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}{l r}
1011 \hline
1012 Basics & Details\\
1013 \hline
1014 Microscopic description of N particle system & \\
1015 Analytical interaction potential & Tersoff-like bond order potential (Erhart/Albe) \\
1016 Numerical integration using Newtons equation of motion as a propagation rule in 6N-dimensional phase space & Velocity Verlet | timestep: \unit[1]{fs} \\
1017 Observables obtained by time and/or ensemble averages & NpT (isothermal-isobaric)\\
1018 %\begin{itemize}
1019 %\item Berendsen thermostat:
1020 %      $\tau_{\text{T}}=100\text{ fs}$
1021 %\item Berendsen barostat:\\
1022 %      $\tau_{\text{P}}=100\text{ fs}$,
1023 %      $\beta^{-1}=100\text{ GPa}$
1024 %\end{itemize}\\
1025 \hline
1026 \end{tabular}
1027
1028  \begin{itemize}
1029   \item Microscopic description of N particle system
1030   \item Analytical interaction potential
1031   \item Numerical integration using Newtons equation of motion\\
1032         as a propagation rule in 6N-dimensional phase space
1033   \item Observables obtained by time and/or ensemble averages
1034  \end{itemize}
1035  {\bf Details of the simulation:}
1036  \begin{itemize}
1037   \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
1038   \item Ensemble: NpT (isothermal-isobaric)
1039         \begin{itemize}
1040          \item Berendsen thermostat:
1041                $\tau_{\text{T}}=100\text{ fs}$
1042          \item Berendsen barostat:\\
1043                $\tau_{\text{P}}=100\text{ fs}$,
1044                $\beta^{-1}=100\text{ GPa}$
1045         \end{itemize}
1046   \item Erhart/Albe potential: Tersoff-like bond order potential
1047   \vspace*{12pt}
1048         \[
1049         E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
1050         \pot_{ij} = {\color{red}f_C(r_{ij})}
1051         \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
1052         \]
1053  \end{itemize}
1054
1055  \begin{picture}(0,0)(-230,-30)
1056   \includegraphics[width=5cm]{tersoff_angle.eps}
1057  \end{picture}
1058
1059 \end{slide}
1060
1061 \end{document}
1062 \ifnum1=0
1063
1064 \begin{slide}
1065
1066  {\large\bf
1067   Density functional theory (DFT) calculations
1068  }
1069
1070  \small
1071
1072  Basic ingredients necessary for DFT
1073
1074  \begin{itemize}
1075   \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
1076         \begin{itemize}
1077          \item ... uniquely determines the ground state potential
1078                / wavefunctions
1079          \item ... minimizes the systems total energy
1080         \end{itemize}
1081   \item \underline{Born-Oppenheimer}
1082         - $N$ moving electrons in an external potential of static nuclei
1083 \[
1084 H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
1085               +\sum_i^N V_{\text{ext}}(r_i)
1086               +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
1087 \]
1088   \item \underline{Effective potential}
1089         - averaged electrostatic potential \& exchange and correlation
1090 \[
1091 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
1092                  +V_{\text{XC}}[n(r)]
1093 \]
1094   \item \underline{Kohn-Sham system}
1095         - Schr\"odinger equation of N non-interacting particles
1096 \[
1097 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
1098 =\epsilon_i\Phi_i(r)
1099 \quad
1100 \Rightarrow
1101 \quad
1102 n(r)=\sum_i^N|\Phi_i(r)|^2
1103 \]
1104   \item \underline{Self-consistent solution}\\
1105 $n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
1106 which in turn depends on $n(r)$
1107   \item \underline{Variational principle}
1108         - minimize total energy with respect to $n(r)$
1109  \end{itemize}
1110
1111 \end{slide}
1112
1113 \begin{slide}
1114
1115  {\large\bf
1116   Density functional theory (DFT) calculations
1117  }
1118
1119  \small
1120
1121  \vspace*{0.2cm}
1122
1123  Details of applied DFT calculations in this work
1124
1125  \begin{itemize}
1126   \item \underline{Exchange correlation functional}
1127         - approximations for the inhomogeneous electron gas
1128         \begin{itemize}
1129          \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
1130          \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
1131         \end{itemize}
1132   \item \underline{Plane wave basis set}
1133         - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
1134 \[
1135 \rightarrow
1136 \text{Fourier series: } \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r), \quad E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}
1137 \qquad ({\color{blue}300\text{ eV}})
1138 \]
1139   \item \underline{Brillouin zone sampling} -
1140         {\color{blue}$\Gamma$-point only} calculations
1141   \item \underline{Pseudo potential}
1142         - consider only the valence electrons
1143   \item \underline{Code} - VASP 4.6
1144  \end{itemize}
1145
1146  \vspace*{0.2cm}
1147
1148  MD and structural optimization
1149
1150  \begin{itemize}
1151   \item MD integration: Gear predictor corrector algorithm
1152   \item Pressure control: Parrinello-Rahman pressure control
1153   \item Structural optimization: Conjugate gradient method
1154  \end{itemize}
1155
1156 \begin{pspicture}(0,0)(0,0)
1157 \psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
1158 \end{pspicture}
1159
1160 \end{slide}
1161
1162 \begin{slide}
1163
1164  {\large\bf
1165   C and Si self-interstitial point defects in silicon
1166  }
1167
1168  \small
1169
1170  \vspace*{0.3cm}
1171
1172 \begin{minipage}{8cm}
1173 Procedure:\\[0.3cm]
1174   \begin{pspicture}(0,0)(7,5)
1175   \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1176    \parbox{7cm}{
1177    \begin{itemize}
1178     \item Creation of c-Si simulation volume
1179     \item Periodic boundary conditions
1180     \item $T=0\text{ K}$, $p=0\text{ bar}$
1181    \end{itemize}
1182   }}}}
1183 \rput(3.5,2.1){\rnode{insert}{\psframebox{
1184  \parbox{7cm}{
1185   \begin{center}
1186   Insertion of interstitial C/Si atoms
1187   \end{center}
1188   }}}}
1189   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1190    \parbox{7cm}{
1191    \begin{center}
1192    Relaxation / structural energy minimization
1193    \end{center}
1194   }}}}
1195   \ncline[]{->}{init}{insert}
1196   \ncline[]{->}{insert}{cool}
1197  \end{pspicture}
1198 \end{minipage}
1199 \begin{minipage}{5cm}
1200   \includegraphics[width=5cm]{unit_cell_e.eps}\\
1201 \end{minipage}
1202
1203 \begin{minipage}{9cm}
1204  \begin{tabular}{l c c}
1205  \hline
1206  & size [unit cells] & \# atoms\\
1207 \hline
1208 VASP & $3\times 3\times 3$ & $216\pm 1$ \\
