posic/talks/mpi_app.tex

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  36
  37 % units
  38 \usepackage{units}
  39
  40 \usepackage{semcolor}
  41 \usepackage{semlayer}           % Seminar overlays
  42 \usepackage{slidesec}           % Seminar sections and list of slides
  43
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  80 \begin{document}
  81
  82 \extraslideheight{10in}
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  84
  85 \pagestyle{empty}
  86
  87 % specify width and height
  88 \slidewidth 26.3cm
  89 \slideheight 19.9cm
  90
  91 % margin
  92 \def\slidetopmargin{-0.15cm}
  93
  94 \newcommand{\ham}{\mathcal{H}}
  95 \newcommand{\pot}{\mathcal{V}}
  96 \newcommand{\foo}{\mathcal{U}}
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  98
  99 % itemize level ii
 100 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
 101
 102 % nice phi
 103 \renewcommand{\phi}{\varphi}
 104
 105 % roman letters
 106 \newcommand{\RM}[1]{\MakeUppercase{\romannumeral #1{}}}
 107
 108 % colors
 109 \newrgbcolor{si-yellow}{.6 .6 0}
 110 \newrgbcolor{hb}{0.75 0.77 0.89}
 111 \newrgbcolor{lbb}{0.75 0.8 0.88}
 112 \newrgbcolor{hlbb}{0.825 0.88 0.968}
 113 \newrgbcolor{lachs}{1.0 .93 .81}
 114
 115 % shortcuts
 116 \newcommand{\si}{Si$_{\text{i}}${}}
 117 \newcommand{\ci}{C$_{\text{i}}${}}
 118 \newcommand{\cs}{C$_{\text{sub}}${}}
 119 \newcommand{\degc}[1]{\unit[#1]{$^{\circ}$C}{}}
 120 \newcommand{\distn}[1]{\unit[#1]{nm}{}}
 121 \newcommand{\dista}[1]{\unit[#1]{\AA}{}}
 122 \newcommand{\perc}[1]{\unit[#1]{\%}{}}
 123
 124 % no vertical centering
 125 %\centerslidesfalse
 126
 127 % layout check
 128 %\layout
 129 \begin{slide}
 130 \center
 131 {\Huge
 132 E\\
 133 F\\
 134 G\\
 135 A B C D E F G H G F E D C B A
 136 G\\
 137 F\\
 138 E\\
 139 }
 140 \end{slide}
 141
 142 % topic
 143
 144 \begin{slide}
 145 \begin{center}
 146
 147  \vspace{16pt}
 148
 149  {\LARGE\bf
 150   Atomistic simulation studies\\[0.2cm]
 151   in the C/Si system
 152  }
 153
 154  \vspace{48pt}
 155
 156  \textsc{Frank Zirkelbach}
 157
 158  \vspace{48pt}
 159
 160  Application talk at the Max Planck Institute for Solid State Research
 161
 162  \vspace{08pt}
 163
 164  Stuttgart, November 2011
 165
 166 \end{center}
 167 \end{slide}
 168
 169 % no vertical centering
 170 \centerslidesfalse
 171
 172 \ifnum1=0
 173
 174 % intro
 175
 176 \begin{slide}
 177
 178 %{\large\bf
 179 % Phase diagram of the C/Si system\\
 180 %}
 181
 182 \vspace*{0.2cm}
 183
 184 \begin{minipage}{6.5cm}
 185 \includegraphics[width=6.5cm]{si-c_phase.eps}
 186 \begin{center}
 187 {\tiny
 188 R. I. Scace and G. A. Slack, J. Chem. Phys. 30, 1551 (1959)
 189 }
 190 \end{center}
 191 \begin{pspicture}(0,0)(0,0)
 192 \psellipse[linecolor=blue,linewidth=0.1cm](3.55,4.0)(0.5,2.9)
 193 \end{pspicture}
 194 \end{minipage}
 195 \begin{minipage}{6cm}
 196 {\bf Phase diagram of the C/Si system}\\[0.2cm]
 197 {\color{blue}Stoichiometric composition}
 198 \begin{itemize}
 199 \item only chemical stable compound
 200 \item wide band gap semiconductor\\
 201       \underline{silicon carbide}, SiC
 202 \end{itemize}
 203 \end{minipage}
 204
 205 \end{slide}
 206
 207 % motivation / properties / applications of silicon carbide
 208
 209 \begin{slide}
 210
 211 \vspace*{1.8cm}
 212
 213 \small
 214
 215 \begin{pspicture}(0,0)(13.5,5)
 216
 217  \psframe*[linecolor=hb](-0.2,0)(12.9,5)
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 221
 222  \rput[lt](0,4.6){\color{gray}PROPERTIES}
 223
 224  \rput[lt](0.3,4){wide band gap}
 225  \rput[lt](0.3,3.5){high electric breakdown field}
 226  \rput[lt](0.3,3){good electron mobility}
 227  \rput[lt](0.3,2.5){high electron saturation drift velocity}
 228  \rput[lt](0.3,2){high thermal conductivity}
 229
 230  \rput[lt](0.3,1.5){hard and mechanically stable}
 231  \rput[lt](0.3,1){chemically inert}
 232
 233  \rput[lt](0.3,0.5){radiation hardness}
 234
 235  \rput[rt](12.7,4.6){\color{gray}APPLICATIONS}
 236
 237  \rput[rt](12.5,3.85){high-temperature, high power}
 238  \rput[rt](12.5,3.5){and high-frequency}
 239  \rput[rt](12.5,3.15){electronic and optoelectronic devices}
 240
 241  \rput[rt](12.5,2.35){material suitable for extreme conditions}
 242  \rput[rt](12.5,2){microelectromechanical systems}
 243  \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements}
 244
 245  \rput[rt](12.5,0.85){first wall reactor material, detectors}
 246  \rput[rt](12.5,0.5){and electronic devices for space}
 247
 248 \end{pspicture}
 249
 250 \begin{picture}(0,0)(5,-162)
 251 \includegraphics[height=2.2cm]{3C_SiC_bs.eps}
 252 \end{picture}
 253 \begin{picture}(0,0)(-120,-162)
 254 \includegraphics[height=2.2cm]{nasa_600c_led.eps}
 255 \end{picture}
 256 \begin{picture}(0,0)(-270,-162)
 257 \includegraphics[height=2.2cm]{6h-sic_3c-sic.eps}
 258 \end{picture}
 259 %%%%
 260 \begin{picture}(0,0)(10,65)
 261 \includegraphics[height=2.8cm]{sic_switch.eps}
 262 \end{picture}
 263 %\begin{picture}(0,0)(-243,65)
 264 \begin{picture}(0,0)(-110,65)
 265 \includegraphics[height=2.8cm]{ise_99.eps}
 266 \end{picture}
 267 %\begin{picture}(0,0)(-135,65)
 268 \begin{picture}(0,0)(-100,65)
 269 \includegraphics[height=1.2cm]{infineon_schottky.eps}
 270 \end{picture}
 271 \begin{picture}(0,0)(-233,65)
 272 \includegraphics[height=2.8cm]{solar_car.eps}
 273 \end{picture}
 274
 275 \end{slide}
 276
 277 % motivation
 278
 279 \begin{slide}
 280
 281  {\large\bf
 282   Polytypes of SiC\\[0.4cm]
 283  }
 284
 285 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
 286 \begin{minipage}{1.9cm}
 287 {\tiny cubic (twist)}
 288 \end{minipage}
 289 \begin{minipage}{2.9cm}
 290 {\tiny hexagonal (no twist)}
 291 \end{minipage}
 292
 293 \begin{picture}(0,0)(-150,0)
 294  \includegraphics[width=7cm]{polytypes.eps}
 295 \end{picture}
 296
 297 \vspace{0.6cm}
 298
 299 \footnotesize
 300
 301 \begin{tabular}{l c c c c c c}
 302 \hline
 303  & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
 304 \hline
 305 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
 306 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
 307 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
 308 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
 309 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
 310 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
 311 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
 312 \hline
 313 \end{tabular}
 314
 315 \begin{pspicture}(0,0)(0,0)
 316 \psellipse[linecolor=green](5.7,2.10)(0.4,0.5)
 317 \end{pspicture}
 318 \begin{pspicture}(0,0)(0,0)
 319 \psellipse[linecolor=green](5.6,0.92)(0.4,0.2)
 320 \end{pspicture}
 321 \begin{pspicture}(0,0)(0,0)
 322 \psellipse[linecolor=red](10.45,0.45)(0.4,0.2)
 323 \end{pspicture}
 324
 325 \end{slide}
 326
 327 % fabrication
 328
 329 \begin{slide}
 330
 331  {\large\bf
 332   Fabrication of silicon carbide
 333  }
 334
 335  \small
 336
 337  \vspace{2pt}
 338
 339 \begin{center}
 340  {\color{gray}
 341  \emph{Silicon carbide --- Born from the stars, perfected on earth.}
 342  }
 343 \end{center}
 344
 345 \vspace{2pt}
 346
 347 SiC thin films by MBE \& CVD
 348 \begin{itemize}
 349  \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
 350  \item \underline{Commercially available} semiconductor power devices based on
 351        \underline{\foreignlanguage{greek}{a}-SiC}
 352  \item Production of favored \underline{3C-SiC} material
 353        \underline{less advanced}
 354  \item Quality and size not yet sufficient
 355 \end{itemize}
 356 \begin{picture}(0,0)(-310,-20)
 357   \includegraphics[width=2.0cm]{cree.eps}
 358 \end{picture}
 359
 360 \vspace{-0.2cm}
 361
 362 Alternative approach:
 363 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
 364
 365 \vspace{0.2cm}
 366
 367 \scriptsize
 368
 369 \framebox{
 370 \begin{minipage}{3.15cm}
 371  \begin{center}
 372 \includegraphics[width=3cm]{imp.eps}\\
 373  {\tiny
 374   Carbon implantation
 375  }
 376  \end{center}
 377 \end{minipage}
 378 \begin{minipage}{3.15cm}
 379  \begin{center}
 380 \includegraphics[width=3cm]{annealing.eps}\\
 381  {\tiny
 382   \unit[12]{h} annealing at \degc{1200}
 383  }
 384  \end{center}
