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{0.2cm}
1005
1006 \small
1007
1008 {\bf Molecular dynamics (MD)}\\
1009 \scriptsize
1010 \begin{tabular}{p{4.5cm} p{7.5cm}}
1011 %\hline
1012 Basics & Details\\
1013 \hline
1014 System of $N$ particles &
1015 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
1016 \hline
1017 Phase space propagation &
1018 Velocity Verlet | timestep: \unit[1]{fs} \\
1019 \hline
1020 Analytical interaction potential &
1021 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
1022 (Erhart/Albe)
1023 $\displaystyle
1024 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
1025     \pot_{ij} = {\color{red}f_C(r_{ij})}
1026     \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
1027 $\\
1028 \hline
1029 %\multicolumn{2}{c}{}\\
1030 Observables: time/ensemble averages &
1031 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
1032 %\begin{itemize}
1033 %\item Berendsen thermostat:
1034 %      $\tau_{\text{T}}=100\text{ fs}$
1035 %\item Berendsen barostat:\\
1036 %      $\tau_{\text{P}}=100\text{ fs}$,
1037 %      $\beta^{-1}=100\text{ GPa}$
1038 %\end{itemize}\\
1039 \hline
1040 \end{tabular}
1041
1042 \small
1043
1044 \vspace{0.1cm}
1045
1046 {\bf Density functional theory (DFT)}
1047
1048 \scriptsize
1049
1050 \begin{minipage}[t]{6cm}
1051 \underline{Basics}
1052 \begin{itemize}
1053  \item Born-Oppenheimer approximation:\\
1054        Decouple electronic \& ionic motion
1055  \item Hohenberg-Kohn theorem:\\
1056        $n_0(r) \stackrel{\text{uniquely}}{\rightarrow}$
1057        $V_0$ / $H$ / $\Phi_i$ / \underline{$E_0$}
1058 \end{itemize}
1059 \underline{Details}
1060 \begin{itemize}
1061 \item Code: \textsc{vasp}
1062 \item Plane wave basis set $\{\phi_j\}$\\[0.1cm]
1063 $\displaystyle
1064 \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r)
1065 $\\
1066 $\displaystyle
1067 E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
1068 $
1069 \item Ultrasoft pseudopotential
1070 \item Brillouin zone sampling: $\Gamma$-point
1071 \end{itemize}
1072 \end{minipage}
1073 \begin{minipage}[t]{6cm}
1074 \end{minipage}
1075
1076 \end{slide}
1077
1078 \end{document}
1079 \ifnum1=0
1080
1081 \begin{slide}
1082
1083  \small
1084  {\large\bf
1085   Density functional theory (DFT) calculations
1086  }
1087
1088  Basic ingredients necessary for DFT
1089
1090  \begin{itemize}
1091   \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
1092         \begin{itemize}
1093          \item ... uniquely determines the ground state potential
1094                / wavefunctions
1095          \item ... minimizes the systems total energy
1096         \end{itemize}
1097   \item \underline{Born-Oppenheimer}
1098         - $N$ moving electrons in an external potential of static nuclei
1099 \[
1100 H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
1101               +\sum_i^N V_{\text{ext}}(r_i)
1102               +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
1103 \]
1104   \item \underline{Effective potential}
1105         - averaged electrostatic potential \& exchange and correlation
1106 \[
1107 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
1108                  +V_{\text{XC}}[n(r)]
1109 \]
1110   \item \underline{Kohn-Sham system}
1111         - Schr\"odinger equation of N non-interacting particles
1112 \[
1113 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
1114 =\epsilon_i\Phi_i(r)
1115 \quad
1116 \Rightarrow
1117 \quad
1118 n(r)=\sum_i^N|\Phi_i(r)|^2
1119 \]
1120   \item \underline{Self-consistent solution}\\
1121 $n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
1122 which in turn depends on $n(r)$
1123   \item \underline{Variational principle}
1124         - minimize total energy with respect to $n(r)$
1125  \end{itemize}
1126
1127 \end{slide}
1128
1129 \begin{slide}
1130
1131  {\large\bf
1132   Density functional theory (DFT) calculations
1133  }
1134
1135  \small
1136
1137  \vspace*{0.2cm}
1138
1139  Details of applied DFT calculations in this work
1140
1141  \begin{itemize}
1142   \item \underline{Exchange correlation functional}
1143         - approximations for the inhomogeneous electron gas
1144         \begin{itemize}
1145          \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
1146          \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
1147         \end{itemize}
1148   \item \underline{Plane wave basis set}
1149         - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
1150   \item \underline{Brillouin zone sampling} -
1151         {\color{blue}$\Gamma$-point only} calculations
1152   \item \underline{Pseudo potential}
1153         - consider only the valence electrons
1154   \item \underline{Code} - VASP 4.6
1155  \end{itemize}
1156
1157  \vspace*{0.2cm}
1158
1159  MD and structural optimization
1160
1161  \begin{itemize}
1162   \item MD integration: Gear predictor corrector algorithm
1163   \item Pressure control: Parrinello-Rahman pressure control
1164   \item Structural optimization: Conjugate gradient method
1165  \end{itemize}
1166
1167 \begin{pspicture}(0,0)(0,0)
1168 \psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
1169 \end{pspicture}
1170
1171 \end{slide}
1172
1173 \begin{slide}
1174
1175  {\large\bf
1176   C and Si self-interstitial point defects in silicon
1177  }
1178
1179  \small
1180
1181  \vspace*{0.3cm}
1182
1183 \begin{minipage}{8cm}
1184 Procedure:\\[0.3cm]
1185   \begin{pspicture}(0,0)(7,5)
1186   \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1187    \parbox{7cm}{
1188    \begin{itemize}
1189     \item Creation of c-Si simulation volume
1190     \item Periodic boundary conditions
1191     \item $T=0\text{ K}$, $p=0\text{ bar}$
1192    \end{itemize}
1193   }}}}
1194 \rput(3.5,2.1){\rnode{insert}{\psframebox{
1195  \parbox{7cm}{
1196   \begin{center}
1197   Insertion of interstitial C/Si atoms
1198   \end{center}
1199   }}}}
1200   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1201    \parbox{7cm}{
1202    \begin{center}
1203    Relaxation / structural energy minimization
1204    \end{center}
1205   }}}}
1206   \ncline[]{->}{init}{insert}
1207   \ncline[]{->}{insert}{cool}
1208  \end{pspicture}
1209 \end{minipage}
1210 \begin{minipage}{5cm}
1211   \includegraphics[width=5cm]{unit_cell_e.eps}\\
1212 \end{minipage}
1213
1214 \begin{minipage}{9cm}
1215  \begin{tabular}{l c c}
1216  \hline
1217  & size [unit cells] & \# atoms\\
1218 \hline
1219 VASP & $3\times 3\times 3$ & $216\pm 1$ \\
1220 Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
1221 \hline