1209 Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
1210 \hline
1211  \end{tabular}
1212 \end{minipage}
1213 \begin{minipage}{4cm}
1214 {\color{red}$\bullet$} Tetrahedral\\
1215 {\color{green}$\bullet$} Hexagonal\\
1216 {\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
1217 {\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
1218 {\color{cyan}$\bullet$} Bond-centered\\
1219 {\color{black}$\bullet$} Vacancy / Substitutional
1220 \end{minipage}
1221
1222 \end{slide}
1223
1224 \begin{slide}
1225
1226  \footnotesize
1227
1228 \begin{minipage}{9.5cm}
1229
1230  {\large\bf
1231   Si self-interstitial point defects in silicon\\
1232  }
1233
1234 \begin{tabular}{l c c c c c}
1235 \hline
1236  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
1237 \hline
1238  VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
1239  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
1240 \hline
1241 \end{tabular}\\[0.2cm]
1242
1243 \begin{minipage}{4.7cm}
1244 \includegraphics[width=4.7cm]{e_kin_si_hex.ps}
1245 \end{minipage}
1246 \begin{minipage}{4.7cm}
1247 \begin{center}
1248 {\tiny nearly T $\rightarrow$ T}\\
1249 \end{center}
1250 \includegraphics[width=4.7cm]{nhex_tet.ps}
1251 \end{minipage}\\
1252
1253 \underline{Hexagonal} \hspace{2pt}
1254 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
1255 \framebox{
1256 \begin{minipage}{2.7cm}
1257 $E_{\text{f}}^*=4.48\text{ eV}$\\
1258 \includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
1259 \end{minipage}
1260 \begin{minipage}{0.4cm}
1261 \begin{center}
1262 $\Rightarrow$
1263 \end{center}
1264 \end{minipage}
1265 \begin{minipage}{2.7cm}
1266 $E_{\text{f}}=3.96\text{ eV}$\\
1267 \includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
1268 \end{minipage}
1269 }
1270 \begin{minipage}{2.9cm}
1271 \begin{flushright}
1272 \underline{Vacancy}\\
1273 \includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
1274 \end{flushright}
1275 \end{minipage}
1276
1277 \end{minipage}
1278 \begin{minipage}{3.5cm}
1279
1280 \begin{flushright}
1281 \underline{\hkl<1 1 0> dumbbell}\\
1282 \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
1283 \underline{Tetrahedral}\\
1284 \includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
1285 \underline{\hkl<1 0 0> dumbbell}\\
1286 \includegraphics[width=3.0cm]{si_pd_albe/100.eps}
1287 \end{flushright}
1288
1289 \end{minipage}
1290
1291 \end{slide}
1292
1293 \begin{slide}
1294
1295 \footnotesize
1296
1297  {\large\bf
1298   C interstitial point defects in silicon\\[-0.1cm]
1299  }
1300
1301 \begin{tabular}{l c c c c c c r}
1302 \hline
1303  $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\
1304 \hline
1305  VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1306  Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1307 \hline
1308 \end{tabular}\\[0.1cm]
1309
1310 \framebox{
1311 \begin{minipage}{2.7cm}
1312 \underline{Hexagonal} \hspace{2pt}
1313 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1314 $E_{\text{f}}^*=9.05\text{ eV}$\\
1315 \includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
1316 \end{minipage}
1317 \begin{minipage}{0.4cm}
1318 \begin{center}
1319 $\Rightarrow$
1320 \end{center}
1321 \end{minipage}
1322 \begin{minipage}{2.7cm}
1323 \underline{\hkl<1 0 0>}\\
1324 $E_{\text{f}}=3.88\text{ eV}$\\
1325 \includegraphics[width=2.7cm]{c_pd_albe/100.eps}
1326 \end{minipage}
1327 }
1328 \begin{minipage}{2cm}
1329 \hfill
1330 \end{minipage}
1331 \begin{minipage}{3cm}
1332 \begin{flushright}
1333 \underline{Tetrahedral}\\
1334 \includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
1335 \end{flushright}
1336 \end{minipage}
1337
1338 \framebox{
1339 \begin{minipage}{2.7cm}
1340 \underline{Bond-centered}\\
1341 $E_{\text{f}}^*=5.59\text{ eV}$\\
1342 \includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
1343 \end{minipage}
1344 \begin{minipage}{0.4cm}
1345 \begin{center}
1346 $\Rightarrow$
1347 \end{center}
1348 \end{minipage}
1349 \begin{minipage}{2.7cm}
1350 \underline{\hkl<1 1 0> dumbbell}\\
1351 $E_{\text{f}}=5.18\text{ eV}$\\
1352 \includegraphics[width=2.7cm]{c_pd_albe/110.eps}
1353 \end{minipage}
1354 }
1355 \begin{minipage}{2cm}
1356 \hfill
1357 \end{minipage}
1358 \begin{minipage}{3cm}
1359 \begin{flushright}
1360 \underline{Substitutional}\\
1361 \includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
1362 \end{flushright}
1363 \end{minipage}
1364
1365 \end{slide}
1366
1367 \begin{slide}
1368
1369 \footnotesize
1370
1371  {\large\bf\boldmath
1372   C \hkl<1 0 0> dumbbell interstitial configuration\\
1373  }
1374
1375 {\tiny
1376 \begin{tabular}{l c c c c c c c c}
1377 \hline
1378  Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
1379 \hline
1380 Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
1381 VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
1382 \hline
1383 \end{tabular}\\[0.2cm]
1384 \begin{tabular}{l c c c c }
1385 \hline
1386  Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
1387 \hline
1388 Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
1389 VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
1390 \hline
1391 \end{tabular}\\[0.2cm]
1392 \begin{tabular}{l c c c}
1393 \hline
1394  Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
1395 \hline
1396 Erhart/Albe & 0.084 & -0.091 & 0.175 \\
1397 VASP & 0.109 & -0.065 & 0.174 \\
1398 \hline
1399 \end{tabular}\\[0.6cm]
1400 }
1401
1402 \begin{minipage}{3.0cm}
1403 \begin{center}
1404 \underline{Erhart/Albe}
1405 \includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
1406 \end{center}
1407 \end{minipage}
1408 \begin{minipage}{3.0cm}
1409 \begin{center}
1410 \underline{VASP}
1411 \includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
1412 \end{center}
1413 \end{minipage}\\
1414
1415 \begin{picture}(0,0)(-185,10)
1416 \includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
1417 \end{picture}
1418 \begin{picture}(0,0)(-280,-150)
1419 \includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
1420 \end{picture}
1421
1422 \begin{pspicture}(0,0)(0,0)
1423 \psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
1424 \psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
1425 \psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
1426 \psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
1427 \end{pspicture}
1428
1429 \end{slide}
1430
1431 \begin{slide}
1432
1433 \small
1434
1435 \begin{minipage}{8.5cm}
1436
1437  {\large\bf
1438   Bond-centered interstitial configuration\\[-0.1cm]
1439  }
1440
1441 \begin{minipage}{3.0cm}
1442 \includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1443 \end{minipage}
