posic/talks/mpi_app.tex

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  42 \usepackage{semlayer}           % Seminar overlays
  43 \usepackage{slidesec}           % Seminar sections and list of slides
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  81 \begin{document}
  82
  83 \extraslideheight{10in}
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  85
  86 \pagestyle{empty}
  87
  88 % specify width and height
  89 \slidewidth 26.3cm
  90 \slideheight 19.9cm
  91
  92 % margin
  93 \def\slidetopmargin{-0.15cm}
  94
  95 \newcommand{\ham}{\mathcal{H}}
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  99
 100 % itemize level ii
 101 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
 102
 103 % nice phi
 104 \renewcommand{\phi}{\varphi}
 105
 106 % roman letters
 107 \newcommand{\RM}[1]{\MakeUppercase{\romannumeral #1{}}}
 108
 109 % colors
 110 \newrgbcolor{si-yellow}{.6 .6 0}
 111 \newrgbcolor{hb}{0.75 0.77 0.89}
 112 \newrgbcolor{lbb}{0.75 0.8 0.88}
 113 \newrgbcolor{hlbb}{0.825 0.88 0.968}
 114 \newrgbcolor{lachs}{1.0 .93 .81}
 115
 116 % shortcuts
 117 \newcommand{\si}{Si$_{\text{i}}${}}
 118 \newcommand{\ci}{C$_{\text{i}}${}}
 119 \newcommand{\cs}{C$_{\text{sub}}${}}
 120 \newcommand{\degc}[1]{\unit[#1]{$^{\circ}$C}{}}
 121 \newcommand{\distn}[1]{\unit[#1]{nm}{}}
 122 \newcommand{\dista}[1]{\unit[#1]{\AA}{}}
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 124
 125 % no vertical centering
 126 %\centerslidesfalse
 127
 128 % layout check
 129 %\layout
 130 \begin{slide}
 131 \center
 132 {\Huge
 133 E\\
 134 F\\
 135 G\\
 136 A B C D E F G H G F E D C B A
 137 G\\
 138 F\\
 139 E\\
 140 }
 141 \end{slide}
 142
 143 % topic
 144
 145 \begin{slide}
 146 \begin{center}
 147
 148  \vspace{16pt}
 149
 150  {\LARGE\bf
 151   Atomistic simulation studies\\[0.2cm]
 152   in the C/Si system
 153  }
 154
 155  \vspace{48pt}
 156
 157  \textsc{Frank Zirkelbach}
 158
 159  \vspace{48pt}
 160
 161  Application talk at the Max Planck Institute for Solid State Research
 162
 163  \vspace{08pt}
 164
 165  Stuttgart, November 2011
 166
 167 \end{center}
 168 \end{slide}
 169
 170 % no vertical centering
 171 \centerslidesfalse
 172
 173 \ifnum1=0
 174
 175 % intro
 176
 177 \begin{slide}
 178
 179 %{\large\bf
 180 % Phase diagram of the C/Si system\\
 181 %}
 182
 183 \vspace*{0.2cm}
 184
 185 \begin{minipage}{6.5cm}
 186 \includegraphics[width=6.5cm]{si-c_phase.eps}
 187 \begin{center}
 188 {\tiny
 189 R. I. Scace and G. A. Slack, J. Chem. Phys. 30, 1551 (1959)
 190 }
 191 \end{center}
 192 \begin{pspicture}(0,0)(0,0)
 193 \psellipse[linecolor=blue,linewidth=0.1cm](3.55,4.0)(0.5,2.9)
 194 \end{pspicture}
 195 \end{minipage}
 196 \begin{minipage}{6cm}
 197 {\bf Phase diagram of the C/Si system}\\[0.2cm]
 198 {\color{blue}Stoichiometric composition}
 199 \begin{itemize}
 200 \item only chemical stable compound
 201 \item wide band gap semiconductor\\
 202       \underline{silicon carbide}, SiC
 203 \end{itemize}
 204 \end{minipage}
 205
 206 \end{slide}
 207
 208 % motivation / properties / applications of silicon carbide
 209
 210 \begin{slide}
 211
 212 \vspace*{1.8cm}
 213
 214 \small
 215
 216 \begin{pspicture}(0,0)(13.5,5)
 217
 218  \psframe*[linecolor=hb](-0.2,0)(12.9,5)
 219
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 222
 223  \rput[lt](0,4.6){\color{gray}PROPERTIES}
 224
 225  \rput[lt](0.3,4){wide band gap}
 226  \rput[lt](0.3,3.5){high electric breakdown field}
 227  \rput[lt](0.3,3){good electron mobility}
 228  \rput[lt](0.3,2.5){high electron saturation drift velocity}
 229  \rput[lt](0.3,2){high thermal conductivity}
 230
 231  \rput[lt](0.3,1.5){hard and mechanically stable}
 232  \rput[lt](0.3,1){chemically inert}
 233
 234  \rput[lt](0.3,0.5){radiation hardness}
 235
 236  \rput[rt](12.7,4.6){\color{gray}APPLICATIONS}
 237
 238  \rput[rt](12.5,3.85){high-temperature, high power}
 239  \rput[rt](12.5,3.5){and high-frequency}
 240  \rput[rt](12.5,3.15){electronic and optoelectronic devices}
 241
 242  \rput[rt](12.5,2.35){material suitable for extreme conditions}
 243  \rput[rt](12.5,2){microelectromechanical systems}
 244  \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements}
 245
 246  \rput[rt](12.5,0.85){first wall reactor material, detectors}
 247  \rput[rt](12.5,0.5){and electronic devices for space}
 248
 249 \end{pspicture}
 250
 251 \begin{picture}(0,0)(5,-162)
 252 \includegraphics[height=2.2cm]{3C_SiC_bs.eps}
 253 \end{picture}
 254 \begin{picture}(0,0)(-120,-162)
 255 \includegraphics[height=2.2cm]{nasa_600c_led.eps}
 256 \end{picture}
 257 \begin{picture}(0,0)(-270,-162)
 258 \includegraphics[height=2.2cm]{6h-sic_3c-sic.eps}
 259 \end{picture}
 260 %%%%
 261 \begin{picture}(0,0)(10,65)
 262 \includegraphics[height=2.8cm]{sic_switch.eps}
 263 \end{picture}
 264 %\begin{picture}(0,0)(-243,65)
 265 \begin{picture}(0,0)(-110,65)
 266 \includegraphics[height=2.8cm]{ise_99.eps}
 267 \end{picture}
 268 %\begin{picture}(0,0)(-135,65)
 269 \begin{picture}(0,0)(-100,65)
 270 \includegraphics[height=1.2cm]{infineon_schottky.eps}
 271 \end{picture}
 272 \begin{picture}(0,0)(-233,65)
 273 \includegraphics[height=2.8cm]{solar_car.eps}
 274 \end{picture}
 275
 276 \end{slide}
 277
 278 % motivation
 279
 280 \begin{slide}
 281
 282  {\large\bf
 283   Polytypes of SiC\\[0.4cm]
 284  }
 285
 286 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
 287 \begin{minipage}{1.9cm}
 288 {\tiny cubic (twist)}
 289 \end{minipage}
 290 \begin{minipage}{2.9cm}
 291 {\tiny hexagonal (no twist)}
 292 \end{minipage}
 293
 294 \begin{picture}(0,0)(-150,0)
 295  \includegraphics[width=7cm]{polytypes.eps}
 296 \end{picture}
 297
 298 \vspace{0.6cm}
 299
 300 \footnotesize
 301
 302 \begin{tabular}{l c c c c c c}
 303 \hline
 304  & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
 305 \hline
 306 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
 307 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
 308 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
 309 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
 310 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
 311 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
 312 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
 313 \hline
 314 \end{tabular}
 315
 316 \begin{pspicture}(0,0)(0,0)
 317 \psellipse[linecolor=green](5.7,2.10)(0.4,0.5)
 318 \end{pspicture}
 319 \begin{pspicture}(0,0)(0,0)
 320 \psellipse[linecolor=green](5.6,0.92)(0.4,0.2)
 321 \end{pspicture}
 322 \begin{pspicture}(0,0)(0,0)
 323 \psellipse[linecolor=red](10.45,0.45)(0.4,0.2)
 324 \end{pspicture}
 325
 326 \end{slide}
 327
 328 % fabrication
 329
 330 \begin{slide}
 331
 332  {\large\bf
 333   Fabrication of silicon carbide
 334  }
 335
 336  \small
 337
 338  \vspace{2pt}
 339
 340 \begin{center}
 341  {\color{gray}
 342  \emph{Silicon carbide --- Born from the stars, perfected on earth.}
 343  }
 344 \end{center}
 345
 346 \vspace{2pt}
 347
 348 SiC thin films by MBE \& CVD
 349 \begin{itemize}
 350  \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
 351  \item \underline{Commercially available} semiconductor power devices based on
 352        \underline{\foreignlanguage{greek}{a}-SiC}
 353  \item Production of favored \underline{3C-SiC} material
 354        \underline{less advanced}
 355  \item Quality and size not yet sufficient
 356 \end{itemize}
 357 \begin{picture}(0,0)(-310,-20)
 358   \includegraphics[width=2.0cm]{cree.eps}
 359 \end{picture}
 360
 361 \vspace{-0.2cm}
 362
 363 Alternative approach:
 364 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
 365
 366 \vspace{0.2cm}
 367
 368 \scriptsize
 369
 370 \framebox{
 371 \begin{minipage}{3.15cm}
 372  \begin{center}
 373 \includegraphics[width=3cm]{imp.eps}\\
 374  {\tiny
 375   Carbon implantation
 376  }
 377  \end{center}
 378 \end{minipage}
 379 \begin{minipage}{3.15cm}
 380  \begin{center}
 381 \includegraphics[width=3cm]{annealing.eps}\\
 382  {\tiny
 383   \unit[12]{h} annealing at \degc{1200}
 384  }
 385  \end{center}
 386 \end{minipage}
 387 }
 388 \begin{minipage}{5.5cm}
