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 % continue here
1462 \fi
1463
1464 \begin{slide}
1465
1466 \headphd
1467 {\large\bf\boldmath
1468  C interstitial migration --- ab initio
1469 }
1470
1471 \scriptsize
1472
1473 \vspace{0.1cm}
1474
1475 \begin{minipage}{6.8cm}
1476 \underline{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
1477 \begin{minipage}{2.0cm}
1478 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1479 \end{minipage}
1480 \begin{minipage}{0.2cm}
1481 $\rightarrow$
1482 \end{minipage}
1483 \begin{minipage}{2.0cm}
1484 \includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps}
1485 \end{minipage}
1486 \begin{minipage}{0.2cm}
1487 $\rightarrow$
1488 \end{minipage}
1489 \begin{minipage}{2.0cm}
1490 \includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps}
1491 \end{minipage}\\[0.1cm]
1492 Spin polarization\\
1493 $\Rightarrow$ BC configuration constitutes local minimum\\
1494 $\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$
1495 \end{minipage}
1496 \begin{minipage}{5.4cm}
1497 \includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
1498 \end{minipage}\\[0.4cm]
1499 %
1500 \begin{minipage}{6.8cm}
1501 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
1502 \begin{minipage}{2.0cm}
1503 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1504 \end{minipage}
1505 \begin{minipage}{0.2cm}
1506 $\rightarrow$
1507 \end{minipage}
1508 \begin{minipage}{2.0cm}
1509 \includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
1510 \end{minipage}
1511 \begin{minipage}{0.2cm}
1512 $\rightarrow$
1513 \end{minipage}
1514 \begin{minipage}{2.0cm}
1515 \includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
1516 \end{minipage}\\[0.1cm]
1517 $\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
1518 $\Rightarrow$ {\color{red}Migration mechanism identified!}\\
1519 Note: Change in orientation
1520 \end{minipage}
1521 \begin{minipage}{5.4cm}
1522 \includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
1523 \end{minipage}\\[0.2cm]
1524 %
1525 \begin{center}
1526 Reorientation pathway composed of two consecutive processes of the above type
1527 \end{center}
1528
1529 \end{slide}
1530
1531 \end{document}
1532 \ifnum1=0
1533
1534 \begin{slide}
1535
1536  {\large\bf\boldmath
1537   Migration of the C \hkl<1 0 0> dumbbell interstitial
1538  }
1539
1540 \scriptsize
1541
1542 \framebox{
1543 \begin{minipage}{5.9cm}
1544 \begin{flushleft}
1545 \includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
1546 \end{flushleft}
1547 \begin{center}
1548 \begin{picture}(0,0)(60,0)
1549 \includegraphics[width=1cm]{vasp_mig/00-1.eps}
1550 \end{picture}
1551 \begin{picture}(0,0)(-5,0)
1552 \includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
1553 \end{picture}
1554 \begin{picture}(0,0)(-55,0)
1555 \includegraphics[width=1cm]{vasp_mig/bc.eps}
1556 \end{picture}
1557 \begin{picture}(0,0)(12.5,10)
1558 \includegraphics[width=1cm]{110_arrow.eps}
1559 \end{picture}
1560 \begin{picture}(0,0)(90,0)
1561 \includegraphics[height=0.9cm]{001_arrow.eps}
1562 \end{picture}
1563 \end{center}
1564 \vspace*{0.35cm}
1565 \end{minipage}
1566 }
1567 \begin{minipage}{0.3cm}
1568 \hfill
1569 \end{minipage}
1570 \framebox{
1571 \begin{minipage}{5.9cm}
1572 \begin{flushright}
1573 \includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
1574 \end{flushright}
1575 \begin{center}
1576 \begin{picture}(0,0)(60,0)
1577 \includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
1578 \end{picture}
1579 \begin{picture}(0,0)(5,0)
1580 \includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
1581 \end{picture}
1582 \begin{picture}(0,0)(-55,0)
1583 \includegraphics[width=1cm]{vasp_mig/0-10.eps}
1584 \end{picture}
1585 \begin{picture}(0,0)(12.5,10)
1586 \includegraphics[width=1cm]{100_arrow.eps}
1587 \end{picture}
1588 \begin{picture}(0,0)(90,0)
1589 \includegraphics[height=0.9cm]{001_arrow.eps}
1590 \end{picture}
1591 \end{center}
1592 \vspace*{0.3cm}
1593 \end{minipage}\\
1594 }
1595
1596 \vspace*{0.05cm}
1597
1598 \framebox{
1599 \begin{minipage}{5.9cm}
1600 \begin{flushleft}
1601 \includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
1602 \end{flushleft}
1603 \begin{center}
1604 \begin{picture}(0,0)(60,0)
1605 \includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps}
1606 \end{picture}
1607 \begin{picture}(0,0)(10,0)
1608 \includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
1609 \end{picture}
1610 \begin{picture}(0,0)(-60,0)
1611 \includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps}
1612 \end{picture}
1613 \begin{picture}(0,0)(12.5,10)
1614 \includegraphics[width=1cm]{100_arrow.eps}
1615 \end{picture}
1616 \begin{picture}(0,0)(90,0)
1617 \includegraphics[height=0.9cm]{001_arrow.eps}
1618 \end{picture}
1619 \end{center}
1620 \vspace*{0.3cm}
1621 \end{minipage}
1622 }
1623 \begin{minipage}{0.3cm}
1624 \hfill
1625 \end{minipage}
1626 \begin{minipage}{6.5cm}
1627 VASP results
1628 \begin{itemize}
1629  \item Energetically most favorable path
1630        \begin{itemize}
1631         \item Path 2
1632         \item Activation energy: $\approx$ 0.9 eV
1633         \item Experimental values: 0.73 ... 0.87 eV
1634        \end{itemize}
1635        $\Rightarrow$ {\color{blue}Diffusion} path identified!