1444 \begin{minipage}{5.2cm}
1445 \begin{itemize}
1446  \item Linear Si-C-Si bond
1447  \item Si: one C \& 3 Si neighbours
1448  \item Spin polarized calculations
1449  \item No saddle point!\\
1450        Real local minimum!
1451 \end{itemize}
1452 \end{minipage}
1453
1454 \framebox{
1455  \tiny
1456  \begin{minipage}[t]{6.5cm}
1457   \begin{minipage}[t]{1.2cm}
1458   {\color{red}Si}\\
1459   {\tiny sp$^3$}\\[0.8cm]
1460   \underline{${\color{black}\uparrow}$}
1461   \underline{${\color{black}\uparrow}$}
1462   \underline{${\color{black}\uparrow}$}
1463   \underline{${\color{red}\uparrow}$}\\
1464   sp$^3$
1465   \end{minipage}
1466   \begin{minipage}[t]{1.4cm}
1467   \begin{center}
1468   {\color{red}M}{\color{blue}O}\\[0.8cm]
1469   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1470   $\sigma_{\text{ab}}$\\[0.5cm]
1471   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1472   $\sigma_{\text{b}}$
1473   \end{center}
1474   \end{minipage}
1475   \begin{minipage}[t]{1.0cm}
1476   \begin{center}
1477   {\color{blue}C}\\
1478   {\tiny sp}\\[0.2cm]
1479   \underline{${\color{white}\uparrow\uparrow}$}
1480   \underline{${\color{white}\uparrow\uparrow}$}\\
1481   2p\\[0.4cm]
1482   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1483   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1484   sp
1485   \end{center}
1486   \end{minipage}
1487   \begin{minipage}[t]{1.4cm}
1488   \begin{center}
1489   {\color{blue}M}{\color{green}O}\\[0.8cm]
1490   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1491   $\sigma_{\text{ab}}$\\[0.5cm]
1492   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1493   $\sigma_{\text{b}}$
1494   \end{center}
1495   \end{minipage}
1496   \begin{minipage}[t]{1.2cm}
1497   \begin{flushright}
1498   {\color{green}Si}\\
1499   {\tiny sp$^3$}\\[0.8cm]
1500   \underline{${\color{green}\uparrow}$}
1501   \underline{${\color{black}\uparrow}$}
1502   \underline{${\color{black}\uparrow}$}
1503   \underline{${\color{black}\uparrow}$}\\
1504   sp$^3$
1505   \end{flushright}
1506   \end{minipage}
1507  \end{minipage}
1508 }\\[0.1cm]
1509
1510 \framebox{
1511 \begin{minipage}{4.5cm}
1512 \includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
1513 \end{minipage}
1514 \begin{minipage}{3.5cm}
1515 {\color{gray}$\bullet$} Spin up\\
1516 {\color{green}$\bullet$} Spin down\\
1517 {\color{blue}$\bullet$} Resulting spin up\\
1518 {\color{yellow}$\bullet$} Si atoms\\
1519 {\color{red}$\bullet$} C atom
1520 \end{minipage}
1521 }
1522
1523 \end{minipage}
1524 \begin{minipage}{4.2cm}
1525 \begin{flushright}
1526 \includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
1527 {\color{green}$\Box$} {\tiny unoccupied}\\
1528 {\color{red}$\bullet$} {\tiny occupied}
1529 \end{flushright}
1530 \end{minipage}
1531
1532 \end{slide}
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  {\small Investigated pathways}
1543
1544 \begin{minipage}{8.5cm}
1545 \begin{minipage}{8.3cm}
1546 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
1547 \begin{minipage}{2.4cm}
1548 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1549 \end{minipage}
1550 \begin{minipage}{0.4cm}
1551 $\rightarrow$
1552 \end{minipage}
1553 \begin{minipage}{2.4cm}
1554 \includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
1555 \end{minipage}
1556 \begin{minipage}{0.4cm}
1557 $\rightarrow$
1558 \end{minipage}
1559 \begin{minipage}{2.4cm}
1560 \includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
1561 \end{minipage}
1562 \end{minipage}\\
1563 \begin{minipage}{8.3cm}
1564 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
1565 \begin{minipage}{2.4cm}
1566 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1567 \end{minipage}
1568 \begin{minipage}{0.4cm}
1569 $\rightarrow$
1570 \end{minipage}
1571 \begin{minipage}{2.4cm}
1572 \includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
1573 \end{minipage}
1574 \begin{minipage}{0.4cm}
1575 $\rightarrow$
1576 \end{minipage}
1577 \begin{minipage}{2.4cm}
1578 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
1579 \end{minipage}
1580 \end{minipage}\\
1581 \begin{minipage}{8.3cm}
1582 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
1583 \begin{minipage}{2.4cm}
1584 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1585 \end{minipage}
1586 \begin{minipage}{0.4cm}
1587 $\rightarrow$
1588 \end{minipage}
1589 \begin{minipage}{2.4cm}
1590 \includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
1591 \end{minipage}
1592 \begin{minipage}{0.4cm}
1593 $\rightarrow$
1594 \end{minipage}
1595 \begin{minipage}{2.4cm}
1596 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
1597 \end{minipage}
1598 \end{minipage}
1599 \end{minipage}
1600 \framebox{
1601 \begin{minipage}{4.2cm}
1602  {\small Constrained relaxation\\
1603          technique (CRT) method}\\
1604 \includegraphics[width=4cm]{crt_orig.eps}
1605 \begin{itemize}
1606  \item Constrain diffusing atom
1607  \item Static constraints
1608 \end{itemize}
1609 \vspace*{0.3cm}
1610  {\small Modifications}\\
1611 \includegraphics[width=4cm]{crt_mod.eps}
1612 \begin{itemize}
1613  \item Constrain all atoms
1614  \item Update individual\\
1615        constraints
1616 \end{itemize}
1617 \end{minipage}
1618 }
1619
1620 \end{slide}
1621
1622 \begin{slide}
1623
1624  {\large\bf\boldmath
1625   Migration of the C \hkl<1 0 0> dumbbell interstitial
1626  }
1627
1628 \scriptsize
1629
1630 \framebox{
1631 \begin{minipage}{5.9cm}
1632 \begin{flushleft}
1633 \includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
1634 \end{flushleft}
1635 \begin{center}
1636 \begin{picture}(0,0)(60,0)
1637 \includegraphics[width=1cm]{vasp_mig/00-1.eps}
1638 \end{picture}
1639 \begin{picture}(0,0)(-5,0)
1640 \includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
1641 \end{picture}
1642 \begin{picture}(0,0)(-55,0)
1643 \includegraphics[width=1cm]{vasp_mig/bc.eps}
1644 \end{picture}
1645 \begin{picture}(0,0)(12.5,10)
1646 \includegraphics[width=1cm]{110_arrow.eps}
1647 \end{picture}
1648 \begin{picture}(0,0)(90,0)
1649 \includegraphics[height=0.9cm]{001_arrow.eps}
1650 \end{picture}
1651 \end{center}
1652 \vspace*{0.35cm}
1653 \end{minipage}
1654 }
1655 \begin{minipage}{0.3cm}
1656 \hfill
1657 \end{minipage}
1658 \framebox{
1659 \begin{minipage}{5.9cm}
1660 \begin{flushright}
1661 \includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
1662 \end{flushright}
1663 \begin{center}
1664 \begin{picture}(0,0)(60,0)
1665 \includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
1666 \end{picture}
1667 \begin{picture}(0,0)(5,0)
1668 \includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
