071        (stress compensation)
2072  \item C-Si indeed favored compared to
2073        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2074  \item Possible low interaction capture radius of
2075        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2076  \item Low barrier for
2077        \ci{} \hkl<1 0 0> $\rightarrow$ \cs{} \& \si{} \hkl<1 1 0>
2078  \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
2079        C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
2080 \end{itemize}
2081 \begin{center}
2082 {\color{blue}Results suggest increased participation of \cs}
2083 \end{center}
2084
2085 \end{slide}
2086
2087 \begin{slide}
2088
2089  {\large\bf
2090   Silicon carbide precipitation simulations
2091  }
2092
2093  \small
2094
2095 {\scriptsize
2096  \begin{pspicture}(0,0)(12,6.5)
2097   % nodes
2098   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
2099    \parbox{7cm}{
2100    \begin{itemize}
2101     \item Create c-Si volume
2102     \item Periodc boundary conditions
2103     \item Set requested $T$ and $p=0\text{ bar}$
2104     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
2105    \end{itemize}
2106   }}}}
2107   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
2108    \parbox{7cm}{
2109    Insertion of C atoms at constant T
2110    \begin{itemize}
2111     \item total simulation volume {\pnode{in1}}
2112     \item volume of minimal SiC precipitate {\pnode{in2}}
2113     \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
2114           precipitate
2115    \end{itemize}
2116   }}}}
2117   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
2118    \parbox{7.0cm}{
2119    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
2120   }}}}
2121   \ncline[]{->}{init}{insert}
2122   \ncline[]{->}{insert}{cool}
2123   \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
2124   \rput(7.8,6){\footnotesize $V_1$}
2125   \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
2126   \rput(9.2,4.85){\tiny $V_2$}
2127   \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
2128   \rput(9.55,4.45){\footnotesize $V_3$}
2129   \rput(7.9,3.2){\pnode{ins1}}
2130   \rput(9.22,2.8){\pnode{ins2}}
2131   \rput(11.0,2.4){\pnode{ins3}}
2132   \ncline[]{->}{in1}{ins1}
2133   \ncline[]{->}{in2}{ins2}
2134   \ncline[]{->}{in3}{ins3}
2135  \end{pspicture}
2136 }
2137
2138 \begin{itemize}
2139  \item Restricted to classical potential simulations
2140  \item $V_2$ and $V_3$ considered due to low diffusion
2141  \item Amount of C atoms: 6000
2142        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
2143  \item Simulation volume: $31\times 31\times 31$ unit cells
2144        (238328 Si atoms)
2145 \end{itemize}
2146
2147 \end{slide}
2148
2149 \begin{slide}
2150
2151  {\large\bf\boldmath
2152   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2153  }
2154
2155  \small
2156
2157 \begin{minipage}{6.5cm}
2158 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2159 \end{minipage}
2160 \begin{minipage}{6.5cm}
2161 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2162 \end{minipage}
2163
2164 \begin{minipage}{6.5cm}
2165 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2166 \end{minipage}
2167 \begin{minipage}{6.5cm}
2168 \scriptsize
2169 \underline{Low C concentration ($V_1$)}\\
2170 \hkl<1 0 0> C-Si dumbbell dominated structure
2171 \begin{itemize}
2172  \item Si-C bumbs around 0.19 nm
2173  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2174        concatenated dumbbells of various orientation
2175  \item Si-Si NN distance stretched to 0.3 nm
2176 \end{itemize}
2177 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2178 \underline{High C concentration ($V_2$, $V_3$)}\\
2179 High amount of strongly bound C-C bonds\\
2180 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2181 Only short range order observable\\
2182 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2183 \end{minipage}
2184
2185 \end{slide}
2186
2187 \begin{slide}
2188
2189  {\large\bf\boldmath
2190   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2191  }
2192
2193  \small
2194
2195 \begin{minipage}{6.5cm}
2196 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2197 \end{minipage}
2198 \begin{minipage}{6.5cm}
2199 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2200 \end{minipage}
2201
2202 \begin{minipage}{6.5cm}
