posic/talks/defense.tex

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  26 %\usepackage{epic}
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  37
  38 % units
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  40
  41 \usepackage{semcolor}
  42 \usepackage{semlayer}           % Seminar overlays
  43 \usepackage{slidesec}           % Seminar sections and list of slides
  44
  45 \input{seminar.bug}             % Official bugs corrections
  46 \input{seminar.bg2}             % Unofficial bugs corrections
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  64 \begin{document}
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  78 \newcommand{\ham}{\mathcal{H}}
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  82
  83 % itemize level ii
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  85
  86 % nice phi
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  88
  89 % roman letters
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  98
  99 % head
 100 \newcommand{\headphd}{
 101 \begin{pspicture}(0,0)(0,0)
 102 \rput(6.0,0.2){\psframebox[fillstyle=gradient,gradbegin=hb,gradend=white,gradlines=1000,gradmidpoint=1,linestyle=none]{
 103 \begin{minipage}{14cm}
 104 \hfill
 105 \vspace{0.7cm}
 106 \end{minipage}
 107 }}
 108 \end{pspicture}
 109 }
 110
 111 % shortcuts
 112 \newcommand{\si}{Si$_{\text{i}}${}}
 113 \newcommand{\ci}{C$_{\text{i}}${}}
 114 \newcommand{\cs}{C$_{\text{sub}}${}}
 115 \newcommand{\degc}[1]{\unit[#1]{$^{\circ}$C}{}}
 116 \newcommand{\distn}[1]{\unit[#1]{nm}{}}
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 125 \ifnum1=0
 126 \begin{slide}
 127 \center
 128 {\Huge
 129 E\\
 130 F\\
 131 G\\
 132 A B C D E F G H G F E D C B A
 133 G\\
 134 F\\
 135 E\\
 136 }
 137 \end{slide}
 138 \fi
 139
 140 % topic
 141
 142 \begin{slide}
 143 \begin{center}
 144
 145  \vspace{16pt}
 146
 147  {\Large\bf
 148   \hrule
 149   \vspace{5pt}
 150   Atomistic simulation study on silicon carbide\\[0.2cm]
 151   precipitation in silicon\\
 152   \vspace{10pt}
 153   \hrule
 154  }
 155
 156  \vspace{60pt}
 157
 158  \textsc{Frank Zirkelbach}
 159
 160  \vspace{60pt}
 161
 162  Defense of doctor's thesis
 163
 164  \vspace{08pt}
 165
 166  Augsburg, 10.01.2012
 167
 168 \end{center}
 169 \end{slide}
 170
 171 % no vertical centering
 172 \centerslidesfalse
 173
 174 % skip for preparation
 175 %\ifnum1=0
 176
 177 % intro
 178
 179 % motivation / properties / applications of silicon carbide
 180
 181 \begin{slide}
 182
 183 \vspace*{1.8cm}
 184
 185 \small
 186
 187 \begin{pspicture}(0,0)(13.5,5)
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 189  \psframe*[linecolor=hb](-0.2,0)(12.9,5)
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 193
 194  \rput[lt](0,4.6){\color{gray}PROPERTIES}
 195
 196  \rput[lt](0.3,4){wide band gap}
 197  \rput[lt](0.3,3.5){high electric breakdown field}
 198  \rput[lt](0.3,3){good electron mobility}
 199  \rput[lt](0.3,2.5){high electron saturation drift velocity}
 200  \rput[lt](0.3,2){high thermal conductivity}
 201
 202  \rput[lt](0.3,1.5){hard and mechanically stable}
 203  \rput[lt](0.3,1){chemically inert}
 204
 205  \rput[lt](0.3,0.5){radiation hardness}
 206
 207  \rput[rt](12.7,4.6){\color{gray}APPLICATIONS}
 208
 209  \rput[rt](12.5,3.85){high-temperature, high power}
 210  \rput[rt](12.5,3.5){and high-frequency}
 211  \rput[rt](12.5,3.15){electronic and optoelectronic devices}
 212
 213  \rput[rt](12.5,2.35){material suitable for extreme conditions}
 214  \rput[rt](12.5,2){microelectromechanical systems}
 215  \rput[rt](12.5,1.65){abrasives, cutting tools, heating elements}
 216
 217  \rput[rt](12.5,0.85){first wall reactor material, detectors}
 218  \rput[rt](12.5,0.5){and electronic devices for space}
 219
 220 \end{pspicture}
 221
 222 \begin{picture}(0,0)(5,-162)
 223 \includegraphics[height=2.2cm]{3C_SiC_bs.eps}
 224 \end{picture}
 225 \begin{picture}(0,0)(-120,-162)
 226 \includegraphics[height=2.2cm]{nasa_600c_led.eps}
 227 \end{picture}
 228 \begin{picture}(0,0)(-270,-162)
 229 \includegraphics[height=2.2cm]{6h-sic_3c-sic.eps}
 230 \end{picture}
 231 %%%%
 232 \begin{picture}(0,0)(10,65)
 233 \includegraphics[height=2.8cm]{sic_switch.eps}
 234 \end{picture}
 235 %\begin{picture}(0,0)(-243,65)
 236 \begin{picture}(0,0)(-110,65)
 237 \includegraphics[height=2.8cm]{ise_99.eps}
 238 \end{picture}
 239 %\begin{picture}(0,0)(-135,65)
 240 \begin{picture}(0,0)(-100,65)
 241 \includegraphics[height=1.2cm]{infineon_schottky.eps}
 242 \end{picture}
 243 \begin{picture}(0,0)(-233,65)
 244 \includegraphics[height=2.8cm]{solar_car.eps}
 245 \end{picture}
 246
 247 \end{slide}
 248
 249 % fabrication
 250
 251 \begin{slide}
 252
 253 \headphd
 254 {\large\bf
 255  IBS of epitaxial single crystalline 3C-SiC
 256 }
 257
 258 \footnotesize
 259
 260 \vspace{0.2cm}
 261
 262 \begin{center}
 263 \begin{itemize}
 264  \item \underline{Implantation step 1}\\[0.1cm]
 265         Almost stoichiometric dose | \unit[180]{keV} | \degc{500}\\
 266         $\Rightarrow$ Epitaxial {\color{blue}3C-SiC} layer \&
 267         {\color{blue}precipitates}
 268  \item \underline{Implantation step 2}\\[0.1cm]
 269         Low remaining amount of dose | \unit[180]{keV} | \degc{250}\\
 270         $\Rightarrow$
 271         Destruction/Amorphization of precipitates at layer interface
 272  \item \underline{Annealing}\\[0.1cm]
 273        \unit[10]{h} at \degc{1250}\\
 274        $\Rightarrow$ Homogeneous 3C-SiC layer with sharp interfaces
 275 \end{itemize}
 276 \end{center}
 277
 278 \begin{minipage}{6.9cm}
 279 \includegraphics[width=7cm]{ibs_3c-sic.eps}\\[-0.4cm]
 280 \begin{center}
 281 {\tiny
 282  XTEM: single crystalline 3C-SiC in Si\hkl(1 0 0)
 283 }
 284 \end{center}
 285 \end{minipage}
 286 \begin{minipage}{5cm}
 287 \begin{center}
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 289 \rnode{box}{
 290 \psframebox[fillstyle=solid,fillcolor=white,linecolor=blue,linestyle=solid]{
 291 \begin{minipage}{3.3cm}
 292  \begin{center}
 293  {\color{blue}
 294   3C-SiC precipitation\\
 295   not yet fully understood
 296  }
 297  \end{center}
 298 % \vspace*{0.1cm}
 299 % \renewcommand\labelitemi{$\Rightarrow$}
 300 % Details of the SiC precipitation
 301 % \begin{itemize}
