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 % continue here
1326 \fi
1327
1328 \begin{slide}
1329
1330 \headphd
1331 {\large\bf\boldmath
1332  C-Si dimer \& bond-centered interstitial configuration
1333 }
1334
1335 \footnotesize
1336
1337 \vspace{0.1cm}
1338
1339 \begin{minipage}[t]{4.1cm}
1340 {\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
1341 \begin{minipage}{2.0cm}
1342 \begin{center}
1343 \underline{Erhart/Albe}
1344 \includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
1345 \end{center}
1346 \end{minipage}
1347 \begin{minipage}{2.0cm}
1348 \begin{center}
1349 \underline{\textsc{vasp}}
1350 \includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
1351 \end{center}
1352 \end{minipage}\\[0.2cm]
1353 Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
1354 $\Rightarrow$ $sp$ hybridization\\[0.1cm]
1355 Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
1356 $\Rightarrow$ $sp^2$ hybridization
1357 \begin{center}
1358 \includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
1359 {\tiny Charge density isosurface}
1360 \end{center}
1361 \end{minipage}
1362 \begin{minipage}{0.2cm}
1363 \hfill
1364 \end{minipage}
1365 \begin{minipage}[t]{8.1cm}
1366 \begin{flushright}
1367 {\bf Bond-centered interstitial}\\[0.1cm]
1368 \begin{minipage}{4.4cm}
1369 \scriptsize
1370 \begin{itemize}
1371  \item Linear Si-C-Si bond
1372  \item Si: one C \& 3 Si neighbours
1373  \item Spin polarized calculations
1374  \item No saddle point!\\
1375        Real local minimum!
1376 \end{itemize}
1377 \end{minipage}
1378 \begin{minipage}{2.7cm}
1379 \includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1380 \end{minipage}
1381
1382 \framebox{
1383  \tiny
1384  \begin{minipage}[t]{6.5cm}
1385   \begin{minipage}[t]{1.2cm}
1386   {\color{red}Si}\\
1387   {\tiny sp$^3$}\\[0.8cm]
1388   \underline{${\color{black}\uparrow}$}
1389   \underline{${\color{black}\uparrow}$}
1390   \underline{${\color{black}\uparrow}$}
1391   \underline{${\color{red}\uparrow}$}\\
1392   sp$^3$
1393   \end{minipage}
1394   \begin{minipage}[t]{1.4cm}
1395   \begin{center}
1396   {\color{red}M}{\color{blue}O}\\[0.8cm]
1397   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1398   $\sigma_{\text{ab}}$\\[0.5cm]
1399   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1400   $\sigma_{\text{b}}$
1401   \end{center}
1402   \end{minipage}
1403   \begin{minipage}[t]{1.0cm}
1404   \begin{center}
1405   {\color{blue}C}\\
1406   {\tiny sp}\\[0.2cm]
1407   \underline{${\color{white}\uparrow\uparrow}$}
1408   \underline{${\color{white}\uparrow\uparrow}$}\\
1409   2p\\[0.4cm]
1410   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1411   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1412   sp
1413   \end{center}
1414   \end{minipage}
1415   \begin{minipage}[t]{1.4cm}
1416   \begin{center}
1417   {\color{blue}M}{\color{green}O}\\[0.8cm]
1418   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1419   $\sigma_{\text{ab}}$\\[0.5cm]
1420   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1421   $\sigma_{\text{b}}$
1422   \end{center}
1423   \end{minipage}
1424   \begin{minipage}[t]{1.2cm}
1425   \begin{flushright}
1426   {\color{green}Si}\\
1427   {\tiny sp$^3$}\\[0.8cm]
1428   \underline{${\color{green}\uparrow}$}
1429   \underline{${\color{black}\uparrow}$}
1430   \underline{${\color{black}\uparrow}$}
1431   \underline{${\color{black}\uparrow}$}\\
1432   sp$^3$
1433   \end{flushright}
1434   \end{minipage}
1435  \end{minipage}
1436 }\\[0.4cm]
1437
1438 %\framebox{
1439 \begin{minipage}{2.8cm}
1440 \scriptsize
1441 Charge density\\
1442 {\color{gray}$\bullet$} Spin up\\
1443 {\color{green}$\bullet$} Spin down\\
1444 {\color{blue}$\bullet$} Resulting spin up\\
1445 {\color{yellow}$\bullet$} Si atoms\\
1446 {\color{red}$\bullet$} C atom
1447 \end{minipage}
1448 \begin{minipage}{3.6cm}
1449 \includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
1450 \end{minipage}
1451 %}
1452
1453 \end{flushright}
1454
1455 \end{minipage}
1456
1457 \end{slide}
1458
1459 \end{document}
1460 \ifnum1=0
1461
1462 \begin{slide}
1463
1464  {\large\bf\boldmath
1465   Migration of the C \hkl<1 0 0> dumbbell interstitial
1466  }
1467
1468 \scriptsize
1469
1470  {\small Investigated pathways}
1471
1472 \begin{minipage}{8.5cm}
1473 \begin{minipage}{8.3cm}
1474 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
1475 \begin{minipage}{2.4cm}
1476 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1477 \end{minipage}
1478 \begin{minipage}{0.4cm}
1479 $\rightarrow$
1480 \end{minipage}
1481 \begin{minipage}{2.4cm}
1482 \includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
1483 \end{minipage}
1484 \begin{minipage}{0.4cm}