 389  \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm]
 390  \begin{center}
 391  {\tiny
 392   XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
 393  }
 394  \end{center}
 395 \end{minipage}
 396
 397 \end{slide}
 398
 399 % contents
 400
 401 \begin{slide}
 402
 403 {\large\bf
 404  Systematic investigation of C implantations into Si
 405 }
 406
 407 \vspace{1.7cm}
 408 \begin{center}
 409 \hspace{-1.0cm}
 410 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
 411 \end{center}
 412
 413 \end{slide}
 414
 415 % outline
 416
 417 \begin{slide}
 418
 419 {\large\bf
 420  Outline
 421 }
 422
 423 \vspace{1.7cm}
 424 \begin{center}
 425 \hspace{-1.0cm}
 426 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
 427 \end{center}
 428
 429 \begin{pspicture}(0,0)(0,0)
 430 \rput(6.0,7.0){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{
 431 \begin{minipage}{11cm}
 432 {\color{black}Diploma thesis}\\
 433  \underline{Monte Carlo} simulation modeling the selforganization process\\
 434  leading to periodic arrays of nanometric amorphous SiC precipitates
 435 \end{minipage}
 436 }}}
 437 \end{pspicture}
 438 \begin{pspicture}(0,0)(0,0)
 439 \rput(6.0,-0.5){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=blue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{
 440 \begin{minipage}{11cm}
 441 {\color{black}Doctoral studies}\\
 442  Classical potential \underline{molecular dynamics} simulations \ldots\\
 443  \underline{Density functional theory} calculations \ldots\\[0.2cm]
 444  \ldots on defect formation and SiC precipitation in Si
 445 \end{minipage}
 446 }}}
 447 \end{pspicture}
 448 \begin{pspicture}(0,0)(0,0)
 449 \psellipse[linecolor=red,linewidth=0.05cm](5,3.0)(0.8,1.0)
 450 \end{pspicture}
 451 \begin{pspicture}(0,0)(0,0)
 452 \psellipse[linecolor=blue,linewidth=0.05cm](8.2,3.2)(1.5,1.6)
 453 \end{pspicture}
 454
 455 \end{slide}
 456
 457 \begin{slide}
 458
 459 \headdiplom
 460 {\large\bf
 461  Selforganization of nanometric amorphous SiC lamellae
 462 }
 463
 464 \small
 465
 466 \vspace{0.2cm}
 467
 468 \begin{itemize}
 469  \item Regularly spaced, nanometric spherical\\
 470        and lamellar amorphous inclusions\\
 471        at the upper a/c interface
 472  \item Carbon accumulation\\
 473        in amorphous volumes
 474 \end{itemize}
 475
 476 \vspace{0.4cm}
 477
 478 \begin{minipage}{12cm}
 479 \includegraphics[width=9cm]{../../nlsop/img/k393abild1_e_l.eps}\\
 480 {\scriptsize
 481 XTEM bright-field, \unit[180]{keV} C$^+ \rightarrow$ Si,
 482 {\color{red}\underline{\degc{150}}},
 483 Dose: \unit[4.3 $\times 10^{17}$]{cm$^{-2}$}
 484 }
 485 \end{minipage}
 486
 487 \begin{picture}(0,0)(-182,-215)
 488 \begin{minipage}{6.5cm}
 489 \begin{center}
 490 \includegraphics[width=6.5cm]{../../nlsop/img/eftem.eps}\\[-0.2cm]
 491 {\scriptsize
 492 XTEM bright-field and respective EFTEM C map
 493 }
 494 \end{center}
 495 \end{minipage}
 496 \end{picture}
 497
 498 \end{slide}
 499
 500 \begin{slide}
 501
 502 \headdiplom
 503 {\large\bf
 504  Model displaying the formation of ordered lamellae
 505 }
 506
 507 \vspace{0.1cm}
 508
 509 \begin{center}
 510  \includegraphics[width=8.0cm]{../../nlsop/img/modell_ng_e.eps}
 511 \end{center}
 512
 513 \footnotesize
 514
 515 \begin{itemize}
 516 \item Supersaturation of C in c-Si\\
 517       $\rightarrow$ {\bf Carbon induced} nucleation of spherical
 518       SiC$_x$-precipitates
 519 \item High interfacial energy between 3C-SiC and c-Si\\
 520       $\rightarrow$ {\bf Amorphous} precipitates
 521 \item \unit[20-- 30]{\%} lower silicon density of a-SiC$_x$ compared to c-Si\\
 522       $\rightarrow$ {\bf Lateral strain} (black arrows)
 523 \item Implantation range near surface\\
 524       $\rightarrow$ {\bf Relaxation} of {\bf vertical strain component}
 525 \item Reduction of the carbon supersaturation in c-Si\\
 526       $\rightarrow$ {\bf Carbon diffusion} into amorphous volumina
 527       (white arrows)
 528 \item Remaining lateral strain\\
 529       $\rightarrow$ {\bf Strain enhanced} lateral amorphisation
 530 \item Absence of crystalline neighbours (structural information)\\
 531       $\rightarrow$ {\bf Stabilization} of amorphous inclusions
 532       {\bf against recrystallization}
 533 \end{itemize}
 534
 535 \end{slide}
 536
 537 \begin{slide}
 538
 539 \headdiplom
 540 {\large\bf
 541  Implementation of the Monte Carlo code
 542 }
 543
 544 \small
 545
 546 \begin{enumerate}
 547  \item \underline{Amorphization / Recrystallization}\\
 548        Ion collision in discretized target determined by random numbers
 549        distributed according to nuclear energy loss.
 550        Amorphization/recrystallization probability:
 551 \[
 552 p_{c \rightarrow a}(\vec{r}) = {\color{green} p_b} + {\color{blue} p_c c_C(\vec{r})} + {\color{red} \sum_{\textrm{amorphous neighbours}} \frac{p_s c_C(\vec{r'})}{(r-r')^2}}
 553 \]
 554 \begin{itemize}
 555  \item {\color{green} $p_b$} normal `ballistic' amorphization
 556  \item {\color{blue} $p_c$} carbon induced amorphization
 557  \item {\color{red} $p_s$} stress enhanced amorphization
 558 \end{itemize}
 559 \[
 560 p_{a \rightarrow c}(\vec r) = (1 - p_{c \rightarrow a}(\vec r)) \Big(1 - \frac{\sum_{direct \, neighbours} \delta (\vec{r'})}{6} \Big) \, \textrm{,}
 561 \]
 562 \[
 563 \delta (\vec r) = \left\{
 564 \begin{array}{ll}
 565         1 & \textrm{if volume at position $\vec r$ is amorphous} \\
 566         0 & \textrm{otherwise} \\
 567 \end{array}
 568 \right.
 569 \]
 570  \item \underline{Carbon incorporation}\\
 571        Incorporation volume determined according to implantation profile
 572  \item \underline{Diffusion / Sputtering}
 573        \begin{itemize}
 574         \item Transfer fraction of C atoms
 575               of crystalline into neighbored amorphous volumes
 576         \item Remove surface layer
 577        \end{itemize}
 578 \end{enumerate}
 579
 580 \end{slide}
 581
 582 \begin{slide}
 583
 584 \begin{minipage}{3.7cm}
 585 \begin{pspicture}(0,0)(0,0)
 586 \rput(1.7,0.2){\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradangle=10,gradmidpoint=1,linestyle=none]{
 587 \begin{minipage}{3.7cm}
 588 \hfill
 589 \vspace{0.7cm}
 590 \end{minipage}
 591 }}
 592 \end{pspicture}
 593 {\large\bf
 594  Results
 595 }
 596
 597 \footnotesize
 598
 599 \vspace{1.2cm}
 600
 601 Evolution of the \ldots
 602 \begin{itemize}
 603  \item continuous\\
 604        amorphous layer
 605  \item a/c interface
 606  \item lamellar precipitates
 607 \end{itemize}
 608 \ldots reproduced!\\[1.4cm]
 609
 610 {\color{blue}
 611 \begin{center}
 612 Experiment \& simulation\\
 613 in good agreement\\[1.0cm]
 614
 615 Simulation is able to model the whole depth region\\[1.2cm]
 616 \end{center}
 617 }
 618
 619 \end{minipage}
 620 \begin{minipage}{0.5cm}
 621 \vfill
 622 \end{minipage}
 623 \begin{minipage}{8.0cm}
 624  \vspace{-0.3cm}
 625  \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e_1-2.eps}\\
 626  \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e2_2-2.eps}
 627 \end{minipage}
 628
 629 \end{slide}
 630
 631 \begin{slide}
 632
 633 \headdiplom
 634 {\large\bf
 635  Structural \& compositional details
 636 }
 637
 638 \begin{minipage}[t]{7.5cm}
 639 \includegraphics[height=6.5cm]{../../nlsop/img/ac_cconc_ver2_e.eps}\\
 640 \end{minipage}
 641 \begin{minipage}[t]{5.0cm}
 642 \includegraphics[height=6.5cm]{../../nlsop/img/97_98_e.eps}
 643 \end{minipage}
 644
 645 \footnotesize
 646
 647 \vspace{-0.1cm}
 648
 649 \begin{itemize}
 650  \item Fluctuation of C concentration in lamellae region
 651  \item \unit[8--10]{at.\%} C saturation limit
 652        within the respective conditions
 653  \item Complementarily arranged and alternating sequence of layers\\
 654        with a high and low amount of amorphous regions
 655  \item C accumulation in the amorphous phase / Origin of stress
 656 \end{itemize}
 657
 658 \begin{picture}(0,0)(-260,-50)
 659 \framebox{
 660 \begin{minipage}{3cm}
 661 \begin{center}
 662 {\color{blue}
 663 Precipitation process\\
 664 gets traceable\\
 665 by simulation!