1636  \item Reorientation (path 3)
1637        \begin{itemize}
1638         \item More likely composed of two consecutive steps of type 2
1639         \item Experimental values: 0.77 ... 0.88 eV
1640        \end{itemize}
1641        $\Rightarrow$ {\color{blue}Reorientation} transition identified!
1642 \end{itemize}
1643 \end{minipage}
1644
1645 \end{slide}
1646
1647 \begin{slide}
1648
1649  {\large\bf\boldmath
1650   Migration of the C \hkl<1 0 0> dumbbell interstitial
1651  }
1652
1653 \scriptsize
1654
1655  \vspace{0.1cm}
1656
1657 \begin{minipage}{6.5cm}
1658
1659 \framebox{
1660 \begin{minipage}[t]{5.9cm}
1661 \begin{flushleft}
1662 \includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
1663 \end{flushleft}
1664 \begin{center}
1665 \begin{pspicture}(0,0)(0,0)
1666 \psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
1667 \end{pspicture}
1668 \begin{picture}(0,0)(60,-50)
1669 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
1670 \end{picture}
1671 \begin{picture}(0,0)(5,-50)
1672 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
1673 \end{picture}
1674 \begin{picture}(0,0)(-55,-50)
1675 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
1676 \end{picture}
1677 \begin{picture}(0,0)(12.5,-40)
1678 \includegraphics[width=1cm]{110_arrow.eps}
1679 \end{picture}
1680 \begin{picture}(0,0)(90,-45)
1681 \includegraphics[height=0.9cm]{001_arrow.eps}
1682 \end{picture}\\
1683 \begin{pspicture}(0,0)(0,0)
1684 \psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
1685 \end{pspicture}
1686 \begin{picture}(0,0)(60,-15)
1687 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
1688 \end{picture}
1689 \begin{picture}(0,0)(35,-15)
1690 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
1691 \end{picture}
1692 \begin{picture}(0,0)(-5,-15)
1693 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
1694 \end{picture}
1695 \begin{picture}(0,0)(-55,-15)
1696 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
1697 \end{picture}
1698 \begin{picture}(0,0)(12.5,-5)
1699 \includegraphics[width=1cm]{100_arrow.eps}
1700 \end{picture}
1701 \begin{picture}(0,0)(90,-15)
1702 \includegraphics[height=0.9cm]{010_arrow.eps}
1703 \end{picture}
1704 \end{center}
1705 \end{minipage}
1706 }\\[0.1cm]
1707
1708 \begin{minipage}{5.9cm}
1709 Erhart/Albe results
1710 \begin{itemize}
1711  \item Lowest activation energy: $\approx$ 2.2 eV
1712  \item 2.4 times higher than VASP
1713  \item Different pathway
1714 \end{itemize}
1715 \end{minipage}
1716
1717 \end{minipage}
1718 \begin{minipage}{6.5cm}
1719
1720 \framebox{
1721 \begin{minipage}{5.9cm}
1722 %\begin{flushright}
1723 %\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
1724 %\end{flushright}
1725 %\begin{center}
1726 %\begin{pspicture}(0,0)(0,0)
1727 %\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
1728 %\end{pspicture}
1729 %\begin{picture}(0,0)(60,-5)
1730 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
1731 %\end{picture}
1732 %\begin{picture}(0,0)(0,-5)
1733 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
1734 %\end{picture}
1735 %\begin{picture}(0,0)(-55,-5)
1736 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
1737 %\end{picture}
1738 %\begin{picture}(0,0)(12.5,5)
1739 %\includegraphics[width=1cm]{100_arrow.eps}
1740 %\end{picture}
1741 %\begin{picture}(0,0)(90,0)
1742 %\includegraphics[height=0.9cm]{001_arrow.eps}
1743 %\end{picture}
1744 %\end{center}
1745 %\vspace{0.2cm}
1746 %\end{minipage}
1747 %}\\[0.2cm]
1748 %
1749 %\framebox{
1750 %\begin{minipage}{5.9cm}
1751 \includegraphics[width=5.9cm]{00-1_110_0-10_mig_albe.ps}
1752 \end{minipage}
1753 }\\[0.1cm]
1754
1755 \begin{minipage}{5.9cm}
1756 Transition involving \ci{} \hkl<1 1 0>
1757 \begin{itemize}
1758  \item Bond-centered configuration unstable\\
1759        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1760  \item Transition minima of path 2 \& 3\\
1761        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1762  \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV
1763  \item 2.4 - 3.4 times higher than VASP
1764  \item Rotation of dumbbell orientation
1765 \end{itemize}
1766 \vspace{0.1cm}
1767 \begin{center}
1768 {\color{blue}Overestimated diffusion barrier}
1769 \end{center}
1770 \end{minipage}
1771
1772 \end{minipage}
1773
1774 \end{slide}
1775
1776 \begin{slide}
1777
1778  {\large\bf\boldmath
1779   Combinations with a C-Si \hkl<1 0 0>-type interstitial
1780  }
1781
1782 \small
1783
1784 \vspace*{0.1cm}
1785
1786 Binding energy:
