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 % continue here
 995 \fi
 996
 997 \begin{slide}
 998
 999 \headphd
1000 {\large\bf
1001  Utilized computational methods
1002 }
1003
1004  \vspace{0.1cm}
1005
1006  \small
1007
1008 {\bf Molecular dynamics (MD):}\\
1009 \scriptsize
1010 \begin{tabular}{p{5cm}|p{7cm}}
1011 \hline
1012 Basics & Details\\
1013 \hline
1014 Microscopic description of N particle system & \\
1015 \multicolumn{2}{c}{}\\
1016 Numerical integration using Newtons equation of motion as a propagation rule in 6N-dimensional phase space & Velocity Verlet | timestep: \unit[1]{fs} \\
1017 \multicolumn{2}{c}{}\\
1018 Analytical interaction potential & Tersoff-like bond order potential (Erhart/Albe) \\
1019 \multicolumn{2}{c}{}\\
1020 Observables obtained by time and/or ensemble averages & NpT (isothermal-isobaric)\\
1021 %\begin{itemize}
1022 %\item Berendsen thermostat:
1023 %      $\tau_{\text{T}}=100\text{ fs}$
1024 %\item Berendsen barostat:\\
1025 %      $\tau_{\text{P}}=100\text{ fs}$,
1026 %      $\beta^{-1}=100\text{ GPa}$
1027 %\end{itemize}\\
1028 \hline
1029 \end{tabular}
1030
1031  \begin{itemize}
1032   \item Microscopic description of N particle system
1033   \item Analytical interaction potential
1034   \item Numerical integration using Newtons equation of motion\\
1035         as a propagation rule in 6N-dimensional phase space
1036   \item Observables obtained by time and/or ensemble averages
1037  \end{itemize}
1038  {\bf Details of the simulation:}
1039  \begin{itemize}
1040   \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
1041   \item Ensemble: NpT (isothermal-isobaric)
1042         \begin{itemize}
1043          \item Berendsen thermostat:
1044                $\tau_{\text{T}}=100\text{ fs}$
1045          \item Berendsen barostat:\\
1046                $\tau_{\text{P}}=100\text{ fs}$,
1047                $\beta^{-1}=100\text{ GPa}$
1048         \end{itemize}
1049   \item Erhart/Albe potential: Tersoff-like bond order potential
1050   \vspace*{12pt}
1051         \[
1052         E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
1053         \pot_{ij} = {\color{red}f_C(r_{ij})}
1054         \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
1055         \]
1056  \end{itemize}
1057
1058  \begin{picture}(0,0)(-230,-30)
1059   \includegraphics[width=5cm]{tersoff_angle.eps}
1060  \end{picture}
1061
1062 \end{slide}
1063
1064 \end{document}
1065 \ifnum1=0
1066
1067 \begin{slide}
1068
1069  {\large\bf
1070   Density functional theory (DFT) calculations
1071  }
1072
1073  \small
1074
1075  Basic ingredients necessary for DFT
1076
1077  \begin{itemize}
1078   \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
1079         \begin{itemize}
1080          \item ... uniquely determines the ground state potential
1081                / wavefunctions
1082          \item ... minimizes the systems total energy
1083         \end{itemize}
1084   \item \underline{Born-Oppenheimer}
1085         - $N$ moving electrons in an external potential of static nuclei
1086 \[
1087 H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
1088               +\sum_i^N V_{\text{ext}}(r_i)
1089               +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
1090 \]
1091   \item \underline{Effective potential}
1092         - averaged electrostatic potential \& exchange and correlation
1093 \[
1094 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
1095                  +V_{\text{XC}}[n(r)]
1096 \]
1097   \item \underline{Kohn-Sham system}
1098         - Schr\"odinger equation of N non-interacting particles
1099 \[
1100 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
1101 =\epsilon_i\Phi_i(r)
1102 \quad
1103 \Rightarrow
1104 \quad
1105 n(r)=\sum_i^N|\Phi_i(r)|^2
1106 \]
1107   \item \underline{Self-consistent solution}\\
1108 $n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
1109 which in turn depends on $n(r)$
1110   \item \underline{Variational principle}
1111         - minimize total energy with respect to $n(r)$
1112  \end{itemize}
1113
1114 \end{slide}
1115
1116 \begin{slide}
1117
1118  {\large\bf
1119   Density functional theory (DFT) calculations
1120  }
1121
1122  \small
1123
1124  \vspace*{0.2cm}
1125
1126  Details of applied DFT calculations in this work
1127
1128  \begin{itemize}
1129   \item \underline{Exchange correlation functional}
1130         - approximations for the inhomogeneous electron gas
1131         \begin{itemize}
1132          \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
1133          \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
1134         \end{itemize}
1135   \item \underline{Plane wave basis set}
1136         - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
1137 \[
1138 \rightarrow
1139 \text{Fourier series: } \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r), \quad E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}
1140 \qquad ({\color{blue}300\text{ eV}})
1141 \]
1142   \item \underline{Brillouin zone sampling} -
1143         {\color{blue}$\Gamma$-point only} calculations
1144   \item \underline{Pseudo potential}
1145         - consider only the valence electrons
1146   \item \underline{Code} - VASP 4.6
1147  \end{itemize}
1148
1149  \vspace*{0.2cm}
1150
1151  MD and structural optimization
1152
1153  \begin{itemize}
1154   \item MD integration: Gear predictor corrector algorithm
1155   \item Pressure control: Parrinello-Rahman pressure control
1156   \item Structural optimization: Conjugate gradient method
1157  \end{itemize}
1158
1159 \begin{pspicture}(0,0)(0,0)
1160 \psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
1161 \end{pspicture}
1162
1163 \end{slide}
1164
1165 \begin{slide}
1166
1167  {\large\bf
1168   C and Si self-interstitial point defects in silicon
1169  }
1170
1171  \small
1172
1173  \vspace*{0.3cm}
1174
1175 \begin{minipage}{8cm}
1176 Procedure:\\[0.3cm]
1177   \begin{pspicture}(0,0)(7,5)
1178   \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1179    \parbox{7cm}{
1180    \begin{itemize}
1181     \item Creation of c-Si simulation volume
1182     \item Periodic boundary conditions
1183     \item $T=0\text{ K}$, $p=0\text{ bar}$
1184    \end{itemize}
1185   }}}}
1186 \rput(3.5,2.1){\rnode{insert}{\psframebox{
1187  \parbox{7cm}{
1188   \begin{center}
1189   Insertion of interstitial C/Si atoms
1190   \end{center}
1191   }}}}
1192   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1193    \parbox{7cm}{
1194    \begin{center}
1195    Relaxation / structural energy minimization
1196    \end{center}
1197   }}}}
1198   \ncline[]{->}{init}{insert}
1199   \ncline[]{->}{insert}{cool}
1200  \end{pspicture}
1201 \end{minipage}
1202 \begin{minipage}{5cm}
1203   \includegraphics[width=5cm]{unit_cell_e.eps}\\