 666 }
 667 \end{center}
 668 \end{minipage}
 669 }
 670 \end{picture}
 671
 672 \end{slide}
 673
 674 \begin{slide}
 675
 676 \headphd
 677 {\large\bf
 678  Formation of epitaxial single crystalline 3C-SiC
 679 }
 680
 681 \footnotesize
 682
 683 \vspace{0.2cm}
 684
 685 \begin{center}
 686 \begin{itemize}
 687  \item \underline{Implantation step 1}\\[0.1cm]
 688         Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
 689         $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
 690         {\color{blue}precipitates}
 691  \item \underline{Implantation step 2}\\[0.1cm]
 692         Little remaining dose | \unit[180]{keV} | \degc{250}\\
 693         $\Rightarrow$
 694         Destruction/Amorphization of precipitates at layer interface
 695  \item \underline{Annealing}\\[0.1cm]
 696        \unit[10]{h} at \degc{1250}\\
 697        $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
 698 \end{itemize}
 699 \end{center}
 700
 701 \begin{minipage}{7cm}
 702 \includegraphics[width=7cm]{ibs_3c-sic.eps}
 703 \end{minipage}
 704 \begin{minipage}{5cm}
 705 \begin{pspicture}(0,0)(0,0)
 706 \rnode{box}{
 707 \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
 708 \begin{minipage}{5.3cm}
 709  \begin{center}
 710  {\color{blue}
 711   3C-SiC precipitation\\
 712   not yet fully understood
 713  }
 714  \end{center}
 715  \vspace*{0.1cm}
 716  \renewcommand\labelitemi{$\Rightarrow$}
 717  Details of the SiC precipitation
 718  \begin{itemize}
 719   \item significant technological progress\\
 720         in SiC thin film formation
 721   \item perspectives for processes relying\\
 722         upon prevention of SiC precipitation
 723  \end{itemize}
 724 \end{minipage}
 725 }}
 726 \rput(-6.8,5.4){\pnode{h0}}
 727 \rput(-3.0,5.4){\pnode{h1}}
 728 \ncline[linecolor=blue]{-}{h0}{h1}
 729 \ncline[linecolor=blue]{->}{h1}{box}
 730 \end{pspicture}
 731 \end{minipage}
 732
 733 \end{slide}
 734
 735 \begin{slide}
 736
 737 \headphd
 738 {\large\bf
 739   Supposed precipitation mechanism of SiC in Si
 740 }
 741
 742  \scriptsize
 743
 744  \vspace{0.1cm}
 745
 746  \framebox{
 747  \begin{minipage}{3.6cm}
 748  \begin{center}
 749  Si \& SiC lattice structure\\[0.1cm]
 750  \includegraphics[width=2.3cm]{sic_unit_cell.eps}
 751  \end{center}
 752 {\tiny
 753  \begin{minipage}{1.7cm}
 754 \underline{Silicon}\\
 755 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
 756 $a=\unit[5.429]{\\A}$\\
 757 $\rho^*_{\text{Si}}=\unit[100]{\%}$
 758  \end{minipage}
 759  \begin{minipage}{1.7cm}
 760 \underline{Silicon carbide}\\
 761 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
 762 $a=\unit[4.359]{\\A}$\\
 763 $\rho^*_{\text{Si}}=\unit[97]{\%}$
 764  \end{minipage}
 765 }
 766  \end{minipage}
 767  }
 768  \hspace{0.1cm}
 769  \begin{minipage}{4.1cm}
 770  \begin{center}
 771  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 772  \end{center}
 773  \end{minipage}
 774  \hspace{0.1cm}
 775  \begin{minipage}{4.0cm}
 776  \begin{center}
 777  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 778  \end{center}
 779  \end{minipage}
 780
 781  \vspace{0.1cm}
 782
 783  \begin{minipage}{4.0cm}
 784  \begin{center}
 785  C-Si dimers (dumbbells)\\[-0.1cm]
 786  on Si interstitial sites
 787  \end{center}
 788  \end{minipage}
 789  \hspace{0.1cm}
 790  \begin{minipage}{4.1cm}
 791  \begin{center}
 792  Agglomeration of C-Si dumbbells\\[-0.1cm]
 793  $\Rightarrow$ dark contrasts
 794  \end{center}
 795  \end{minipage}
 796  \hspace{0.1cm}
 797  \begin{minipage}{4.0cm}
 798  \begin{center}
 799  Precipitation of 3C-SiC in Si\\[-0.1cm]
 800  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 801  \& release of Si self-interstitials
 802  \end{center}
 803  \end{minipage}
 804
 805  \vspace{0.1cm}
 806
 807  \begin{minipage}{4.0cm}
 808  \begin{center}
 809  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 810  \end{center}
 811  \end{minipage}
 812  \hspace{0.1cm}
 813  \begin{minipage}{4.1cm}
 814  \begin{center}
 815  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 816  \end{center}
 817  \end{minipage}
 818  \hspace{0.1cm}
 819  \begin{minipage}{4.0cm}
 820  \begin{center}
 821  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 822  \end{center}
 823  \end{minipage}
 824
 825 \begin{pspicture}(0,0)(0,0)
 826 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
 827 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
 828 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
 829 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
 830 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 831  $4a_{\text{Si}}=5a_{\text{SiC}}$
 832  }}}
 833 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 834 \hkl(h k l) planes match
 835  }}}
 836 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 837 r = \unit[2--4]{nm}
 838  }}}
 839 \end{pspicture}
 840
 841 \end{slide}
 842
 843 \begin{slide}
 844
 845 \headphd
 846 {\large\bf
 847  Supposed precipitation mechanism of SiC in Si
 848 }
 849
 850  \scriptsize
 851
 852  \vspace{0.1cm}
 853
 854  \framebox{
 855  \begin{minipage}{3.6cm}
 856  \begin{center}
 857  Si \& SiC lattice structure\\[0.1cm]
 858  \includegraphics[width=2.3cm]{sic_unit_cell.eps}
 859  \end{center}
 860 {\tiny
 861  \begin{minipage}{1.7cm}
 862 \underline{Silicon}\\
 863 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
 864 $a=\unit[5.429]{\\A}$\\
 865 $\rho^*_{\text{Si}}=\unit[100]{\%}$
 866  \end{minipage}
 867  \begin{minipage}{1.7cm}
 868 \underline{Silicon carbide}\\
 869 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
 870 $a=\unit[4.359]{\\A}$\\
 871 $\rho^*_{\text{Si}}=\unit[97]{\%}$
 872  \end{minipage}
 873 }
 874  \end{minipage}
 875  }
 876  \hspace{0.1cm}
 877  \begin{minipage}{4.1cm}
 878  \begin{center}
 879  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 880  \end{center}
 881  \end{minipage}
 882  \hspace{0.1cm}
 883  \begin{minipage}{4.0cm}
 884  \begin{center}
 885  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 886  \end{center}
 887  \end{minipage}
 888
 889  \vspace{0.1cm}
 890
 891  \begin{minipage}{4.0cm}
 892  \begin{center}
 893  C-Si dimers (dumbbells)\\[-0.1cm]
 894  on Si interstitial sites
 895  \end{center}
 896  \end{minipage}
 897  \hspace{0.1cm}
 898  \begin{minipage}{4.1cm}
 899  \begin{center}
 900  Agglomeration of C-Si dumbbells\\[-0.1cm]
 901  $\Rightarrow$ dark contrasts
 902  \end{center}
 903  \end{minipage}
 904  \hspace{0.1cm}
 905  \begin{minipage}{4.0cm}
 906  \begin{center}
 907  Precipitation of 3C-SiC in Si\\[-0.1cm]
 908  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 909  \& release of Si self-interstitials
 910  \end{center}
 911  \end{minipage}
 912
 913  \vspace{0.1cm}
 914
 915  \begin{minipage}{4.0cm}
 916  \begin{center}
 917  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 918  \end{center}
 919  \end{minipage}
 920  \hspace{0.1cm}
 921  \begin{minipage}{4.1cm}
 922  \begin{center}
 923  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 924  \end{center}
 925  \end{minipage}
 926  \hspace{0.1cm}
 927  \begin{minipage}{4.0cm}
 928  \begin{center}
 929  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 930  \end{center}
 931  \end{minipage}
 932
 933 \begin{pspicture}(0,0)(0,0)
 934 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
 935 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
 936 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
 937 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
 938 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 939  $4a_{\text{Si}}=5a_{\text{SiC}}$
 940  }}}
 941 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 942 \hkl(h k l) planes match
 943  }}}
 944 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 945 r = \unit[2--4]{nm}
 946  }}}
 947 % controversial view!