1787 $
1788 E_{\text{b}}=
1789 E_{\text{f}}^{\text{defect combination}}-
1790 E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
1791 E_{\text{f}}^{\text{2nd defect}}
1792 $
1793
1794 \vspace*{0.1cm}
1795
1796 {\scriptsize
1797 \begin{tabular}{l c c c c c c}
1798 \hline
1799  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1800  \hline
1801  \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1802  \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1803  \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}\\
1804  \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}\\
1805  \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}\\
1806  \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}\\
1807  \hline
1808  C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1809  Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1810 \hline
1811 \end{tabular}
1812 }
1813
1814 \vspace*{0.3cm}
1815
1816 \footnotesize
1817
1818 \begin{minipage}[t]{3.8cm}
1819 \underline{\hkl<1 0 0> at position 1}\\[0.1cm]
1820 \includegraphics[width=3.5cm]{00-1dc/2-25.eps}
1821 \end{minipage}
1822 \begin{minipage}[t]{3.5cm}
1823 \underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
1824 \includegraphics[width=3.2cm]{00-1dc/2-39.eps}
1825 \end{minipage}
1826 \begin{minipage}[t]{5.5cm}
1827 \begin{itemize}
1828  \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\
1829        $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
1830  \item Stress compensation / increase
1831  \item Unfavored: antiparallel orientations
1832  \item Indication of energetically favored\\
1833        agglomeration
1834  \item Most favorable: C clustering
1835  \item However: High barrier ($>4\,\text{eV}$)
1836  \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$
1837        (Entropy)
1838 \end{itemize}
1839 \end{minipage}
1840
1841 \begin{picture}(0,0)(-295,-130)
1842 \includegraphics[width=3.5cm]{comb_pos.eps}
1843 \end{picture}
1844
1845 \end{slide}
1846
1847 \begin{slide}
1848
1849  {\large\bf\boldmath
1850   Combinations of C-Si \hkl<1 0 0>-type interstitials
1851  }
1852
1853 \small
1854
1855 \vspace*{0.1cm}
1856
1857 Energetically most favorable combinations along \hkl<1 1 0>
1858
1859 \vspace*{0.1cm}
1860
1861 {\scriptsize
1862 \begin{tabular}{l c c c c c c}
1863 \hline
1864  & 1 & 2 & 3 & 4 & 5 & 6\\
1865 \hline
1866 $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
1867 C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
1868 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>\\
1869 \hline
1870 \end{tabular}
1871 }
1872
1873 \vspace*{0.3cm}
1874
1875 \begin{minipage}{7.0cm}
1876 \includegraphics[width=7cm]{db_along_110_cc.ps}
1877 \end{minipage}
1878 \begin{minipage}{6.0cm}
1879 \begin{itemize}
1880  \item Interaction proportional to reciprocal cube of C-C distance
1881  \item Saturation in the immediate vicinity
1882  \renewcommand\labelitemi{$\Rightarrow$}
1883  \item Agglomeration of \ci{} expected
1884  \item Absence of C clustering
1885 \end{itemize}
1886 \begin{center}
1887 {\color{blue}
1888  Consisten with initial precipitation model
1889 }
1890 \end{center}
1891 \end{minipage}
1892
1893 \vspace{0.2cm}
1894
1895 \end{slide}
1896
1897 \begin{slide}
1898
1899  {\large\bf\boldmath
1900   Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
1901  }
1902
1903  \scriptsize
1904
1905 %\begin{center}
1906 %\begin{minipage}{3.2cm}
1907 %\includegraphics[width=3cm]{sub_110_combo.eps}
1908 %\end{minipage}
1909 %\begin{minipage}{7.8cm}
1910 %\begin{tabular}{l c c c c c c}
1911 %\hline
1912 %C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
1913 %                   \hkl<1 0 1> & \hkl<-1 0 1> \\
1914 %\hline
1915 %1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
1916 %2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
1917 %3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
1918 %4 & \RM{4} & B & D & E & E & D \\
1919 %5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
1920 %\hline
1921 %\end{tabular}
1922 %\end{minipage}
1923 %\end{center}
1924
1925 %\begin{center}
1926 %\begin{tabular}{l c c c c c c c c c c}
1927 %\hline
1928 %Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
1929 %\hline
1930 %$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
1931 %$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
1932 %$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
1933 %\hline
1934 %\end{tabular}
1935 %\end{center}
1936
1937 \begin{minipage}{6.0cm}
