posic/talks/mpi_app.tex

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  42 \usepackage{semlayer}           % Seminar overlays
  43 \usepackage{slidesec}           % Seminar sections and list of slides
  44
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  86 \begin{document}
  87
  88 \extraslideheight{10in}
  89 \slideframe{plain}
  90
  91 \pagestyle{empty}
  92
  93 % specify width and height
  94 \slidewidth 26.3cm
  95 \slideheight 19.9cm
  96
  97 % margin
  98 \def\slidetopmargin{-0.15cm}
  99
 100 \newcommand{\ham}{\mathcal{H}}
 101 \newcommand{\pot}{\mathcal{V}}
 102 \newcommand{\foo}{\mathcal{U}}
 103 \newcommand{\vir}{\mathcal{W}}
 104
 105 % itemize level ii
 106 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
 107
 108 % nice phi
 109 \renewcommand{\phi}{\varphi}
 110
 111 % roman letters
 112 \newcommand{\RM}[1]{\MakeUppercase{\romannumeral #1{}}}
 113
 114 % colors
 115 \newrgbcolor{si-yellow}{.6 .6 0}
 116 \newrgbcolor{hb}{0.75 0.77 0.89}
 117 \newrgbcolor{lbb}{0.75 0.8 0.88}
 118 \newrgbcolor{hlbb}{0.825 0.88 0.968}
 119 \newrgbcolor{lachs}{1.0 .93 .81}
 120
 121 % shortcuts
 122 \newcommand{\si}{Si$_{\text{i}}${}}
 123 \newcommand{\ci}{C$_{\text{i}}${}}
 124 \newcommand{\cs}{C$_{\text{sub}}${}}
 125 \newcommand{\degc}[1]{\unit[#1]{$^{\circ}$C}{}}
 126 \newcommand{\distn}[1]{\unit[#1]{nm}{}}
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 129
 130 % no vertical centering
 131 %\centerslidesfalse
 132
 133 % layout check
 134 %\layout
 135 \begin{slide}
 136 \center
 137 {\Huge
 138 E\\
 139 F\\
 140 G\\
 141 A B C D E F G H G F E D C B A
 142 G\\
 143 F\\
 144 E\\
 145 }
 146 \end{slide}
 147
 148 % topic
 149
 150 \begin{slide}
 151 \begin{center}
 152
 153  \vspace{16pt}
 154
 155  {\LARGE\bf
 156   Atomistic simulation studies\\[0.2cm]
 157   in the C/Si system
 158  }
 159
 160  \vspace{48pt}
 161
 162  \textsc{Frank Zirkelbach}
 163
 164  \vspace{48pt}
 165
 166  Application talk at the Max Planck Institute for Solid State Research
 167
 168  \vspace{08pt}
 169
 170  Stuttgart, November 2011
 171
 172 \end{center}
 173 \end{slide}
 174
 175 % no vertical centering
 176 \centerslidesfalse
 177
 178 % intro
 179
 180 \begin{slide}
 181
 182 %{\large\bf
 183 % Phase diagram of the C/Si system\\
 184 %}
 185
 186 \vspace*{0.2cm}
 187
 188 \begin{minipage}{6.5cm}
 189 \includegraphics[width=6.5cm]{si-c_phase.eps}
 190 \begin{center}
 191 {\tiny
 192 R. I. Scace and G. A. Slack, J. Chem. Phys. 30, 1551 (1959)
 193 }
 194 \end{center}
 195 \begin{pspicture}(0,0)(0,0)
 196 \psellipse[linecolor=blue,linewidth=0.1cm](3.55,4.0)(0.5,2.9)
 197 \end{pspicture}
 198 \end{minipage}
 199 \begin{minipage}{6cm}
 200 {\bf Phase diagram of the C/Si system}\\[0.2cm]
 201 {\color{blue}Stoichiometric composition}
 202 \begin{itemize}
 203 \item only chemical stable compound
 204 \item wide band gap semiconductor\\
 205       \underline{silicon carbide}, SiC
 206 \end{itemize}
 207 \end{minipage}
 208
 209 \end{slide}
 210
 211 % motivation / properties / applications of silicon carbide
 212
 213 \begin{slide}
 214
 215 \vspace*{1.8cm}
 216
 217 \small
 218
 219 \begin{pspicture}(0,0)(13.5,5)
 220
 221  \psframe*[linecolor=hb](-0.2,0)(12.9,5)
 222
 223  \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](5.2,1)(6.5,1)(6.5,3)(5.2,3)
 224  \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](6.4,0.5)(7.7,2)(7.7,2)(6.4,3.5)
 225
 226  \rput[lt](0,4.6){\color{gray}PROPERTIES}
 227
 228  \rput[lt](0.3,4){wide band gap}
 229  \rput[lt](0.3,3.5){high electric breakdown field}
 230  \rput[lt](0.3,3){good electron mobility}
 231  \rput[lt](0.3,2.5){high electron saturation drift velocity}
 232  \rput[lt](0.3,2){high thermal conductivity}
 233
 234  \rput[lt](0.3,1.5){hard and mechanically stable}
 235  \rput[lt](0.3,1){chemically inert}
 236
 237  \rput[lt](0.3,0.5){radiation hardness}
 238
 239  \rput[rt](12.7,4.6){\color{gray}APPLICATIONS}
 240
 241  \rput[rt](12.5,3.85){high-temperature, high power}
 242  \rput[rt](12.5,3.5){and high-frequency}
 243  \rput[rt](12.5,3.15){electronic and optoelectronic devices}
 244
 245  \rput[rt](12.5,2.35){material suitable for extreme conditions}
 246  \rput[rt](12.5,2){microelectromechanical systems}
 247  \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements}
 248
 249  \rput[rt](12.5,0.85){first wall reactor material, detectors}
 250  \rput[rt](12.5,0.5){and electronic devices for space}
 251
 252 \end{pspicture}
 253
 254 \begin{picture}(0,0)(5,-162)
 255 \includegraphics[height=2.2cm]{3C_SiC_bs.eps}
 256 \end{picture}
 257 \begin{picture}(0,0)(-120,-162)
 258 \includegraphics[height=2.2cm]{nasa_600c_led.eps}
 259 \end{picture}
 260 \begin{picture}(0,0)(-270,-162)
 261 \includegraphics[height=2.2cm]{6h-sic_3c-sic.eps}
 262 \end{picture}
 263 %%%%
 264 \begin{picture}(0,0)(10,65)
 265 \includegraphics[height=2.8cm]{sic_switch.eps}
 266 \end{picture}
 267 %\begin{picture}(0,0)(-243,65)
 268 \begin{picture}(0,0)(-110,65)
 269 \includegraphics[height=2.8cm]{ise_99.eps}
 270 \end{picture}
 271 %\begin{picture}(0,0)(-135,65)
 272 \begin{picture}(0,0)(-100,65)
 273 \includegraphics[height=1.2cm]{infineon_schottky.eps}
 274 \end{picture}
 275 \begin{picture}(0,0)(-233,65)
 276 \includegraphics[height=2.8cm]{solar_car.eps}
 277 \end{picture}
 278
 279 \end{slide}
 280
 281 % motivation
 282
 283 \begin{slide}
 284
 285  {\large\bf
 286   Polytypes of SiC\\[0.4cm]
 287  }
 288
 289 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
 290 \begin{minipage}{1.9cm}
 291 {\tiny cubic (twist)}
 292 \end{minipage}
 293 \begin{minipage}{2.9cm}
 294 {\tiny hexagonal (no twist)}
 295 \end{minipage}
 296
 297 \begin{picture}(0,0)(-150,0)
 298  \includegraphics[width=7cm]{polytypes.eps}
 299 \end{picture}
 300
 301 \vspace{0.6cm}
 302
 303 \footnotesize
 304
 305 \begin{tabular}{l c c c c c c}
 306 \hline
 307  & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
 308 \hline
 309 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
 310 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
 311 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
 312 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
 313 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
 314 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
 315 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
 316 \hline
 317 \end{tabular}
 318
 319 \begin{pspicture}(0,0)(0,0)
 320 \psellipse[linecolor=green](5.7,2.10)(0.4,0.5)
 321 \end{pspicture}
 322 \begin{pspicture}(0,0)(0,0)
 323 \psellipse[linecolor=green](5.6,0.92)(0.4,0.2)
 324 \end{pspicture}
 325 \begin{pspicture}(0,0)(0,0)
 326 \psellipse[linecolor=red](10.45,0.45)(0.4,0.2)
 327 \end{pspicture}
 328
 329 \end{slide}
 330
 331 % fabrication
 332
 333 \begin{slide}
 334
 335  {\large\bf
 336   Fabrication of silicon carbide
 337  }
 338
 339  \small
 340
 341  \vspace{2pt}
 342
 343 \begin{center}
 344  {\color{gray}
 345  \emph{Silicon carbide --- Born from the stars, perfected on earth.}
 346  }
 347 \end{center}
 348
 349 \vspace{2pt}
 350
 351 SiC thin films by MBE \& CVD
 352 \begin{itemize}
 353  \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
 354  \item \underline{Commercially available} semiconductor power devices based on
 355        \underline{\foreignlanguage{greek}{a}-SiC}
 356  \item Production of favored \underline{3C-SiC} material
 357        \underline{less advanced}
 358  \item Quality and size not yet sufficient
 359 \end{itemize}
 360 \begin{picture}(0,0)(-310,-20)
 361   \includegraphics[width=2.0cm]{cree.eps}
 362 \end{picture}
 363
 364 \vspace{-0.2cm}
 365
 366 Alternative approach:
 367 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
 368
 369 \vspace{0.2cm}
 370
 371 \scriptsize
 372
 373 \framebox{
 374 \begin{minipage}{3.15cm}
 375  \begin{center}
 376 \includegraphics[width=3cm]{imp.eps}\\
 377  {\tiny
 378   Carbon implantation
 379  }
 380  \end{center}
 381 \end{minipage}
 382 \begin{minipage}{3.15cm}
 383  \begin{center}
 384 \includegraphics[width=3cm]{annealing.eps}\\
 385  {\tiny
 386   \unit[12]{h} annealing at \degc{1200}
 387  }
 388  \end{center}
 389 \end{minipage}
 390 }
 391 \begin{minipage}{5.5cm}