1485 $\rightarrow$
1486 \end{minipage}
1487 \begin{minipage}{2.4cm}
1488 \includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
1489 \end{minipage}
1490 \end{minipage}\\
1491 \begin{minipage}{8.3cm}
1492 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
1493 \begin{minipage}{2.4cm}
1494 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1495 \end{minipage}
1496 \begin{minipage}{0.4cm}
1497 $\rightarrow$
1498 \end{minipage}
1499 \begin{minipage}{2.4cm}
1500 \includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
1501 \end{minipage}
1502 \begin{minipage}{0.4cm}
1503 $\rightarrow$
1504 \end{minipage}
1505 \begin{minipage}{2.4cm}
1506 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
1507 \end{minipage}
1508 \end{minipage}\\
1509 \begin{minipage}{8.3cm}
1510 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
1511 \begin{minipage}{2.4cm}
1512 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1513 \end{minipage}
1514 \begin{minipage}{0.4cm}
1515 $\rightarrow$
1516 \end{minipage}
1517 \begin{minipage}{2.4cm}
1518 \includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
1519 \end{minipage}
1520 \begin{minipage}{0.4cm}
1521 $\rightarrow$
1522 \end{minipage}
1523 \begin{minipage}{2.4cm}
1524 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
1525 \end{minipage}
1526 \end{minipage}
1527 \end{minipage}
1528
1529 \end{slide}
1530
1531 \begin{slide}
1532
1533  {\large\bf\boldmath
1534   Migration of the C \hkl<1 0 0> dumbbell interstitial
1535  }
1536
1537 \scriptsize
1538
1539 \framebox{
1540 \begin{minipage}{5.9cm}
1541 \begin{flushleft}
1542 \includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
1543 \end{flushleft}
1544 \begin{center}
1545 \begin{picture}(0,0)(60,0)
1546 \includegraphics[width=1cm]{vasp_mig/00-1.eps}
1547 \end{picture}
1548 \begin{picture}(0,0)(-5,0)
1549 \includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
1550 \end{picture}
1551 \begin{picture}(0,0)(-55,0)
1552 \includegraphics[width=1cm]{vasp_mig/bc.eps}
1553 \end{picture}
1554 \begin{picture}(0,0)(12.5,10)
1555 \includegraphics[width=1cm]{110_arrow.eps}
1556 \end{picture}
1557 \begin{picture}(0,0)(90,0)
1558 \includegraphics[height=0.9cm]{001_arrow.eps}
1559 \end{picture}
1560 \end{center}
1561 \vspace*{0.35cm}
1562 \end{minipage}
1563 }
1564 \begin{minipage}{0.3cm}
1565 \hfill
1566 \end{minipage}
1567 \framebox{
1568 \begin{minipage}{5.9cm}
1569 \begin{flushright}
1570 \includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
1571 \end{flushright}
1572 \begin{center}
1573 \begin{picture}(0,0)(60,0)
1574 \includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
1575 \end{picture}
1576 \begin{picture}(0,0)(5,0)
1577 \includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
1578 \end{picture}
1579 \begin{picture}(0,0)(-55,0)
1580 \includegraphics[width=1cm]{vasp_mig/0-10.eps}
1581 \end{picture}
1582 \begin{picture}(0,0)(12.5,10)
1583 \includegraphics[width=1cm]{100_arrow.eps}
1584 \end{picture}
1585 \begin{picture}(0,0)(90,0)
1586 \includegraphics[height=0.9cm]{001_arrow.eps}
1587 \end{picture}
1588 \end{center}
1589 \vspace*{0.3cm}
1590 \end{minipage}\\
1591 }
1592
1593 \vspace*{0.05cm}
1594
1595 \framebox{
1596 \begin{minipage}{5.9cm}
1597 \begin{flushleft}
1598 \includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
1599 \end{flushleft}
1600 \begin{center}
1601 \begin{picture}(0,0)(60,0)
1602 \includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps}
1603 \end{picture}
1604 \begin{picture}(0,0)(10,0)
1605 \includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
1606 \end{picture}
1607 \begin{picture}(0,0)(-60,0)
1608 \includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps}
1609 \end{picture}
1610 \begin{picture}(0,0)(12.5,10)
1611 \includegraphics[width=1cm]{100_arrow.eps}
1612 \end{picture}
1613 \begin{picture}(0,0)(90,0)
1614 \includegraphics[height=0.9cm]{001_arrow.eps}
1615 \end{picture}
1616 \end{center}
1617 \vspace*{0.3cm}
1618 \end{minipage}
1619 }
1620 \begin{minipage}{0.3cm}
1621 \hfill
1622 \end{minipage}
1623 \begin{minipage}{6.5cm}
1624 VASP results
1625 \begin{itemize}
1626  \item Energetically most favorable path
1627        \begin{itemize}
1628         \item Path 2
1629         \item Activation energy: $\approx$ 0.9 eV
1630         \item Experimental values: 0.73 ... 0.87 eV
1631        \end{itemize}
1632        $\Rightarrow$ {\color{blue}Diffusion} path identified!
1633  \item Reorientation (path 3)
1634        \begin{itemize}
1635         \item More likely composed of two consecutive steps of type 2
1636         \item Experimental values: 0.77 ... 0.88 eV
1637        \end{itemize}
1638        $\Rightarrow$ {\color{blue}Reorientation} transition identified!