 385 \end{minipage}
 386 }
 387 \begin{minipage}{5.5cm}
 388  \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm]
 389  \begin{center}
 390  {\tiny
 391   XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
 392  }
 393  \end{center}
 394 \end{minipage}
 395
 396 \end{slide}
 397
 398 % contents
 399
 400 \begin{slide}
 401
 402 {\large\bf
 403  Systematic investigation of C implantations into Si
 404 }
 405
 406 \vspace{1.7cm}
 407 \begin{center}
 408 \hspace{-1.0cm}
 409 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
 410 \end{center}
 411
 412 \end{slide}
 413
 414 % outline
 415
 416 \begin{slide}
 417
 418 {\large\bf
 419  Outline
 420 }
 421
 422 \vspace{1.7cm}
 423 \begin{center}
 424 \hspace{-1.0cm}
 425 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
 426 \end{center}
 427
 428 \begin{pspicture}(0,0)(0,0)
 429 \rput(6.0,7.0){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{
 430 \begin{minipage}{11cm}
 431 {\color{black}Diploma thesis}\\
 432  \underline{Monte Carlo} simulation modeling the selforganization process\\
 433  leading to periodic arrays of nanometric amorphous SiC precipitates
 434 \end{minipage}
 435 }}}
 436 \end{pspicture}
 437 \begin{pspicture}(0,0)(0,0)
 438 \rput(6.0,-0.5){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=blue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{
 439 \begin{minipage}{11cm}
 440 {\color{black}Doctoral studies}\\
 441  Classical potential \underline{molecular dynamics} simulations \ldots\\
 442  \underline{Density functional theory} calculations \ldots\\[0.2cm]
 443  \ldots on defect formation and SiC precipitation in Si
 444 \end{minipage}
 445 }}}
 446 \end{pspicture}
 447 \begin{pspicture}(0,0)(0,0)
 448 \psellipse[linecolor=red,linewidth=0.05cm](5,3.0)(0.8,1.0)
 449 \end{pspicture}
 450 \begin{pspicture}(0,0)(0,0)
 451 \psellipse[linecolor=blue,linewidth=0.05cm](8.2,3.2)(1.5,1.6)
 452 \end{pspicture}
 453
 454 \end{slide}
 455
 456 \begin{slide}
 457
 458 \headdiplom
 459 {\large\bf
 460  Selforganization of nanometric amorphous SiC lamellae
 461 }
 462
 463 \small
 464
 465 \vspace{0.2cm}
 466
 467 \begin{itemize}
 468  \item Regularly spaced, nanometric spherical\\
 469        and lamellar amorphous inclusions\\
 470        at the upper a/c interface
 471  \item Carbon accumulation\\
 472        in amorphous volumes
 473 \end{itemize}
 474
 475 \vspace{0.4cm}
 476
 477 \begin{minipage}{12cm}
 478 \includegraphics[width=9cm]{../../nlsop/img/k393abild1_e_l.eps}\\
 479 {\scriptsize
 480 XTEM bright-field, \unit[180]{keV} C$^+ \rightarrow$ Si,
 481 {\color{red}\underline{\degc{150}}},
 482 Dose: \unit[4.3 $\times 10^{17}$]{cm$^{-2}$}
 483 }
 484 \end{minipage}
 485
 486 \begin{picture}(0,0)(-182,-215)
 487 \begin{minipage}{6.5cm}
 488 \begin{center}
 489 \includegraphics[width=6.5cm]{../../nlsop/img/eftem.eps}\\[-0.2cm]
 490 {\scriptsize
 491 XTEM bright-field and respective EFTEM C map
 492 }
 493 \end{center}
 494 \end{minipage}
 495 \end{picture}
 496
 497 \end{slide}
 498
 499 \begin{slide}
 500
 501 \headdiplom
 502 {\large\bf
 503  Model displaying the formation of ordered lamellae
 504 }
 505
 506 \vspace{0.1cm}
 507
 508 \begin{center}
 509  \includegraphics[width=8.0cm]{../../nlsop/img/modell_ng_e.eps}
 510 \end{center}
 511
 512 \footnotesize
 513
 514 \begin{itemize}
 515 \item Supersaturation of C in c-Si\\
 516       $\rightarrow$ {\bf Carbon induced} nucleation of spherical
 517       SiC$_x$-precipitates
 518 \item High interfacial energy between 3C-SiC and c-Si\\
 519       $\rightarrow$ {\bf Amorphous} precipitates
 520 \item \unit[20-- 30]{\%} lower silicon density of a-SiC$_x$ compared to c-Si\\
 521       $\rightarrow$ {\bf Lateral strain} (black arrows)
 522 \item Implantation range near surface\\
 523       $\rightarrow$ {\bf Relaxation} of {\bf vertical strain component}
 524 \item Reduction of the carbon supersaturation in c-Si\\
 525       $\rightarrow$ {\bf Carbon diffusion} into amorphous volumina
 526       (white arrows)
 527 \item Remaining lateral strain\\
 528       $\rightarrow$ {\bf Strain enhanced} lateral amorphisation
 529 \item Absence of crystalline neighbours (structural information)\\
 530       $\rightarrow$ {\bf Stabilization} of amorphous inclusions
 531       {\bf against recrystallization}
 532 \end{itemize}
 533
 534 \end{slide}
 535
 536 \begin{slide}
 537
 538 \headdiplom
 539 {\large\bf
 540  Implementation of the Monte Carlo code
 541 }
 542
 543 \small
 544
 545 \begin{enumerate}
 546  \item \underline{Amorphization / Recrystallization}\\
 547        Ion collision in discretized target determined by random numbers
 548        distributed according to nuclear energy loss.
 549        Amorphization/recrystallization probability:
 550 \[
 551 p_{c \rightarrow a}(\vec{r}) = {\color{green} p_b} + {\color{blue} p_c c_C(\vec{r})} + {\color{red} \sum_{\textrm{amorphous neighbours}} \frac{p_s c_C(\vec{r'})}{(r-r')^2}}
 552 \]
 553 \begin{itemize}
 554  \item {\color{green} $p_b$} normal `ballistic' amorphization
 555  \item {\color{blue} $p_c$} carbon induced amorphization
 556  \item {\color{red} $p_s$} stress enhanced amorphization
 557 \end{itemize}
 558 \[
 559 p_{a \rightarrow c}(\vec r) = (1 - p_{c \rightarrow a}(\vec r)) \Big(1 - \frac{\sum_{direct \, neighbours} \delta (\vec{r'})}{6} \Big) \, \textrm{,}
 560 \]
 561 \[
 562 \delta (\vec r) = \left\{
 563 \begin{array}{ll}
 564         1 & \textrm{if volume at position $\vec r$ is amorphous} \\
 565         0 & \textrm{otherwise} \\
 566 \end{array}
 567 \right.
 568 \]
 569  \item \underline{Carbon incorporation}\\
 570        Incorporation volume determined according to implantation profile
 571  \item \underline{Diffusion / Sputtering}
 572        \begin{itemize}
 573         \item Transfer fraction of C atoms
 574               of crystalline into neighbored amorphous volumes
 575         \item Remove surface layer
 576        \end{itemize}
 577 \end{enumerate}
 578
 579 \end{slide}
 580
 581 \begin{slide}
 582
 583 \begin{minipage}{3.7cm}
 584 \begin{pspicture}(0,0)(0,0)
 585 \rput(1.7,0.2){\psframebox[fillstyle=gradient,gradbegin=red,gradend=white,gradlines=1000,gradangle=10,gradmidpoint=1,linestyle=none]{
 586 \begin{minipage}{3.7cm}
 587 \hfill
 588 \vspace{0.7cm}
 589 \end{minipage}
 590 }}
 591 \end{pspicture}
 592 {\large\bf
 593  Results
 594 }
 595
 596 \footnotesize
 597
 598 \vspace{1.2cm}
 599
 600 Evolution of the \ldots
 601 \begin{itemize}
 602  \item continuous\\
 603        amorphous layer
 604  \item a/c interface
 605  \item lamellar precipitates
 606 \end{itemize}
 607 \ldots reproduced!\\[1.4cm]
 608
 609 {\color{blue}
 610 \begin{center}
 611 Experiment \& simulation\\
 612 in good agreement\\[1.0cm]
 613
 614 Simulation is able to model the whole depth region\\[1.2cm]
 615 \end{center}
 616 }
 617
 618 \end{minipage}
 619 \begin{minipage}{0.5cm}
 620 \vfill
 621 \end{minipage}
 622 \begin{minipage}{8.0cm}
 623  \vspace{-0.3cm}
 624  \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e_1-2.eps}\\
 625  \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e2_2-2.eps}
 626 \end{minipage}
 627
 628 \end{slide}
 629
 630 \begin{slide}
 631
 632 \headdiplom
 633 {\large\bf
 634  Structural \& compositional details
 635 }
 636
 637 \begin{minipage}[t]{7.5cm}
 638 \includegraphics[height=6.5cm]{../../nlsop/img/ac_cconc_ver2_e.eps}\\
 639 \end{minipage}
 640 \begin{minipage}[t]{5.0cm}
 641 \includegraphics[height=6.5cm]{../../nlsop/img/97_98_e.eps}
 642 \end{minipage}
 643
 644 \footnotesize
 645
 646 \vspace{-0.1cm}
 647
 648 \begin{itemize}
 649  \item Fluctuation of C concentration in lamellae region
 650  \item \unit[8--10]{at.\%} C saturation limit
 651        within the respective conditions
 652  \item Complementarily arranged and alternating sequence of layers\\
 653        with a high and low amount of amorphous regions
 654  \item C accumulation in the amorphous phase / Origin of stress
 655 \end{itemize}
 656
 657 \begin{picture}(0,0)(-260,-50)
 658 \framebox{
 659 \begin{minipage}{3cm}
 660 \begin{center}
 661 {\color{blue}
 662 Precipitation process\\
 663 gets traceable\\
 664 by simulation!