1938 \includegraphics[width=5.8cm]{c_sub_si110.ps}
1939 \end{minipage}
1940 \begin{minipage}{7cm}
1941 \scriptsize
1942 \begin{itemize}
1943  \item IBS: C may displace Si\\
1944        $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
1945  \item Assumption:\\
1946        \hkl<1 1 0>-type $\rightarrow$ favored combination
1947  \renewcommand\labelitemi{$\Rightarrow$}
1948  \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
1949  \item Less favorable than C-Si \hkl<1 0 0> dumbbell
1950  \item Interaction drops quickly to zero\\
1951        $\rightarrow$ low capture radius
1952 \end{itemize}
1953 \begin{center}
1954  {\color{blue}
1955  IBS process far from equilibrium\\
1956  \cs{} \& \si{} instead of thermodynamic ground state
1957  }
1958 \end{center}
1959 \end{minipage}
1960
1961 \begin{minipage}{6.5cm}
1962 \includegraphics[width=6.0cm]{162-097.ps}
1963 \begin{itemize}
1964  \item Low migration barrier
1965 \end{itemize}
1966 \end{minipage}
1967 \begin{minipage}{6.5cm}
1968 \begin{center}
1969 Ab initio MD at \degc{900}\\
1970 \includegraphics[width=3.3cm]{md_vasp_01.eps}
1971 $t=\unit[2230]{fs}$\\
1972 \includegraphics[width=3.3cm]{md_vasp_02.eps}
1973 $t=\unit[2900]{fs}$
1974 \end{center}
1975 {\color{blue}
1976 Contribution of entropy to structural formation
1977 }
1978 \end{minipage}
1979
1980 \end{slide}
1981
1982 \begin{slide}
1983
1984  {\large\bf\boldmath
1985   Migration in C-Si \hkl<1 0 0> and vacancy combinations
1986  }
1987
1988  \footnotesize
1989
1990 \vspace{0.1cm}
1991
1992 \begin{minipage}[t]{3cm}
1993 \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
1994 \includegraphics[width=2.8cm]{00-1dc/0-59.eps}
1995 \end{minipage}
1996 \begin{minipage}[t]{7cm}
1997 \vspace{0.2cm}
1998 \begin{center}
1999  Low activation energies\\
2000  High activation energies for reverse processes\\
2001  $\Downarrow$\\
2002  {\color{blue}C$_{\text{sub}}$ very stable}\\
2003 \vspace*{0.1cm}
2004  \hrule
2005 \vspace*{0.1cm}
2006  Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
2007  $\Downarrow$\\
2008  {\color{blue}Formation of SiC by successive substitution by C}
2009
2010 \end{center}
2011 \end{minipage}
2012 \begin{minipage}[t]{3cm}
2013 \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
2014 \includegraphics[width=2.8cm]{00-1dc/3-14.eps}
2015 \end{minipage}
2016
2017
2018 \framebox{
2019 \begin{minipage}{5.9cm}
2020 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
2021 \begin{center}
2022 \begin{picture}(0,0)(70,0)
2023 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
2024 \end{picture}
2025 \begin{picture}(0,0)(30,0)
2026 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
2027 \end{picture}
2028 \begin{picture}(0,0)(-10,0)
2029 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
2030 \end{picture}
2031 \begin{picture}(0,0)(-48,0)
2032 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
2033 \end{picture}
2034 \begin{picture}(0,0)(12.5,5)
2035 \includegraphics[width=1cm]{100_arrow.eps}
2036 \end{picture}
2037 \begin{picture}(0,0)(97,-10)
2038 \includegraphics[height=0.9cm]{001_arrow.eps}
2039 \end{picture}
2040 \end{center}
2041 \vspace{0.1cm}
2042 \end{minipage}
2043 }
2044 \begin{minipage}{0.3cm}
2045 \hfill
2046 \end{minipage}
2047 \framebox{
2048 \begin{minipage}{5.9cm}
2049 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
2050 \begin{center}
2051 \begin{picture}(0,0)(60,0)
2052 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
2053 \end{picture}
2054 \begin{picture}(0,0)(25,0)
2055 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
2056 \end{picture}
2057 \begin{picture}(0,0)(-20,0)
2058 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
2059 \end{picture}
2060 \begin{picture}(0,0)(-55,0)
2061 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
2062 \end{picture}
2063 \begin{picture}(0,0)(12.5,5)
2064 \includegraphics[width=1cm]{100_arrow.eps}
2065 \end{picture}
2066 \begin{picture}(0,0)(95,0)
2067 \includegraphics[height=0.9cm]{001_arrow.eps}
2068 \end{picture}
2069 \end{center}
2070 \vspace{0.1cm}
2071 \end{minipage}
2072 }
2073
2074 \end{slide}
2075
2076 \begin{slide}
2077
2078  {\large\bf
2079   Conclusion of defect / migration / combined defect simulations
2080  }
2081
2082  \footnotesize
2083
2084 \vspace*{0.1cm}
2085
2086 Defect structures
2087 \begin{itemize}
2088  \item Accurately described by quantum-mechanical simulations
2089  \item Less accurate description by classical potential simulations
2090  \item Underestimated formation energy of \cs{} by classical approach