1204 \end{minipage}
1205
1206 \begin{minipage}{9cm}
1207  \begin{tabular}{l c c}
1208  \hline
1209  & size [unit cells] & \# atoms\\
1210 \hline
1211 VASP & $3\times 3\times 3$ & $216\pm 1$ \\
1212 Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
1213 \hline
1214  \end{tabular}
1215 \end{minipage}
1216 \begin{minipage}{4cm}
1217 {\color{red}$\bullet$} Tetrahedral\\
1218 {\color{green}$\bullet$} Hexagonal\\
1219 {\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
1220 {\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
1221 {\color{cyan}$\bullet$} Bond-centered\\
1222 {\color{black}$\bullet$} Vacancy / Substitutional
1223 \end{minipage}
1224
1225 \end{slide}
1226
1227 \begin{slide}
1228
1229  \footnotesize
1230
1231 \begin{minipage}{9.5cm}
1232
1233  {\large\bf
1234   Si self-interstitial point defects in silicon\\
1235  }
1236
1237 \begin{tabular}{l c c c c c}
1238 \hline
1239  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
1240 \hline
1241  VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
1242  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
1243 \hline
1244 \end{tabular}\\[0.2cm]
1245
1246 \begin{minipage}{4.7cm}
1247 \includegraphics[width=4.7cm]{e_kin_si_hex.ps}
1248 \end{minipage}
1249 \begin{minipage}{4.7cm}
1250 \begin{center}
1251 {\tiny nearly T $\rightarrow$ T}\\
1252 \end{center}
1253 \includegraphics[width=4.7cm]{nhex_tet.ps}
1254 \end{minipage}\\
1255
1256 \underline{Hexagonal} \hspace{2pt}
1257 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
1258 \framebox{
1259 \begin{minipage}{2.7cm}
1260 $E_{\text{f}}^*=4.48\text{ eV}$\\
1261 \includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
1262 \end{minipage}
1263 \begin{minipage}{0.4cm}
1264 \begin{center}
1265 $\Rightarrow$
1266 \end{center}
1267 \end{minipage}
1268 \begin{minipage}{2.7cm}
1269 $E_{\text{f}}=3.96\text{ eV}$\\
1270 \includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
1271 \end{minipage}
1272 }
1273 \begin{minipage}{2.9cm}
1274 \begin{flushright}
1275 \underline{Vacancy}\\
1276 \includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
1277 \end{flushright}
1278 \end{minipage}
1279
1280 \end{minipage}
1281 \begin{minipage}{3.5cm}
1282
1283 \begin{flushright}
1284 \underline{\hkl<1 1 0> dumbbell}\\
1285 \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
1286 \underline{Tetrahedral}\\
1287 \includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
1288 \underline{\hkl<1 0 0> dumbbell}\\
1289 \includegraphics[width=3.0cm]{si_pd_albe/100.eps}
1290 \end{flushright}
1291
1292 \end{minipage}
1293
1294 \end{slide}
1295
1296 \begin{slide}
1297
1298 \footnotesize
1299
1300  {\large\bf
1301   C interstitial point defects in silicon\\[-0.1cm]
1302  }
1303
1304 \begin{tabular}{l c c c c c c r}
1305 \hline
1306  $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\
1307 \hline
1308  VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1309  Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1310 \hline
1311 \end{tabular}\\[0.1cm]
1312
1313 \framebox{
1314 \begin{minipage}{2.7cm}
1315 \underline{Hexagonal} \hspace{2pt}
1316 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1317 $E_{\text{f}}^*=9.05\text{ eV}$\\
1318 \includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
1319 \end{minipage}
1320 \begin{minipage}{0.4cm}
1321 \begin{center}
1322 $\Rightarrow$
1323 \end{center}
1324 \end{minipage}
1325 \begin{minipage}{2.7cm}
1326 \underline{\hkl<1 0 0>}\\
1327 $E_{\text{f}}=3.88\text{ eV}$\\
1328 \includegraphics[width=2.7cm]{c_pd_albe/100.eps}
1329 \end{minipage}
1330 }
1331 \begin{minipage}{2cm}
1332 \hfill
1333 \end{minipage}
1334 \begin{minipage}{3cm}
1335 \begin{flushright}
1336 \underline{Tetrahedral}\\
1337 \includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
1338 \end{flushright}
1339 \end{minipage}
1340
1341 \framebox{
1342 \begin{minipage}{2.7cm}
1343 \underline{Bond-centered}\\
1344 $E_{\text{f}}^*=5.59\text{ eV}$\\
1345 \includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
1346 \end{minipage}
1347 \begin{minipage}{0.4cm}
1348 \begin{center}
1349 $\Rightarrow$
1350 \end{center}
1351 \end{minipage}
1352 \begin{minipage}{2.7cm}
1353 \underline{\hkl<1 1 0> dumbbell}\\
1354 $E_{\text{f}}=5.18\text{ eV}$\\
1355 \includegraphics[width=2.7cm]{c_pd_albe/110.eps}
1356 \end{minipage}
1357 }
1358 \begin{minipage}{2cm}
1359 \hfill
1360 \end{minipage}
1361 \begin{minipage}{3cm}
1362 \begin{flushright}
1363 \underline{Substitutional}\\
1364 \includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
1365 \end{flushright}
1366 \end{minipage}
1367
1368 \end{slide}
1369
1370 \begin{slide}
1371
1372 \footnotesize
1373
1374  {\large\bf\boldmath
1375   C \hkl<1 0 0> dumbbell interstitial configuration\\
1376  }
1377
1378 {\tiny
1379 \begin{tabular}{l c c c c c c c c}
1380 \hline
1381  Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
1382 \hline
1383 Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
1384 VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
1385 \hline
1386 \end{tabular}\\[0.2cm]
1387 \begin{tabular}{l c c c c }
1388 \hline
1389  Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
1390 \hline
1391 Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
1392 VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
1393 \hline
1394 \end{tabular}\\[0.2cm]
1395 \begin{tabular}{l c c c}
1396 \hline
1397  Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
1398 \hline
1399 Erhart/Albe & 0.084 & -0.091 & 0.175 \\
1400 VASP & 0.109 & -0.065 & 0.174 \\
1401 \hline
1402 \end{tabular}\\[0.6cm]
1403 }
1404
1405 \begin{minipage}{3.0cm}
1406 \begin{center}
1407 \underline{Erhart/Albe}
1408 \includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
1409 \end{center}
1410 \end{minipage}
1411 \begin{minipage}{3.0cm}
1412 \begin{center}
1413 \underline{VASP}
1414 \includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
1415 \end{center}
1416 \end{minipage}\\
1417
1418 \begin{picture}(0,0)(-185,10)
1419 \includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
1420 \end{picture}
1421 \begin{picture}(0,0)(-280,-150)
1422 \includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
1423 \end{picture}
1424
1425 \begin{pspicture}(0,0)(0,0)
1426 \psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
1427 \psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
1428 \psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
1429 \psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
1430 \end{pspicture}
1431
1432 \end{slide}
1433
1434 \begin{slide}
1435
1436 \small
1437
1438 \begin{minipage}{8.5cm}
1439
1440  {\large\bf
1441   Bond-centered interstitial configuration\\[-0.1cm]
1442  }
1443
1444 \begin{minipage}{3.0cm}
1445 \includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1446 \end{minipage}