1669 \end{picture}
1670 \begin{picture}(0,0)(-55,0)
1671 \includegraphics[width=1cm]{vasp_mig/0-10.eps}
1672 \end{picture}
1673 \begin{picture}(0,0)(12.5,10)
1674 \includegraphics[width=1cm]{100_arrow.eps}
1675 \end{picture}
1676 \begin{picture}(0,0)(90,0)
1677 \includegraphics[height=0.9cm]{001_arrow.eps}
1678 \end{picture}
1679 \end{center}
1680 \vspace*{0.3cm}
1681 \end{minipage}\\
1682 }
1683
1684 \vspace*{0.05cm}
1685
1686 \framebox{
1687 \begin{minipage}{5.9cm}
1688 \begin{flushleft}
1689 \includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
1690 \end{flushleft}
1691 \begin{center}
1692 \begin{picture}(0,0)(60,0)
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1694 \end{picture}
1695 \begin{picture}(0,0)(10,0)
1696 \includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
1697 \end{picture}
1698 \begin{picture}(0,0)(-60,0)
1699 \includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps}
1700 \end{picture}
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1702 \includegraphics[width=1cm]{100_arrow.eps}
1703 \end{picture}
1704 \begin{picture}(0,0)(90,0)
1705 \includegraphics[height=0.9cm]{001_arrow.eps}
1706 \end{picture}
1707 \end{center}
1708 \vspace*{0.3cm}
1709 \end{minipage}
1710 }
1711 \begin{minipage}{0.3cm}
1712 \hfill
1713 \end{minipage}
1714 \begin{minipage}{6.5cm}
1715 VASP results
1716 \begin{itemize}
1717  \item Energetically most favorable path
1718        \begin{itemize}
1719         \item Path 2
1720         \item Activation energy: $\approx$ 0.9 eV
1721         \item Experimental values: 0.73 ... 0.87 eV
1722        \end{itemize}
1723        $\Rightarrow$ {\color{blue}Diffusion} path identified!
1724  \item Reorientation (path 3)
1725        \begin{itemize}
1726         \item More likely composed of two consecutive steps of type 2
1727         \item Experimental values: 0.77 ... 0.88 eV
1728        \end{itemize}
1729        $\Rightarrow$ {\color{blue}Reorientation} transition identified!
1730 \end{itemize}
1731 \end{minipage}
1732
1733 \end{slide}
1734
1735 \begin{slide}
1736
1737  {\large\bf\boldmath
1738   Migration of the C \hkl<1 0 0> dumbbell interstitial
1739  }
1740
1741 \scriptsize
1742
1743  \vspace{0.1cm}
1744
1745 \begin{minipage}{6.5cm}
1746
1747 \framebox{
1748 \begin{minipage}[t]{5.9cm}
1749 \begin{flushleft}
1750 \includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
1751 \end{flushleft}
1752 \begin{center}
1753 \begin{pspicture}(0,0)(0,0)
1754 \psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
1755 \end{pspicture}
1756 \begin{picture}(0,0)(60,-50)
1757 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
1758 \end{picture}
1759 \begin{picture}(0,0)(5,-50)
1760 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
1761 \end{picture}
1762 \begin{picture}(0,0)(-55,-50)
1763 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
1764 \end{picture}
1765 \begin{picture}(0,0)(12.5,-40)
1766 \includegraphics[width=1cm]{110_arrow.eps}
1767 \end{picture}
1768 \begin{picture}(0,0)(90,-45)
1769 \includegraphics[height=0.9cm]{001_arrow.eps}
1770 \end{picture}\\
1771 \begin{pspicture}(0,0)(0,0)
1772 \psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
1773 \end{pspicture}
1774 \begin{picture}(0,0)(60,-15)
1775 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
1776 \end{picture}
1777 \begin{picture}(0,0)(35,-15)
1778 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
1779 \end{picture}
1780 \begin{picture}(0,0)(-5,-15)
1781 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
1782 \end{picture}
1783 \begin{picture}(0,0)(-55,-15)
1784 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
1785 \end{picture}
1786 \begin{picture}(0,0)(12.5,-5)
1787 \includegraphics[width=1cm]{100_arrow.eps}
1788 \end{picture}
1789 \begin{picture}(0,0)(90,-15)
1790 \includegraphics[height=0.9cm]{010_arrow.eps}
1791 \end{picture}
1792 \end{center}
1793 \end{minipage}
1794 }\\[0.1cm]
1795
1796 \begin{minipage}{5.9cm}
1797 Erhart/Albe results
1798 \begin{itemize}
1799  \item Lowest activation energy: $\approx$ 2.2 eV
1800  \item 2.4 times higher than VASP
1801  \item Different pathway
1802 \end{itemize}
1803 \end{minipage}
1804
1805 \end{minipage}
1806 \begin{minipage}{6.5cm}
1807
1808 \framebox{
1809 \begin{minipage}{5.9cm}
1810 %\begin{flushright}
1811 %\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
1812 %\end{flushright}
1813 %\begin{center}
1814 %\begin{pspicture}(0,0)(0,0)
1815 %\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
1816 %\end{pspicture}
1817 %\begin{picture}(0,0)(60,-5)
1818 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
1819 %\end{picture}
1820 %\begin{picture}(0,0)(0,-5)
1821 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
1822 %\end{picture}
1823 %\begin{picture}(0,0)(-55,-5)
1824 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
1825 %\end{picture}
1826 %\begin{picture}(0,0)(12.5,5)
1827 %\includegraphics[width=1cm]{100_arrow.eps}
1828 %\end{picture}
1829 %\begin{picture}(0,0)(90,0)
1830 %\includegraphics[height=0.9cm]{001_arrow.eps}
1831 %\end{picture}
1832 %\end{center}
1833 %\vspace{0.2cm}
1834 %\end{minipage}
1835 %}\\[0.2cm]
1836 %
1837 %\framebox{
1838 %\begin{minipage}{5.9cm}
1839 \includegraphics[width=5.9cm]{00-1_110_0-10_mig_albe.ps}
1840 \end{minipage}
1841 }\\[0.1cm]
1842
1843 \begin{minipage}{5.9cm}
1844 Transition involving \ci{} \hkl<1 1 0>
1845 \begin{itemize}
1846  \item Bond-centered configuration unstable\\
1847        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1848  \item Transition minima of path 2 \& 3\\
1849        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1850  \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV
1851  \item 2.4 - 3.4 times higher than VASP
1852  \item Rotation of dumbbell orientation
1853 \end{itemize}
1854 \vspace{0.1cm}
1855 \begin{center}
1856 {\color{blue}Overestimated diffusion barrier}
1857 \end{center}
1858 \end{minipage}
1859
1860 \end{minipage}
1861
1862 \end{slide}
1863
1864 \begin{slide}
1865
1866  {\large\bf\boldmath
1867   Combinations with a C-Si \hkl<1 0 0>-type interstitial
1868  }
1869
1870 \small
1871
1872 \vspace*{0.1cm}
1873
1874 Binding energy:
1875 $
1876 E_{\text{b}}=
1877 E_{\text{f}}^{\text{defect combination}}-
1878 E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
1879 E_{\text{f}}^{\text{2nd defect}}
1880 $
1881
1882 \vspace*{0.1cm}
1883
1884 {\scriptsize
1885 \begin{tabular}{l c c c c c c}
1886 \hline
1887  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1888  \hline
1889  \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1890  \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1891  \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}\\