2091  \item Both methods predict same ground state: \ci{} \hkl<1 0 0> dumbbell
2092 \end{itemize}
2093
2094 Migration
2095 \begin{itemize}
2096  \item C migration pathway in Si identified
2097  \item Consistent with reorientation and diffusion experiments
2098 \end{itemize}
2099 \begin{itemize}
2100  \item Different path and ...
2101  \item overestimated barrier by classical potential calculations
2102 \end{itemize}
2103
2104 Concerning the precipitation mechanism
2105 \begin{itemize}
2106  \item Agglomeration of C-Si dumbbells energetically favorable
2107        (stress compensation)
2108  \item C-Si indeed favored compared to
2109        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2110  \item Possible low interaction capture radius of
2111        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2112  \item Low barrier for
2113        \ci{} \hkl<1 0 0> $\rightarrow$ \cs{} \& \si{} \hkl<1 1 0>
2114  \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
2115        C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
2116 \end{itemize}
2117 \begin{center}
2118 {\color{blue}Results suggest increased participation of \cs}
2119 \end{center}
2120
2121 \end{slide}
2122
2123 \begin{slide}
2124
2125  {\large\bf
2126   Silicon carbide precipitation simulations
2127  }
2128
2129  \small
2130
2131 {\scriptsize
2132  \begin{pspicture}(0,0)(12,6.5)
2133   % nodes
2134   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
2135    \parbox{7cm}{
2136    \begin{itemize}
2137     \item Create c-Si volume
2138     \item Periodc boundary conditions
2139     \item Set requested $T$ and $p=0\text{ bar}$
2140     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
2141    \end{itemize}
2142   }}}}
2143   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
2144    \parbox{7cm}{
2145    Insertion of C atoms at constant T
2146    \begin{itemize}
2147     \item total simulation volume {\pnode{in1}}
2148     \item volume of minimal SiC precipitate {\pnode{in2}}
2149     \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
2150           precipitate
2151    \end{itemize}
2152   }}}}
2153   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
2154    \parbox{7.0cm}{
2155    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
2156   }}}}
2157   \ncline[]{->}{init}{insert}
2158   \ncline[]{->}{insert}{cool}
2159   \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
2160   \rput(7.8,6){\footnotesize $V_1$}
2161   \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
2162   \rput(9.2,4.85){\tiny $V_2$}
2163   \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
2164   \rput(9.55,4.45){\footnotesize $V_3$}
2165   \rput(7.9,3.2){\pnode{ins1}}
2166   \rput(9.22,2.8){\pnode{ins2}}
2167   \rput(11.0,2.4){\pnode{ins3}}
2168   \ncline[]{->}{in1}{ins1}
2169   \ncline[]{->}{in2}{ins2}
2170   \ncline[]{->}{in3}{ins3}
2171  \end{pspicture}
2172 }
2173
2174 \begin{itemize}
2175  \item Restricted to classical potential simulations
2176  \item $V_2$ and $V_3$ considered due to low diffusion
2177  \item Amount of C atoms: 6000
2178        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
2179  \item Simulation volume: $31\times 31\times 31$ unit cells
2180        (238328 Si atoms)
2181 \end{itemize}
2182
2183 \end{slide}
2184
2185 \begin{slide}
2186
2187  {\large\bf\boldmath
2188   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2189  }
2190
2191  \small
2192
2193 \begin{minipage}{6.5cm}
2194 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2195 \end{minipage}
2196 \begin{minipage}{6.5cm}
2197 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2198 \end{minipage}
2199
2200 \begin{minipage}{6.5cm}
2201 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2202 \end{minipage}
2203 \begin{minipage}{6.5cm}
2204 \scriptsize
2205 \underline{Low C concentration ($V_1$)}\\
2206 \hkl<1 0 0> C-Si dumbbell dominated structure
2207 \begin{itemize}
2208  \item Si-C bumbs around 0.19 nm
2209  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2210        concatenated dumbbells of various orientation
2211  \item Si-Si NN distance stretched to 0.3 nm
2212 \end{itemize}
2213 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2214 \underline{High C concentration ($V_2$, $V_3$)}\\
2215 High amount of strongly bound C-C bonds\\
2216 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2217 Only short range order observable\\
2218 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2219 \end{minipage}