 665 }
 666 \end{center}
 667 \end{minipage}
 668 }
 669 \end{picture}
 670
 671 \end{slide}
 672
 673 \fi
 674
 675 \begin{slide}
 676
 677 \headphd
 678 {\large\bf
 679  Formation of epitaxial single crystalline 3C-SiC
 680 }
 681
 682 \footnotesize
 683
 684 \vspace{0.2cm}
 685
 686 \begin{center}
 687 \begin{itemize}
 688  \item \underline{Implantation step 1}\\[0.1cm]
 689         Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
 690         $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
 691         {\color{blue}precipitates}
 692  \item \underline{Implantation step 2}\\[0.1cm]
 693         Little remaining dose | \unit[180]{keV} | \degc{250}\\
 694         $\Rightarrow$
 695         Destruction/Amorphization of precipitates at layer interface
 696  \item \underline{Annealing}\\[0.1cm]
 697        \unit[10]{h} at \degc{1250}\\
 698        $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
 699 \end{itemize}
 700 \end{center}
 701
 702 \begin{minipage}{7cm}
 703 \includegraphics[width=7cm]{ibs_3c-sic.eps}
 704 \end{minipage}
 705 \begin{minipage}{5cm}
 706 \begin{pspicture}(0,0)(0,0)
 707 \rnode{box}{
 708 \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
 709 \begin{minipage}{5.3cm}
 710  \begin{center}
 711  {\color{blue}
 712   3C-SiC precipitation\\
 713   not yet fully understood
 714  }
 715  \end{center}
 716  \vspace*{0.1cm}
 717  \renewcommand\labelitemi{$\Rightarrow$}
 718  Details of the SiC precipitation
 719  \begin{itemize}
 720   \item significant technological progress\\
 721         in SiC thin film formation
 722   \item perspectives for processes relying\\
 723         upon prevention of SiC precipitation
 724  \end{itemize}
 725 \end{minipage}
 726 }}
 727 \rput(-6.8,5.4){\pnode{h0}}
 728 \rput(-3.0,5.4){\pnode{h1}}
 729 \ncline[linecolor=blue]{-}{h0}{h1}
 730 \ncline[linecolor=blue]{->}{h1}{box}
 731 \end{pspicture}
 732 \end{minipage}
 733
 734 \end{slide}
 735
 736
 737 \end{document}
 738
 739 \ifnum1=0
 740
 741 % continue here
 742 %\fi
 743
 744 \begin{slide}
 745
 746 {\large\bf
 747  Model displaying the formation of ordered lamellae
 748 }
 749
 750
 751 \end{slide}
 752
 753 \begin{slide}
 754
 755  {\large\bf
 756   Supposed precipitation mechanism of SiC in Si
 757  }
 758
 759  \scriptsize
 760
 761  \vspace{0.1cm}
 762
 763  \begin{minipage}{3.8cm}
 764  Si \& SiC lattice structure\\[0.2cm]
 765  \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
 766  \hrule
 767  \end{minipage}
 768  \hspace{0.6cm}
 769  \begin{minipage}{3.8cm}
 770  \begin{center}
 771  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 772  \end{center}
 773  \end{minipage}
 774  \hspace{0.6cm}
 775  \begin{minipage}{3.8cm}
 776  \begin{center}
 777  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 778  \end{center}
 779  \end{minipage}
 780
 781  \begin{minipage}{4cm}
 782  \begin{center}
 783  C-Si dimers (dumbbells)\\[-0.1cm]
 784  on Si interstitial sites
 785  \end{center}
 786  \end{minipage}
 787  \hspace{0.2cm}
 788  \begin{minipage}{4.2cm}
 789  \begin{center}
 790  Agglomeration of C-Si dumbbells\\[-0.1cm]
 791  $\Rightarrow$ dark contrasts
 792  \end{center}
 793  \end{minipage}
 794  \hspace{0.2cm}
 795  \begin{minipage}{4cm}
 796  \begin{center}
 797  Precipitation of 3C-SiC in Si\\[-0.1cm]
 798  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 799  \& release of Si self-interstitials
 800  \end{center}
 801  \end{minipage}
 802
 803  \begin{minipage}{3.8cm}
 804  \begin{center}
 805  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 806  \end{center}
 807  \end{minipage}
 808  \hspace{0.6cm}
 809  \begin{minipage}{3.8cm}
 810  \begin{center}
 811  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 812  \end{center}
 813  \end{minipage}
 814  \hspace{0.6cm}
 815  \begin{minipage}{3.8cm}
 816  \begin{center}
 817  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 818  \end{center}
 819  \end{minipage}
 820
 821 \begin{pspicture}(0,0)(0,0)
 822 \psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
 823 \psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
 824 \rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
 825 \psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
 826 \rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 827  $4a_{\text{Si}}=5a_{\text{SiC}}$
 828  }}}
 829 \rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 830 \hkl(h k l) planes match
 831  }}}
 832 \rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 833 r = 2 - 4 nm
 834  }}}
 835 \end{pspicture}
 836
 837 \end{slide}
 838
 839 \begin{slide}
 840
 841  {\large\bf
 842   Supposed precipitation mechanism of SiC in Si
 843  }
 844
 845  \scriptsize
 846
 847  \vspace{0.1cm}
 848
 849  \begin{minipage}{3.8cm}
 850  Si \& SiC lattice structure\\[0.2cm]
 851  \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
 852  \hrule
 853  \end{minipage}
 854  \hspace{0.6cm}
 855  \begin{minipage}{3.8cm}
 856  \begin{center}
 857  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 858  \end{center}
 859  \end{minipage}
 860  \hspace{0.6cm}
 861  \begin{minipage}{3.8cm}
 862  \begin{center}
 863  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 864  \end{center}
 865  \end{minipage}
 866
 867  \begin{minipage}{4cm}
 868  \begin{center}
 869  C-Si dimers (dumbbells)\\[-0.1cm]
 870  on Si interstitial sites
 871  \end{center}
 872  \end{minipage}
 873  \hspace{0.2cm}
 874  \begin{minipage}{4.2cm}
 875  \begin{center}
 876  Agglomeration of C-Si dumbbells\\[-0.1cm]
 877  $\Rightarrow$ dark contrasts
 878  \end{center}
 879  \end{minipage}
 880  \hspace{0.2cm}
 881  \begin{minipage}{4cm}
 882  \begin{center}
 883  Precipitation of 3C-SiC in Si\\[-0.1cm]
 884  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 885  \& release of Si self-interstitials
 886  \end{center}
 887  \end{minipage}
 888
 889  \begin{minipage}{3.8cm}
 890  \begin{center}
 891  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 892  \end{center}
 893  \end{minipage}
 894  \hspace{0.6cm}
 895  \begin{minipage}{3.8cm}
 896  \begin{center}
 897  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 898  \end{center}
 899  \end{minipage}
 900  \hspace{0.6cm}
 901  \begin{minipage}{3.8cm}
 902  \begin{center}
 903  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 904  \end{center}
 905  \end{minipage}
 906
 907 \begin{pspicture}(0,0)(0,0)
 908 \psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
 909 \psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
 910 \rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
 911 \psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
 912 \rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 913  $4a_{\text{Si}}=5a_{\text{SiC}}$
 914  }}}
 915 \rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 916 \hkl(h k l) planes match
 917  }}}
 918 \rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 919 r = 2 - 4 nm
 920  }}}
 921 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
 922 \begin{minipage}{10cm}
 923 \small
 924 {\color{red}\bf Controversial views}
 925 \begin{itemize}
 926 \item Implantations at high T (Nejim et al.)
 927  \begin{itemize}
 928   \item Topotactic transformation based on \cs
 929   \item \si{} as supply reacting with further C in cleared volume
 930  \end{itemize}
 931 \item Annealing behavior (Serre et al.)
 932  \begin{itemize}
 933   \item Room temperature implants $\rightarrow$ highly mobile C
 934   \item Elevated T implants $\rightarrow$ no/low C redistribution/migration\\
 935         (indicate stable \cs{} configurations)
 936  \end{itemize}
 937 \item Strained silicon \& Si/SiC heterostructures
 938  \begin{itemize}
 939   \item Coherent SiC precipitates (tensile strain)
 940   \item Incoherent SiC (strain relaxation)
 941  \end{itemize}
 942 \end{itemize}
 943 \end{minipage}
 944  }}}
 945 \end{pspicture}
 946
 947 \end{slide}
 948
 949 \begin{slide}
 950
 951  {\large\bf
 952   Molecular dynamics (MD) simulations
 953  }
 954
 955  \vspace{12pt}
 956
 957  \small
 958
 959  {\bf MD basics:}
 960  \begin{itemize}
 961   \item Microscopic description of N particle system
 962   \item Analytical interaction potential
 963   \item Numerical integration using Newtons equation of motion\\
 964         as a propagation rule in 6N-dimensional phase space
 965   \item Observables obtained by time and/or ensemble averages
 966  \end{itemize}
 967  {\bf Details of the simulation:}
 968  \begin{itemize}
 969   \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
 970   \item Ensemble: NpT (isothermal-isobaric)
 971         \begin{itemize}
 972          \item Berendsen thermostat:
 973                $\tau_{\text{T}}=100\text{ fs}$
 974          \item Berendsen barostat:\\
 975                $\tau_{\text{P}}=100\text{ fs}$,
 976                $\beta^{-1}=100\text{ GPa}$
 977         \end{itemize}
 978   \item Erhart/Albe potential: Tersoff-like bond order potential
 979   \vspace*{12pt}
 980         \[
 981         E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
 982         \pot_{ij} = {\color{red}f_C(r_{ij})}
 983         \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
 984         \]
 985  \end{itemize}
 986
 987  \begin{picture}(0,0)(-230,-30)
 988   \includegraphics[width=5cm]{tersoff_angle.eps}
 989  \end{picture}
 990
 991 \end{slide}
 992
 993 \begin{slide}
 994
 995  {\large\bf
 996   Density functional theory (DFT) calculations
 997  }
 998
 999  \small
1000
1001  Basic ingredients necessary for DFT
1002
1003  \begin{itemize}
1004   \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
1005         \begin{itemize}
1006          \item ... uniquely determines the ground state potential
1007                / wavefunctions
1008          \item ... minimizes the systems total energy
1009         \end{itemize}
1010   \item \underline{Born-Oppenheimer}
1011         - $N$ moving electrons in an external potential of static nuclei
1012 \[
1013 H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
1014               +\sum_i^N V_{\text{ext}}(r_i)
1015               +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
1016 \]
1017   \item \underline{Effective potential}