1222  \end{tabular}
1223 \end{minipage}
1224 \begin{minipage}{4cm}
1225 {\color{red}$\bullet$} Tetrahedral\\
1226 {\color{green}$\bullet$} Hexagonal\\
1227 {\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
1228 {\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
1229 {\color{cyan}$\bullet$} Bond-centered\\
1230 {\color{black}$\bullet$} Vacancy / Substitutional
1231 \end{minipage}
1232
1233 \end{slide}
1234
1235 \begin{slide}
1236
1237  \footnotesize
1238
1239 \begin{minipage}{9.5cm}
1240
1241  {\large\bf
1242   Si self-interstitial point defects in silicon\\
1243  }
1244
1245 \begin{tabular}{l c c c c c}
1246 \hline
1247  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
1248 \hline
1249  VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
1250  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
1251 \hline
1252 \end{tabular}\\[0.2cm]
1253
1254 \begin{minipage}{4.7cm}
1255 \includegraphics[width=4.7cm]{e_kin_si_hex.ps}
1256 \end{minipage}
1257 \begin{minipage}{4.7cm}
1258 \begin{center}
1259 {\tiny nearly T $\rightarrow$ T}\\
1260 \end{center}
1261 \includegraphics[width=4.7cm]{nhex_tet.ps}
1262 \end{minipage}\\
1263
1264 \underline{Hexagonal} \hspace{2pt}
1265 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
1266 \framebox{
1267 \begin{minipage}{2.7cm}
1268 $E_{\text{f}}^*=4.48\text{ eV}$\\
1269 \includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
1270 \end{minipage}
1271 \begin{minipage}{0.4cm}
1272 \begin{center}
1273 $\Rightarrow$
1274 \end{center}
1275 \end{minipage}
1276 \begin{minipage}{2.7cm}
1277 $E_{\text{f}}=3.96\text{ eV}$\\
1278 \includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
1279 \end{minipage}
1280 }
1281 \begin{minipage}{2.9cm}
1282 \begin{flushright}
1283 \underline{Vacancy}\\
1284 \includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
1285 \end{flushright}
1286 \end{minipage}
1287
1288 \end{minipage}
1289 \begin{minipage}{3.5cm}
1290
1291 \begin{flushright}
1292 \underline{\hkl<1 1 0> dumbbell}\\
1293 \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
1294 \underline{Tetrahedral}\\
1295 \includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
1296 \underline{\hkl<1 0 0> dumbbell}\\
1297 \includegraphics[width=3.0cm]{si_pd_albe/100.eps}
1298 \end{flushright}
1299
1300 \end{minipage}
1301
1302 \end{slide}
1303
1304 \begin{slide}
1305
1306 \footnotesize
1307
1308  {\large\bf
1309   C interstitial point defects in silicon\\[-0.1cm]
1310  }
1311
1312 \begin{tabular}{l c c c c c c r}
1313 \hline
1314  $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\
1315 \hline
1316  VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1317  Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1318 \hline
1319 \end{tabular}\\[0.1cm]
1320
1321 \framebox{
1322 \begin{minipage}{2.7cm}
1323 \underline{Hexagonal} \hspace{2pt}
1324 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1325 $E_{\text{f}}^*=9.05\text{ eV}$\\
1326 \includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
1327 \end{minipage}
1328 \begin{minipage}{0.4cm}
1329 \begin{center}
1330 $\Rightarrow$
1331 \end{center}
1332 \end{minipage}
1333 \begin{minipage}{2.7cm}
1334 \underline{\hkl<1 0 0>}\\
1335 $E_{\text{f}}=3.88\text{ eV}$\\
1336 \includegraphics[width=2.7cm]{c_pd_albe/100.eps}
1337 \end{minipage}
1338 }
1339 \begin{minipage}{2cm}
1340 \hfill
1341 \end{minipage}
1342 \begin{minipage}{3cm}
1343 \begin{flushright}
1344 \underline{Tetrahedral}\\
1345 \includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
1346 \end{flushright}
1347 \end{minipage}
1348
1349 \framebox{
1350 \begin{minipage}{2.7cm}
1351 \underline{Bond-centered}\\
1352 $E_{\text{f}}^*=5.59\text{ eV}$\\
1353 \includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
1354 \end{minipage}
1355 \begin{minipage}{0.4cm}
1356 \begin{center}
1357 $\Rightarrow$
1358 \end{center}
1359 \end{minipage}
1360 \begin{minipage}{2.7cm}
1361 \underline{\hkl<1 1 0> dumbbell}\\
1362 $E_{\text{f}}=5.18\text{ eV}$\\
1363 \includegraphics[width=2.7cm]{c_pd_albe/110.eps}
1364 \end{minipage}
1365 }
1366 \begin{minipage}{2cm}
1367 \hfill
1368 \end{minipage}
1369 \begin{minipage}{3cm}
1370 \begin{flushright}
1371 \underline{Substitutional}\\
1372 \includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
1373 \end{flushright}
1374 \end{minipage}
1375
1376 \end{slide}
1377
1378 \begin{slide}
1379
1380 \footnotesize
1381
1382  {\large\bf\boldmath
1383   C \hkl<1 0 0> dumbbell interstitial configuration\\
1384  }
1385
1386 {\tiny
1387 \begin{tabular}{l c c c c c c c c}
1388 \hline
1389  Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
1390 \hline
1391 Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
1392 VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
1393 \hline
1394 \end{tabular}\\[0.2cm]
1395 \begin{tabular}{l c c c c }
1396 \hline
1397  Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
1398 \hline
1399 Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
1400 VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
1401 \hline
1402 \end{tabular}\\[0.2cm]
1403 \begin{tabular}{l c c c}
1404 \hline
1405  Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
1406 \hline
1407 Erhart/Albe & 0.084 & -0.091 & 0.175 \\
1408 VASP & 0.109 & -0.065 & 0.174 \\
1409 \hline
1410 \end{tabular}\\[0.6cm]
1411 }
1412
1413 \begin{minipage}{3.0cm}
1414 \begin{center}
1415 \underline{Erhart/Albe}
1416 \includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
1417 \end{center}
1418 \end{minipage}
1419 \begin{minipage}{3.0cm}
1420 \begin{center}
1421 \underline{VASP}
1422 \includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
1423 \end{center}
1424 \end{minipage}\\
1425
1426 \begin{picture}(0,0)(-185,10)
1427 \includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
1428 \end{picture}
1429 \begin{picture}(0,0)(-280,-150)
1430 \includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
1431 \end{picture}
1432
1433 \begin{pspicture}(0,0)(0,0)
1434 \psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
1435 \psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
1436 \psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
1437 \psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
1438 \end{pspicture}
1439
1440 \end{slide}
1441
1442 \begin{slide}
1443
1444 \small
1445
1446 \begin{minipage}{8.5cm}
1447
1448  {\large\bf
1449   Bond-centered interstitial configuration\\[-0.1cm]
1450  }
1451
1452 \begin{minipage}{3.0cm}
1453 \includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1454 \end{minipage}
