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 \includegraphics[width=7cm]{ibs_3c-sic.eps}\\
 687
 688 \begin{itemize}
 689  \item \underline{Implantation step 1}\\[0.1cm]
 690         Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
 691         $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
 692         {\color{blue}precipitates}
 693  \item \underline{Implantation step 2}\\[0.1cm]
 694         Little remaining dose | \unit[180]{keV} | \degc{250}\\
 695         $\Rightarrow$
 696         Destruction/Amorphization of precipitates at layer interface
 697  \item \underline{Annealing}\\[0.1cm]
 698        \unit[10]{h} at \degc{1250}\\
 699        $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
 700 \end{itemize}
 701
 702 \begin{pspicture}(0,0)(0,0)
 703 \rput(10.0,4.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
 704 \begin{minipage}{5.3cm}
 705  \begin{center}
 706  {\color{blue}
 707   3C-SiC precipitation\\
 708   not yet fully understood
 709  }
 710  \end{center}
 711  \vspace*{0.1cm}
 712  \renewcommand\labelitemi{$\Rightarrow$}
 713  Details of the SiC precipitation
 714  \begin{itemize}
 715   \item significant technological progress\\
 716         in SiC thin film formation
 717   \item perspectives for processes relying\\
 718         upon prevention of SiC precipitation
 719  \end{itemize}
 720 \end{minipage}
 721 }}}
 722 \end{pspicture}
 723
 724
 725 \end{slide}
 726
 727
 728 \end{document}
 729
 730 \ifnum1=0
 731
 732 % continue here
 733 %\fi
 734
 735 \begin{slide}
 736
 737 {\large\bf
 738  Model displaying the formation of ordered lamellae
 739 }
 740
 741
 742 \end{slide}
 743
 744 \begin{slide}
 745
 746  {\large\bf
 747   Supposed precipitation mechanism of SiC in Si
 748  }
 749
 750  \scriptsize
 751
 752  \vspace{0.1cm}
 753
 754  \begin{minipage}{3.8cm}
 755  Si \& SiC lattice structure\\[0.2cm]
 756  \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
 757  \hrule
 758  \end{minipage}
 759  \hspace{0.6cm}
 760  \begin{minipage}{3.8cm}
 761  \begin{center}
 762  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 763  \end{center}
 764  \end{minipage}
 765  \hspace{0.6cm}
 766  \begin{minipage}{3.8cm}
 767  \begin{center}
 768  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 769  \end{center}
 770  \end{minipage}
 771
 772  \begin{minipage}{4cm}
 773  \begin{center}
 774  C-Si dimers (dumbbells)\\[-0.1cm]
 775  on Si interstitial sites
 776  \end{center}
 777  \end{minipage}
 778  \hspace{0.2cm}
 779  \begin{minipage}{4.2cm}
 780  \begin{center}
 781  Agglomeration of C-Si dumbbells\\[-0.1cm]
 782  $\Rightarrow$ dark contrasts
 783  \end{center}
 784  \end{minipage}
 785  \hspace{0.2cm}
 786  \begin{minipage}{4cm}
 787  \begin{center}
 788  Precipitation of 3C-SiC in Si\\[-0.1cm]
 789  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 790  \& release of Si self-interstitials
 791  \end{center}
 792  \end{minipage}
 793
 794  \begin{minipage}{3.8cm}
 795  \begin{center}
 796  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 797  \end{center}
 798  \end{minipage}
 799  \hspace{0.6cm}
 800  \begin{minipage}{3.8cm}
 801  \begin{center}
 802  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 803  \end{center}
 804  \end{minipage}
 805  \hspace{0.6cm}
 806  \begin{minipage}{3.8cm}
 807  \begin{center}
 808  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 809  \end{center}
 810  \end{minipage}
 811
 812 \begin{pspicture}(0,0)(0,0)
 813 \psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
 814 \psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
 815 \rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
 816 \psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
 817 \rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 818  $4a_{\text{Si}}=5a_{\text{SiC}}$
 819  }}}
 820 \rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 821 \hkl(h k l) planes match
 822  }}}
 823 \rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 824 r = 2 - 4 nm
 825  }}}
 826 \end{pspicture}
 827
 828 \end{slide}
 829
 830 \begin{slide}
 831
 832  {\large\bf
 833   Supposed precipitation mechanism of SiC in Si
 834  }
 835
 836  \scriptsize
 837
 838  \vspace{0.1cm}
 839
 840  \begin{minipage}{3.8cm}
 841  Si \& SiC lattice structure\\[0.2cm]
 842  \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
 843  \hrule
 844  \end{minipage}
 845  \hspace{0.6cm}
 846  \begin{minipage}{3.8cm}
 847  \begin{center}
 848  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 849  \end{center}
 850  \end{minipage}
 851  \hspace{0.6cm}
 852  \begin{minipage}{3.8cm}
 853  \begin{center}
 854  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 855  \end{center}
 856  \end{minipage}
 857
 858  \begin{minipage}{4cm}
 859  \begin{center}
 860  C-Si dimers (dumbbells)\\[-0.1cm]
 861  on Si interstitial sites
 862  \end{center}
 863  \end{minipage}
 864  \hspace{0.2cm}
 865  \begin{minipage}{4.2cm}
 866  \begin{center}
 867  Agglomeration of C-Si dumbbells\\[-0.1cm]
 868  $\Rightarrow$ dark contrasts
 869  \end{center}
 870  \end{minipage}
 871  \hspace{0.2cm}
 872  \begin{minipage}{4cm}
 873  \begin{center}
 874  Precipitation of 3C-SiC in Si\\[-0.1cm]
 875  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 876  \& release of Si self-interstitials
 877  \end{center}
 878  \end{minipage}
 879
 880  \begin{minipage}{3.8cm}
 881  \begin{center}
 882  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 883  \end{center}
 884  \end{minipage}
 885  \hspace{0.6cm}
 886  \begin{minipage}{3.8cm}
 887  \begin{center}
 888  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 889  \end{center}
 890  \end{minipage}
 891  \hspace{0.6cm}
 892  \begin{minipage}{3.8cm}
 893  \begin{center}
 894  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 895  \end{center}
 896  \end{minipage}
 897
 898 \begin{pspicture}(0,0)(0,0)
 899 \psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
 900 \psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
 901 \rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
 902 \psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
 903 \rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 904  $4a_{\text{Si}}=5a_{\text{SiC}}$
 905  }}}
 906 \rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 907 \hkl(h k l) planes match
 908  }}}
 909 \rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 910 r = 2 - 4 nm
 911  }}}
 912 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
 913 \begin{minipage}{10cm}
 914 \small
 915 {\color{red}\bf Controversial views}
 916 \begin{itemize}
 917 \item Implantations at high T (Nejim et al.)
 918  \begin{itemize}
 919   \item Topotactic transformation based on \cs
 920   \item \si{} as supply reacting with further C in cleared volume
 921  \end{itemize}
 922 \item Annealing behavior (Serre et al.)