 948 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
 949 \begin{minipage}{14cm}
 950 \hfill
 951 \vspace{12cm}
 952 \end{minipage}
 953 }}
 954 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
 955 \begin{minipage}{10cm}
 956 \small
 957 \vspace*{0.2cm}
 958 \begin{center}
 959 {\color{gray}\bf Controversial findings}
 960 \end{center}
 961 \begin{itemize}
 962 \item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
 963  \begin{itemize}
 964   \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites
 965   \item \si{} reacting with further C in cleared volume
 966  \end{itemize}
 967 \item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
 968  \begin{itemize}
 969   \item Room temperature implantation $\rightarrow$ high C diffusion
 970   \item Elevated temperature implantation $\rightarrow$ no C redistribution
 971  \end{itemize}
 972  $\Rightarrow$ mobile {\color{red}\ci} opposed to
 973  stable {\color{blue}\cs{}} configurations
 974 \item Strained silicon \& Si/SiC heterostructures
 975       {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
 976  \begin{itemize}
 977   \item {\color{blue}Coherent} SiC precipitates (tensile strain)
 978   \item Incoherent SiC (strain relaxation)
 979  \end{itemize}
 980 \end{itemize}
 981 \vspace{0.1cm}
 982 \begin{center}
 983 {\Huge${\lightning}$} \hspace{0.3cm}
 984 {\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
 985 {\Huge${\lightning}$}
 986 \end{center}
 987 \vspace{0.2cm}
 988 \end{minipage}
 989  }}}
 990 \end{pspicture}
 991
 992 \end{slide}
 993
 994 \begin{slide}
 995
 996 \headphd
 997 {\large\bf
 998  Utilized computational methods
 999 }
1000
1001 \vspace{0.3cm}
1002
1003 \small
1004
1005 {\bf Molecular dynamics (MD)}\\[0.1cm]
1006 \scriptsize
1007 \begin{tabular}{| p{4.5cm} | p{7.5cm} |}
1008 \hline
1009 System of $N$ particles &
1010 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
1011 Phase space propagation &
1012 Velocity Verlet | timestep: \unit[1]{fs} \\
1013 Analytical interaction potential &
1014 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
1015 (Erhart/Albe)
1016 $\displaystyle
1017 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
1018     \pot_{ij} = {\color{red}f_C(r_{ij})}
1019     \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
1020 $\\
1021 Observables: time/ensemble averages &
1022 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
1023 \hline
1024 \end{tabular}
1025
1026 \small
1027
1028 \vspace{0.3cm}
1029
1030 {\bf Density functional theory (DFT)}
1031
1032 \scriptsize
1033
1034 \begin{minipage}[t]{6cm}
1035 \begin{itemize}
1036  \item Hohenberg-Kohn theorem:\\
1037        $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
1038  \item Kohn-Sham approach:\\
1039        Single-particle effective theory
1040 \end{itemize}
1041 \hrule
1042 \begin{itemize}
1043 \item Code: \textsc{vasp}
1044 \item Plane wave basis set
1045 %$\displaystyle
1046 %\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
1047 %$\\
1048 %$\displaystyle
1049 %E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
1050 %$
1051 \item Ultrasoft pseudopotential
1052 \item Exchange \& correlation: GGA
1053 \item Brillouin zone sampling: $\Gamma$-point
1054 \item Supercell: $N=216\pm2$
1055 \end{itemize}
1056 \end{minipage}
1057 \begin{minipage}{6cm}
1058 \begin{pspicture}(0,0)(0,0)
1059 \pscircle[fillcolor=yellow,fillstyle=solid,linestyle=none](3.5,-2.0){2.5}
1060 \rput(2.7,-0.7){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
1061 $\displaystyle
1062 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
1063 $
1064 }}
1065 \rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
1066 $\displaystyle
1067 n(r)=\sum_i^N|\Phi_i(r)|^2
1068 $
1069 }}
1070 \rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
1071 $\displaystyle
1072 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
1073                  +V_{\text{XC}}[n(r)]
1074 $
1075 }}
1076 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
1077 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165}
1078 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
1079
1080 \end{pspicture}
1081 \end{minipage}
1082
1083 \end{slide}
1084
1085 \begin{slide}
1086
1087 \headphd
1088  {\large\bf
1089   Point defects \& defect migration
1090  }
1091
1092  \small
1093
1094  \vspace{0.2cm}
1095
1096 \begin{minipage}[b]{7.5cm}
1097 {\bf Defect structure}\\
1098   \begin{pspicture}(0,0)(7,4.4)
1099   \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1100    \parbox{7cm}{
1101    \begin{itemize}
1102     \item Creation of c-Si simulation volume
1103     \item Periodic boundary conditions
1104     \item $T=0\text{ K}$, $p=0\text{ bar}$
1105    \end{itemize}
1106   }}}}
1107 \rput(3.5,1.3){\rnode{insert}{\psframebox{
1108  \parbox{7cm}{
1109   \begin{center}
1110   Insertion of interstitial C/Si atoms
1111   \end{center}
1112   }}}}
1113   \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1114    \parbox{7cm}{
1115    \begin{center}
1116    Relaxation / structural energy minimization
1117    \end{center}
1118   }}}}
1119   \ncline[]{->}{init}{insert}
1120   \ncline[]{->}{insert}{cool}
1121  \end{pspicture}
1122 \end{minipage}
1123 \begin{minipage}[b]{4.5cm}
1124 \begin{center}
1125 \includegraphics[width=3.8cm]{unit_cell_e.eps}\\
1126 \end{center}
1127 \begin{minipage}{2.21cm}
1128 {\scriptsize
1129 {\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
1130 {\color{green}$\bullet$} Hexagonal\\[-0.1cm]
1131 {\color{yellow}$\bullet$} \hkl<1 0 0> DB
1132 }
1133 \end{minipage}
1134 \begin{minipage}{2.21cm}
1135 {\scriptsize
1136 {\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
1137 {\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
1138 {\color{black}$\bullet$} Vac. / Sub.
1139 }
1140 \end{minipage}
1141 \end{minipage}
1142
1143 \vspace{0.2cm}
1144
1145 \begin{minipage}[b]{6cm}
1146 {\bf Defect formation energy}\\
1147 \framebox{
1148 $E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm]
1149 Particle reservoir: Si \& SiC\\[0.2cm]
1150 {\bf Binding energy}\\
1151 \framebox{
1152 $
1153 E_{\text{b}}=
1154 E_{\text{f}}^{\text{comb}}-
1155 E_{\text{f}}^{1^{\text{st}}}-
1156 E_{\text{f}}^{2^{\text{nd}}}
1157 $
1158 }\\[0.1cm]
1159 \footnotesize
1160 $E_{\text{b}}<0$: energetically favorable configuration\\
1161 $E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
1162 \end{minipage}
1163 \begin{minipage}[b]{6cm}
1164 {\bf Migration barrier}
1165 \footnotesize
1166 \begin{itemize}
1167  \item Displace diffusing atom
1168  \item Constrain relaxation of (diffusing) atoms
1169  \item Record configurational energy
1170 \end{itemize}
1171 \begin{picture}(0,0)(-60,-33)
1172 \includegraphics[width=4.5cm]{crt_mod.eps}
1173 \end{picture}
1174 \end{minipage}
1175
1176 \end{slide}
1177
1178 \begin{slide}
1179
1180 \footnotesize
1181
1182 \headphd
1183 {\large\bf
1184  Si self-interstitial point defects in silicon\\[0.1cm]
1185 }
1186
1187 \begin{center}
1188 \begin{tabular}{l c c c c c}
1189 \hline
1190  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
1191 \hline
1192  \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
1193  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
1194 \hline
1195 \end{tabular}\\[0.4cm]
1196 \end{center}
1197
1198 \begin{minipage}{3cm}
1199 \begin{center}
1200 \underline{Vacancy}\\
1201 \includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
1202 \end{center}
1203 \end{minipage}
1204 \begin{minipage}{3cm}
1205 \begin{center}
1206 \underline{\hkl<1 1 0> DB}\\
1207 \includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
1208 \end{center}
1209 \end{minipage}
1210 \begin{minipage}{3cm}
1211 \begin{center}
1212 \underline{\hkl<1 0 0> DB}\\
1213 \includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
1214 \end{center}
1215 \end{minipage}
1216 \begin{minipage}{3cm}
1217 \begin{center}
1218 \underline{Tetrahedral}\\
1219 \includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
1220 \end{center}
1221 \end{minipage}\\
1222
1223 \underline{Hexagonal} \hspace{2pt}
1224 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
1225 \framebox{
1226 \begin{minipage}{2.7cm}
1227 $E_{\text{f}}^*=4.48\text{ eV}$\\
1228 \includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
1229 \end{minipage}
1230 \begin{minipage}{0.4cm}
1231 \begin{center}
1232 $\Rightarrow$
1233 \end{center}
1234 \end{minipage}
1235 \begin{minipage}{2.7cm}
1236 $E_{\text{f}}=3.96\text{ eV}$\\
1237 \includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps}
1238 \end{minipage}
1239 }
1240 \begin{minipage}{5.5cm}
1241 \begin{center}
1242 {\tiny nearly T $\rightarrow$ T}\\
1243 \end{center}
1244 \includegraphics[width=6.0cm]{nhex_tet.ps}
1245 \end{minipage}
1246
1247 \end{slide}
1248
1249 \begin{slide}
1250
1251 \footnotesize
1252
1253 \headphd
1254 {\large\bf
1255  C interstitial point defects in silicon\\
1256 }
1257
1258 \begin{tabular}{l c c c c c c r}
1259 \hline
1260  $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B &
1261  {\color{black} \cs{} \& \si}\\
1262 \hline
1263  \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1264  Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1265 \hline
1266 \end{tabular}\\[0.1cm]
1267
1268 \framebox{
1269 \begin{minipage}{2.8cm}
1270 \underline{Hexagonal} \hspace{2pt}
1271 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1272 $E_{\text{f}}^*=9.05\text{ eV}$\\
1273 \includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps}
1274 \end{minipage}
1275 \begin{minipage}{0.4cm}
1276 \begin{center}
1277 $\Rightarrow$
1278 \end{center}
1279 \end{minipage}
1280 \begin{minipage}{2.8cm}
1281 \underline{\hkl<1 0 0>}\\
1282 $E_{\text{f}}=3.88\text{ eV}$\\
1283 \includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps}
1284 \end{minipage}
1285 }
1286 \begin{minipage}{1.4cm}
1287 \hfill
1288 \end{minipage}
1289 \begin{minipage}{3.0cm}
1290 \begin{flushright}
1291 \underline{Tetrahedral}\\
1292 \includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps}
1293 \end{flushright}
1294 \end{minipage}
1295
1296 \framebox{
1297 \begin{minipage}{2.8cm}
1298 \underline{Bond-centered}\\
1299 $E_{\text{f}}^*=5.59\text{ eV}$\\
1300 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}
1301 \end{minipage}
1302 \begin{minipage}{0.4cm}
1303 \begin{center}
1304 $\Rightarrow$
1305 \end{center}
1306 \end{minipage}
1307 \begin{minipage}{2.8cm}
1308 \underline{\hkl<1 1 0> dumbbell}\\
1309 $E_{\text{f}}=5.18\text{ eV}$\\
1310 \includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps}
1311 \end{minipage}
1312 }
1313 \begin{minipage}{1.4cm}
1314 \hfill
1315 \end{minipage}
1316 \begin{minipage}{3.0cm}
1317 \begin{flushright}
1318 \underline{Substitutional}\\
1319 \includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps}
1320 \end{flushright}
1321 \end{minipage}
1322
1323 \end{slide}
1324
1325 \begin{slide}
1326
1327 \headphd
1328 {\large\bf\boldmath
1329  C-Si dimer \& bond-centered interstitial configuration
1330 }
1331
1332 \footnotesize
1333
1334 \vspace{0.1cm}
1335
1336 \begin{minipage}[t]{4.1cm}
1337 {\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
1338 \begin{minipage}{2.0cm}
1339 \begin{center}
1340 \underline{Erhart/Albe}
1341 \includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
1342 \end{center}
1343 \end{minipage}
1344 \begin{minipage}{2.0cm}
1345 \begin{center}
1346 \underline{\textsc{vasp}}
1347 \includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
1348 \end{center}
1349 \end{minipage}\\[0.2cm]
1350 Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
1351 $\Rightarrow$ $sp$ hybridization\\[0.1cm]
1352 Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
1353 $\Rightarrow$ $sp^2$ hybridization
1354 \begin{center}
1355 \includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
1356 {\tiny Charge density isosurface}
1357 \end{center}
1358 \end{minipage}
1359 \begin{minipage}{0.2cm}
1360 \hfill
1361 \end{minipage}
1362 \begin{minipage}[t]{8.1cm}
1363 \begin{flushright}
1364 {\bf Bond-centered interstitial}\\[0.1cm]