 302 %  \item significant technological progress\\
 303 %        in SiC thin film formation
 304 %  \item perspectives for processes relying\\
 305 %        upon prevention of SiC precipitation
 306 % \end{itemize}
 307 \end{minipage}
 308 }}
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 313 \end{pspicture}
 314 \end{center}
 315 \end{minipage}
 316
 317 \end{slide}
 318
 319 \begin{slide}
 320
 321 \headphd
 322 {\large\bf
 323   Supposed precipitation mechanism of SiC in Si
 324 }
 325
 326  \scriptsize
 327
 328  \vspace{0.1cm}
 329
 330  \framebox{
 331  \begin{minipage}{3.6cm}
 332  \begin{center}
 333  Si \& SiC lattice structure\\[0.1cm]
 334  \includegraphics[width=2.3cm]{sic_unit_cell.eps}
 335  \end{center}
 336 {\tiny
 337  \begin{minipage}{1.7cm}
 338 \underline{Silicon}\\
 339 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
 340 $a=\unit[5.429]{\\A}$\\
 341 $\rho^*_{\text{Si}}=\unit[100]{\%}$
 342  \end{minipage}
 343  \begin{minipage}{1.7cm}
 344 \underline{Silicon carbide}\\
 345 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
 346 $a=\unit[4.359]{\\A}$\\
 347 $\rho^*_{\text{Si}}=\unit[97]{\%}$
 348  \end{minipage}
 349 }
 350  \end{minipage}
 351  }
 352  \hspace{0.1cm}
 353  \begin{minipage}{4.1cm}
 354  \begin{center}
 355  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 356  \end{center}
 357  \end{minipage}
 358  \hspace{0.1cm}
 359  \begin{minipage}{4.0cm}
 360  \begin{center}
 361  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 362  \end{center}
 363  \end{minipage}
 364
 365  \vspace{0.1cm}
 366
 367  \begin{minipage}{4.0cm}
 368  \begin{center}
 369  C-Si dimers (dumbbells)\\[-0.1cm]
 370  on Si lattice sites
 371  \end{center}
 372  \end{minipage}
 373  \hspace{0.1cm}
 374  \begin{minipage}{4.1cm}
 375  \begin{center}
 376  Agglomeration of C-Si dumbbells\\[-0.1cm]
 377  $\Rightarrow$ dark contrasts
 378  \end{center}
 379  \end{minipage}
 380  \hspace{0.1cm}
 381  \begin{minipage}{4.0cm}
 382  \begin{center}
 383  Precipitation of 3C-SiC in Si\\[-0.1cm]
 384  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 385  \& release of Si self-interstitials
 386  \end{center}
 387  \end{minipage}
 388
 389  \vspace{0.1cm}
 390
 391  \begin{minipage}{4.0cm}
 392  \begin{center}
 393  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 394  \end{center}
 395  \end{minipage}
 396  \hspace{0.1cm}
 397  \begin{minipage}{4.1cm}
 398  \begin{center}
 399  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 400  \end{center}
 401  \end{minipage}
 402  \hspace{0.1cm}
 403  \begin{minipage}{4.0cm}
 404  \begin{center}
 405  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 406  \end{center}
 407  \end{minipage}
 408
 409 \begin{pspicture}(0,0)(0,0)
 410 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
 411 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
 412 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
 413 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
 414 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 415  $4a_{\text{Si}}=5a_{\text{SiC}}$
 416  }}}
 417 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 418 \hkl(h k l) planes match
 419  }}}
 420 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 421 r = \unit[2--4]{nm}
 422  }}}
 423 \end{pspicture}
 424
 425 \end{slide}
 426
 427 \begin{slide}
 428
 429 \headphd
 430 {\large\bf
 431  Supposed precipitation mechanism of SiC in Si
 432 }
 433
 434  \scriptsize
 435
 436  \vspace{0.1cm}
 437
 438  \framebox{
 439  \begin{minipage}{3.6cm}
 440  \begin{center}
 441  Si \& SiC lattice structure\\[0.1cm]
 442  \includegraphics[width=2.3cm]{sic_unit_cell.eps}
 443  \end{center}
 444 {\tiny
 445  \begin{minipage}{1.7cm}
 446 \underline{Silicon}\\
 447 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} Si\\
 448 $a=\unit[5.429]{\\A}$\\
 449 $\rho^*_{\text{Si}}=\unit[100]{\%}$
 450  \end{minipage}
 451  \begin{minipage}{1.7cm}
 452 \underline{Silicon carbide}\\
 453 {\color{yellow}$\bullet$} Si | {\color{gray}$\bullet$} C\\
 454 $a=\unit[4.359]{\\A}$\\
 455 $\rho^*_{\text{Si}}=\unit[97]{\%}$
 456  \end{minipage}
 457 }
 458  \end{minipage}
 459  }
 460  \hspace{0.1cm}
 461  \begin{minipage}{4.1cm}
 462  \begin{center}
 463  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 464  \end{center}
 465  \end{minipage}
 466  \hspace{0.1cm}
 467  \begin{minipage}{4.0cm}
 468  \begin{center}
 469  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 470  \end{center}
 471  \end{minipage}
 472
 473  \vspace{0.1cm}
 474
 475  \begin{minipage}{4.0cm}
 476  \begin{center}
 477  C-Si dimers (dumbbells)\\[-0.1cm]
 478  on Si interstitial sites
 479  \end{center}
 480  \end{minipage}
 481  \hspace{0.1cm}
 482  \begin{minipage}{4.1cm}
 483  \begin{center}
 484  Agglomeration of C-Si dumbbells\\[-0.1cm]
 485  $\Rightarrow$ dark contrasts
 486  \end{center}
 487  \end{minipage}
 488  \hspace{0.1cm}
 489  \begin{minipage}{4.0cm}
 490  \begin{center}
 491  Precipitation of 3C-SiC in Si\\[-0.1cm]
 492  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 493  \& release of Si self-interstitials
 494  \end{center}
 495  \end{minipage}
 496
 497  \vspace{0.1cm}
 498
 499  \begin{minipage}{4.0cm}
 500  \begin{center}
 501  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 502  \end{center}
 503  \end{minipage}
 504  \hspace{0.1cm}
 505  \begin{minipage}{4.1cm}
 506  \begin{center}
 507  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 508  \end{center}
 509  \end{minipage}
 510  \hspace{0.1cm}
 511  \begin{minipage}{4.0cm}
 512  \begin{center}
 513  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 514  \end{center}
 515  \end{minipage}
 516
 517 \begin{pspicture}(0,0)(0,0)
 518 \psline[linewidth=2pt]{->}(8.3,2)(8.8,2)
 519 \psellipse[linecolor=blue](11.1,6.0)(0.3,0.5)
 520 \rput{-20}{\psellipse[linecolor=blue](3.1,8.2)(0.3,0.5)}
 521 \psline[linewidth=2pt]{->}(3.9,2)(4.4,2)
 522 \rput(11.8,0.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 523  $4a_{\text{Si}}=5a_{\text{SiC}}$
 524  }}}
 525 \rput(11.5,8){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 526 \hkl(h k l) planes match
 527  }}}
 528 \rput(8.5,6.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 529 r = \unit[2--4]{nm}
 530  }}}
 531 % controversial view!