 923  \begin{itemize}
 924   \item Room temperature implants $\rightarrow$ highly mobile C
 925   \item Elevated T implants $\rightarrow$ no/low C redistribution/migration\\
 926         (indicate stable \cs{} configurations)
 927  \end{itemize}
 928 \item Strained silicon \& Si/SiC heterostructures
 929  \begin{itemize}
 930   \item Coherent SiC precipitates (tensile strain)
 931   \item Incoherent SiC (strain relaxation)
 932  \end{itemize}
 933 \end{itemize}
 934 \end{minipage}
 935  }}}
 936 \end{pspicture}
 937
 938 \end{slide}
 939
 940 \begin{slide}
 941
 942  {\large\bf
 943   Molecular dynamics (MD) simulations
 944  }
 945
 946  \vspace{12pt}
 947
 948  \small
 949
 950  {\bf MD basics:}
 951  \begin{itemize}
 952   \item Microscopic description of N particle system
 953   \item Analytical interaction potential
 954   \item Numerical integration using Newtons equation of motion\\
 955         as a propagation rule in 6N-dimensional phase space
 956   \item Observables obtained by time and/or ensemble averages
 957  \end{itemize}
 958  {\bf Details of the simulation:}
 959  \begin{itemize}
 960   \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
 961   \item Ensemble: NpT (isothermal-isobaric)
 962         \begin{itemize}
 963          \item Berendsen thermostat:
 964                $\tau_{\text{T}}=100\text{ fs}$
 965          \item Berendsen barostat:\\
 966                $\tau_{\text{P}}=100\text{ fs}$,
 967                $\beta^{-1}=100\text{ GPa}$
 968         \end{itemize}
 969   \item Erhart/Albe potential: Tersoff-like bond order potential
 970   \vspace*{12pt}
 971         \[
 972         E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
 973         \pot_{ij} = {\color{red}f_C(r_{ij})}
 974         \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
 975         \]
 976  \end{itemize}
 977
 978  \begin{picture}(0,0)(-230,-30)
 979   \includegraphics[width=5cm]{tersoff_angle.eps}
 980  \end{picture}
 981
 982 \end{slide}
 983
 984 \begin{slide}
 985
 986  {\large\bf
 987   Density functional theory (DFT) calculations
 988  }
 989
 990  \small
 991
 992  Basic ingredients necessary for DFT
 993
 994  \begin{itemize}
 995   \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
 996         \begin{itemize}
 997          \item ... uniquely determines the ground state potential
 998                / wavefunctions
 999          \item ... minimizes the systems total energy
1000         \end{itemize}
1001   \item \underline{Born-Oppenheimer}
1002         - $N$ moving electrons in an external potential of static nuclei
1003 \[
1004 H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
1005               +\sum_i^N V_{\text{ext}}(r_i)
1006               +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
1007 \]
1008   \item \underline{Effective potential}
1009         - averaged electrostatic potential \& exchange and correlation
1010 \[
1011 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
1012                  +V_{\text{XC}}[n(r)]
1013 \]
1014   \item \underline{Kohn-Sham system}
1015         - Schr\"odinger equation of N non-interacting particles
1016 \[
1017 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
1018 =\epsilon_i\Phi_i(r)
1019 \quad
1020 \Rightarrow
1021 \quad
1022 n(r)=\sum_i^N|\Phi_i(r)|^2
1023 \]
1024   \item \underline{Self-consistent solution}\\
1025 $n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
1026 which in turn depends on $n(r)$
1027   \item \underline{Variational principle}
1028         - minimize total energy with respect to $n(r)$
1029  \end{itemize}
1030
1031 \end{slide}
1032
1033 \begin{slide}
1034
1035  {\large\bf
1036   Density functional theory (DFT) calculations
1037  }
1038
1039  \small
1040
1041  \vspace*{0.2cm}
1042
1043  Details of applied DFT calculations in this work
1044
1045  \begin{itemize}
1046   \item \underline{Exchange correlation functional}
1047         - approximations for the inhomogeneous electron gas
1048         \begin{itemize}
1049          \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
1050          \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
1051         \end{itemize}
1052   \item \underline{Plane wave basis set}
1053         - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
1054 \[
1055 \rightarrow
1056 \text{Fourier series: } \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r), \quad E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}
1057 \qquad ({\color{blue}300\text{ eV}})
1058 \]
1059   \item \underline{Brillouin zone sampling} -
1060         {\color{blue}$\Gamma$-point only} calculations
1061   \item \underline{Pseudo potential}
1062         - consider only the valence electrons
1063   \item \underline{Code} - VASP 4.6
1064  \end{itemize}
1065
1066  \vspace*{0.2cm}
1067
1068  MD and structural optimization
1069
1070  \begin{itemize}
1071   \item MD integration: Gear predictor corrector algorithm
1072   \item Pressure control: Parrinello-Rahman pressure control
1073   \item Structural optimization: Conjugate gradient method
1074  \end{itemize}
1075
1076 \begin{pspicture}(0,0)(0,0)
1077 \psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
1078 \end{pspicture}
1079
1080 \end{slide}
1081
1082 \begin{slide}
1083
1084  {\large\bf
1085   C and Si self-interstitial point defects in silicon
1086  }
1087
1088  \small
1089
1090  \vspace*{0.3cm}
1091
1092 \begin{minipage}{8cm}
1093 Procedure:\\[0.3cm]
1094   \begin{pspicture}(0,0)(7,5)
1095   \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1096    \parbox{7cm}{
1097    \begin{itemize}
1098     \item Creation of c-Si simulation volume
1099     \item Periodic boundary conditions
1100     \item $T=0\text{ K}$, $p=0\text{ bar}$
1101    \end{itemize}
1102   }}}}
1103 \rput(3.5,2.1){\rnode{insert}{\psframebox{
1104  \parbox{7cm}{
1105   \begin{center}
1106   Insertion of interstitial C/Si atoms
1107   \end{center}
1108   }}}}
1109   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1110    \parbox{7cm}{
1111    \begin{center}
1112    Relaxation / structural energy minimization
1113    \end{center}
1114   }}}}
1115   \ncline[]{->}{init}{insert}
1116   \ncline[]{->}{insert}{cool}
1117  \end{pspicture}
1118 \end{minipage}
1119 \begin{minipage}{5cm}
1120   \includegraphics[width=5cm]{unit_cell_e.eps}\\
1121 \end{minipage}
1122
1123 \begin{minipage}{9cm}
1124  \begin{tabular}{l c c}
1125  \hline
1126  & size [unit cells] & \# atoms\\
1127 \hline
1128 VASP & $3\times 3\times 3$ & $216\pm 1$ \\
1129 Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
1130 \hline
1131  \end{tabular}
1132 \end{minipage}
1133 \begin{minipage}{4cm}
1134 {\color{red}$\bullet$} Tetrahedral\\
1135 {\color{green}$\bullet$} Hexagonal\\
1136 {\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
1137 {\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
1138 {\color{cyan}$\bullet$} Bond-centered\\
1139 {\color{black}$\bullet$} Vacancy / Substitutional
1140 \end{minipage}
1141
1142 \end{slide}
1143
1144 \begin{slide}
1145
1146  \footnotesize
1147
1148 \begin{minipage}{9.5cm}
1149
1150  {\large\bf
1151   Si self-interstitial point defects in silicon\\
1152  }
1153
1154 \begin{tabular}{l c c c c c}
1155 \hline
1156  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