1018         - averaged electrostatic potential \& exchange and correlation
1019 \[
1020 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
1021                  +V_{\text{XC}}[n(r)]
1022 \]
1023   \item \underline{Kohn-Sham system}
1024         - Schr\"odinger equation of N non-interacting particles
1025 \[
1026 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
1027 =\epsilon_i\Phi_i(r)
1028 \quad
1029 \Rightarrow
1030 \quad
1031 n(r)=\sum_i^N|\Phi_i(r)|^2
1032 \]
1033   \item \underline{Self-consistent solution}\\
1034 $n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
1035 which in turn depends on $n(r)$
1036   \item \underline{Variational principle}
1037         - minimize total energy with respect to $n(r)$
1038  \end{itemize}
1039
1040 \end{slide}
1041
1042 \begin{slide}
1043
1044  {\large\bf
1045   Density functional theory (DFT) calculations
1046  }
1047
1048  \small
1049
1050  \vspace*{0.2cm}
1051
1052  Details of applied DFT calculations in this work
1053
1054  \begin{itemize}
1055   \item \underline{Exchange correlation functional}
1056         - approximations for the inhomogeneous electron gas
1057         \begin{itemize}
1058          \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
1059          \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
1060         \end{itemize}
1061   \item \underline{Plane wave basis set}
1062         - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
1063 \[
1064 \rightarrow
1065 \text{Fourier series: } \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r), \quad E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}
1066 \qquad ({\color{blue}300\text{ eV}})
1067 \]
1068   \item \underline{Brillouin zone sampling} -
1069         {\color{blue}$\Gamma$-point only} calculations
1070   \item \underline{Pseudo potential}
1071         - consider only the valence electrons
1072   \item \underline{Code} - VASP 4.6
1073  \end{itemize}
1074
1075  \vspace*{0.2cm}
1076
1077  MD and structural optimization
1078
1079  \begin{itemize}
1080   \item MD integration: Gear predictor corrector algorithm
1081   \item Pressure control: Parrinello-Rahman pressure control
1082   \item Structural optimization: Conjugate gradient method
1083  \end{itemize}
1084
1085 \begin{pspicture}(0,0)(0,0)
1086 \psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
1087 \end{pspicture}
1088
1089 \end{slide}
1090
1091 \begin{slide}
1092
1093  {\large\bf
1094   C and Si self-interstitial point defects in silicon
1095  }
1096
1097  \small
1098
1099  \vspace*{0.3cm}
1100
1101 \begin{minipage}{8cm}
1102 Procedure:\\[0.3cm]
1103   \begin{pspicture}(0,0)(7,5)
1104   \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1105    \parbox{7cm}{
1106    \begin{itemize}
1107     \item Creation of c-Si simulation volume
1108     \item Periodic boundary conditions
1109     \item $T=0\text{ K}$, $p=0\text{ bar}$
1110    \end{itemize}
1111   }}}}
1112 \rput(3.5,2.1){\rnode{insert}{\psframebox{
1113  \parbox{7cm}{
1114   \begin{center}
1115   Insertion of interstitial C/Si atoms
1116   \end{center}
1117   }}}}
1118   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1119    \parbox{7cm}{
1120    \begin{center}
1121    Relaxation / structural energy minimization
1122    \end{center}
1123   }}}}
1124   \ncline[]{->}{init}{insert}
1125   \ncline[]{->}{insert}{cool}
1126  \end{pspicture}
1127 \end{minipage}
1128 \begin{minipage}{5cm}
1129   \includegraphics[width=5cm]{unit_cell_e.eps}\\
1130 \end{minipage}
1131
1132 \begin{minipage}{9cm}
1133  \begin{tabular}{l c c}
1134  \hline
1135  & size [unit cells] & \# atoms\\
1136 \hline
1137 VASP & $3\times 3\times 3$ & $216\pm 1$ \\
1138 Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
1139 \hline
1140  \end{tabular}
1141 \end{minipage}
1142 \begin{minipage}{4cm}
1143 {\color{red}$\bullet$} Tetrahedral\\
1144 {\color{green}$\bullet$} Hexagonal\\
1145 {\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
1146 {\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
1147 {\color{cyan}$\bullet$} Bond-centered\\
1148 {\color{black}$\bullet$} Vacancy / Substitutional
1149 \end{minipage}
1150
1151 \end{slide}
1152
1153 \begin{slide}
1154
1155  \footnotesize
1156
1157 \begin{minipage}{9.5cm}
1158
1159  {\large\bf
1160   Si self-interstitial point defects in silicon\\
1161  }
1162
1163 \begin{tabular}{l c c c c c}
1164 \hline
1165  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
1166 \hline
1167  VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
1168  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
1169 \hline
1170 \end{tabular}\\[0.2cm]
1171
1172 \begin{minipage}{4.7cm}
1173 \includegraphics[width=4.7cm]{e_kin_si_hex.ps}
1174 \end{minipage}
1175 \begin{minipage}{4.7cm}
1176 \begin{center}
1177 {\tiny nearly T $\rightarrow$ T}\\
1178 \end{center}
1179 \includegraphics[width=4.7cm]{nhex_tet.ps}
1180 \end{minipage}\\
1181
1182 \underline{Hexagonal} \hspace{2pt}
1183 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
1184 \framebox{
1185 \begin{minipage}{2.7cm}
1186 $E_{\text{f}}^*=4.48\text{ eV}$\\
1187 \includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
1188 \end{minipage}
1189 \begin{minipage}{0.4cm}
1190 \begin{center}
1191 $\Rightarrow$
1192 \end{center}
1193 \end{minipage}
1194 \begin{minipage}{2.7cm}
1195 $E_{\text{f}}=3.96\text{ eV}$\\
1196 \includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
1197 \end{minipage}
1198 }
1199 \begin{minipage}{2.9cm}
1200 \begin{flushright}
1201 \underline{Vacancy}\\
1202 \includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
1203 \end{flushright}
1204 \end{minipage}
1205
1206 \end{minipage}
1207 \begin{minipage}{3.5cm}
1208
1209 \begin{flushright}
1210 \underline{\hkl<1 1 0> dumbbell}\\
1211 \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
1212 \underline{Tetrahedral}\\
1213 \includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
1214 \underline{\hkl<1 0 0> dumbbell}\\
1215 \includegraphics[width=3.0cm]{si_pd_albe/100.eps}
1216 \end{flushright}
1217
1218 \end{minipage}
1219
1220 \end{slide}
1221
1222 \begin{slide}
1223
1224 \footnotesize
1225
1226  {\large\bf
1227   C interstitial point defects in silicon\\[-0.1cm]
1228  }
1229
1230 \begin{tabular}{l c c c c c c r}
1231 \hline
1232  $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\
1233 \hline
1234  VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1235  Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1236 \hline
1237 \end{tabular}\\[0.1cm]
1238
1239 \framebox{
1240 \begin{minipage}{2.7cm}
1241 \underline{Hexagonal} \hspace{2pt}
1242 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1243 $E_{\text{f}}^*=9.05\text{ eV}$\\
1244 \includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
1245 \end{minipage}
1246 \begin{minipage}{0.4cm}
1247 \begin{center}
1248 $\Rightarrow$
1249 \end{center}
1250 \end{minipage}
1251 \begin{minipage}{2.7cm}
1252 \underline{\hkl<1 0 0>}\\
1253 $E_{\text{f}}=3.88\text{ eV}$\\
1254 \includegraphics[width=2.7cm]{c_pd_albe/100.eps}
1255 \end{minipage}
1256 }
1257 \begin{minipage}{2cm}
1258 \hfill
1259 \end{minipage}
1260 \begin{minipage}{3cm}
1261 \begin{flushright}
1262 \underline{Tetrahedral}\\
1263 \includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
1264 \end{flushright}
1265 \end{minipage}
1266
1267 \framebox{
1268 \begin{minipage}{2.7cm}
1269 \underline{Bond-centered}\\
1270 $E_{\text{f}}^*=5.59\text{ eV}$\\
1271 \includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
1272 \end{minipage}
1273 \begin{minipage}{0.4cm}
1274 \begin{center}
1275 $\Rightarrow$
1276 \end{center}
1277 \end{minipage}
1278 \begin{minipage}{2.7cm}
1279 \underline{\hkl<1 1 0> dumbbell}\\
1280 $E_{\text{f}}=5.18\text{ eV}$\\
1281 \includegraphics[width=2.7cm]{c_pd_albe/110.eps}
1282 \end{minipage}
1283 }
1284 \begin{minipage}{2cm}
1285 \hfill
1286 \end{minipage}
1287 \begin{minipage}{3cm}
1288 \begin{flushright}
1289 \underline{Substitutional}\\
1290 \includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
1291 \end{flushright}
1292 \end{minipage}
1293
1294 \end{slide}
1295
1296 \begin{slide}
1297
1298 \footnotesize
1299
1300  {\large\bf\boldmath
1301   C \hkl<1 0 0> dumbbell interstitial configuration\\
1302  }
1303
1304 {\tiny
1305 \begin{tabular}{l c c c c c c c c}
1306 \hline
1307  Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
1308 \hline
1309 Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
1310 VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
1311 \hline
1312 \end{tabular}\\[0.2cm]
1313 \begin{tabular}{l c c c c }
1314 \hline
1315  Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
1316 \hline
1317 Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
1318 VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
1319 \hline
1320 \end{tabular}\\[0.2cm]
1321 \begin{tabular}{l c c c}
1322 \hline
1323  Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
1324 \hline
1325 Erhart/Albe & 0.084 & -0.091 & 0.175 \\
1326 VASP & 0.109 & -0.065 & 0.174 \\
1327 \hline
1328 \end{tabular}\\[0.6cm]
1329 }
1330
1331 \begin{minipage}{3.0cm}
1332 \begin{center}
1333 \underline{Erhart/Albe}
1334 \includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
1335 \end{center}
1336 \end{minipage}
1337 \begin{minipage}{3.0cm}
1338 \begin{center}
1339 \underline{VASP}
1340 \includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
1341 \end{center}
1342 \end{minipage}\\
1343
1344 \begin{picture}(0,0)(-185,10)
1345 \includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
1346 \end{picture}
1347 \begin{picture}(0,0)(-280,-150)
1348 \includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
1349 \end{picture}
1350
1351 \begin{pspicture}(0,0)(0,0)
1352 \psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
1353 \psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
1354 \psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
1355 \psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
1356 \end{pspicture}
1357
1358 \end{slide}
1359
1360 \begin{slide}
1361
1362 \small
1363
1364 \begin{minipage}{8.5cm}
1365
1366  {\large\bf
1367   Bond-centered interstitial configuration\\[-0.1cm]
1368  }
1369
1370 \begin{minipage}{3.0cm}
1371 \includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1372 \end{minipage}