1639 \end{itemize}
1640 \end{minipage}
1641
1642 \end{slide}
1643
1644 \begin{slide}
1645
1646  {\large\bf\boldmath
1647   Migration of the C \hkl<1 0 0> dumbbell interstitial
1648  }
1649
1650 \scriptsize
1651
1652  \vspace{0.1cm}
1653
1654 \begin{minipage}{6.5cm}
1655
1656 \framebox{
1657 \begin{minipage}[t]{5.9cm}
1658 \begin{flushleft}
1659 \includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
1660 \end{flushleft}
1661 \begin{center}
1662 \begin{pspicture}(0,0)(0,0)
1663 \psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
1664 \end{pspicture}
1665 \begin{picture}(0,0)(60,-50)
1666 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
1667 \end{picture}
1668 \begin{picture}(0,0)(5,-50)
1669 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
1670 \end{picture}
1671 \begin{picture}(0,0)(-55,-50)
1672 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
1673 \end{picture}
1674 \begin{picture}(0,0)(12.5,-40)
1675 \includegraphics[width=1cm]{110_arrow.eps}
1676 \end{picture}
1677 \begin{picture}(0,0)(90,-45)
1678 \includegraphics[height=0.9cm]{001_arrow.eps}
1679 \end{picture}\\
1680 \begin{pspicture}(0,0)(0,0)
1681 \psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
1682 \end{pspicture}
1683 \begin{picture}(0,0)(60,-15)
1684 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
1685 \end{picture}
1686 \begin{picture}(0,0)(35,-15)
1687 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
1688 \end{picture}
1689 \begin{picture}(0,0)(-5,-15)
1690 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
1691 \end{picture}
1692 \begin{picture}(0,0)(-55,-15)
1693 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
1694 \end{picture}
1695 \begin{picture}(0,0)(12.5,-5)
1696 \includegraphics[width=1cm]{100_arrow.eps}
1697 \end{picture}
1698 \begin{picture}(0,0)(90,-15)
1699 \includegraphics[height=0.9cm]{010_arrow.eps}
1700 \end{picture}
1701 \end{center}
1702 \end{minipage}
1703 }\\[0.1cm]
1704
1705 \begin{minipage}{5.9cm}
1706 Erhart/Albe results
1707 \begin{itemize}
1708  \item Lowest activation energy: $\approx$ 2.2 eV
1709  \item 2.4 times higher than VASP
1710  \item Different pathway
1711 \end{itemize}
1712 \end{minipage}
1713
1714 \end{minipage}
1715 \begin{minipage}{6.5cm}
1716
1717 \framebox{
1718 \begin{minipage}{5.9cm}
1719 %\begin{flushright}
1720 %\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
1721 %\end{flushright}
1722 %\begin{center}
1723 %\begin{pspicture}(0,0)(0,0)
1724 %\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
1725 %\end{pspicture}
1726 %\begin{picture}(0,0)(60,-5)
1727 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
1728 %\end{picture}
1729 %\begin{picture}(0,0)(0,-5)
1730 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
1731 %\end{picture}
1732 %\begin{picture}(0,0)(-55,-5)
1733 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
1734 %\end{picture}
1735 %\begin{picture}(0,0)(12.5,5)
1736 %\includegraphics[width=1cm]{100_arrow.eps}
1737 %\end{picture}
1738 %\begin{picture}(0,0)(90,0)
1739 %\includegraphics[height=0.9cm]{001_arrow.eps}
1740 %\end{picture}
1741 %\end{center}
1742 %\vspace{0.2cm}
1743 %\end{minipage}
1744 %}\\[0.2cm]
1745 %
1746 %\framebox{
1747 %\begin{minipage}{5.9cm}
1748 \includegraphics[width=5.9cm]{00-1_110_0-10_mig_albe.ps}
1749 \end{minipage}
1750 }\\[0.1cm]
1751
1752 \begin{minipage}{5.9cm}
1753 Transition involving \ci{} \hkl<1 1 0>
1754 \begin{itemize}
1755  \item Bond-centered configuration unstable\\
1756        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1757  \item Transition minima of path 2 \& 3\\
1758        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1759  \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV
1760  \item 2.4 - 3.4 times higher than VASP
1761  \item Rotation of dumbbell orientation
1762 \end{itemize}
1763 \vspace{0.1cm}
1764 \begin{center}
1765 {\color{blue}Overestimated diffusion barrier}
1766 \end{center}
1767 \end{minipage}
1768
1769 \end{minipage}
1770
1771 \end{slide}
1772
1773 \begin{slide}
1774
1775  {\large\bf\boldmath
1776   Combinations with a C-Si \hkl<1 0 0>-type interstitial
1777  }
1778
1779 \small
1780
1781 \vspace*{0.1cm}
1782
1783 Binding energy:
1784 $
1785 E_{\text{b}}=
1786 E_{\text{f}}^{\text{defect combination}}-
1787 E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
1788 E_{\text{f}}^{\text{2nd defect}}
1789 $
1790
1791 \vspace*{0.1cm}
1792
1793 {\scriptsize
1794 \begin{tabular}{l c c c c c c}
1795 \hline
1796  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1797  \hline