1365 \begin{minipage}{4.4cm}
1366 %\scriptsize
1367 \begin{itemize}
1368  \item Linear Si-C-Si bond
1369  \item Si: one C \& 3 Si neighbours
1370  \item Spin polarized calculations
1371  \item No saddle point!\\
1372        Real local minimum!
1373 \end{itemize}
1374 \end{minipage}
1375 \begin{minipage}{2.7cm}
1376 %\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1377 \vspace{0.2cm}
1378 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\
1379 \end{minipage}
1380
1381 \framebox{
1382  \tiny
1383  \begin{minipage}[t]{6.5cm}
1384   \begin{minipage}[t]{1.2cm}
1385   {\color{red}Si}\\
1386   {\tiny sp$^3$}\\[0.8cm]
1387   \underline{${\color{black}\uparrow}$}
1388   \underline{${\color{black}\uparrow}$}
1389   \underline{${\color{black}\uparrow}$}
1390   \underline{${\color{red}\uparrow}$}\\
1391   sp$^3$
1392   \end{minipage}
1393   \begin{minipage}[t]{1.4cm}
1394   \begin{center}
1395   {\color{red}M}{\color{blue}O}\\[0.8cm]
1396   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1397   $\sigma_{\text{ab}}$\\[0.5cm]
1398   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1399   $\sigma_{\text{b}}$
1400   \end{center}
1401   \end{minipage}
1402   \begin{minipage}[t]{1.0cm}
1403   \begin{center}
1404   {\color{blue}C}\\
1405   {\tiny sp}\\[0.2cm]
1406   \underline{${\color{white}\uparrow\uparrow}$}
1407   \underline{${\color{white}\uparrow\uparrow}$}\\
1408   2p\\[0.4cm]
1409   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1410   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1411   sp
1412   \end{center}
1413   \end{minipage}
1414   \begin{minipage}[t]{1.4cm}
1415   \begin{center}
1416   {\color{blue}M}{\color{green}O}\\[0.8cm]
1417   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1418   $\sigma_{\text{ab}}$\\[0.5cm]
1419   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1420   $\sigma_{\text{b}}$
1421   \end{center}
1422   \end{minipage}
1423   \begin{minipage}[t]{1.2cm}
1424   \begin{flushright}
1425   {\color{green}Si}\\
1426   {\tiny sp$^3$}\\[0.8cm]
1427   \underline{${\color{green}\uparrow}$}
1428   \underline{${\color{black}\uparrow}$}
1429   \underline{${\color{black}\uparrow}$}
1430   \underline{${\color{black}\uparrow}$}\\
1431   sp$^3$
1432   \end{flushright}
1433   \end{minipage}
1434  \end{minipage}
1435 }\\[0.4cm]
1436
1437 %\framebox{
1438 \begin{minipage}{3.0cm}
1439 %\scriptsize
1440 \underline{Charge density}\\
1441 {\color{gray}$\bullet$} Spin up\\
1442 {\color{green}$\bullet$} Spin down\\
1443 {\color{blue}$\bullet$} Resulting spin up\\
1444 {\color{yellow}$\bullet$} Si atoms\\
1445 {\color{red}$\bullet$} C atom
1446 \end{minipage}
1447 \begin{minipage}{3.6cm}
1448 \includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
1449 \end{minipage}
1450 %}
1451
1452 \end{flushright}
1453
1454 \end{minipage}
1455 \begin{pspicture}(0,0)(0,0)
1456 \psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0)
1457 \end{pspicture}
1458
1459 \end{slide}
1460
1461 \begin{slide}
1462
1463 \headphd
1464 {\large\bf\boldmath
1465  C interstitial migration --- ab initio
1466 }
1467
1468 \scriptsize
1469
1470 \vspace{0.1cm}
1471
1472 \begin{minipage}{6.8cm}
1473 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
1474 \begin{minipage}{2.0cm}
1475 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1476 \end{minipage}
1477 \begin{minipage}{0.2cm}
1478 $\rightarrow$
1479 \end{minipage}
1480 \begin{minipage}{2.0cm}
1481 \includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps}
1482 \end{minipage}
1483 \begin{minipage}{0.2cm}
1484 $\rightarrow$
1485 \end{minipage}
1486 \begin{minipage}{2.0cm}
1487 \includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps}
1488 \end{minipage}\\[0.1cm]
1489 Spin polarization\\
1490 $\Rightarrow$ BC configuration constitutes local minimum\\
1491 $\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$
1492 \end{minipage}
1493 \begin{minipage}{5.4cm}
1494 \includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
1495 \end{minipage}\\[0.2cm]
1496 %\hrule
1497 %
1498 \begin{minipage}{6.8cm}
1499 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\
1500 \begin{minipage}{2.0cm}
1501 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1502 \end{minipage}
1503 \begin{minipage}{0.2cm}
1504 $\rightarrow$
1505 \end{minipage}
1506 \begin{minipage}{2.0cm}
1507 \includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
1508 \end{minipage}
1509 \begin{minipage}{0.2cm}
1510 $\rightarrow$
1511 \end{minipage}
1512 \begin{minipage}{2.0cm}
1513 \includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
1514 \end{minipage}\\[0.1cm]
1515 $\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
1516 $\Rightarrow$ {\color{red}Migration mechanism identified!}\\
1517 Note: Change in orientation
1518 \end{minipage}
1519 \begin{minipage}{5.4cm}
1520 \includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
1521 \end{minipage}\\[0.1cm]
1522 %
1523 \begin{center}
1524 Reorientation pathway composed of two consecutive processes of the above type
1525 \end{center}
1526
1527 \end{slide}
1528
1529 \begin{slide}
1530
1531 \headphd
1532 {\large\bf\boldmath
1533  C interstitial migration --- analytical potential
1534 }
1535
1536 \scriptsize
1537
1538 \vspace{0.3cm}
1539
1540 \begin{minipage}[t]{6.0cm}
1541 {\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm]
1542 \includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\
1543 \begin{itemize}
1544  \item Lowermost migration barrier
1545  \item $\Delta E \approx \unit[2.2]{eV}$
1546  \item 2.4 times higher than ab initio result
1547  \item Different pathway
1548 \end{itemize}
1549 \end{minipage}
1550 \begin{minipage}[t]{0.2cm}
1551 \hfill
1552 \end{minipage}
1553 \begin{minipage}[t]{6.0cm}
1554 {\bf\boldmath Transition involving a \hkl<1 1 0> configuration}
1555 \vspace{0.1cm}
1556 \begin{itemize}
1557  \item Bond-centered configuration unstable\\
1558        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1559  \item Minima of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
1560        $\rightarrow$ \ci{} \hkl<1 1 0> DB
1561 \end{itemize}
1562 \vspace{0.1cm}
1563 \includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps}
1564 \begin{itemize}
1565  \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$
1566  \item 2.4 -- 3.4 times higher than ab initio result
1567  \item After all: Change of the DB orientation
1568 \end{itemize}
1569 \end{minipage}
1570
1571 \vspace{0.5cm}
1572 \begin{center}
1573 {\color{red}\bf Drastically overestimated diffusion barrier}
1574 \end{center}
1575
1576 \begin{pspicture}(0,0)(0,0)
1577 \psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3)
1578 \end{pspicture}
1579
1580 \end{slide}
1581
1582 \begin{slide}
1583
1584 \headphd
1585 {\large\bf\boldmath
1586  Defect combinations
1587 }
1588
1589 \footnotesize
1590
1591 \vspace{0.3cm}
1592
1593 \begin{minipage}{9cm}
1594 {\bf
1595  Summary of combinations}\\[0.1cm]
1596 {\scriptsize
1597 \begin{tabular}{l c c c c c c}
1598 \hline
1599  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1600  \hline
1601  \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1602  \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1603  \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}\\
1604  \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}\\
1605  \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}\\
1606  \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}\\
1607  \hline
1608  C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1609  Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1610 \hline
1611 \end{tabular}
1612 }
1613 \vspace{0.2cm}
1614 \begin{center}
1615 {\color{blue}
1616  $E_{\text{b}}$ explainable by stress compensation / increase
1617 }
1618 \end{center}
1619 \end{minipage}
1620 \begin{minipage}{3cm}
1621 \includegraphics[width=3.5cm]{comb_pos.eps}
1622 \end{minipage}
1623
1624 \vspace{0.2cm}
1625
1626 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1627 \begin{minipage}[t]{3.2cm}
1628 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1629 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1630 \end{minipage}
1631 \begin{minipage}[t]{3.0cm}
1632 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1633 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1634 \end{minipage}
1635 \begin{minipage}[t]{6.1cm}
1636 \vspace{0.7cm}
1637 \begin{itemize}
1638  \item \ci{} agglomeration energetically favorable