1373 \begin{minipage}{5.2cm}
1374 \begin{itemize}
1375  \item Linear Si-C-Si bond
1376  \item Si: one C \& 3 Si neighbours
1377  \item Spin polarized calculations
1378  \item No saddle point!\\
1379        Real local minimum!
1380 \end{itemize}
1381 \end{minipage}
1382
1383 \framebox{
1384  \tiny
1385  \begin{minipage}[t]{6.5cm}
1386   \begin{minipage}[t]{1.2cm}
1387   {\color{red}Si}\\
1388   {\tiny sp$^3$}\\[0.8cm]
1389   \underline{${\color{black}\uparrow}$}
1390   \underline{${\color{black}\uparrow}$}
1391   \underline{${\color{black}\uparrow}$}
1392   \underline{${\color{red}\uparrow}$}\\
1393   sp$^3$
1394   \end{minipage}
1395   \begin{minipage}[t]{1.4cm}
1396   \begin{center}
1397   {\color{red}M}{\color{blue}O}\\[0.8cm]
1398   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1399   $\sigma_{\text{ab}}$\\[0.5cm]
1400   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1401   $\sigma_{\text{b}}$
1402   \end{center}
1403   \end{minipage}
1404   \begin{minipage}[t]{1.0cm}
1405   \begin{center}
1406   {\color{blue}C}\\
1407   {\tiny sp}\\[0.2cm]
1408   \underline{${\color{white}\uparrow\uparrow}$}
1409   \underline{${\color{white}\uparrow\uparrow}$}\\
1410   2p\\[0.4cm]
1411   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1412   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1413   sp
1414   \end{center}
1415   \end{minipage}
1416   \begin{minipage}[t]{1.4cm}
1417   \begin{center}
1418   {\color{blue}M}{\color{green}O}\\[0.8cm]
1419   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1420   $\sigma_{\text{ab}}$\\[0.5cm]
1421   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1422   $\sigma_{\text{b}}$
1423   \end{center}
1424   \end{minipage}
1425   \begin{minipage}[t]{1.2cm}
1426   \begin{flushright}
1427   {\color{green}Si}\\
1428   {\tiny sp$^3$}\\[0.8cm]
1429   \underline{${\color{green}\uparrow}$}
1430   \underline{${\color{black}\uparrow}$}
1431   \underline{${\color{black}\uparrow}$}
1432   \underline{${\color{black}\uparrow}$}\\
1433   sp$^3$
1434   \end{flushright}
1435   \end{minipage}
1436  \end{minipage}
1437 }\\[0.1cm]
1438
1439 \framebox{
1440 \begin{minipage}{4.5cm}
1441 \includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
1442 \end{minipage}
1443 \begin{minipage}{3.5cm}
1444 {\color{gray}$\bullet$} Spin up\\
1445 {\color{green}$\bullet$} Spin down\\
1446 {\color{blue}$\bullet$} Resulting spin up\\
1447 {\color{yellow}$\bullet$} Si atoms\\
1448 {\color{red}$\bullet$} C atom
1449 \end{minipage}
1450 }
1451
1452 \end{minipage}
1453 \begin{minipage}{4.2cm}
1454 \begin{flushright}
1455 \includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
1456 {\color{green}$\Box$} {\tiny unoccupied}\\
1457 {\color{red}$\bullet$} {\tiny occupied}
1458 \end{flushright}
1459 \end{minipage}
1460
1461 \end{slide}
1462
1463 \begin{slide}
1464
1465  {\large\bf\boldmath
1466   Migration of the C \hkl<1 0 0> dumbbell interstitial
1467  }
1468
1469 \scriptsize
1470
1471  {\small Investigated pathways}
1472
1473 \begin{minipage}{8.5cm}
1474 \begin{minipage}{8.3cm}
1475 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
1476 \begin{minipage}{2.4cm}
1477 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1478 \end{minipage}
1479 \begin{minipage}{0.4cm}
1480 $\rightarrow$
1481 \end{minipage}
1482 \begin{minipage}{2.4cm}
1483 \includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
1484 \end{minipage}
1485 \begin{minipage}{0.4cm}
1486 $\rightarrow$
1487 \end{minipage}
1488 \begin{minipage}{2.4cm}
1489 \includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
1490 \end{minipage}
1491 \end{minipage}\\
1492 \begin{minipage}{8.3cm}
1493 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
1494 \begin{minipage}{2.4cm}
1495 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1496 \end{minipage}
1497 \begin{minipage}{0.4cm}
1498 $\rightarrow$
1499 \end{minipage}
1500 \begin{minipage}{2.4cm}
1501 \includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
1502 \end{minipage}
1503 \begin{minipage}{0.4cm}
1504 $\rightarrow$
1505 \end{minipage}
1506 \begin{minipage}{2.4cm}
1507 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
1508 \end{minipage}
1509 \end{minipage}\\
1510 \begin{minipage}{8.3cm}
1511 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
1512 \begin{minipage}{2.4cm}
1513 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1514 \end{minipage}
1515 \begin{minipage}{0.4cm}
1516 $\rightarrow$
1517 \end{minipage}
1518 \begin{minipage}{2.4cm}
1519 \includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
1520 \end{minipage}
1521 \begin{minipage}{0.4cm}
1522 $\rightarrow$
1523 \end{minipage}
1524 \begin{minipage}{2.4cm}
1525 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
1526 \end{minipage}
1527 \end{minipage}
1528 \end{minipage}
1529 \framebox{
1530 \begin{minipage}{4.2cm}
1531  {\small Constrained relaxation\\
1532          technique (CRT) method}\\
1533 \includegraphics[width=4cm]{crt_orig.eps}
1534 \begin{itemize}
1535  \item Constrain diffusing atom
1536  \item Static constraints
1537 \end{itemize}
1538 \vspace*{0.3cm}
1539  {\small Modifications}\\
1540 \includegraphics[width=4cm]{crt_mod.eps}
1541 \begin{itemize}
1542  \item Constrain all atoms
1543  \item Update individual\\
1544        constraints
1545 \end{itemize}
1546 \end{minipage}
1547 }
1548
1549 \end{slide}
1550
1551 \begin{slide}
1552
1553  {\large\bf\boldmath
1554   Migration of the C \hkl<1 0 0> dumbbell interstitial
1555  }
1556
1557 \scriptsize
1558
1559 \framebox{
1560 \begin{minipage}{5.9cm}
1561 \begin{flushleft}
1562 \includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
1563 \end{flushleft}
1564 \begin{center}
1565 \begin{picture}(0,0)(60,0)
1566 \includegraphics[width=1cm]{vasp_mig/00-1.eps}
1567 \end{picture}
1568 \begin{picture}(0,0)(-5,0)
1569 \includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
1570 \end{picture}
1571 \begin{picture}(0,0)(-55,0)
1572 \includegraphics[width=1cm]{vasp_mig/bc.eps}
1573 \end{picture}
1574 \begin{picture}(0,0)(12.5,10)
1575 \includegraphics[width=1cm]{110_arrow.eps}
1576 \end{picture}
1577 \begin{picture}(0,0)(90,0)
1578 \includegraphics[height=0.9cm]{001_arrow.eps}
1579 \end{picture}
1580 \end{center}
1581 \vspace*{0.35cm}
1582 \end{minipage}
1583 }
1584 \begin{minipage}{0.3cm}
1585 \hfill
1586 \end{minipage}
1587 \framebox{
1588 \begin{minipage}{5.9cm}
1589 \begin{flushright}
1590 \includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
1591 \end{flushright}
1592 \begin{center}
1593 \begin{picture}(0,0)(60,0)
1594 \includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
1595 \end{picture}
1596 \begin{picture}(0,0)(5,0)
1597 \includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
1598 \end{picture}
1599 \begin{picture}(0,0)(-55,0)
1600 \includegraphics[width=1cm]{vasp_mig/0-10.eps}
1601 \end{picture}
1602 \begin{picture}(0,0)(12.5,10)
1603 \includegraphics[width=1cm]{100_arrow.eps}
1604 \end{picture}
1605 \begin{picture}(0,0)(90,0)
1606 \includegraphics[height=0.9cm]{001_arrow.eps}
1607 \end{picture}
1608 \end{center}
1609 \vspace*{0.3cm}
1610 \end{minipage}\\
1611 }
1612
1613 \vspace*{0.05cm}
1614
1615 \framebox{
1616 \begin{minipage}{5.9cm}
1617 \begin{flushleft}
1618 \includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
1619 \end{flushleft}
1620 \begin{center}
1621 \begin{picture}(0,0)(60,0)
1622 \includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps}
1623 \end{picture}
1624 \begin{picture}(0,0)(10,0)
1625 \includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
1626 \end{picture}
1627 \begin{picture}(0,0)(-60,0)
1628 \includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps}
1629 \end{picture}
1630 \begin{picture}(0,0)(12.5,10)
1631 \includegraphics[width=1cm]{100_arrow.eps}
1632 \end{picture}
1633 \begin{picture}(0,0)(90,0)
1634 \includegraphics[height=0.9cm]{001_arrow.eps}
1635 \end{picture}
1636 \end{center}
1637 \vspace*{0.3cm}
1638 \end{minipage}
1639 }
1640 \begin{minipage}{0.3cm}
1641 \hfill
1642 \end{minipage}
1643 \begin{minipage}{6.5cm}
1644 VASP results
1645 \begin{itemize}
1646  \item Energetically most favorable path
1647        \begin{itemize}
1648         \item Path 2
1649         \item Activation energy: $\approx$ 0.9 eV
1650         \item Experimental values: 0.73 ... 0.87 eV
1651        \end{itemize}
1652        $\Rightarrow$ {\color{blue}Diffusion} path identified!
1653  \item Reorientation (path 3)
1654        \begin{itemize}
1655         \item More likely composed of two consecutive steps of type 2
1656         \item Experimental values: 0.77 ... 0.88 eV
1657        \end{itemize}
1658        $\Rightarrow$ {\color{blue}Reorientation} transition identified!