 532 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
 533 \begin{minipage}{14cm}
 534 \hfill
 535 \vspace{12cm}
 536 \end{minipage}
 537 }}
 538 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
 539 \begin{minipage}{10cm}
 540 \small
 541 \vspace*{0.2cm}
 542 \begin{center}
 543 {\color{gray}\bf Controversial findings}
 544 \end{center}
 545 \begin{itemize}
 546 \item High-temperature implantation {\tiny\color{gray}/Nejim~et~al./}
 547  \begin{itemize}
 548   \item {\color{blue}Substitutionally} incorporated C on regular Si lattice sites
 549   \item \si{} reacting with further C in cleared volume
 550  \end{itemize}
 551 \item Annealing behavior {\tiny\color{gray}/Serre~et~al./}
 552  \begin{itemize}
 553   \item Room temperature implantation $\rightarrow$ high C diffusion
 554   \item Elevated temperature implantation $\rightarrow$ no C redistribution
 555  \end{itemize}
 556  $\Rightarrow$ mobile {\color{red}\ci} opposed to
 557  stable {\color{blue}\cs{}} configurations
 558 \item Strained Si$_{1-y}$C$_y$/Si heterostructures
 559       {\tiny\color{gray}/Strane~et~al./Guedj~et~al./}
 560  \begin{itemize}
 561   \item Initial {\color{blue}coherent} SiC structures (tensile strain)
 562   \item Incoherent SiC nanocrystals (strain relaxation)
 563  \end{itemize}
 564 \end{itemize}
 565 \vspace{0.1cm}
 566 \begin{center}
 567 {\Huge${\lightning}$} \hspace{0.3cm}
 568 {\color{blue}\cs{}} --- vs --- {\color{red}\ci} \hspace{0.3cm}
 569 {\Huge${\lightning}$}
 570 \end{center}
 571 \vspace{0.2cm}
 572 \end{minipage}
 573  }}}
 574 \end{pspicture}
 575
 576 \end{slide}
 577
 578 \begin{slide}
 579
 580 % contents
 581
 582 \headphd
 583 {\large\bf
 584  Outline
 585 }
 586
 587  \begin{itemize}
 588   {\color{gray}
 589   \item Introduction / Motivation
 590   \item Assumed SiC precipitation mechanisms / Controversy
 591   }
 592   \item Utilized simulation techniques
 593         \begin{itemize}
 594          \item Molecular dynamics (MD) simulations
 595          \item Density functional theory (DFT) calculations
 596         \end{itemize}
 597   \item Simulation results
 598         \begin{itemize}
 599          \item C and Si self-interstitial point defects in silicon
 600          \item Silicon carbide precipitation simulations
 601         \end{itemize}
 602   \item Summary / Conclusion
 603  \end{itemize}
 604
 605 \end{slide}
 606
 607 \begin{slide}
 608
 609 \headphd
 610 {\large\bf
 611  Utilized computational methods
 612 }
 613
 614 \vspace{0.3cm}
 615
 616 \small
 617
 618 {\bf Molecular dynamics (MD)}\\[0.1cm]
 619 \scriptsize
 620 \begin{tabular}{| p{4.5cm} | p{7.5cm} |}
 621 \hline
 622 System of $N$ particles &
 623 $N=5832\pm 1$ (Defects), $N=238328+6000$ (Precipitation)\\
 624 Phase space propagation &
 625 Velocity Verlet | timestep: \unit[1]{fs} \\
 626 Analytical interaction potential &
 627 Tersoff-like {\color{red}short-range}, {\color{blue}bond order} potential
 628 (Erhart/Albe)
 629 $\displaystyle
 630 E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
 631     \pot_{ij} = {\color{red}f_C(r_{ij})}
 632     \left[ f_R(r_{ij}) + {\color{blue}b_{ij}} f_A(r_{ij}) \right]
 633 $\\
 634 Observables: time/ensemble averages &
 635 NpT (isothermal-isobaric) | Berendsen thermostat/barostat\\
 636 \hline
 637 \end{tabular}
 638
 639 \small
 640
 641 \vspace{0.3cm}
 642
 643 {\bf Density functional theory (DFT)}
 644
 645 \scriptsize
 646
 647 \begin{minipage}[t]{6cm}
 648 \begin{itemize}
 649  \item Hohenberg-Kohn theorem:\\
 650        $\Psi_0(r_1,r_2,\ldots,r_N)=\Psi[n_0(r)]$, $E_0=E[n_0]$
 651  \item Kohn-Sham approach:\\
 652        Single-particle effective theory
 653 \end{itemize}
 654 \hrule
 655 \begin{itemize}
 656 \item Code: \textsc{vasp}
 657 \item Plane wave basis set | $E_{\text{cut}}=\unit[300]{eV}$
 658 %$\displaystyle
 659 %\Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_{i,k+G} \exp{\left(i(k+G)r\right)}
 660 %$\\
 661 %$\displaystyle
 662 %E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}=\unit[300]{eV}
 663 %$
 664 \item Ultrasoft pseudopotential
 665 \item Exchange \& correlation: GGA
 666 \item Brillouin zone sampling: $\Gamma$-point
 667 \item Supercell: $N=216\pm2$
 668 \end{itemize}
 669 \end{minipage}
 670 \begin{minipage}{6cm}
 671 \begin{pspicture}(0,0)(0,0)
 672 \pscircle[fillcolor=yellow,fillstyle=solid,linestyle=none](3.5,-2.0){2.5}
 673 \rput(2.7,-0.7){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
 674 $\displaystyle
 675 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) - \epsilon_i \right] \Phi_i(r) = 0
 676 $
 677 }}
 678 \rput(5.2,-2.0){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
 679 $\displaystyle
 680 n(r)=\sum_i^N|\Phi_i(r)|^2
 681 $
 682 }}
 683 \rput(3.0,-4.5){\psframebox[fillstyle=solid,opacity=0.8,fillcolor=white]{
 684 $\displaystyle
 685 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
 686                  +V_{\text{XC}}[n(r)]
 687 $
 688 }}
 689 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{130}{15}
 690 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{230}{165}
 691 \psarcn[linewidth=0.07cm,linestyle=dashed]{->}(3.5,-2.0){2.5}{345}{310}
 692
 693 \end{pspicture}
 694 \end{minipage}
 695
 696 \end{slide}
 697
 698 \begin{slide}
 699
 700 \headphd
 701  {\large\bf
 702   Point defects \& defect migration
 703  }
 704
 705  \small
 706
 707  \vspace{0.2cm}
 708
 709 \begin{minipage}[b]{7.5cm}
 710 {\bf Defect structure}\\
 711   \begin{pspicture}(0,0)(7,4.4)
 712   \rput(3.5,3.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 713    \parbox{7cm}{
 714    \begin{itemize}
 715     \item Creation of c-Si simulation volume
 716     \item Periodic boundary conditions
 717     \item $T=0\text{ K}$, $p=0\text{ bar}$
 718    \end{itemize}
 719   }}}}
 720 \rput(3.5,1.3){\rnode{insert}{\psframebox{
 721  \parbox{7cm}{
 722   \begin{center}
 723   Insertion of interstitial C/Si atoms
 724   \end{center}
 725   }}}}
 726   \rput(3.5,0.2){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
 727    \parbox{7cm}{
 728    \begin{center}
 729    Relaxation / structural energy minimization
 730    \end{center}
 731   }}}}
 732   \ncline[]{->}{init}{insert}
 733   \ncline[]{->}{insert}{cool}
 734  \end{pspicture}
 735 \end{minipage}
 736 \begin{minipage}[b]{4.5cm}
 737 \begin{center}
 738 \includegraphics[width=3.8cm]{unit_cell_e.eps}\\
 739 \end{center}
 740 \begin{minipage}{2.21cm}
 741 {\scriptsize
 742 {\color{red}$\bullet$} Tetrahedral\\[-0.1cm]
 743 {\color{green}$\bullet$} Hexagonal\\[-0.1cm]
 744 {\color{yellow}$\bullet$} \hkl<1 0 0> DB
 745 }
 746 \end{minipage}
 747 \begin{minipage}{2.21cm}
 748 {\scriptsize
 749 {\color{magenta}$\bullet$} \hkl<1 1 0> DB\\[-0.1cm]
 750 {\color{cyan}$\bullet$} Bond-centered\\[-0.1cm]
 751 {\color{black}$\bullet$} Vac. / Sub.