1455 \begin{minipage}{5.2cm}
1456 \begin{itemize}
1457  \item Linear Si-C-Si bond
1458  \item Si: one C \& 3 Si neighbours
1459  \item Spin polarized calculations
1460  \item No saddle point!\\
1461        Real local minimum!
1462 \end{itemize}
1463 \end{minipage}
1464
1465 \framebox{
1466  \tiny
1467  \begin{minipage}[t]{6.5cm}
1468   \begin{minipage}[t]{1.2cm}
1469   {\color{red}Si}\\
1470   {\tiny sp$^3$}\\[0.8cm]
1471   \underline{${\color{black}\uparrow}$}
1472   \underline{${\color{black}\uparrow}$}
1473   \underline{${\color{black}\uparrow}$}
1474   \underline{${\color{red}\uparrow}$}\\
1475   sp$^3$
1476   \end{minipage}
1477   \begin{minipage}[t]{1.4cm}
1478   \begin{center}
1479   {\color{red}M}{\color{blue}O}\\[0.8cm]
1480   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1481   $\sigma_{\text{ab}}$\\[0.5cm]
1482   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1483   $\sigma_{\text{b}}$
1484   \end{center}
1485   \end{minipage}
1486   \begin{minipage}[t]{1.0cm}
1487   \begin{center}
1488   {\color{blue}C}\\
1489   {\tiny sp}\\[0.2cm]
1490   \underline{${\color{white}\uparrow\uparrow}$}
1491   \underline{${\color{white}\uparrow\uparrow}$}\\
1492   2p\\[0.4cm]
1493   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1494   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1495   sp
1496   \end{center}
1497   \end{minipage}
1498   \begin{minipage}[t]{1.4cm}
1499   \begin{center}
1500   {\color{blue}M}{\color{green}O}\\[0.8cm]
1501   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1502   $\sigma_{\text{ab}}$\\[0.5cm]
1503   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1504   $\sigma_{\text{b}}$
1505   \end{center}
1506   \end{minipage}
1507   \begin{minipage}[t]{1.2cm}
1508   \begin{flushright}
1509   {\color{green}Si}\\
1510   {\tiny sp$^3$}\\[0.8cm]
1511   \underline{${\color{green}\uparrow}$}
1512   \underline{${\color{black}\uparrow}$}
1513   \underline{${\color{black}\uparrow}$}
1514   \underline{${\color{black}\uparrow}$}\\
1515   sp$^3$
1516   \end{flushright}
1517   \end{minipage}
1518  \end{minipage}
1519 }\\[0.1cm]
1520
1521 \framebox{
1522 \begin{minipage}{4.5cm}
1523 \includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
1524 \end{minipage}
1525 \begin{minipage}{3.5cm}
1526 {\color{gray}$\bullet$} Spin up\\
1527 {\color{green}$\bullet$} Spin down\\
1528 {\color{blue}$\bullet$} Resulting spin up\\
1529 {\color{yellow}$\bullet$} Si atoms\\
1530 {\color{red}$\bullet$} C atom
1531 \end{minipage}
1532 }
1533
1534 \end{minipage}
1535 \begin{minipage}{4.2cm}
1536 \begin{flushright}
1537 \includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
1538 {\color{green}$\Box$} {\tiny unoccupied}\\
1539 {\color{red}$\bullet$} {\tiny occupied}
1540 \end{flushright}
1541 \end{minipage}
1542
1543 \end{slide}
1544
1545 \begin{slide}
1546
1547  {\large\bf\boldmath
1548   Migration of the C \hkl<1 0 0> dumbbell interstitial
1549  }
1550
1551 \scriptsize
1552
1553  {\small Investigated pathways}
1554
1555 \begin{minipage}{8.5cm}
1556 \begin{minipage}{8.3cm}
1557 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
1558 \begin{minipage}{2.4cm}
1559 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1560 \end{minipage}
1561 \begin{minipage}{0.4cm}
1562 $\rightarrow$
1563 \end{minipage}
1564 \begin{minipage}{2.4cm}
1565 \includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
1566 \end{minipage}
1567 \begin{minipage}{0.4cm}
1568 $\rightarrow$
1569 \end{minipage}
1570 \begin{minipage}{2.4cm}
1571 \includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
1572 \end{minipage}
1573 \end{minipage}\\
1574 \begin{minipage}{8.3cm}
1575 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
1576 \begin{minipage}{2.4cm}
1577 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1578 \end{minipage}
1579 \begin{minipage}{0.4cm}
1580 $\rightarrow$
1581 \end{minipage}
1582 \begin{minipage}{2.4cm}
1583 \includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
1584 \end{minipage}
1585 \begin{minipage}{0.4cm}
1586 $\rightarrow$
1587 \end{minipage}
1588 \begin{minipage}{2.4cm}
1589 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
1590 \end{minipage}
1591 \end{minipage}\\
1592 \begin{minipage}{8.3cm}
1593 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
1594 \begin{minipage}{2.4cm}
1595 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1596 \end{minipage}
1597 \begin{minipage}{0.4cm}
1598 $\rightarrow$
1599 \end{minipage}
1600 \begin{minipage}{2.4cm}
1601 \includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
1602 \end{minipage}
1603 \begin{minipage}{0.4cm}
1604 $\rightarrow$
1605 \end{minipage}
1606 \begin{minipage}{2.4cm}
1607 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
1608 \end{minipage}
1609 \end{minipage}
1610 \end{minipage}
1611 \framebox{
1612 \begin{minipage}{4.2cm}
1613  {\small Constrained relaxation\\
1614          technique (CRT) method}\\
1615 \includegraphics[width=4cm]{crt_orig.eps}
1616 \begin{itemize}
1617  \item Constrain diffusing atom
1618  \item Static constraints
1619 \end{itemize}
1620 \vspace*{0.3cm}
1621  {\small Modifications}\\
1622 \includegraphics[width=4cm]{crt_mod.eps}
1623 \begin{itemize}
1624  \item Constrain all atoms
1625  \item Update individual\\
1626        constraints
1627 \end{itemize}
1628 \end{minipage}
1629 }
1630
1631 \end{slide}
1632
1633 \begin{slide}
1634
1635  {\large\bf\boldmath
1636   Migration of the C \hkl<1 0 0> dumbbell interstitial
1637  }
1638
1639 \scriptsize
1640
1641 \framebox{
1642 \begin{minipage}{5.9cm}
1643 \begin{flushleft}
1644 \includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
1645 \end{flushleft}
1646 \begin{center}
1647 \begin{picture}(0,0)(60,0)
1648 \includegraphics[width=1cm]{vasp_mig/00-1.eps}
1649 \end{picture}
1650 \begin{picture}(0,0)(-5,0)
1651 \includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
1652 \end{picture}
1653 \begin{picture}(0,0)(-55,0)
1654 \includegraphics[width=1cm]{vasp_mig/bc.eps}
1655 \end{picture}
1656 \begin{picture}(0,0)(12.5,10)
1657 \includegraphics[width=1cm]{110_arrow.eps}
1658 \end{picture}
1659 \begin{picture}(0,0)(90,0)
1660 \includegraphics[height=0.9cm]{001_arrow.eps}
1661 \end{picture}
1662 \end{center}
1663 \vspace*{0.35cm}
1664 \end{minipage}
1665 }
1666 \begin{minipage}{0.3cm}
1667 \hfill
1668 \end{minipage}
1669 \framebox{
1670 \begin{minipage}{5.9cm}
1671 \begin{flushright}
1672 \includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
1673 \end{flushright}
1674 \begin{center}
1675 \begin{picture}(0,0)(60,0)
1676 \includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
1677 \end{picture}
1678 \begin{picture}(0,0)(5,0)