1447 \begin{minipage}{5.2cm}
1448 \begin{itemize}
1449  \item Linear Si-C-Si bond
1450  \item Si: one C \& 3 Si neighbours
1451  \item Spin polarized calculations
1452  \item No saddle point!\\
1453        Real local minimum!
1454 \end{itemize}
1455 \end{minipage}
1456
1457 \framebox{
1458  \tiny
1459  \begin{minipage}[t]{6.5cm}
1460   \begin{minipage}[t]{1.2cm}
1461   {\color{red}Si}\\
1462   {\tiny sp$^3$}\\[0.8cm]
1463   \underline{${\color{black}\uparrow}$}
1464   \underline{${\color{black}\uparrow}$}
1465   \underline{${\color{black}\uparrow}$}
1466   \underline{${\color{red}\uparrow}$}\\
1467   sp$^3$
1468   \end{minipage}
1469   \begin{minipage}[t]{1.4cm}
1470   \begin{center}
1471   {\color{red}M}{\color{blue}O}\\[0.8cm]
1472   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1473   $\sigma_{\text{ab}}$\\[0.5cm]
1474   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1475   $\sigma_{\text{b}}$
1476   \end{center}
1477   \end{minipage}
1478   \begin{minipage}[t]{1.0cm}
1479   \begin{center}
1480   {\color{blue}C}\\
1481   {\tiny sp}\\[0.2cm]
1482   \underline{${\color{white}\uparrow\uparrow}$}
1483   \underline{${\color{white}\uparrow\uparrow}$}\\
1484   2p\\[0.4cm]
1485   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1486   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1487   sp
1488   \end{center}
1489   \end{minipage}
1490   \begin{minipage}[t]{1.4cm}
1491   \begin{center}
1492   {\color{blue}M}{\color{green}O}\\[0.8cm]
1493   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1494   $\sigma_{\text{ab}}$\\[0.5cm]
1495   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1496   $\sigma_{\text{b}}$
1497   \end{center}
1498   \end{minipage}
1499   \begin{minipage}[t]{1.2cm}
1500   \begin{flushright}
1501   {\color{green}Si}\\
1502   {\tiny sp$^3$}\\[0.8cm]
1503   \underline{${\color{green}\uparrow}$}
1504   \underline{${\color{black}\uparrow}$}
1505   \underline{${\color{black}\uparrow}$}
1506   \underline{${\color{black}\uparrow}$}\\
1507   sp$^3$
1508   \end{flushright}
1509   \end{minipage}
1510  \end{minipage}
1511 }\\[0.1cm]
1512
1513 \framebox{
1514 \begin{minipage}{4.5cm}
1515 \includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
1516 \end{minipage}
1517 \begin{minipage}{3.5cm}
1518 {\color{gray}$\bullet$} Spin up\\
1519 {\color{green}$\bullet$} Spin down\\
1520 {\color{blue}$\bullet$} Resulting spin up\\
1521 {\color{yellow}$\bullet$} Si atoms\\
1522 {\color{red}$\bullet$} C atom
1523 \end{minipage}
1524 }
1525
1526 \end{minipage}
1527 \begin{minipage}{4.2cm}
1528 \begin{flushright}
1529 \includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
1530 {\color{green}$\Box$} {\tiny unoccupied}\\
1531 {\color{red}$\bullet$} {\tiny occupied}
1532 \end{flushright}
1533 \end{minipage}
1534
1535 \end{slide}
1536
1537 \begin{slide}
1538
1539  {\large\bf\boldmath
1540   Migration of the C \hkl<1 0 0> dumbbell interstitial
1541  }
1542
1543 \scriptsize
1544
1545  {\small Investigated pathways}
1546
1547 \begin{minipage}{8.5cm}
1548 \begin{minipage}{8.3cm}
1549 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
1550 \begin{minipage}{2.4cm}
1551 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1552 \end{minipage}
1553 \begin{minipage}{0.4cm}
1554 $\rightarrow$
1555 \end{minipage}
1556 \begin{minipage}{2.4cm}
1557 \includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
1558 \end{minipage}
1559 \begin{minipage}{0.4cm}
1560 $\rightarrow$
1561 \end{minipage}
1562 \begin{minipage}{2.4cm}
1563 \includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
1564 \end{minipage}
1565 \end{minipage}\\
1566 \begin{minipage}{8.3cm}
1567 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
1568 \begin{minipage}{2.4cm}
1569 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1570 \end{minipage}
1571 \begin{minipage}{0.4cm}
1572 $\rightarrow$
1573 \end{minipage}
1574 \begin{minipage}{2.4cm}
1575 \includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
1576 \end{minipage}
1577 \begin{minipage}{0.4cm}
1578 $\rightarrow$
1579 \end{minipage}
1580 \begin{minipage}{2.4cm}
1581 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
1582 \end{minipage}
1583 \end{minipage}\\
1584 \begin{minipage}{8.3cm}
1585 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
1586 \begin{minipage}{2.4cm}
1587 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1588 \end{minipage}
1589 \begin{minipage}{0.4cm}
1590 $\rightarrow$
1591 \end{minipage}
1592 \begin{minipage}{2.4cm}
1593 \includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
1594 \end{minipage}
1595 \begin{minipage}{0.4cm}
1596 $\rightarrow$
1597 \end{minipage}
1598 \begin{minipage}{2.4cm}
1599 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
1600 \end{minipage}
1601 \end{minipage}
1602 \end{minipage}
1603 \framebox{
1604 \begin{minipage}{4.2cm}
1605  {\small Constrained relaxation\\
1606          technique (CRT) method}\\
1607 \includegraphics[width=4cm]{crt_orig.eps}
1608 \begin{itemize}
1609  \item Constrain diffusing atom
1610  \item Static constraints
1611 \end{itemize}
1612 \vspace*{0.3cm}
1613  {\small Modifications}\\
1614 \includegraphics[width=4cm]{crt_mod.eps}
1615 \begin{itemize}
1616  \item Constrain all atoms
1617  \item Update individual\\
1618        constraints
1619 \end{itemize}
1620 \end{minipage}
1621 }
1622
1623 \end{slide}
1624
1625 \begin{slide}
1626
1627  {\large\bf\boldmath
1628   Migration of the C \hkl<1 0 0> dumbbell interstitial
1629  }
1630
1631 \scriptsize
1632
1633 \framebox{
1634 \begin{minipage}{5.9cm}
1635 \begin{flushleft}
1636 \includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
1637 \end{flushleft}
1638 \begin{center}
1639 \begin{picture}(0,0)(60,0)
1640 \includegraphics[width=1cm]{vasp_mig/00-1.eps}
1641 \end{picture}
1642 \begin{picture}(0,0)(-5,0)
1643 \includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
1644 \end{picture}
1645 \begin{picture}(0,0)(-55,0)
1646 \includegraphics[width=1cm]{vasp_mig/bc.eps}
1647 \end{picture}
1648 \begin{picture}(0,0)(12.5,10)
1649 \includegraphics[width=1cm]{110_arrow.eps}
1650 \end{picture}
1651 \begin{picture}(0,0)(90,0)
1652 \includegraphics[height=0.9cm]{001_arrow.eps}
1653 \end{picture}
1654 \end{center}
1655 \vspace*{0.35cm}
1656 \end{minipage}
1657 }
1658 \begin{minipage}{0.3cm}
1659 \hfill
1660 \end{minipage}
1661 \framebox{
1662 \begin{minipage}{5.9cm}
1663 \begin{flushright}
1664 \includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
1665 \end{flushright}
1666 \begin{center}
1667 \begin{picture}(0,0)(60,0)
1668 \includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
1669 \end{picture}