 752 }
 753 \end{minipage}
 754 \end{minipage}
 755
 756 \vspace{0.3cm}
 757
 758 \begin{minipage}[t]{6cm}
 759 {\bf Defect formation energy}\\
 760 \framebox{
 761 $E_{\text{f}}=E-\sum_i N_i\mu_i$}\\[0.5cm]
 762 %Particle reservoir: Si \& SiC\\[0.2cm]
 763 {\bf Binding energy}\\
 764 \framebox{
 765 $
 766 E_{\text{b}}=
 767 E_{\text{f}}^{\text{comb}}-
 768 E_{\text{f}}^{1^{\text{st}}}-
 769 E_{\text{f}}^{2^{\text{nd}}}
 770 $
 771 }\\[0.1cm]
 772 \footnotesize
 773 $E_{\text{b}}<0$: energetically favorable configuration\\
 774 $E_{\text{b}}\rightarrow 0$: non-interacting, isolated defects\\
 775 \end{minipage}
 776 \begin{minipage}[t]{6cm}
 777 \vspace{1.4cm}
 778 {\bf Migration barrier}
 779 \footnotesize
 780 \begin{itemize}
 781  \item Displace diffusing atom
 782  \item Constrain relaxation of (diffusing) atoms
 783  \item Record configurational energy
 784 \end{itemize}
 785 \begin{picture}(0,0)(-60,-33)
 786 \includegraphics[width=4.5cm]{crt_mod.eps}
 787 \end{picture}
 788 \end{minipage}
 789
 790 \end{slide}
 791
 792 \begin{slide}
 793
 794 \footnotesize
 795
 796 \headphd
 797 {\large\bf
 798  C interstitial point defects in silicon\\
 799 }
 800
 801 \begin{tabular}{l c c c c c c r}
 802 \hline
 803  $E_{\text{f}}$ [eV] & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B &
 804  {\color{black} \cs{} \& \si}\\
 805 \hline
 806  \textsc{vasp} & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 & {\color{green}4.17}\\
 807  Erhart/Albe & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & {\color{red}0.75} & 5.59$^*$ & {\color{green}4.43} \\
 808 \hline
 809 \end{tabular}\\[0.1cm]
 810
 811 \framebox{
 812 \begin{minipage}{2.8cm}
 813 \underline{Hexagonal} \hspace{2pt}
 814 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
 815 $E_{\text{f}}^*=9.05\text{ eV}$\\
 816 \includegraphics[width=2.8cm]{c_pd_albe/hex_bonds.eps}
 817 \end{minipage}
 818 \begin{minipage}{0.4cm}
 819 \begin{center}
 820 $\Rightarrow$
 821 \end{center}
 822 \end{minipage}
 823 \begin{minipage}{2.8cm}
 824 \underline{\hkl<1 0 0>}\\
 825 $E_{\text{f}}=3.88\text{ eV}$\\
 826 \includegraphics[width=2.8cm]{c_pd_albe/100_bonds.eps}
 827 \end{minipage}
 828 }
 829 \begin{minipage}{1.4cm}
 830 \hfill
 831 \end{minipage}
 832 \begin{minipage}{3.0cm}
 833 \begin{flushright}
 834 \underline{Tetrahedral}\\
 835 \includegraphics[width=3.0cm]{c_pd_albe/tet_bonds.eps}
 836 \end{flushright}
 837 \end{minipage}
 838
 839 \framebox{
 840 \begin{minipage}{2.8cm}
 841 \underline{Bond-centered}\\
 842 $E_{\text{f}}^*=5.59\text{ eV}$\\
 843 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}
 844 \end{minipage}
 845 \begin{minipage}{0.4cm}
 846 \begin{center}
 847 $\Rightarrow$
 848 \end{center}
 849 \end{minipage}
 850 \begin{minipage}{2.8cm}
 851 \underline{\hkl<1 1 0> dumbbell}\\
 852 $E_{\text{f}}=5.18\text{ eV}$\\
 853 \includegraphics[width=2.8cm]{c_pd_albe/110_bonds.eps}
 854 \end{minipage}
 855 }
 856 \begin{minipage}{1.4cm}
 857 \hfill
 858 \end{minipage}
 859 \begin{minipage}{3.0cm}
 860 \begin{flushright}
 861 \underline{Substitutional}\\
 862 \includegraphics[width=3.0cm]{c_pd_albe/sub_bonds.eps}
 863 \end{flushright}
 864 \end{minipage}
 865
 866 \end{slide}
 867
 868 \begin{slide}
 869
 870 \headphd
 871 {\large\bf\boldmath
 872  C interstitial migration --- ab initio
 873 }
 874
 875 \scriptsize
 876
 877 \vspace{0.3cm}
 878
 879 \begin{minipage}{6.8cm}
 880 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 0 1]}\\
 881 \begin{minipage}{2.0cm}
 882 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
 883 \end{minipage}
 884 \begin{minipage}{0.2cm}
 885 $\rightarrow$
 886 \end{minipage}
 887 \begin{minipage}{2.0cm}
 888 \includegraphics[width=2.0cm]{c_pd_vasp/bc_2333.eps}
 889 \end{minipage}
 890 \begin{minipage}{0.2cm}
 891 $\rightarrow$
 892 \end{minipage}
 893 \begin{minipage}{2.0cm}
 894 \includegraphics[width=2.0cm]{c_pd_vasp/100_next_2333.eps}
 895 \end{minipage}\\[0.1cm]
 896 Symmetry:\\
 897 $\Rightarrow$ Sufficient to consider \hkl[00-1] to BC transition\\
 898 $\Rightarrow$ Migration barrier to reach BC | $\Delta E=\unit[1.2]{eV}$
 899 \end{minipage}
 900 \begin{minipage}{5.4cm}
 901 \includegraphics[width=6.0cm]{im_00-1_nosym_sp_fullct_thesis_vasp_s.ps}
 902 %\end{minipage}\\[0.2cm]
 903 \end{minipage}\\[0.4cm]
 904 %\hrule
 905 %
 906 \begin{minipage}{6.8cm}
 907 \framebox{\hkl[0 0 -1] $\rightarrow$ \hkl[0 -1 0]}\\
 908 \begin{minipage}{2.0cm}
 909 \includegraphics[width=2.0cm]{c_pd_vasp/100_2333.eps}
 910 \end{minipage}
 911 \begin{minipage}{0.2cm}
 912 $\rightarrow$
 913 \end{minipage}
 914 \begin{minipage}{2.0cm}
 915 \includegraphics[width=2.0cm]{c_pd_vasp/00-1-0-10_2333.eps}
 916 \end{minipage}
 917 \begin{minipage}{0.2cm}
 918 $\rightarrow$
 919 \end{minipage}
 920 \begin{minipage}{2.0cm}
 921 \includegraphics[width=2.0cm]{c_pd_vasp/0-10_2333.eps}
 922 \end{minipage}\\[0.1cm]
 923 $\Delta E=\unit[0.9]{eV}$ | Experimental values: \unit[0.70--0.87]{eV}\\
 924 $\Rightarrow$ {\color{red}Migration mechanism identified!}\\
 925 Note: Change in orientation
 926 \end{minipage}
 927 \begin{minipage}{5.4cm}
 928 \includegraphics[width=6.0cm]{00-1_0-10_vasp_s.ps}
 929 \end{minipage}\\[0.1cm]
 930 %
 931 %\begin{center}
 932 %Reorientation pathway composed of two consecutive processes of the above type
 933 %\end{center}
 934
 935 \end{slide}
 936
 937 \begin{slide}
 938
 939 \headphd
 940 {\large\bf\boldmath
 941  C interstitial migration --- analytical potential
 942 }
 943
 944 \scriptsize
 945
 946 \vspace{0.3cm}
 947
 948 \begin{minipage}[t]{6.0cm}
 949 {\bf\boldmath BC to \hkl[0 0 -1] transition}\\[0.2cm]
 950 \includegraphics[width=6.0cm]{bc_00-1_albe_s.ps}\\
 951 \begin{itemize}
 952  \item Lowermost migration barrier
 953  \item $\Delta E \approx \unit[2.2]{eV}$
 954  \item 2.4 times higher than ab initio result
 955  \item Different pathway
 956 \end{itemize}
 957 \end{minipage}
 958 \begin{minipage}[t]{0.2cm}
 959 \hfill
 960 \end{minipage}
 961 \begin{minipage}[t]{6.0cm}
 962 {\bf\boldmath Transition involving a \hkl<1 1 0> configuration}
 963 \vspace{0.1cm}
 964 \begin{itemize}
 965  \item Bond-centered configuration unstable\\
 966        $\rightarrow$ \ci{} \hkl<1 1 0> dumbbell
 967  \item Minimum of the \hkl[0 0 -1] to \hkl[0 -1 0] transition\\
 968        $\rightarrow$ \ci{} \hkl<1 1 0> DB
 969 \end{itemize}
 970 \vspace{0.1cm}
 971 \includegraphics[width=6.0cm]{00-1_110_0-10_mig_albe.ps}
 972 \begin{itemize}
 973  \item $\Delta E \approx \unit[2.2]{eV} \text{ \& } \unit[0.9]{eV}$
 974  \item 2.4 -- 3.4 times higher than ab initio result
 975  \item After all: Change of the DB orientation
 976 \end{itemize}
 977 \end{minipage}
 978
 979 \vspace{0.5cm}
 980 \begin{center}
 981 {\color{red}\bf Drastically overestimated diffusion barrier}
 982 \end{center}
 983
 984 \begin{pspicture}(0,0)(0,0)
 985 \psline[linewidth=0.05cm,linecolor=gray](6.1,1.0)(6.1,9.3)
 986 \end{pspicture}
 987
 988 \end{slide}
 989
 990 \begin{slide}
 991
 992 \headphd
 993 {\large\bf\boldmath
 994  Defect combinations --- ab inito
 995 }
 996
 997 \footnotesize
 998
 999 \vspace{0.3cm}
1000
1001 \begin{minipage}{9cm}
1002 {\bf
1003  Summary of combinations}\\[0.1cm]
1004 {\scriptsize
1005 \begin{tabular}{l c c c c c c}
1006 \hline