2203 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2204 \end{minipage}
2205 \begin{minipage}{6.5cm}
2206 \scriptsize
2207 \underline{Low C concentration ($V_1$)}\\
2208 \hkl<1 0 0> C-Si dumbbell dominated structure
2209 \begin{itemize}
2210  \item Si-C bumbs around 0.19 nm
2211  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2212        concatenated dumbbells of various orientation
2213  \item Si-Si NN distance stretched to 0.3 nm
2214 \end{itemize}
2215 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2216 \underline{High C concentration ($V_2$, $V_3$)}\\
2217 High amount of strongly bound C-C bonds\\
2218 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2219 Only short range order observable\\
2220 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2221 \end{minipage}
2222
2223 \begin{pspicture}(0,0)(0,0)
2224 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2225 \begin{minipage}{10cm}
2226 \small
2227 {\color{red}\bf 3C-SiC formation fails to appear}
2228 \begin{itemize}
2229 \item Low C concentration simulations
2230  \begin{itemize}
2231   \item Formation of \ci{} indeed occurs
2232   \item Agllomeration not observed
2233  \end{itemize}
2234 \item High C concentration simulations
2235  \begin{itemize}
2236   \item Amorphous SiC-like structure\\
2237         (not expected at prevailing temperatures)
2238   \item Rearrangement and transition into 3C-SiC structure missing
2239  \end{itemize}
2240 \end{itemize}
2241 \end{minipage}
2242  }}}
2243 \end{pspicture}
2244
2245 \end{slide}
2246
2247 \begin{slide}
2248
2249  {\large\bf
2250   Limitations of molecular dynamics and short range potentials
2251  }
2252
2253 \footnotesize
2254
2255 \vspace{0.2cm}
2256
2257 \underline{Time scale problem of MD}\\[0.2cm]
2258 Minimize integration error\\
2259 $\Rightarrow$ discretization considerably smaller than
2260               reciprocal of fastest vibrational mode\\[0.1cm]
2261 Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
2262 $\Rightarrow$ suitable choice of time step:
2263               $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
2264 $\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
2265 Several local minima in energy surface separated by large energy barriers\\
2266 $\Rightarrow$ transition event corresponds to a multiple
2267               of vibrational periods\\
2268 $\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
2269               infrequent transition events\\[0.1cm]
2270 {\color{blue}Accelerated methods:}
2271 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
2272
2273 \vspace{0.3cm}
2274
2275 \underline{Limitations related to the short range potential}\\[0.2cm]
2276 Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
2277 and 2$^{\text{nd}}$ next neighbours\\
2278 $\Rightarrow$ overestimated unphysical high forces of next neighbours
2279
2280 \vspace{0.3cm}
2281
2282 \framebox{
2283 \color{red}
2284 Potential enhanced problem of slow phase space propagation
2285 }
2286
2287 \vspace{0.3cm}
2288
2289 \underline{Approach to the (twofold) problem}\\[0.2cm]
2290 Increased temperature simulations without TAD corrections\\
2291 (accelerated methods or higher time scales exclusively not sufficient)
2292
2293 \begin{picture}(0,0)(-260,-30)
2294 \framebox{
2295 \begin{minipage}{4.2cm}
2296 \tiny
2297 \begin{center}
2298 \vspace{0.03cm}
2299 \underline{IBS}
2300 \end{center}
2301 \begin{itemize}
2302 \item 3C-SiC also observed for higher T
2303 \item higher T inside sample
2304 \item structural evolution vs.\\
2305       equilibrium properties
2306 \end{itemize}
2307 \end{minipage}
2308 }
2309 \end{picture}
2310
2311 \begin{picture}(0,0)(-305,-155)
2312 \framebox{
2313 \begin{minipage}{2.5cm}
2314 \tiny
2315 \begin{center}
2316 retain proper\\
2317 thermodynmic sampling
2318 \end{center}
2319 \end{minipage}
2320 }
2321 \end{picture}
2322
2323 \end{slide}
2324
2325 \begin{slide}
2326
2327  {\large\bf
2328   Increased temperature simulations at low C concentration
2329  }
2330
2331 \small
2332
2333 \begin{minipage}{6.5cm}
2334 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2335 \end{minipage}
2336 \begin{minipage}{6.5cm}
2337 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2338 \end{minipage}
2339
2340 \begin{minipage}{6.5cm}
2341 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2342 \end{minipage}