1670 \begin{picture}(0,0)(5,0)
1671 \includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
1672 \end{picture}
1673 \begin{picture}(0,0)(-55,0)
1674 \includegraphics[width=1cm]{vasp_mig/0-10.eps}
1675 \end{picture}
1676 \begin{picture}(0,0)(12.5,10)
1677 \includegraphics[width=1cm]{100_arrow.eps}
1678 \end{picture}
1679 \begin{picture}(0,0)(90,0)
1680 \includegraphics[height=0.9cm]{001_arrow.eps}
1681 \end{picture}
1682 \end{center}
1683 \vspace*{0.3cm}
1684 \end{minipage}\\
1685 }
1686
1687 \vspace*{0.05cm}
1688
1689 \framebox{
1690 \begin{minipage}{5.9cm}
1691 \begin{flushleft}
1692 \includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
1693 \end{flushleft}
1694 \begin{center}
1695 \begin{picture}(0,0)(60,0)
1696 \includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps}
1697 \end{picture}
1698 \begin{picture}(0,0)(10,0)
1699 \includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
1700 \end{picture}
1701 \begin{picture}(0,0)(-60,0)
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1706 \end{picture}
1707 \begin{picture}(0,0)(90,0)
1708 \includegraphics[height=0.9cm]{001_arrow.eps}
1709 \end{picture}
1710 \end{center}
1711 \vspace*{0.3cm}
1712 \end{minipage}
1713 }
1714 \begin{minipage}{0.3cm}
1715 \hfill
1716 \end{minipage}
1717 \begin{minipage}{6.5cm}
1718 VASP results
1719 \begin{itemize}
1720  \item Energetically most favorable path
1721        \begin{itemize}
1722         \item Path 2
1723         \item Activation energy: $\approx$ 0.9 eV
1724         \item Experimental values: 0.73 ... 0.87 eV
1725        \end{itemize}
1726        $\Rightarrow$ {\color{blue}Diffusion} path identified!
1727  \item Reorientation (path 3)
1728        \begin{itemize}
1729         \item More likely composed of two consecutive steps of type 2
1730         \item Experimental values: 0.77 ... 0.88 eV
1731        \end{itemize}
1732        $\Rightarrow$ {\color{blue}Reorientation} transition identified!
1733 \end{itemize}
1734 \end{minipage}
1735
1736 \end{slide}
1737
1738 \begin{slide}
1739
1740  {\large\bf\boldmath
1741   Migration of the C \hkl<1 0 0> dumbbell interstitial
1742  }
1743
1744 \scriptsize
1745
1746  \vspace{0.1cm}
1747
1748 \begin{minipage}{6.5cm}
1749
1750 \framebox{
1751 \begin{minipage}[t]{5.9cm}
1752 \begin{flushleft}
1753 \includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
1754 \end{flushleft}
1755 \begin{center}
1756 \begin{pspicture}(0,0)(0,0)
1757 \psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
1758 \end{pspicture}
1759 \begin{picture}(0,0)(60,-50)
1760 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
1761 \end{picture}
1762 \begin{picture}(0,0)(5,-50)
1763 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
1764 \end{picture}
1765 \begin{picture}(0,0)(-55,-50)
1766 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
1767 \end{picture}
1768 \begin{picture}(0,0)(12.5,-40)
1769 \includegraphics[width=1cm]{110_arrow.eps}
1770 \end{picture}
1771 \begin{picture}(0,0)(90,-45)
1772 \includegraphics[height=0.9cm]{001_arrow.eps}
1773 \end{picture}\\
1774 \begin{pspicture}(0,0)(0,0)
1775 \psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
1776 \end{pspicture}
1777 \begin{picture}(0,0)(60,-15)
1778 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
1779 \end{picture}
1780 \begin{picture}(0,0)(35,-15)
1781 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
1782 \end{picture}
1783 \begin{picture}(0,0)(-5,-15)
1784 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
1785 \end{picture}
1786 \begin{picture}(0,0)(-55,-15)
1787 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
1788 \end{picture}
1789 \begin{picture}(0,0)(12.5,-5)
1790 \includegraphics[width=1cm]{100_arrow.eps}
1791 \end{picture}
1792 \begin{picture}(0,0)(90,-15)
1793 \includegraphics[height=0.9cm]{010_arrow.eps}
1794 \end{picture}
1795 \end{center}
1796 \end{minipage}
1797 }\\[0.1cm]
1798
1799 \begin{minipage}{5.9cm}
1800 Erhart/Albe results
1801 \begin{itemize}
1802  \item Lowest activation energy: $\approx$ 2.2 eV
1803  \item 2.4 times higher than VASP
1804  \item Different pathway
1805 \end{itemize}
1806 \end{minipage}
1807
1808 \end{minipage}
1809 \begin{minipage}{6.5cm}
1810
1811 \framebox{
1812 \begin{minipage}{5.9cm}
1813 %\begin{flushright}
1814 %\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
1815 %\end{flushright}
1816 %\begin{center}
1817 %\begin{pspicture}(0,0)(0,0)
1818 %\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
1819 %\end{pspicture}
1820 %\begin{picture}(0,0)(60,-5)
1821 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
1822 %\end{picture}
1823 %\begin{picture}(0,0)(0,-5)
1824 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
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1826 %\begin{picture}(0,0)(-55,-5)
1827 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
1828 %\end{picture}
1829 %\begin{picture}(0,0)(12.5,5)
1830 %\includegraphics[width=1cm]{100_arrow.eps}
1831 %\end{picture}
1832 %\begin{picture}(0,0)(90,0)
1833 %\includegraphics[height=0.9cm]{001_arrow.eps}
1834 %\end{picture}
1835 %\end{center}
1836 %\vspace{0.2cm}
1837 %\end{minipage}
1838 %}\\[0.2cm]
1839 %
1840 %\framebox{
1841 %\begin{minipage}{5.9cm}
1842 \includegraphics[width=5.9cm]{00-1_110_0-10_mig_albe.ps}
1843 \end{minipage}
1844 }\\[0.1cm]
1845
1846 \begin{minipage}{5.9cm}
1847 Transition involving \ci{} \hkl<1 1 0>
1848 \begin{itemize}
1849  \item Bond-centered configuration unstable\\
1850        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1851  \item Transition minima of path 2 \& 3\\
1852        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1853  \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV
1854  \item 2.4 - 3.4 times higher than VASP
1855  \item Rotation of dumbbell orientation
1856 \end{itemize}
1857 \vspace{0.1cm}
1858 \begin{center}
1859 {\color{blue}Overestimated diffusion barrier}
1860 \end{center}
1861 \end{minipage}
1862
1863 \end{minipage}
1864
1865 \end{slide}
1866
1867 \begin{slide}
1868
1869  {\large\bf\boldmath
1870   Combinations with a C-Si \hkl<1 0 0>-type interstitial
1871  }
1872
1873 \small
1874
1875 \vspace*{0.1cm}
1876
1877 Binding energy:
1878 $
1879 E_{\text{b}}=
1880 E_{\text{f}}^{\text{defect combination}}-
1881 E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
1882 E_{\text{f}}^{\text{2nd defect}}
1883 $
1884
1885 \vspace*{0.1cm}
1886
1887 {\scriptsize
1888 \begin{tabular}{l c c c c c c}
1889 \hline
1890  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1891  \hline
1892  \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1893  \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1894  \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}\\
