posic/talks/mpi_app.tex

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   2 %\documentclass[landscape,semhelv,draft]{seminar}
   3 \documentclass[landscape,semhelv]{seminar}
   4
   5 \usepackage{verbatim}
   6 \usepackage[greek,german]{babel}
   7 \usepackage[latin1]{inputenc}
   8 \usepackage[T1]{fontenc}
   9 \usepackage{amsmath}
  10 \usepackage{latexsym}
  11 \usepackage{ae}
  12
  13 \usepackage{calc}               % Simple computations with LaTeX variables
  14 \usepackage{caption}            % Improved captions
  15 \usepackage{fancybox}           % To have several backgrounds
  16
  17 \usepackage{fancyhdr}           % Headers and footers definitions
  18 \usepackage{fancyvrb}           % Fancy verbatim environments
  19 \usepackage{pstricks}           % PSTricks with the standard color package
  20
  21 \usepackage{pstricks}
  22 \usepackage{pst-node}
  23
  24 %\usepackage{epic}
  25 %\usepackage{eepic}
  26
  27 \usepackage{layout}
  28
  29 \usepackage{graphicx}
  30 \graphicspath{{../img/}}
  31
  32 \usepackage{miller}
  33
  34 \usepackage[setpagesize=false]{hyperref}
  35
  36 % units
  37 \usepackage{units}
  38
  39 \usepackage{semcolor}
  40 \usepackage{semlayer}           % Seminar overlays
  41 \usepackage{slidesec}           % Seminar sections and list of slides
  42
  43 \input{seminar.bug}             % Official bugs corrections
  44 \input{seminar.bg2}             % Unofficial bugs corrections
  45
  46 \articlemag{1}
  47
  48 \special{landscape}
  49
  50 % font
  51 %\usepackage{cmbright}
  52 %\renewcommand{\familydefault}{\sfdefault}
  53 %\usepackage{mathptmx}
  54
  55 \usepackage{upgreek}
  56
  57 \begin{document}
  58
  59 \extraslideheight{10in}
  60 \slideframe{plain}
  61
  62 \pagestyle{empty}
  63
  64 % specify width and height
  65 \slidewidth 26.3cm
  66 \slideheight 19.9cm
  67
  68 % margin
  69 \def\slidetopmargin{-0.15cm}
  70
  71 \newcommand{\ham}{\mathcal{H}}
  72 \newcommand{\pot}{\mathcal{V}}
  73 \newcommand{\foo}{\mathcal{U}}
  74 \newcommand{\vir}{\mathcal{W}}
  75
  76 % itemize level ii
  77 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
  78
  79 % nice phi
  80 \renewcommand{\phi}{\varphi}
  81
  82 % roman letters
  83 \newcommand{\RM}[1]{\MakeUppercase{\romannumeral #1{}}}
  84
  85 % colors
  86 \newrgbcolor{si-yellow}{.6 .6 0}
  87 \newrgbcolor{hb}{0.75 0.77 0.89}
  88 \newrgbcolor{lbb}{0.75 0.8 0.88}
  89 \newrgbcolor{hlbb}{0.825 0.88 0.968}
  90 \newrgbcolor{lachs}{1.0 .93 .81}
  91
  92 % shortcuts
  93 \newcommand{\si}{Si$_{\text{i}}${}}
  94 \newcommand{\ci}{C$_{\text{i}}${}}
  95 \newcommand{\cs}{C$_{\text{sub}}${}}
  96 \newcommand{\degc}[1]{\unit[#1]{$^{\circ}$C}{}}
  97 \newcommand{\distn}[1]{\unit[#1]{nm}{}}
  98 \newcommand{\dista}[1]{\unit[#1]{\AA}{}}
  99 \newcommand{\perc}[1]{\unit[#1]{\%}{}}
 100
 101 % no vertical centering
 102 %\centerslidesfalse
 103
 104 % layout check
 105 %\layout
 106 \begin{slide}
 107 \center
 108 {\Huge
 109 E\\
 110 F\\
 111 G\\
 112 A B C D E F G H G F E D C B A
 113 G\\
 114 F\\
 115 E\\
 116 }
 117 \end{slide}
 118
 119 % topic
 120
 121 \begin{slide}
 122 \begin{center}
 123
 124  \vspace{16pt}
 125
 126  {\LARGE\bf
 127   Atomistic simulation studies\\[0.2cm]
 128   in the C/Si system
 129  }
 130
 131  \vspace{48pt}
 132
 133  \textsc{Frank Zirkelbach}
 134
 135  \vspace{48pt}
 136
 137  Application talk at the Max Planck Institute for Solid State Research
 138
 139  \vspace{08pt}
 140
 141  Stuttgart, November 2011
 142
 143 \end{center}
 144 \end{slide}
 145
 146 % no vertical centering
 147 \centerslidesfalse
 148
 149 \ifnum1=0
 150
 151 % intro
 152
 153 \begin{slide}
 154
 155 %{\large\bf
 156 % Phase diagram of the C/Si system\\
 157 %}
 158
 159 \vspace*{0.2cm}
 160
 161 \begin{minipage}{6.5cm}
 162 \includegraphics[width=6.5cm]{si-c_phase.eps}
 163 \begin{center}
 164 {\tiny
 165 R. I. Scace and G. A. Slack, J. Chem. Phys. 30, 1551 (1959)
 166 }
 167 \end{center}
 168 \begin{pspicture}(0,0)(0,0)
 169 \psellipse[linecolor=blue,linewidth=0.1cm](3.55,4.0)(0.5,2.9)
 170 \end{pspicture}
 171 \end{minipage}
 172 \begin{minipage}{6cm}
 173 {\bf Phase diagram of the C/Si system}\\[0.2cm]
 174 {\color{blue}Stoichiometric composition}
 175 \begin{itemize}
 176 \item only chemical stable compound
 177 \item wide band gap semiconductor\\
 178       \underline{silicon carbide}, SiC
 179 \end{itemize}
 180 \end{minipage}
 181
 182 \end{slide}
 183
 184 % motivation / properties / applications of silicon carbide
 185
 186 \begin{slide}
 187
 188 \small
 189
 190 \begin{pspicture}(0,0)(13.5,5)
 191
 192  \psframe*[linecolor=hb](-0.2,0)(12.9,5)
 193
 194  \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](5.2,1)(6.5,1)(6.5,3)(5.2,3)
 195  \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](6.4,0.5)(7.7,2)(7.7,2)(6.4,3.5)
 196
 197  \rput[lt](0,4.6){\color{gray}PROPERTIES}
 198
 199  \rput[lt](0.3,4){wide band gap}
 200  \rput[lt](0.3,3.5){high electric breakdown field}
 201  \rput[lt](0.3,3){good electron mobility}
 202  \rput[lt](0.3,2.5){high electron saturation drift velocity}
 203  \rput[lt](0.3,2){high thermal conductivity}
 204
 205  \rput[lt](0.3,1.5){hard and mechanically stable}
 206  \rput[lt](0.3,1){chemically inert}
 207
 208  \rput[lt](0.3,0.5){radiation hardness}
 209
 210  \rput[rt](12.7,4.6){\color{gray}APPLICATIONS}
 211
 212  \rput[rt](12.5,3.85){high-temperature, high power}
 213  \rput[rt](12.5,3.5){and high-frequency}
 214  \rput[rt](12.5,3.15){electronic and optoelectronic devices}
 215
 216  \rput[rt](12.5,2.35){material suitable for extreme conditions}
 217  \rput[rt](12.5,2){microelectromechanical systems}
 218  \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements}
 219
 220  \rput[rt](12.5,0.85){first wall reactor material, detectors}
 221  \rput[rt](12.5,0.5){and electronic devices for space}
 222
 223 \end{pspicture}
 224
 225 \begin{picture}(0,0)(5,-162)
 226 \includegraphics[height=2.2cm]{3C_SiC_bs.eps}
 227 \end{picture}
 228 \begin{picture}(0,0)(-120,-162)
 229 \includegraphics[height=2.2cm]{nasa_600c_led.eps}
 230 \end{picture}
 231 \begin{picture}(0,0)(-270,-162)
 232 \includegraphics[height=2.2cm]{6h-sic_3c-sic.eps}
 233 \end{picture}
 234 %%%%
 235 \begin{picture}(0,0)(10,65)
 236 \includegraphics[height=2.8cm]{sic_switch.eps}
 237 \end{picture}
 238 %\begin{picture}(0,0)(-243,65)
 239 \begin{picture}(0,0)(-110,65)
 240 \includegraphics[height=2.8cm]{ise_99.eps}
 241 \end{picture}
 242 %\begin{picture}(0,0)(-135,65)
 243 \begin{picture}(0,0)(-100,65)
 244 \includegraphics[height=1.2cm]{infineon_schottky.eps}
 245 \end{picture}
 246 \begin{picture}(0,0)(-233,65)
 247 \includegraphics[height=2.8cm]{solar_car.eps}
 248 \end{picture}
 249
 250 \end{slide}
 251
 252 % motivation
 253
 254 \begin{slide}
 255
 256  {\large\bf
 257   Polytypes of SiC\\[0.4cm]
 258  }
 259
 260 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
 261 \begin{minipage}{1.9cm}
 262 {\tiny cubic (twist)}
 263 \end{minipage}
 264 \begin{minipage}{2.9cm}
 265 {\tiny hexagonal (no twist)}
 266 \end{minipage}
 267
 268 \begin{picture}(0,0)(-150,0)
 269  \includegraphics[width=7cm]{polytypes.eps}
 270 \end{picture}
 271
 272 \vspace{0.6cm}
 273
 274 \footnotesize
 275
 276 \begin{tabular}{l c c c c c c}
 277 \hline
 278  & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
 279 \hline
 280 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
 281 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
 282 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
 283 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
 284 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
 285 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
 286 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
 287 \hline
 288 \end{tabular}
 289
 290 \begin{pspicture}(0,0)(0,0)
 291 \psellipse[linecolor=green](5.7,2.10)(0.4,0.5)
 292 \end{pspicture}
 293 \begin{pspicture}(0,0)(0,0)
 294 \psellipse[linecolor=green](5.6,0.92)(0.4,0.2)
 295 \end{pspicture}
 296 \begin{pspicture}(0,0)(0,0)
 297 \psellipse[linecolor=red](10.45,0.45)(0.4,0.2)
 298 \end{pspicture}
 299
 300 \end{slide}
 301
 302 % fabrication
 303
 304 \begin{slide}
 305
 306  {\large\bf
 307   Fabrication of silicon carbide
 308  }
 309
 310  \small
 311
 312  \vspace{2pt}
 313
 314 \begin{center}
 315  {\color{gray}
 316  \emph{Silicon carbide --- Born from the stars, perfected on earth.}
 317  }
 318 \end{center}
 319
 320 \vspace{2pt}
 321
 322 SiC thin films by MBE \& CVD
 323 \begin{itemize}
 324  \item Much progress achieved in homo/heteroepitaxial SiC thin film growth
 325  \item \underline{Commercially available} semiconductor power devices based on