1157 \hline
1158  VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
1159  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
1160 \hline
1161 \end{tabular}\\[0.2cm]
1162
1163 \begin{minipage}{4.7cm}
1164 \includegraphics[width=4.7cm]{e_kin_si_hex.ps}
1165 \end{minipage}
1166 \begin{minipage}{4.7cm}
1167 \begin{center}
1168 {\tiny nearly T $\rightarrow$ T}\\
1169 \end{center}
1170 \includegraphics[width=4.7cm]{nhex_tet.ps}
1171 \end{minipage}\\
1172
1173 \underline{Hexagonal} \hspace{2pt}
1174 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
1175 \framebox{
1176 \begin{minipage}{2.7cm}
1177 $E_{\text{f}}^*=4.48\text{ eV}$\\
1178 \includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
1179 \end{minipage}
1180 \begin{minipage}{0.4cm}
1181 \begin{center}
1182 $\Rightarrow$
1183 \end{center}
1184 \end{minipage}
1185 \begin{minipage}{2.7cm}
1186 $E_{\text{f}}=3.96\text{ eV}$\\
1187 \includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
1188 \end{minipage}
1189 }
1190 \begin{minipage}{2.9cm}
1191 \begin{flushright}
1192 \underline{Vacancy}\\
1193 \includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
1194 \end{flushright}
1195 \end{minipage}
1196
1197 \end{minipage}
1198 \begin{minipage}{3.5cm}
1199
1200 \begin{flushright}
1201 \underline{\hkl<1 1 0> dumbbell}\\
1202 \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
1203 \underline{Tetrahedral}\\
1204 \includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
1205 \underline{\hkl<1 0 0> dumbbell}\\
1206 \includegraphics[width=3.0cm]{si_pd_albe/100.eps}
1207 \end{flushright}
1208
1209 \end{minipage}
1210
1211 \end{slide}
1212
1213 \begin{slide}
1214
1215 \footnotesize
1216
1217  {\large\bf
1218   C interstitial point defects in silicon\\[-0.1cm]
1219  }
1220
1221 \begin{tabular}{l c c c c c c r}
1222 \hline
1223  $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\
1224 \hline
1225  VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1226  Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1227 \hline
1228 \end{tabular}\\[0.1cm]
1229
1230 \framebox{
1231 \begin{minipage}{2.7cm}
1232 \underline{Hexagonal} \hspace{2pt}
1233 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1234 $E_{\text{f}}^*=9.05\text{ eV}$\\
1235 \includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
1236 \end{minipage}
1237 \begin{minipage}{0.4cm}
1238 \begin{center}
1239 $\Rightarrow$
1240 \end{center}
1241 \end{minipage}
1242 \begin{minipage}{2.7cm}
1243 \underline{\hkl<1 0 0>}\\
1244 $E_{\text{f}}=3.88\text{ eV}$\\
1245 \includegraphics[width=2.7cm]{c_pd_albe/100.eps}
1246 \end{minipage}
1247 }
1248 \begin{minipage}{2cm}
1249 \hfill
1250 \end{minipage}
1251 \begin{minipage}{3cm}
1252 \begin{flushright}
1253 \underline{Tetrahedral}\\
1254 \includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
1255 \end{flushright}
1256 \end{minipage}
1257
1258 \framebox{
1259 \begin{minipage}{2.7cm}
1260 \underline{Bond-centered}\\
1261 $E_{\text{f}}^*=5.59\text{ eV}$\\
1262 \includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
1263 \end{minipage}
1264 \begin{minipage}{0.4cm}
1265 \begin{center}
1266 $\Rightarrow$
1267 \end{center}
1268 \end{minipage}
1269 \begin{minipage}{2.7cm}
1270 \underline{\hkl<1 1 0> dumbbell}\\
1271 $E_{\text{f}}=5.18\text{ eV}$\\
1272 \includegraphics[width=2.7cm]{c_pd_albe/110.eps}
1273 \end{minipage}
1274 }
1275 \begin{minipage}{2cm}
1276 \hfill
1277 \end{minipage}
1278 \begin{minipage}{3cm}
1279 \begin{flushright}
1280 \underline{Substitutional}\\
1281 \includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
1282 \end{flushright}
1283 \end{minipage}
1284
1285 \end{slide}
1286
1287 \begin{slide}
1288
1289 \footnotesize
1290
1291  {\large\bf\boldmath
1292   C \hkl<1 0 0> dumbbell interstitial configuration\\
1293  }
1294
1295 {\tiny
1296 \begin{tabular}{l c c c c c c c c}
1297 \hline
1298  Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
1299 \hline
1300 Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
1301 VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
1302 \hline
1303 \end{tabular}\\[0.2cm]
1304 \begin{tabular}{l c c c c }
1305 \hline
1306  Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
1307 \hline
1308 Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
1309 VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
1310 \hline
1311 \end{tabular}\\[0.2cm]
1312 \begin{tabular}{l c c c}
1313 \hline
1314  Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
1315 \hline
1316 Erhart/Albe & 0.084 & -0.091 & 0.175 \\
1317 VASP & 0.109 & -0.065 & 0.174 \\
1318 \hline
1319 \end{tabular}\\[0.6cm]
1320 }
1321
1322 \begin{minipage}{3.0cm}
1323 \begin{center}
1324 \underline{Erhart/Albe}
1325 \includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
1326 \end{center}
1327 \end{minipage}
1328 \begin{minipage}{3.0cm}
1329 \begin{center}
1330 \underline{VASP}
1331 \includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
1332 \end{center}
1333 \end{minipage}\\
1334
1335 \begin{picture}(0,0)(-185,10)
1336 \includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
1337 \end{picture}
1338 \begin{picture}(0,0)(-280,-150)
1339 \includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
1340 \end{picture}
1341
1342 \begin{pspicture}(0,0)(0,0)
1343 \psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
1344 \psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
1345 \psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
1346 \psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
1347 \end{pspicture}
1348
1349 \end{slide}
1350
1351 \begin{slide}
1352
1353 \small
1354
1355 \begin{minipage}{8.5cm}
1356
1357  {\large\bf
1358   Bond-centered interstitial configuration\\[-0.1cm]
1359  }
1360
1361 \begin{minipage}{3.0cm}
1362 \includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1363 \end{minipage}
1364 \begin{minipage}{5.2cm}
1365 \begin{itemize}
1366  \item Linear Si-C-Si bond
1367  \item Si: one C \& 3 Si neighbours
1368  \item Spin polarized calculations
1369  \item No saddle point!\\
1370        Real local minimum!
1371 \end{itemize}
1372 \end{minipage}
1373
1374 \framebox{
1375  \tiny
1376  \begin{minipage}[t]{6.5cm}
1377   \begin{minipage}[t]{1.2cm}
1378   {\color{red}Si}\\
1379   {\tiny sp$^3$}\\[0.8cm]
1380   \underline{${\color{black}\uparrow}$}
1381   \underline{${\color{black}\uparrow}$}
1382   \underline{${\color{black}\uparrow}$}
1383   \underline{${\color{red}\uparrow}$}\\
1384   sp$^3$
1385   \end{minipage}
1386   \begin{minipage}[t]{1.4cm}
1387   \begin{center}
1388   {\color{red}M}{\color{blue}O}\\[0.8cm]
1389   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1390   $\sigma_{\text{ab}}$\\[0.5cm]
1391   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1392   $\sigma_{\text{b}}$
1393   \end{center}
1394   \end{minipage}
1395   \begin{minipage}[t]{1.0cm}
1396   \begin{center}
1397   {\color{blue}C}\\
1398   {\tiny sp}\\[0.2cm]
1399   \underline{${\color{white}\uparrow\uparrow}$}
1400   \underline{${\color{white}\uparrow\uparrow}$}\\
1401   2p\\[0.4cm]
1402   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1403   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1404   sp
1405   \end{center}
1406   \end{minipage}
1407   \begin{minipage}[t]{1.4cm}