 392  \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm]
 393  \begin{center}
 394  {\tiny
 395   XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
 396  }
 397  \end{center}
 398 \end{minipage}
 399
 400 \end{slide}
 401
 402 % contents
 403
 404 \begin{slide}
 405
 406 {\large\bf
 407  Systematic investigation of C implantations into Si
 408 }
 409
 410 \vspace{1.7cm}
 411 \begin{center}
 412 \hspace{-1.0cm}
 413 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
 414 \end{center}
 415
 416 \end{slide}
 417
 418 % outline
 419
 420 \begin{slide}
 421
 422 {\large\bf
 423  Outline
 424 }
 425
 426 \vspace{1.7cm}
 427 \begin{center}
 428 \hspace{-1.0cm}
 429 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
 430 \end{center}
 431
 432 \begin{pspicture}(0,0)(0,0)
 433 \rput(6.0,7.0){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=hred,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{
 434 \begin{minipage}{11cm}
 435 {\color{black}Diploma thesis}\\
 436  \underline{Monte Carlo} simulation modeling the selforganization process\\
 437  leading to periodic arrays of nanometric amorphous SiC precipitates
 438 \end{minipage}
 439 }}}
 440 \end{pspicture}
 441 \begin{pspicture}(0,0)(0,0)
 442 \rput(6.0,-0.5){\rnode{init}{\psframebox[fillstyle=gradient,gradbegin=hblue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{
 443 \begin{minipage}{11cm}
 444 {\color{black}Doctoral studies}\\
 445  Classical potential \underline{molecular dynamics} simulations \ldots\\
 446  \underline{Density functional theory} calculations \ldots\\[0.2cm]
 447  \ldots on defect formation and SiC precipitation in Si
 448 \end{minipage}
 449 }}}
 450 \end{pspicture}
 451 \begin{pspicture}(0,0)(0,0)
 452 \psellipse[linecolor=red,linewidth=0.05cm](5,3.0)(0.8,1.0)
 453 \end{pspicture}
 454 \begin{pspicture}(0,0)(0,0)
 455 \psellipse[linecolor=blue,linewidth=0.05cm](8.2,3.2)(1.5,1.6)
 456 \end{pspicture}
 457
 458 \end{slide}
 459
 460 \begin{slide}
 461
 462 \headdiplom
 463 {\large\bf
 464  Selforganization of nanometric amorphous SiC lamellae
 465 }
 466
 467 \small
 468
 469 \vspace{0.2cm}
 470
 471 \begin{itemize}
 472  \item Regularly spaced, nanometric spherical\\
 473        and lamellar amorphous inclusions\\
 474        at the upper a/c interface
 475  \item Carbon accumulation\\
 476        in amorphous volumes
 477 \end{itemize}
 478
 479 \vspace{0.4cm}
 480
 481 \begin{minipage}{12cm}
 482 \includegraphics[width=9cm]{../../nlsop/img/k393abild1_e_l.eps}\\
 483 {\scriptsize
 484 XTEM bright-field, \unit[180]{keV} C$^+ \rightarrow$ Si,
 485 {\color{red}\underline{\degc{150}}},
 486 Dose: \unit[4.3 $\times 10^{17}$]{cm$^{-2}$}
 487 }
 488 \end{minipage}
 489
 490 \begin{picture}(0,0)(-182,-215)
 491 \begin{minipage}{6.5cm}
 492 \begin{center}
 493 \includegraphics[width=6.5cm]{../../nlsop/img/eftem.eps}\\[-0.2cm]
 494 {\scriptsize
 495 XTEM bright-field and respective EFTEM C map
 496 }
 497 \end{center}
 498 \end{minipage}
 499 \end{picture}
 500
 501 \end{slide}
 502
 503 \begin{slide}
 504
 505 \headdiplom
 506 {\large\bf
 507  Model displaying the formation of ordered lamellae
 508 }
 509
 510 \vspace{0.1cm}
 511
 512 \begin{center}
 513  \includegraphics[width=8.0cm]{../../nlsop/img/modell_ng_e.eps}
 514 \end{center}
 515
 516 \footnotesize
 517
 518 \begin{itemize}
 519 \item Supersaturation of C in c-Si\\
 520       $\rightarrow$ {\bf Carbon induced} nucleation of spherical
 521       SiC$_x$-precipitates
 522 \item High interfacial energy between 3C-SiC and c-Si\\
 523       $\rightarrow$ {\bf Amorphous} precipitates
 524 \item \unit[20-- 30]{\%} lower silicon density of a-SiC$_x$ compared to c-Si\\
 525       $\rightarrow$ {\bf Lateral strain} (black arrows)
 526 \item Implantation range near surface\\
 527       $\rightarrow$ {\bf Relaxation} of {\bf vertical strain component}
 528 \item Reduction of the carbon supersaturation in c-Si\\
 529       $\rightarrow$ {\bf Carbon diffusion} into amorphous volumina
 530       (white arrows)
 531 \item Remaining lateral strain\\
 532       $\rightarrow$ {\bf Strain enhanced} lateral amorphisation
 533 \item Absence of crystalline neighbours (structural information)\\
 534       $\rightarrow$ {\bf Stabilization} of amorphous inclusions
 535       {\bf against recrystallization}
 536 \end{itemize}
 537
 538 \end{slide}
 539
 540 \begin{slide}
 541
 542 \headdiplom
 543 {\large\bf
 544  Implementation of the Monte Carlo code
 545 }
 546
 547 \small
 548
 549 \begin{enumerate}
 550  \item \underline{Amorphization / Recrystallization}\\
 551        Ion collision in discretized target determined by random numbers
 552        distributed according to nuclear energy loss.
 553        Amorphization/recrystallization probability:
 554 \[
 555 p_{c \rightarrow a}(\vec{r}) = {\color{green} p_b} + {\color{blue} p_c c_C(\vec{r})} + {\color{red} \sum_{\textrm{amorphous neighbours}} \frac{p_s c_C(\vec{r'})}{(r-r')^2}}
 556 \]
 557 \begin{itemize}
 558  \item {\color{green} $p_b$} normal `ballistic' amorphization
 559  \item {\color{blue} $p_c$} carbon induced amorphization
 560  \item {\color{red} $p_s$} stress enhanced amorphization
 561 \end{itemize}
 562 \[
 563 p_{a \rightarrow c}(\vec r) = (1 - p_{c \rightarrow a}(\vec r)) \Big(1 - \frac{\sum_{direct \, neighbours} \delta (\vec{r'})}{6} \Big) \, \textrm{,}
 564 \]
 565 \[
 566 \delta (\vec r) = \left\{
 567 \begin{array}{ll}
 568         1 & \textrm{if volume at position $\vec r$ is amorphous} \\
 569         0 & \textrm{otherwise} \\
 570 \end{array}
 571 \right.
 572 \]
 573  \item \underline{Carbon incorporation}\\
 574        Incorporation volume determined according to implantation profile
 575  \item \underline{Diffusion / Sputtering}
 576        \begin{itemize}
 577         \item Transfer fraction of C atoms
 578               of crystalline into neighbored amorphous volumes
 579         \item Remove surface layer
 580        \end{itemize}
 581 \end{enumerate}
 582
 583 \end{slide}
 584
 585 \begin{slide}
 586
 587 \begin{minipage}{3.7cm}
 588 \begin{pspicture}(0,0)(0,0)
 589 \rput(1.7,0.2){\psframebox[fillstyle=gradient,gradbegin=hred,gradend=white,gradlines=1000,gradangle=10,gradmidpoint=1,linestyle=none]{
 590 \begin{minipage}{3.7cm}
 591 \hfill
 592 \vspace{0.7cm}
 593 \end{minipage}
 594 }}
 595 \end{pspicture}
 596 {\large\bf
 597  Results
 598 }
 599
 600 \footnotesize
 601
 602 \vspace{1.2cm}
 603
 604 Evolution of the \ldots
 605 \begin{itemize}
 606  \item continuous\\
 607        amorphous layer
 608  \item a/c interface
 609  \item lamellar precipitates
 610 \end{itemize}
 611 \ldots reproduced!\\[1.4cm]
 612
 613 {\color{blue}
 614 \begin{center}
 615 Experiment \& simulation\\
 616 in good agreement\\[1.0cm]
 617
 618 Simulation is able to model the whole depth region\\[1.2cm]
 619 \end{center}
 620 }
 621
 622 \end{minipage}
 623 \begin{minipage}{0.5cm}
 624 \vfill
 625 \end{minipage}
 626 \begin{minipage}{8.0cm}
 627  \vspace{-0.3cm}
 628  \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e_1-2.eps}\\
 629  \includegraphics[width=9cm]{../../nlsop/img/dosis_entwicklung_ng_e2_2-2.eps}
 630 \end{minipage}
 631
 632 \end{slide}
 633
 634 \begin{slide}
 635
 636 \headdiplom
 637 {\large\bf
 638  Structural \& compositional details
 639 }
 640
 641 \begin{minipage}[t]{7.5cm}
 642 \includegraphics[height=6.5cm]{../../nlsop/img/ac_cconc_ver2_e.eps}\\
 643 \end{minipage}
 644 \begin{minipage}[t]{5.0cm}
 645 \includegraphics[height=6.5cm]{../../nlsop/img/97_98_e.eps}
 646 \end{minipage}
 647
 648 \footnotesize
 649
 650 \vspace{-0.1cm}
 651
 652 \begin{itemize}
 653  \item Fluctuation of C concentration in lamellae region
 654  \item \unit[8--10]{at.\%} C saturation limit
 655        within the respective conditions
 656  \item Complementarily arranged and alternating sequence of layers\\
 657        with a high and low amount of amorphous regions
 658  \item C accumulation in the amorphous phase / Origin of stress
 659 \end{itemize}
 660
 661 \begin{picture}(0,0)(-260,-50)
 662 \framebox{
 663 \begin{minipage}{3cm}
 664 \begin{center}
 665 {\color{blue}
 666 Precipitation process\\
 667 gets traceable\\
 668 by simulation!