 326        \underline{\foreignlanguage{greek}{a}-SiC}
 327  \item Production of favored \underline{3C-SiC} material
 328        \underline{less advanced}
 329  \item Quality and size not yet sufficient
 330 \end{itemize}
 331 \begin{picture}(0,0)(-310,-20)
 332   \includegraphics[width=2.0cm]{cree.eps}
 333 \end{picture}
 334
 335 \vspace{-0.2cm}
 336
 337 Alternative approach:
 338 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
 339
 340 \vspace{0.2cm}
 341
 342 \scriptsize
 343
 344 \framebox{
 345 \begin{minipage}{3.15cm}
 346  \begin{center}
 347 \includegraphics[width=3cm]{imp.eps}\\
 348  {\tiny
 349   Carbon implantation
 350  }
 351  \end{center}
 352 \end{minipage}
 353 \begin{minipage}{3.15cm}
 354  \begin{center}
 355 \includegraphics[width=3cm]{annealing.eps}\\
 356  {\tiny
 357   \unit[12]{h} annealing at \degc{1200}
 358  }
 359  \end{center}
 360 \end{minipage}
 361 }
 362 \begin{minipage}{5.5cm}
 363  \includegraphics[width=5.8cm]{ibs_3c-sic.eps}\\[-0.2cm]
 364  \begin{center}
 365  {\tiny
 366   XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
 367  }
 368  \end{center}
 369 \end{minipage}
 370
 371 \end{slide}
 372
 373 % contents
 374
 375 \begin{slide}
 376
 377 {\large\bf
 378  Systematic investigation of C implantations into Si
 379 }
 380
 381 \vspace{1.7cm}
 382 \begin{center}
 383 \hspace{-1.0cm}
 384 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
 385 \end{center}
 386
 387 \end{slide}
 388
 389 % outline
 390
 391 \begin{slide}
 392
 393 {\large\bf
 394  Outline
 395 }
 396
 397 \vspace{1.7cm}
 398 \begin{center}
 399 \hspace{-1.0cm}
 400 \includegraphics[width=0.75\textwidth]{imp_inv.eps}
 401 \end{center}
 402
 403 \begin{pspicture}(0,0)(0,0)
 404 \rput(6.0,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
 405 \begin{minipage}{11cm}
 406 {\color{red}Diploma thesis}\\
 407  \underline{Monte Carlo} simulation modeling the selforganization process\\
 408  leading to periodic arrays of nanometric amorphous SiC precipitates
 409 \end{minipage}
 410 }}}
 411 \end{pspicture}
 412 \begin{pspicture}(0,0)(0,0)
 413 \rput(6.0,-0.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
 414 \begin{minipage}{11cm}
 415 {\color{blue}Doctoral studies}\\
 416  Classical potential \underline{molecular dynamics} simulations \ldots\\
 417  \underline{Density functional theory} calculations \ldots\\[0.2cm]
 418  \ldots on defect formation and SiC precipitation in Si
 419 \end{minipage}
 420 }}}
 421 \end{pspicture}
 422 \begin{pspicture}(0,0)(0,0)
 423 \psellipse[linecolor=red,linewidth=0.05cm](5,3.0)(0.8,1.0)
 424 \end{pspicture}
 425 \begin{pspicture}(0,0)(0,0)
 426 \psellipse[linecolor=blue,linewidth=0.05cm](8.2,3.2)(1.5,1.6)
 427 \end{pspicture}
 428
 429 \end{slide}
 430
 431 % continue here
 432 \fi
 433 \begin{slide}
 434
 435 {\large\bf
 436  Selforganization of nanometric amorphous SiC lamellae
 437 }
 438
 439 \begin{minipage}{6cm}
 440 \includegraphics[width=6cm]{}
 441 \end{minipage}
 442
 443 \end{slide}
 444
 445
 446 \end{document}
 447 \ifnum1=0
 448
 449 \begin{slide}
 450
 451 {\large\bf
 452  Selforganization of nanometric amorphous SiC lamellae
 453 }
 454
 455 \framebox{
 456  \begin{minipage}{6.3cm}
 457  \begin{center}
 458  {\color{blue}
 459   Precipitation mechanism not yet fully understood!
 460  }
 461  \renewcommand\labelitemi{$\Rightarrow$}
 462  \small
 463  \underline{Understanding the SiC precipitation}
 464  \begin{itemize}
 465   \item significant technological progress in SiC thin film formation
 466   \item perspectives for processes relying upon prevention of SiC precipitation
 467  \end{itemize}
 468  \end{center}
 469  \end{minipage}
 470 }
 471
 472 \end{slide}
 473
 474 \begin{slide}
 475
 476  {\large\bf
 477   Supposed precipitation mechanism of SiC in Si
 478  }
 479
 480  \scriptsize
 481
 482  \vspace{0.1cm}
 483
 484  \begin{minipage}{3.8cm}
 485  Si \& SiC lattice structure\\[0.2cm]
 486  \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
 487  \hrule
 488  \end{minipage}
 489  \hspace{0.6cm}
 490  \begin{minipage}{3.8cm}
 491  \begin{center}
 492  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 493  \end{center}
 494  \end{minipage}
 495  \hspace{0.6cm}
 496  \begin{minipage}{3.8cm}
 497  \begin{center}
 498  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 499  \end{center}
 500  \end{minipage}
 501
 502  \begin{minipage}{4cm}
 503  \begin{center}
 504  C-Si dimers (dumbbells)\\[-0.1cm]
 505  on Si interstitial sites
 506  \end{center}
 507  \end{minipage}
 508  \hspace{0.2cm}
 509  \begin{minipage}{4.2cm}
 510  \begin{center}
 511  Agglomeration of C-Si dumbbells\\[-0.1cm]
 512  $\Rightarrow$ dark contrasts
 513  \end{center}
 514  \end{minipage}
 515  \hspace{0.2cm}
 516  \begin{minipage}{4cm}
 517  \begin{center}
 518  Precipitation of 3C-SiC in Si\\[-0.1cm]
 519  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 520  \& release of Si self-interstitials
 521  \end{center}
 522  \end{minipage}
 523
 524  \begin{minipage}{3.8cm}
 525  \begin{center}
 526  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 527  \end{center}
 528  \end{minipage}
 529  \hspace{0.6cm}
 530  \begin{minipage}{3.8cm}
 531  \begin{center}
 532  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 533  \end{center}
 534  \end{minipage}
 535  \hspace{0.6cm}
 536  \begin{minipage}{3.8cm}
 537  \begin{center}
 538  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 539  \end{center}
 540  \end{minipage}
 541
 542 \begin{pspicture}(0,0)(0,0)
 543 \psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
 544 \psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
 545 \rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
 546 \psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
 547 \rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 548  $4a_{\text{Si}}=5a_{\text{SiC}}$
 549  }}}
 550 \rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 551 \hkl(h k l) planes match
 552  }}}
 553 \rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 554 r = 2 - 4 nm
 555  }}}
 556 \end{pspicture}
 557
 558 \end{slide}
 559
 560 \begin{slide}
 561
 562  {\large\bf
 563   Supposed precipitation mechanism of SiC in Si
 564  }
 565
 566  \scriptsize
 567
 568  \vspace{0.1cm}
 569
 570  \begin{minipage}{3.8cm}
 571  Si \& SiC lattice structure\\[0.2cm]
 572  \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
 573  \hrule
 574  \end{minipage}
 575  \hspace{0.6cm}
 576  \begin{minipage}{3.8cm}
 577  \begin{center}
 578  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 579  \end{center}
 580  \end{minipage}
 581  \hspace{0.6cm}
 582  \begin{minipage}{3.8cm}
 583  \begin{center}
 584  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 585  \end{center}
 586  \end{minipage}
 587
 588  \begin{minipage}{4cm}
 589  \begin{center}
 590  C-Si dimers (dumbbells)\\[-0.1cm]
 591  on Si interstitial sites
 592  \end{center}
 593  \end{minipage}
 594  \hspace{0.2cm}
 595  \begin{minipage}{4.2cm}
 596  \begin{center}
 597  Agglomeration of C-Si dumbbells\\[-0.1cm]
 598  $\Rightarrow$ dark contrasts
 599  \end{center}
 600  \end{minipage}
 601  \hspace{0.2cm}
 602  \begin{minipage}{4cm}
 603  \begin{center}
 604  Precipitation of 3C-SiC in Si\\[-0.1cm]
 605  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 606  \& release of Si self-interstitials
 607  \end{center}
 608  \end{minipage}
 609
 610  \begin{minipage}{3.8cm}
 611  \begin{center}
 612  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 613  \end{center}
 614  \end{minipage}
 615  \hspace{0.6cm}
 616  \begin{minipage}{3.8cm}
 617  \begin{center}
 618  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 619  \end{center}
 620  \end{minipage}
 621  \hspace{0.6cm}
 622  \begin{minipage}{3.8cm}
 623  \begin{center}
 624  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 625  \end{center}
 626  \end{minipage}
 627
 628 \begin{pspicture}(0,0)(0,0)
 629 \psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
 630 \psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
 631 \rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
 632 \psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
 633 \rput(12.7,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 634  $4a_{\text{Si}}=5a_{\text{SiC}}$
 635  }}}
 636 \rput(12.2,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 637 \hkl(h k l) planes match
 638  }}}
 639 \rput(9.7,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 640 r = 2 - 4 nm
 641  }}}
 642 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
 643 \begin{minipage}{10cm}
 644 \small
 645 {\color{red}\bf Controversial views}
 646 \begin{itemize}
 647 \item Implantations at high T (Nejim et al.)