1007  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1008  \hline
1009  \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1010  \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1011  \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}\\
1012  \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}\\
1013  \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}\\
1014  \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}\\
1015  \hline
1016  C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1017  Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1018 \hline
1019 \end{tabular}
1020 }
1021 \vspace{0.2cm}
1022 \begin{center}
1023 {\color{blue}
1024  $E_{\text{b}}$ explainable by stress compensation / increase
1025 }
1026 \end{center}
1027 \end{minipage}
1028 \begin{minipage}{3cm}
1029 \includegraphics[width=3.5cm]{comb_pos.eps}
1030 \end{minipage}
1031
1032 \vspace{0.2cm}
1033
1034 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1035 \begin{minipage}[t]{3.2cm}
1036 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1037 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1038 \end{minipage}
1039 \begin{minipage}[t]{3.0cm}
1040 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1041 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1042 \end{minipage}
1043 \begin{minipage}[t]{6.1cm}
1044 \vspace{0.7cm}
1045 \begin{itemize}
1046  \item \ci{} agglomeration energetically favorable
1047  \item Most favorable: C clustering\\
1048        {\color{red}However \ldots}\\
1049         \ldots high migration barrier ($>4\,\text{eV}$)\\
1050         \ldots entropy:
1051         $4\times{\color{cyan}[-2.25]}$ versus
1052         $2\times{\color{orange}[-2.39]}$
1053 \end{itemize}
1054 \begin{center}
1055 {\color{blue}\ci{} agglomeration / no C clustering}
1056 \end{center}
1057 \end{minipage}
1058
1059 \end{slide}
1060
1061 \begin{slide}
1062
1063 \headphd
1064 {\large\bf\boldmath
1065  Defect combinations
1066 }
1067
1068 \footnotesize
1069
1070 \vspace{0.3cm}
1071
1072 \begin{minipage}{9cm}
1073 {\bf
1074  Summary of combinations}\\[0.1cm]
1075 {\scriptsize
1076 \begin{tabular}{l c c c c c c}
1077 \hline
1078  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1079  \hline
1080  \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1081  \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1082  \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}\\
1083  \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}\\
1084  \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}\\
1085  \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}\\
1086  \hline
1087  C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1088  Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1089 \hline
1090 \end{tabular}
1091 }
1092 \vspace{0.2cm}
1093 \begin{center}
1094 {\color{blue}
1095  $E_{\text{b}}$ explainable by stress compensation / increase
1096 }
1097 \end{center}
1098 \end{minipage}
1099 \begin{minipage}{3cm}
1100 \includegraphics[width=3.5cm]{comb_pos.eps}
1101 \end{minipage}
1102
1103 \vspace{0.2cm}
1104
1105 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1106 \begin{minipage}[t]{3.2cm}
1107 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1108 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1109 \end{minipage}
1110 \begin{minipage}[t]{3.0cm}
1111 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1112 \includegraphics[width=2.8cm]{00-1dc/2-39.eps}
1113 \end{minipage}
1114 \begin{minipage}[t]{6.1cm}
1115 \vspace{0.7cm}
1116 \begin{itemize}
1117  \item \ci{} agglomeration energetically favorable
1118  \item Most favorable: C clustering\\
1119        {\color{red}However \ldots}\\
1120         \ldots high migration barrier ($>4\,\text{eV}$)\\
1121         \ldots entropy:
1122         $4\times{\color{cyan}[-2.25]}$ versus
1123         $2\times{\color{orange}[-2.39]}$
1124 \end{itemize}
1125 \begin{center}
1126 {\color{blue}\ci{} agglomeration / no C clustering}
1127 \end{center}
1128 \end{minipage}
1129
1130 % insert graph ...
1131 \begin{pspicture}(0,0)(0,0)
1132 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1133 \begin{minipage}{14cm}
1134 \hfill
1135 \vspace{12cm}
1136 \end{minipage}
1137 }}
1138 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1139 \begin{minipage}{8cm}
1140 \begin{center}
1141 \vspace{0.2cm}
1142 \scriptsize
1143 Interaction along \hkl[1 1 0]
1144 \includegraphics[width=7cm]{db_along_110_cc.ps}
1145 \end{center}
1146 \end{minipage}
1147 }}}
1148 \end{pspicture}
1149
1150 \end{slide}
1151
1152 \begin{slide}
1153
1154 \headphd
1155 {\large\bf
1156  Defect combinations of C-Si dimers and vacancies
1157 }
1158 \footnotesize
1159
1160 \vspace{0.2cm}
1161
1162 \begin{minipage}[b]{2.6cm}
1163 \begin{flushleft}
1164 \underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm]
1165 \includegraphics[width=2.5cm]{00-1dc/0-59.eps}
1166 \end{flushleft}
1167 \end{minipage}
1168 \begin{minipage}[b]{7cm}
1169 \hfill
1170 \end{minipage}
1171 \begin{minipage}[b]{2.6cm}
1172 \begin{flushright}
1173 \underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm]
1174 \includegraphics[width=2.5cm]{00-1dc/3-14.eps}
1175 \end{flushright}
1176 \end{minipage}\\[0.2cm]
1177
1178 \begin{minipage}{6.5cm}
1179 \includegraphics[width=6.0cm]{059-539.ps}
1180 \end{minipage}
1181 \begin{minipage}{5.7cm}
1182 \includegraphics[width=6.0cm]{314-539.ps}
1183 \end{minipage}
1184
1185 \begin{pspicture}(0,0)(0,0)
1186 \psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0)
1187
1188 \rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{
1189 \begin{minipage}{6.5cm}
1190 \begin{center}
1191 IBS: Impinging C creates V \& far away \si\\[0.3cm]
1192 Low migration barrier towards C$_{\text{sub}}$\\
1193 \&\\
1194 High barrier for reverse process\\[0.3cm]
1195 {\color{blue}
1196 High probability of stable C$_{\text{sub}}$ configuration
1197 }
1198 \end{center}
1199 \end{minipage}
1200 }}}
1201 \end{pspicture}
1202
1203 \end{slide}
1204
1205 \begin{slide}
1206
1207 \headphd
1208 {\large\bf
1209  Combinations of substitutional C and Si self-interstitials
1210 }
1211
1212 \scriptsize
1213
1214 \vspace{0.3cm}
1215
1216 \begin{minipage}{6.2cm}
1217 \begin{center}
1218 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1219 \begin{itemize}
1220  \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1221  \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1222  \item Interaction drops quickly to zero\\
1223        $\rightarrow$ low capture radius
1224 \end{itemize}
1225 \end{center}
1226 \end{minipage}
1227 \begin{minipage}{0.2cm}
1228 \hfill
1229 \end{minipage}
1230 \begin{minipage}{6.0cm}
1231 \begin{center}
1232 {\bf Transition from the ground state}
1233 \begin{itemize}
1234  \item Low transition barrier
1235  \item Barrier smaller than \ci{} migration barrier
1236  \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1237        $\rightarrow$ Separation of \cs{} \& \si{} most probable
1238 \end{itemize}
1239 \end{center}
1240 \end{minipage}\\[0.3cm]
1241
1242 \begin{minipage}{6.0cm}
1243 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1244 \end{minipage}
1245 \begin{minipage}{0.4cm}
1246 \hfill
1247 \end{minipage}
1248 \begin{minipage}{6.0cm}
1249 \begin{flushright}
1250 \includegraphics[width=6.0cm]{162-097.ps}