 669 }
 670 \end{center}
 671 \end{minipage}
 672 }
 673 \end{picture}
 674
 675 \end{slide}
 676
 677 \begin{slide}
 678
 679 \headphd
 680 {\large\bf
 681  Formation of epitaxial single crystalline 3C-SiC
 682 }
 683
 684 \footnotesize
 685
 686 \vspace{0.2cm}
 687
 688 \begin{center}
 689 \begin{itemize}
 690  \item \underline{Implantation step 1}\\[0.1cm]
 691         Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
 692         $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
 693         {\color{blue}precipitates}
 694  \item \underline{Implantation step 2}\\[0.1cm]
 695         Little remaining dose | \unit[180]{keV} | \degc{250}\\
 696         $\Rightarrow$
 697         Destruction/Amorphization of precipitates at layer interface
 698  \item \underline{Annealing}\\[0.1cm]
 699        \unit[10]{h} at \degc{1250}\\
 700        $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
 701 \end{itemize}
 702 \end{center}
 703
 704 \begin{minipage}{7cm}
 705 \includegraphics[width=7cm]{ibs_3c-sic.eps}
 706 \end{minipage}
 707 \begin{minipage}{5cm}
 708 \begin{pspicture}(0,0)(0,0)
 709 \rnode{box}{
 710 \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
 711 \begin{minipage}{5.3cm}
 712  \begin{center}
 713  {\color{blue}
 714   3C-SiC precipitation\\
 715   not yet fully understood
 716  }
 717  \end{center}
 718  \vspace*{0.1cm}
 719  \renewcommand\labelitemi{$\Rightarrow$}
 720  Details of the SiC precipitation
 721  \begin{itemize}
 722   \item significant technological progress\\
 723         in SiC thin film formation
 724   \item perspectives for processes relying\\
 725         upon prevention of SiC precipitation
 726  \end{itemize}
 727 \end{minipage}
 728 }}
 729 \rput(-6.8,5.4){\pnode{h0}}
 730 \rput(-3.0,5.4){\pnode{h1}}
 731 \ncline[linecolor=blue]{-}{h0}{h1}
 732 \ncline[linecolor=blue]{->}{h1}{box}
 733 \end{pspicture}
 734 \end{minipage}
 735
 736 \end{slide}
 737
 738 \begin{slide}
 739
 740 \headphd
 741 {\large\bf
 742   Supposed precipitation mechanism of SiC in Si
 743 }
 744
 745  \scriptsize
 746
 747  \vspace{0.1cm}
 748
 749  \framebox{
 750  \begin{minipage}{3.6cm}
 751  \begin{center}
 752  Si \& SiC lattice structure\\[0.1cm]
 753  \includegraphics[width=2.3cm]{sic_unit_cell.eps}
 754  \end{center}
 755 {\tiny
 756  \begin{minipage}{1.7cm}
 757 \underline{Silicon}\\
 758 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
 759 $a=\unit[5.429]{\\A}$\\
 760 $\rho^*_{\text{Si}}=\unit[100]{\%}$
 761  \end{minipage}
 762  \begin{minipage}{1.7cm}
 763 \underline{Silicon carbide}\\
 764 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
 765 $a=\unit[4.359]{\\A}$\\
 766 $\rho^*_{\text{Si}}=\unit[97]{\%}$
 767  \end{minipage}
 768 }
 769  \end{minipage}
 770  }
 771  \hspace{0.1cm}
 772  \begin{minipage}{4.1cm}
 773  \begin{center}
 774  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 775  \end{center}
 776  \end{minipage}
 777  \hspace{0.1cm}
 778  \begin{minipage}{4.0cm}
 779  \begin{center}
 780  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 781  \end{center}
 782  \end{minipage}
 783
 784  \vspace{0.1cm}
 785
 786  \begin{minipage}{4.0cm}
 787  \begin{center}
 788  C-Si dimers (dumbbells)\\[-0.1cm]
 789  on Si interstitial sites
 790  \end{center}
 791  \end{minipage}
 792  \hspace{0.1cm}
 793  \begin{minipage}{4.1cm}
 794  \begin{center}
 795  Agglomeration of C-Si dumbbells\\[-0.1cm]
 796  $\Rightarrow$ dark contrasts
 797  \end{center}
 798  \end{minipage}
 799  \hspace{0.1cm}
 800  \begin{minipage}{4.0cm}
 801  \begin{center}
 802  Precipitation of 3C-SiC in Si\\[-0.1cm]
 803  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 804  \& release of Si self-interstitials
 805  \end{center}
 806  \end{minipage}
 807
 808  \vspace{0.1cm}
 809
 810  \begin{minipage}{4.0cm}
 811  \begin{center}
 812  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 813  \end{center}
 814  \end{minipage}
 815  \hspace{0.1cm}
 816  \begin{minipage}{4.1cm}
 817  \begin{center}
 818  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 819  \end{center}
 820  \end{minipage}
 821  \hspace{0.1cm}
 822  \begin{minipage}{4.0cm}
 823  \begin{center}
 824  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 825  \end{center}
 826  \end{minipage}
 827
 828 \begin{pspicture}(0,0)(0,0)
 829 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
 830 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
 831 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
 832 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
 833 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 834  $4a_{\text{Si}}=5a_{\text{SiC}}$
 835  }}}
 836 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 837 \hkl(h k l) planes match
 838  }}}
 839 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 840 r = \unit[2--4]{nm}
 841  }}}
 842 \end{pspicture}
 843
 844 \end{slide}
 845
 846 \begin{slide}
 847
 848 \headphd
 849 {\large\bf
 850  Supposed precipitation mechanism of SiC in Si
 851 }
 852
 853  \scriptsize
 854
 855  \vspace{0.1cm}
 856
 857  \framebox{
 858  \begin{minipage}{3.6cm}
 859  \begin{center}
 860  Si \& SiC lattice structure\\[0.1cm]
 861  \includegraphics[width=2.3cm]{sic_unit_cell.eps}
 862  \end{center}
 863 {\tiny
 864  \begin{minipage}{1.7cm}
 865 \underline{Silicon}\\
 866 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
 867 $a=\unit[5.429]{\\A}$\\
 868 $\rho^*_{\text{Si}}=\unit[100]{\%}$
 869  \end{minipage}
 870  \begin{minipage}{1.7cm}
 871 \underline{Silicon carbide}\\
 872 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
 873 $a=\unit[4.359]{\\A}$\\
 874 $\rho^*_{\text{Si}}=\unit[97]{\%}$
 875  \end{minipage}
 876 }
 877  \end{minipage}
 878  }
 879  \hspace{0.1cm}
 880  \begin{minipage}{4.1cm}
 881  \begin{center}
 882  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 883  \end{center}
 884  \end{minipage}
 885  \hspace{0.1cm}
 886  \begin{minipage}{4.0cm}
 887  \begin{center}
 888  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 889  \end{center}
 890  \end{minipage}
 891
 892  \vspace{0.1cm}
 893
 894  \begin{minipage}{4.0cm}
 895  \begin{center}
 896  C-Si dimers (dumbbells)\\[-0.1cm]
 897  on Si interstitial sites
 898  \end{center}
 899  \end{minipage}
 900  \hspace{0.1cm}
 901  \begin{minipage}{4.1cm}
 902  \begin{center}
 903  Agglomeration of C-Si dumbbells\\[-0.1cm]
 904  $\Rightarrow$ dark contrasts
 905  \end{center}
 906  \end{minipage}
 907  \hspace{0.1cm}
 908  \begin{minipage}{4.0cm}
 909  \begin{center}
 910  Precipitation of 3C-SiC in Si\\[-0.1cm]
 911  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 912  \& release of Si self-interstitials
 913  \end{center}
 914  \end{minipage}
 915
 916  \vspace{0.1cm}
 917
 918  \begin{minipage}{4.0cm}
 919  \begin{center}
 920  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 921  \end{center}
 922  \end{minipage}
 923  \hspace{0.1cm}
 924  \begin{minipage}{4.1cm}
 925  \begin{center}
 926  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 927  \end{center}
 928  \end{minipage}
 929  \hspace{0.1cm}
 930  \begin{minipage}{4.0cm}
 931  \begin{center}
 932  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 933  \end{center}
 934  \end{minipage}
 935
 936 \begin{pspicture}(0,0)(0,0)
 937 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
 938 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
 939 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
 940 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
 941 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 942  $4a_{\text{Si}}=5a_{\text{SiC}}$
 943  }}}
 944 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 945 \hkl(h k l) planes match
 946  }}}
 947 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 948 r = \unit[2--4]{nm}
 949  }}}
 950 % controversial view!