1408   \begin{center}
1409   {\color{blue}M}{\color{green}O}\\[0.8cm]
1410   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1411   $\sigma_{\text{ab}}$\\[0.5cm]
1412   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1413   $\sigma_{\text{b}}$
1414   \end{center}
1415   \end{minipage}
1416   \begin{minipage}[t]{1.2cm}
1417   \begin{flushright}
1418   {\color{green}Si}\\
1419   {\tiny sp$^3$}\\[0.8cm]
1420   \underline{${\color{green}\uparrow}$}
1421   \underline{${\color{black}\uparrow}$}
1422   \underline{${\color{black}\uparrow}$}
1423   \underline{${\color{black}\uparrow}$}\\
1424   sp$^3$
1425   \end{flushright}
1426   \end{minipage}
1427  \end{minipage}
1428 }\\[0.1cm]
1429
1430 \framebox{
1431 \begin{minipage}{4.5cm}
1432 \includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
1433 \end{minipage}
1434 \begin{minipage}{3.5cm}
1435 {\color{gray}$\bullet$} Spin up\\
1436 {\color{green}$\bullet$} Spin down\\
1437 {\color{blue}$\bullet$} Resulting spin up\\
1438 {\color{yellow}$\bullet$} Si atoms\\
1439 {\color{red}$\bullet$} C atom
1440 \end{minipage}
1441 }
1442
1443 \end{minipage}
1444 \begin{minipage}{4.2cm}
1445 \begin{flushright}
1446 \includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
1447 {\color{green}$\Box$} {\tiny unoccupied}\\
1448 {\color{red}$\bullet$} {\tiny occupied}
1449 \end{flushright}
1450 \end{minipage}
1451
1452 \end{slide}
1453
1454 \begin{slide}
1455
1456  {\large\bf\boldmath
1457   Migration of the C \hkl<1 0 0> dumbbell interstitial
1458  }
1459
1460 \scriptsize
1461
1462  {\small Investigated pathways}
1463
1464 \begin{minipage}{8.5cm}
1465 \begin{minipage}{8.3cm}
1466 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
1467 \begin{minipage}{2.4cm}
1468 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1469 \end{minipage}
1470 \begin{minipage}{0.4cm}
1471 $\rightarrow$
1472 \end{minipage}
1473 \begin{minipage}{2.4cm}
1474 \includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
1475 \end{minipage}
1476 \begin{minipage}{0.4cm}
1477 $\rightarrow$
1478 \end{minipage}
1479 \begin{minipage}{2.4cm}
1480 \includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
1481 \end{minipage}
1482 \end{minipage}\\
1483 \begin{minipage}{8.3cm}
1484 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
1485 \begin{minipage}{2.4cm}
1486 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1487 \end{minipage}
1488 \begin{minipage}{0.4cm}
1489 $\rightarrow$
1490 \end{minipage}
1491 \begin{minipage}{2.4cm}
1492 \includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
1493 \end{minipage}
1494 \begin{minipage}{0.4cm}
1495 $\rightarrow$
1496 \end{minipage}
1497 \begin{minipage}{2.4cm}
1498 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
1499 \end{minipage}
1500 \end{minipage}\\
1501 \begin{minipage}{8.3cm}
1502 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
1503 \begin{minipage}{2.4cm}
1504 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1505 \end{minipage}
1506 \begin{minipage}{0.4cm}
1507 $\rightarrow$
1508 \end{minipage}
1509 \begin{minipage}{2.4cm}
1510 \includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
1511 \end{minipage}
1512 \begin{minipage}{0.4cm}
1513 $\rightarrow$
1514 \end{minipage}
1515 \begin{minipage}{2.4cm}
1516 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
1517 \end{minipage}
1518 \end{minipage}
1519 \end{minipage}
1520 \framebox{
1521 \begin{minipage}{4.2cm}
1522  {\small Constrained relaxation\\
1523          technique (CRT) method}\\
1524 \includegraphics[width=4cm]{crt_orig.eps}
1525 \begin{itemize}
1526  \item Constrain diffusing atom
1527  \item Static constraints
1528 \end{itemize}
1529 \vspace*{0.3cm}
1530  {\small Modifications}\\
1531 \includegraphics[width=4cm]{crt_mod.eps}
1532 \begin{itemize}
1533  \item Constrain all atoms
1534  \item Update individual\\
1535        constraints
1536 \end{itemize}
1537 \end{minipage}
1538 }
1539
1540 \end{slide}
1541
1542 \begin{slide}
1543
1544  {\large\bf\boldmath
1545   Migration of the C \hkl<1 0 0> dumbbell interstitial
1546  }
1547
1548 \scriptsize
1549
1550 \framebox{
1551 \begin{minipage}{5.9cm}
1552 \begin{flushleft}
1553 \includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
1554 \end{flushleft}
1555 \begin{center}
1556 \begin{picture}(0,0)(60,0)
1557 \includegraphics[width=1cm]{vasp_mig/00-1.eps}
1558 \end{picture}
1559 \begin{picture}(0,0)(-5,0)
1560 \includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
1561 \end{picture}
1562 \begin{picture}(0,0)(-55,0)
1563 \includegraphics[width=1cm]{vasp_mig/bc.eps}
1564 \end{picture}
1565 \begin{picture}(0,0)(12.5,10)
1566 \includegraphics[width=1cm]{110_arrow.eps}
1567 \end{picture}
1568 \begin{picture}(0,0)(90,0)
1569 \includegraphics[height=0.9cm]{001_arrow.eps}
1570 \end{picture}
1571 \end{center}
1572 \vspace*{0.35cm}
1573 \end{minipage}
1574 }
1575 \begin{minipage}{0.3cm}
1576 \hfill
1577 \end{minipage}
1578 \framebox{
1579 \begin{minipage}{5.9cm}
1580 \begin{flushright}
1581 \includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
1582 \end{flushright}
1583 \begin{center}
1584 \begin{picture}(0,0)(60,0)
1585 \includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
1586 \end{picture}
1587 \begin{picture}(0,0)(5,0)
1588 \includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
1589 \end{picture}
1590 \begin{picture}(0,0)(-55,0)
1591 \includegraphics[width=1cm]{vasp_mig/0-10.eps}
1592 \end{picture}
1593 \begin{picture}(0,0)(12.5,10)
1594 \includegraphics[width=1cm]{100_arrow.eps}
1595 \end{picture}
1596 \begin{picture}(0,0)(90,0)
1597 \includegraphics[height=0.9cm]{001_arrow.eps}
1598 \end{picture}
1599 \end{center}
1600 \vspace*{0.3cm}
1601 \end{minipage}\\
1602 }
1603
1604 \vspace*{0.05cm}
1605
1606 \framebox{
1607 \begin{minipage}{5.9cm}
1608 \begin{flushleft}
1609 \includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
1610 \end{flushleft}
1611 \begin{center}
1612 \begin{picture}(0,0)(60,0)
1613 \includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps}
1614 \end{picture}
1615 \begin{picture}(0,0)(10,0)
1616 \includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
1617 \end{picture}
1618 \begin{picture}(0,0)(-60,0)
1619 \includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps}
1620 \end{picture}
1621 \begin{picture}(0,0)(12.5,10)
1622 \includegraphics[width=1cm]{100_arrow.eps}
1623 \end{picture}
1624 \begin{picture}(0,0)(90,0)
1625 \includegraphics[height=0.9cm]{001_arrow.eps}
1626 \end{picture}
1627 \end{center}
1628 \vspace*{0.3cm}
1629 \end{minipage}
1630 }
1631 \begin{minipage}{0.3cm}
1632 \hfill
1633 \end{minipage}
1634 \begin{minipage}{6.5cm}
1635 VASP results
1636 \begin{itemize}
1637  \item Energetically most favorable path
1638        \begin{itemize}
1639         \item Path 2
1640         \item Activation energy: $\approx$ 0.9 eV
1641         \item Experimental values: 0.73 ... 0.87 eV
1642        \end{itemize}
1643        $\Rightarrow$ {\color{blue}Diffusion} path identified!
1644  \item Reorientation (path 3)
1645        \begin{itemize}
1646         \item More likely composed of two consecutive steps of type 2
1647         \item Experimental values: 0.77 ... 0.88 eV
1648        \end{itemize}
1649        $\Rightarrow$ {\color{blue}Reorientation} transition identified!