 648  \begin{itemize}
 649   \item Topotactic transformation based on \cs
 650   \item \si{} as supply reacting with further C in cleared volume
 651  \end{itemize}
 652 \item Annealing behavior (Serre et al.)
 653  \begin{itemize}
 654   \item Room temperature implants $\rightarrow$ highly mobile C
 655   \item Elevated T implants $\rightarrow$ no/low C redistribution/migration\\
 656         (indicate stable \cs{} configurations)
 657  \end{itemize}
 658 \item Strained silicon \& Si/SiC heterostructures
 659  \begin{itemize}
 660   \item Coherent SiC precipitates (tensile strain)
 661   \item Incoherent SiC (strain relaxation)
 662  \end{itemize}
 663 \end{itemize}
 664 \end{minipage}
 665  }}}
 666 \end{pspicture}
 667
 668 \end{slide}
 669
 670 \begin{slide}
 671
 672  {\large\bf
 673   Molecular dynamics (MD) simulations
 674  }
 675
 676  \vspace{12pt}
 677
 678  \small
 679
 680  {\bf MD basics:}
 681  \begin{itemize}
 682   \item Microscopic description of N particle system
 683   \item Analytical interaction potential
 684   \item Numerical integration using Newtons equation of motion\\
 685         as a propagation rule in 6N-dimensional phase space
 686   \item Observables obtained by time and/or ensemble averages
 687  \end{itemize}
 688  {\bf Details of the simulation:}
 689  \begin{itemize}
 690   \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
 691   \item Ensemble: NpT (isothermal-isobaric)
 692         \begin{itemize}
 693          \item Berendsen thermostat:
 694                $\tau_{\text{T}}=100\text{ fs}$
 695          \item Berendsen barostat:\\
 696                $\tau_{\text{P}}=100\text{ fs}$,
 697                $\beta^{-1}=100\text{ GPa}$
 698         \end{itemize}
 699   \item Erhart/Albe potential: Tersoff-like bond order potential
 700   \vspace*{12pt}
 701         \[
 702         E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
 703         \pot_{ij} = {\color{red}f_C(r_{ij})}
 704         \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
 705         \]
 706  \end{itemize}
 707
 708  \begin{picture}(0,0)(-230,-30)
 709   \includegraphics[width=5cm]{tersoff_angle.eps}
 710  \end{picture}
 711
 712 \end{slide}
 713
 714 \begin{slide}
 715
 716  {\large\bf
 717   Density functional theory (DFT) calculations
 718  }
 719
 720  \small
 721
 722  Basic ingredients necessary for DFT
 723
 724  \begin{itemize}
 725   \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
 726         \begin{itemize}
 727          \item ... uniquely determines the ground state potential
 728                / wavefunctions
 729          \item ... minimizes the systems total energy
 730         \end{itemize}
 731   \item \underline{Born-Oppenheimer}
 732         - $N$ moving electrons in an external potential of static nuclei
 733 \[
 734 H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
 735               +\sum_i^N V_{\text{ext}}(r_i)
 736               +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
 737 \]
 738   \item \underline{Effective potential}
 739         - averaged electrostatic potential \& exchange and correlation
 740 \[
 741 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
 742                  +V_{\text{XC}}[n(r)]
 743 \]
 744   \item \underline{Kohn-Sham system}
 745         - Schr\"odinger equation of N non-interacting particles
 746 \[
 747 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
 748 =\epsilon_i\Phi_i(r)
 749 \quad
 750 \Rightarrow
 751 \quad
 752 n(r)=\sum_i^N|\Phi_i(r)|^2
 753 \]
 754   \item \underline{Self-consistent solution}\\
 755 $n(r)$ depends on $\Phi_i$, which depend on $V_{\text{eff}}$,
 756 which in turn depends on $n(r)$
 757   \item \underline{Variational principle}
 758         - minimize total energy with respect to $n(r)$
 759  \end{itemize}
 760
 761 \end{slide}
 762
 763 \begin{slide}
 764
 765  {\large\bf
 766   Density functional theory (DFT) calculations
 767  }
 768
 769  \small
 770
 771  \vspace*{0.2cm}
 772
 773  Details of applied DFT calculations in this work
 774
 775  \begin{itemize}
 776   \item \underline{Exchange correlation functional}
 777         - approximations for the inhomogeneous electron gas
 778         \begin{itemize}
 779          \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
 780          \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
 781         \end{itemize}
 782   \item \underline{Plane wave basis set}
 783         - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
 784 \[
 785 \rightarrow
 786 \text{Fourier series: } \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r), \quad E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}
 787 \qquad ({\color{blue}300\text{ eV}})
 788 \]
 789   \item \underline{Brillouin zone sampling} -
 790         {\color{blue}$\Gamma$-point only} calculations
 791   \item \underline{Pseudo potential}
 792         - consider only the valence electrons
 793   \item \underline{Code} - VASP 4.6
 794  \end{itemize}
 795
 796  \vspace*{0.2cm}
 797
 798  MD and structural optimization
 799
 800  \begin{itemize}
 801   \item MD integration: Gear predictor corrector algorithm
 802   \item Pressure control: Parrinello-Rahman pressure control
 803   \item Structural optimization: Conjugate gradient method
 804  \end{itemize}
 805
 806 \begin{pspicture}(0,0)(0,0)
 807 \psellipse[linecolor=blue](1.5,6.75)(0.5,0.3)
 808 \end{pspicture}
 809
 810 \end{slide}
 811
 812 \begin{slide}
 813
 814  {\large\bf
 815   C and Si self-interstitial point defects in silicon
 816  }
 817
 818  \small
 819
 820  \vspace*{0.3cm}
 821
 822 \begin{minipage}{8cm}
 823 Procedure:\\[0.3cm]
 824   \begin{pspicture}(0,0)(7,5)
 825   \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 826    \parbox{7cm}{
 827    \begin{itemize}
 828     \item Creation of c-Si simulation volume
 829     \item Periodic boundary conditions
 830     \item $T=0\text{ K}$, $p=0\text{ bar}$
 831    \end{itemize}
 832   }}}}
 833 \rput(3.5,2.1){\rnode{insert}{\psframebox{
 834  \parbox{7cm}{
 835   \begin{center}
 836   Insertion of interstitial C/Si atoms
 837   \end{center}
 838   }}}}
 839   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
 840    \parbox{7cm}{
 841    \begin{center}
 842    Relaxation / structural energy minimization
 843    \end{center}
 844   }}}}
 845   \ncline[]{->}{init}{insert}
 846   \ncline[]{->}{insert}{cool}
 847  \end{pspicture}
 848 \end{minipage}
 849 \begin{minipage}{5cm}
 850   \includegraphics[width=5cm]{unit_cell_e.eps}\\
 851 \end{minipage}
 852
 853 \begin{minipage}{9cm}
 854  \begin{tabular}{l c c}
 855  \hline
 856  & size [unit cells] & \# atoms\\
 857 \hline
 858 VASP & $3\times 3\times 3$ & $216\pm 1$ \\
 859 Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
 860 \hline
 861  \end{tabular}
 862 \end{minipage}
 863 \begin{minipage}{4cm}
 864 {\color{red}$\bullet$} Tetrahedral\\
 865 {\color{green}$\bullet$} Hexagonal\\
 866 {\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
 867 {\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
 868 {\color{cyan}$\bullet$} Bond-centered\\
 869 {\color{black}$\bullet$} Vacancy / Substitutional
 870 \end{minipage}
 871
 872 \end{slide}
 873
 874 \begin{slide}
 875
 876  \footnotesize
 877
 878 \begin{minipage}{9.5cm}
 879
 880  {\large\bf
 881   Si self-interstitial point defects in silicon\\
 882  }
 883
 884 \begin{tabular}{l c c c c c}
 885 \hline
 886  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
 887 \hline
 888  VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
 889  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
 890 \hline
 891 \end{tabular}\\[0.2cm]
 892
 893 \begin{minipage}{4.7cm}
 894 \includegraphics[width=4.7cm]{e_kin_si_hex.ps}
 895 \end{minipage}
 896 \begin{minipage}{4.7cm}
 897 \begin{center}
 898 {\tiny nearly T $\rightarrow$ T}\\
 899 \end{center}
 900 \includegraphics[width=4.7cm]{nhex_tet.ps}
 901 \end{minipage}\\
 902
 903 \underline{Hexagonal} \hspace{2pt}
 904 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
 905 \framebox{
 906 \begin{minipage}{2.7cm}
 907 $E_{\text{f}}^*=4.48\text{ eV}$\\
 908 \includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
 909 \end{minipage}
 910 \begin{minipage}{0.4cm}
 911 \begin{center}
 912 $\Rightarrow$
 913 \end{center}
 914 \end{minipage}
 915 \begin{minipage}{2.7cm}
 916 $E_{\text{f}}=3.96\text{ eV}$\\
 917 \includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
 918 \end{minipage}
 919 }
 920 \begin{minipage}{2.9cm}
 921 \begin{flushright}
 922 \underline{Vacancy}\\
 923 \includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
 924 \end{flushright}
 925 \end{minipage}
 926
 927 \end{minipage}
 928 \begin{minipage}{3.5cm}
 929
 930 \begin{flushright}
 931 \underline{\hkl<1 1 0> dumbbell}\\
 932 \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
 933 \underline{Tetrahedral}\\
 934 \includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
 935 \underline{\hkl<1 0 0> dumbbell}\\