 951 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
 952 \begin{minipage}{14cm}
 953 \hfill
 954 \vspace{12cm}
 955 \end{minipage}
 956 }}
 957 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
 958 \begin{minipage}{10cm}
 959 \small
 960 \vspace*{0.2cm}
 961 \begin{center}
 962 {\color{gray}\bf Controversial findings}
 963 \end{center}
 964 \begin{itemize}
 965 \item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
 966  \begin{itemize}
 967   \item C incorporated {\color{blue}substitutionally} on regular Si lattice sites
 968   \item \si{} reacting with further C in cleared volume
 969  \end{itemize}
 970 \item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
 971  \begin{itemize}
 972   \item Room temperature implantation $\rightarrow$ high C diffusion
 973   \item Elevated temperature implantation $\rightarrow$ no C redistribution
 974  \end{itemize}
 975  $\Rightarrow$ mobile {\color{red}\ci} opposed to
 976  stable {\color{blue}\cs{}} configurations
 977 \item Strained silicon \& Si/SiC heterostructures
 978       {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
 979  \begin{itemize}
 980   \item {\color{blue}Coherent} SiC precipitates (tensile strain)
 981   \item Incoherent SiC (strain relaxation)
 982  \end{itemize}
 983 \end{itemize}
 984 \vspace{0.1cm}
 985 \begin{center}
 986 {\Huge${\lightning}$} \hspace{0.3cm}
 987 {\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
 988 {\Huge${\lightning}$}
 989 \end{center}
 990 \vspace{0.2cm}
 991 \end{minipage}
 992  }}}
 993 \end{pspicture}
 994
 995 \end{slide}
 996
 997 \begin{slide}
 998
 999 \headphd
1000 {\large\bf
1001  Utilized computational methods
1002 }
1003
1004 \vspace{0.3cm}
1005
1006 \small
1007
1008 {\bf Molecular dynamics (MD)}\\[0.1cm]
1009 \scriptsize
1010 \begin{tabular}{| p{4.5cm} | p{7.5cm} |}
1011 \hline
1012 System of $N$ particles &
1013 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
1014 Phase space propagation &
1015 Velocity Verlet | timestep: \unit[1]{fs} \\
1016 Analytical interaction potential &
1017 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
1018 (Erhart/Albe)
1019 $\displaystyle
1020 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
1021     \pot_{ij} = {\color{red}f_C(r_{ij})}
1022     \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
1023 $\\
1024 Observables: time/ensemble averages &
1025 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
1026 \hline
1027 \end{tabular}
1028
1029 \small
1030
1031 \vspace{0.3cm}
1032
1033 {\bf Density functional theory (DFT)}
1034
1035 \scriptsize
1036
1037 \begin{minipage}[t]{6cm}
1038 \begin{itemize}
1039  \item Hohenberg-Kohn theorem:\\
1040        $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
1041  \item Kohn-Sham approach:\\
1042        Single-particle effective theory
1043 \end{itemize}
1044 \hrule
1045 \begin{itemize}
1046 \item Code: \textsc{vasp}
1047 \item Plane wave basis set
1048 %$\displaystyle
1049 %\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
1050 %$\\
1051 %$\displaystyle
1052 %E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
1053 %$
1054 \item Ultrasoft pseudopotential
1055 \item Exchange \& correlation: GGA
1056 \item Brillouin zone sampling: $\Gamma$-point
1057 \item Supercell: $N=216\pm2$
1058 \end{itemize}
1059 \end{minipage}
1060 \begin{minipage}{6cm}
1061 \begin{pspicture}(0,0)(0,0)
1062 \pscircle[fillcolor=yellow,fillstyle=solid,linestyle=none](3.5,-2.0){2.5}
1063 \rput(2.7,-0.7){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
1064 $\displaystyle
1065 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
1066 $
1067 }}
1068 \rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
1069 $\displaystyle
1070 n(r)=\sum_i^N|\Phi_i(r)|^2
1071 $
1072 }}
1073 \rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
1074 $\displaystyle
1075 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
1076                  +V_{\text{XC}}[n(r)]
1077 $
1078 }}
1079 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
1080 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165}
1081 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
1082
1083 \end{pspicture}
1084 \end{minipage}
1085
1086 \end{slide}
1087
1088 \begin{slide}
1089
1090 \headphd
1091  {\large\bf
1092   Point defects \& defect migration
1093  }
1094
1095  \small
1096
1097  \vspace{0.2cm}
1098
1099 \begin{minipage}[b]{7.5cm}
1100 {\bf Defect structure}\\
1101   \begin{pspicture}(0,0)(7,4.4)
1102   \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1103    \parbox{7cm}{
1104    \begin{itemize}
1105     \item Creation of c-Si simulation volume
1106     \item Periodic boundary conditions
1107     \item $T=0\text{ K}$, $p=0\text{ bar}$
1108    \end{itemize}
1109   }}}}
1110 \rput(3.5,1.3){\rnode{insert}{\psframebox{
1111  \parbox{7cm}{
1112   \begin{center}
1113   Insertion of interstitial C/Si atoms
1114   \end{center}
1115   }}}}
1116   \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1117    \parbox{7cm}{
1118    \begin{center}
1119    Relaxation / structural energy minimization
1120    \end{center}
1121   }}}}
1122   \ncline[]{->}{init}{insert}
1123   \ncline[]{->}{insert}{cool}
1124  \end{pspicture}
1125 \end{minipage}
1126 \begin{minipage}[b]{4.5cm}
1127 \begin{center}
1128 \includegraphics[width=3.8cm]{unit_cell_e.eps}\\
1129 \end{center}
1130 \begin{minipage}{2.21cm}
1131 {\scriptsize
1132 {\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
1133 {\color{green}$\bullet$} Hexagonal\\[-0.1cm]
1134 {\color{yellow}$\bullet$} \hkl<1 0 0> DB
1135 }
1136 \end{minipage}
1137 \begin{minipage}{2.21cm}
1138 {\scriptsize
1139 {\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
1140 {\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
1141 {\color{black}$\bullet$} Vac. / Sub.
1142 }
1143 \end{minipage}
1144 \end{minipage}
1145
1146 \vspace{0.2cm}
1147
1148 \begin{minipage}[b]{6cm}
1149 {\bf Defect formation energy}\\
1150 \framebox{
1151 $E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.1cm]
1152 Particle reservoir: Si \& SiC\\[0.2cm]
1153 {\bf Binding energy}\\
1154 \framebox{
1155 $
1156 E_{\text{b}}=
1157 E_{\text{f}}^{\text{comb}}-
1158 E_{\text{f}}^{1^{\text{st}}}-
1159 E_{\text{f}}^{2^{\text{nd}}}
1160 $
1161 }\\[0.1cm]
1162 \footnotesize
1163 $E_{\text{b}}<0$: energetically favorable configuration\\
1164 $E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
1165 \end{minipage}
1166 \begin{minipage}[b]{6cm}
1167 {\bf Migration barrier}
1168 \footnotesize
1169 \begin{itemize}
1170  \item Displace diffusing atom
1171  \item Constrain relaxation of (diffusing) atoms
1172  \item Record configurational energy
1173 \end{itemize}
1174 \begin{picture}(0,0)(-60,-33)
1175 \includegraphics[width=4.5cm]{crt_mod.eps}
1176 \end{picture}
1177 \end{minipage}
1178
1179 \end{slide}
1180
1181 \begin{slide}
1182
1183 \footnotesize
1184
1185 \headphd
1186 {\large\bf
1187  Si self-interstitial point defects in silicon\\[0.1cm]
1188 }
1189
1190 \begin{center}
1191 \begin{tabular}{l c c c c c}
1192 \hline
1193  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
1194 \hline
1195  \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
1196  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
1197 \hline
1198 \end{tabular}\\[0.4cm]
1199 \end{center}
1200
1201 \begin{minipage}{3cm}
1202 \begin{center}
1203 \underline{Vacancy}\\
1204 \includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
1205 \end{center}
1206 \end{minipage}
1207 \begin{minipage}{3cm}
1208 \begin{center}
1209 \underline{\hkl<1 1 0> DB}\\
1210 \includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
1211 \end{center}
1212 \end{minipage}
1213 \begin{minipage}{3cm}
1214 \begin{center}
1215 \underline{\hkl<1 0 0> DB}\\
1216 \includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
1217 \end{center}
1218 \end{minipage}
1219 \begin{minipage}{3cm}
1220 \begin{center}
1221 \underline{Tetrahedral}\\
1222 \includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
1223 \end{center}
1224 \end{minipage}\\
1225
1226 \underline{Hexagonal} \hspace{2pt}
1227 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
1228 \framebox{
1229 \begin{minipage}{2.7cm}
1230 $E_{\text{f}}^*=4.48\text{ eV}$\\
1231 \includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
1232 \end{minipage}
1233 \begin{minipage}{0.4cm}
1234 \begin{center}
1235 $\Rightarrow$
1236 \end{center}
1237 \end{minipage}
1238 \begin{minipage}{2.7cm}
1239 $E_{\text{f}}=3.96\text{ eV}$\\
1240 \includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps}
1241 \end{minipage}
1242 }
1243 \begin{minipage}{5.5cm}
1244 \begin{center}
1245 {\tiny nearly T $\rightarrow$ T}\\
1246 \end{center}
1247 \includegraphics[width=6.0cm]{nhex_tet.ps}
1248 \end{minipage}
1249
1250 \end{slide}
1251
1252 \begin{slide}
1253
1254 \footnotesize
1255
1256 \headphd
1257 {\large\bf
1258  C interstitial point defects in silicon\\
1259 }
1260
1261 \begin{tabular}{l c c c c c c r}
1262 \hline
1263  $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B &
1264  {\color{black} \cs{} \& \si}\\
1265 \hline
1266  \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
1267  Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
1268 \hline
1269 \end{tabular}\\[0.1cm]
1270
1271 \framebox{
1272 \begin{minipage}{2.8cm}
1273 \underline{Hexagonal} \hspace{2pt}
1274 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
1275 $E_{\text{f}}^*=9.05\text{ eV}$\\
1276 \includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps}
1277 \end{minipage}
1278 \begin{minipage}{0.4cm}
1279 \begin{center}
1280 $\Rightarrow$
1281 \end{center}
1282 \end{minipage}
1283 \begin{minipage}{2.8cm}
1284 \underline{\hkl<1 0 0>}\\
1285 $E_{\text{f}}=3.88\text{ eV}$\\
1286 \includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps}
1287 \end{minipage}
1288 }
1289 \begin{minipage}{1.4cm}
1290 \hfill
1291 \end{minipage}
1292 \begin{minipage}{3.0cm}
1293 \begin{flushright}
1294 \underline{Tetrahedral}\\
1295 \includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps}
1296 \end{flushright}
1297 \end{minipage}
1298
1299 \framebox{
1300 \begin{minipage}{2.8cm}
1301 \underline{Bond-centered}\\
1302 $E_{\text{f}}^*=5.59\text{ eV}$\\
1303 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}
1304 \end{minipage}
1305 \begin{minipage}{0.4cm}
1306 \begin{center}
1307 $\Rightarrow$
1308 \end{center}
1309 \end{minipage}
1310 \begin{minipage}{2.8cm}
1311 \underline{\hkl<1 1 0> dumbbell}\\
1312 $E_{\text{f}}=5.18\text{ eV}$\\
1313 \includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps}
1314 \end{minipage}
1315 }
1316 \begin{minipage}{1.4cm}
1317 \hfill
1318 \end{minipage}
1319 \begin{minipage}{3.0cm}
1320 \begin{flushright}
1321 \underline{Substitutional}\\
1322 \includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps}
1323 \end{flushright}
1324 \end{minipage}
1325
1326 \end{slide}
1327
1328 \begin{slide}
1329
1330 \headphd
1331 {\large\bf\boldmath
1332  C-Si dimer \& bond-centered interstitial configuration
1333 }
1334
1335 \footnotesize
1336
1337 \vspace{0.1cm}
1338
1339 \begin{minipage}[t]{4.1cm}
1340 {\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
1341 \begin{minipage}{2.0cm}
1342 \begin{center}
1343 \underline{Erhart/Albe}
1344 \includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
1345 \end{center}
1346 \end{minipage}
1347 \begin{minipage}{2.0cm}
1348 \begin{center}
1349 \underline{\textsc{vasp}}
1350 \includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
1351 \end{center}
1352 \end{minipage}\\[0.2cm]
1353 Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
1354 $\Rightarrow$ $sp$ hybridization\\[0.1cm]
1355 Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
1356 $\Rightarrow$ $sp^2$ hybridization
1357 \begin{center}
1358 \includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
1359 {\tiny Charge density isosurface}
1360 \end{center}
1361 \end{minipage}
1362 \begin{minipage}{0.2cm}
1363 \hfill
1364 \end{minipage}
1365 \begin{minipage}[t]{8.1cm}
1366 \begin{flushright}
1367 {\bf Bond-centered interstitial}\\[0.1cm]