1659 \end{itemize}
1660 \end{minipage}
1661
1662 \end{slide}
1663
1664 \begin{slide}
1665
1666  {\large\bf\boldmath
1667   Migration of the C \hkl<1 0 0> dumbbell interstitial
1668  }
1669
1670 \scriptsize
1671
1672  \vspace{0.1cm}
1673
1674 \begin{minipage}{6.5cm}
1675
1676 \framebox{
1677 \begin{minipage}[t]{5.9cm}
1678 \begin{flushleft}
1679 \includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
1680 \end{flushleft}
1681 \begin{center}
1682 \begin{pspicture}(0,0)(0,0)
1683 \psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
1684 \end{pspicture}
1685 \begin{picture}(0,0)(60,-50)
1686 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
1687 \end{picture}
1688 \begin{picture}(0,0)(5,-50)
1689 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
1690 \end{picture}
1691 \begin{picture}(0,0)(-55,-50)
1692 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
1693 \end{picture}
1694 \begin{picture}(0,0)(12.5,-40)
1695 \includegraphics[width=1cm]{110_arrow.eps}
1696 \end{picture}
1697 \begin{picture}(0,0)(90,-45)
1698 \includegraphics[height=0.9cm]{001_arrow.eps}
1699 \end{picture}\\
1700 \begin{pspicture}(0,0)(0,0)
1701 \psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
1702 \end{pspicture}
1703 \begin{picture}(0,0)(60,-15)
1704 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
1705 \end{picture}
1706 \begin{picture}(0,0)(35,-15)
1707 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
1708 \end{picture}
1709 \begin{picture}(0,0)(-5,-15)
1710 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
1711 \end{picture}
1712 \begin{picture}(0,0)(-55,-15)
1713 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
1714 \end{picture}
1715 \begin{picture}(0,0)(12.5,-5)
1716 \includegraphics[width=1cm]{100_arrow.eps}
1717 \end{picture}
1718 \begin{picture}(0,0)(90,-15)
1719 \includegraphics[height=0.9cm]{010_arrow.eps}
1720 \end{picture}
1721 \end{center}
1722 \end{minipage}
1723 }\\[0.1cm]
1724
1725 \begin{minipage}{5.9cm}
1726 Erhart/Albe results
1727 \begin{itemize}
1728  \item Lowest activation energy: $\approx$ 2.2 eV
1729  \item 2.4 times higher than VASP
1730  \item Different pathway
1731 \end{itemize}
1732 \end{minipage}
1733
1734 \end{minipage}
1735 \begin{minipage}{6.5cm}
1736
1737 \framebox{
1738 \begin{minipage}{5.9cm}
1739 %\begin{flushright}
1740 %\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
1741 %\end{flushright}
1742 %\begin{center}
1743 %\begin{pspicture}(0,0)(0,0)
1744 %\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
1745 %\end{pspicture}
1746 %\begin{picture}(0,0)(60,-5)
1747 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
1748 %\end{picture}
1749 %\begin{picture}(0,0)(0,-5)
1750 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
1751 %\end{picture}
1752 %\begin{picture}(0,0)(-55,-5)
1753 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
1754 %\end{picture}
1755 %\begin{picture}(0,0)(12.5,5)
1756 %\includegraphics[width=1cm]{100_arrow.eps}
1757 %\end{picture}
1758 %\begin{picture}(0,0)(90,0)
1759 %\includegraphics[height=0.9cm]{001_arrow.eps}
1760 %\end{picture}
1761 %\end{center}
1762 %\vspace{0.2cm}
1763 %\end{minipage}
1764 %}\\[0.2cm]
1765 %
1766 %\framebox{
1767 %\begin{minipage}{5.9cm}
1768 \includegraphics[width=5.9cm]{00-1_110_0-10_mig_albe.ps}
1769 \end{minipage}
1770 }\\[0.1cm]
1771
1772 \begin{minipage}{5.9cm}
1773 Transition involving \ci{} \hkl<1 1 0>
1774 \begin{itemize}
1775  \item Bond-centered configuration unstable\\
1776        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1777  \item Transition minima of path 2 \& 3\\
1778        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1779  \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV
1780  \item 2.4 - 3.4 times higher than VASP
1781  \item Rotation of dumbbell orientation
1782 \end{itemize}
1783 \vspace{0.1cm}
1784 \begin{center}
1785 {\color{blue}Overestimated diffusion barrier}
1786 \end{center}
1787 \end{minipage}
1788
1789 \end{minipage}
1790
1791 \end{slide}
1792
1793 \begin{slide}
1794
1795  {\large\bf\boldmath
1796   Combinations with a C-Si \hkl<1 0 0>-type interstitial
1797  }
1798
1799 \small
1800
1801 \vspace*{0.1cm}
1802
1803 Binding energy:
1804 $
1805 E_{\text{b}}=
1806 E_{\text{f}}^{\text{defect combination}}-
1807 E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
1808 E_{\text{f}}^{\text{2nd defect}}
1809 $
1810
1811 \vspace*{0.1cm}
1812
1813 {\scriptsize
1814 \begin{tabular}{l c c c c c c}
1815 \hline
1816  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1817  \hline
1818  \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1819  \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1820  \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}\\
1821  \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}\\
1822  \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}\\
1823  \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}\\
1824  \hline
1825  C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1826  Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1827 \hline
1828 \end{tabular}
1829 }
1830
1831 \vspace*{0.3cm}
1832
1833 \footnotesize
1834
1835 \begin{minipage}[t]{3.8cm}
1836 \underline{\hkl<1 0 0> at position 1}\\[0.1cm]
1837 \includegraphics[width=3.5cm]{00-1dc/2-25.eps}
1838 \end{minipage}
1839 \begin{minipage}[t]{3.5cm}
1840 \underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
1841 \includegraphics[width=3.2cm]{00-1dc/2-39.eps}
1842 \end{minipage}
1843 \begin{minipage}[t]{5.5cm}
1844 \begin{itemize}
1845  \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\
1846        $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
1847  \item Stress compensation / increase
1848  \item Unfavored: antiparallel orientations
1849  \item Indication of energetically favored\\
1850        agglomeration
1851  \item Most favorable: C clustering
1852  \item However: High barrier ($>4\,\text{eV}$)
1853  \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$
1854        (Entropy)
1855 \end{itemize}
1856 \end{minipage}
1857
1858 \begin{picture}(0,0)(-295,-130)
1859 \includegraphics[width=3.5cm]{comb_pos.eps}
1860 \end{picture}
1861
1862 \end{slide}
1863
1864 \begin{slide}
1865
1866  {\large\bf\boldmath
1867   Combinations of C-Si \hkl<1 0 0>-type interstitials
1868  }
1869
1870 \small
1871
1872 \vspace*{0.1cm}
1873
1874 Energetically most favorable combinations along \hkl<1 1 0>
1875
1876 \vspace*{0.1cm}
1877
1878 {\scriptsize
1879 \begin{tabular}{l c c c c c c}
1880 \hline
1881  & 1 & 2 & 3 & 4 & 5 & 6\\
1882 \hline
1883 $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
1884 C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
1885 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>\\
1886 \hline
1887 \end{tabular}
1888 }
1889
1890 \vspace*{0.3cm}
1891
1892 \begin{minipage}{7.0cm}
1893 \includegraphics[width=7cm]{db_along_110_cc.ps}
1894 \end{minipage}
1895 \begin{minipage}{6.0cm}
1896 \begin{itemize}
1897  \item Interaction proportional to reciprocal cube of C-C distance
1898  \item Saturation in the immediate vicinity
1899  \renewcommand\labelitemi{$\Rightarrow$}
1900  \item Agglomeration of \ci{} expected
1901  \item Absence of C clustering
1902 \end{itemize}
1903 \begin{center}
1904 {\color{blue}
1905  Consisten with initial precipitation model
1906 }
1907 \end{center}
1908 \end{minipage}
1909
1910 \vspace{0.2cm}
1911
1912 \end{slide}
1913
1914 \begin{slide}
1915
1916  {\large\bf\boldmath
1917   Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
1918  }
1919
1920  \scriptsize
1921
1922 %\begin{center}
1923 %\begin{minipage}{3.2cm}
1924 %\includegraphics[width=3cm]{sub_110_combo.eps}
1925 %\end{minipage}
1926 %\begin{minipage}{7.8cm}
1927 %\begin{tabular}{l c c c c c c}
1928 %\hline
1929 %C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
1930 %                   \hkl<1 0 1> & \hkl<-1 0 1> \\
1931 %\hline
1932 %1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
1933 %2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
1934 %3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
1935 %4 & \RM{4} & B & D & E & E & D \\
1936 %5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
1937 %\hline
1938 %\end{tabular}
1939 %\end{minipage}
1940 %\end{center}
1941
1942 %\begin{center}
1943 %\begin{tabular}{l c c c c c c c c c c}
1944 %\hline
1945 %Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
1946 %\hline
1947 %$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
1948 %$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
1949 %$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
1950 %\hline
1951 %\end{tabular}
1952 %\end{center}
1953
1954 \begin{minipage}{6.0cm}
1955 \includegraphics[width=5.8cm]{c_sub_si110.ps}
1956 \end{minipage}
1957 \begin{minipage}{7cm}
1958 \scriptsize
1959 \begin{itemize}
1960  \item IBS: C may displace Si\\
1961        $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
1962  \item Assumption:\\
1963        \hkl<1 1 0>-type $\rightarrow$ favored combination
1964  \renewcommand\labelitemi{$\Rightarrow$}
1965  \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
1966  \item Less favorable than C-Si \hkl<1 0 0> dumbbell
1967  \item Interaction drops quickly to zero\\
1968        $\rightarrow$ low capture radius
1969 \end{itemize}
1970 \begin{center}
1971  {\color{blue}
1972  IBS process far from equilibrium\\
1973  \cs{} \& \si{} instead of thermodynamic ground state
1974  }
1975 \end{center}
1976 \end{minipage}
1977
1978 \begin{minipage}{6.5cm}
1979 \includegraphics[width=6.0cm]{162-097.ps}
1980 \begin{itemize}
1981  \item Low migration barrier
1982 \end{itemize}
1983 \end{minipage}
1984 \begin{minipage}{6.5cm}
1985 \begin{center}
1986 Ab initio MD at \degc{900}\\
1987 \includegraphics[width=3.3cm]{md_vasp_01.eps}
1988 $t=\unit[2230]{fs}$\\
1989 \includegraphics[width=3.3cm]{md_vasp_02.eps}
1990 $t=\unit[2900]{fs}$
1991 \end{center}
1992 {\color{blue}
1993 Contribution of entropy to structural formation
1994 }
1995 \end{minipage}
1996
1997 \end{slide}
1998
1999 \begin{slide}
2000
2001  {\large\bf\boldmath
2002   Migration in C-Si \hkl<1 0 0> and vacancy combinations
2003  }
2004
2005  \footnotesize
2006
2007 \vspace{0.1cm}
2008
2009 \begin{minipage}[t]{3cm}
2010 \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
2011 \includegraphics[width=2.8cm]{00-1dc/0-59.eps}
2012 \end{minipage}
2013 \begin{minipage}[t]{7cm}