2220
2221 \end{slide}
2222
2223 \begin{slide}
2224
2225  {\large\bf\boldmath
2226   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2227  }
2228
2229  \small
2230
2231 \begin{minipage}{6.5cm}
2232 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2233 \end{minipage}
2234 \begin{minipage}{6.5cm}
2235 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2236 \end{minipage}
2237
2238 \begin{minipage}{6.5cm}
2239 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2240 \end{minipage}
2241 \begin{minipage}{6.5cm}
2242 \scriptsize
2243 \underline{Low C concentration ($V_1$)}\\
2244 \hkl<1 0 0> C-Si dumbbell dominated structure
2245 \begin{itemize}
2246  \item Si-C bumbs around 0.19 nm
2247  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2248        concatenated dumbbells of various orientation
2249  \item Si-Si NN distance stretched to 0.3 nm
2250 \end{itemize}
2251 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2252 \underline{High C concentration ($V_2$, $V_3$)}\\
2253 High amount of strongly bound C-C bonds\\
2254 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2255 Only short range order observable\\
2256 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2257 \end{minipage}
2258
2259 \begin{pspicture}(0,0)(0,0)
2260 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2261 \begin{minipage}{10cm}
2262 \small
2263 {\color{red}\bf 3C-SiC formation fails to appear}
2264 \begin{itemize}
2265 \item Low C concentration simulations
2266  \begin{itemize}
2267   \item Formation of \ci{} indeed occurs
2268   \item Agllomeration not observed
2269  \end{itemize}
2270 \item High C concentration simulations
2271  \begin{itemize}
2272   \item Amorphous SiC-like structure\\
2273         (not expected at prevailing temperatures)
2274   \item Rearrangement and transition into 3C-SiC structure missing
2275  \end{itemize}
2276 \end{itemize}
2277 \end{minipage}
2278  }}}
2279 \end{pspicture}
2280
2281 \end{slide}
2282
2283 \begin{slide}
2284
2285  {\large\bf
2286   Limitations of molecular dynamics and short range potentials
2287  }
2288
2289 \footnotesize
2290
2291 \vspace{0.2cm}
2292
2293 \underline{Time scale problem of MD}\\[0.2cm]
2294 Minimize integration error\\
2295 $\Rightarrow$ discretization considerably smaller than
2296               reciprocal of fastest vibrational mode\\[0.1cm]
2297 Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
2298 $\Rightarrow$ suitable choice of time step:
2299               $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
2300 $\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
2301 Several local minima in energy surface separated by large energy barriers\\
2302 $\Rightarrow$ transition event corresponds to a multiple
2303               of vibrational periods\\
2304 $\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
2305               infrequent transition events\\[0.1cm]
2306 {\color{blue}Accelerated methods:}
2307 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
2308
2309 \vspace{0.3cm}
2310
2311 \underline{Limitations related to the short range potential}\\[0.2cm]
2312 Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
2313 and 2$^{\text{nd}}$ next neighbours\\
2314 $\Rightarrow$ overestimated unphysical high forces of next neighbours
2315
2316 \vspace{0.3cm}
2317
2318 \framebox{
2319 \color{red}
2320 Potential enhanced problem of slow phase space propagation
2321 }
2322
2323 \vspace{0.3cm}
2324
2325 \underline{Approach to the (twofold) problem}\\[0.2cm]
2326 Increased temperature simulations without TAD corrections\\
2327 (accelerated methods or higher time scales exclusively not sufficient)
2328
2329 \begin{picture}(0,0)(-260,-30)
2330 \framebox{
2331 \begin{minipage}{4.2cm}
2332 \tiny
2333 \begin{center}
2334 \vspace{0.03cm}
2335 \underline{IBS}
2336 \end{center}
2337 \begin{itemize}
2338 \item 3C-SiC also observed for higher T
2339 \item higher T inside sample
2340 \item structural evolution vs.\\
2341       equilibrium properties
2342 \end{itemize}
2343 \end{minipage}
2344 }
2345 \end{picture}
2346
2347 \begin{picture}(0,0)(-305,-155)
2348 \framebox{
2349 \begin{minipage}{2.5cm}
2350 \tiny
2351 \begin{center}
2352 retain proper\\
2353 thermodynmic sampling
2354 \end{center}
2355 \end{minipage}
2356 }
2357 \end{picture}
2358
2359 \end{slide}
2360
2361 \begin{slide}
2362
2363  {\large\bf
2364   Increased temperature simulations at low C concentration
2365  }
2366
2367 \small
2368