 936 \includegraphics[width=3.0cm]{si_pd_albe/100.eps}
 937 \end{flushright}
 938
 939 \end{minipage}
 940
 941 \end{slide}
 942
 943 \begin{slide}
 944
 945 \footnotesize
 946
 947  {\large\bf
 948   C interstitial point defects in silicon\\[-0.1cm]
 949  }
 950
 951 \begin{tabular}{l c c c c c c r}
 952 \hline
 953  $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B & \cs{} \& \si\\
 954 \hline
 955  VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
 956  Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
 957 \hline
 958 \end{tabular}\\[0.1cm]
 959
 960 \framebox{
 961 \begin{minipage}{2.7cm}
 962 \underline{Hexagonal} \hspace{2pt}
 963 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
 964 $E_{\text{f}}^*=9.05\text{ eV}$\\
 965 \includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
 966 \end{minipage}
 967 \begin{minipage}{0.4cm}
 968 \begin{center}
 969 $\Rightarrow$
 970 \end{center}
 971 \end{minipage}
 972 \begin{minipage}{2.7cm}
 973 \underline{\hkl<1 0 0>}\\
 974 $E_{\text{f}}=3.88\text{ eV}$\\
 975 \includegraphics[width=2.7cm]{c_pd_albe/100.eps}
 976 \end{minipage}
 977 }
 978 \begin{minipage}{2cm}
 979 \hfill
 980 \end{minipage}
 981 \begin{minipage}{3cm}
 982 \begin{flushright}
 983 \underline{Tetrahedral}\\
 984 \includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
 985 \end{flushright}
 986 \end{minipage}
 987
 988 \framebox{
 989 \begin{minipage}{2.7cm}
 990 \underline{Bond-centered}\\
 991 $E_{\text{f}}^*=5.59\text{ eV}$\\
 992 \includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
 993 \end{minipage}
 994 \begin{minipage}{0.4cm}
 995 \begin{center}
 996 $\Rightarrow$
 997 \end{center}
 998 \end{minipage}
 999 \begin{minipage}{2.7cm}
1000 \underline{\hkl<1 1 0> dumbbell}\\
1001 $E_{\text{f}}=5.18\text{ eV}$\\
1002 \includegraphics[width=2.7cm]{c_pd_albe/110.eps}
1003 \end{minipage}
1004 }
1005 \begin{minipage}{2cm}
1006 \hfill
1007 \end{minipage}
1008 \begin{minipage}{3cm}
1009 \begin{flushright}
1010 \underline{Substitutional}\\
1011 \includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
1012 \end{flushright}
1013 \end{minipage}
1014
1015 \end{slide}
1016
1017 \begin{slide}
1018
1019 \footnotesize
1020
1021  {\large\bf\boldmath
1022   C \hkl<1 0 0> dumbbell interstitial configuration\\
1023  }
1024
1025 {\tiny
1026 \begin{tabular}{l c c c c c c c c}
1027 \hline
1028  Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
1029 \hline
1030 Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
1031 VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
1032 \hline
1033 \end{tabular}\\[0.2cm]
1034 \begin{tabular}{l c c c c }
1035 \hline
1036  Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
1037 \hline
1038 Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
1039 VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
1040 \hline
1041 \end{tabular}\\[0.2cm]
1042 \begin{tabular}{l c c c}
1043 \hline
1044  Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
1045 \hline
1046 Erhart/Albe & 0.084 & -0.091 & 0.175 \\
1047 VASP & 0.109 & -0.065 & 0.174 \\
1048 \hline
1049 \end{tabular}\\[0.6cm]
1050 }
1051
1052 \begin{minipage}{3.0cm}
1053 \begin{center}
1054 \underline{Erhart/Albe}
1055 \includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
1056 \end{center}
1057 \end{minipage}
1058 \begin{minipage}{3.0cm}
1059 \begin{center}
1060 \underline{VASP}
1061 \includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
1062 \end{center}
1063 \end{minipage}\\
1064
1065 \begin{picture}(0,0)(-185,10)
1066 \includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
1067 \end{picture}
1068 \begin{picture}(0,0)(-280,-150)
1069 \includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
1070 \end{picture}
1071
1072 \begin{pspicture}(0,0)(0,0)
1073 \psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
1074 \psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
1075 \psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
1076 \psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
1077 \end{pspicture}
1078
1079 \end{slide}
1080
1081 \begin{slide}
1082
1083 \small
1084
1085 \begin{minipage}{8.5cm}
1086
1087  {\large\bf
1088   Bond-centered interstitial configuration\\[-0.1cm]
1089  }
1090
1091 \begin{minipage}{3.0cm}
1092 \includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
1093 \end{minipage}
1094 \begin{minipage}{5.2cm}
1095 \begin{itemize}
1096  \item Linear Si-C-Si bond
1097  \item Si: one C \& 3 Si neighbours
1098  \item Spin polarized calculations
1099  \item No saddle point!\\
1100        Real local minimum!
1101 \end{itemize}
1102 \end{minipage}
1103
1104 \framebox{
1105  \tiny
1106  \begin{minipage}[t]{6.5cm}
1107   \begin{minipage}[t]{1.2cm}
1108   {\color{red}Si}\\
1109   {\tiny sp$^3$}\\[0.8cm]
1110   \underline{${\color{black}\uparrow}$}
1111   \underline{${\color{black}\uparrow}$}
1112   \underline{${\color{black}\uparrow}$}
1113   \underline{${\color{red}\uparrow}$}\\
1114   sp$^3$
1115   \end{minipage}
1116   \begin{minipage}[t]{1.4cm}
1117   \begin{center}
1118   {\color{red}M}{\color{blue}O}\\[0.8cm]
1119   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1120   $\sigma_{\text{ab}}$\\[0.5cm]
1121   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
1122   $\sigma_{\text{b}}$
1123   \end{center}
1124   \end{minipage}
1125   \begin{minipage}[t]{1.0cm}
1126   \begin{center}
1127   {\color{blue}C}\\
1128   {\tiny sp}\\[0.2cm]
1129   \underline{${\color{white}\uparrow\uparrow}$}
1130   \underline{${\color{white}\uparrow\uparrow}$}\\
1131   2p\\[0.4cm]
1132   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
1133   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
1134   sp
1135   \end{center}
1136   \end{minipage}
1137   \begin{minipage}[t]{1.4cm}
1138   \begin{center}
1139   {\color{blue}M}{\color{green}O}\\[0.8cm]
1140   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
1141   $\sigma_{\text{ab}}$\\[0.5cm]
1142   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
1143   $\sigma_{\text{b}}$
1144   \end{center}
1145   \end{minipage}
1146   \begin{minipage}[t]{1.2cm}
1147   \begin{flushright}
1148   {\color{green}Si}\\
1149   {\tiny sp$^3$}\\[0.8cm]
1150   \underline{${\color{green}\uparrow}$}
1151   \underline{${\color{black}\uparrow}$}
1152   \underline{${\color{black}\uparrow}$}
1153   \underline{${\color{black}\uparrow}$}\\
1154   sp$^3$
1155   \end{flushright}
1156   \end{minipage}
1157  \end{minipage}
1158 }\\[0.1cm]
1159
1160 \framebox{
1161 \begin{minipage}{4.5cm}
1162 \includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
1163 \end{minipage}
1164 \begin{minipage}{3.5cm}
1165 {\color{gray}$\bullet$} Spin up\\
1166 {\color{green}$\bullet$} Spin down\\
1167 {\color{blue}$\bullet$} Resulting spin up\\
1168 {\color{yellow}$\bullet$} Si atoms\\
1169 {\color{red}$\bullet$} C atom
1170 \end{minipage}
1171 }
1172
1173 \end{minipage}
1174 \begin{minipage}{4.2cm}
1175 \begin{flushright}
1176 \includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
1177 {\color{green}$\Box$} {\tiny unoccupied}\\
1178 {\color{red}$\bullet$} {\tiny occupied}
1179 \end{flushright}
1180 \end{minipage}
1181
1182 \end{slide}
1183
1184 \begin{slide}
1185
1186  {\large\bf\boldmath
1187   Migration of the C \hkl<1 0 0> dumbbell interstitial
1188  }
1189
1190 \scriptsize
1191
1192  {\small Investigated pathways}
1193
1194 \begin{minipage}{8.5cm}
1195 \begin{minipage}{8.3cm}
1196 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
1197 \begin{minipage}{2.4cm}
1198 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1199 \end{minipage}
1200 \begin{minipage}{0.4cm}
1201 $\rightarrow$
1202 \end{minipage}
1203 \begin{minipage}{2.4cm}
1204 \includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
1205 \end{minipage}
1206 \begin{minipage}{0.4cm}
1207 $\rightarrow$
1208 \end{minipage}
1209 \begin{minipage}{2.4cm}
1210 \includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
1211 \end{minipage}
1212 \end{minipage}\\
1213 \begin{minipage}{8.3cm}
1214 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
1215 \begin{minipage}{2.4cm}
1216 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1217 \end{minipage}
1218 \begin{minipage}{0.4cm}
1219 $\rightarrow$
1220 \end{minipage}
1221 \begin{minipage}{2.4cm}
1222 \includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
1223 \end{minipage}
1224 \begin{minipage}{0.4cm}
1225 $\rightarrow$
1226 \end{minipage}
1227 \begin{minipage}{2.4cm}
1228 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
1229 \end{minipage}
1230 \end{minipage}\\
1231 \begin{minipage}{8.3cm}
1232 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
1233 \begin{minipage}{2.4cm}
1234 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
1235 \end{minipage}
1236 \begin{minipage}{0.4cm}
1237 $\rightarrow$
1238 \end{minipage}
1239 \begin{minipage}{2.4cm}
1240 \includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
1241 \end{minipage}
1242 \begin{minipage}{0.4cm}
1243 $\rightarrow$
1244 \end{minipage}
1245 \begin{minipage}{2.4cm}