1798  \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1799  \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1800  \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}\\
1801  \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}\\
1802  \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}\\
1803  \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}\\
1804  \hline
1805  C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1806  Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1807 \hline
1808 \end{tabular}
1809 }
1810
1811 \vspace*{0.3cm}
1812
1813 \footnotesize
1814
1815 \begin{minipage}[t]{3.8cm}
1816 \underline{\hkl<1 0 0> at position 1}\\[0.1cm]
1817 \includegraphics[width=3.5cm]{00-1dc/2-25.eps}
1818 \end{minipage}
1819 \begin{minipage}[t]{3.5cm}
1820 \underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
1821 \includegraphics[width=3.2cm]{00-1dc/2-39.eps}
1822 \end{minipage}
1823 \begin{minipage}[t]{5.5cm}
1824 \begin{itemize}
1825  \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\
1826        $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
1827  \item Stress compensation / increase
1828  \item Unfavored: antiparallel orientations
1829  \item Indication of energetically favored\\
1830        agglomeration
1831  \item Most favorable: C clustering
1832  \item However: High barrier ($>4\,\text{eV}$)
1833  \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$
1834        (Entropy)
1835 \end{itemize}
1836 \end{minipage}
1837
1838 \begin{picture}(0,0)(-295,-130)
1839 \includegraphics[width=3.5cm]{comb_pos.eps}
1840 \end{picture}
1841
1842 \end{slide}
1843
1844 \begin{slide}
1845
1846  {\large\bf\boldmath
1847   Combinations of C-Si \hkl<1 0 0>-type interstitials
1848  }
1849
1850 \small
1851
1852 \vspace*{0.1cm}
1853
1854 Energetically most favorable combinations along \hkl<1 1 0>
1855
1856 \vspace*{0.1cm}
1857
1858 {\scriptsize
1859 \begin{tabular}{l c c c c c c}
1860 \hline
1861  & 1 & 2 & 3 & 4 & 5 & 6\\
1862 \hline
1863 $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
1864 C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
1865 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>\\
1866 \hline
1867 \end{tabular}
1868 }
1869
1870 \vspace*{0.3cm}
1871
1872 \begin{minipage}{7.0cm}
1873 \includegraphics[width=7cm]{db_along_110_cc.ps}
1874 \end{minipage}
1875 \begin{minipage}{6.0cm}
1876 \begin{itemize}
1877  \item Interaction proportional to reciprocal cube of C-C distance
1878  \item Saturation in the immediate vicinity
1879  \renewcommand\labelitemi{$\Rightarrow$}
1880  \item Agglomeration of \ci{} expected
1881  \item Absence of C clustering
1882 \end{itemize}
1883 \begin{center}
1884 {\color{blue}
1885  Consisten with initial precipitation model
1886 }
1887 \end{center}
1888 \end{minipage}
1889
1890 \vspace{0.2cm}
1891
1892 \end{slide}
1893
1894 \begin{slide}
1895
1896  {\large\bf\boldmath
1897   Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
1898  }
1899
1900  \scriptsize
1901
1902 %\begin{center}
1903 %\begin{minipage}{3.2cm}
1904 %\includegraphics[width=3cm]{sub_110_combo.eps}
1905 %\end{minipage}
1906 %\begin{minipage}{7.8cm}
1907 %\begin{tabular}{l c c c c c c}
1908 %\hline
1909 %C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
1910 %                   \hkl<1 0 1> & \hkl<-1 0 1> \\
1911 %\hline
1912 %1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
1913 %2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
1914 %3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
1915 %4 & \RM{4} & B & D & E & E & D \\
1916 %5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
1917 %\hline
1918 %\end{tabular}
1919 %\end{minipage}
1920 %\end{center}
1921
1922 %\begin{center}
1923 %\begin{tabular}{l c c c c c c c c c c}
1924 %\hline
1925 %Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
1926 %\hline
1927 %$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
1928 %$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
1929 %$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
1930 %\hline
1931 %\end{tabular}
1932 %\end{center}
1933
1934 \begin{minipage}{6.0cm}
1935 \includegraphics[width=5.8cm]{c_sub_si110.ps}
1936 \end{minipage}
1937 \begin{minipage}{7cm}
1938 \scriptsize
1939 \begin{itemize}
1940  \item IBS: C may displace Si\\
1941        $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
1942  \item Assumption:\\
1943        \hkl<1 1 0>-type $\rightarrow$ favored combination
1944  \renewcommand\labelitemi{$\Rightarrow$}