1679 \includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
1680 \end{picture}
1681 \begin{picture}(0,0)(-55,0)
1682 \includegraphics[width=1cm]{vasp_mig/0-10.eps}
1683 \end{picture}
1684 \begin{picture}(0,0)(12.5,10)
1685 \includegraphics[width=1cm]{100_arrow.eps}
1686 \end{picture}
1687 \begin{picture}(0,0)(90,0)
1688 \includegraphics[height=0.9cm]{001_arrow.eps}
1689 \end{picture}
1690 \end{center}
1691 \vspace*{0.3cm}
1692 \end{minipage}\\
1693 }
1694
1695 \vspace*{0.05cm}
1696
1697 \framebox{
1698 \begin{minipage}{5.9cm}
1699 \begin{flushleft}
1700 \includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
1701 \end{flushleft}
1702 \begin{center}
1703 \begin{picture}(0,0)(60,0)
1704 \includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps}
1705 \end{picture}
1706 \begin{picture}(0,0)(10,0)
1707 \includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
1708 \end{picture}
1709 \begin{picture}(0,0)(-60,0)
1710 \includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps}
1711 \end{picture}
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1713 \includegraphics[width=1cm]{100_arrow.eps}
1714 \end{picture}
1715 \begin{picture}(0,0)(90,0)
1716 \includegraphics[height=0.9cm]{001_arrow.eps}
1717 \end{picture}
1718 \end{center}
1719 \vspace*{0.3cm}
1720 \end{minipage}
1721 }
1722 \begin{minipage}{0.3cm}
1723 \hfill
1724 \end{minipage}
1725 \begin{minipage}{6.5cm}
1726 VASP results
1727 \begin{itemize}
1728  \item Energetically most favorable path
1729        \begin{itemize}
1730         \item Path 2
1731         \item Activation energy: $\approx$ 0.9 eV
1732         \item Experimental values: 0.73 ... 0.87 eV
1733        \end{itemize}
1734        $\Rightarrow$ {\color{blue}Diffusion} path identified!
1735  \item Reorientation (path 3)
1736        \begin{itemize}
1737         \item More likely composed of two consecutive steps of type 2
1738         \item Experimental values: 0.77 ... 0.88 eV
1739        \end{itemize}
1740        $\Rightarrow$ {\color{blue}Reorientation} transition identified!
1741 \end{itemize}
1742 \end{minipage}
1743
1744 \end{slide}
1745
1746 \begin{slide}
1747
1748  {\large\bf\boldmath
1749   Migration of the C \hkl<1 0 0> dumbbell interstitial
1750  }
1751
1752 \scriptsize
1753
1754  \vspace{0.1cm}
1755
1756 \begin{minipage}{6.5cm}
1757
1758 \framebox{
1759 \begin{minipage}[t]{5.9cm}
1760 \begin{flushleft}
1761 \includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
1762 \end{flushleft}
1763 \begin{center}
1764 \begin{pspicture}(0,0)(0,0)
1765 \psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
1766 \end{pspicture}
1767 \begin{picture}(0,0)(60,-50)
1768 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
1769 \end{picture}
1770 \begin{picture}(0,0)(5,-50)
1771 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
1772 \end{picture}
1773 \begin{picture}(0,0)(-55,-50)
1774 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
1775 \end{picture}
1776 \begin{picture}(0,0)(12.5,-40)
1777 \includegraphics[width=1cm]{110_arrow.eps}
1778 \end{picture}
1779 \begin{picture}(0,0)(90,-45)
1780 \includegraphics[height=0.9cm]{001_arrow.eps}
1781 \end{picture}\\
1782 \begin{pspicture}(0,0)(0,0)
1783 \psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
1784 \end{pspicture}
1785 \begin{picture}(0,0)(60,-15)
1786 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
1787 \end{picture}
1788 \begin{picture}(0,0)(35,-15)
1789 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
1790 \end{picture}
1791 \begin{picture}(0,0)(-5,-15)
1792 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
1793 \end{picture}
1794 \begin{picture}(0,0)(-55,-15)
1795 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
1796 \end{picture}
1797 \begin{picture}(0,0)(12.5,-5)
1798 \includegraphics[width=1cm]{100_arrow.eps}
1799 \end{picture}
1800 \begin{picture}(0,0)(90,-15)
1801 \includegraphics[height=0.9cm]{010_arrow.eps}
1802 \end{picture}
1803 \end{center}
1804 \end{minipage}
1805 }\\[0.1cm]
1806
1807 \begin{minipage}{5.9cm}
1808 Erhart/Albe results
1809 \begin{itemize}
1810  \item Lowest activation energy: $\approx$ 2.2 eV
1811  \item 2.4 times higher than VASP
1812  \item Different pathway
1813 \end{itemize}
1814 \end{minipage}
1815
1816 \end{minipage}
1817 \begin{minipage}{6.5cm}
1818
1819 \framebox{
1820 \begin{minipage}{5.9cm}
1821 %\begin{flushright}
1822 %\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
1823 %\end{flushright}
1824 %\begin{center}
1825 %\begin{pspicture}(0,0)(0,0)
1826 %\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
1827 %\end{pspicture}
1828 %\begin{picture}(0,0)(60,-5)
1829 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
1830 %\end{picture}
1831 %\begin{picture}(0,0)(0,-5)
1832 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
1833 %\end{picture}
1834 %\begin{picture}(0,0)(-55,-5)
1835 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
1836 %\end{picture}
1837 %\begin{picture}(0,0)(12.5,5)
1838 %\includegraphics[width=1cm]{100_arrow.eps}
1839 %\end{picture}
1840 %\begin{picture}(0,0)(90,0)
1841 %\includegraphics[height=0.9cm]{001_arrow.eps}
1842 %\end{picture}
1843 %\end{center}
1844 %\vspace{0.2cm}
1845 %\end{minipage}
1846 %}\\[0.2cm]
1847 %
1848 %\framebox{
1849 %\begin{minipage}{5.9cm}
1850 \includegraphics[width=5.9cm]{00-1_110_0-10_mig_albe.ps}
1851 \end{minipage}
1852 }\\[0.1cm]
1853
1854 \begin{minipage}{5.9cm}
1855 Transition involving \ci{} \hkl<1 1 0>
1856 \begin{itemize}
1857  \item Bond-centered configuration unstable\\
1858        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1859  \item Transition minima of path 2 \& 3\\
1860        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1861  \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV
1862  \item 2.4 - 3.4 times higher than VASP
1863  \item Rotation of dumbbell orientation
1864 \end{itemize}
1865 \vspace{0.1cm}
1866 \begin{center}
1867 {\color{blue}Overestimated diffusion barrier}
1868 \end{center}
1869 \end{minipage}
1870
1871 \end{minipage}
1872
1873 \end{slide}
1874
1875 \begin{slide}
1876
1877  {\large\bf\boldmath
1878   Combinations with a C-Si \hkl<1 0 0>-type interstitial
1879  }
1880
1881 \small
1882
1883 \vspace*{0.1cm}
1884
1885 Binding energy:
1886 $
1887 E_{\text{b}}=
1888 E_{\text{f}}^{\text{defect combination}}-
1889 E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
1890 E_{\text{f}}^{\text{2nd defect}}
1891 $
1892
1893 \vspace*{0.1cm}
1894
1895 {\scriptsize
1896 \begin{tabular}{l c c c c c c}
1897 \hline
1898  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1899  \hline