2343 \begin{minipage}{6.5cm}
2344 \scriptsize
2345  \underline{Si-C bonds:}
2346  \begin{itemize}
2347   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2348   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2349  \end{itemize}
2350  \underline{Si-Si bonds:}
2351  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2352  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2353  \underline{C-C bonds:}
2354  \begin{itemize}
2355   \item C-C next neighbour pairs reduced (mandatory)
2356   \item Peak at 0.3 nm slightly shifted
2357         \begin{itemize}
2358          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2359                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2360                combinations (|)\\
2361                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2362                ($\downarrow$)
2363          \item Range [|-$\downarrow$]:
2364                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2365                with nearby Si$_{\text{I}}$}
2366         \end{itemize}
2367  \end{itemize}
2368 \end{minipage}
2369
2370 \begin{picture}(0,0)(-330,-74)
2371 \color{blue}
2372 \framebox{
2373 \begin{minipage}{1.6cm}
2374 \tiny
2375 \begin{center}
2376 stretched SiC\\[-0.1cm]
2377 in c-Si
2378 \end{center}
2379 \end{minipage}
2380 }
2381 \end{picture}
2382
2383 \end{slide}
2384
2385 \begin{slide}
2386
2387  {\large\bf
2388   Increased temperature simulations at low C concentration
2389  }
2390
2391 \small
2392
2393 \begin{minipage}{6.5cm}
2394 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2395 \end{minipage}
2396 \begin{minipage}{6.5cm}
2397 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2398 \end{minipage}
2399
2400 \begin{minipage}{6.5cm}
2401 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2402 \end{minipage}
2403 \begin{minipage}{6.5cm}
2404 \scriptsize
2405  \underline{Si-C bonds:}
2406  \begin{itemize}
2407   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2408   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2409  \end{itemize}
2410  \underline{Si-Si bonds:}
2411  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2412  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2413  \underline{C-C bonds:}
2414  \begin{itemize}
2415   \item C-C next neighbour pairs reduced (mandatory)
2416   \item Peak at 0.3 nm slightly shifted
2417         \begin{itemize}
2418          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2419                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2420                combinations (|)\\
2421                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2422                ($\downarrow$)
2423          \item Range [|-$\downarrow$]:
2424                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2425                with nearby Si$_{\text{I}}$}
2426         \end{itemize}
2427  \end{itemize}
2428 \end{minipage}
2429
2430 %\begin{picture}(0,0)(-330,-74)
2431 %\color{blue}
2432 %\framebox{
2433 %\begin{minipage}{1.6cm}
2434 %\tiny
2435 %\begin{center}
2436 %stretched SiC\\[-0.1cm]
2437 %in c-Si
2438 %\end{center}
2439 %\end{minipage}
2440 %}
2441 %\end{picture}
2442
2443 \begin{pspicture}(0,0)(0,0)
2444 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2445 \begin{minipage}{10cm}
2446 \small
2447 {\color{blue}\bf Stretched SiC in c-Si}
2448 \begin{itemize}
2449 \item Consistent to precipitation model involving \cs{}
2450 \item Explains annealing behavior of high/low T C implants
2451       \begin{itemize}
2452        \item Low T: highly mobiel \ci{}
2453        \item High T: stable configurations of \cs{}
2454       \end{itemize}
2455 \end{itemize}
2456 $\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2457 $\Rightarrow$ Precipitation mechanism involving \cs{}
2458 \end{minipage}
2459  }}}
2460 \end{pspicture}
2461
2462 \end{slide}
2463
2464 \begin{slide}
2465
2466  {\large\bf
2467   Increased temperature simulations at high C concentration
2468  }
2469
2470 \footnotesize
2471
2472 \begin{minipage}{6.5cm}
2473 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2474 \end{minipage}
2475 \begin{minipage}{6.5cm}
2476 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2477 \end{minipage}
2478
2479 \vspace{0.1cm}
2480
2481 \scriptsize
2482
2483 \framebox{
2484 \begin{minipage}[t]{6.0cm}