1892  \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}\\
1893  \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}\\
1894  \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}\\
1895  \hline
1896  C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1897  Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1898 \hline
1899 \end{tabular}
1900 }
1901
1902 \vspace*{0.3cm}
1903
1904 \footnotesize
1905
1906 \begin{minipage}[t]{3.8cm}
1907 \underline{\hkl<1 0 0> at position 1}\\[0.1cm]
1908 \includegraphics[width=3.5cm]{00-1dc/2-25.eps}
1909 \end{minipage}
1910 \begin{minipage}[t]{3.5cm}
1911 \underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
1912 \includegraphics[width=3.2cm]{00-1dc/2-39.eps}
1913 \end{minipage}
1914 \begin{minipage}[t]{5.5cm}
1915 \begin{itemize}
1916  \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\
1917        $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
1918  \item Stress compensation / increase
1919  \item Unfavored: antiparallel orientations
1920  \item Indication of energetically favored\\
1921        agglomeration
1922  \item Most favorable: C clustering
1923  \item However: High barrier ($>4\,\text{eV}$)
1924  \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$
1925        (Entropy)
1926 \end{itemize}
1927 \end{minipage}
1928
1929 \begin{picture}(0,0)(-295,-130)
1930 \includegraphics[width=3.5cm]{comb_pos.eps}
1931 \end{picture}
1932
1933 \end{slide}
1934
1935 \begin{slide}
1936
1937  {\large\bf\boldmath
1938   Combinations of C-Si \hkl<1 0 0>-type interstitials
1939  }
1940
1941 \small
1942
1943 \vspace*{0.1cm}
1944
1945 Energetically most favorable combinations along \hkl<1 1 0>
1946
1947 \vspace*{0.1cm}
1948
1949 {\scriptsize
1950 \begin{tabular}{l c c c c c c}
1951 \hline
1952  & 1 & 2 & 3 & 4 & 5 & 6\\
1953 \hline
1954 $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
1955 C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
1956 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>\\
1957 \hline
1958 \end{tabular}
1959 }
1960
1961 \vspace*{0.3cm}
1962
1963 \begin{minipage}{7.0cm}
1964 \includegraphics[width=7cm]{db_along_110_cc.ps}
1965 \end{minipage}
1966 \begin{minipage}{6.0cm}
1967 \begin{itemize}
1968  \item Interaction proportional to reciprocal cube of C-C distance
1969  \item Saturation in the immediate vicinity
1970  \renewcommand\labelitemi{$\Rightarrow$}
1971  \item Agglomeration of \ci{} expected
1972  \item Absence of C clustering
1973 \end{itemize}
1974 \begin{center}
1975 {\color{blue}
1976  Consisten with initial precipitation model
1977 }
1978 \end{center}
1979 \end{minipage}
1980
1981 \vspace{0.2cm}
1982
1983 \end{slide}
1984
1985 \begin{slide}
1986
1987  {\large\bf\boldmath
1988   Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
1989  }
1990
1991  \scriptsize
1992
1993 %\begin{center}
1994 %\begin{minipage}{3.2cm}
1995 %\includegraphics[width=3cm]{sub_110_combo.eps}
1996 %\end{minipage}
1997 %\begin{minipage}{7.8cm}
1998 %\begin{tabular}{l c c c c c c}
1999 %\hline
2000 %C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
2001 %                   \hkl<1 0 1> & \hkl<-1 0 1> \\
2002 %\hline
2003 %1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
2004 %2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
2005 %3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
2006 %4 & \RM{4} & B & D & E & E & D \\
2007 %5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
2008 %\hline
2009 %\end{tabular}
2010 %\end{minipage}
2011 %\end{center}
2012
2013 %\begin{center}
2014 %\begin{tabular}{l c c c c c c c c c c}
2015 %\hline
2016 %Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
2017 %\hline
2018 %$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
2019 %$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
2020 %$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
2021 %\hline
2022 %\end{tabular}
2023 %\end{center}
2024
2025 \begin{minipage}{6.0cm}
2026 \includegraphics[width=5.8cm]{c_sub_si110.ps}
2027 \end{minipage}
2028 \begin{minipage}{7cm}
2029 \scriptsize
2030 \begin{itemize}
2031  \item IBS: C may displace Si\\
2032        $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
2033  \item Assumption:\\
2034        \hkl<1 1 0>-type $\rightarrow$ favored combination
2035  \renewcommand\labelitemi{$\Rightarrow$}
2036  \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
2037  \item Less favorable than C-Si \hkl<1 0 0> dumbbell
2038  \item Interaction drops quickly to zero\\
2039        $\rightarrow$ low capture radius
2040 \end{itemize}
2041 \begin{center}
2042  {\color{blue}
2043  IBS process far from equilibrium\\
2044  \cs{} \& \si{} instead of thermodynamic ground state
2045  }
2046 \end{center}
2047 \end{minipage}
2048
2049 \begin{minipage}{6.5cm}
2050 \includegraphics[width=6.0cm]{162-097.ps}
2051 \begin{itemize}
2052  \item Low migration barrier
2053 \end{itemize}
2054 \end{minipage}
2055 \begin{minipage}{6.5cm}
2056 \begin{center}
2057 Ab initio MD at \degc{900}\\
2058 \includegraphics[width=3.3cm]{md_vasp_01.eps}
2059 $t=\unit[2230]{fs}$\\
2060 \includegraphics[width=3.3cm]{md_vasp_02.eps}
2061 $t=\unit[2900]{fs}$
2062 \end{center}
2063 {\color{blue}
2064 Contribution of entropy to structural formation
2065 }
2066 \end{minipage}
2067
2068 \end{slide}
2069
2070 \begin{slide}
2071
2072  {\large\bf\boldmath
2073   Migration in C-Si \hkl<1 0 0> and vacancy combinations
2074  }
2075
2076  \footnotesize
2077
2078 \vspace{0.1cm}
2079
2080 \begin{minipage}[t]{3cm}
2081 \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
2082 \includegraphics[width=2.8cm]{00-1dc/0-59.eps}
2083 \end{minipage}
2084 \begin{minipage}[t]{7cm}
2085 \vspace{0.2cm}
2086 \begin{center}
2087  Low activation energies\\
2088  High activation energies for reverse processes\\
2089  $\Downarrow$\\
2090  {\color{blue}C$_{\text{sub}}$ very stable}\\
2091 \vspace*{0.1cm}
2092  \hrule
2093 \vspace*{0.1cm}
2094  Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
2095  $\Downarrow$\\
2096  {\color{blue}Formation of SiC by successive substitution by C}
2097
2098 \end{center}
2099 \end{minipage}
2100 \begin{minipage}[t]{3cm}
2101 \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
2102 \includegraphics[width=2.8cm]{00-1dc/3-14.eps}
2103 \end{minipage}
2104
2105
2106 \framebox{
2107 \begin{minipage}{5.9cm}
2108 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
2109 \begin{center}
2110 \begin{picture}(0,0)(70,0)
2111 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
2112 \end{picture}
2113 \begin{picture}(0,0)(30,0)