1639  \item Most favorable: C clustering\\
1640        {\color{red}However \ldots}\\
1641         \ldots high migration barrier ($>4\,\text{eV}$)\\
1642         \ldots entropy:
1643         $4\times{\color{cyan}[-2.25]}$ versus
1644         $2\times{\color{orange}[-2.39]}$
1645 \end{itemize}
1646 \begin{center}
1647 {\color{blue}\ci{} agglomeration / no C clustering}
1648 \end{center}
1649 \end{minipage}
1650
1651 \end{slide}
1652
1653 \begin{slide}
1654
1655 \headphd
1656 {\large\bf\boldmath
1657  Defect combinations
1658 }
1659
1660 \footnotesize
1661
1662 \vspace{0.3cm}
1663
1664 \begin{minipage}{9cm}
1665 {\bf
1666  Summary of combinations}\\[0.1cm]
1667 {\scriptsize
1668 \begin{tabular}{l c c c c c c}
1669 \hline
1670  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1671  \hline
1672  \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1673  \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1674  \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}\\
1675  \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}\\
1676  \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}\\
1677  \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}\\
1678  \hline
1679  C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1680  Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1681 \hline
1682 \end{tabular}
1683 }
1684 \vspace{0.2cm}
1685 \begin{center}
1686 {\color{blue}
1687  $E_{\text{b}}$ explainable by stress compensation / increase
1688 }
1689 \end{center}
1690 \end{minipage}
1691 \begin{minipage}{3cm}
1692 \includegraphics[width=3.5cm]{comb_pos.eps}
1693 \end{minipage}
1694
1695 \vspace{0.2cm}
1696
1697 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1698 \begin{minipage}[t]{3.2cm}
1699 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1700 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1701 \end{minipage}
1702 \begin{minipage}[t]{3.0cm}
1703 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1704 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1705 \end{minipage}
1706 \begin{minipage}[t]{6.1cm}
1707 \vspace{0.7cm}
1708 \begin{itemize}
1709  \item \ci{} agglomeration energetically favorable
1710  \item Most favorable: C clustering\\
1711        {\color{red}However \ldots}\\
1712         \ldots high migration barrier ($>4\,\text{eV}$)\\
1713         \ldots entropy:
1714         $4\times{\color{cyan}[-2.25]}$ versus
1715         $2\times{\color{orange}[-2.39]}$
1716 \end{itemize}
1717 \begin{center}
1718 {\color{blue}\ci{} agglomeration / no C clustering}
1719 \end{center}
1720 \end{minipage}
1721
1722 % insert graph ...
1723 \begin{pspicture}(0,0)(0,0)
1724 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1725 \begin{minipage}{14cm}
1726 \hfill
1727 \vspace{12cm}
1728 \end{minipage}
1729 }}
1730 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1731 \begin{minipage}{8cm}
1732 \begin{center}
1733 \vspace{0.2cm}
1734 \scriptsize
1735 Interaction along \hkl[1 1 0]
1736 \includegraphics[width=7cm]{db_along_110_cc.ps}
1737 \end{center}
1738 \end{minipage}
1739 }}}
1740 \end{pspicture}
1741
1742 \end{slide}
1743
1744 \begin{slide}
1745
1746 \headphd
1747 {\large\bf
1748  Defect combinations of C-Si dimers and vacancies
1749 }
1750 \footnotesize
1751
1752 \vspace{0.2cm}
1753
1754 \begin{minipage}[b]{2.6cm}
1755 \begin{flushleft}
1756 \underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm]
1757 \includegraphics[width=2.5cm]{00-1dc/0-59.eps}
1758 \end{flushleft}
1759 \end{minipage}
1760 \begin{minipage}[b]{7cm}
1761 \hfill
1762 \end{minipage}
1763 \begin{minipage}[b]{2.6cm}
1764 \begin{flushright}
1765 \underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm]
1766 \includegraphics[width=2.5cm]{00-1dc/3-14.eps}
1767 \end{flushright}
1768 \end{minipage}\\[0.2cm]
1769
1770 \begin{minipage}{6.5cm}
1771 \includegraphics[width=6.0cm]{059-539.ps}
1772 \end{minipage}
1773 \begin{minipage}{5.7cm}
1774 \includegraphics[width=6.0cm]{314-539.ps}
1775 \end{minipage}
1776
1777 \begin{pspicture}(0,0)(0,0)
1778 \psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0)
1779
1780 \rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{
1781 \begin{minipage}{6.5cm}
1782 \begin{center}
1783 IBS: Impinging C creates V \& far away \si\\[0.3cm]
1784 Low migration barrier towards C$_{\text{sub}}$\\
1785 \&\\
1786 High barrier for reverse process\\[0.3cm]
1787 {\color{blue}
1788 High probability of stable C$_{\text{sub}}$ configuration
1789 }
1790 \end{center}
1791 \end{minipage}
1792 }}}
1793 \end{pspicture}
1794
1795 \end{slide}
1796
1797 \begin{slide}
1798
1799 \headphd
1800 {\large\bf
1801  Combinations of substitutional C and Si self-interstitials
1802 }
1803
1804 \scriptsize
1805
1806 \vspace{0.3cm}
1807
1808 \begin{minipage}{6.2cm}
1809 \begin{center}
1810 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1811 \begin{itemize}
1812  \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1813  \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1814  \item Interaction drops quickly to zero\\
1815        $\rightarrow$ low capture radius
1816 \end{itemize}
1817 \end{center}
1818 \end{minipage}
1819 \begin{minipage}{0.2cm}
1820 \hfill
1821 \end{minipage}
1822 \begin{minipage}{6.0cm}
1823 \begin{center}
1824 {\bf Transition from the ground state}
1825 \begin{itemize}
1826  \item Low transition barrier
1827  \item Barrier smaller than \ci{} migration barrier
1828  \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1829        $\rightarrow$ Separation of \cs{} \& \si{} most probable
1830 \end{itemize}
1831 \end{center}
1832 \end{minipage}\\[0.3cm]
1833
1834 \begin{minipage}{6.0cm}
1835 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1836 \end{minipage}
1837 \begin{minipage}{0.4cm}
1838 \hfill
1839 \end{minipage}
1840 \begin{minipage}{6.0cm}
1841 \begin{flushright}
1842 \includegraphics[width=6.0cm]{162-097.ps}
1843 \end{flushright}
1844 \end{minipage}
1845
1846 \begin{pspicture}(0,0)(0,0)
1847 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1848 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1849 \begin{minipage}{8cm}
1850 \begin{center}
1851 \vspace{0.1cm}
1852 {\color{black}
1853 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1854 IBS --- process far from equilibrium\\
1855 }
1856 \end{center}
1857 \end{minipage}
1858 }}}
1859 \end{pspicture}
1860
1861 \end{slide}
1862
1863 \begin{slide}
1864
1865 \headphd
1866 {\large\bf
1867  Combinations of substitutional C and Si self-interstitials
1868 }
1869
1870 \scriptsize
1871
1872 \vspace{0.3cm}
1873
1874 \begin{minipage}{6.2cm}
1875 \begin{center}
1876 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1877 \begin{itemize}
1878  \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1879  \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1880  \item Interaction drops quickly to zero\\
1881        $\rightarrow$ low capture radius
1882 \end{itemize}
1883 \end{center}
1884 \end{minipage}
1885 \begin{minipage}{0.2cm}
1886 \hfill
1887 \end{minipage}
1888 \begin{minipage}{6.0cm}
1889 \begin{center}
1890 {\bf Transition from the ground state}
1891 \begin{itemize}
1892  \item Low transition barrier
1893  \item Barrier smaller than \ci{} migration barrier
1894  \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1895        $\rightarrow$ Separation of \cs{} \& \si{} most probable
1896 \end{itemize}
1897 \end{center}
1898 \end{minipage}\\[0.3cm]
1899
1900 \begin{minipage}{6.0cm}
1901 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1902 \end{minipage}
1903 \begin{minipage}{0.4cm}
1904 \hfill
1905 \end{minipage}
1906 \begin{minipage}{6.0cm}
1907 \begin{flushright}
1908 \includegraphics[width=6.0cm]{162-097.ps}
1909 \end{flushright}
1910 \end{minipage}
1911
1912 \begin{pspicture}(0,0)(0,0)
1913 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1914 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1915 \begin{minipage}{8cm}
1916 \begin{center}
1917 \vspace{0.1cm}
1918 {\color{black}
1919 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1920 IBS --- process far from equilibrium\\
1921 }
1922 \end{center}
1923 \end{minipage}
1924 }}}
1925 \end{pspicture}
1926
1927 % md support
1928 \begin{pspicture}(0,0)(0,0)
1929 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1930 \begin{minipage}{14cm}
1931 \hfill
1932 \vspace{14cm}
1933 \end{minipage}
1934 }}
1935 \rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1936 \begin{minipage}{11cm}
1937 \begin{center}
1938 \vspace{0.2cm}