1246 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
1247 \end{minipage}
1248 \end{minipage}
1249 \end{minipage}
1250 \framebox{
1251 \begin{minipage}{4.2cm}
1252  {\small Constrained relaxation\\
1253          technique (CRT) method}\\
1254 \includegraphics[width=4cm]{crt_orig.eps}
1255 \begin{itemize}
1256  \item Constrain diffusing atom
1257  \item Static constraints
1258 \end{itemize}
1259 \vspace*{0.3cm}
1260  {\small Modifications}\\
1261 \includegraphics[width=4cm]{crt_mod.eps}
1262 \begin{itemize}
1263  \item Constrain all atoms
1264  \item Update individual\\
1265        constraints
1266 \end{itemize}
1267 \end{minipage}
1268 }
1269
1270 \end{slide}
1271
1272 \begin{slide}
1273
1274  {\large\bf\boldmath
1275   Migration of the C \hkl<1 0 0> dumbbell interstitial
1276  }
1277
1278 \scriptsize
1279
1280 \framebox{
1281 \begin{minipage}{5.9cm}
1282 \begin{flushleft}
1283 \includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
1284 \end{flushleft}
1285 \begin{center}
1286 \begin{picture}(0,0)(60,0)
1287 \includegraphics[width=1cm]{vasp_mig/00-1.eps}
1288 \end{picture}
1289 \begin{picture}(0,0)(-5,0)
1290 \includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
1291 \end{picture}
1292 \begin{picture}(0,0)(-55,0)
1293 \includegraphics[width=1cm]{vasp_mig/bc.eps}
1294 \end{picture}
1295 \begin{picture}(0,0)(12.5,10)
1296 \includegraphics[width=1cm]{110_arrow.eps}
1297 \end{picture}
1298 \begin{picture}(0,0)(90,0)
1299 \includegraphics[height=0.9cm]{001_arrow.eps}
1300 \end{picture}
1301 \end{center}
1302 \vspace*{0.35cm}
1303 \end{minipage}
1304 }
1305 \begin{minipage}{0.3cm}
1306 \hfill
1307 \end{minipage}
1308 \framebox{
1309 \begin{minipage}{5.9cm}
1310 \begin{flushright}
1311 \includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
1312 \end{flushright}
1313 \begin{center}
1314 \begin{picture}(0,0)(60,0)
1315 \includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
1316 \end{picture}
1317 \begin{picture}(0,0)(5,0)
1318 \includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
1319 \end{picture}
1320 \begin{picture}(0,0)(-55,0)
1321 \includegraphics[width=1cm]{vasp_mig/0-10.eps}
1322 \end{picture}
1323 \begin{picture}(0,0)(12.5,10)
1324 \includegraphics[width=1cm]{100_arrow.eps}
1325 \end{picture}
1326 \begin{picture}(0,0)(90,0)
1327 \includegraphics[height=0.9cm]{001_arrow.eps}
1328 \end{picture}
1329 \end{center}
1330 \vspace*{0.3cm}
1331 \end{minipage}\\
1332 }
1333
1334 \vspace*{0.05cm}
1335
1336 \framebox{
1337 \begin{minipage}{5.9cm}
1338 \begin{flushleft}
1339 \includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
1340 \end{flushleft}
1341 \begin{center}
1342 \begin{picture}(0,0)(60,0)
1343 \includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps}
1344 \end{picture}
1345 \begin{picture}(0,0)(10,0)
1346 \includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
1347 \end{picture}
1348 \begin{picture}(0,0)(-60,0)
1349 \includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps}
1350 \end{picture}
1351 \begin{picture}(0,0)(12.5,10)
1352 \includegraphics[width=1cm]{100_arrow.eps}
1353 \end{picture}
1354 \begin{picture}(0,0)(90,0)
1355 \includegraphics[height=0.9cm]{001_arrow.eps}
1356 \end{picture}
1357 \end{center}
1358 \vspace*{0.3cm}
1359 \end{minipage}
1360 }
1361 \begin{minipage}{0.3cm}
1362 \hfill
1363 \end{minipage}
1364 \begin{minipage}{6.5cm}
1365 VASP results
1366 \begin{itemize}
1367  \item Energetically most favorable path
1368        \begin{itemize}
1369         \item Path 2
1370         \item Activation energy: $\approx$ 0.9 eV
1371         \item Experimental values: 0.73 ... 0.87 eV
1372        \end{itemize}
1373        $\Rightarrow$ {\color{blue}Diffusion} path identified!
1374  \item Reorientation (path 3)
1375        \begin{itemize}
1376         \item More likely composed of two consecutive steps of type 2
1377         \item Experimental values: 0.77 ... 0.88 eV
1378        \end{itemize}
1379        $\Rightarrow$ {\color{blue}Reorientation} transition identified!
1380 \end{itemize}
1381 \end{minipage}
1382
1383 \end{slide}
1384
1385 \begin{slide}
1386
1387  {\large\bf\boldmath
1388   Migration of the C \hkl<1 0 0> dumbbell interstitial
1389  }
1390
1391 \scriptsize
1392
1393  \vspace{0.1cm}
1394
1395 \begin{minipage}{6.5cm}
1396
1397 \framebox{
1398 \begin{minipage}[t]{5.9cm}
1399 \begin{flushleft}
1400 \includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
1401 \end{flushleft}
1402 \begin{center}
1403 \begin{pspicture}(0,0)(0,0)
1404 \psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
1405 \end{pspicture}
1406 \begin{picture}(0,0)(60,-50)
1407 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
1408 \end{picture}
1409 \begin{picture}(0,0)(5,-50)
1410 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
1411 \end{picture}
1412 \begin{picture}(0,0)(-55,-50)
1413 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
1414 \end{picture}
1415 \begin{picture}(0,0)(12.5,-40)
1416 \includegraphics[width=1cm]{110_arrow.eps}
1417 \end{picture}
1418 \begin{picture}(0,0)(90,-45)
1419 \includegraphics[height=0.9cm]{001_arrow.eps}
1420 \end{picture}\\
1421 \begin{pspicture}(0,0)(0,0)
1422 \psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
1423 \end{pspicture}
1424 \begin{picture}(0,0)(60,-15)
1425 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
1426 \end{picture}
1427 \begin{picture}(0,0)(35,-15)
1428 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
1429 \end{picture}
1430 \begin{picture}(0,0)(-5,-15)
1431 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
1432 \end{picture}
1433 \begin{picture}(0,0)(-55,-15)
1434 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
1435 \end{picture}
1436 \begin{picture}(0,0)(12.5,-5)
1437 \includegraphics[width=1cm]{100_arrow.eps}
1438 \end{picture}
1439 \begin{picture}(0,0)(90,-15)
1440 \includegraphics[height=0.9cm]{010_arrow.eps}
1441 \end{picture}
1442 \end{center}
1443 \end{minipage}
1444 }\\[0.1cm]
1445
1446 \begin{minipage}{5.9cm}
1447 Erhart/Albe results
1448 \begin{itemize}
1449  \item Lowest activation energy: $\approx$ 2.2 eV
1450  \item 2.4 times higher than VASP
1451  \item Different pathway
1452 \end{itemize}
1453 \end{minipage}
1454
1455 \end{minipage}
1456 \begin{minipage}{6.5cm}
1457
1458 \framebox{
1459 \begin{minipage}{5.9cm}
1460 %\begin{flushright}
1461 %\includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
1462 %\end{flushright}
1463 %\begin{center}
1464 %\begin{pspicture}(0,0)(0,0)
1465 %\psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
1466 %\end{pspicture}
1467 %\begin{picture}(0,0)(60,-5)
1468 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
1469 %\end{picture}
1470 %\begin{picture}(0,0)(0,-5)
1471 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
1472 %\end{picture}
1473 %\begin{picture}(0,0)(-55,-5)
1474 %\includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
1475 %\end{picture}
1476 %\begin{picture}(0,0)(12.5,5)
1477 %\includegraphics[width=1cm]{100_arrow.eps}
1478 %\end{picture}
1479 %\begin{picture}(0,0)(90,0)
1480 %\includegraphics[height=0.9cm]{001_arrow.eps}
1481 %\end{picture}
1482 %\end{center}
1483 %\vspace{0.2cm}
1484 %\end{minipage}
1485 %}\\[0.2cm]
1486 %
1487 %\framebox{
1488 %\begin{minipage}{5.9cm}
1489 \includegraphics[width=5.9cm]{00-1_110_0-10_mig_albe.ps}
1490 \end{minipage}
1491 }\\[0.1cm]
1492
1493 \begin{minipage}{5.9cm}
1494 Transition involving \ci{} \hkl<1 1 0>
1495 \begin{itemize}
1496  \item Bond-centered configuration unstable\\
1497        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1498  \item Transition minima of path 2 \& 3\\
1499        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
1500  \item Activation energy: $\approx$ 2.2 eV \& 0.9 eV
1501  \item 2.4 - 3.4 times higher than VASP
1502  \item Rotation of dumbbell orientation
1503 \end{itemize}
1504 \vspace{0.1cm}
1505 \begin{center}
1506 {\color{blue}Overestimated diffusion barrier}
1507 \end{center}
1508 \end{minipage}
1509
1510 \end{minipage}
1511
1512 \end{slide}
1513
1514 \begin{slide}
1515
1516  {\large\bf\boldmath
1517   Combinations with a C-Si \hkl<1 0 0>-type interstitial
1518  }
1519
1520 \small
1521
1522 \vspace*{0.1cm}
1523
1524 Binding energy:
1525 $
1526 E_{\text{b}}=
1527 E_{\text{f}}^{\text{defect combination}}-
1528 E_{\text{f}}^{\text{C \hkl<0 0 -1> dumbbell}}-
1529 E_{\text{f}}^{\text{2nd defect}}
1530 $
1531
1532 \vspace*{0.1cm}
1533
1534 {\scriptsize
1535 \begin{tabular}{l c c c c c c}
1536 \hline
1537  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1538  \hline
1539  \hkl<0 0 -1> & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1540  \hkl<0 0 1> & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1541  \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}\\
1542  \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}\\
1543  \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}\\
1544  \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}\\
1545  \hline