2114 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
2115 \end{picture}
2116 \begin{picture}(0,0)(-10,0)
2117 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
2118 \end{picture}
2119 \begin{picture}(0,0)(-48,0)
2120 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
2121 \end{picture}
2122 \begin{picture}(0,0)(12.5,5)
2123 \includegraphics[width=1cm]{100_arrow.eps}
2124 \end{picture}
2125 \begin{picture}(0,0)(97,-10)
2126 \includegraphics[height=0.9cm]{001_arrow.eps}
2127 \end{picture}
2128 \end{center}
2129 \vspace{0.1cm}
2130 \end{minipage}
2131 }
2132 \begin{minipage}{0.3cm}
2133 \hfill
2134 \end{minipage}
2135 \framebox{
2136 \begin{minipage}{5.9cm}
2137 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
2138 \begin{center}
2139 \begin{picture}(0,0)(60,0)
2140 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
2141 \end{picture}
2142 \begin{picture}(0,0)(25,0)
2143 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
2144 \end{picture}
2145 \begin{picture}(0,0)(-20,0)
2146 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
2147 \end{picture}
2148 \begin{picture}(0,0)(-55,0)
2149 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
2150 \end{picture}
2151 \begin{picture}(0,0)(12.5,5)
2152 \includegraphics[width=1cm]{100_arrow.eps}
2153 \end{picture}
2154 \begin{picture}(0,0)(95,0)
2155 \includegraphics[height=0.9cm]{001_arrow.eps}
2156 \end{picture}
2157 \end{center}
2158 \vspace{0.1cm}
2159 \end{minipage}
2160 }
2161
2162 \end{slide}
2163
2164 \begin{slide}
2165
2166  {\large\bf
2167   Conclusion of defect / migration / combined defect simulations
2168  }
2169
2170  \footnotesize
2171
2172 \vspace*{0.1cm}
2173
2174 Defect structures
2175 \begin{itemize}
2176  \item Accurately described by quantum-mechanical simulations
2177  \item Less accurate description by classical potential simulations
2178  \item Underestimated formation energy of \cs{} by classical approach
2179  \item Both methods predict same ground state: \ci{} \hkl<1 0 0> dumbbell
2180 \end{itemize}
2181
2182 Migration
2183 \begin{itemize}
2184  \item C migration pathway in Si identified
2185  \item Consistent with reorientation and diffusion experiments
2186 \end{itemize}
2187 \begin{itemize}
2188  \item Different path and ...
2189  \item overestimated barrier by classical potential calculations
2190 \end{itemize}
2191
2192 Concerning the precipitation mechanism
2193 \begin{itemize}
2194  \item Agglomeration of C-Si dumbbells energetically favorable
2195        (stress compensation)
2196  \item C-Si indeed favored compared to
2197        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2198  \item Possible low interaction capture radius of
2199        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2200  \item Low barrier for
2201        \ci{} \hkl<1 0 0> $\rightarrow$ \cs{} \& \si{} \hkl<1 1 0>
2202  \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
2203        C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
2204 \end{itemize}
2205 \begin{center}
2206 {\color{blue}Results suggest increased participation of \cs}
2207 \end{center}
2208
2209 \end{slide}
2210
2211 \begin{slide}
2212
2213  {\large\bf
2214   Silicon carbide precipitation simulations
2215  }
2216
2217  \small
2218
2219 {\scriptsize
2220  \begin{pspicture}(0,0)(12,6.5)
2221   % nodes
2222   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
2223    \parbox{7cm}{
2224    \begin{itemize}
2225     \item Create c-Si volume
2226     \item Periodc boundary conditions
2227     \item Set requested $T$ and $p=0\text{ bar}$
2228     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
2229    \end{itemize}
2230   }}}}
2231   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
2232    \parbox{7cm}{
2233    Insertion of C atoms at constant T
2234    \begin{itemize}
2235     \item total simulation volume {\pnode{in1}}
2236     \item volume of minimal SiC precipitate {\pnode{in2}}
2237     \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
2238           precipitate
2239    \end{itemize}
2240   }}}}
2241   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
2242    \parbox{7.0cm}{
2243    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
2244   }}}}
2245   \ncline[]{->}{init}{insert}
2246   \ncline[]{->}{insert}{cool}
2247   \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
2248   \rput(7.8,6){\footnotesize $V_1$}
2249   \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
2250   \rput(9.2,4.85){\tiny $V_2$}
2251   \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
2252   \rput(9.55,4.45){\footnotesize $V_3$}
2253   \rput(7.9,3.2){\pnode{ins1}}
2254   \rput(9.22,2.8){\pnode{ins2}}
2255   \rput(11.0,2.4){\pnode{ins3}}
2256   \ncline[]{->}{in1}{ins1}
2257   \ncline[]{->}{in2}{ins2}
2258   \ncline[]{->}{in3}{ins3}
2259  \end{pspicture}
2260 }
2261
2262 \begin{itemize}
2263  \item Restricted to classical potential simulations
2264  \item $V_2$ and $V_3$ considered due to low diffusion
2265  \item Amount of C atoms: 6000
2266        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
2267  \item Simulation volume: $31\times 31\times 31$ unit cells
2268        (238328 Si atoms)
2269 \end{itemize}
2270
2271 \end{slide}
2272
2273 \begin{slide}
2274
2275  {\large\bf\boldmath
2276   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2277  }
2278
2279  \small
2280
2281 \begin{minipage}{6.5cm}
2282 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2283 \end{minipage}
2284 \begin{minipage}{6.5cm}
2285 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2286 \end{minipage}
2287
2288 \begin{minipage}{6.5cm}
2289 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2290 \end{minipage}
2291 \begin{minipage}{6.5cm}
2292 \scriptsize
2293 \underline{Low C concentration ($V_1$)}\\
2294 \hkl<1 0 0> C-Si dumbbell dominated structure
2295 \begin{itemize}
2296  \item Si-C bumbs around 0.19 nm
2297  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2298        concatenated dumbbells of various orientation
2299  \item Si-Si NN distance stretched to 0.3 nm
2300 \end{itemize}
2301 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2302 \underline{High C concentration ($V_2$, $V_3$)}\\
2303 High amount of strongly bound C-C bonds\\
2304 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2305 Only short range order observable\\
2306 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2307 \end{minipage}
2308
2309 \end{slide}
2310
2311 \begin{slide}
2312
2313  {\large\bf\boldmath
2314   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2315  }
2316
2317  \small
2318
2319 \begin{minipage}{6.5cm}