1900  \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1901  \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1902  \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}\\
1903  \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}\\
1904  \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}\\
1905  \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}\\
1906  \hline
1907  C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1908  Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1909 \hline
1910 \end{tabular}
1911 }
1912
1913 \vspace*{0.3cm}
1914
1915 \footnotesize
1916
1917 \begin{minipage}[t]{3.8cm}
1918 \underline{\hkl<1 0 0> at position 1}\\[0.1cm]
1919 \includegraphics[width=3.5cm]{00-1dc/2-25.eps}
1920 \end{minipage}
1921 \begin{minipage}[t]{3.5cm}
1922 \underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
1923 \includegraphics[width=3.2cm]{00-1dc/2-39.eps}
1924 \end{minipage}
1925 \begin{minipage}[t]{5.5cm}
1926 \begin{itemize}
1927  \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\
1928        $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
1929  \item Stress compensation / increase
1930  \item Unfavored: antiparallel orientations
1931  \item Indication of energetically favored\\
1932        agglomeration
1933  \item Most favorable: C clustering
1934  \item However: High barrier ($>4\,\text{eV}$)
1935  \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$
1936        (Entropy)
1937 \end{itemize}
1938 \end{minipage}
1939
1940 \begin{picture}(0,0)(-295,-130)
1941 \includegraphics[width=3.5cm]{comb_pos.eps}
1942 \end{picture}
1943
1944 \end{slide}
1945
1946 \begin{slide}
1947
1948  {\large\bf\boldmath
1949   Combinations of C-Si \hkl<1 0 0>-type interstitials
1950  }
1951
1952 \small
1953
1954 \vspace*{0.1cm}
1955
1956 Energetically most favorable combinations along \hkl<1 1 0>
1957
1958 \vspace*{0.1cm}
1959
1960 {\scriptsize
1961 \begin{tabular}{l c c c c c c}
1962 \hline
1963  & 1 & 2 & 3 & 4 & 5 & 6\\
1964 \hline
1965 $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
1966 C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
1967 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>\\
1968 \hline
1969 \end{tabular}
1970 }
1971
1972 \vspace*{0.3cm}
1973
1974 \begin{minipage}{7.0cm}
1975 \includegraphics[width=7cm]{db_along_110_cc.ps}
1976 \end{minipage}
1977 \begin{minipage}{6.0cm}
1978 \begin{itemize}
1979  \item Interaction proportional to reciprocal cube of C-C distance
1980  \item Saturation in the immediate vicinity
1981  \renewcommand\labelitemi{$\Rightarrow$}
1982  \item Agglomeration of \ci{} expected
1983  \item Absence of C clustering
1984 \end{itemize}
1985 \begin{center}
1986 {\color{blue}
1987  Consisten with initial precipitation model
1988 }
1989 \end{center}
1990 \end{minipage}
1991
1992 \vspace{0.2cm}
1993
1994 \end{slide}
1995
1996 \begin{slide}
1997
1998  {\large\bf\boldmath
1999   Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
2000  }
2001
2002  \scriptsize
2003
2004 %\begin{center}
2005 %\begin{minipage}{3.2cm}
2006 %\includegraphics[width=3cm]{sub_110_combo.eps}
2007 %\end{minipage}
2008 %\begin{minipage}{7.8cm}
2009 %\begin{tabular}{l c c c c c c}
2010 %\hline
2011 %C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
2012 %                   \hkl<1 0 1> & \hkl<-1 0 1> \\
2013 %\hline
2014 %1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
2015 %2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
2016 %3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
2017 %4 & \RM{4} & B & D & E & E & D \\
2018 %5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
2019 %\hline
2020 %\end{tabular}
2021 %\end{minipage}
2022 %\end{center}
2023
2024 %\begin{center}
2025 %\begin{tabular}{l c c c c c c c c c c}
2026 %\hline
2027 %Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
2028 %\hline
2029 %$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
2030 %$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
2031 %$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
2032 %\hline
2033 %\end{tabular}
2034 %\end{center}
2035
2036 \begin{minipage}{6.0cm}
2037 \includegraphics[width=5.8cm]{c_sub_si110.ps}
2038 \end{minipage}
2039 \begin{minipage}{7cm}
2040 \scriptsize
2041 \begin{itemize}
2042  \item IBS: C may displace Si\\
2043        $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
2044  \item Assumption:\\
2045        \hkl<1 1 0>-type $\rightarrow$ favored combination
2046  \renewcommand\labelitemi{$\Rightarrow$}
2047  \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
2048  \item Less favorable than C-Si \hkl<1 0 0> dumbbell
2049  \item Interaction drops quickly to zero\\
2050        $\rightarrow$ low capture radius
2051 \end{itemize}
2052 \begin{center}
2053  {\color{blue}
2054  IBS process far from equilibrium\\
2055  \cs{} \& \si{} instead of thermodynamic ground state
2056  }
2057 \end{center}
2058 \end{minipage}
2059
2060 \begin{minipage}{6.5cm}
2061 \includegraphics[width=6.0cm]{162-097.ps}
2062 \begin{itemize}
2063  \item Low migration barrier
2064 \end{itemize}
2065 \end{minipage}
2066 \begin{minipage}{6.5cm}
2067 \begin{center}
2068 Ab initio MD at \degc{900}\\
2069 \includegraphics[width=3.3cm]{md_vasp_01.eps}
2070 $t=\unit[2230]{fs}$\\
2071 \includegraphics[width=3.3cm]{md_vasp_02.eps}
2072 $t=\unit[2900]{fs}$
2073 \end{center}
2074 {\color{blue}
2075 Contribution of entropy to structural formation
2076 }
2077 \end{minipage}
2078
2079 \end{slide}
2080
2081 \begin{slide}
2082
2083  {\large\bf\boldmath
2084   Migration in C-Si \hkl<1 0 0> and vacancy combinations
2085  }
2086
2087  \footnotesize
2088
2089 \vspace{0.1cm}
2090
2091 \begin{minipage}[t]{3cm}
2092 \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
2093 \includegraphics[width=2.8cm]{00-1dc/0-59.eps}
2094 \end{minipage}
2095 \begin{minipage}[t]{7cm}
2096 \vspace{0.2cm}
2097 \begin{center}
2098  Low activation energies\\
2099  High activation energies for reverse processes\\
2100  $\Downarrow$\\
2101  {\color{blue}C$_{\text{sub}}$ very stable}\\
2102 \vspace*{0.1cm}
2103  \hrule
2104 \vspace*{0.1cm}
2105  Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
2106  $\Downarrow$\\
2107  {\color{blue}Formation of SiC by successive substitution by C}
2108
2109 \end{center}
2110 \end{minipage}
2111 \begin{minipage}[t]{3cm}
2112 \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
2113 \includegraphics[width=2.8cm]{00-1dc/3-14.eps}
2114 \end{minipage}
2115
2116
2117 \framebox{
2118 \begin{minipage}{5.9cm}
2119 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
2120 \begin{center}
2121 \begin{picture}(0,0)(70,0)
2122 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