1650 \end{itemize}
1651 \end{minipage}
1652
1653 \end{slide}
1654
1655 \begin{slide}
1656
1657  {\large\bf\boldmath
1658   Migration of the C \hkl<1 0 0> dumbbell interstitial
1659  }
1660
1661 \scriptsize
1662
1663  \vspace{0.1cm}
1664
1665 \begin{minipage}{6.5cm}
1666
1667 \framebox{
1668 \begin{minipage}[t]{5.9cm}
1669 \begin{flushleft}
1670 \includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
1671 \end{flushleft}
1672 \begin{center}
1673 \begin{pspicture}(0,0)(0,0)
1674 \psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
1675 \end{pspicture}
1676 \begin{picture}(0,0)(60,-50)
1677 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
1678 \end{picture}
1679 \begin{picture}(0,0)(5,-50)
1680 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
1681 \end{picture}
1682 \begin{picture}(0,0)(-55,-50)
1683 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
1684 \end{picture}
1685 \begin{picture}(0,0)(12.5,-40)
1686 \includegraphics[width=1cm]{110_arrow.eps}
1687 \end{picture}
1688 \begin{picture}(0,0)(90,-45)
1689 \includegraphics[height=0.9cm]{001_arrow.eps}
1690 \end{picture}\\
1691 \begin{pspicture}(0,0)(0,0)
1692 \psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
1693 \end{pspicture}
1694 \begin{picture}(0,0)(60,-15)
1695 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
1696 \end{picture}
1697 \begin{picture}(0,0)(35,-15)
1698 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
1699 \end{picture}
1700 \begin{picture}(0,0)(-5,-15)
1701 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
1702 \end{picture}
1703 \begin{picture}(0,0)(-55,-15)
1704 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
1705 \end{picture}
1706 \begin{picture}(0,0)(12.5,-5)
1707 \includegraphics[width=1cm]{100_arrow.eps}
1708 \end{picture}
1709 \begin{picture}(0,0)(90,-15)
1710 \includegraphics[height=0.9cm]{010_arrow.eps}
1711 \end{picture}
1712 \end{center}
1713 \end{minipage}
1714 }\\[0.1cm]
1715
1716 \begin{minipage}{5.9cm}
1717 Erhart/Albe results
1718 \begin{itemize}
1719  \item Lowest activation energy: $\approx$ 2.2 eV
1720  \item 2.4 times higher than VASP
1721  \item Different pathway
1722 \end{itemize}
1723 \end{minipage}
1724
1725 \end{minipage}
1726 \begin{minipage}{6.5cm}
1727
1728 \framebox{
1729 \begin{minipage}{5.9cm}
1730 %\begin{flushright}
1731 %\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
1732 %\end{flushright}
1733 %\begin{center}
1734 %\begin{pspicture}(0,0)(0,0)
1735 %\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
1736 %\end{pspicture}
1737 %\begin{picture}(0,0)(60,-5)
1738 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
1739 %\end{picture}
1740 %\begin{picture}(0,0)(0,-5)
1741 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
1742 %\end{picture}
1743 %\begin{picture}(0,0)(-55,-5)
1744 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
1745 %\end{picture}
1746 %\begin{picture}(0,0)(12.5,5)
1747 %\includegraphics[width=1cm]{100_arrow.eps}
1748 %\end{picture}
1749 %\begin{picture}(0,0)(90,0)
1750 %\includegraphics[height=0.9cm]{001_arrow.eps}
1751 %\end{picture}
1752 %\end{center}
1753 %\vspace{0.2cm}
1754 %\end{minipage}
1755 %}\\[0.2cm]
1756 %
1757 %\framebox{
1758 %\begin{minipage}{5.9cm}
1759 \includegraphics[width=5.9cm]{00-1_110_0-10_mig_albe.ps}
1760 \end{minipage}
1761 }\\[0.1cm]
1762
1763 \begin{minipage}{5.9cm}
1764 Transition involving \ci{} \hkl<1 1 0>
1765 \begin{itemize}
1766  \item Bond-centered configuration unstable\\
1767        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1768  \item Transition minima of path 2 \& 3\\
1769        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1770  \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV
1771  \item 2.4 - 3.4 times higher than VASP
1772  \item Rotation of dumbbell orientation
1773 \end{itemize}
1774 \vspace{0.1cm}
1775 \begin{center}
1776 {\color{blue}Overestimated diffusion barrier}
1777 \end{center}
1778 \end{minipage}
1779
1780 \end{minipage}
1781
1782 \end{slide}
1783
1784 \begin{slide}
1785
1786  {\large\bf\boldmath
1787   Combinations with a C-Si \hkl<1 0 0>-type interstitial
1788  }
1789
1790 \small
1791
1792 \vspace*{0.1cm}
1793
1794 Binding energy:
1795 $
1796 E_{\text{b}}=
1797 E_{\text{f}}^{\text{defect combination}}-
1798 E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
1799 E_{\text{f}}^{\text{2nd defect}}
1800 $
1801
1802 \vspace*{0.1cm}
1803
1804 {\scriptsize
1805 \begin{tabular}{l c c c c c c}
1806 \hline
1807  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1808  \hline
1809  \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1810  \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1811  \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}\\
1812  \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}\\
1813  \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}\\
1814  \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}\\
1815  \hline
1816  C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1817  Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1818 \hline
1819 \end{tabular}
1820 }
1821
1822 \vspace*{0.3cm}
1823
1824 \footnotesize
1825
1826 \begin{minipage}[t]{3.8cm}
1827 \underline{\hkl<1 0 0> at position 1}\\[0.1cm]
1828 \includegraphics[width=3.5cm]{00-1dc/2-25.eps}
1829 \end{minipage}
1830 \begin{minipage}[t]{3.5cm}
1831 \underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
1832 \includegraphics[width=3.2cm]{00-1dc/2-39.eps}
1833 \end{minipage}
1834 \begin{minipage}[t]{5.5cm}
1835 \begin{itemize}
1836  \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\
1837        $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
1838  \item Stress compensation / increase
1839  \item Unfavored: antiparallel orientations
1840  \item Indication of energetically favored\\
1841        agglomeration
1842  \item Most favorable: C clustering
1843  \item However: High barrier ($>4\,\text{eV}$)
1844  \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$
1845        (Entropy)
1846 \end{itemize}
1847 \end{minipage}
1848
1849 \begin{picture}(0,0)(-295,-130)
1850 \includegraphics[width=3.5cm]{comb_pos.eps}
1851 \end{picture}
1852
1853 \end{slide}
1854
1855 \begin{slide}
1856
1857  {\large\bf\boldmath
1858   Combinations of C-Si \hkl<1 0 0>-type interstitials
1859  }
1860
1861 \small
1862
1863 \vspace*{0.1cm}
1864
1865 Energetically most favorable combinations along \hkl<1 1 0>
1866
1867 \vspace*{0.1cm}
1868
1869 {\scriptsize
1870 \begin{tabular}{l c c c c c c}
1871 \hline
1872  & 1 & 2 & 3 & 4 & 5 & 6\\
1873 \hline
1874 $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
1875 C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
1876 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>\\
1877 \hline
1878 \end{tabular}
1879 }
1880