2485 0.186 nm: Si-C pairs $\uparrow$\\
2486 (as expected in 3C-SiC)\\[0.2cm]
2487 0.282 nm: Si-C-C\\[0.2cm]
2488 $\approx$0.35 nm: C-Si-Si
2489 \end{minipage}
2490 }
2491 \begin{minipage}{0.2cm}
2492 \hfill
2493 \end{minipage}
2494 \framebox{
2495 \begin{minipage}[t]{6.0cm}
2496 0.15 nm: C-C pairs $\uparrow$\\
2497 (as expected in graphite/diamond)\\[0.2cm]
2498 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2499 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2500 \end{minipage}
2501 }
2502
2503 \begin{itemize}
2504 \item Decreasing cut-off artifact
2505 \item {\color{red}Amorphous} SiC-like phase remains
2506 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2507 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2508 \end{itemize}
2509
2510 \vspace{-0.1cm}
2511
2512 \begin{center}
2513 {\color{blue}
2514 \framebox{
2515 {\color{black}
2516 High C \& small $V$ \& short $t$
2517 $\Rightarrow$
2518 }
2519 Slow restructuring due to strong C-C bonds
2520 {\color{black}
2521 $\Leftarrow$
2522 High C \& low T implants
2523 }
2524 }
2525 }
2526 \end{center}
2527
2528 \end{slide}
2529
2530 \begin{slide}
2531
2532  {\large\bf
2533   Summary and Conclusions
2534  }
2535
2536  \scriptsize
2537
2538 %\vspace{0.1cm}
2539
2540 \framebox{
2541 \begin{minipage}[t]{12.9cm}
2542  \underline{Pecipitation simulations}
2543  \begin{itemize}
2544   \item High C concentration $\rightarrow$ amorphous SiC like phase
2545   \item Problem of potential enhanced slow phase space propagation
2546   \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2547   \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2548   \item High T necessary to simulate IBS conditions (far from equilibrium)
2549   \item Precipitation by successive agglomeration of \cs (epitaxy)
2550   \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2551         (stretched SiC, interface)
2552  \end{itemize}
2553 \end{minipage}
2554 }
2555
2556 %\vspace{0.1cm}
2557
2558 \framebox{
2559 \begin{minipage}{12.9cm}
2560  \underline{Defects}
2561  \begin{itemize}
2562    \item DFT / EA
2563         \begin{itemize}
2564          \item Point defects excellently / fairly well described
2565                by DFT / EA
2566          \item C$_{\text{sub}}$ drastically underestimated by EA
2567          \item EA predicts correct ground state:
2568                C$_{\text{sub}}$ \& \si{} $>$ \ci{}
2569          \item Identified migration path explaining
2570                diffusion and reorientation experiments by DFT
2571          \item EA fails to describe \ci{} migration:
2572                Wrong path \& overestimated barrier
2573         \end{itemize}
2574    \item Combinations of defects
2575          \begin{itemize}
2576           \item Agglomeration of point defects energetically favorable
2577                 by compensation of stress
2578           \item Formation of C-C unlikely
2579           \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2580           \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2581                 Low barrier (\unit[0.77]{eV}) \& low capture radius
2582         \end{itemize}
2583  \end{itemize}
2584 \end{minipage}
2585 }
2586
2587 \begin{center}
2588 {\color{blue}
2589 \framebox{Precipitation by successive agglomeration of \cs{}}
2590 }
2591 \end{center}
2592
2593 \end{slide}
2594
2595 \begin{slide}
2596
2597  {\large\bf
2598   Acknowledgements
2599  }
2600
2601  \vspace{0.1cm}
2602
2603  \small
2604
2605  Thanks to \ldots
2606
2607  \underline{Augsburg}
2608  \begin{itemize}
2609   \item Prof. B. Stritzker (accomodation at EP \RM{4})
2610   \item Ralf Utermann (EDV)
2611  \end{itemize}
2612
2613  \underline{Helsinki}
2614  \begin{itemize}
2615   \item Prof. K. Nordlund (MD)
2616  \end{itemize}
2617
2618  \underline{Munich}
2619  \begin{itemize}
2620   \item Bayerische Forschungsstiftung (financial support)
2621  \end{itemize}
2622
2623  \underline{Paderborn}
2624  \begin{itemize}
2625   \item Prof. J. Lindner (SiC)
2626   \item Prof. G. Schmidt (DFT + financial support)
2627   \item Dr. E. Rauls (DFT + SiC)
2628   \item Dr. S. Sanna (VASP)
2629  \end{itemize}
2630
2631 \vspace{0.2cm}
2632
2633 \begin{center}
2634 \framebox{
2635 \bf Thank you for your attention!
2636 }
2637 \end{center}
2638
2639 \end{slide}
2640
2641 \end{document}
2642
2643 \fi