1368 \begin{minipage}{4.4cm}
1369 %\scriptsize
1370 \begin{itemize}
1371  \item Linear Si-C-Si bond
1372  \item Si: one C \& 3 Si neighbours
1373  \item Spin polarized calculations
1374  \item No saddle point!\\
1375        Real local minimum!
1376 \end{itemize}
1377 \end{minipage}
1378 \begin{minipage}{2.7cm}
1379 %\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1380 \vspace{0.2cm}
1381 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\
1382 \end{minipage}
1383
1384 \framebox{
1385  \tiny
1386  \begin{minipage}[t]{6.5cm}
1387   \begin{minipage}[t]{1.2cm}
1388   {\color{red}Si}\\
1389   {\tiny sp$^3$}\\[0.8cm]
1390   \underline{${\color{black}\uparrow}$}
1391   \underline{${\color{black}\uparrow}$}
1392   \underline{${\color{black}\uparrow}$}
1393   \underline{${\color{red}\uparrow}$}\\
1394   sp$^3$
1395   \end{minipage}
1396   \begin{minipage}[t]{1.4cm}
1397   \begin{center}
1398   {\color{red}M}{\color{blue}O}\\[0.8cm]
1399   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1400   $\sigma_{\text{ab}}$\\[0.5cm]
1401   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1402   $\sigma_{\text{b}}$
1403   \end{center}
1404   \end{minipage}
1405   \begin{minipage}[t]{1.0cm}
1406   \begin{center}
1407   {\color{blue}C}\\
1408   {\tiny sp}\\[0.2cm]
1409   \underline{${\color{white}\uparrow\uparrow}$}
1410   \underline{${\color{white}\uparrow\uparrow}$}\\
1411   2p\\[0.4cm]
1412   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1413   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1414   sp
1415   \end{center}
1416   \end{minipage}
1417   \begin{minipage}[t]{1.4cm}
1418   \begin{center}
1419   {\color{blue}M}{\color{green}O}\\[0.8cm]
1420   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1421   $\sigma_{\text{ab}}$\\[0.5cm]
1422   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1423   $\sigma_{\text{b}}$
1424   \end{center}
1425   \end{minipage}
1426   \begin{minipage}[t]{1.2cm}
1427   \begin{flushright}
1428   {\color{green}Si}\\
1429   {\tiny sp$^3$}\\[0.8cm]
1430   \underline{${\color{green}\uparrow}$}
1431   \underline{${\color{black}\uparrow}$}
1432   \underline{${\color{black}\uparrow}$}
1433   \underline{${\color{black}\uparrow}$}\\
1434   sp$^3$
1435   \end{flushright}
1436   \end{minipage}
1437  \end{minipage}
1438 }\\[0.4cm]
1439
1440 %\framebox{
1441 \begin{minipage}{3.0cm}
1442 %\scriptsize
1443 \underline{Charge density}\\
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 \begin{minipage}{3.6cm}
1451 \includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
1452 \end{minipage}
1453 %}
1454
1455 \end{flushright}
1456
1457 \end{minipage}
1458 \begin{pspicture}(0,0)(0,0)
1459 \psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0)
1460 \end{pspicture}
1461
1462 \end{slide}
1463
1464 \begin{slide}
1465
1466 \headphd
1467 {\large\bf\boldmath
1468  C interstitial migration --- ab initio
1469 }
1470
1471 \scriptsize
1472
1473 \vspace{0.1cm}
1474
1475 \begin{minipage}{6.8cm}
1476 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
1477 \begin{minipage}{2.0cm}
1478 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1479 \end{minipage}
1480 \begin{minipage}{0.2cm}
1481 $\rightarrow$
1482 \end{minipage}
1483 \begin{minipage}{2.0cm}
1484 \includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps}
1485 \end{minipage}
1486 \begin{minipage}{0.2cm}
1487 $\rightarrow$
1488 \end{minipage}
1489 \begin{minipage}{2.0cm}
1490 \includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps}
1491 \end{minipage}\\[0.1cm]
1492 Spin polarization\\
1493 $\Rightarrow$ BC configuration constitutes local minimum\\
1494 $\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$
1495 \end{minipage}
1496 \begin{minipage}{5.4cm}
1497 \includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
1498 \end{minipage}\\[0.2cm]
1499 %\hrule
1500 %
1501 \begin{minipage}{6.8cm}
1502 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\
1503 \begin{minipage}{2.0cm}
1504 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
1505 \end{minipage}
1506 \begin{minipage}{0.2cm}
1507 $\rightarrow$
1508 \end{minipage}
1509 \begin{minipage}{2.0cm}
1510 \includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
1511 \end{minipage}
1512 \begin{minipage}{0.2cm}
1513 $\rightarrow$
1514 \end{minipage}
1515 \begin{minipage}{2.0cm}
1516 \includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
1517 \end{minipage}\\[0.1cm]
1518 $\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
1519 $\Rightarrow$ {\color{red}Migration mechanism identified!}\\
1520 Note: Change in orientation
1521 \end{minipage}
1522 \begin{minipage}{5.4cm}
1523 \includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
1524 \end{minipage}\\[0.1cm]
1525 %
1526 \begin{center}
1527 Reorientation pathway composed of two consecutive processes of the above type
1528 \end{center}
1529
1530 \end{slide}
1531
1532 \begin{slide}
1533
1534 \headphd
1535 {\large\bf\boldmath
1536  C interstitial migration --- analytical potential
1537 }
1538
1539 \scriptsize
1540
1541 \vspace{0.3cm}
1542
1543 \begin{minipage}[t]{6.0cm}
1544 {\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm]
1545 \includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\
1546 \begin{itemize}
1547  \item Lowermost migration barrier
1548  \item $\Delta E \approx \unit[2.2]{eV}$
1549  \item 2.4 times higher than ab initio result
1550  \item Different pathway
1551 \end{itemize}
1552 \end{minipage}
1553 \begin{minipage}[t]{0.2cm}
1554 \hfill
1555 \end{minipage}
1556 \begin{minipage}[t]{6.0cm}
1557 {\bf\boldmath Transition involving a \hkl<1 1 0> configuration}
1558 \vspace{0.1cm}
1559 \begin{itemize}
1560  \item Bond-centered configuration unstable\\
1561        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1562  \item Minima of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
1563        $\rightarrow$ \ci{} \hkl<1 1 0> DB
1564 \end{itemize}
1565 \vspace{0.1cm}
1566 \includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps}
1567 \begin{itemize}
1568  \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$
1569  \item 2.4 -- 3.4 times higher than ab initio result
1570  \item After all: Change of the DB orientation
1571 \end{itemize}
1572 \end{minipage}
1573
1574 \vspace{0.5cm}
1575 \begin{center}
1576 {\color{red}\bf Drastically overestimated diffusion barrier}
1577 \end{center}
1578
1579 \begin{pspicture}(0,0)(0,0)
1580 \psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3)
1581 \end{pspicture}
1582
1583 \end{slide}
1584
1585 \begin{slide}
1586
1587 \headphd
1588 {\large\bf\boldmath
1589  Defect combinations
1590 }
1591
1592 \footnotesize
1593
1594 \vspace{0.3cm}
1595
1596 \begin{minipage}{9cm}
1597 {\bf
1598  Summary of combinations}\\[0.1cm]
1599 {\scriptsize
1600 \begin{tabular}{l c c c c c c}
1601 \hline
1602  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1603  \hline
1604  \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1605  \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1606  \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}\\
1607  \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}\\
1608  \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}\\
1609  \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}\\
1610  \hline
1611  C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1612  Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1613 \hline
1614 \end{tabular}
1615 }
1616 \vspace{0.2cm}
1617 \begin{center}
1618 {\color{blue}
1619  $E_{\text{b}}$ explainable by stress compensation / increase
1620 }
1621 \end{center}
1622 \end{minipage}
1623 \begin{minipage}{3cm}
1624 \includegraphics[width=3.5cm]{comb_pos.eps}
1625 \end{minipage}
1626
1627 \vspace{0.2cm}
1628
1629 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1630 \begin{minipage}[t]{3.2cm}
1631 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1632 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1633 \end{minipage}
1634 \begin{minipage}[t]{3.0cm}
1635 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1636 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1637 \end{minipage}
1638 \begin{minipage}[t]{6.1cm}
1639 \vspace{0.7cm}
1640 \begin{itemize}
1641  \item \ci{} agglomeration energetically favorable
1642  \item Most favorable: C clustering\\
1643        {\color{red}However \ldots}\\
1644         \ldots high migration barrier ($>4\,\text{eV}$)\\