1895  \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}\\
1896  \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}\\
1897  \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}\\
1898  \hline
1899  C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1900  Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1901 \hline
1902 \end{tabular}
1903 }
1904
1905 \vspace*{0.3cm}
1906
1907 \footnotesize
1908
1909 \begin{minipage}[t]{3.8cm}
1910 \underline{\hkl<1 0 0> at position 1}\\[0.1cm]
1911 \includegraphics[width=3.5cm]{00-1dc/2-25.eps}
1912 \end{minipage}
1913 \begin{minipage}[t]{3.5cm}
1914 \underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
1915 \includegraphics[width=3.2cm]{00-1dc/2-39.eps}
1916 \end{minipage}
1917 \begin{minipage}[t]{5.5cm}
1918 \begin{itemize}
1919  \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\
1920        $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
1921  \item Stress compensation / increase
1922  \item Unfavored: antiparallel orientations
1923  \item Indication of energetically favored\\
1924        agglomeration
1925  \item Most favorable: C clustering
1926  \item However: High barrier ($>4\,\text{eV}$)
1927  \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$
1928        (Entropy)
1929 \end{itemize}
1930 \end{minipage}
1931
1932 \begin{picture}(0,0)(-295,-130)
1933 \includegraphics[width=3.5cm]{comb_pos.eps}
1934 \end{picture}
1935
1936 \end{slide}
1937
1938 \begin{slide}
1939
1940  {\large\bf\boldmath
1941   Combinations of C-Si \hkl<1 0 0>-type interstitials
1942  }
1943
1944 \small
1945
1946 \vspace*{0.1cm}
1947
1948 Energetically most favorable combinations along \hkl<1 1 0>
1949
1950 \vspace*{0.1cm}
1951
1952 {\scriptsize
1953 \begin{tabular}{l c c c c c c}
1954 \hline
1955  & 1 & 2 & 3 & 4 & 5 & 6\\
1956 \hline
1957 $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
1958 C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
1959 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>\\
1960 \hline
1961 \end{tabular}
1962 }
1963
1964 \vspace*{0.3cm}
1965
1966 \begin{minipage}{7.0cm}
1967 \includegraphics[width=7cm]{db_along_110_cc.ps}
1968 \end{minipage}
1969 \begin{minipage}{6.0cm}
1970 \begin{itemize}
1971  \item Interaction proportional to reciprocal cube of C-C distance
1972  \item Saturation in the immediate vicinity
1973  \renewcommand\labelitemi{$\Rightarrow$}
1974  \item Agglomeration of \ci{} expected
1975  \item Absence of C clustering
1976 \end{itemize}
1977 \begin{center}
1978 {\color{blue}
1979  Consisten with initial precipitation model
1980 }
1981 \end{center}
1982 \end{minipage}
1983
1984 \vspace{0.2cm}
1985
1986 \end{slide}
1987
1988 \begin{slide}
1989
1990  {\large\bf\boldmath
1991   Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
1992  }
1993
1994  \scriptsize
1995
1996 %\begin{center}
1997 %\begin{minipage}{3.2cm}
1998 %\includegraphics[width=3cm]{sub_110_combo.eps}
1999 %\end{minipage}
2000 %\begin{minipage}{7.8cm}
2001 %\begin{tabular}{l c c c c c c}
2002 %\hline
2003 %C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
2004 %                   \hkl<1 0 1> & \hkl<-1 0 1> \\
2005 %\hline
2006 %1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
2007 %2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
2008 %3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
2009 %4 & \RM{4} & B & D & E & E & D \\
2010 %5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
2011 %\hline
2012 %\end{tabular}
2013 %\end{minipage}
2014 %\end{center}
2015
2016 %\begin{center}
2017 %\begin{tabular}{l c c c c c c c c c c}
2018 %\hline
2019 %Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
2020 %\hline
2021 %$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
2022 %$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
2023 %$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
2024 %\hline
2025 %\end{tabular}
2026 %\end{center}
2027
2028 \begin{minipage}{6.0cm}
2029 \includegraphics[width=5.8cm]{c_sub_si110.ps}
2030 \end{minipage}
2031 \begin{minipage}{7cm}
2032 \scriptsize
2033 \begin{itemize}
2034  \item IBS: C may displace Si\\
2035        $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
2036  \item Assumption:\\
2037        \hkl<1 1 0>-type $\rightarrow$ favored combination
2038  \renewcommand\labelitemi{$\Rightarrow$}
2039  \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
2040  \item Less favorable than C-Si \hkl<1 0 0> dumbbell
2041  \item Interaction drops quickly to zero\\
2042        $\rightarrow$ low capture radius
2043 \end{itemize}
2044 \begin{center}
2045  {\color{blue}
2046  IBS process far from equilibrium\\
2047  \cs{} \& \si{} instead of thermodynamic ground state
2048  }
2049 \end{center}
2050 \end{minipage}
2051
2052 \begin{minipage}{6.5cm}
2053 \includegraphics[width=6.0cm]{162-097.ps}
2054 \begin{itemize}
2055  \item Low migration barrier
2056 \end{itemize}
2057 \end{minipage}
2058 \begin{minipage}{6.5cm}
2059 \begin{center}
2060 Ab initio MD at \degc{900}\\
2061 \includegraphics[width=3.3cm]{md_vasp_01.eps}
2062 $t=\unit[2230]{fs}$\\
2063 \includegraphics[width=3.3cm]{md_vasp_02.eps}
2064 $t=\unit[2900]{fs}$
2065 \end{center}
2066 {\color{blue}
2067 Contribution of entropy to structural formation
2068 }
2069 \end{minipage}
2070
2071 \end{slide}
2072
2073 \begin{slide}
2074
2075  {\large\bf\boldmath
2076   Migration in C-Si \hkl<1 0 0> and vacancy combinations
2077  }
2078
2079  \footnotesize
2080
2081 \vspace{0.1cm}
2082
2083 \begin{minipage}[t]{3cm}
2084 \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
2085 \includegraphics[width=2.8cm]{00-1dc/0-59.eps}
2086 \end{minipage}
2087 \begin{minipage}[t]{7cm}
2088 \vspace{0.2cm}
2089 \begin{center}
2090  Low activation energies\\
2091  High activation energies for reverse processes\\
2092  $\Downarrow$\\
2093  {\color{blue}C$_{\text{sub}}$ very stable}\\
2094 \vspace*{0.1cm}
2095  \hrule
2096 \vspace*{0.1cm}
2097  Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
2098  $\Downarrow$\\
2099  {\color{blue}Formation of SiC by successive substitution by C}
2100
2101 \end{center}
2102 \end{minipage}
2103 \begin{minipage}[t]{3cm}
2104 \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
2105 \includegraphics[width=2.8cm]{00-1dc/3-14.eps}
2106 \end{minipage}
2107
2108
2109 \framebox{
2110 \begin{minipage}{5.9cm}
2111 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
2112 \begin{center}
2113 \begin{picture}(0,0)(70,0)
2114 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
2115 \end{picture}
2116 \begin{picture}(0,0)(30,0)