2123 \end{picture}
2124 \begin{picture}(0,0)(30,0)
2125 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
2126 \end{picture}
2127 \begin{picture}(0,0)(-10,0)
2128 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
2129 \end{picture}
2130 \begin{picture}(0,0)(-48,0)
2131 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
2132 \end{picture}
2133 \begin{picture}(0,0)(12.5,5)
2134 \includegraphics[width=1cm]{100_arrow.eps}
2135 \end{picture}
2136 \begin{picture}(0,0)(97,-10)
2137 \includegraphics[height=0.9cm]{001_arrow.eps}
2138 \end{picture}
2139 \end{center}
2140 \vspace{0.1cm}
2141 \end{minipage}
2142 }
2143 \begin{minipage}{0.3cm}
2144 \hfill
2145 \end{minipage}
2146 \framebox{
2147 \begin{minipage}{5.9cm}
2148 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
2149 \begin{center}
2150 \begin{picture}(0,0)(60,0)
2151 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
2152 \end{picture}
2153 \begin{picture}(0,0)(25,0)
2154 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
2155 \end{picture}
2156 \begin{picture}(0,0)(-20,0)
2157 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
2158 \end{picture}
2159 \begin{picture}(0,0)(-55,0)
2160 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
2161 \end{picture}
2162 \begin{picture}(0,0)(12.5,5)
2163 \includegraphics[width=1cm]{100_arrow.eps}
2164 \end{picture}
2165 \begin{picture}(0,0)(95,0)
2166 \includegraphics[height=0.9cm]{001_arrow.eps}
2167 \end{picture}
2168 \end{center}
2169 \vspace{0.1cm}
2170 \end{minipage}
2171 }
2172
2173 \end{slide}
2174
2175 \begin{slide}
2176
2177  {\large\bf
2178   Conclusion of defect / migration / combined defect simulations
2179  }
2180
2181  \footnotesize
2182
2183 \vspace*{0.1cm}
2184
2185 Defect structures
2186 \begin{itemize}
2187  \item Accurately described by quantum-mechanical simulations
2188  \item Less accurate description by classical potential simulations
2189  \item Underestimated formation energy of \cs{} by classical approach
2190  \item Both methods predict same ground state: \ci{} \hkl<1 0 0> dumbbell
2191 \end{itemize}
2192
2193 Migration
2194 \begin{itemize}
2195  \item C migration pathway in Si identified
2196  \item Consistent with reorientation and diffusion experiments
2197 \end{itemize}
2198 \begin{itemize}
2199  \item Different path and ...
2200  \item overestimated barrier by classical potential calculations
2201 \end{itemize}
2202
2203 Concerning the precipitation mechanism
2204 \begin{itemize}
2205  \item Agglomeration of C-Si dumbbells energetically favorable
2206        (stress compensation)
2207  \item C-Si indeed favored compared to
2208        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2209  \item Possible low interaction capture radius of
2210        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2211  \item Low barrier for
2212        \ci{} \hkl<1 0 0> $\rightarrow$ \cs{} \& \si{} \hkl<1 1 0>
2213  \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
2214        C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
2215 \end{itemize}
2216 \begin{center}
2217 {\color{blue}Results suggest increased participation of \cs}
2218 \end{center}
2219
2220 \end{slide}
2221
2222 \begin{slide}
2223
2224  {\large\bf
2225   Silicon carbide precipitation simulations
2226  }
2227
2228  \small
2229
2230 {\scriptsize
2231  \begin{pspicture}(0,0)(12,6.5)
2232   % nodes
2233   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
2234    \parbox{7cm}{
2235    \begin{itemize}
2236     \item Create c-Si volume
2237     \item Periodc boundary conditions
2238     \item Set requested $T$ and $p=0\text{ bar}$
2239     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
2240    \end{itemize}
2241   }}}}
2242   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
2243    \parbox{7cm}{
2244    Insertion of C atoms at constant T
2245    \begin{itemize}
2246     \item total simulation volume {\pnode{in1}}
2247     \item volume of minimal SiC precipitate {\pnode{in2}}
2248     \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
2249           precipitate
2250    \end{itemize}
2251   }}}}
2252   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
2253    \parbox{7.0cm}{
2254    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
2255   }}}}
2256   \ncline[]{->}{init}{insert}
2257   \ncline[]{->}{insert}{cool}
2258   \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
2259   \rput(7.8,6){\footnotesize $V_1$}
2260   \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
2261   \rput(9.2,4.85){\tiny $V_2$}
2262   \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
2263   \rput(9.55,4.45){\footnotesize $V_3$}
2264   \rput(7.9,3.2){\pnode{ins1}}
2265   \rput(9.22,2.8){\pnode{ins2}}
2266   \rput(11.0,2.4){\pnode{ins3}}
2267   \ncline[]{->}{in1}{ins1}
2268   \ncline[]{->}{in2}{ins2}
2269   \ncline[]{->}{in3}{ins3}
2270  \end{pspicture}
2271 }
2272
2273 \begin{itemize}
2274  \item Restricted to classical potential simulations
2275  \item $V_2$ and $V_3$ considered due to low diffusion
2276  \item Amount of C atoms: 6000
2277        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
2278  \item Simulation volume: $31\times 31\times 31$ unit cells
2279        (238328 Si atoms)
2280 \end{itemize}
2281
2282 \end{slide}
2283
2284 \begin{slide}
2285
2286  {\large\bf\boldmath
2287   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2288  }
2289
2290  \small
2291
2292 \begin{minipage}{6.5cm}
2293 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2294 \end{minipage}
2295 \begin{minipage}{6.5cm}
2296 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2297 \end{minipage}
2298
2299 \begin{minipage}{6.5cm}
2300 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2301 \end{minipage}
2302 \begin{minipage}{6.5cm}
2303 \scriptsize
2304 \underline{Low C concentration ($V_1$)}\\
2305 \hkl<1 0 0> C-Si dumbbell dominated structure
2306 \begin{itemize}
2307  \item Si-C bumbs around 0.19 nm
2308  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2309        concatenated dumbbells of various orientation
2310  \item Si-Si NN distance stretched to 0.3 nm
2311 \end{itemize}
2312 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2313 \underline{High C concentration ($V_2$, $V_3$)}\\
2314 High amount of strongly bound C-C bonds\\
2315 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2316 Only short range order observable\\
2317 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2318 \end{minipage}
2319
2320 \end{slide}
2321
2322 \begin{slide}
2323
2324  {\large\bf\boldmath
2325   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2326  }
2327
2328  \small
2329