1945  \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
1946  \item Less favorable than C-Si \hkl<1 0 0> dumbbell
1947  \item Interaction drops quickly to zero\\
1948        $\rightarrow$ low capture radius
1949 \end{itemize}
1950 \begin{center}
1951  {\color{blue}
1952  IBS process far from equilibrium\\
1953  \cs{} \& \si{} instead of thermodynamic ground state
1954  }
1955 \end{center}
1956 \end{minipage}
1957
1958 \begin{minipage}{6.5cm}
1959 \includegraphics[width=6.0cm]{162-097.ps}
1960 \begin{itemize}
1961  \item Low migration barrier
1962 \end{itemize}
1963 \end{minipage}
1964 \begin{minipage}{6.5cm}
1965 \begin{center}
1966 Ab initio MD at \degc{900}\\
1967 \includegraphics[width=3.3cm]{md_vasp_01.eps}
1968 $t=\unit[2230]{fs}$\\
1969 \includegraphics[width=3.3cm]{md_vasp_02.eps}
1970 $t=\unit[2900]{fs}$
1971 \end{center}
1972 {\color{blue}
1973 Contribution of entropy to structural formation
1974 }
1975 \end{minipage}
1976
1977 \end{slide}
1978
1979 \begin{slide}
1980
1981  {\large\bf\boldmath
1982   Migration in C-Si \hkl<1 0 0> and vacancy combinations
1983  }
1984
1985  \footnotesize
1986
1987 \vspace{0.1cm}
1988
1989 \begin{minipage}[t]{3cm}
1990 \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
1991 \includegraphics[width=2.8cm]{00-1dc/0-59.eps}
1992 \end{minipage}
1993 \begin{minipage}[t]{7cm}
1994 \vspace{0.2cm}
1995 \begin{center}
1996  Low activation energies\\
1997  High activation energies for reverse processes\\
1998  $\Downarrow$\\
1999  {\color{blue}C$_{\text{sub}}$ very stable}\\
2000 \vspace*{0.1cm}
2001  \hrule
2002 \vspace*{0.1cm}
2003  Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
2004  $\Downarrow$\\
2005  {\color{blue}Formation of SiC by successive substitution by C}
2006
2007 \end{center}
2008 \end{minipage}
2009 \begin{minipage}[t]{3cm}
2010 \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
2011 \includegraphics[width=2.8cm]{00-1dc/3-14.eps}
2012 \end{minipage}
2013
2014
2015 \framebox{
2016 \begin{minipage}{5.9cm}
2017 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
2018 \begin{center}
2019 \begin{picture}(0,0)(70,0)
2020 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
2021 \end{picture}
2022 \begin{picture}(0,0)(30,0)
2023 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
2024 \end{picture}
2025 \begin{picture}(0,0)(-10,0)
2026 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
2027 \end{picture}
2028 \begin{picture}(0,0)(-48,0)
2029 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
2030 \end{picture}
2031 \begin{picture}(0,0)(12.5,5)
2032 \includegraphics[width=1cm]{100_arrow.eps}
2033 \end{picture}
2034 \begin{picture}(0,0)(97,-10)
2035 \includegraphics[height=0.9cm]{001_arrow.eps}
2036 \end{picture}
2037 \end{center}
2038 \vspace{0.1cm}
2039 \end{minipage}
2040 }
2041 \begin{minipage}{0.3cm}
2042 \hfill
2043 \end{minipage}
2044 \framebox{
2045 \begin{minipage}{5.9cm}
2046 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
2047 \begin{center}
2048 \begin{picture}(0,0)(60,0)
2049 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
2050 \end{picture}
2051 \begin{picture}(0,0)(25,0)
2052 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
2053 \end{picture}
2054 \begin{picture}(0,0)(-20,0)
2055 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
2056 \end{picture}
2057 \begin{picture}(0,0)(-55,0)
2058 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
2059 \end{picture}
2060 \begin{picture}(0,0)(12.5,5)
2061 \includegraphics[width=1cm]{100_arrow.eps}
2062 \end{picture}
2063 \begin{picture}(0,0)(95,0)
2064 \includegraphics[height=0.9cm]{001_arrow.eps}
2065 \end{picture}
2066 \end{center}
2067 \vspace{0.1cm}
2068 \end{minipage}
2069 }
2070
2071 \end{slide}
2072
2073 \begin{slide}
2074
2075  {\large\bf
2076   Conclusion of defect / migration / combined defect simulations
2077  }
2078
2079  \footnotesize
2080
2081 \vspace*{0.1cm}
2082
2083 Defect structures
2084 \begin{itemize}
2085  \item Accurately described by quantum-mechanical simulations
2086  \item Less accurate description by classical potential simulations
2087  \item Underestimated formation energy of \cs{} by classical approach
2088  \item Both methods predict same ground state: \ci{} \hkl<1 0 0> dumbbell
2089 \end{itemize}
2090
2091 Migration
2092 \begin{itemize}
2093  \item C migration pathway in Si identified
2094  \item Consistent with reorientation and diffusion experiments
2095 \end{itemize}
2096 \begin{itemize}
2097  \item Different path and ...