2369 \begin{minipage}{6.5cm}
2370 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2371 \end{minipage}
2372 \begin{minipage}{6.5cm}
2373 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2374 \end{minipage}
2375
2376 \begin{minipage}{6.5cm}
2377 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2378 \end{minipage}
2379 \begin{minipage}{6.5cm}
2380 \scriptsize
2381  \underline{Si-C bonds:}
2382  \begin{itemize}
2383   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2384   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2385  \end{itemize}
2386  \underline{Si-Si bonds:}
2387  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2388  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2389  \underline{C-C bonds:}
2390  \begin{itemize}
2391   \item C-C next neighbour pairs reduced (mandatory)
2392   \item Peak at 0.3 nm slightly shifted
2393         \begin{itemize}
2394          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2395                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2396                combinations (|)\\
2397                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2398                ($\downarrow$)
2399          \item Range [|-$\downarrow$]:
2400                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2401                with nearby Si$_{\text{I}}$}
2402         \end{itemize}
2403  \end{itemize}
2404 \end{minipage}
2405
2406 \begin{picture}(0,0)(-330,-74)
2407 \color{blue}
2408 \framebox{
2409 \begin{minipage}{1.6cm}
2410 \tiny
2411 \begin{center}
2412 stretched SiC\\[-0.1cm]
2413 in c-Si
2414 \end{center}
2415 \end{minipage}
2416 }
2417 \end{picture}
2418
2419 \end{slide}
2420
2421 \begin{slide}
2422
2423  {\large\bf
2424   Increased temperature simulations at low C concentration
2425  }
2426
2427 \small
2428
2429 \begin{minipage}{6.5cm}
2430 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2431 \end{minipage}
2432 \begin{minipage}{6.5cm}
2433 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2434 \end{minipage}
2435
2436 \begin{minipage}{6.5cm}
2437 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2438 \end{minipage}
2439 \begin{minipage}{6.5cm}
2440 \scriptsize
2441  \underline{Si-C bonds:}
2442  \begin{itemize}
2443   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2444   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2445  \end{itemize}
2446  \underline{Si-Si bonds:}
2447  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2448  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2449  \underline{C-C bonds:}
2450  \begin{itemize}
2451   \item C-C next neighbour pairs reduced (mandatory)
2452   \item Peak at 0.3 nm slightly shifted
2453         \begin{itemize}
2454          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2455                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2456                combinations (|)\\
2457                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2458                ($\downarrow$)
2459          \item Range [|-$\downarrow$]:
2460                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2461                with nearby Si$_{\text{I}}$}
2462         \end{itemize}
2463  \end{itemize}
2464 \end{minipage}
2465
2466 %\begin{picture}(0,0)(-330,-74)
2467 %\color{blue}
2468 %\framebox{
2469 %\begin{minipage}{1.6cm}
2470 %\tiny
2471 %\begin{center}
2472 %stretched SiC\\[-0.1cm]
2473 %in c-Si
2474 %\end{center}
2475 %\end{minipage}
2476 %}
2477 %\end{picture}
2478
2479 \begin{pspicture}(0,0)(0,0)
2480 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2481 \begin{minipage}{10cm}
2482 \small
2483 {\color{blue}\bf Stretched SiC in c-Si}
2484 \begin{itemize}
2485 \item Consistent to precipitation model involving \cs{}
2486 \item Explains annealing behavior of high/low T C implants
2487       \begin{itemize}
2488        \item Low T: highly mobiel \ci{}
2489        \item High T: stable configurations of \cs{}
2490       \end{itemize}
2491 \end{itemize}
2492 $\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2493 $\Rightarrow$ Precipitation mechanism involving \cs{}
2494 \end{minipage}
2495  }}}
2496 \end{pspicture}
2497
2498 \end{slide}
2499
2500 \begin{slide}
2501
2502  {\large\bf
2503   Increased temperature simulations at high C concentration
2504  }
2505
2506 \footnotesize
2507
2508 \begin{minipage}{6.5cm}
2509 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2510 \end{minipage}
2511 \begin{minipage}{6.5cm}