2320 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2321 \end{minipage}
2322 \begin{minipage}{6.5cm}
2323 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2324 \end{minipage}
2325
2326 \begin{minipage}{6.5cm}
2327 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2328 \end{minipage}
2329 \begin{minipage}{6.5cm}
2330 \scriptsize
2331 \underline{Low C concentration ($V_1$)}\\
2332 \hkl<1 0 0> C-Si dumbbell dominated structure
2333 \begin{itemize}
2334  \item Si-C bumbs around 0.19 nm
2335  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2336        concatenated dumbbells of various orientation
2337  \item Si-Si NN distance stretched to 0.3 nm
2338 \end{itemize}
2339 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2340 \underline{High C concentration ($V_2$, $V_3$)}\\
2341 High amount of strongly bound C-C bonds\\
2342 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2343 Only short range order observable\\
2344 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2345 \end{minipage}
2346
2347 \begin{pspicture}(0,0)(0,0)
2348 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2349 \begin{minipage}{10cm}
2350 \small
2351 {\color{red}\bf 3C-SiC formation fails to appear}
2352 \begin{itemize}
2353 \item Low C concentration simulations
2354  \begin{itemize}
2355   \item Formation of \ci{} indeed occurs
2356   \item Agllomeration not observed
2357  \end{itemize}
2358 \item High C concentration simulations
2359  \begin{itemize}
2360   \item Amorphous SiC-like structure\\
2361         (not expected at prevailing temperatures)
2362   \item Rearrangement and transition into 3C-SiC structure missing
2363  \end{itemize}
2364 \end{itemize}
2365 \end{minipage}
2366  }}}
2367 \end{pspicture}
2368
2369 \end{slide}
2370
2371 \begin{slide}
2372
2373  {\large\bf
2374   Limitations of molecular dynamics and short range potentials
2375  }
2376
2377 \footnotesize
2378
2379 \vspace{0.2cm}
2380
2381 \underline{Time scale problem of MD}\\[0.2cm]
2382 Minimize integration error\\
2383 $\Rightarrow$ discretization considerably smaller than
2384               reciprocal of fastest vibrational mode\\[0.1cm]
2385 Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
2386 $\Rightarrow$ suitable choice of time step:
2387               $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
2388 $\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
2389 Several local minima in energy surface separated by large energy barriers\\
2390 $\Rightarrow$ transition event corresponds to a multiple
2391               of vibrational periods\\
2392 $\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
2393               infrequent transition events\\[0.1cm]
2394 {\color{blue}Accelerated methods:}
2395 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
2396
2397 \vspace{0.3cm}
2398
2399 \underline{Limitations related to the short range potential}\\[0.2cm]
2400 Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
2401 and 2$^{\text{nd}}$ next neighbours\\
2402 $\Rightarrow$ overestimated unphysical high forces of next neighbours
2403
2404 \vspace{0.3cm}
2405
2406 \framebox{
2407 \color{red}
2408 Potential enhanced problem of slow phase space propagation
2409 }
2410
2411 \vspace{0.3cm}
2412
2413 \underline{Approach to the (twofold) problem}\\[0.2cm]
2414 Increased temperature simulations without TAD corrections\\
2415 (accelerated methods or higher time scales exclusively not sufficient)
2416
2417 \begin{picture}(0,0)(-260,-30)
2418 \framebox{
2419 \begin{minipage}{4.2cm}
2420 \tiny
2421 \begin{center}
2422 \vspace{0.03cm}
2423 \underline{IBS}
2424 \end{center}
2425 \begin{itemize}
2426 \item 3C-SiC also observed for higher T
2427 \item higher T inside sample
2428 \item structural evolution vs.\\
2429       equilibrium properties
2430 \end{itemize}
2431 \end{minipage}
2432 }
2433 \end{picture}
2434
2435 \begin{picture}(0,0)(-305,-155)
2436 \framebox{
2437 \begin{minipage}{2.5cm}
2438 \tiny
2439 \begin{center}
2440 retain proper\\
2441 thermodynmic sampling
2442 \end{center}
2443 \end{minipage}
2444 }
2445 \end{picture}
2446
2447 \end{slide}
2448
2449 \begin{slide}
2450
2451  {\large\bf
2452   Increased temperature simulations at low C concentration
2453  }
2454
2455 \small
2456
2457 \begin{minipage}{6.5cm}
2458 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2459 \end{minipage}
2460 \begin{minipage}{6.5cm}
2461 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2462 \end{minipage}
2463
2464 \begin{minipage}{6.5cm}
2465 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2466 \end{minipage}
2467 \begin{minipage}{6.5cm}
2468 \scriptsize
2469  \underline{Si-C bonds:}
2470  \begin{itemize}
2471   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2472   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2473  \end{itemize}
2474  \underline{Si-Si bonds:}
2475  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2476  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2477  \underline{C-C bonds:}
2478  \begin{itemize}
2479   \item C-C next neighbour pairs reduced (mandatory)
2480   \item Peak at 0.3 nm slightly shifted
2481         \begin{itemize}
2482          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2483                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2484                combinations (|)\\
2485                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2486                ($\downarrow$)
2487          \item Range [|-$\downarrow$]:
2488                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2489                with nearby Si$_{\text{I}}$}
2490         \end{itemize}
2491  \end{itemize}
2492 \end{minipage}
2493
2494 \begin{picture}(0,0)(-330,-74)
2495 \color{blue}
2496 \framebox{
2497 \begin{minipage}{1.6cm}
2498 \tiny
2499 \begin{center}
2500 stretched SiC\\[-0.1cm]
2501 in c-Si
2502 \end{center}
2503 \end{minipage}
2504 }
2505 \end{picture}
2506
2507 \end{slide}
2508
2509 \begin{slide}
2510
2511  {\large\bf
2512   Increased temperature simulations at low C concentration
2513  }
2514
2515 \small
2516
2517 \begin{minipage}{6.5cm}
2518 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2519 \end{minipage}
2520 \begin{minipage}{6.5cm}
2521 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2522 \end{minipage}
2523
2524 \begin{minipage}{6.5cm}
2525 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2526 \end{minipage}
2527 \begin{minipage}{6.5cm}
2528 \scriptsize
2529  \underline{Si-C bonds:}
2530  \begin{itemize}
2531   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2532   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2533  \end{itemize}