2117 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
2118 \end{picture}
2119 \begin{picture}(0,0)(-10,0)
2120 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
2121 \end{picture}
2122 \begin{picture}(0,0)(-48,0)
2123 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
2124 \end{picture}
2125 \begin{picture}(0,0)(12.5,5)
2126 \includegraphics[width=1cm]{100_arrow.eps}
2127 \end{picture}
2128 \begin{picture}(0,0)(97,-10)
2129 \includegraphics[height=0.9cm]{001_arrow.eps}
2130 \end{picture}
2131 \end{center}
2132 \vspace{0.1cm}
2133 \end{minipage}
2134 }
2135 \begin{minipage}{0.3cm}
2136 \hfill
2137 \end{minipage}
2138 \framebox{
2139 \begin{minipage}{5.9cm}
2140 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
2141 \begin{center}
2142 \begin{picture}(0,0)(60,0)
2143 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
2144 \end{picture}
2145 \begin{picture}(0,0)(25,0)
2146 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
2147 \end{picture}
2148 \begin{picture}(0,0)(-20,0)
2149 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
2150 \end{picture}
2151 \begin{picture}(0,0)(-55,0)
2152 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
2153 \end{picture}
2154 \begin{picture}(0,0)(12.5,5)
2155 \includegraphics[width=1cm]{100_arrow.eps}
2156 \end{picture}
2157 \begin{picture}(0,0)(95,0)
2158 \includegraphics[height=0.9cm]{001_arrow.eps}
2159 \end{picture}
2160 \end{center}
2161 \vspace{0.1cm}
2162 \end{minipage}
2163 }
2164
2165 \end{slide}
2166
2167 \begin{slide}
2168
2169  {\large\bf
2170   Conclusion of defect / migration / combined defect simulations
2171  }
2172
2173  \footnotesize
2174
2175 \vspace*{0.1cm}
2176
2177 Defect structures
2178 \begin{itemize}
2179  \item Accurately described by quantum-mechanical simulations
2180  \item Less accurate description by classical potential simulations
2181  \item Underestimated formation energy of \cs{} by classical approach
2182  \item Both methods predict same ground state: \ci{} \hkl<1 0 0> dumbbell
2183 \end{itemize}
2184
2185 Migration
2186 \begin{itemize}
2187  \item C migration pathway in Si identified
2188  \item Consistent with reorientation and diffusion experiments
2189 \end{itemize}
2190 \begin{itemize}
2191  \item Different path and ...
2192  \item overestimated barrier by classical potential calculations
2193 \end{itemize}
2194
2195 Concerning the precipitation mechanism
2196 \begin{itemize}
2197  \item Agglomeration of C-Si dumbbells energetically favorable
2198        (stress compensation)
2199  \item C-Si indeed favored compared to
2200        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2201  \item Possible low interaction capture radius of
2202        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2203  \item Low barrier for
2204        \ci{} \hkl<1 0 0> $\rightarrow$ \cs{} \& \si{} \hkl<1 1 0>
2205  \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
2206        C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
2207 \end{itemize}
2208 \begin{center}
2209 {\color{blue}Results suggest increased participation of \cs}
2210 \end{center}
2211
2212 \end{slide}
2213
2214 \begin{slide}
2215
2216  {\large\bf
2217   Silicon carbide precipitation simulations
2218  }
2219
2220  \small
2221
2222 {\scriptsize
2223  \begin{pspicture}(0,0)(12,6.5)
2224   % nodes
2225   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
2226    \parbox{7cm}{
2227    \begin{itemize}
2228     \item Create c-Si volume
2229     \item Periodc boundary conditions
2230     \item Set requested $T$ and $p=0\text{ bar}$
2231     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
2232    \end{itemize}
2233   }}}}
2234   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
2235    \parbox{7cm}{
2236    Insertion of C atoms at constant T
2237    \begin{itemize}
2238     \item total simulation volume {\pnode{in1}}
2239     \item volume of minimal SiC precipitate {\pnode{in2}}
2240     \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
2241           precipitate
2242    \end{itemize}
2243   }}}}
2244   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
2245    \parbox{7.0cm}{
2246    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
2247   }}}}
2248   \ncline[]{->}{init}{insert}
2249   \ncline[]{->}{insert}{cool}
2250   \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
2251   \rput(7.8,6){\footnotesize $V_1$}
2252   \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
2253   \rput(9.2,4.85){\tiny $V_2$}
2254   \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
2255   \rput(9.55,4.45){\footnotesize $V_3$}
2256   \rput(7.9,3.2){\pnode{ins1}}
2257   \rput(9.22,2.8){\pnode{ins2}}
2258   \rput(11.0,2.4){\pnode{ins3}}
2259   \ncline[]{->}{in1}{ins1}
2260   \ncline[]{->}{in2}{ins2}
2261   \ncline[]{->}{in3}{ins3}
2262  \end{pspicture}
2263 }
2264
2265 \begin{itemize}
2266  \item Restricted to classical potential simulations
2267  \item $V_2$ and $V_3$ considered due to low diffusion
2268  \item Amount of C atoms: 6000
2269        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
2270  \item Simulation volume: $31\times 31\times 31$ unit cells
2271        (238328 Si atoms)
2272 \end{itemize}
2273
2274 \end{slide}
2275
2276 \begin{slide}
2277
2278  {\large\bf\boldmath
2279   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2280  }
2281
2282  \small
2283
2284 \begin{minipage}{6.5cm}
2285 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2286 \end{minipage}
2287 \begin{minipage}{6.5cm}
2288 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2289 \end{minipage}
2290
2291 \begin{minipage}{6.5cm}
2292 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2293 \end{minipage}
2294 \begin{minipage}{6.5cm}
2295 \scriptsize
2296 \underline{Low C concentration ($V_1$)}\\
2297 \hkl<1 0 0> C-Si dumbbell dominated structure
2298 \begin{itemize}
2299  \item Si-C bumbs around 0.19 nm
2300  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2301        concatenated dumbbells of various orientation
2302  \item Si-Si NN distance stretched to 0.3 nm
2303 \end{itemize}
2304 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2305 \underline{High C concentration ($V_2$, $V_3$)}\\
2306 High amount of strongly bound C-C bonds\\
2307 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2308 Only short range order observable\\
2309 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2310 \end{minipage}
2311
2312 \end{slide}
2313
2314 \begin{slide}
2315
2316  {\large\bf\boldmath
2317   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2318  }
2319
2320  \small
2321
2322 \begin{minipage}{6.5cm}