2098  \item overestimated barrier by classical potential calculations
2099 \end{itemize}
2100
2101 Concerning the precipitation mechanism
2102 \begin{itemize}
2103  \item Agglomeration of C-Si dumbbells energetically favorable
2104        (stress compensation)
2105  \item C-Si indeed favored compared to
2106        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2107  \item Possible low interaction capture radius of
2108        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2109  \item Low barrier for
2110        \ci{} \hkl<1 0 0> $\rightarrow$ \cs{} \& \si{} \hkl<1 1 0>
2111  \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
2112        C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
2113 \end{itemize}
2114 \begin{center}
2115 {\color{blue}Results suggest increased participation of \cs}
2116 \end{center}
2117
2118 \end{slide}
2119
2120 \begin{slide}
2121
2122  {\large\bf
2123   Silicon carbide precipitation simulations
2124  }
2125
2126  \small
2127
2128 {\scriptsize
2129  \begin{pspicture}(0,0)(12,6.5)
2130   % nodes
2131   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
2132    \parbox{7cm}{
2133    \begin{itemize}
2134     \item Create c-Si volume
2135     \item Periodc boundary conditions
2136     \item Set requested $T$ and $p=0\text{ bar}$
2137     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
2138    \end{itemize}
2139   }}}}
2140   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
2141    \parbox{7cm}{
2142    Insertion of C atoms at constant T
2143    \begin{itemize}
2144     \item total simulation volume {\pnode{in1}}
2145     \item volume of minimal SiC precipitate {\pnode{in2}}
2146     \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
2147           precipitate
2148    \end{itemize}
2149   }}}}
2150   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
2151    \parbox{7.0cm}{
2152    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
2153   }}}}
2154   \ncline[]{->}{init}{insert}
2155   \ncline[]{->}{insert}{cool}
2156   \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
2157   \rput(7.8,6){\footnotesize $V_1$}
2158   \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
2159   \rput(9.2,4.85){\tiny $V_2$}
2160   \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
2161   \rput(9.55,4.45){\footnotesize $V_3$}
2162   \rput(7.9,3.2){\pnode{ins1}}
2163   \rput(9.22,2.8){\pnode{ins2}}
2164   \rput(11.0,2.4){\pnode{ins3}}
2165   \ncline[]{->}{in1}{ins1}
2166   \ncline[]{->}{in2}{ins2}
2167   \ncline[]{->}{in3}{ins3}
2168  \end{pspicture}
2169 }
2170
2171 \begin{itemize}
2172  \item Restricted to classical potential simulations
2173  \item $V_2$ and $V_3$ considered due to low diffusion
2174  \item Amount of C atoms: 6000
2175        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
2176  \item Simulation volume: $31\times 31\times 31$ unit cells
2177        (238328 Si atoms)
2178 \end{itemize}
2179
2180 \end{slide}
2181
2182 \begin{slide}
2183
2184  {\large\bf\boldmath
2185   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2186  }
2187
2188  \small
2189
2190 \begin{minipage}{6.5cm}
2191 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2192 \end{minipage}
2193 \begin{minipage}{6.5cm}
2194 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2195 \end{minipage}
2196
2197 \begin{minipage}{6.5cm}
2198 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2199 \end{minipage}
2200 \begin{minipage}{6.5cm}
2201 \scriptsize
2202 \underline{Low C concentration ($V_1$)}\\
2203 \hkl<1 0 0> C-Si dumbbell dominated structure
2204 \begin{itemize}
2205  \item Si-C bumbs around 0.19 nm
2206  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2207        concatenated dumbbells of various orientation
2208  \item Si-Si NN distance stretched to 0.3 nm
2209 \end{itemize}
2210 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2211 \underline{High C concentration ($V_2$, $V_3$)}\\
2212 High amount of strongly bound C-C bonds\\
2213 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2214 Only short range order observable\\
2215 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2216 \end{minipage}
2217
2218 \end{slide}
2219
2220 \begin{slide}
2221
2222  {\large\bf\boldmath
2223   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2224  }
2225
2226  \small
2227
2228 \begin{minipage}{6.5cm}
2229 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2230 \end{minipage}
2231 \begin{minipage}{6.5cm}
2232 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2233 \end{minipage}
2234
2235 \begin{minipage}{6.5cm}
2236 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2237 \end{minipage}
2238 \begin{minipage}{6.5cm}
2239 \scriptsize
2240 \underline{Low C concentration ($V_1$)}\\
2241 \hkl<1 0 0> C-Si dumbbell dominated structure
2242 \begin{itemize}
2243  \item Si-C bumbs around 0.19 nm
2244  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2245        concatenated dumbbells of various orientation
2246  \item Si-Si NN distance stretched to 0.3 nm
2247 \end{itemize}
2248 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2249 \underline{High C concentration ($V_2$, $V_3$)}\\
2250 High amount of strongly bound C-C bonds\\
2251 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2252 Only short range order observable\\
2253 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2254 \end{minipage}
2255
2256 \begin{pspicture}(0,0)(0,0)
2257 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2258 \begin{minipage}{10cm}
2259 \small
2260 {\color{red}\bf 3C-SiC formation fails to appear}
2261 \begin{itemize}
2262 \item Low C concentration simulations
2263  \begin{itemize}
2264   \item Formation of \ci{} indeed occurs
2265   \item Agllomeration not observed
2266  \end{itemize}
2267 \item High C concentration simulations
2268  \begin{itemize}
2269   \item Amorphous SiC-like structure\\