2014 \vspace{0.2cm}
2015 \begin{center}
2016  Low activation energies\\
2017  High activation energies for reverse processes\\
2018  $\Downarrow$\\
2019  {\color{blue}C$_{\text{sub}}$ very stable}\\
2020 \vspace*{0.1cm}
2021  \hrule
2022 \vspace*{0.1cm}
2023  Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
2024  $\Downarrow$\\
2025  {\color{blue}Formation of SiC by successive substitution by C}
2026
2027 \end{center}
2028 \end{minipage}
2029 \begin{minipage}[t]{3cm}
2030 \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
2031 \includegraphics[width=2.8cm]{00-1dc/3-14.eps}
2032 \end{minipage}
2033
2034
2035 \framebox{
2036 \begin{minipage}{5.9cm}
2037 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
2038 \begin{center}
2039 \begin{picture}(0,0)(70,0)
2040 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
2041 \end{picture}
2042 \begin{picture}(0,0)(30,0)
2043 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
2044 \end{picture}
2045 \begin{picture}(0,0)(-10,0)
2046 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
2047 \end{picture}
2048 \begin{picture}(0,0)(-48,0)
2049 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
2050 \end{picture}
2051 \begin{picture}(0,0)(12.5,5)
2052 \includegraphics[width=1cm]{100_arrow.eps}
2053 \end{picture}
2054 \begin{picture}(0,0)(97,-10)
2055 \includegraphics[height=0.9cm]{001_arrow.eps}
2056 \end{picture}
2057 \end{center}
2058 \vspace{0.1cm}
2059 \end{minipage}
2060 }
2061 \begin{minipage}{0.3cm}
2062 \hfill
2063 \end{minipage}
2064 \framebox{
2065 \begin{minipage}{5.9cm}
2066 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
2067 \begin{center}
2068 \begin{picture}(0,0)(60,0)
2069 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
2070 \end{picture}
2071 \begin{picture}(0,0)(25,0)
2072 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
2073 \end{picture}
2074 \begin{picture}(0,0)(-20,0)
2075 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
2076 \end{picture}
2077 \begin{picture}(0,0)(-55,0)
2078 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
2079 \end{picture}
2080 \begin{picture}(0,0)(12.5,5)
2081 \includegraphics[width=1cm]{100_arrow.eps}
2082 \end{picture}
2083 \begin{picture}(0,0)(95,0)
2084 \includegraphics[height=0.9cm]{001_arrow.eps}
2085 \end{picture}
2086 \end{center}
2087 \vspace{0.1cm}
2088 \end{minipage}
2089 }
2090
2091 \end{slide}
2092
2093 \begin{slide}
2094
2095  {\large\bf
2096   Conclusion of defect / migration / combined defect simulations
2097  }
2098
2099  \footnotesize
2100
2101 \vspace*{0.1cm}
2102
2103 Defect structures
2104 \begin{itemize}
2105  \item Accurately described by quantum-mechanical simulations
2106  \item Less accurate description by classical potential simulations
2107  \item Underestimated formation energy of \cs{} by classical approach
2108  \item Both methods predict same ground state: \ci{} \hkl<1 0 0> dumbbell
2109 \end{itemize}
2110
2111 Migration
2112 \begin{itemize}
2113  \item C migration pathway in Si identified
2114  \item Consistent with reorientation and diffusion experiments
2115 \end{itemize}
2116 \begin{itemize}
2117  \item Different path and ...
2118  \item overestimated barrier by classical potential calculations
2119 \end{itemize}
2120
2121 Concerning the precipitation mechanism
2122 \begin{itemize}
2123  \item Agglomeration of C-Si dumbbells energetically favorable
2124        (stress compensation)
2125  \item C-Si indeed favored compared to
2126        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2127  \item Possible low interaction capture radius of
2128        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2129  \item Low barrier for
2130        \ci{} \hkl<1 0 0> $\rightarrow$ \cs{} \& \si{} \hkl<1 1 0>
2131  \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
2132        C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
2133 \end{itemize}
2134 \begin{center}
2135 {\color{blue}Results suggest increased participation of \cs}
2136 \end{center}
2137
2138 \end{slide}
2139
2140 \begin{slide}
2141
2142  {\large\bf
2143   Silicon carbide precipitation simulations
2144  }
2145
2146  \small
2147
2148 {\scriptsize
2149  \begin{pspicture}(0,0)(12,6.5)
2150   % nodes
2151   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
2152    \parbox{7cm}{
2153    \begin{itemize}
2154     \item Create c-Si volume
2155     \item Periodc boundary conditions
2156     \item Set requested $T$ and $p=0\text{ bar}$
2157     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
2158    \end{itemize}
2159   }}}}
2160   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
2161    \parbox{7cm}{
2162    Insertion of C atoms at constant T
2163    \begin{itemize}
2164     \item total simulation volume {\pnode{in1}}
2165     \item volume of minimal SiC precipitate {\pnode{in2}}
2166     \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
2167           precipitate
2168    \end{itemize}
2169   }}}}
2170   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
2171    \parbox{7.0cm}{
2172    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
2173   }}}}
2174   \ncline[]{->}{init}{insert}
2175   \ncline[]{->}{insert}{cool}
2176   \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
2177   \rput(7.8,6){\footnotesize $V_1$}
2178   \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
2179   \rput(9.2,4.85){\tiny $V_2$}
2180   \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
2181   \rput(9.55,4.45){\footnotesize $V_3$}
2182   \rput(7.9,3.2){\pnode{ins1}}
2183   \rput(9.22,2.8){\pnode{ins2}}
2184   \rput(11.0,2.4){\pnode{ins3}}
2185   \ncline[]{->}{in1}{ins1}
2186   \ncline[]{->}{in2}{ins2}
2187   \ncline[]{->}{in3}{ins3}
2188  \end{pspicture}
2189 }
2190
2191 \begin{itemize}
2192  \item Restricted to classical potential simulations
2193  \item $V_2$ and $V_3$ considered due to low diffusion
2194  \item Amount of C atoms: 6000
2195        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
2196  \item Simulation volume: $31\times 31\times 31$ unit cells
2197        (238328 Si atoms)
2198 \end{itemize}
2199
2200 \end{slide}
2201
2202 \begin{slide}
2203
2204  {\large\bf\boldmath
2205   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2206  }
2207
2208  \small
2209
2210 \begin{minipage}{6.5cm}
2211 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2212 \end{minipage}
2213 \begin{minipage}{6.5cm}
2214 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2215 \end{minipage}
2216
2217 \begin{minipage}{6.5cm}
2218 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2219 \end{minipage}
2220 \begin{minipage}{6.5cm}
2221 \scriptsize
2222 \underline{Low C concentration ($V_1$)}\\
2223 \hkl<1 0 0> C-Si dumbbell dominated structure
2224 \begin{itemize}
2225  \item Si-C bumbs around 0.19 nm
2226  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2227        concatenated dumbbells of various orientation
2228  \item Si-Si NN distance stretched to 0.3 nm
2229 \end{itemize}
2230 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2231 \underline{High C concentration ($V_2$, $V_3$)}\\
2232 High amount of strongly bound C-C bonds\\
2233 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2234 Only short range order observable\\
2235 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2236 \end{minipage}
2237
2238 \end{slide}
2239
2240 \begin{slide}
2241
2242  {\large\bf\boldmath
2243   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2244  }
2245
2246  \small
2247
2248 \begin{minipage}{6.5cm}
2249 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2250 \end{minipage}
2251 \begin{minipage}{6.5cm}
2252 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2253 \end{minipage}
2254
2255 \begin{minipage}{6.5cm}
2256 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2257 \end{minipage}
2258 \begin{minipage}{6.5cm}
2259 \scriptsize
2260 \underline{Low C concentration ($V_1$)}\\
2261 \hkl<1 0 0> C-Si dumbbell dominated structure
2262 \begin{itemize}
2263  \item Si-C bumbs around 0.19 nm
2264  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2265        concatenated dumbbells of various orientation
2266  \item Si-Si NN distance stretched to 0.3 nm
2267 \end{itemize}
2268 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2269 \underline{High C concentration ($V_2$, $V_3$)}\\
2270 High amount of strongly bound C-C bonds\\
2271 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2272 Only short range order observable\\
2273 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2274 \end{minipage}
2275
2276 \begin{pspicture}(0,0)(0,0)
2277 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2278 \begin{minipage}{10cm}
2279 \small
2280 {\color{red}\bf 3C-SiC formation fails to appear}
2281 \begin{itemize}
2282 \item Low C concentration simulations
2283  \begin{itemize}
2284   \item Formation of \ci{} indeed occurs
2285   \item Agllomeration not observed
2286  \end{itemize}
2287 \item High C concentration simulations
2288  \begin{itemize}
2289   \item Amorphous SiC-like structure\\
2290         (not expected at prevailing temperatures)
2291   \item Rearrangement and transition into 3C-SiC structure missing
2292  \end{itemize}
2293 \end{itemize}
2294 \end{minipage}
2295  }}}
2296 \end{pspicture}
2297
2298 \end{slide}
2299
2300 \begin{slide}
2301
2302  {\large\bf
2303   Limitations of molecular dynamics and short range potentials
2304  }
2305
2306 \footnotesize
2307
2308 \vspace{0.2cm}
2309
2310 \underline{Time scale problem of MD}\\[0.2cm]
2311 Minimize integration error\\
2312 $\Rightarrow$ discretization considerably smaller than
2313               reciprocal of fastest vibrational mode\\[0.1cm]
2314 Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
2315 $\Rightarrow$ suitable choice of time step:
2316               $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
2317 $\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
2318 Several local minima in energy surface separated by large energy barriers\\
2319 $\Rightarrow$ transition event corresponds to a multiple
2320               of vibrational periods\\
2321 $\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
2322               infrequent transition events\\[0.1cm]
2323 {\color{blue}Accelerated methods:}
2324 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
2325
2326 \vspace{0.3cm}
2327
2328 \underline{Limitations related to the short range potential}\\[0.2cm]