2323 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2324 \end{minipage}
2325 \begin{minipage}{6.5cm}
2326 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2327 \end{minipage}
2328
2329 \begin{minipage}{6.5cm}
2330 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2331 \end{minipage}
2332 \begin{minipage}{6.5cm}
2333 \scriptsize
2334 \underline{Low C concentration ($V_1$)}\\
2335 \hkl<1 0 0> C-Si dumbbell dominated structure
2336 \begin{itemize}
2337  \item Si-C bumbs around 0.19 nm
2338  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2339        concatenated dumbbells of various orientation
2340  \item Si-Si NN distance stretched to 0.3 nm
2341 \end{itemize}
2342 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2343 \underline{High C concentration ($V_2$, $V_3$)}\\
2344 High amount of strongly bound C-C bonds\\
2345 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2346 Only short range order observable\\
2347 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2348 \end{minipage}
2349
2350 \begin{pspicture}(0,0)(0,0)
2351 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2352 \begin{minipage}{10cm}
2353 \small
2354 {\color{red}\bf 3C-SiC formation fails to appear}
2355 \begin{itemize}
2356 \item Low C concentration simulations
2357  \begin{itemize}
2358   \item Formation of \ci{} indeed occurs
2359   \item Agllomeration not observed
2360  \end{itemize}
2361 \item High C concentration simulations
2362  \begin{itemize}
2363   \item Amorphous SiC-like structure\\
2364         (not expected at prevailing temperatures)
2365   \item Rearrangement and transition into 3C-SiC structure missing
2366  \end{itemize}
2367 \end{itemize}
2368 \end{minipage}
2369  }}}
2370 \end{pspicture}
2371
2372 \end{slide}
2373
2374 \begin{slide}
2375
2376  {\large\bf
2377   Limitations of molecular dynamics and short range potentials
2378  }
2379
2380 \footnotesize
2381
2382 \vspace{0.2cm}
2383
2384 \underline{Time scale problem of MD}\\[0.2cm]
2385 Minimize integration error\\
2386 $\Rightarrow$ discretization considerably smaller than
2387               reciprocal of fastest vibrational mode\\[0.1cm]
2388 Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
2389 $\Rightarrow$ suitable choice of time step:
2390               $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
2391 $\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
2392 Several local minima in energy surface separated by large energy barriers\\
2393 $\Rightarrow$ transition event corresponds to a multiple
2394               of vibrational periods\\
2395 $\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
2396               infrequent transition events\\[0.1cm]
2397 {\color{blue}Accelerated methods:}
2398 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
2399
2400 \vspace{0.3cm}
2401
2402 \underline{Limitations related to the short range potential}\\[0.2cm]
2403 Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
2404 and 2$^{\text{nd}}$ next neighbours\\
2405 $\Rightarrow$ overestimated unphysical high forces of next neighbours
2406
2407 \vspace{0.3cm}
2408
2409 \framebox{
2410 \color{red}
2411 Potential enhanced problem of slow phase space propagation
2412 }
2413
2414 \vspace{0.3cm}
2415
2416 \underline{Approach to the (twofold) problem}\\[0.2cm]
2417 Increased temperature simulations without TAD corrections\\
2418 (accelerated methods or higher time scales exclusively not sufficient)
2419
2420 \begin{picture}(0,0)(-260,-30)
2421 \framebox{
2422 \begin{minipage}{4.2cm}
2423 \tiny
2424 \begin{center}
2425 \vspace{0.03cm}
2426 \underline{IBS}
2427 \end{center}
2428 \begin{itemize}
2429 \item 3C-SiC also observed for higher T
2430 \item higher T inside sample
2431 \item structural evolution vs.\\
2432       equilibrium properties
2433 \end{itemize}
2434 \end{minipage}
2435 }
2436 \end{picture}
2437
2438 \begin{picture}(0,0)(-305,-155)
2439 \framebox{
2440 \begin{minipage}{2.5cm}
2441 \tiny
2442 \begin{center}
2443 retain proper\\
2444 thermodynmic sampling
2445 \end{center}
2446 \end{minipage}
2447 }
2448 \end{picture}
2449
2450 \end{slide}
2451
2452 \begin{slide}
2453
2454  {\large\bf
2455   Increased temperature simulations at low C concentration
2456  }
2457
2458 \small
2459
2460 \begin{minipage}{6.5cm}
2461 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2462 \end{minipage}
2463 \begin{minipage}{6.5cm}
2464 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2465 \end{minipage}
2466
2467 \begin{minipage}{6.5cm}
2468 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2469 \end{minipage}
2470 \begin{minipage}{6.5cm}
2471 \scriptsize
2472  \underline{Si-C bonds:}
2473  \begin{itemize}
2474   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2475   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2476  \end{itemize}
2477  \underline{Si-Si bonds:}
2478  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2479  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2480  \underline{C-C bonds:}
2481  \begin{itemize}
2482   \item C-C next neighbour pairs reduced (mandatory)
2483   \item Peak at 0.3 nm slightly shifted
2484         \begin{itemize}
2485          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2486                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2487                combinations (|)\\
2488                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2489                ($\downarrow$)
2490          \item Range [|-$\downarrow$]:
2491                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2492                with nearby Si$_{\text{I}}$}
2493         \end{itemize}
2494  \end{itemize}
2495 \end{minipage}
2496
2497 \begin{picture}(0,0)(-330,-74)
2498 \color{blue}
2499 \framebox{
2500 \begin{minipage}{1.6cm}
2501 \tiny
2502 \begin{center}
2503 stretched SiC\\[-0.1cm]
2504 in c-Si
2505 \end{center}
2506 \end{minipage}
2507 }
2508 \end{picture}
2509
2510 \end{slide}
2511
2512 \begin{slide}
2513
2514  {\large\bf
2515   Increased temperature simulations at low C concentration
2516  }
2517
2518 \small
2519
2520 \begin{minipage}{6.5cm}
2521 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2522 \end{minipage}
2523 \begin{minipage}{6.5cm}
2524 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2525 \end{minipage}
2526
2527 \begin{minipage}{6.5cm}
2528 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2529 \end{minipage}
2530 \begin{minipage}{6.5cm}
2531 \scriptsize
2532  \underline{Si-C bonds:}
2533  \begin{itemize}
2534   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2535   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2536  \end{itemize}