2330 \begin{minipage}{6.5cm}
2331 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2332 \end{minipage}
2333 \begin{minipage}{6.5cm}
2334 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2335 \end{minipage}
2336
2337 \begin{minipage}{6.5cm}
2338 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2339 \end{minipage}
2340 \begin{minipage}{6.5cm}
2341 \scriptsize
2342 \underline{Low C concentration ($V_1$)}\\
2343 \hkl<1 0 0> C-Si dumbbell dominated structure
2344 \begin{itemize}
2345  \item Si-C bumbs around 0.19 nm
2346  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2347        concatenated dumbbells of various orientation
2348  \item Si-Si NN distance stretched to 0.3 nm
2349 \end{itemize}
2350 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2351 \underline{High C concentration ($V_2$, $V_3$)}\\
2352 High amount of strongly bound C-C bonds\\
2353 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2354 Only short range order observable\\
2355 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2356 \end{minipage}
2357
2358 \begin{pspicture}(0,0)(0,0)
2359 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2360 \begin{minipage}{10cm}
2361 \small
2362 {\color{red}\bf 3C-SiC formation fails to appear}
2363 \begin{itemize}
2364 \item Low C concentration simulations
2365  \begin{itemize}
2366   \item Formation of \ci{} indeed occurs
2367   \item Agllomeration not observed
2368  \end{itemize}
2369 \item High C concentration simulations
2370  \begin{itemize}
2371   \item Amorphous SiC-like structure\\
2372         (not expected at prevailing temperatures)
2373   \item Rearrangement and transition into 3C-SiC structure missing
2374  \end{itemize}
2375 \end{itemize}
2376 \end{minipage}
2377  }}}
2378 \end{pspicture}
2379
2380 \end{slide}
2381
2382 \begin{slide}
2383
2384  {\large\bf
2385   Limitations of molecular dynamics and short range potentials
2386  }
2387
2388 \footnotesize
2389
2390 \vspace{0.2cm}
2391
2392 \underline{Time scale problem of MD}\\[0.2cm]
2393 Minimize integration error\\
2394 $\Rightarrow$ discretization considerably smaller than
2395               reciprocal of fastest vibrational mode\\[0.1cm]
2396 Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
2397 $\Rightarrow$ suitable choice of time step:
2398               $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
2399 $\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
2400 Several local minima in energy surface separated by large energy barriers\\
2401 $\Rightarrow$ transition event corresponds to a multiple
2402               of vibrational periods\\
2403 $\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
2404               infrequent transition events\\[0.1cm]
2405 {\color{blue}Accelerated methods:}
2406 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
2407
2408 \vspace{0.3cm}
2409
2410 \underline{Limitations related to the short range potential}\\[0.2cm]
2411 Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
2412 and 2$^{\text{nd}}$ next neighbours\\
2413 $\Rightarrow$ overestimated unphysical high forces of next neighbours
2414
2415 \vspace{0.3cm}
2416
2417 \framebox{
2418 \color{red}
2419 Potential enhanced problem of slow phase space propagation
2420 }
2421
2422 \vspace{0.3cm}
2423
2424 \underline{Approach to the (twofold) problem}\\[0.2cm]
2425 Increased temperature simulations without TAD corrections\\
2426 (accelerated methods or higher time scales exclusively not sufficient)
2427
2428 \begin{picture}(0,0)(-260,-30)
2429 \framebox{
2430 \begin{minipage}{4.2cm}
2431 \tiny
2432 \begin{center}
2433 \vspace{0.03cm}
2434 \underline{IBS}
2435 \end{center}
2436 \begin{itemize}
2437 \item 3C-SiC also observed for higher T
2438 \item higher T inside sample
2439 \item structural evolution vs.\\
2440       equilibrium properties
2441 \end{itemize}
2442 \end{minipage}
2443 }
2444 \end{picture}
2445
2446 \begin{picture}(0,0)(-305,-155)
2447 \framebox{
2448 \begin{minipage}{2.5cm}
2449 \tiny
2450 \begin{center}
2451 retain proper\\
2452 thermodynmic sampling
2453 \end{center}
2454 \end{minipage}
2455 }
2456 \end{picture}
2457
2458 \end{slide}
2459
2460 \begin{slide}
2461
2462  {\large\bf
2463   Increased temperature simulations at low C concentration
2464  }
2465
2466 \small
2467
2468 \begin{minipage}{6.5cm}
2469 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2470 \end{minipage}
2471 \begin{minipage}{6.5cm}
2472 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2473 \end{minipage}
2474
2475 \begin{minipage}{6.5cm}
2476 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2477 \end{minipage}
2478 \begin{minipage}{6.5cm}
2479 \scriptsize
2480  \underline{Si-C bonds:}
2481  \begin{itemize}
2482   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2483   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2484  \end{itemize}
2485  \underline{Si-Si bonds:}
2486  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2487  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2488  \underline{C-C bonds:}
2489  \begin{itemize}
2490   \item C-C next neighbour pairs reduced (mandatory)
2491   \item Peak at 0.3 nm slightly shifted
2492         \begin{itemize}
2493          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2494                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2495                combinations (|)\\
2496                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2497                ($\downarrow$)
2498          \item Range [|-$\downarrow$]:
2499                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2500                with nearby Si$_{\text{I}}$}
2501         \end{itemize}
2502  \end{itemize}
2503 \end{minipage}
2504
2505 \begin{picture}(0,0)(-330,-74)
2506 \color{blue}
2507 \framebox{
2508 \begin{minipage}{1.6cm}
2509 \tiny
2510 \begin{center}
2511 stretched SiC\\[-0.1cm]
2512 in c-Si
2513 \end{center}
2514 \end{minipage}
2515 }
2516 \end{picture}
2517
2518 \end{slide}
2519
2520 \begin{slide}
2521
2522  {\large\bf
2523   Increased temperature simulations at low C concentration
2524  }
2525
2526 \small
2527
2528 \begin{minipage}{6.5cm}
2529 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2530 \end{minipage}
2531 \begin{minipage}{6.5cm}
2532 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2533 \end{minipage}
2534
2535 \begin{minipage}{6.5cm}
2536 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2537 \end{minipage}
2538 \begin{minipage}{6.5cm}
2539 \scriptsize
2540  \underline{Si-C bonds:}
2541  \begin{itemize}
2542   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2543   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2544  \end{itemize}