1546  C substitutional (C$_{\text{S}}$) & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1547  Vacancy & -5.39 ($\rightarrow$ C$_{\text{S}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1548 \hline
1549 \end{tabular}
1550 }
1551
1552 \vspace*{0.3cm}
1553
1554 \footnotesize
1555
1556 \begin{minipage}[t]{3.8cm}
1557 \underline{\hkl<1 0 0> at position 1}\\[0.1cm]
1558 \includegraphics[width=3.5cm]{00-1dc/2-25.eps}
1559 \end{minipage}
1560 \begin{minipage}[t]{3.5cm}
1561 \underline{\hkl<0 -1 0> at position 1}\\[0.1cm]
1562 \includegraphics[width=3.2cm]{00-1dc/2-39.eps}
1563 \end{minipage}
1564 \begin{minipage}[t]{5.5cm}
1565 \begin{itemize}
1566  \item $E_{\text{b}}=0$ $\Leftrightarrow$ non-interacting defects\\
1567        $E_{\text{b}} \rightarrow 0$ for increasing distance (R)
1568  \item Stress compensation / increase
1569  \item Unfavored: antiparallel orientations
1570  \item Indication of energetically favored\\
1571        agglomeration
1572  \item Most favorable: C clustering
1573  \item However: High barrier ($>4\,\text{eV}$)
1574  \item $4\times{\color{cyan}-2.25}$ versus $2\times{\color{orange}-2.39}$
1575        (Entropy)
1576 \end{itemize}
1577 \end{minipage}
1578
1579 \begin{picture}(0,0)(-295,-130)
1580 \includegraphics[width=3.5cm]{comb_pos.eps}
1581 \end{picture}
1582
1583 \end{slide}
1584
1585 \begin{slide}
1586
1587  {\large\bf\boldmath
1588   Combinations of C-Si \hkl<1 0 0>-type interstitials
1589  }
1590
1591 \small
1592
1593 \vspace*{0.1cm}
1594
1595 Energetically most favorable combinations along \hkl<1 1 0>
1596
1597 \vspace*{0.1cm}
1598
1599 {\scriptsize
1600 \begin{tabular}{l c c c c c c}
1601 \hline
1602  & 1 & 2 & 3 & 4 & 5 & 6\\
1603 \hline
1604 $E_{\text{b}}$ [eV] & -2.39 & -1.88 & -0.59 & -0.31 & -0.24 & -0.21 \\
1605 C-C distance [\AA] & 1.4 & 4.6 & 6.5 & 8.6 & 10.5 & 10.8 \\
1606 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>\\
1607 \hline
1608 \end{tabular}
1609 }
1610
1611 \vspace*{0.3cm}
1612
1613 \begin{minipage}{7.0cm}
1614 \includegraphics[width=7cm]{db_along_110_cc.ps}
1615 \end{minipage}
1616 \begin{minipage}{6.0cm}
1617 \begin{itemize}
1618  \item Interaction proportional to reciprocal cube of C-C distance
1619  \item Saturation in the immediate vicinity
1620  \renewcommand\labelitemi{$\Rightarrow$}
1621  \item Agglomeration of \ci{} expected
1622  \item Absence of C clustering
1623 \end{itemize}
1624 \begin{center}
1625 {\color{blue}
1626  Consisten with initial precipitation model
1627 }
1628 \end{center}
1629 \end{minipage}
1630
1631 \vspace{0.2cm}
1632
1633 \end{slide}
1634
1635 \begin{slide}
1636
1637  {\large\bf\boldmath
1638   Combinations of substitutional C and \hkl<1 1 0> Si self-interstitials
1639  }
1640
1641  \scriptsize
1642
1643 %\begin{center}
1644 %\begin{minipage}{3.2cm}
1645 %\includegraphics[width=3cm]{sub_110_combo.eps}
1646 %\end{minipage}
1647 %\begin{minipage}{7.8cm}
1648 %\begin{tabular}{l c c c c c c}
1649 %\hline
1650 %C$_{\text{sub}}$ & \hkl<1 1 0> & \hkl<-1 1 0> & \hkl<0 1 1> & \hkl<0 -1 1> &
1651 %                   \hkl<1 0 1> & \hkl<-1 0 1> \\
1652 %\hline
1653 %1 & \RM{1} & \RM{3} & \RM{3} & \RM{1} & \RM{3} & \RM{1} \\
1654 %2 & \RM{2} & A & A & \RM{2} & C & \RM{5} \\
1655 %3 & \RM{3} & \RM{1} & \RM{3} & \RM{1} & \RM{1} & \RM{3} \\
1656 %4 & \RM{4} & B & D & E & E & D \\
1657 %5 & \RM{5} & C & A & \RM{2} & A & \RM{2} \\
1658 %\hline
1659 %\end{tabular}
1660 %\end{minipage}
1661 %\end{center}
1662
1663 %\begin{center}
1664 %\begin{tabular}{l c c c c c c c c c c}
1665 %\hline
1666 %Conf & \RM{1} & \RM{2} & \RM{3} & \RM{4} & \RM{5} & A & B & C & D & E \\
1667 %\hline
1668 %$E_{\text{f}}$ [eV]& 4.37 & 5.26 & 5.57 & 5.37 & 5.12 & 5.10 & 5.32 & 5.28 & 5.39 & 5.32 \\
1669 %$E_{\text{b}}$ [eV] & -0.97 & -0.08 & 0.22 & -0.02 & -0.23 & -0.25 & -0.02 & -0.06 & 0.05 & -0.03 \\
1670 %$r$ [nm] & 0.292 & 0.394 & 0.241 & 0.453 & 0.407 & 0.408 & 0.452 & 0.392 & 0.456 & 0.453\\
1671 %\hline
1672 %\end{tabular}
1673 %\end{center}
1674
1675 \begin{minipage}{6.0cm}
1676 \includegraphics[width=5.8cm]{c_sub_si110.ps}
1677 \end{minipage}
1678 \begin{minipage}{7cm}
1679 \scriptsize
1680 \begin{itemize}
1681  \item IBS: C may displace Si\\
1682        $\Rightarrow$ C$_{\text{sub}}$ + \hkl<1 1 0> Si self-interstitial
1683  \item Assumption:\\
1684        \hkl<1 1 0>-type $\rightarrow$ favored combination
1685  \renewcommand\labelitemi{$\Rightarrow$}
1686  \item Most favorable: \cs{} along \hkl<1 1 0> chain \si{}
1687  \item Less favorable than C-Si \hkl<1 0 0> dumbbell
1688  \item Interaction drops quickly to zero\\
1689        $\rightarrow$ low capture radius
1690 \end{itemize}
1691 \begin{center}
1692  {\color{blue}
1693  IBS process far from equilibrium\\
1694  \cs{} \& \si{} instead of thermodynamic ground state
1695  }
1696 \end{center}
1697 \end{minipage}
1698
1699 \begin{minipage}{6.5cm}
1700 \includegraphics[width=6.0cm]{162-097.ps}
1701 \begin{itemize}
1702  \item Low migration barrier
1703 \end{itemize}
1704 \end{minipage}
1705 \begin{minipage}{6.5cm}
1706 \begin{center}
1707 Ab initio MD at \degc{900}\\
1708 \includegraphics[width=3.3cm]{md_vasp_01.eps}
1709 $t=\unit[2230]{fs}$\\
1710 \includegraphics[width=3.3cm]{md_vasp_02.eps}
1711 $t=\unit[2900]{fs}$
1712 \end{center}
1713 {\color{blue}
1714 Contribution of entropy to structural formation
1715 }
1716 \end{minipage}
1717
1718 \end{slide}
1719
1720 \begin{slide}
1721
1722  {\large\bf\boldmath
1723   Migration in C-Si \hkl<1 0 0> and vacancy combinations
1724  }
1725
1726  \footnotesize
1727
1728 \vspace{0.1cm}
1729
1730 \begin{minipage}[t]{3cm}
1731 \underline{Pos 2, $E_{\text{b}}=-0.59\text{ eV}$}\\
1732 \includegraphics[width=2.8cm]{00-1dc/0-59.eps}
1733 \end{minipage}
1734 \begin{minipage}[t]{7cm}
1735 \vspace{0.2cm}
1736 \begin{center}
1737  Low activation energies\\
1738  High activation energies for reverse processes\\
1739  $\Downarrow$\\
1740  {\color{blue}C$_{\text{sub}}$ very stable}\\
1741 \vspace*{0.1cm}
1742  \hrule
1743 \vspace*{0.1cm}
1744  Without nearby \hkl<1 1 0> Si self-interstitial (IBS)\\
1745  $\Downarrow$\\
1746  {\color{blue}Formation of SiC by successive substitution by C}
1747
1748 \end{center}
1749 \end{minipage}
1750 \begin{minipage}[t]{3cm}
1751 \underline{Pos 3, $E_{\text{b}}=-3.14\text{ eV}$}\\
1752 \includegraphics[width=2.8cm]{00-1dc/3-14.eps}
1753 \end{minipage}
1754
1755
1756 \framebox{
1757 \begin{minipage}{5.9cm}
1758 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_3-2_vac_fullct.ps}\\[0.6cm]
1759 \begin{center}
1760 \begin{picture}(0,0)(70,0)
1761 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_init.eps}
1762 \end{picture}
1763 \begin{picture}(0,0)(30,0)
1764 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_03.eps}
1765 \end{picture}
1766 \begin{picture}(0,0)(-10,0)
1767 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_seq_06.eps}
1768 \end{picture}
1769 \begin{picture}(0,0)(-48,0)
1770 \includegraphics[width=1.4cm]{vasp_mig/comb_2-1_final.eps}
1771 \end{picture}
1772 \begin{picture}(0,0)(12.5,5)
1773 \includegraphics[width=1cm]{100_arrow.eps}
1774 \end{picture}
1775 \begin{picture}(0,0)(97,-10)
1776 \includegraphics[height=0.9cm]{001_arrow.eps}
1777 \end{picture}
1778 \end{center}
1779 \vspace{0.1cm}
1780 \end{minipage}
1781 }
1782 \begin{minipage}{0.3cm}
1783 \hfill
1784 \end{minipage}
1785 \framebox{
1786 \begin{minipage}{5.9cm}
1787 \includegraphics[width=5.9cm]{vasp_mig/comb_mig_4-2_vac_fullct.ps}\\[0.1cm]
1788 \begin{center}
1789 \begin{picture}(0,0)(60,0)
1790 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_init.eps}
1791 \end{picture}
1792 \begin{picture}(0,0)(25,0)
1793 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_03.eps}
1794 \end{picture}
1795 \begin{picture}(0,0)(-20,0)
1796 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_seq_07.eps}
1797 \end{picture}
1798 \begin{picture}(0,0)(-55,0)
1799 \includegraphics[width=0.9cm]{vasp_mig/comb_3-1_final.eps}
1800 \end{picture}
1801 \begin{picture}(0,0)(12.5,5)
1802 \includegraphics[width=1cm]{100_arrow.eps}
1803 \end{picture}
1804 \begin{picture}(0,0)(95,0)
1805 \includegraphics[height=0.9cm]{001_arrow.eps}
1806 \end{picture}
1807 \end{center}
1808 \vspace{0.1cm}
1809 \end{minipage}
1810 }
1811
1812 \end{slide}
1813
1814 \begin{slide}
1815
1816  {\large\bf
1817   Conclusion of defect / migration / combined defect simulations
1818  }
1819
1820  \footnotesize
1821
1822 \vspace*{0.1cm}
1823
1824 Defect structures
1825 \begin{itemize}
1826  \item Accurately described by quantum-mechanical simulations
1827  \item Less accurate description by classical potential simulations
1828  \item Underestimated formation energy of \cs{} by classical approach
1829  \item Both methods predict same ground state: \ci{} \hkl<1 0 0> dumbbell
1830 \end{itemize}
1831
1832 Migration
1833 \begin{itemize}
1834  \item C migration pathway in Si identified
1835  \item Consistent with reorientation and diffusion experiments
1836 \end{itemize}
1837 \begin{itemize}
1838  \item Different path and ...