2537  \underline{Si-Si bonds:}
2538  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2539  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2540  \underline{C-C bonds:}
2541  \begin{itemize}
2542   \item C-C next neighbour pairs reduced (mandatory)
2543   \item Peak at 0.3 nm slightly shifted
2544         \begin{itemize}
2545          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2546                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2547                combinations (|)\\
2548                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2549                ($\downarrow$)
2550          \item Range [|-$\downarrow$]:
2551                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2552                with nearby Si$_{\text{I}}$}
2553         \end{itemize}
2554  \end{itemize}
2555 \end{minipage}
2556
2557 %\begin{picture}(0,0)(-330,-74)
2558 %\color{blue}
2559 %\framebox{
2560 %\begin{minipage}{1.6cm}
2561 %\tiny
2562 %\begin{center}
2563 %stretched SiC\\[-0.1cm]
2564 %in c-Si
2565 %\end{center}
2566 %\end{minipage}
2567 %}
2568 %\end{picture}
2569
2570 \begin{pspicture}(0,0)(0,0)
2571 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2572 \begin{minipage}{10cm}
2573 \small
2574 {\color{blue}\bf Stretched SiC in c-Si}
2575 \begin{itemize}
2576 \item Consistent to precipitation model involving \cs{}
2577 \item Explains annealing behavior of high/low T C implants
2578       \begin{itemize}
2579        \item Low T: highly mobiel \ci{}
2580        \item High T: stable configurations of \cs{}
2581       \end{itemize}
2582 \end{itemize}
2583 $\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2584 $\Rightarrow$ Precipitation mechanism involving \cs{}
2585 \end{minipage}
2586  }}}
2587 \end{pspicture}
2588
2589 \end{slide}
2590
2591 \begin{slide}
2592
2593  {\large\bf
2594   Increased temperature simulations at high C concentration
2595  }
2596
2597 \footnotesize
2598
2599 \begin{minipage}{6.5cm}
2600 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2601 \end{minipage}
2602 \begin{minipage}{6.5cm}
2603 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2604 \end{minipage}
2605
2606 \vspace{0.1cm}
2607
2608 \scriptsize
2609
2610 \framebox{
2611 \begin{minipage}[t]{6.0cm}
2612 0.186 nm: Si-C pairs $\uparrow$\\
2613 (as expected in 3C-SiC)\\[0.2cm]
2614 0.282 nm: Si-C-C\\[0.2cm]
2615 $\approx$0.35 nm: C-Si-Si
2616 \end{minipage}
2617 }
2618 \begin{minipage}{0.2cm}
2619 \hfill
2620 \end{minipage}
2621 \framebox{
2622 \begin{minipage}[t]{6.0cm}
2623 0.15 nm: C-C pairs $\uparrow$\\
2624 (as expected in graphite/diamond)\\[0.2cm]
2625 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2626 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2627 \end{minipage}
2628 }
2629
2630 \begin{itemize}
2631 \item Decreasing cut-off artifact
2632 \item {\color{red}Amorphous} SiC-like phase remains
2633 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2634 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2635 \end{itemize}
2636
2637 \vspace{-0.1cm}
2638
2639 \begin{center}
2640 {\color{blue}
2641 \framebox{
2642 {\color{black}
2643 High C \& small $V$ \& short $t$
2644 $\Rightarrow$
2645 }
2646 Slow restructuring due to strong C-C bonds
2647 {\color{black}
2648 $\Leftarrow$
2649 High C \& low T implants
2650 }
2651 }
2652 }
2653 \end{center}
2654
2655 \end{slide}
2656
2657 \begin{slide}
2658
2659  {\large\bf
2660   Summary and Conclusions
2661  }
2662
2663  \scriptsize
2664
2665 %\vspace{0.1cm}
2666
2667 \framebox{
2668 \begin{minipage}[t]{12.9cm}
2669  \underline{Pecipitation simulations}
2670  \begin{itemize}
2671   \item High C concentration $\rightarrow$ amorphous SiC like phase
2672   \item Problem of potential enhanced slow phase space propagation
2673   \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2674   \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2675   \item High T necessary to simulate IBS conditions (far from equilibrium)
2676   \item Precipitation by successive agglomeration of \cs (epitaxy)
2677   \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2678         (stretched SiC, interface)
2679  \end{itemize}
2680 \end{minipage}
2681 }
2682
2683 %\vspace{0.1cm}
2684
2685 \framebox{
2686 \begin{minipage}{12.9cm}
2687  \underline{Defects}
2688  \begin{itemize}
2689    \item DFT / EA
2690         \begin{itemize}
2691          \item Point defects excellently / fairly well described
2692                by DFT / EA
2693          \item C$_{\text{sub}}$ drastically underestimated by EA
2694          \item EA predicts correct ground state:
2695                C$_{\text{sub}}$ \& \si{} $>$ \ci{}
2696          \item Identified migration path explaining
2697                diffusion and reorientation experiments by DFT
2698          \item EA fails to describe \ci{} migration:
2699                Wrong path \& overestimated barrier
2700         \end{itemize}
2701    \item Combinations of defects
2702          \begin{itemize}
2703           \item Agglomeration of point defects energetically favorable
2704                 by compensation of stress
2705           \item Formation of C-C unlikely
2706           \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2707           \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2708                 Low barrier (\unit[0.77]{eV}) \& low capture radius
2709         \end{itemize}
2710  \end{itemize}
2711 \end{minipage}
2712 }
2713
2714 \begin{center}
2715 {\color{blue}
2716 \framebox{Precipitation by successive agglomeration of \cs{}}
2717 }
2718 \end{center}
2719
2720 \end{slide}
2721
2722 \begin{slide}
2723
2724  {\large\bf
2725   Acknowledgements
2726  }
2727
2728  \vspace{0.1cm}
2729
2730  \small
2731
2732  Thanks to \ldots
2733
2734  \underline{Augsburg}
2735  \begin{itemize}
2736   \item Prof. B. Stritzker (accomodation at EP \RM{4})
2737   \item Ralf Utermann (EDV)
2738  \end{itemize}
2739
2740  \underline{Helsinki}
2741  \begin{itemize}
2742   \item Prof. K. Nordlund (MD)
2743  \end{itemize}
2744
2745  \underline{Munich}
2746  \begin{itemize}
2747   \item Bayerische Forschungsstiftung (financial support)
2748  \end{itemize}
2749
2750  \underline{Paderborn}
2751  \begin{itemize}
2752   \item Prof. J. Lindner (SiC)
2753   \item Prof. G. Schmidt (DFT + financial support)
2754   \item Dr. E. Rauls (DFT + SiC)
2755   \item Dr. S. Sanna (VASP)
2756  \end{itemize}
2757
2758 \vspace{0.2cm}
2759
2760 \begin{center}
2761 \framebox{
2762 \bf Thank you for your attention!
2763 }
2764 \end{center}
2765
2766 \end{slide}
2767
2768 \end{document}
2769
2770 \fi