1645         \ldots entropy:
1646         $4\times{\color{cyan}[-2.25]}$ versus
1647         $2\times{\color{orange}[-2.39]}$
1648 \end{itemize}
1649 \begin{center}
1650 {\color{blue}\ci{} agglomeration / no C clustering}
1651 \end{center}
1652 \end{minipage}
1653
1654 \end{slide}
1655
1656 \begin{slide}
1657
1658 \headphd
1659 {\large\bf\boldmath
1660  Defect combinations
1661 }
1662
1663 \footnotesize
1664
1665 \vspace{0.3cm}
1666
1667 \begin{minipage}{9cm}
1668 {\bf
1669  Summary of combinations}\\[0.1cm]
1670 {\scriptsize
1671 \begin{tabular}{l c c c c c c}
1672 \hline
1673  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1674  \hline
1675  \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1676  \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1677  \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}\\
1678  \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}\\
1679  \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}\\
1680  \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}\\
1681  \hline
1682  C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1683  Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1684 \hline
1685 \end{tabular}
1686 }
1687 \vspace{0.2cm}
1688 \begin{center}
1689 {\color{blue}
1690  $E_{\text{b}}$ explainable by stress compensation / increase
1691 }
1692 \end{center}
1693 \end{minipage}
1694 \begin{minipage}{3cm}
1695 \includegraphics[width=3.5cm]{comb_pos.eps}
1696 \end{minipage}
1697
1698 \vspace{0.2cm}
1699
1700 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1701 \begin{minipage}[t]{3.2cm}
1702 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1703 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1704 \end{minipage}
1705 \begin{minipage}[t]{3.0cm}
1706 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1707 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1708 \end{minipage}
1709 \begin{minipage}[t]{6.1cm}
1710 \vspace{0.7cm}
1711 \begin{itemize}
1712  \item \ci{} agglomeration energetically favorable
1713  \item Most favorable: C clustering\\
1714        {\color{red}However \ldots}\\
1715         \ldots high migration barrier ($>4\,\text{eV}$)\\
1716         \ldots entropy:
1717         $4\times{\color{cyan}[-2.25]}$ versus
1718         $2\times{\color{orange}[-2.39]}$
1719 \end{itemize}
1720 \begin{center}
1721 {\color{blue}\ci{} agglomeration / no C clustering}
1722 \end{center}
1723 \end{minipage}
1724
1725 % insert graph ...
1726 \begin{pspicture}(0,0)(0,0)
1727 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1728 \begin{minipage}{14cm}
1729 \hfill
1730 \vspace{12cm}
1731 \end{minipage}
1732 }}
1733 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1734 \begin{minipage}{8cm}
1735 \begin{center}
1736 \vspace{0.2cm}
1737 \scriptsize
1738 Interaction along \hkl[1 1 0]
1739 \includegraphics[width=7cm]{db_along_110_cc.ps}
1740 \end{center}
1741 \end{minipage}
1742 }}}
1743 \end{pspicture}
1744
1745 \end{slide}
1746
1747 \begin{slide}
1748
1749 \headphd
1750 {\large\bf
1751  Defect combinations of C-Si dimers and vacancies
1752 }
1753 \footnotesize
1754
1755 \vspace{0.2cm}
1756
1757 \begin{minipage}[b]{2.6cm}
1758 \begin{flushleft}
1759 \underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm]
1760 \includegraphics[width=2.5cm]{00-1dc/0-59.eps}
1761 \end{flushleft}
1762 \end{minipage}
1763 \begin{minipage}[b]{7cm}
1764 \hfill
1765 \end{minipage}
1766 \begin{minipage}[b]{2.6cm}
1767 \begin{flushright}
1768 \underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm]
1769 \includegraphics[width=2.5cm]{00-1dc/3-14.eps}
1770 \end{flushright}
1771 \end{minipage}\\[0.2cm]
1772
1773 \begin{minipage}{6.5cm}
1774 \includegraphics[width=6.0cm]{059-539.ps}
1775 \end{minipage}
1776 \begin{minipage}{5.7cm}
1777 \includegraphics[width=6.0cm]{314-539.ps}
1778 \end{minipage}
1779
1780 \begin{pspicture}(0,0)(0,0)
1781 \psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0)
1782
1783 \rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{
1784 \begin{minipage}{6.5cm}
1785 \begin{center}
1786 IBS: Impinging C creates V \& far away \si\\[0.3cm]
1787 Low migration barrier towards C$_{\text{sub}}$\\
1788 \&\\
1789 High barrier for reverse process\\[0.3cm]
1790 {\color{blue}
1791 High probability of stable C$_{\text{sub}}$ configuration
1792 }
1793 \end{center}
1794 \end{minipage}
1795 }}}
1796 \end{pspicture}
1797
1798 \end{slide}
1799
1800 \begin{slide}
1801
1802 \headphd
1803 {\large\bf
1804  Combinations of substitutional C and Si self-interstitials
1805 }
1806
1807 \scriptsize
1808
1809 \vspace{0.3cm}
1810
1811 \begin{minipage}{6.2cm}
1812 \begin{center}
1813 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1814 \begin{itemize}
1815  \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1816  \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1817  \item Interaction drops quickly to zero\\
1818        $\rightarrow$ low capture radius
1819 \end{itemize}
1820 \end{center}
1821 \end{minipage}
1822 \begin{minipage}{0.2cm}
1823 \hfill
1824 \end{minipage}
1825 \begin{minipage}{6.0cm}
1826 \begin{center}
1827 {\bf Transition from the ground state}
1828 \begin{itemize}
1829  \item Low transition barrier
1830  \item Barrier smaller than \ci{} migration barrier
1831  \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1832        $\rightarrow$ Separation of \cs{} \& \si{} most probable
1833 \end{itemize}
1834 \end{center}
1835 \end{minipage}\\[0.3cm]
1836
1837 \begin{minipage}{6.0cm}
1838 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1839 \end{minipage}
1840 \begin{minipage}{0.4cm}
1841 \hfill
1842 \end{minipage}
1843 \begin{minipage}{6.0cm}
1844 \begin{flushright}
1845 \includegraphics[width=6.0cm]{162-097.ps}
1846 \end{flushright}
1847 \end{minipage}
1848
1849 \begin{pspicture}(0,0)(0,0)
1850 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1851 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1852 \begin{minipage}{8cm}
1853 \begin{center}
1854 \vspace{0.1cm}
1855 {\color{black}
1856 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1857 IBS --- process far from equilibrium\\
1858 }
1859 \end{center}
1860 \end{minipage}
1861 }}}
1862 \end{pspicture}
1863
1864 \end{slide}
1865
1866 \begin{slide}
1867
1868 \headphd
1869 {\large\bf
1870  Combinations of substitutional C and Si self-interstitials
1871 }
1872
1873 \scriptsize
1874
1875 \vspace{0.3cm}
1876
1877 \begin{minipage}{6.2cm}
1878 \begin{center}
1879 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1880 \begin{itemize}
1881  \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1882  \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1883  \item Interaction drops quickly to zero\\
1884        $\rightarrow$ low capture radius
1885 \end{itemize}
1886 \end{center}
1887 \end{minipage}
1888 \begin{minipage}{0.2cm}
1889 \hfill
1890 \end{minipage}
1891 \begin{minipage}{6.0cm}
1892 \begin{center}
1893 {\bf Transition from the ground state}
1894 \begin{itemize}
1895  \item Low transition barrier
1896  \item Barrier smaller than \ci{} migration barrier
1897  \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1898        $\rightarrow$ Separation of \cs{} \& \si{} most probable
1899 \end{itemize}
1900 \end{center}
1901 \end{minipage}\\[0.3cm]
1902
1903 \begin{minipage}{6.0cm}
1904 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1905 \end{minipage}
1906 \begin{minipage}{0.4cm}
1907 \hfill
1908 \end{minipage}
1909 \begin{minipage}{6.0cm}
1910 \begin{flushright}
1911 \includegraphics[width=6.0cm]{162-097.ps}
1912 \end{flushright}
1913 \end{minipage}
1914
1915 \begin{pspicture}(0,0)(0,0)
1916 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1917 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1918 \begin{minipage}{8cm}
1919 \begin{center}
1920 \vspace{0.1cm}
1921 {\color{black}
1922 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1923 IBS --- process far from equilibrium\\
1924 }
1925 \end{center}
1926 \end{minipage}
1927 }}}
1928 \end{pspicture}
1929
1930 % md support
1931 \begin{pspicture}(0,0)(0,0)
1932 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1933 \begin{minipage}{14cm}
1934 \hfill
1935 \vspace{14cm}
1936 \end{minipage}
1937 }}
1938 \rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1939 \begin{minipage}{11cm}
1940 \begin{center}
1941 \vspace{0.2cm}
1942 \scriptsize
1943 Ab initio MD at \degc{900}\\[0.4cm]
1944 \begin{minipage}{5.4cm}