1939 \scriptsize
1940 Ab initio MD at \degc{900}\\[0.4cm]
1941 \begin{minipage}{5.4cm}
1942 \centering
1943 \includegraphics[width=4.3cm]{md01_bonds.eps}\\
1944 $t=\unit[2230]{fs}$
1945 \end{minipage}
1946 \begin{minipage}{5.4cm}
1947 \centering
1948 \includegraphics[width=4.3cm]{md02_bonds.eps}\\
1949 $t=\unit[2900]{fs}$
1950 \end{minipage}\\[0.5cm]
1951 {\color{blue}
1952 Contribution of entropy to structural formation\\[0.1cm]
1953 }
1954 \end{center}
1955 \end{minipage}
1956 }}}
1957 \end{pspicture}
1958
1959 \end{slide}
1960
1961 \begin{slide}
1962
1963 \headphd
1964 {\large\bf
1965  Silicon carbide precipitation simulations
1966 }
1967
1968 \small
1969
1970 \vspace{0.2cm}
1971
1972 {\bf Procedure}
1973
1974 {\scriptsize
1975  \begin{pspicture}(0,0)(12,6.5)
1976   % nodes
1977   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1978    \parbox{7cm}{
1979    \begin{itemize}
1980     \item Create c-Si volume
1981     \item Periodc boundary conditions
1982     \item Set requested $T$ and $p=0\text{ bar}$
1983     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1984    \end{itemize}
1985   }}}}
1986   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1987    \parbox{7cm}{
1988    Insertion of C atoms at constant T
1989    \begin{itemize}
1990     \item total simulation volume {\pnode{in1}}
1991     \item volume of minimal SiC precipitate size {\pnode{in2}}
1992     \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1993           precipitate
1994    \end{itemize}
1995   }}}}
1996   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1997    \parbox{7.0cm}{
1998    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
1999   }}}}
2000   \ncline[]{->}{init}{insert}
2001   \ncline[]{->}{insert}{cool}
2002   \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3)
2003   \rput(7.6,6){\footnotesize $V_1$}
2004   \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5)
2005   \rput(8.9,4.85){\tiny $V_2$}
2006   \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75)
2007   \rput(9.25,4.45){\footnotesize $V_3$}
2008   \rput(7.9,3.2){\pnode{ins1}}
2009   \rput(8.92,2.8){\pnode{ins2}}
2010   \rput(10.8,2.4){\pnode{ins3}}
2011   \ncline[]{->}{in1}{ins1}
2012   \ncline[]{->}{in2}{ins2}
2013   \ncline[]{->}{in3}{ins3}
2014  \end{pspicture}
2015 }
2016
2017 \vspace{-0.5cm}
2018
2019 {\bf Note}
2020
2021 \footnotesize
2022
2023 \begin{minipage}{5.7cm}
2024 \begin{itemize}
2025  \item Amount of C atoms: 6000\\
2026        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm})
2027  \item Simulation volume: $31^3$ Si unit cells\\
2028        (238328 Si atoms)
2029 \end{itemize}
2030 \end{minipage}
2031 \begin{minipage}{0.3cm}
2032 \hfill
2033 \end{minipage}
2034 \framebox{
2035 \begin{minipage}{6.0cm}
2036 Restricted to classical potential caclulations\\
2037 $\rightarrow$ Low C diffusion / overestimated barrier\\
2038 $\rightarrow$ Consider $V_2$ and $V_3$
2039 %\begin{itemize}
2040 % \item $V_2$ and $V_3$ considered due to expected low C diffusion
2041 %\end{itemize}
2042 \end{minipage}
2043 }
2044
2045 \end{slide}
2046
2047 \begin{slide}
2048
2049 \headphd
2050 {\large\bf\boldmath
2051  Silicon carbide precipitation simulations at \degc{450} as in IBS
2052 }
2053
2054 \small
2055
2056 \begin{minipage}{6.3cm}
2057 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
2058 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
2059 \hfill
2060 \end{minipage}
2061 \begin{minipage}{6.1cm}
2062 \scriptsize
2063 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
2064 \hkl<1 0 0> C-Si dumbbell dominated structure
2065 \begin{itemize}
2066  \item Si-C bumbs around \unit[0.19]{nm}
2067  \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
2068        concatenated differently oriented \ci{} DBs
2069  \item Si-Si NN distance stretched to \unit[0.3]{nm}
2070 \end{itemize}
2071 \begin{pspicture}(0,0)(6.0,1.0)
2072 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
2073 \begin{minipage}{6cm}
2074 \centering
2075 Formation of \ci{} dumbbells\\
2076 C atoms in proper 3C-SiC distance first
2077 \end{minipage}
2078 }}
2079 \end{pspicture}\\[0.1cm]
2080 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
2081 \begin{itemize}
2082 \item High amount of strongly bound C-C bonds
2083 \item Increased defect \& damage density\\
2084       $\rightarrow$ Arrangements hard to categorize and trace
2085 \item Only short range order observable
2086 \end{itemize}
2087 \begin{pspicture}(0,0)(6.0,0.8)
2088 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
2089 \begin{minipage}{6cm}
2090 \centering
2091 Amorphous SiC-like phase
2092 \end{minipage}
2093 }}
2094 \end{pspicture}\\[0.3cm]
2095 \begin{pspicture}(0,0)(6.0,2.0)
2096 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{
2097 \begin{minipage}{6cm}
2098 \hfill
2099 \vspace{2.5cm}
2100 \end{minipage}
2101 }}
2102 \end{pspicture}
2103 \end{minipage}
2104
2105 \end{slide}
2106
2107 \begin{slide}
2108
2109 \headphd
2110 {\large\bf\boldmath
2111  Silicon carbide precipitation simulations at \degc{450} as in IBS
2112 }
2113
2114 \small
2115
2116 \begin{minipage}{6.3cm}
2117 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
2118 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
2119 \hfill
2120 \end{minipage}
2121 \begin{minipage}{6.1cm}
2122 \scriptsize
2123 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
2124 \hkl<1 0 0> C-Si dumbbell dominated structure
2125 \begin{itemize}
2126  \item Si-C bumbs around \unit[0.19]{nm}
2127  \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
2128        concatenated differently oriented \ci{} DBs
2129  \item Si-Si NN distance stretched to \unit[0.3]{nm}
2130 \end{itemize}
2131 \begin{pspicture}(0,0)(6.0,1.0)
2132 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
2133 \begin{minipage}{6cm}
2134 \centering
2135 Formation of \ci{} dumbbells\\
2136 C atoms in proper 3C-SiC distance first
2137 \end{minipage}
2138 }}
2139 \end{pspicture}\\[0.1cm]
2140 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
2141 \begin{itemize}
2142 \item High amount of strongly bound C-C bonds
2143 \item Increased defect \& damage density\\
2144       $\rightarrow$ Arrangements hard to categorize and trace
2145 \item Only short range order observable
2146 \end{itemize}
2147 \begin{pspicture}(0,0)(6.0,0.8)
2148 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
2149 \begin{minipage}{6cm}
2150 \centering
2151 Amorphous SiC-like phase
2152 \end{minipage}
2153 }}
2154 \end{pspicture}\\[0.3cm]
2155 \begin{pspicture}(0,0)(6.0,2.0)
2156 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{
2157 \begin{minipage}{6cm}
2158 \vspace{0.1cm}
2159 \centering
2160 {\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm]
2161 \begin{minipage}{0.8cm}
2162 {\bf\boldmath $V_1$:}
2163 \end{minipage}
2164 \begin{minipage}{5.1cm}
2165 Formation of \ci{} indeed occurs\\
2166 Agllomeration not observed
2167 \end{minipage}\\[0.3cm]
2168 \begin{minipage}{0.8cm}
2169 {\bf\boldmath $V_{2,3}$:}
2170 \end{minipage}
2171 \begin{minipage}{5.1cm}
2172 Amorphous SiC-like structure\\
2173 (not expected at \degc{450})\\[0.05cm]
2174 No rearrangement/transition into 3C-SiC
2175 \end{minipage}\\[0.1cm]
2176 \end{minipage}
2177 }}
2178 \end{pspicture}
2179 \end{minipage}
2180
2181 \end{slide}
2182
2183 \begin{slide}
2184
2185 \headphd
2186 {\large\bf
2187  Limitations of MD and short range potentials
2188 }
2189
2190 \small
2191
2192 \vspace{0.2cm}
2193
2194 {\bf Time scale problem of MD}\\[0.2cm]
2195 Precise integration \& thermodynamic sampling\\
2196 $\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
2197               $\omega$: vibrational mode\\
2198 $\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
2199 Several local minima separated by large energy barriers\\
2200 $\Rightarrow$ Transition event corresponds to a multiple
2201               of vibrational periods\\
2202 $\Rightarrow$ Phase transition consists of {\color{red}\underline{many}}
2203               infrequent transition events\\[0.2cm]
2204 {\color{blue}Accelerated methods:}
2205 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
2206
2207 \vspace{0.2cm}
2208
2209 {\bf Limitations related to the short range potential}\\[0.2cm]
2210 Cut-off function limits interaction to next neighbours\\
2211 $\Rightarrow$ Overestimated unphysical high forces of next neighbours
2212
2213 \vspace{1.4cm}
2214
2215 {\bf Approach to the (twofold) problem}\\[0.2cm]