2270         (not expected at prevailing temperatures)
2271   \item Rearrangement and transition into 3C-SiC structure missing
2272  \end{itemize}
2273 \end{itemize}
2274 \end{minipage}
2275  }}}
2276 \end{pspicture}
2277
2278 \end{slide}
2279
2280 \begin{slide}
2281
2282  {\large\bf
2283   Limitations of molecular dynamics and short range potentials
2284  }
2285
2286 \footnotesize
2287
2288 \vspace{0.2cm}
2289
2290 \underline{Time scale problem of MD}\\[0.2cm]
2291 Minimize integration error\\
2292 $\Rightarrow$ discretization considerably smaller than
2293               reciprocal of fastest vibrational mode\\[0.1cm]
2294 Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
2295 $\Rightarrow$ suitable choice of time step:
2296               $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
2297 $\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
2298 Several local minima in energy surface separated by large energy barriers\\
2299 $\Rightarrow$ transition event corresponds to a multiple
2300               of vibrational periods\\
2301 $\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
2302               infrequent transition events\\[0.1cm]
2303 {\color{blue}Accelerated methods:}
2304 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
2305
2306 \vspace{0.3cm}
2307
2308 \underline{Limitations related to the short range potential}\\[0.2cm]
2309 Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
2310 and 2$^{\text{nd}}$ next neighbours\\
2311 $\Rightarrow$ overestimated unphysical high forces of next neighbours
2312
2313 \vspace{0.3cm}
2314
2315 \framebox{
2316 \color{red}
2317 Potential enhanced problem of slow phase space propagation
2318 }
2319
2320 \vspace{0.3cm}
2321
2322 \underline{Approach to the (twofold) problem}\\[0.2cm]
2323 Increased temperature simulations without TAD corrections\\
2324 (accelerated methods or higher time scales exclusively not sufficient)
2325
2326 \begin{picture}(0,0)(-260,-30)
2327 \framebox{
2328 \begin{minipage}{4.2cm}
2329 \tiny
2330 \begin{center}
2331 \vspace{0.03cm}
2332 \underline{IBS}
2333 \end{center}
2334 \begin{itemize}
2335 \item 3C-SiC also observed for higher T
2336 \item higher T inside sample
2337 \item structural evolution vs.\\
2338       equilibrium properties
2339 \end{itemize}
2340 \end{minipage}
2341 }
2342 \end{picture}
2343
2344 \begin{picture}(0,0)(-305,-155)
2345 \framebox{
2346 \begin{minipage}{2.5cm}
2347 \tiny
2348 \begin{center}
2349 retain proper\\
2350 thermodynmic sampling
2351 \end{center}
2352 \end{minipage}
2353 }
2354 \end{picture}
2355
2356 \end{slide}
2357
2358 \begin{slide}
2359
2360  {\large\bf
2361   Increased temperature simulations at low C concentration
2362  }
2363
2364 \small
2365
2366 \begin{minipage}{6.5cm}
2367 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2368 \end{minipage}
2369 \begin{minipage}{6.5cm}
2370 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2371 \end{minipage}
2372
2373 \begin{minipage}{6.5cm}
2374 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2375 \end{minipage}
2376 \begin{minipage}{6.5cm}
2377 \scriptsize
2378  \underline{Si-C bonds:}
2379  \begin{itemize}
2380   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2381   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2382  \end{itemize}
2383  \underline{Si-Si bonds:}
2384  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2385  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2386  \underline{C-C bonds:}
2387  \begin{itemize}
2388   \item C-C next neighbour pairs reduced (mandatory)
2389   \item Peak at 0.3 nm slightly shifted
2390         \begin{itemize}
2391          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2392                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2393                combinations (|)\\
2394                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2395                ($\downarrow$)
2396          \item Range [|-$\downarrow$]:
2397                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2398                with nearby Si$_{\text{I}}$}
2399         \end{itemize}
2400  \end{itemize}
2401 \end{minipage}
2402
2403 \begin{picture}(0,0)(-330,-74)
2404 \color{blue}
2405 \framebox{
2406 \begin{minipage}{1.6cm}
2407 \tiny
2408 \begin{center}
2409 stretched SiC\\[-0.1cm]
2410 in c-Si
2411 \end{center}
2412 \end{minipage}
2413 }
2414 \end{picture}
2415
2416 \end{slide}
2417
2418 \begin{slide}
2419
2420  {\large\bf
2421   Increased temperature simulations at low C concentration
2422  }
2423
2424 \small
2425
2426 \begin{minipage}{6.5cm}
2427 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2428 \end{minipage}
2429 \begin{minipage}{6.5cm}
2430 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2431 \end{minipage}
2432
2433 \begin{minipage}{6.5cm}
2434 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2435 \end{minipage}
2436 \begin{minipage}{6.5cm}
2437 \scriptsize
2438  \underline{Si-C bonds:}
2439  \begin{itemize}
2440   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2441   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2442  \end{itemize}
2443  \underline{Si-Si bonds:}
2444  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2445  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2446  \underline{C-C bonds:}
2447  \begin{itemize}
2448   \item C-C next neighbour pairs reduced (mandatory)
2449   \item Peak at 0.3 nm slightly shifted
2450         \begin{itemize}
2451          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2452                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2453                combinations (|)\\
2454                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2455                ($\downarrow$)
2456          \item Range [|-$\downarrow$]:
2457                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2458                with nearby Si$_{\text{I}}$}