2545  \underline{Si-Si bonds:}
2546  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2547  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2548  \underline{C-C bonds:}
2549  \begin{itemize}
2550   \item C-C next neighbour pairs reduced (mandatory)
2551   \item Peak at 0.3 nm slightly shifted
2552         \begin{itemize}
2553          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2554                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2555                combinations (|)\\
2556                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2557                ($\downarrow$)
2558          \item Range [|-$\downarrow$]:
2559                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2560                with nearby Si$_{\text{I}}$}
2561         \end{itemize}
2562  \end{itemize}
2563 \end{minipage}
2564
2565 %\begin{picture}(0,0)(-330,-74)
2566 %\color{blue}
2567 %\framebox{
2568 %\begin{minipage}{1.6cm}
2569 %\tiny
2570 %\begin{center}
2571 %stretched SiC\\[-0.1cm]
2572 %in c-Si
2573 %\end{center}
2574 %\end{minipage}
2575 %}
2576 %\end{picture}
2577
2578 \begin{pspicture}(0,0)(0,0)
2579 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2580 \begin{minipage}{10cm}
2581 \small
2582 {\color{blue}\bf Stretched SiC in c-Si}
2583 \begin{itemize}
2584 \item Consistent to precipitation model involving \cs{}
2585 \item Explains annealing behavior of high/low T C implants
2586       \begin{itemize}
2587        \item Low T: highly mobiel \ci{}
2588        \item High T: stable configurations of \cs{}
2589       \end{itemize}
2590 \end{itemize}
2591 $\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2592 $\Rightarrow$ Precipitation mechanism involving \cs{}
2593 \end{minipage}
2594  }}}
2595 \end{pspicture}
2596
2597 \end{slide}
2598
2599 \begin{slide}
2600
2601  {\large\bf
2602   Increased temperature simulations at high C concentration
2603  }
2604
2605 \footnotesize
2606
2607 \begin{minipage}{6.5cm}
2608 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2609 \end{minipage}
2610 \begin{minipage}{6.5cm}
2611 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2612 \end{minipage}
2613
2614 \vspace{0.1cm}
2615
2616 \scriptsize
2617
2618 \framebox{
2619 \begin{minipage}[t]{6.0cm}
2620 0.186 nm: Si-C pairs $\uparrow$\\
2621 (as expected in 3C-SiC)\\[0.2cm]
2622 0.282 nm: Si-C-C\\[0.2cm]
2623 $\approx$0.35 nm: C-Si-Si
2624 \end{minipage}
2625 }
2626 \begin{minipage}{0.2cm}
2627 \hfill
2628 \end{minipage}
2629 \framebox{
2630 \begin{minipage}[t]{6.0cm}
2631 0.15 nm: C-C pairs $\uparrow$\\
2632 (as expected in graphite/diamond)\\[0.2cm]
2633 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2634 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2635 \end{minipage}
2636 }
2637
2638 \begin{itemize}
2639 \item Decreasing cut-off artifact
2640 \item {\color{red}Amorphous} SiC-like phase remains
2641 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2642 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2643 \end{itemize}
2644
2645 \vspace{-0.1cm}
2646
2647 \begin{center}
2648 {\color{blue}
2649 \framebox{
2650 {\color{black}
2651 High C \& small $V$ \& short $t$
2652 $\Rightarrow$
2653 }
2654 Slow restructuring due to strong C-C bonds
2655 {\color{black}
2656 $\Leftarrow$
2657 High C \& low T implants
2658 }
2659 }
2660 }
2661 \end{center}
2662
2663 \end{slide}
2664
2665 \begin{slide}
2666
2667  {\large\bf
2668   Summary and Conclusions
2669  }
2670
2671  \scriptsize
2672
2673 %\vspace{0.1cm}
2674
2675 \framebox{
2676 \begin{minipage}[t]{12.9cm}
2677  \underline{Pecipitation simulations}
2678  \begin{itemize}
2679   \item High C concentration $\rightarrow$ amorphous SiC like phase
2680   \item Problem of potential enhanced slow phase space propagation
2681   \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2682   \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2683   \item High T necessary to simulate IBS conditions (far from equilibrium)
2684   \item Precipitation by successive agglomeration of \cs (epitaxy)
2685   \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2686         (stretched SiC, interface)
2687  \end{itemize}
2688 \end{minipage}
2689 }
2690
2691 %\vspace{0.1cm}
2692
2693 \framebox{
2694 \begin{minipage}{12.9cm}
2695  \underline{Defects}
2696  \begin{itemize}
2697    \item DFT / EA
2698         \begin{itemize}
2699          \item Point defects excellently / fairly well described
2700                by DFT / EA
2701          \item C$_{\text{sub}}$ drastically underestimated by EA
2702          \item EA predicts correct ground state:
2703                C$_{\text{sub}}$ \& \si{} $>$ \ci{}
2704          \item Identified migration path explaining
2705                diffusion and reorientation experiments by DFT
2706          \item EA fails to describe \ci{} migration:
2707                Wrong path \& overestimated barrier
2708         \end{itemize}
2709    \item Combinations of defects
2710          \begin{itemize}
2711           \item Agglomeration of point defects energetically favorable
2712                 by compensation of stress
2713           \item Formation of C-C unlikely
2714           \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2715           \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2716                 Low barrier (\unit[0.77]{eV}) \& low capture radius
2717         \end{itemize}
2718  \end{itemize}
2719 \end{minipage}
2720 }
2721
2722 \begin{center}
2723 {\color{blue}
2724 \framebox{Precipitation by successive agglomeration of \cs{}}
2725 }
2726 \end{center}
2727
2728 \end{slide}
2729
2730 \begin{slide}
2731
2732  {\large\bf
2733   Acknowledgements
2734  }
2735
2736  \vspace{0.1cm}
2737
2738  \small
2739
2740  Thanks to \ldots
2741
2742  \underline{Augsburg}
2743  \begin{itemize}
2744   \item Prof. B. Stritzker (accomodation at EP \RM{4})
2745   \item Ralf Utermann (EDV)
2746  \end{itemize}
2747
2748  \underline{Helsinki}
2749  \begin{itemize}
2750   \item Prof. K. Nordlund (MD)
2751  \end{itemize}
2752
2753  \underline{Munich}
2754  \begin{itemize}
2755   \item Bayerische Forschungsstiftung (financial support)
2756  \end{itemize}
2757
2758  \underline{Paderborn}
2759  \begin{itemize}
2760   \item Prof. J. Lindner (SiC)
2761   \item Prof. G. Schmidt (DFT + financial support)
2762   \item Dr. E. Rauls (DFT + SiC)
2763   \item Dr. S. Sanna (VASP)
2764  \end{itemize}
2765
2766 \vspace{0.2cm}
2767
2768 \begin{center}
2769 \framebox{
2770 \bf Thank you for your attention!
2771 }
2772 \end{center}
2773
2774 \end{slide}
2775
2776 \end{document}
2777
2778 \fi