1881 \vspace*{0.3cm}
1882
1883 \begin{minipage}{7.0cm}
1884 \includegraphics[width=7cm]{db_along_110_cc.ps}
1885 \end{minipage}
1886 \begin{minipage}{6.0cm}
1887 \begin{itemize}
1888  \item Interaction proportional to reciprocal cube of C-C distance
1889  \item Saturation in the immediate vicinity
1890  \renewcommand\labelitemi{$\Rightarrow$}
1891  \item Agglomeration of \ci{} expected
1892  \item Absence of C clustering
1893 \end{itemize}
1894 \begin{center}
1895 {\color{blue}
1896  Consisten with initial precipitation model
1897 }
1898 \end{center}
1899 \end{minipage}
1900
1901 \vspace{0.2cm}
1902
1903 \end{slide}
1904
1905 \begin{slide}
1906
1907  {\large\bf\boldmath
1908   Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
1909  }
1910
1911  \scriptsize
1912
1913 %\begin{center}
1914 %\begin{minipage}{3.2cm}
1915 %\includegraphics[width=3cm]{sub_110_combo.eps}
1916 %\end{minipage}
1917 %\begin{minipage}{7.8cm}
1918 %\begin{tabular}{l c c c c c c}
1919 %\hline
1920 %C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
1921 %                   \hkl<1 0 1> & \hkl<-1 0 1> \\
1922 %\hline
1923 %1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
1924 %2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
1925 %3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
1926 %4 & \RM{4} & B & D & E & E & D \\
1927 %5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
1928 %\hline
1929 %\end{tabular}
1930 %\end{minipage}
1931 %\end{center}
1932
1933 %\begin{center}
1934 %\begin{tabular}{l c c c c c c c c c c}
1935 %\hline
1936 %Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
1937 %\hline
1938 %$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
1939 %$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
1940 %$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
1941 %\hline
1942 %\end{tabular}
1943 %\end{center}
1944
1945 \begin{minipage}{6.0cm}
1946 \includegraphics[width=5.8cm]{c_sub_si110.ps}
1947 \end{minipage}
1948 \begin{minipage}{7cm}
1949 \scriptsize
1950 \begin{itemize}
1951  \item IBS: C may displace Si\\
1952        $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
1953  \item Assumption:\\
1954        \hkl<1 1 0>-type $\rightarrow$ favored combination
1955  \renewcommand\labelitemi{$\Rightarrow$}
1956  \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
1957  \item Less favorable than C-Si \hkl<1 0 0> dumbbell
1958  \item Interaction drops quickly to zero\\
1959        $\rightarrow$ low capture radius
1960 \end{itemize}
1961 \begin{center}
1962  {\color{blue}
1963  IBS process far from equilibrium\\
1964  \cs{} \& \si{} instead of thermodynamic ground state
1965  }
1966 \end{center}
1967 \end{minipage}
1968
1969 \begin{minipage}{6.5cm}
1970 \includegraphics[width=6.0cm]{162-097.ps}
1971 \begin{itemize}
1972  \item Low migration barrier
1973 \end{itemize}
1974 \end{minipage}
1975 \begin{minipage}{6.5cm}
1976 \begin{center}
1977 Ab initio MD at \degc{900}\\
1978 \includegraphics[width=3.3cm]{md_vasp_01.eps}
1979 $t=\unit[2230]{fs}$\\
1980 \includegraphics[width=3.3cm]{md_vasp_02.eps}
1981 $t=\unit[2900]{fs}$
1982 \end{center}
1983 {\color{blue}
1984 Contribution of entropy to structural formation
1985 }
1986 \end{minipage}
1987
1988 \end{slide}
1989
1990 \begin{slide}
1991
1992  {\large\bf\boldmath
1993   Migration in C-Si \hkl<1 0 0> and vacancy combinations
1994  }
1995
1996  \footnotesize
1997
1998 \vspace{0.1cm}
1999
2000 \begin{minipage}[t]{3cm}
2001 \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
2002 \includegraphics[width=2.8cm]{00-1dc/0-59.eps}
2003 \end{minipage}
2004 \begin{minipage}[t]{7cm}
2005 \vspace{0.2cm}
2006 \begin{center}
2007  Low activation energies\\
2008  High activation energies for reverse processes\\
2009  $\Downarrow$\\
2010  {\color{blue}C$_{\text{sub}}$ very stable}\\
2011 \vspace*{0.1cm}
2012  \hrule
2013 \vspace*{0.1cm}
2014  Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
2015  $\Downarrow$\\
2016  {\color{blue}Formation of SiC by successive substitution by C}
2017
2018 \end{center}
2019 \end{minipage}
2020 \begin{minipage}[t]{3cm}
2021 \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
2022 \includegraphics[width=2.8cm]{00-1dc/3-14.eps}
2023 \end{minipage}
2024
2025
2026 \framebox{
2027 \begin{minipage}{5.9cm}
2028 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
2029 \begin{center}
2030 \begin{picture}(0,0)(70,0)
2031 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
2032 \end{picture}
2033 \begin{picture}(0,0)(30,0)
2034 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
2035 \end{picture}
2036 \begin{picture}(0,0)(-10,0)
2037 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
2038 \end{picture}
2039 \begin{picture}(0,0)(-48,0)
2040 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
2041 \end{picture}
2042 \begin{picture}(0,0)(12.5,5)
2043 \includegraphics[width=1cm]{100_arrow.eps}
2044 \end{picture}
2045 \begin{picture}(0,0)(97,-10)
2046 \includegraphics[height=0.9cm]{001_arrow.eps}
2047 \end{picture}
2048 \end{center}
2049 \vspace{0.1cm}
2050 \end{minipage}
2051 }
2052 \begin{minipage}{0.3cm}
2053 \hfill
2054 \end{minipage}
2055 \framebox{
2056 \begin{minipage}{5.9cm}
2057 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
2058 \begin{center}
2059 \begin{picture}(0,0)(60,0)
2060 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
2061 \end{picture}
2062 \begin{picture}(0,0)(25,0)
2063 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
2064 \end{picture}
2065 \begin{picture}(0,0)(-20,0)
2066 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
2067 \end{picture}
2068 \begin{picture}(0,0)(-55,0)
2069 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
2070 \end{picture}
2071 \begin{picture}(0,0)(12.5,5)
2072 \includegraphics[width=1cm]{100_arrow.eps}
2073 \end{picture}
2074 \begin{picture}(0,0)(95,0)
2075 \includegraphics[height=0.9cm]{001_arrow.eps}
2076 \end{picture}
2077 \end{center}
2078 \vspace{0.1cm}
2079 \end{minipage}
2080 }
2081
2082 \end{slide}
2083
2084 \begin{slide}
2085
2086  {\large\bf
2087   Conclusion of defect / migration / combined defect simulations
2088  }
2089
2090  \footnotesize
2091
2092 \vspace*{0.1cm}
2093
2094 Defect structures
2095 \begin{itemize}
2096  \item Accurately described by quantum-mechanical simulations
2097  \item Less accurate description by classical potential simulations
2098  \item Underestimated formation energy of \cs{} by classical approach
2099  \item Both methods predict same ground state: \ci{} \hkl<1 0 0> dumbbell
2100 \end{itemize}
2101
2102 Migration
2103 \begin{itemize}
2104  \item C migration pathway in Si identified
2105  \item Consistent with reorientation and diffusion experiments
2106 \end{itemize}
2107 \begin{itemize}
2108  \item Different path and ...