1251 \end{flushright}
1252 \end{minipage}
1253
1254 \begin{pspicture}(0,0)(0,0)
1255 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1256 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1257 \begin{minipage}{8cm}
1258 \begin{center}
1259 \vspace{0.1cm}
1260 {\color{black}
1261 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1262 IBS --- process far from equilibrium\\
1263 }
1264 \end{center}
1265 \end{minipage}
1266 }}}
1267 \end{pspicture}
1268
1269 \end{slide}
1270
1271 \begin{slide}
1272
1273 \headphd
1274 {\large\bf
1275  Combinations of substitutional C and Si self-interstitials
1276 }
1277
1278 \scriptsize
1279
1280 \vspace{0.3cm}
1281
1282 \begin{minipage}{6.2cm}
1283 \begin{center}
1284 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1285 \begin{itemize}
1286  \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1287  \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1288  \item Interaction drops quickly to zero\\
1289        $\rightarrow$ low capture radius
1290 \end{itemize}
1291 \end{center}
1292 \end{minipage}
1293 \begin{minipage}{0.2cm}
1294 \hfill
1295 \end{minipage}
1296 \begin{minipage}{6.0cm}
1297 \begin{center}
1298 {\bf Transition from the ground state}
1299 \begin{itemize}
1300  \item Low transition barrier
1301  \item Barrier smaller than \ci{} migration barrier
1302  \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1303        $\rightarrow$ Separation of \cs{} \& \si{} most probable
1304 \end{itemize}
1305 \end{center}
1306 \end{minipage}\\[0.3cm]
1307
1308 \begin{minipage}{6.0cm}
1309 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1310 \end{minipage}
1311 \begin{minipage}{0.4cm}
1312 \hfill
1313 \end{minipage}
1314 \begin{minipage}{6.0cm}
1315 \begin{flushright}
1316 \includegraphics[width=6.0cm]{162-097.ps}
1317 \end{flushright}
1318 \end{minipage}
1319
1320 \begin{pspicture}(0,0)(0,0)
1321 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1322 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1323 \begin{minipage}{8cm}
1324 \begin{center}
1325 \vspace{0.1cm}
1326 {\color{black}
1327 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1328 IBS --- process far from equilibrium\\
1329 }
1330 \end{center}
1331 \end{minipage}
1332 }}}
1333 \end{pspicture}
1334
1335 % md support
1336 \begin{pspicture}(0,0)(0,0)
1337 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1338 \begin{minipage}{14cm}
1339 \hfill
1340 \vspace{14cm}
1341 \end{minipage}
1342 }}
1343 \rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1344 \begin{minipage}{11cm}
1345 \begin{center}
1346 \vspace{0.2cm}
1347 \scriptsize
1348 Ab initio MD at \degc{900}\\[0.4cm]
1349 \begin{minipage}{5.4cm}
1350 \centering
1351 \includegraphics[width=4.3cm]{md01_bonds.eps}\\
1352 $t=\unit[2230]{fs}$
1353 \end{minipage}
1354 \begin{minipage}{5.4cm}
1355 \centering
1356 \includegraphics[width=4.3cm]{md02_bonds.eps}\\
1357 $t=\unit[2900]{fs}$
1358 \end{minipage}\\[0.5cm]
1359 {\color{blue}
1360 Contribution of entropy to structural formation\\[0.1cm]
1361 }
1362 \end{center}
1363 \end{minipage}
1364 }}}
1365 \end{pspicture}
1366
1367 \end{slide}
1368
1369 \begin{slide}
1370
1371 \headphd
1372 {\large\bf
1373  Silicon carbide precipitation simulations
1374 }
1375
1376 \small
1377
1378 \vspace{0.2cm}
1379
1380 {\bf Procedure}
1381
1382 {\scriptsize
1383  \begin{pspicture}(0,0)(12,6.5)
1384   % nodes
1385   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1386    \parbox{7cm}{
1387    \begin{itemize}
1388     \item Create c-Si volume
1389     \item Periodc boundary conditions
1390     \item Set requested $T$ and $p=0\text{ bar}$
1391     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1392    \end{itemize}
1393   }}}}
1394   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1395    \parbox{7cm}{
1396    Insertion of C atoms at constant T
1397    \begin{itemize}
1398     \item total simulation volume {\pnode{in1}}
1399     \item volume of minimal SiC precipitate size {\pnode{in2}}
1400     \item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1401           precipitate
1402    \end{itemize}
1403   }}}}
1404   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1405    \parbox{7.0cm}{
1406    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
1407   }}}}
1408   \ncline[]{->}{init}{insert}
1409   \ncline[]{->}{insert}{cool}
1410   \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3)
1411   \rput(7.6,6){\footnotesize $V_1$}
1412   \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5)
1413   \rput(8.9,4.85){\tiny $V_2$}
1414   \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75)
1415   \rput(9.25,4.45){\footnotesize $V_3$}
1416   \rput(7.9,3.2){\pnode{ins1}}
1417   \rput(8.92,2.8){\pnode{ins2}}
1418   \rput(10.8,2.4){\pnode{ins3}}
1419   \ncline[]{->}{in1}{ins1}
1420   \ncline[]{->}{in2}{ins2}
1421   \ncline[]{->}{in3}{ins3}
1422  \end{pspicture}
1423 }
1424
1425 \vspace{-0.5cm}
1426
1427 {\bf Note}
1428
1429 \footnotesize
1430
1431 \begin{minipage}{5.7cm}
1432 \begin{itemize}
1433  \item Amount of C atoms: 6000\\
1434        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm})
1435  \item Simulation volume: $31^3$ Si unit cells\\
1436        (238328 Si atoms)
1437 \end{itemize}
1438 \end{minipage}
1439 \begin{minipage}{0.3cm}
1440 \hfill
1441 \end{minipage}
1442 \framebox{
1443 \begin{minipage}{6.0cm}
1444 Restricted to classical potential caclulations\\
1445 $\rightarrow$ Low C diffusion / overestimated barrier\\
1446 $\rightarrow$ Consider $V_2$ and $V_3$
1447 %\begin{itemize}
1448 % \item $V_2$ and $V_3$ considered due to expected low C diffusion
1449 %\end{itemize}
1450 \end{minipage}
1451 }
1452
1453 \end{slide}
1454
1455 \begin{slide}
1456
1457 \headphd
1458 {\large\bf\boldmath
1459  Silicon carbide precipitation simulations at \degc{450} as in IBS
1460 }
1461
1462 \small
1463
1464 \begin{minipage}{6.3cm}
1465 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1466 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1467 \hfill
1468 \end{minipage}
1469 \begin{minipage}{6.1cm}
1470 \scriptsize
1471 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1472 \ci{} \hkl<1 0 0> dumbbell dominated structure
1473 \begin{itemize}
1474  \item Si-C bumbs around \unit[0.19]{nm}
1475  \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1476        concatenated differently oriented \ci{} DBs
1477  \item Si-Si NN distance stretched to \unit[0.3]{nm}
1478 \end{itemize}
1479 \begin{pspicture}(0,0)(6.0,1.0)
1480 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1481 \begin{minipage}{6cm}
1482 \centering
1483 Formation of \ci{} dumbbells\\
1484 C atoms separated as expected in 3C-SiC
1485 \end{minipage}
1486 }}
1487 \end{pspicture}\\[0.1cm]
1488 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1489 \begin{itemize}
1490 \item High amount of strongly bound C-C bonds
1491 \item Increased defect \& damage density\\
1492       $\rightarrow$ Arrangements hard to categorize and trace
1493 \item Only short range order observable
1494 \end{itemize}
1495 \begin{pspicture}(0,0)(6.0,0.8)
1496 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1497 \begin{minipage}{6cm}
1498 \centering
1499 Amorphous SiC-like phase
1500 \end{minipage}
1501 }}
1502 \end{pspicture}\\[0.3cm]