2534  \underline{Si-Si bonds:}
2535  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2536  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2537  \underline{C-C bonds:}
2538  \begin{itemize}
2539   \item C-C next neighbour pairs reduced (mandatory)
2540   \item Peak at 0.3 nm slightly shifted
2541         \begin{itemize}
2542          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2543                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2544                combinations (|)\\
2545                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2546                ($\downarrow$)
2547          \item Range [|-$\downarrow$]:
2548                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2549                with nearby Si$_{\text{I}}$}
2550         \end{itemize}
2551  \end{itemize}
2552 \end{minipage}
2553
2554 %\begin{picture}(0,0)(-330,-74)
2555 %\color{blue}
2556 %\framebox{
2557 %\begin{minipage}{1.6cm}
2558 %\tiny
2559 %\begin{center}
2560 %stretched SiC\\[-0.1cm]
2561 %in c-Si
2562 %\end{center}
2563 %\end{minipage}
2564 %}
2565 %\end{picture}
2566
2567 \begin{pspicture}(0,0)(0,0)
2568 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2569 \begin{minipage}{10cm}
2570 \small
2571 {\color{blue}\bf Stretched SiC in c-Si}
2572 \begin{itemize}
2573 \item Consistent to precipitation model involving \cs{}
2574 \item Explains annealing behavior of high/low T C implants
2575       \begin{itemize}
2576        \item Low T: highly mobiel \ci{}
2577        \item High T: stable configurations of \cs{}
2578       \end{itemize}
2579 \end{itemize}
2580 $\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2581 $\Rightarrow$ Precipitation mechanism involving \cs{}
2582 \end{minipage}
2583  }}}
2584 \end{pspicture}
2585
2586 \end{slide}
2587
2588 \begin{slide}
2589
2590  {\large\bf
2591   Increased temperature simulations at high C concentration
2592  }
2593
2594 \footnotesize
2595
2596 \begin{minipage}{6.5cm}
2597 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2598 \end{minipage}
2599 \begin{minipage}{6.5cm}
2600 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2601 \end{minipage}
2602
2603 \vspace{0.1cm}
2604
2605 \scriptsize
2606
2607 \framebox{
2608 \begin{minipage}[t]{6.0cm}
2609 0.186 nm: Si-C pairs $\uparrow$\\
2610 (as expected in 3C-SiC)\\[0.2cm]
2611 0.282 nm: Si-C-C\\[0.2cm]
2612 $\approx$0.35 nm: C-Si-Si
2613 \end{minipage}
2614 }
2615 \begin{minipage}{0.2cm}
2616 \hfill
2617 \end{minipage}
2618 \framebox{
2619 \begin{minipage}[t]{6.0cm}
2620 0.15 nm: C-C pairs $\uparrow$\\
2621 (as expected in graphite/diamond)\\[0.2cm]
2622 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2623 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2624 \end{minipage}
2625 }
2626
2627 \begin{itemize}
2628 \item Decreasing cut-off artifact
2629 \item {\color{red}Amorphous} SiC-like phase remains
2630 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2631 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2632 \end{itemize}
2633
2634 \vspace{-0.1cm}
2635
2636 \begin{center}
2637 {\color{blue}
2638 \framebox{
2639 {\color{black}
2640 High C \& small $V$ \& short $t$
2641 $\Rightarrow$
2642 }
2643 Slow restructuring due to strong C-C bonds
2644 {\color{black}
2645 $\Leftarrow$
2646 High C \& low T implants
2647 }
2648 }
2649 }
2650 \end{center}
2651
2652 \end{slide}
2653
2654 \begin{slide}
2655
2656  {\large\bf
2657   Summary and Conclusions
2658  }
2659
2660  \scriptsize
2661
2662 %\vspace{0.1cm}
2663
2664 \framebox{
2665 \begin{minipage}[t]{12.9cm}
2666  \underline{Pecipitation simulations}
2667  \begin{itemize}
2668   \item High C concentration $\rightarrow$ amorphous SiC like phase
2669   \item Problem of potential enhanced slow phase space propagation
2670   \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2671   \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2672   \item High T necessary to simulate IBS conditions (far from equilibrium)
2673   \item Precipitation by successive agglomeration of \cs (epitaxy)
2674   \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2675         (stretched SiC, interface)
2676  \end{itemize}
2677 \end{minipage}
2678 }
2679
2680 %\vspace{0.1cm}
2681
2682 \framebox{
2683 \begin{minipage}{12.9cm}
2684  \underline{Defects}
2685  \begin{itemize}
2686    \item DFT / EA
2687         \begin{itemize}
2688          \item Point defects excellently / fairly well described
2689                by DFT / EA
2690          \item C$_{\text{sub}}$ drastically underestimated by EA
2691          \item EA predicts correct ground state:
2692                C$_{\text{sub}}$ \& \si{} $>$ \ci{}
2693          \item Identified migration path explaining
2694                diffusion and reorientation experiments by DFT
2695          \item EA fails to describe \ci{} migration:
2696                Wrong path \& overestimated barrier
2697         \end{itemize}
2698    \item Combinations of defects
2699          \begin{itemize}
2700           \item Agglomeration of point defects energetically favorable
2701                 by compensation of stress
2702           \item Formation of C-C unlikely
2703           \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2704           \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2705                 Low barrier (\unit[0.77]{eV}) \& low capture radius
2706         \end{itemize}
2707  \end{itemize}
2708 \end{minipage}
2709 }
2710
2711 \begin{center}
2712 {\color{blue}
2713 \framebox{Precipitation by successive agglomeration of \cs{}}
2714 }
2715 \end{center}
2716
2717 \end{slide}
2718
2719 \begin{slide}
2720
2721  {\large\bf
2722   Acknowledgements
2723  }
2724
2725  \vspace{0.1cm}
2726
2727  \small
2728
2729  Thanks to \ldots
2730
2731  \underline{Augsburg}
2732  \begin{itemize}
2733   \item Prof. B. Stritzker (accomodation at EP \RM{4})
2734   \item Ralf Utermann (EDV)
2735  \end{itemize}
2736
2737  \underline{Helsinki}
2738  \begin{itemize}
2739   \item Prof. K. Nordlund (MD)
2740  \end{itemize}
2741
2742  \underline{Munich}
2743  \begin{itemize}
2744   \item Bayerische Forschungsstiftung (financial support)
2745  \end{itemize}
2746
2747  \underline{Paderborn}
2748  \begin{itemize}
2749   \item Prof. J. Lindner (SiC)
2750   \item Prof. G. Schmidt (DFT + financial support)
2751   \item Dr. E. Rauls (DFT + SiC)
2752   \item Dr. S. Sanna (VASP)
2753  \end{itemize}
2754
2755 \vspace{0.2cm}
2756
2757 \begin{center}
2758 \framebox{
2759 \bf Thank you for your attention!
2760 }
2761 \end{center}
2762
2763 \end{slide}
2764
2765 \end{document}
2766
2767 \fi