1839  \item overestimated barrier by classical potential calculations
1840 \end{itemize}
1841
1842 Concerning the precipitation mechanism
1843 \begin{itemize}
1844  \item Agglomeration of C-Si dumbbells energetically favorable
1845        (stress compensation)
1846  \item C-Si indeed favored compared to
1847        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
1848  \item Possible low interaction capture radius of
1849        C$_{\text{sub}}$ \& \hkl<1 1 0> Si self-interstitial
1850  \item Low barrier for
1851        \ci{} \hkl<1 0 0> $\rightarrow$ \cs{} \& \si{} \hkl<1 1 0>
1852  \item In absence of nearby \hkl<1 1 0> Si self-interstitial:
1853        C-Si \hkl<1 0 0> + Vacancy $\rightarrow$ C$_{\text{sub}}$ (SiC)
1854 \end{itemize}
1855 \begin{center}
1856 {\color{blue}Results suggest increased participation of \cs}
1857 \end{center}
1858
1859 \end{slide}
1860
1861 \begin{slide}
1862
1863  {\large\bf
1864   Silicon carbide precipitation simulations
1865  }
1866
1867  \small
1868
1869 {\scriptsize
1870  \begin{pspicture}(0,0)(12,6.5)
1871   % nodes
1872   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1873    \parbox{7cm}{
1874    \begin{itemize}
1875     \item Create c-Si volume
1876     \item Periodc boundary conditions
1877     \item Set requested $T$ and $p=0\text{ bar}$
1878     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1879    \end{itemize}
1880   }}}}
1881   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1882    \parbox{7cm}{
1883    Insertion of C atoms at constant T
1884    \begin{itemize}
1885     \item total simulation volume {\pnode{in1}}
1886     \item volume of minimal SiC precipitate {\pnode{in2}}
1887     \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1888           precipitate
1889    \end{itemize}
1890   }}}}
1891   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1892    \parbox{7.0cm}{
1893    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
1894   }}}}
1895   \ncline[]{->}{init}{insert}
1896   \ncline[]{->}{insert}{cool}
1897   \psframe[fillstyle=solid,fillcolor=white](7.5,0.7)(13.5,6.3)
1898   \rput(7.8,6){\footnotesize $V_1$}
1899   \psframe[fillstyle=solid,fillcolor=lightgray](9,2)(12,5)
1900   \rput(9.2,4.85){\tiny $V_2$}
1901   \psframe[fillstyle=solid,fillcolor=gray](9.25,2.25)(11.75,4.75)
1902   \rput(9.55,4.45){\footnotesize $V_3$}
1903   \rput(7.9,3.2){\pnode{ins1}}
1904   \rput(9.22,2.8){\pnode{ins2}}
1905   \rput(11.0,2.4){\pnode{ins3}}
1906   \ncline[]{->}{in1}{ins1}
1907   \ncline[]{->}{in2}{ins2}
1908   \ncline[]{->}{in3}{ins3}
1909  \end{pspicture}
1910 }
1911
1912 \begin{itemize}
1913  \item Restricted to classical potential simulations
1914  \item $V_2$ and $V_3$ considered due to low diffusion
1915  \item Amount of C atoms: 6000
1916        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: 2 ... 4 nm)
1917  \item Simulation volume: $31\times 31\times 31$ unit cells
1918        (238328 Si atoms)
1919 \end{itemize}
1920
1921 \end{slide}
1922
1923 \begin{slide}
1924
1925  {\large\bf\boldmath
1926   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
1927  }
1928
1929  \small
1930
1931 \begin{minipage}{6.5cm}
1932 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
1933 \end{minipage}
1934 \begin{minipage}{6.5cm}
1935 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
1936 \end{minipage}
1937
1938 \begin{minipage}{6.5cm}
1939 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
1940 \end{minipage}
1941 \begin{minipage}{6.5cm}
1942 \scriptsize
1943 \underline{Low C concentration ($V_1$)}\\
1944 \hkl<1 0 0> C-Si dumbbell dominated structure
1945 \begin{itemize}
1946  \item Si-C bumbs around 0.19 nm
1947  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
1948        concatenated dumbbells of various orientation
1949  \item Si-Si NN distance stretched to 0.3 nm
1950 \end{itemize}
1951 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
1952 \underline{High C concentration ($V_2$, $V_3$)}\\
1953 High amount of strongly bound C-C bonds\\
1954 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
1955 Only short range order observable\\
1956 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
1957 \end{minipage}
1958
1959 \end{slide}
1960
1961 \begin{slide}
1962
1963  {\large\bf\boldmath
1964   Silicon carbide precipitation simulations at $450\,^{\circ}\mathrm{C}$ as in IBS
1965  }
1966
1967  \small
1968
1969 \begin{minipage}{6.5cm}
1970 \includegraphics[width=6.4cm]{sic_prec_450_si-si_c-c.ps}
1971 \end{minipage}
1972 \begin{minipage}{6.5cm}
1973 \includegraphics[width=6.4cm]{sic_prec_450_energy.ps}
1974 \end{minipage}
1975
1976 \begin{minipage}{6.5cm}
1977 \includegraphics[width=6.4cm]{sic_prec_450_si-c.ps}
1978 \end{minipage}
1979 \begin{minipage}{6.5cm}
1980 \scriptsize
1981 \underline{Low C concentration ($V_1$)}\\
1982 \hkl<1 0 0> C-Si dumbbell dominated structure
1983 \begin{itemize}
1984  \item Si-C bumbs around 0.19 nm
1985  \item C-C peak at 0.31 nm (as expected in 3C-SiC):\\
1986        concatenated dumbbells of various orientation
1987  \item Si-Si NN distance stretched to 0.3 nm
1988 \end{itemize}
1989 {\color{blue}$\Rightarrow$ C atoms in proper 3C-SiC distance first}\\
1990 \underline{High C concentration ($V_2$, $V_3$)}\\
1991 High amount of strongly bound C-C bonds\\
1992 Defect density $\uparrow$ $\Rightarrow$ considerable amount of damage\\
1993 Only short range order observable\\
1994 {\color{blue}$\Rightarrow$ amorphous SiC-like phase}
1995 \end{minipage}
1996
1997 \begin{pspicture}(0,0)(0,0)
1998 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
1999 \begin{minipage}{10cm}
2000 \small
2001 {\color{red}\bf 3C-SiC formation fails to appear}
2002 \begin{itemize}
2003 \item Low C concentration simulations
2004  \begin{itemize}
2005   \item Formation of \ci{} indeed occurs
2006   \item Agllomeration not observed
2007  \end{itemize}
2008 \item High C concentration simulations
2009  \begin{itemize}
2010   \item Amorphous SiC-like structure\\
2011         (not expected at prevailing temperatures)
2012   \item Rearrangement and transition into 3C-SiC structure missing
2013  \end{itemize}
2014 \end{itemize}
2015 \end{minipage}
2016  }}}
2017 \end{pspicture}
2018
2019 \end{slide}
2020
2021 \begin{slide}
2022
2023  {\large\bf
2024   Limitations of molecular dynamics and short range potentials
2025  }
2026
2027 \footnotesize
2028
2029 \vspace{0.2cm}
2030
2031 \underline{Time scale problem of MD}\\[0.2cm]
2032 Minimize integration error\\
2033 $\Rightarrow$ discretization considerably smaller than
2034               reciprocal of fastest vibrational mode\\[0.1cm]
2035 Order of fastest vibrational mode: $10^{13} - 10^{14}\text{ Hz}$\\
2036 $\Rightarrow$ suitable choice of time step:
2037               $\tau=1\text{ fs}=10^{-15}\text{ s}$\\
2038 $\Rightarrow$ {\color{red}\underline{slow}} phase space propagation\\[0.1cm]
2039 Several local minima in energy surface separated by large energy barriers\\
2040 $\Rightarrow$ transition event corresponds to a multiple
2041               of vibrational periods\\
2042 $\Rightarrow$ phase transition made up of {\color{red}\underline{many}}
2043               infrequent transition events\\[0.1cm]
2044 {\color{blue}Accelerated methods:}
2045 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
2046
2047 \vspace{0.3cm}
2048
2049 \underline{Limitations related to the short range potential}\\[0.2cm]
2050 Cut-off function pushing forces and energies to zero between 1$^{\text{st}}$
2051 and 2$^{\text{nd}}$ next neighbours\\
2052 $\Rightarrow$ overestimated unphysical high forces of next neighbours
2053
2054 \vspace{0.3cm}
2055
2056 \framebox{
2057 \color{red}
2058 Potential enhanced problem of slow phase space propagation
2059 }
2060
2061 \vspace{0.3cm}
2062
2063 \underline{Approach to the (twofold) problem}\\[0.2cm]
2064 Increased temperature simulations without TAD corrections\\
2065 (accelerated methods or higher time scales exclusively not sufficient)
2066
2067 \begin{picture}(0,0)(-260,-30)
2068 \framebox{
2069 \begin{minipage}{4.2cm}
2070 \tiny
2071 \begin{center}
2072 \vspace{0.03cm}
2073 \underline{IBS}
2074 \end{center}
2075 \begin{itemize}
2076 \item 3C-SiC also observed for higher T
2077 \item higher T inside sample
2078 \item structural evolution vs.\\
2079       equilibrium properties
2080 \end{itemize}
2081 \end{minipage}
2082 }
2083 \end{picture}
2084
2085 \begin{picture}(0,0)(-305,-155)
2086 \framebox{
2087 \begin{minipage}{2.5cm}
2088 \tiny
2089 \begin{center}
2090 retain proper\\
2091 thermodynmic sampling
2092 \end{center}
2093 \end{minipage}
2094 }
2095 \end{picture}
2096
2097 \end{slide}
2098
2099 \begin{slide}
2100
2101  {\large\bf
2102   Increased temperature simulations at low C concentration
2103  }
2104
2105 \small
2106
2107 \begin{minipage}{6.5cm}
2108 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2109 \end{minipage}
2110 \begin{minipage}{6.5cm}