1503 \begin{pspicture}(0,0)(6.0,2.0)
1504 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{
1505 \begin{minipage}{6cm}
1506 \hfill
1507 \vspace{2.5cm}
1508 \end{minipage}
1509 }}
1510 \end{pspicture}
1511 \end{minipage}
1512
1513 \end{slide}
1514
1515 \begin{slide}
1516
1517 \headphd
1518 {\large\bf\boldmath
1519  Silicon carbide precipitation simulations at \degc{450} as in IBS
1520 }
1521
1522 \small
1523
1524 \begin{minipage}{6.3cm}
1525 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1526 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1527 \hfill
1528 \end{minipage}
1529 \begin{minipage}{6.1cm}
1530 \scriptsize
1531 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1532 \ci{} \hkl<1 0 0> dumbbell dominated structure
1533 \begin{itemize}
1534  \item Si-C bumbs around \unit[0.19]{nm}
1535  \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1536        concatenated differently oriented \ci{} DBs
1537  \item Si-Si NN distance stretched to \unit[0.3]{nm}
1538 \end{itemize}
1539 \begin{pspicture}(0,0)(6.0,1.0)
1540 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1541 \begin{minipage}{6cm}
1542 \centering
1543 Formation of \ci{} dumbbells\\
1544 C atoms separated as expected in 3C-SiC
1545 \end{minipage}
1546 }}
1547 \end{pspicture}\\[0.1cm]
1548 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1549 \begin{itemize}
1550 \item High amount of strongly bound C-C bonds
1551 \item Increased defect \& damage density\\
1552       $\rightarrow$ Arrangements hard to categorize and trace
1553 \item Only short range order observable
1554 \end{itemize}
1555 \begin{pspicture}(0,0)(6.0,0.8)
1556 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1557 \begin{minipage}{6cm}
1558 \centering
1559 Amorphous SiC-like phase
1560 \end{minipage}
1561 }}
1562 \end{pspicture}\\[0.3cm]
1563 \begin{pspicture}(0,0)(6.0,2.0)
1564 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{
1565 \begin{minipage}{6cm}
1566 \vspace{0.1cm}
1567 \centering
1568 {\bf\color{red}3C-SiC formation fails to appear}\\[0.3cm]
1569 \begin{minipage}{0.8cm}
1570 {\bf\boldmath $V_1$:}
1571 \end{minipage}
1572 \begin{minipage}{5.1cm}
1573 Formation of \ci{} indeed occurs\\
1574 Agllomeration not observed
1575 \end{minipage}\\[0.3cm]
1576 \begin{minipage}{0.8cm}
1577 {\bf\boldmath $V_{2,3}$:}
1578 \end{minipage}
1579 \begin{minipage}{5.1cm}
1580 Amorphous SiC-like structure\\
1581 (not expected at \degc{450})\\[0.05cm]
1582 No rearrangement/transition into 3C-SiC
1583 \end{minipage}\\[0.1cm]
1584 \end{minipage}
1585 }}
1586 \end{pspicture}
1587 \end{minipage}
1588
1589 \end{slide}
1590
1591 \begin{slide}
1592
1593 \headphd
1594 {\large\bf
1595  Limitations of MD and short range potentials
1596 }
1597
1598 \small
1599
1600 \vspace{0.2cm}
1601
1602 {\bf Time scale problem of MD}\\[0.2cm]
1603 Minimize integration error \& precise thermodynamic sampling\\
1604 $\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
1605               $\omega$: vibrational mode\\
1606 $\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
1607 Several local minima separated by large energy barriers\\
1608 $\Rightarrow$ Transition event corresponds to a multiple
1609               of vibrational periods\\
1610 $\Rightarrow$ Phase transition consists of {\color{red}\underline{many}}
1611               infrequent transition events\\[0.2cm]
1612 {\color{blue}Accelerated methods:}
1613 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
1614
1615 \vspace{0.2cm}
1616
1617 {\bf Limitations related to the short range potential}\\[0.2cm]
1618 Cut-off function limits interaction to next neighbours\\
1619 $\Rightarrow$ Overestimated diffusion barrier (factor: 2.4--3.4)
1620
1621 \vspace{1.4cm}
1622
1623 {\bf Approach to the (twofold) problem}\\[0.2cm]
1624 Increased temperature simulations without TAD corrections\\
1625 Accelerated methods or higher time scales exclusively not sufficient!
1626
1627 \begin{pspicture}(0,0)(0,0)
1628 \rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{
1629 \begin{minipage}{7.5cm}
1630 \centering
1631 \vspace{0.05cm}
1632 Potential enhanced slow phase space propagation
1633 \end{minipage}
1634 }}
1635 \rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1636 \begin{minipage}{2.7cm}
1637 \tiny
1638 \centering
1639 retain proper\\
1640 thermodynamic sampling
1641 \end{minipage}
1642 }}
1643 \psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7)
1644 \rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{
1645 \begin{minipage}{3.6cm}
1646 \tiny
1647 \centering
1648 \underline{IBS}\\[0.1cm]
1649 3C-SiC also observed for higher T\\[0.1cm]
1650 Higher T inside sample\\[0.1cm]
1651 Structural evolution vs.\\
1652 equilibrium properties
1653 \end{minipage}
1654 }}
1655 \psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0)
1656 \end{pspicture}
1657
1658 \end{slide}
1659
1660 \begin{slide}
1661
1662 \headphd
1663 {\large\bf\boldmath
1664  Increased temperature simulations --- $V_1$
1665 }
1666
1667 \small
1668
1669 \begin{minipage}{6.2cm}
1670 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
1671 \hfill
1672 \end{minipage}
1673 \begin{minipage}{6.2cm}
1674 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
1675 \end{minipage}
1676
1677 \begin{minipage}{6.2cm}
1678 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
1679 \hfill
1680 \end{minipage}
1681 \begin{minipage}{6.3cm}
1682 \scriptsize
1683  \underline{Si-C bonds:}
1684  \begin{itemize}
1685   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
1686   \item Structural change: \ci{} \hkl<1 0 0> DB $\rightarrow$
1687         {\color{blue}\cs{}}
1688  \end{itemize}
1689  \underline{Si-Si bonds:}
1690  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
1691  ($\rightarrow$ 0.325 nm)\\[0.1cm]
1692  \underline{C-C bonds:}
1693  \begin{itemize}
1694   \item C-C next neighbour pairs reduced (mandatory)
1695   \item Peak at 0.3 nm slightly shifted\\[0.05cm]
1696         $\searrow$ \ci{} combinations (dashed arrows)\\
1697         $\nearrow$ \ci{} \hkl<1 0 0> \& {\color{blue}\cs{} combinations} (|)\\
1698         $\nearrow$ \ci{} pure \cs{} combinations ($\downarrow$)\\[0.05cm]
1699         Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si}
1700  \end{itemize}
1701 \end{minipage}
1702
1703 \end{slide}
1704
1705 \begin{slide}
1706
1707 \headphd
1708 {\large\bf\boldmath
1709  Increased temperature simulations --- $V_1$
1710 }
1711
1712 \small
1713
1714 \begin{minipage}{6.2cm}
1715 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
1716 \hfill
1717 \end{minipage}
1718 \begin{minipage}{6.2cm}
1719 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
1720 \end{minipage}
1721
1722 \begin{minipage}{6.2cm}
1723 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
1724 \hfill
1725 \end{minipage}
1726 \begin{minipage}{6.3cm}
1727 \scriptsize
1728  \underline{Si-C bonds:}
1729  \begin{itemize}
1730   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
1731   \item Structural change: \ci{} \hkl<1 0 0> DB $\rightarrow$
1732         {\color{blue}\cs{}}
1733  \end{itemize}
1734  \underline{Si-Si bonds:}
1735  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
1736  ($\rightarrow$ 0.325 nm)\\[0.1cm]
1737  \underline{C-C bonds:}
1738  \begin{itemize}
1739   \item C-C next neighbour pairs reduced (mandatory)