2109  \item overestimated barrier by classical potential calculations
2110 \end{itemize}
2111
2112 Concerning the precipitation mechanism
2113 \begin{itemize}
2114  \item Agglomeration of C-Si dumbbells energetically favorable
2115        (stress compensation)
2116  \item C-Si indeed favored compared to
2117        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2118  \item Possible low interaction capture radius of
2119        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
2120  \item Low barrier for
2121        \ci{} \hkl<1 0 0> $\rightarrow$ \cs{} \& \si{} \hkl<1 1 0>
2122  \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
2123        C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
2124 \end{itemize}
2125 \begin{center}
2126 {\color{blue}Results suggest increased participation of \cs}
2127 \end{center}
2128
2129 \end{slide}
2130
2131 \begin{slide}
2132
2133  {\large\bf
2134   Silicon carbide precipitation simulations
2135  }
2136
2137  \small
2138
2139 {\scriptsize
2140  \begin{pspicture}(0,0)(12,6.5)
2141   % nodes
2142   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
2143    \parbox{7cm}{
2144    \begin{itemize}
2145     \item Create c-Si volume
2146     \item Periodc boundary conditions
2147     \item Set requested $T$ and $p=0\text{ bar}$
2148     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
2149    \end{itemize}
2150   }}}}
2151   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
2152    \parbox{7cm}{
2153    Insertion of C atoms at constant T
2154    \begin{itemize}
2155     \item total simulation volume {\pnode{in1}}
2156     \item volume of minimal SiC precipitate {\pnode{in2}}
2157     \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
2158           precipitate
2159    \end{itemize}
2160   }}}}
2161   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
2162    \parbox{7.0cm}{
2163    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
2164   }}}}
2165   \ncline[]{->}{init}{insert}
2166   \ncline[]{->}{insert}{cool}
2167   \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
2168   \rput(7.8,6){\footnotesize $V_1$}
2169   \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
2170   \rput(9.2,4.85){\tiny $V_2$}
2171   \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
2172   \rput(9.55,4.45){\footnotesize $V_3$}
2173   \rput(7.9,3.2){\pnode{ins1}}
2174   \rput(9.22,2.8){\pnode{ins2}}
2175   \rput(11.0,2.4){\pnode{ins3}}
2176   \ncline[]{->}{in1}{ins1}
2177   \ncline[]{->}{in2}{ins2}
2178   \ncline[]{->}{in3}{ins3}
2179  \end{pspicture}
2180 }
2181
2182 \begin{itemize}
2183  \item Restricted to classical potential simulations
2184  \item $V_2$ and $V_3$ considered due to low diffusion
2185  \item Amount of C atoms: 6000
2186        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
2187  \item Simulation volume: $31\times 31\times 31$ unit cells
2188        (238328 Si atoms)
2189 \end{itemize}
2190
2191 \end{slide}
2192
2193 \begin{slide}
2194
2195  {\large\bf\boldmath
2196   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2197  }
2198
2199  \small
2200
2201 \begin{minipage}{6.5cm}
2202 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2203 \end{minipage}
2204 \begin{minipage}{6.5cm}
2205 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2206 \end{minipage}
2207
2208 \begin{minipage}{6.5cm}
2209 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2210 \end{minipage}
2211 \begin{minipage}{6.5cm}
2212 \scriptsize
2213 \underline{Low C concentration ($V_1$)}\\
2214 \hkl<1 0 0> C-Si dumbbell dominated structure
2215 \begin{itemize}
2216  \item Si-C bumbs around 0.19 nm
2217  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2218        concatenated dumbbells of various orientation
2219  \item Si-Si NN distance stretched to 0.3 nm
2220 \end{itemize}
2221 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2222 \underline{High C concentration ($V_2$, $V_3$)}\\
2223 High amount of strongly bound C-C bonds\\
2224 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2225 Only short range order observable\\
2226 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2227 \end{minipage}
2228
2229 \end{slide}
2230
2231 \begin{slide}
2232
2233  {\large\bf\boldmath
2234   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
2235  }
2236
2237  \small
2238
2239 \begin{minipage}{6.5cm}
2240 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
2241 \end{minipage}
2242 \begin{minipage}{6.5cm}
2243 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
2244 \end{minipage}
2245
2246 \begin{minipage}{6.5cm}
2247 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
2248 \end{minipage}
2249 \begin{minipage}{6.5cm}
2250 \scriptsize
2251 \underline{Low C concentration ($V_1$)}\\
2252 \hkl<1 0 0> C-Si dumbbell dominated structure
2253 \begin{itemize}
2254  \item Si-C bumbs around 0.19 nm
2255  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
2256        concatenated dumbbells of various orientation
2257  \item Si-Si NN distance stretched to 0.3 nm
2258 \end{itemize}
2259 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
2260 \underline{High C concentration ($V_2$, $V_3$)}\\
2261 High amount of strongly bound C-C bonds\\
2262 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
2263 Only short range order observable\\
2264 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
2265 \end{minipage}
2266
2267 \begin{pspicture}(0,0)(0,0)
2268 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2269 \begin{minipage}{10cm}
2270 \small
2271 {\color{red}\bf 3C-SiC formation fails to appear}
2272 \begin{itemize}
2273 \item Low C concentration simulations
2274  \begin{itemize}
2275   \item Formation of \ci{} indeed occurs
2276   \item Agllomeration not observed
2277  \end{itemize}
2278 \item High C concentration simulations
2279  \begin{itemize}
2280   \item Amorphous SiC-like structure\\
2281         (not expected at prevailing temperatures)
2282   \item Rearrangement and transition into 3C-SiC structure missing
2283  \end{itemize}
2284 \end{itemize}
2285 \end{minipage}
2286  }}}
2287 \end{pspicture}
2288
2289 \end{slide}
2290
2291 \begin{slide}
2292
2293  {\large\bf
2294   Limitations of molecular dynamics and short range potentials
2295  }
2296
2297 \footnotesize
2298
2299 \vspace{0.2cm}
2300
2301 \underline{Time scale problem of MD}\\[0.2cm]
2302 Minimize integration error\\
2303 $\Rightarrow$ discretization considerably smaller than
2304               reciprocal of fastest vibrational mode\\[0.1cm]
2305 Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
2306 $\Rightarrow$ suitable choice of time step:
2307               $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
2308 $\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
2309 Several local minima in energy surface separated by large energy barriers\\
2310 $\Rightarrow$ transition event corresponds to a multiple
2311               of vibrational periods\\
2312 $\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
2313               infrequent transition events\\[0.1cm]
2314 {\color{blue}Accelerated methods:}
2315 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
2316
2317 \vspace{0.3cm}
2318
2319 \underline{Limitations related to the short range potential}\\[0.2cm]
2320 Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
2321 and 2$^{\text{nd}}$ next neighbours\\
2322 $\Rightarrow$ overestimated unphysical high forces of next neighbours
2323
2324 \vspace{0.3cm}
2325
2326 \framebox{
2327 \color{red}
2328 Potential enhanced problem of slow phase space propagation
2329 }
2330
2331 \vspace{0.3cm}
2332
2333 \underline{Approach to the (twofold) problem}\\[0.2cm]
2334 Increased temperature simulations without TAD corrections\\
2335 (accelerated methods or higher time scales exclusively not sufficient)
2336
2337 \begin{picture}(0,0)(-260,-30)
2338 \framebox{
2339 \begin{minipage}{4.2cm}
2340 \tiny
2341 \begin{center}
2342 \vspace{0.03cm}
2343 \underline{IBS}
2344 \end{center}
2345 \begin{itemize}
2346 \item 3C-SiC also observed for higher T
2347 \item higher T inside sample
2348 \item structural evolution vs.\\
2349       equilibrium properties
2350 \end{itemize}
2351 \end{minipage}
2352 }
2353 \end{picture}
2354
2355 \begin{picture}(0,0)(-305,-155)
2356 \framebox{
2357 \begin{minipage}{2.5cm}
2358 \tiny
2359 \begin{center}
2360 retain proper\\
2361 thermodynmic sampling
2362 \end{center}
2363 \end{minipage}
2364 }
2365 \end{picture}
2366
2367 \end{slide}
2368
2369 \begin{slide}
2370
2371  {\large\bf
2372   Increased temperature simulations at low C concentration
2373  }
2374
2375 \small
2376
2377 \begin{minipage}{6.5cm}
2378 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2379 \end{minipage}
2380 \begin{minipage}{6.5cm}
2381 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2382 \end{minipage}