2111 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2112 \end{minipage}
2113
2114 \begin{minipage}{6.5cm}
2115 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2116 \end{minipage}
2117 \begin{minipage}{6.5cm}
2118 \scriptsize
2119  \underline{Si-C bonds:}
2120  \begin{itemize}
2121   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2122   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2123  \end{itemize}
2124  \underline{Si-Si bonds:}
2125  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2126  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2127  \underline{C-C bonds:}
2128  \begin{itemize}
2129   \item C-C next neighbour pairs reduced (mandatory)
2130   \item Peak at 0.3 nm slightly shifted
2131         \begin{itemize}
2132          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2133                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2134                combinations (|)\\
2135                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2136                ($\downarrow$)
2137          \item Range [|-$\downarrow$]:
2138                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2139                with nearby Si$_{\text{I}}$}
2140         \end{itemize}
2141  \end{itemize}
2142 \end{minipage}
2143
2144 \begin{picture}(0,0)(-330,-74)
2145 \color{blue}
2146 \framebox{
2147 \begin{minipage}{1.6cm}
2148 \tiny
2149 \begin{center}
2150 stretched SiC\\[-0.1cm]
2151 in c-Si
2152 \end{center}
2153 \end{minipage}
2154 }
2155 \end{picture}
2156
2157 \end{slide}
2158
2159 \begin{slide}
2160
2161  {\large\bf
2162   Increased temperature simulations at low C concentration
2163  }
2164
2165 \small
2166
2167 \begin{minipage}{6.5cm}
2168 \includegraphics[width=6.4cm]{tot_pc_thesis.ps}
2169 \end{minipage}
2170 \begin{minipage}{6.5cm}
2171 \includegraphics[width=6.4cm]{tot_pc3_thesis.ps}
2172 \end{minipage}
2173
2174 \begin{minipage}{6.5cm}
2175 \includegraphics[width=6.4cm]{tot_pc2_thesis.ps}
2176 \end{minipage}
2177 \begin{minipage}{6.5cm}
2178 \scriptsize
2179  \underline{Si-C bonds:}
2180  \begin{itemize}
2181   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
2182   \item Structural change: C-Si \hkl<1 0 0> $\rightarrow$ C$_{\text{sub}}$
2183  \end{itemize}
2184  \underline{Si-Si bonds:}
2185  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
2186  ($\rightarrow$ 0.325 nm)\\[0.1cm]
2187  \underline{C-C bonds:}
2188  \begin{itemize}
2189   \item C-C next neighbour pairs reduced (mandatory)
2190   \item Peak at 0.3 nm slightly shifted
2191         \begin{itemize}
2192          \item C-Si \hkl<1 0 0> combinations (dashed arrows)\\
2193                $\rightarrow$ C-Si \hkl<1 0 0> \& C$_{\text{sub}}$
2194                combinations (|)\\
2195                $\rightarrow$ pure {\color{blue}C$_{\text{sub}}$ combinations}
2196                ($\downarrow$)
2197          \item Range [|-$\downarrow$]:
2198                {\color{blue}C$_{\text{sub}}$ \& C$_{\text{sub}}$
2199                with nearby Si$_{\text{I}}$}
2200         \end{itemize}
2201  \end{itemize}
2202 \end{minipage}
2203
2204 %\begin{picture}(0,0)(-330,-74)
2205 %\color{blue}
2206 %\framebox{
2207 %\begin{minipage}{1.6cm}
2208 %\tiny
2209 %\begin{center}
2210 %stretched SiC\\[-0.1cm]
2211 %in c-Si
2212 %\end{center}
2213 %\end{minipage}
2214 %}
2215 %\end{picture}
2216
2217 \begin{pspicture}(0,0)(0,0)
2218 \rput(6.7,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white]{
2219 \begin{minipage}{10cm}
2220 \small
2221 {\color{blue}\bf Stretched SiC in c-Si}
2222 \begin{itemize}
2223 \item Consistent to precipitation model involving \cs{}
2224 \item Explains annealing behavior of high/low T C implants
2225       \begin{itemize}
2226        \item Low T: highly mobiel \ci{}
2227        \item High T: stable configurations of \cs{}
2228       \end{itemize}
2229 \end{itemize}
2230 $\Rightarrow$ High T $\leftrightarrow$ IBS conditions far from equilibrium\\
2231 $\Rightarrow$ Precipitation mechanism involving \cs{}
2232 \end{minipage}
2233  }}}
2234 \end{pspicture}
2235
2236 \end{slide}
2237
2238 \begin{slide}
2239
2240  {\large\bf
2241   Increased temperature simulations at high C concentration
2242  }
2243
2244 \footnotesize
2245
2246 \begin{minipage}{6.5cm}
2247 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2248 \end{minipage}
2249 \begin{minipage}{6.5cm}
2250 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2251 \end{minipage}
2252
2253 \vspace{0.1cm}
2254
2255 \scriptsize
2256
2257 \framebox{
2258 \begin{minipage}[t]{6.0cm}
2259 0.186 nm: Si-C pairs $\uparrow$\\
2260 (as expected in 3C-SiC)\\[0.2cm]
2261 0.282 nm: Si-C-C\\[0.2cm]
2262 $\approx$0.35 nm: C-Si-Si
2263 \end{minipage}
2264 }
2265 \begin{minipage}{0.2cm}
2266 \hfill
2267 \end{minipage}
2268 \framebox{
2269 \begin{minipage}[t]{6.0cm}
2270 0.15 nm: C-C pairs $\uparrow$\\
2271 (as expected in graphite/diamond)\\[0.2cm]
2272 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2273 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2274 \end{minipage}
2275 }
2276
2277 \begin{itemize}
2278 \item Decreasing cut-off artifact
2279 \item {\color{red}Amorphous} SiC-like phase remains
2280 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2281 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2282 \end{itemize}
2283
2284 \vspace{-0.1cm}
2285
2286 \begin{center}
2287 {\color{blue}
2288 \framebox{
2289 {\color{black}
2290 High C \& small $V$ \& short $t$
2291 $\Rightarrow$
2292 }
2293 Slow restructuring due to strong C-C bonds
2294 {\color{black}
2295 $\Leftarrow$
2296 High C \& low T implants
2297 }
2298 }
2299 }
2300 \end{center}
2301
2302 \end{slide}
2303
2304 \begin{slide}
2305
2306  {\large\bf
2307   Summary and Conclusions
2308  }
2309
2310  \scriptsize
2311
2312 %\vspace{0.1cm}
2313
2314 \framebox{
2315 \begin{minipage}[t]{12.9cm}
2316  \underline{Pecipitation simulations}
2317  \begin{itemize}
2318   \item High C concentration $\rightarrow$ amorphous SiC like phase
2319   \item Problem of potential enhanced slow phase space propagation
2320   \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
2321   \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
2322   \item High T necessary to simulate IBS conditions (far from equilibrium)
2323   \item Precipitation by successive agglomeration of \cs (epitaxy)
2324   \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
2325         (stretched SiC, interface)
2326  \end{itemize}
2327 \end{minipage}
2328 }
2329
2330 %\vspace{0.1cm}
2331
2332 \framebox{
2333 \begin{minipage}{12.9cm}
2334  \underline{Defects}
2335  \begin{itemize}
2336    \item DFT / EA
2337         \begin{itemize}
2338          \item Point defects excellently / fairly well described
2339                by DFT / EA
2340          \item C$_{\text{sub}}$ drastically underestimated by EA
2341          \item EA predicts correct ground state:
2342                C$_{\text{sub}}$ \& \si{} $>$ \ci{}
2343          \item Identified migration path explaining
2344                diffusion and reorientation experiments by DFT
2345          \item EA fails to describe \ci{} migration:
2346                Wrong path \& overestimated barrier
2347         \end{itemize}
2348    \item Combinations of defects
2349          \begin{itemize}
2350           \item Agglomeration of point defects energetically favorable
2351                 by compensation of stress
2352           \item Formation of C-C unlikely
2353           \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
2354           \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
2355                 Low barrier (\unit[0.77]{eV}) \& low capture radius
2356         \end{itemize}
2357  \end{itemize}
2358 \end{minipage}
2359 }
2360
2361 \begin{center}
2362 {\color{blue}
2363 \framebox{Precipitation by successive agglomeration of \cs{}}
2364 }
2365 \end{center}
2366
2367 \end{slide}
2368
2369 \begin{slide}
2370
2371  {\large\bf
2372   Acknowledgements
2373  }
2374
2375  \vspace{0.1cm}
2376
2377  \small
2378
2379  Thanks to \ldots
2380
2381  \underline{Augsburg}
2382  \begin{itemize}
2383   \item Prof. B. Stritzker (accomodation at EP \RM{4})
2384   \item Ralf Utermann (EDV)
2385  \end{itemize}
2386
2387  \underline{Helsinki}
2388  \begin{itemize}
2389   \item Prof. K. Nordlund (MD)
2390  \end{itemize}
2391
2392  \underline{Munich}
2393  \begin{itemize}
2394   \item Bayerische Forschungsstiftung (financial support)
2395  \end{itemize}
2396
2397  \underline{Paderborn}
2398  \begin{itemize}
2399   \item Prof. J. Lindner (SiC)
2400   \item Prof. G. Schmidt (DFT + financial support)
2401   \item Dr. E. Rauls (DFT + SiC)
2402   \item Dr. S. Sanna (VASP)
2403  \end{itemize}
2404
2405 \vspace{0.2cm}
2406
2407 \begin{center}
2408 \framebox{
2409 \bf Thank you for your attention!
2410 }
2411 \end{center}
2412
2413 \end{slide}
2414
2415 \end{document}
2416
2417 \fi