2459         \end{itemize}
2460  \end{itemize}
2461 \end{minipage}
2462
2463 %\begin{picture}(0,0)(-330,-74)
2464 %\color{blue}
2465 %\framebox{
2466 %\begin{minipage}{1.6cm}
2467 %\tiny
2468 %\begin{center}
2469 %stretched SiC\\[-0.1cm]
2470 %in c-Si
2471 %\end{center}
2472 %\end{minipage}
2473 %}
2474 %\end{picture}
2475
2476 \begin{pspicture}(0,0)(0,0)
2477 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2478 \begin{minipage}{10cm}
2479 \small
2480 {\color{blue}\bf Stretched SiC in c-Si}
2481 \begin{itemize}
2482 \item Consistent to precipitation model involving \cs{}
2483 \item Explains annealing behavior of high/low T C implants
2484       \begin{itemize}
2485        \item Low T: highly mobiel \ci{}
2486        \item High T: stable configurations of \cs{}
2487       \end{itemize}
2488 \end{itemize}
2489 $\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2490 $\Rightarrow$ Precipitation mechanism involving \cs{}
2491 \end{minipage}
2492  }}}
2493 \end{pspicture}
2494
2495 \end{slide}
2496
2497 \begin{slide}
2498
2499  {\large\bf
2500   Increased temperature simulations at high C concentration
2501  }
2502
2503 \footnotesize
2504
2505 \begin{minipage}{6.5cm}
2506 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2507 \end{minipage}
2508 \begin{minipage}{6.5cm}
2509 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2510 \end{minipage}
2511
2512 \vspace{0.1cm}
2513
2514 \scriptsize
2515
2516 \framebox{
2517 \begin{minipage}[t]{6.0cm}
2518 0.186 nm: Si-C pairs $\uparrow$\\
2519 (as expected in 3C-SiC)\\[0.2cm]
2520 0.282 nm: Si-C-C\\[0.2cm]
2521 $\approx$0.35 nm: C-Si-Si
2522 \end{minipage}
2523 }
2524 \begin{minipage}{0.2cm}
2525 \hfill
2526 \end{minipage}
2527 \framebox{
2528 \begin{minipage}[t]{6.0cm}
2529 0.15 nm: C-C pairs $\uparrow$\\
2530 (as expected in graphite/diamond)\\[0.2cm]
2531 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2532 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2533 \end{minipage}
2534 }
2535
2536 \begin{itemize}
2537 \item Decreasing cut-off artifact
2538 \item {\color{red}Amorphous} SiC-like phase remains
2539 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2540 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2541 \end{itemize}
2542
2543 \vspace{-0.1cm}
2544
2545 \begin{center}
2546 {\color{blue}
2547 \framebox{
2548 {\color{black}
2549 High C \& small $V$ \& short $t$
2550 $\Rightarrow$
2551 }
2552 Slow restructuring due to strong C-C bonds
2553 {\color{black}
2554 $\Leftarrow$
2555 High C \& low T implants
2556 }
2557 }
2558 }
2559 \end{center}
2560
2561 \end{slide}
2562
2563 \begin{slide}
2564
2565  {\large\bf
2566   Summary and Conclusions
2567  }
2568
2569  \scriptsize
2570
2571 %\vspace{0.1cm}
2572
2573 \framebox{
2574 \begin{minipage}[t]{12.9cm}
2575  \underline{Pecipitation simulations}
2576  \begin{itemize}
2577   \item High C concentration $\rightarrow$ amorphous SiC like phase
2578   \item Problem of potential enhanced slow phase space propagation
2579   \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2580   \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2581   \item High T necessary to simulate IBS conditions (far from equilibrium)
2582   \item Precipitation by successive agglomeration of \cs (epitaxy)
2583   \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2584         (stretched SiC, interface)
2585  \end{itemize}
2586 \end{minipage}
2587 }
2588
2589 %\vspace{0.1cm}
2590
2591 \framebox{
2592 \begin{minipage}{12.9cm}
2593  \underline{Defects}
2594  \begin{itemize}
2595    \item DFT / EA
2596         \begin{itemize}
2597          \item Point defects excellently / fairly well described
2598                by DFT / EA
2599          \item C$_{\text{sub}}$ drastically underestimated by EA
2600          \item EA predicts correct ground state:
2601                C$_{\text{sub}}$ \& \si{} $>$ \ci{}
2602          \item Identified migration path explaining
2603                diffusion and reorientation experiments by DFT
2604          \item EA fails to describe \ci{} migration:
2605                Wrong path \& overestimated barrier
2606         \end{itemize}
2607    \item Combinations of defects
2608          \begin{itemize}
2609           \item Agglomeration of point defects energetically favorable
2610                 by compensation of stress
2611           \item Formation of C-C unlikely
2612           \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2613           \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2614                 Low barrier (\unit[0.77]{eV}) \& low capture radius
2615         \end{itemize}
2616  \end{itemize}
2617 \end{minipage}
2618 }
2619
2620 \begin{center}
2621 {\color{blue}
2622 \framebox{Precipitation by successive agglomeration of \cs{}}
2623 }
2624 \end{center}
2625
2626 \end{slide}
2627
2628 \begin{slide}
2629
2630  {\large\bf
2631   Acknowledgements
2632  }
2633
2634  \vspace{0.1cm}
2635
2636  \small
2637
2638  Thanks to \ldots
2639
2640  \underline{Augsburg}
2641  \begin{itemize}
2642   \item Prof. B. Stritzker (accomodation at EP \RM{4})
2643   \item Ralf Utermann (EDV)
2644  \end{itemize}
2645
2646  \underline{Helsinki}
2647  \begin{itemize}
2648   \item Prof. K. Nordlund (MD)
2649  \end{itemize}
2650
2651  \underline{Munich}
2652  \begin{itemize}
2653   \item Bayerische Forschungsstiftung (financial support)
2654  \end{itemize}
2655
2656  \underline{Paderborn}
2657  \begin{itemize}
2658   \item Prof. J. Lindner (SiC)
2659   \item Prof. G. Schmidt (DFT + financial support)
2660   \item Dr. E. Rauls (DFT + SiC)
2661   \item Dr. S. Sanna (VASP)
2662  \end{itemize}
2663
2664 \vspace{0.2cm}
2665
2666 \begin{center}
2667 \framebox{
2668 \bf Thank you for your attention!
2669 }
2670 \end{center}
2671
2672 \end{slide}
2673
2674 \end{document}
2675
2676 \fi