2329 Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
2330 and 2$^{\text{nd}}$ next neighbours\\
2331 $\Rightarrow$ overestimated unphysical high forces of next neighbours
2332
2333 \vspace{0.3cm}
2334
2335 \framebox{
2336 \color{red}
2337 Potential enhanced problem of slow phase space propagation
2338 }
2339
2340 \vspace{0.3cm}
2341
2342 \underline{Approach to the (twofold) problem}\\[0.2cm]
2343 Increased temperature simulations without TAD corrections\\
2344 (accelerated methods or higher time scales exclusively not sufficient)
2345
2346 \begin{picture}(0,0)(-260,-30)
2347 \framebox{
2348 \begin{minipage}{4.2cm}
2349 \tiny
2350 \begin{center}
2351 \vspace{0.03cm}
2352 \underline{IBS}
2353 \end{center}
2354 \begin{itemize}
2355 \item 3C-SiC also observed for higher T
2356 \item higher T inside sample
2357 \item structural evolution vs.\\
2358       equilibrium properties
2359 \end{itemize}
2360 \end{minipage}
2361 }
2362 \end{picture}
2363
2364 \begin{picture}(0,0)(-305,-155)
2365 \framebox{
2366 \begin{minipage}{2.5cm}
2367 \tiny
2368 \begin{center}
2369 retain proper\\
2370 thermodynmic sampling
2371 \end{center}
2372 \end{minipage}
2373 }
2374 \end{picture}
2375
2376 \end{slide}
2377
2378 \begin{slide}
2379
2380  {\large\bf
2381   Increased temperature simulations at low C concentration
2382  }
2383
2384 \small
2385
2386 \begin{minipage}{6.5cm}
2387 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2388 \end{minipage}
2389 \begin{minipage}{6.5cm}
2390 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2391 \end{minipage}
2392
2393 \begin{minipage}{6.5cm}
2394 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2395 \end{minipage}
2396 \begin{minipage}{6.5cm}
2397 \scriptsize
2398  \underline{Si-C bonds:}
2399  \begin{itemize}
2400   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2401   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2402  \end{itemize}
2403  \underline{Si-Si bonds:}
2404  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2405  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2406  \underline{C-C bonds:}
2407  \begin{itemize}
2408   \item C-C next neighbour pairs reduced (mandatory)
2409   \item Peak at 0.3 nm slightly shifted
2410         \begin{itemize}
2411          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2412                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2413                combinations (|)\\
2414                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2415                ($\downarrow$)
2416          \item Range [|-$\downarrow$]:
2417                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2418                with nearby Si$_{\text{I}}$}
2419         \end{itemize}
2420  \end{itemize}
2421 \end{minipage}
2422
2423 \begin{picture}(0,0)(-330,-74)
2424 \color{blue}
2425 \framebox{
2426 \begin{minipage}{1.6cm}
2427 \tiny
2428 \begin{center}
2429 stretched SiC\\[-0.1cm]
2430 in c-Si
2431 \end{center}
2432 \end{minipage}
2433 }
2434 \end{picture}
2435
2436 \end{slide}
2437
2438 \begin{slide}
2439
2440  {\large\bf
2441   Increased temperature simulations at low C concentration
2442  }
2443
2444 \small
2445
2446 \begin{minipage}{6.5cm}
2447 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2448 \end{minipage}
2449 \begin{minipage}{6.5cm}
2450 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2451 \end{minipage}
2452
2453 \begin{minipage}{6.5cm}
2454 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2455 \end{minipage}
2456 \begin{minipage}{6.5cm}
2457 \scriptsize
2458  \underline{Si-C bonds:}
2459  \begin{itemize}
2460   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2461   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2462  \end{itemize}
2463  \underline{Si-Si bonds:}
2464  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2465  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2466  \underline{C-C bonds:}
2467  \begin{itemize}
2468   \item C-C next neighbour pairs reduced (mandatory)
2469   \item Peak at 0.3 nm slightly shifted
2470         \begin{itemize}
2471          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2472                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2473                combinations (|)\\
2474                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2475                ($\downarrow$)
2476          \item Range [|-$\downarrow$]:
2477                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2478                with nearby Si$_{\text{I}}$}
2479         \end{itemize}
2480  \end{itemize}
2481 \end{minipage}
2482
2483 %\begin{picture}(0,0)(-330,-74)
2484 %\color{blue}
2485 %\framebox{
2486 %\begin{minipage}{1.6cm}
2487 %\tiny
2488 %\begin{center}
2489 %stretched SiC\\[-0.1cm]
2490 %in c-Si
2491 %\end{center}
2492 %\end{minipage}
2493 %}
2494 %\end{picture}
2495
2496 \begin{pspicture}(0,0)(0,0)
2497 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2498 \begin{minipage}{10cm}
2499 \small
2500 {\color{blue}\bf Stretched SiC in c-Si}
2501 \begin{itemize}
2502 \item Consistent to precipitation model involving \cs{}
2503 \item Explains annealing behavior of high/low T C implants
2504       \begin{itemize}
2505        \item Low T: highly mobiel \ci{}
2506        \item High T: stable configurations of \cs{}
2507       \end{itemize}
2508 \end{itemize}
2509 $\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2510 $\Rightarrow$ Precipitation mechanism involving \cs{}
2511 \end{minipage}
2512  }}}
2513 \end{pspicture}
2514
2515 \end{slide}
2516
2517 \begin{slide}
2518
2519  {\large\bf
2520   Increased temperature simulations at high C concentration
2521  }
2522
2523 \footnotesize
2524
2525 \begin{minipage}{6.5cm}
2526 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2527 \end{minipage}
2528 \begin{minipage}{6.5cm}
2529 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2530 \end{minipage}
2531
2532 \vspace{0.1cm}
2533
2534 \scriptsize
2535
2536 \framebox{
2537 \begin{minipage}[t]{6.0cm}
2538 0.186 nm: Si-C pairs $\uparrow$\\
2539 (as expected in 3C-SiC)\\[0.2cm]
2540 0.282 nm: Si-C-C\\[0.2cm]
2541 $\approx$0.35 nm: C-Si-Si
2542 \end{minipage}
2543 }
2544 \begin{minipage}{0.2cm}
2545 \hfill
2546 \end{minipage}
2547 \framebox{
2548 \begin{minipage}[t]{6.0cm}
2549 0.15 nm: C-C pairs $\uparrow$\\
2550 (as expected in graphite/diamond)\\[0.2cm]
2551 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2552 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2553 \end{minipage}
2554 }
2555
2556 \begin{itemize}
2557 \item Decreasing cut-off artifact
2558 \item {\color{red}Amorphous} SiC-like phase remains
2559 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2560 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2561 \end{itemize}
2562
2563 \vspace{-0.1cm}
2564
2565 \begin{center}
2566 {\color{blue}
2567 \framebox{
2568 {\color{black}
2569 High C \& small $V$ \& short $t$
2570 $\Rightarrow$
2571 }
2572 Slow restructuring due to strong C-C bonds
2573 {\color{black}
2574 $\Leftarrow$
2575 High C \& low T implants
2576 }
2577 }
2578 }
2579 \end{center}
2580
2581 \end{slide}
2582
2583 \begin{slide}
2584
2585  {\large\bf
2586   Summary and Conclusions
2587  }
2588
2589  \scriptsize
2590
2591 %\vspace{0.1cm}
2592
2593 \framebox{
2594 \begin{minipage}[t]{12.9cm}
2595  \underline{Pecipitation simulations}
2596  \begin{itemize}
2597   \item High C concentration $\rightarrow$ amorphous SiC like phase
2598   \item Problem of potential enhanced slow phase space propagation
2599   \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2600   \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2601   \item High T necessary to simulate IBS conditions (far from equilibrium)
2602   \item Precipitation by successive agglomeration of \cs (epitaxy)
2603   \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2604         (stretched SiC, interface)
2605  \end{itemize}
2606 \end{minipage}
2607 }
2608
2609 %\vspace{0.1cm}
2610
2611 \framebox{
2612 \begin{minipage}{12.9cm}
2613  \underline{Defects}
2614  \begin{itemize}
2615    \item DFT / EA
2616         \begin{itemize}
2617          \item Point defects excellently / fairly well described
2618                by DFT / EA
2619          \item C$_{\text{sub}}$ drastically underestimated by EA
2620          \item EA predicts correct ground state:
2621                C$_{\text{sub}}$ \& \si{} $>$ \ci{}
2622          \item Identified migration path explaining
2623                diffusion and reorientation experiments by DFT
2624          \item EA fails to describe \ci{} migration:
2625                Wrong path \& overestimated barrier
2626         \end{itemize}
2627    \item Combinations of defects
2628          \begin{itemize}
2629           \item Agglomeration of point defects energetically favorable
2630                 by compensation of stress
2631           \item Formation of C-C unlikely
2632           \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2633           \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2634                 Low barrier (\unit[0.77]{eV}) \& low capture radius
2635         \end{itemize}
2636  \end{itemize}
2637 \end{minipage}
2638 }
2639
2640 \begin{center}
2641 {\color{blue}
2642 \framebox{Precipitation by successive agglomeration of \cs{}}
2643 }
2644 \end{center}
2645
2646 \end{slide}
2647
2648 \begin{slide}
2649
2650  {\large\bf
2651   Acknowledgements
2652  }
2653
2654  \vspace{0.1cm}
2655
2656  \small
2657
2658  Thanks to \ldots
2659
2660  \underline{Augsburg}
2661  \begin{itemize}
2662   \item Prof. B. Stritzker (accomodation at EP \RM{4})
2663   \item Ralf Utermann (EDV)
2664  \end{itemize}
2665
2666  \underline{Helsinki}
2667  \begin{itemize}
2668   \item Prof. K. Nordlund (MD)
2669  \end{itemize}
2670
2671  \underline{Munich}
2672  \begin{itemize}
2673   \item Bayerische Forschungsstiftung (financial support)
2674  \end{itemize}
2675
2676  \underline{Paderborn}
2677  \begin{itemize}
2678   \item Prof. J. Lindner (SiC)
2679   \item Prof. G. Schmidt (DFT + financial support)
2680   \item Dr. E. Rauls (DFT + SiC)
2681   \item Dr. S. Sanna (VASP)
2682  \end{itemize}
2683
2684 \vspace{0.2cm}
2685
2686 \begin{center}
2687 \framebox{
2688 \bf Thank you for your attention!
2689 }
2690 \end{center}
2691
2692 \end{slide}
2693
2694 \end{document}
2695
2696 \fi