1945 \centering
1946 \includegraphics[width=4.3cm]{md01_bonds.eps}\\
1947 $t=\unit[2230]{fs}$
1948 \end{minipage}
1949 \begin{minipage}{5.4cm}
1950 \centering
1951 \includegraphics[width=4.3cm]{md02_bonds.eps}\\
1952 $t=\unit[2900]{fs}$
1953 \end{minipage}\\[0.5cm]
1954 {\color{blue}
1955 Contribution of entropy to structural formation\\[0.1cm]
1956 }
1957 \end{center}
1958 \end{minipage}
1959 }}}
1960 \end{pspicture}
1961
1962 \end{slide}
1963
1964 \begin{slide}
1965
1966 \headphd
1967 {\large\bf
1968  Silicon carbide precipitation simulations
1969 }
1970
1971 \small
1972
1973 \vspace{0.2cm}
1974
1975 {\bf Procedure}
1976
1977 {\scriptsize
1978  \begin{pspicture}(0,0)(12,6.5)
1979   % nodes
1980   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1981    \parbox{7cm}{
1982    \begin{itemize}
1983     \item Create c-Si volume
1984     \item Periodc boundary conditions
1985     \item Set requested $T$ and $p=0\text{ bar}$
1986     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1987    \end{itemize}
1988   }}}}
1989   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1990    \parbox{7cm}{
1991    Insertion of C atoms at constant T
1992    \begin{itemize}
1993     \item total simulation volume {\pnode{in1}}
1994     \item volume of minimal SiC precipitate size {\pnode{in2}}
1995     \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1996           precipitate
1997    \end{itemize}
1998   }}}}
1999   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
2000    \parbox{7.0cm}{
2001    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
2002   }}}}
2003   \ncline[]{->}{init}{insert}
2004   \ncline[]{->}{insert}{cool}
2005   \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3)
2006   \rput(7.6,6){\footnotesize $V_1$}
2007   \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5)
2008   \rput(8.9,4.85){\tiny $V_2$}
2009   \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75)
2010   \rput(9.25,4.45){\footnotesize $V_3$}
2011   \rput(7.9,3.2){\pnode{ins1}}
2012   \rput(8.92,2.8){\pnode{ins2}}
2013   \rput(10.8,2.4){\pnode{ins3}}
2014   \ncline[]{->}{in1}{ins1}
2015   \ncline[]{->}{in2}{ins2}
2016   \ncline[]{->}{in3}{ins3}
2017  \end{pspicture}
2018 }
2019
2020 \vspace{-0.5cm}
2021
2022 {\bf Note}
2023
2024 \footnotesize
2025
2026 \begin{minipage}{5.7cm}
2027 \begin{itemize}
2028  \item Amount of C atoms: 6000\\
2029        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm})
2030  \item Simulation volume: $31^3$ Si unit cells\\
2031        (238328 Si atoms)
2032 \end{itemize}
2033 \end{minipage}
2034 \begin{minipage}{0.3cm}
2035 \hfill
2036 \end{minipage}
2037 \framebox{
2038 \begin{minipage}{6.0cm}
2039 Restricted to classical potential caclulations\\
2040 $\rightarrow$ Low C diffusion / overestimated barrier\\
2041 $\rightarrow$ Consider $V_2$ and $V_3$
2042 %\begin{itemize}
2043 % \item $V_2$ and $V_3$ considered due to expected low C diffusion
2044 %\end{itemize}
2045 \end{minipage}
2046 }
2047
2048 \end{slide}
2049
2050 \begin{slide}
2051
2052 \headphd
2053 {\large\bf\boldmath
2054  Silicon carbide precipitation simulations at \degc{450} as in IBS
2055 }
2056
2057 \small
2058
2059 \begin{minipage}{6.3cm}
2060 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
2061 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
2062 \hfill
2063 \end{minipage}
2064 \begin{minipage}{6.1cm}
2065 \scriptsize
2066 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
2067 \hkl<1 0 0> C-Si dumbbell dominated structure
2068 \begin{itemize}
2069  \item Si-C bumbs around \unit[0.19]{nm}
2070  \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
2071        concatenated differently oriented \ci{} DBs
2072  \item Si-Si NN distance stretched to \unit[0.3]{nm}
2073 \end{itemize}
2074 \begin{pspicture}(0,0)(6.0,1.0)
2075 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
2076 \begin{minipage}{6cm}
2077 \centering
2078 Formation of \ci{} dumbbells\\
2079 C atoms in proper 3C-SiC distance first
2080 \end{minipage}
2081 }}
2082 \end{pspicture}\\[0.1cm]
2083 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
2084 \begin{itemize}
2085 \item High amount of strongly bound C-C bonds
2086 \item Increased defect \& damage density\\
2087       $\rightarrow$ Arrangements hard to categorize and trace
2088 \item Only short range order observable
2089 \end{itemize}
2090 \begin{pspicture}(0,0)(6.0,0.8)
2091 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
2092 \begin{minipage}{6cm}
2093 \centering
2094 Amorphous SiC-like phase
2095 \end{minipage}
2096 }}
2097 \end{pspicture}\\[0.3cm]
2098 \begin{pspicture}(0,0)(6.0,2.0)
2099 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{
2100 \begin{minipage}{6cm}
2101 \hfill
2102 \vspace{2.5cm}
2103 \end{minipage}
2104 }}
2105 \end{pspicture}
2106 \end{minipage}
2107
2108 \end{slide}
2109
2110 \begin{slide}
2111
2112 \headphd
2113 {\large\bf\boldmath
2114  Silicon carbide precipitation simulations at \degc{450} as in IBS
2115 }
2116
2117 \small
2118
2119 \begin{minipage}{6.3cm}
2120 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
2121 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
2122 \hfill
2123 \end{minipage}
2124 \begin{minipage}{6.1cm}
2125 \scriptsize
2126 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
2127 \hkl<1 0 0> C-Si dumbbell dominated structure
2128 \begin{itemize}
2129  \item Si-C bumbs around \unit[0.19]{nm}
2130  \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
2131        concatenated differently oriented \ci{} DBs
2132  \item Si-Si NN distance stretched to \unit[0.3]{nm}
2133 \end{itemize}
2134 \begin{pspicture}(0,0)(6.0,1.0)
2135 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
2136 \begin{minipage}{6cm}
2137 \centering
2138 Formation of \ci{} dumbbells\\
2139 C atoms in proper 3C-SiC distance first
2140 \end{minipage}
2141 }}
2142 \end{pspicture}\\[0.1cm]
2143 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
2144 \begin{itemize}
2145 \item High amount of strongly bound C-C bonds
2146 \item Increased defect \& damage density\\
2147       $\rightarrow$ Arrangements hard to categorize and trace
2148 \item Only short range order observable
2149 \end{itemize}
2150 \begin{pspicture}(0,0)(6.0,0.8)
2151 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
2152 \begin{minipage}{6cm}
2153 \centering
2154 Amorphous SiC-like phase
2155 \end{minipage}
2156 }}
2157 \end{pspicture}\\[0.3cm]
2158 \begin{pspicture}(0,0)(6.0,2.0)
2159 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{
2160 \begin{minipage}{6cm}
2161 \vspace{0.1cm}
2162 \centering
2163 {\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm]
2164 \begin{minipage}{0.8cm}
2165 {\bf\boldmath $V_1$:}
2166 \end{minipage}
2167 \begin{minipage}{5.1cm}
2168 Formation of \ci{} indeed occurs\\
2169 Agllomeration not observed
2170 \end{minipage}\\[0.3cm]
2171 \begin{minipage}{0.8cm}
2172 {\bf\boldmath $V_{2,3}$:}
2173 \end{minipage}
2174 \begin{minipage}{5.1cm}
2175 Amorphous SiC-like structure\\
2176 (not expected at \degc{450})\\[0.05cm]
2177 No rearrangement/transition into 3C-SiC
2178 \end{minipage}\\[0.1cm]
2179 \end{minipage}
2180 }}
2181 \end{pspicture}
2182 \end{minipage}
2183
2184 \end{slide}
2185
2186 \begin{slide}
2187
2188 \headphd
2189 {\large\bf
2190  Limitations of MD and short range potentials
2191 }
2192
2193 \small
2194
2195 \vspace{0.2cm}
2196
2197 {\bf Time scale problem of MD}\\[0.2cm]
2198 Precise integration \& thermodynamic sampling\\
2199 $\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
2200               $\omega$: vibrational mode\\
2201 $\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
2202 Several local minima separated by large energy barriers\\
2203 $\Rightarrow$ Transition event corresponds to a multiple
2204               of vibrational periods\\
2205 $\Rightarrow$ Phase transition consists of {\color{red}\underline{many}}
2206               infrequent transition events\\[0.2cm]
2207 {\color{blue}Accelerated methods:}
2208 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
2209
2210 \vspace{0.2cm}
2211
2212 {\bf Limitations related to the short range potential}\\[0.2cm]
2213 Cut-off function limits interaction to next neighbours\\
2214 $\Rightarrow$ Overestimated unphysical high forces of next neighbours
2215               (factor: 2.4--3.4)
2216
2217 \vspace{1.4cm}
2218
2219 {\bf Approach to the (twofold) problem}\\[0.2cm]