2383
2384 \begin{minipage}{6.5cm}
2385 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2386 \end{minipage}
2387 \begin{minipage}{6.5cm}
2388 \scriptsize
2389  \underline{Si-C bonds:}
2390  \begin{itemize}
2391   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2392   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2393  \end{itemize}
2394  \underline{Si-Si bonds:}
2395  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2396  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2397  \underline{C-C bonds:}
2398  \begin{itemize}
2399   \item C-C next neighbour pairs reduced (mandatory)
2400   \item Peak at 0.3 nm slightly shifted
2401         \begin{itemize}
2402          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2403                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2404                combinations (|)\\
2405                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2406                ($\downarrow$)
2407          \item Range [|-$\downarrow$]:
2408                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2409                with nearby Si$_{\text{I}}$}
2410         \end{itemize}
2411  \end{itemize}
2412 \end{minipage}
2413
2414 \begin{picture}(0,0)(-330,-74)
2415 \color{blue}
2416 \framebox{
2417 \begin{minipage}{1.6cm}
2418 \tiny
2419 \begin{center}
2420 stretched SiC\\[-0.1cm]
2421 in c-Si
2422 \end{center}
2423 \end{minipage}
2424 }
2425 \end{picture}
2426
2427 \end{slide}
2428
2429 \begin{slide}
2430
2431  {\large\bf
2432   Increased temperature simulations at low C concentration
2433  }
2434
2435 \small
2436
2437 \begin{minipage}{6.5cm}
2438 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2439 \end{minipage}
2440 \begin{minipage}{6.5cm}
2441 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2442 \end{minipage}
2443
2444 \begin{minipage}{6.5cm}
2445 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2446 \end{minipage}
2447 \begin{minipage}{6.5cm}
2448 \scriptsize
2449  \underline{Si-C bonds:}
2450  \begin{itemize}
2451   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2452   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2453  \end{itemize}
2454  \underline{Si-Si bonds:}
2455  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2456  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2457  \underline{C-C bonds:}
2458  \begin{itemize}
2459   \item C-C next neighbour pairs reduced (mandatory)
2460   \item Peak at 0.3 nm slightly shifted
2461         \begin{itemize}
2462          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2463                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2464                combinations (|)\\
2465                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2466                ($\downarrow$)
2467          \item Range [|-$\downarrow$]:
2468                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2469                with nearby Si$_{\text{I}}$}
2470         \end{itemize}
2471  \end{itemize}
2472 \end{minipage}
2473
2474 %\begin{picture}(0,0)(-330,-74)
2475 %\color{blue}
2476 %\framebox{
2477 %\begin{minipage}{1.6cm}
2478 %\tiny
2479 %\begin{center}
2480 %stretched SiC\\[-0.1cm]
2481 %in c-Si
2482 %\end{center}
2483 %\end{minipage}
2484 %}
2485 %\end{picture}
2486
2487 \begin{pspicture}(0,0)(0,0)
2488 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2489 \begin{minipage}{10cm}
2490 \small
2491 {\color{blue}\bf Stretched SiC in c-Si}
2492 \begin{itemize}
2493 \item Consistent to precipitation model involving \cs{}
2494 \item Explains annealing behavior of high/low T C implants
2495       \begin{itemize}
2496        \item Low T: highly mobiel \ci{}
2497        \item High T: stable configurations of \cs{}
2498       \end{itemize}
2499 \end{itemize}
2500 $\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2501 $\Rightarrow$ Precipitation mechanism involving \cs{}
2502 \end{minipage}
2503  }}}
2504 \end{pspicture}
2505
2506 \end{slide}
2507
2508 \begin{slide}
2509
2510  {\large\bf
2511   Increased temperature simulations at high C concentration
2512  }
2513
2514 \footnotesize
2515
2516 \begin{minipage}{6.5cm}
2517 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2518 \end{minipage}
2519 \begin{minipage}{6.5cm}
2520 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2521 \end{minipage}
2522
2523 \vspace{0.1cm}
2524
2525 \scriptsize
2526
2527 \framebox{
2528 \begin{minipage}[t]{6.0cm}
2529 0.186 nm: Si-C pairs $\uparrow$\\
2530 (as expected in 3C-SiC)\\[0.2cm]
2531 0.282 nm: Si-C-C\\[0.2cm]
2532 $\approx$0.35 nm: C-Si-Si
2533 \end{minipage}
2534 }
2535 \begin{minipage}{0.2cm}
2536 \hfill
2537 \end{minipage}
2538 \framebox{
2539 \begin{minipage}[t]{6.0cm}
2540 0.15 nm: C-C pairs $\uparrow$\\
2541 (as expected in graphite/diamond)\\[0.2cm]
2542 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2543 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2544 \end{minipage}
2545 }
2546
2547 \begin{itemize}
2548 \item Decreasing cut-off artifact
2549 \item {\color{red}Amorphous} SiC-like phase remains
2550 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2551 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2552 \end{itemize}
2553
2554 \vspace{-0.1cm}
2555
2556 \begin{center}
2557 {\color{blue}
2558 \framebox{
2559 {\color{black}
2560 High C \& small $V$ \& short $t$
2561 $\Rightarrow$
2562 }
2563 Slow restructuring due to strong C-C bonds
2564 {\color{black}
2565 $\Leftarrow$
2566 High C \& low T implants
2567 }
2568 }
2569 }
2570 \end{center}
2571
2572 \end{slide}
2573
2574 \begin{slide}
2575
2576  {\large\bf
2577   Summary and Conclusions
2578  }
2579
2580  \scriptsize
2581
2582 %\vspace{0.1cm}
2583
2584 \framebox{
2585 \begin{minipage}[t]{12.9cm}
2586  \underline{Pecipitation simulations}
2587  \begin{itemize}
2588   \item High C concentration $\rightarrow$ amorphous SiC like phase
2589   \item Problem of potential enhanced slow phase space propagation
2590   \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2591   \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2592   \item High T necessary to simulate IBS conditions (far from equilibrium)
2593   \item Precipitation by successive agglomeration of \cs (epitaxy)
2594   \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2595         (stretched SiC, interface)
2596  \end{itemize}
2597 \end{minipage}
2598 }
2599
2600 %\vspace{0.1cm}
2601
2602 \framebox{
2603 \begin{minipage}{12.9cm}
2604  \underline{Defects}
2605  \begin{itemize}
2606    \item DFT / EA
2607         \begin{itemize}
2608          \item Point defects excellently / fairly well described
2609                by DFT / EA
2610          \item C$_{\text{sub}}$ drastically underestimated by EA
2611          \item EA predicts correct ground state:
2612                C$_{\text{sub}}$ \& \si{} $>$ \ci{}
2613          \item Identified migration path explaining
2614                diffusion and reorientation experiments by DFT
2615          \item EA fails to describe \ci{} migration:
2616                Wrong path \& overestimated barrier
2617         \end{itemize}
2618    \item Combinations of defects
2619          \begin{itemize}
2620           \item Agglomeration of point defects energetically favorable
2621                 by compensation of stress
2622           \item Formation of C-C unlikely
2623           \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2624           \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2625                 Low barrier (\unit[0.77]{eV}) \& low capture radius
2626         \end{itemize}
2627  \end{itemize}
2628 \end{minipage}
2629 }
2630
2631 \begin{center}
2632 {\color{blue}
2633 \framebox{Precipitation by successive agglomeration of \cs{}}
2634 }
2635 \end{center}
2636
2637 \end{slide}
2638
2639 \begin{slide}
2640
2641  {\large\bf
2642   Acknowledgements
2643  }
2644
2645  \vspace{0.1cm}
2646
2647  \small
2648
2649  Thanks to \ldots
2650
2651  \underline{Augsburg}
2652  \begin{itemize}
2653   \item Prof. B. Stritzker (accomodation at EP \RM{4})
2654   \item Ralf Utermann (EDV)
2655  \end{itemize}
2656
2657  \underline{Helsinki}
2658  \begin{itemize}
2659   \item Prof. K. Nordlund (MD)
2660  \end{itemize}
2661
2662  \underline{Munich}
2663  \begin{itemize}
2664   \item Bayerische Forschungsstiftung (financial support)
2665  \end{itemize}
2666
2667  \underline{Paderborn}
2668  \begin{itemize}
2669   \item Prof. J. Lindner (SiC)
2670   \item Prof. G. Schmidt (DFT + financial support)
2671   \item Dr. E. Rauls (DFT + SiC)
2672   \item Dr. S. Sanna (VASP)
2673  \end{itemize}
2674
2675 \vspace{0.2cm}
2676
2677 \begin{center}
2678 \framebox{
2679 \bf Thank you for your attention!
2680 }
2681 \end{center}
2682
2683 \end{slide}
2684
2685 \end{document}
2686
2687 \fi