2216 Increased temperature simulations without TAD corrections\\
2217 Accelerated methods or higher time scales exclusively not sufficient!
2218
2219 \begin{pspicture}(0,0)(0,0)
2220 \rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{
2221 \begin{minipage}{7.5cm}
2222 \centering
2223 \vspace{0.05cm}
2224 Potential enhanced slow phase space propagation
2225 \end{minipage}
2226 }}
2227 \rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
2228 \begin{minipage}{2.7cm}
2229 \tiny
2230 \centering
2231 retain proper\\
2232 thermodynamic sampling
2233 \end{minipage}
2234 }}
2235 \psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7)
2236 \rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{
2237 \begin{minipage}{3.6cm}
2238 \tiny
2239 \centering
2240 \underline{IBS}\\[0.1cm]
2241 3C-SiC also observed for higher T\\[0.1cm]
2242 Higher T inside sample\\[0.1cm]
2243 Structural evolution vs.\\
2244 equilibrium properties
2245 \end{minipage}
2246 }}
2247 \psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0)
2248 \end{pspicture}
2249
2250 \end{slide}
2251
2252 % continue here
2253 \fi
2254
2255 \begin{slide}
2256
2257 \headphd
2258 {\large\bf\boldmath
2259  Increased temperature simulations --- $V_1$
2260 }
2261
2262 \small
2263
2264 \begin{minipage}{6.2cm}
2265 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
2266 \hfill
2267 \end{minipage}
2268 \begin{minipage}{6.2cm}
2269 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
2270 \end{minipage}
2271
2272 \begin{minipage}{6.2cm}
2273 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
2274 \hfill
2275 \end{minipage}
2276 \begin{minipage}{6.3cm}
2277 \scriptsize
2278  \underline{Si-C bonds:}
2279  \begin{itemize}
2280   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2281   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2282  \end{itemize}
2283  \underline{Si-Si bonds:}
2284  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2285  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2286  \underline{C-C bonds:}
2287  \begin{itemize}
2288   \item C-C next neighbour pairs reduced (mandatory)
2289   \item Peak at 0.3 nm slightly shifted
2290         \begin{itemize}
2291          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2292                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2293                combinations (|)\\
2294                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2295                ($\downarrow$)
2296          \item Range [|-$\downarrow$]:
2297                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2298                with nearby Si$_{\text{I}}$}
2299         \end{itemize}
2300  \end{itemize}
2301 \end{minipage}
2302
2303 \end{slide}
2304
2305 \begin{slide}
2306
2307 \headphd
2308 {\large\bf\boldmath
2309  Increased temperature simulations --- $V_1$
2310 }
2311
2312 \small
2313
2314 \begin{minipage}{6.2cm}
2315 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
2316 \hfill
2317 \end{minipage}
2318 \begin{minipage}{6.2cm}
2319 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
2320 \end{minipage}
2321
2322 \begin{minipage}{6.2cm}
2323 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
2324 \hfill
2325 \end{minipage}
2326 \begin{minipage}{6.3cm}
2327 \scriptsize
2328  \underline{Si-C bonds:}
2329  \begin{itemize}
2330   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2331   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2332  \end{itemize}
2333  \underline{Si-Si bonds:}
2334  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2335  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2336  \underline{C-C bonds:}
2337  \begin{itemize}
2338   \item C-C next neighbour pairs reduced (mandatory)
2339   \item Peak at 0.3 nm slightly shifted
2340         \begin{itemize}
2341          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2342                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2343                combinations (|)\\
2344                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2345                ($\downarrow$)
2346          \item Range [|-$\downarrow$]:
2347                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2348                with nearby Si$_{\text{I}}$}
2349         \end{itemize}
2350  \end{itemize}
2351 \end{minipage}
2352
2353 % md support
2354 \begin{pspicture}(0,0)(0,0)
2355 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
2356 \begin{minipage}{14cm}
2357 \hfill
2358 \vspace{14cm}
2359 \end{minipage}
2360 }}
2361 \rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
2362 \begin{minipage}{9cm}
2363 \vspace{0.2cm}
2364 \small
2365 {\color{blue}\bf Stretched structures of SiC in c-Si}
2366 \begin{itemize}
2367 \item Consistent to precipitation model involving \cs{}
2368 \item Explains annealing behavior of high/low T C implants
2369       \begin{itemize}
2370        \item Low T: highly mobiel \ci{}
2371        \item High T: stable configurations of \cs{}
2372       \end{itemize}
2373 \end{itemize}
2374 $\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2375 $\Rightarrow$ Precipitation mechanism involving \cs{}
2376
2377 \end{minipage}
2378 }}
2379 \end{pspicture}
2380
2381 \end{slide}
2382
2383 \begin{slide}
2384
2385  {\large\bf
2386   Increased temperature simulations at high C concentration
2387  }
2388
2389 \footnotesize
2390
2391 \begin{minipage}{6.5cm}
2392 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2393 \end{minipage}
2394 \begin{minipage}{6.5cm}
2395 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2396 \end{minipage}
2397
2398 \vspace{0.1cm}
2399
2400 \scriptsize
2401
2402 \framebox{
2403 \begin{minipage}[t]{6.0cm}
2404 0.186 nm: Si-C pairs $\uparrow$\\
2405 (as expected in 3C-SiC)\\[0.2cm]
2406 0.282 nm: Si-C-C\\[0.2cm]
2407 $\approx$0.35 nm: C-Si-Si
2408 \end{minipage}
2409 }
2410 \begin{minipage}{0.2cm}
2411 \hfill
2412 \end{minipage}
2413 \framebox{
2414 \begin{minipage}[t]{6.0cm}
2415 0.15 nm: C-C pairs $\uparrow$\\
2416 (as expected in graphite/diamond)\\[0.2cm]
2417 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2418 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2419 \end{minipage}
2420 }
2421
2422 \begin{itemize}
2423 \item Decreasing cut-off artifact
2424 \item {\color{red}Amorphous} SiC-like phase remains
2425 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2426 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2427 \end{itemize}
2428
2429 \vspace{-0.1cm}
2430
2431 \begin{center}
2432 {\color{blue}
2433 \framebox{
2434 {\color{black}
2435 High C \& small $V$ \& short $t$
2436 $\Rightarrow$
2437 }
2438 Slow restructuring due to strong C-C bonds
2439 {\color{black}
2440 $\Leftarrow$
2441 High C \& low T implants
2442 }
2443 }
2444 }
2445 \end{center}
2446
2447 \end{slide}
2448
2449 \end{document}
2450 \ifnum1=0
2451
2452 \begin{slide}
2453
2454  {\large\bf
2455   Summary and Conclusions
2456  }
2457
2458  \scriptsize
2459
2460 %\vspace{0.1cm}
2461
2462 \framebox{
2463 \begin{minipage}[t]{12.9cm}
2464  \underline{Pecipitation simulations}
2465  \begin{itemize}
2466   \item High C concentration $\rightarrow$ amorphous SiC like phase
2467   \item Problem of potential enhanced slow phase space propagation
2468   \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2469   \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2470   \item High T necessary to simulate IBS conditions (far from equilibrium)
2471   \item Precipitation by successive agglomeration of \cs (epitaxy)
2472   \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2473         (stretched SiC, interface)
2474  \end{itemize}
2475 \end{minipage}
2476 }
2477
2478 %\vspace{0.1cm}
2479
2480 \framebox{
2481 \begin{minipage}{12.9cm}
2482  \underline{Defects}
2483  \begin{itemize}
2484    \item DFT / EA
2485         \begin{itemize}
2486          \item Point defects excellently / fairly well described
2487                by DFT / EA
2488          \item C$_{\text{sub}}$ drastically underestimated by EA
2489          \item EA predicts correct ground state:
2490                C$_{\text{sub}}$ \& \si{} $>$ \ci{}
2491          \item Identified migration path explaining
2492                diffusion and reorientation experiments by DFT
2493          \item EA fails to describe \ci{} migration:
2494                Wrong path \& overestimated barrier
2495         \end{itemize}
2496    \item Combinations of defects
2497          \begin{itemize}
2498           \item Agglomeration of point defects energetically favorable
2499                 by compensation of stress
2500           \item Formation of C-C unlikely
2501           \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2502           \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2503                 Low barrier (\unit[0.77]{eV}) \& low capture radius
2504         \end{itemize}
2505  \end{itemize}
2506 \end{minipage}
2507 }
2508
2509 \begin{center}
2510 {\color{blue}
2511 \framebox{Precipitation by successive agglomeration of \cs{}}
2512 }
2513 \end{center}
2514
2515 \end{slide}
2516
2517 \begin{slide}
2518
2519  {\large\bf
2520   Acknowledgements
2521  }
2522
2523  \vspace{0.1cm}
2524
2525  \small
2526
2527  Thanks to \ldots
2528
2529  \underline{Augsburg}
2530  \begin{itemize}
2531   \item Prof. B. Stritzker (accomodation at EP \RM{4})
2532   \item Ralf Utermann (EDV)
2533  \end{itemize}
2534
2535  \underline{Helsinki}
2536  \begin{itemize}
2537   \item Prof. K. Nordlund (MD)
2538  \end{itemize}
2539
2540  \underline{Munich}
2541  \begin{itemize}
2542   \item Bayerische Forschungsstiftung (financial support)
2543  \end{itemize}
2544
2545  \underline{Paderborn}
2546  \begin{itemize}
2547   \item Prof. J. Lindner (SiC)
2548   \item Prof. G. Schmidt (DFT + financial support)
2549   \item Dr. E. Rauls (DFT + SiC)
2550   \item Dr. S. Sanna (VASP)
2551  \end{itemize}
2552
2553 \vspace{0.2cm}
2554
2555 \begin{center}
2556 \framebox{
2557 \bf Thank you for your attention!
2558 }
2559 \end{center}
2560
2561 \end{slide}
2562
2563 \end{document}
2564
2565 \fi