2220 Increased temperature simulations without TAD corrections\\
2221 Accelerated methods or higher time scales exclusively not sufficient!
2222
2223 \begin{pspicture}(0,0)(0,0)
2224 \rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{
2225 \begin{minipage}{7.5cm}
2226 \centering
2227 \vspace{0.05cm}
2228 Potential enhanced slow phase space propagation
2229 \end{minipage}
2230 }}
2231 \rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
2232 \begin{minipage}{2.7cm}
2233 \tiny
2234 \centering
2235 retain proper\\
2236 thermodynamic sampling
2237 \end{minipage}
2238 }}
2239 \psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7)
2240 \rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{
2241 \begin{minipage}{3.6cm}
2242 \tiny
2243 \centering
2244 \underline{IBS}\\[0.1cm]
2245 3C-SiC also observed for higher T\\[0.1cm]
2246 Higher T inside sample\\[0.1cm]
2247 Structural evolution vs.\\
2248 equilibrium properties
2249 \end{minipage}
2250 }}
2251 \psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0)
2252 \end{pspicture}
2253
2254 \end{slide}
2255
2256 \begin{slide}
2257
2258 \headphd
2259 {\large\bf\boldmath
2260  Increased temperature simulations --- $V_1$
2261 }
2262
2263 \small
2264
2265 \begin{minipage}{6.2cm}
2266 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
2267 \hfill
2268 \end{minipage}
2269 \begin{minipage}{6.2cm}
2270 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
2271 \end{minipage}
2272
2273 \begin{minipage}{6.2cm}
2274 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
2275 \hfill
2276 \end{minipage}
2277 \begin{minipage}{6.3cm}
2278 \scriptsize
2279  \underline{Si-C bonds:}
2280  \begin{itemize}
2281   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2282   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2283  \end{itemize}
2284  \underline{Si-Si bonds:}
2285  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2286  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2287  \underline{C-C bonds:}
2288  \begin{itemize}
2289   \item C-C next neighbour pairs reduced (mandatory)
2290   \item Peak at 0.3 nm slightly shifted
2291         \begin{itemize}
2292          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2293                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2294                combinations (|)\\
2295                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2296                ($\downarrow$)
2297          \item Range [|-$\downarrow$]:
2298                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2299                with nearby Si$_{\text{I}}$}
2300         \end{itemize}
2301  \end{itemize}
2302 \end{minipage}
2303
2304 \end{slide}
2305
2306 \begin{slide}
2307
2308 \headphd
2309 {\large\bf\boldmath
2310  Increased temperature simulations --- $V_1$
2311 }
2312
2313 \small
2314
2315 \begin{minipage}{6.2cm}
2316 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
2317 \hfill
2318 \end{minipage}
2319 \begin{minipage}{6.2cm}
2320 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
2321 \end{minipage}
2322
2323 \begin{minipage}{6.2cm}
2324 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
2325 \hfill
2326 \end{minipage}
2327 \begin{minipage}{6.3cm}
2328 \scriptsize
2329  \underline{Si-C bonds:}
2330  \begin{itemize}
2331   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2332   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2333  \end{itemize}
2334  \underline{Si-Si bonds:}
2335  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2336  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2337  \underline{C-C bonds:}
2338  \begin{itemize}
2339   \item C-C next neighbour pairs reduced (mandatory)
2340   \item Peak at 0.3 nm slightly shifted
2341         \begin{itemize}
2342          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2343                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2344                combinations (|)\\
2345                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2346                ($\downarrow$)
2347          \item Range [|-$\downarrow$]:
2348                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2349                with nearby Si$_{\text{I}}$}
2350         \end{itemize}
2351  \end{itemize}
2352 \end{minipage}
2353
2354 % conclusions
2355 \begin{pspicture}(0,0)(0,0)
2356 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
2357 \begin{minipage}{14cm}
2358 \hfill
2359 \vspace{14cm}
2360 \end{minipage}
2361 }}
2362 \rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
2363 \begin{minipage}{9cm}
2364 \vspace{0.2cm}
2365 \small
2366 \begin{center}
2367 {\color{gray}\bf Conclusions on SiC precipitation}\\[0.1cm]
2368 {\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\
2369 \end{center}
2370 \begin{itemize}
2371 \item Stretched coherent SiC structures\\
2372 $\Rightarrow$ Precipitation process involves {\color{blue}\cs}
2373 \item Explains annealing behavior of high/low T C implantations
2374       \begin{itemize}
2375        \item Low T: highly mobile {\color{red}\ci}
2376        \item High T: stable configurations of {\color{blue}\cs}
2377       \end{itemize}
2378 \item Role of \si{}
2379       \begin{itemize}
2380        \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
2381        \item Building block for surrounding Si host \& further SiC
2382        \item Strain compensation \ldots\\
2383              \ldots Si/SiC interface\\
2384              \ldots within stretched coherent SiC structure
2385       \end{itemize}
2386 \end{itemize}
2387 \vspace{0.2cm}
2388 \centering
2389 \psframebox[linecolor=blue,linewidth=0.05cm]{
2390 \begin{minipage}{7cm}
2391 \centering
2392 Precipitation mechanism involving \cs\\
2393 High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2394 \end{minipage}
2395 }
2396 \end{minipage}
2397 \vspace{0.2cm}
2398 }}
2399 \end{pspicture}
2400
2401 \end{slide}
2402
2403 % skip high T / C conc ... only here!
2404 \ifnum1=0
2405
2406 \begin{slide}
2407
2408  {\large\bf
2409   Increased temperature simulations at high C concentration
2410  }
2411
2412 \footnotesize
2413
2414 \begin{minipage}{6.5cm}
2415 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2416 \end{minipage}
2417 \begin{minipage}{6.5cm}
2418 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2419 \end{minipage}
2420
2421 \vspace{0.1cm}
2422
2423 \scriptsize
2424
2425 \framebox{
2426 \begin{minipage}[t]{6.0cm}
2427 0.186 nm: Si-C pairs $\uparrow$\\
2428 (as expected in 3C-SiC)\\[0.2cm]
2429 0.282 nm: Si-C-C\\[0.2cm]
2430 $\approx$0.35 nm: C-Si-Si
2431 \end{minipage}
2432 }
2433 \begin{minipage}{0.2cm}
2434 \hfill
2435 \end{minipage}
2436 \framebox{
2437 \begin{minipage}[t]{6.0cm}
2438 0.15 nm: C-C pairs $\uparrow$\\
2439 (as expected in graphite/diamond)\\[0.2cm]
2440 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2441 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2442 \end{minipage}
2443 }
2444
2445 \begin{itemize}
2446 \item Decreasing cut-off artifact
2447 \item {\color{red}Amorphous} SiC-like phase remains
2448 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2449 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2450 \end{itemize}
2451
2452 \vspace{-0.1cm}
2453
2454 \begin{center}
2455 {\color{blue}
2456 \framebox{
2457 {\color{black}
2458 High C \& small $V$ \& short $t$
2459 $\Rightarrow$
2460 }
2461 Slow restructuring due to strong C-C bonds
2462 {\color{black}
2463 $\Leftarrow$
2464 High C \& low T implants
2465 }
2466 }
2467 }
2468 \end{center}
2469
2470 \end{slide}
2471
2472 % skipped high T / C conc
2473 \fi
2474
2475 \begin{slide}
2476
2477 {\large\bf
2478  Summary / Outlook
2479 }
2480
2481 \small
2482
2483 \begin{pspicture}(0,0)(12,1.0)
2484 \psframebox[fillstyle=gradient,gradbegin=hred,gradend=white,gradlines=1000,gradmidpoint=1.0,linestyle=none]{
2485 \begin{minipage}{11cm}
2486 {\color{black}Diploma thesis}\\
2487  \underline{Monte Carlo} simulation modeling the selforganization process\\
2488  leading to periodic arrays of nanometric amorphous SiC precipitates
2489 \end{minipage}
2490 }
2491 \end{pspicture}\\[0.4cm]
2492 \begin{pspicture}(0,0)(12,2)
2493 \psframebox[fillstyle=gradient,gradbegin=hblue,gradend=white,gradmidpoint=1.0,gradlines=1000,linestyle=none]{
2494 \begin{minipage}{11cm}
2495 {\color{black}Doctoral studies}\\
2496  Classical potential \underline{molecular dynamics} simulations \ldots\\
2497  \underline{Density functional theory} calculations \ldots\\[0.2cm]
2498  \ldots on defect formation and SiC precipitation in Si
2499 \end{minipage}
2500 }
2501 \end{pspicture}\\[0.5cm]
2502 \begin{pspicture}(0,0)(12,3)
2503 \psframebox[fillstyle=solid,fillcolor=white,linestyle=solid]{
2504 \begin{minipage}{11cm}
2505 \vspace{0.2cm}
2506 {\color{black}\bf How to proceed \ldots}\\[0.1cm]
2507 MC $\rightarrow$ empirical potential MD $\rightarrow$ Ground-state DFT \ldots
2508 \begin{itemize}
2509  \renewcommand\labelitemi{$\ldots$}
2510  \item beyond LDA/GGA methods \& ground-state DFT
2511 \end{itemize}
2512 Investigation of structure \& structural evolution \ldots
2513 \begin{itemize}
2514  \renewcommand\labelitemi{$\ldots$}
2515  \item electronic/optical properties
2516  \item electronic correlations
2517  \item non-equilibrium systems
2518 \end{itemize}
2519 \end{minipage}
2520 }
2521 \end{pspicture}\\[0.5cm]
2522
2523 \end{slide}
2524
2525 \begin{slide}
2526
2527  {\large\bf
2528   Acknowledgements
2529  }
2530
2531  \vspace{0.1cm}
2532
2533  \small
2534
2535  Thanks to \ldots
2536
2537  \underline{Augsburg}
2538  \begin{itemize}
2539   \item Prof. B. Stritzker (accomodation at EP \RM{4})
2540   \item Ralf Utermann (EDV)
2541  \end{itemize}
2542
2543  \underline{Helsinki}
2544  \begin{itemize}
2545   \item Prof. K. Nordlund (MD)
2546  \end{itemize}
2547
2548  \underline{Munich}
2549  \begin{itemize}
2550   \item Bayerische Forschungsstiftung (financial support)
2551  \end{itemize}
2552
2553  \underline{Paderborn}
2554  \begin{itemize}
2555   \item Prof. J. Lindner (SiC)
2556   \item Prof. G. Schmidt (DFT + financial support)
2557   \item Dr. E. Rauls (DFT + SiC)
2558  \end{itemize}
2559
2560  \underline{Stuttgart}
2561 \begin{center}
2562 \framebox{
2563 \bf Thank you for your attention / invitation!
2564 }
2565 \end{center}
2566
2567 \end{slide}
2568
2569 \end{document}
2570