2512 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2513 \end{minipage}
2514
2515 \vspace{0.1cm}
2516
2517 \scriptsize
2518
2519 \framebox{
2520 \begin{minipage}[t]{6.0cm}
2521 0.186 nm: Si-C pairs $\uparrow$\\
2522 (as expected in 3C-SiC)\\[0.2cm]
2523 0.282 nm: Si-C-C\\[0.2cm]
2524 $\approx$0.35 nm: C-Si-Si
2525 \end{minipage}
2526 }
2527 \begin{minipage}{0.2cm}
2528 \hfill
2529 \end{minipage}
2530 \framebox{
2531 \begin{minipage}[t]{6.0cm}
2532 0.15 nm: C-C pairs $\uparrow$\\
2533 (as expected in graphite/diamond)\\[0.2cm]
2534 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2535 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2536 \end{minipage}
2537 }
2538
2539 \begin{itemize}
2540 \item Decreasing cut-off artifact
2541 \item {\color{red}Amorphous} SiC-like phase remains
2542 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2543 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2544 \end{itemize}
2545
2546 \vspace{-0.1cm}
2547
2548 \begin{center}
2549 {\color{blue}
2550 \framebox{
2551 {\color{black}
2552 High C \& small $V$ \& short $t$
2553 $\Rightarrow$
2554 }
2555 Slow restructuring due to strong C-C bonds
2556 {\color{black}
2557 $\Leftarrow$
2558 High C \& low T implants
2559 }
2560 }
2561 }
2562 \end{center}
2563
2564 \end{slide}
2565
2566 \begin{slide}
2567
2568  {\large\bf
2569   Summary and Conclusions
2570  }
2571
2572  \scriptsize
2573
2574 %\vspace{0.1cm}
2575
2576 \framebox{
2577 \begin{minipage}[t]{12.9cm}
2578  \underline{Pecipitation simulations}
2579  \begin{itemize}
2580   \item High C concentration $\rightarrow$ amorphous SiC like phase
2581   \item Problem of potential enhanced slow phase space propagation
2582   \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2583   \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2584   \item High T necessary to simulate IBS conditions (far from equilibrium)
2585   \item Precipitation by successive agglomeration of \cs (epitaxy)
2586   \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2587         (stretched SiC, interface)
2588  \end{itemize}
2589 \end{minipage}
2590 }
2591
2592 %\vspace{0.1cm}
2593
2594 \framebox{
2595 \begin{minipage}{12.9cm}
2596  \underline{Defects}
2597  \begin{itemize}
2598    \item DFT / EA
2599         \begin{itemize}
2600          \item Point defects excellently / fairly well described
2601                by DFT / EA
2602          \item C$_{\text{sub}}$ drastically underestimated by EA
2603          \item EA predicts correct ground state:
2604                C$_{\text{sub}}$ \& \si{} $>$ \ci{}
2605          \item Identified migration path explaining
2606                diffusion and reorientation experiments by DFT
2607          \item EA fails to describe \ci{} migration:
2608                Wrong path \& overestimated barrier
2609         \end{itemize}
2610    \item Combinations of defects
2611          \begin{itemize}
2612           \item Agglomeration of point defects energetically favorable
2613                 by compensation of stress
2614           \item Formation of C-C unlikely
2615           \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2616           \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2617                 Low barrier (\unit[0.77]{eV}) \& low capture radius
2618         \end{itemize}
2619  \end{itemize}
2620 \end{minipage}
2621 }
2622
2623 \begin{center}
2624 {\color{blue}
2625 \framebox{Precipitation by successive agglomeration of \cs{}}
2626 }
2627 \end{center}
2628
2629 \end{slide}
2630
2631 \begin{slide}
2632
2633  {\large\bf
2634   Acknowledgements
2635  }
2636
2637  \vspace{0.1cm}
2638
2639  \small
2640
2641  Thanks to \ldots
2642
2643  \underline{Augsburg}
2644  \begin{itemize}
2645   \item Prof. B. Stritzker (accomodation at EP \RM{4})
2646   \item Ralf Utermann (EDV)
2647  \end{itemize}
2648
2649  \underline{Helsinki}
2650  \begin{itemize}
2651   \item Prof. K. Nordlund (MD)
2652  \end{itemize}
2653
2654  \underline{Munich}
2655  \begin{itemize}
2656   \item Bayerische Forschungsstiftung (financial support)
2657  \end{itemize}
2658
2659  \underline{Paderborn}
2660  \begin{itemize}
2661   \item Prof. J. Lindner (SiC)
2662   \item Prof. G. Schmidt (DFT + financial support)
2663   \item Dr. E. Rauls (DFT + SiC)
2664   \item Dr. S. Sanna (VASP)
2665  \end{itemize}
2666
2667 \vspace{0.2cm}
2668
2669 \begin{center}
2670 \framebox{
2671 \bf Thank you for your attention!
2672 }
2673 \end{center}
2674
2675 \end{slide}
2676
2677 \end{document}
2678
2679 \fi