1740   \item Peak at 0.3 nm slightly shifted
1741   \item Peak at 0.3 nm slightly shifted\\[0.05cm]
1742         $\searrow$ \ci{} combinations (dashed arrows)\\
1743         $\nearrow$ \ci{} \hkl<1 0 0> \& {\color{blue}\cs{} combinations} (|)\\
1744         $\nearrow$ \ci{} pure \cs{} combinations ($\downarrow$)\\[0.05cm]
1745         Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si}
1746  \end{itemize}
1747 \end{minipage}
1748
1749 % conclusions
1750 \begin{pspicture}(0,0)(0,0)
1751 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1752 \begin{minipage}{14cm}
1753 \hfill
1754 \vspace{14cm}
1755 \end{minipage}
1756 }}
1757 \rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1758 \begin{minipage}{9cm}
1759 \vspace{0.2cm}
1760 \small
1761 \begin{center}
1762 {\color{gray}\bf Conclusions on SiC precipitation}\\[0.1cm]
1763 {\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\
1764 \end{center}
1765 \begin{itemize}
1766 \item Stretched coherent SiC structures directly observed
1767 \begin{center}
1768 \psframebox[linecolor=blue,linewidth=0.05cm]{
1769 \begin{minipage}{7cm}
1770 \centering
1771 \cs{} extensively involved in the precipitation mechanism\\
1772 \end{minipage}
1773 }
1774 \end{center}
1775 \item Emission of \si{} serves several needs:
1776       \begin{itemize}
1777        \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
1778        \item Building block for surrounding Si host \& further SiC
1779        \item Strain compensation \ldots\\
1780              \ldots Si/SiC interface\\
1781              \ldots within stretched coherent SiC structure
1782       \end{itemize}
1783 \item Explains annealing behavior of high/low T C implantations
1784       \begin{itemize}
1785        \item Low T: highly mobile {\color{red}\ci}
1786        \item High T: stable configurations of {\color{blue}\cs}
1787       \end{itemize}
1788 \end{itemize}
1789 \vspace{0.2cm}
1790 \centering
1791 \psframebox[linecolor=blue,linewidth=0.05cm]{
1792 \begin{minipage}{7cm}
1793 \centering
1794 High T $\leftrightarrow$ IBS conditions far from equilibrium\\
1795 \end{minipage}
1796 }
1797 \end{minipage}
1798 \vspace{0.2cm}
1799 }}
1800 \end{pspicture}
1801
1802 \end{slide}
1803
1804 % skip high c conc results
1805 \ifnum1=0
1806
1807 \begin{slide}
1808
1809  {\large\bf
1810   Increased temperature simulations at high C concentration
1811  }
1812
1813 \footnotesize
1814
1815 \begin{minipage}{6.0cm}
1816 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
1817 \end{minipage}
1818 \begin{minipage}{6.0cm}
1819 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
1820 \end{minipage}
1821
1822 \vspace{0.1cm}
1823
1824 \scriptsize
1825
1826 \framebox{
1827 \begin{minipage}[t]{6.0cm}
1828 0.186 nm: Si-C pairs $\uparrow$\\
1829 (as expected in 3C-SiC)\\[0.2cm]
1830 0.282 nm: Si-C-C\\[0.2cm]
1831 $\approx$0.35 nm: C-Si-Si
1832 \end{minipage}
1833 }
1834 \begin{minipage}{0.2cm}
1835 \hfill
1836 \end{minipage}
1837 \framebox{
1838 \begin{minipage}[t]{6.0cm}
1839 0.15 nm: C-C pairs $\uparrow$\\
1840 (as expected in graphite/diamond)\\[0.2cm]
1841 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
1842 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
1843 \end{minipage}
1844 }
1845
1846 \begin{itemize}
1847 \item Decreasing cut-off artifact
1848 \item {\color{red}Amorphous} SiC-like phase remains
1849 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
1850 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
1851 \end{itemize}
1852
1853 \vspace{-0.1cm}
1854
1855 \begin{center}
1856 {\color{blue}
1857 \framebox{
1858 {\color{black}
1859 High C \& small $V$ \& short $t$
1860 $\Rightarrow$
1861 }
1862 Slow restructuring due to strong C-C bonds
1863 {\color{black}
1864 $\Leftarrow$
1865 High C \& low T implants
1866 }
1867 }
1868 }
1869 \end{center}
1870
1871 \end{slide}
1872
1873 % skip high c conc
1874 \fi
1875
1876 \begin{slide}
1877
1878 \headphd
1879 {\large\bf
1880  Summary and Conclusions
1881 }
1882
1883 \footnotesize
1884
1885 \vspace{0.1cm}
1886
1887 \framebox{
1888 \begin{minipage}{12.3cm}
1889  \underline{Defects}
1890  \begin{itemize}
1891    \item DFT / EA
1892         \begin{itemize}
1893          \item Point defects excellently / fairly well described
1894                by DFT / EA
1895          \item Identified \ci{} migration path
1896          \item EA drastically overestimates the diffusion barrier
1897         \end{itemize}
1898    \item Combinations of defects (DFT)
1899          \begin{itemize}
1900           \item Agglomeration of point defects energetically favorable
1901           \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
1902           \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
1903                 Low barrier (\unit[0.77]{eV}) \& low capture radius
1904         \end{itemize}
1905  \end{itemize}
1906 \end{minipage}
1907 }
1908
1909 \framebox{
1910 \begin{minipage}[t]{12.3cm}
1911  \underline{Pecipitation simulations}
1912  \begin{itemize}
1913   \item Problem of potential enhanced slow phase space propagation
1914   \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
1915   \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
1916   \item High T necessary to simulate IBS conditions (far from equilibrium)
1917   \item \cs{} involved in the precipitation process at elevated temperatures
1918   \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
1919         (stretched SiC, interface)
1920  \end{itemize}
1921 \end{minipage}
1922 }
1923
1924 \begin{center}
1925 {\color{blue}\bf
1926 \framebox{IBS: 3C-SiC precipitation occurs by successive agglomeration of \cs{}}
1927 }
1928 \end{center}
1929
1930 \end{slide}
1931
1932 \begin{slide}
1933
1934 \headphd
1935 {\large\bf
1936  Acknowledgements
1937 }
1938
1939  \vspace{0.1cm}
1940
1941  \small
1942
1943  Thanks to \ldots
1944
1945 \begin{minipage}[t]{6cm}
1946  \underline{Augsburg}
1947  \begin{itemize}
1948   \item Prof. B. Stritzker
1949   \item Ralf Utermann
1950   \item EP \RM{4}
1951  \end{itemize}
1952
1953  \underline{Helsinki}
1954  \begin{itemize}
1955   \item Prof. K. Nordlund
1956  \end{itemize}
1957
1958  \underline{Munich}
1959  \begin{itemize}
1960   \item Bayerische Forschungsstiftung
1961  \end{itemize}
1962
1963  \underline{Paderborn}
1964  \begin{itemize}
1965   \item Prof. J. Lindner
1966   \item Prof. G. Schmidt
1967   \item Dr. E. Rauls
1968  \end{itemize}
1969 \end{minipage}
1970 \begin{minipage}[t]{6cm}
1971 \underline{Referees}
1972  \begin{itemize}
1973   \item PD V. Eyert
1974   \item Prof. F. Haider
1975  \end{itemize}
1976 \end{minipage}
1977
1978 \vspace{0.5cm}
1979 \begin{center}
1980 \framebox{
1981 \Large\bf Thank you for your attention!
1982 }
1983 \end{center}
1984
1985 \end{slide}
1986
1987
1988
1989
1990
1991
1992
1993 \begin{slide}
1994
1995 \headphd
1996  {\large\bf
1997   Polytypes of SiC\\[0.6cm]
1998  }
1999
2000 \vspace{0.6cm}
2001
2002 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
2003 \begin{minipage}{1.9cm}
2004 {\tiny cubic (twist)}
2005 \end{minipage}
2006 \begin{minipage}{2.9cm}
2007 {\tiny hexagonal (no twist)}
2008 \end{minipage}
2009
2010 \begin{picture}(0,0)(-150,0)
2011  \includegraphics[width=7cm]{polytypes.eps}
2012 \end{picture}
2013
2014 \vspace{0.6cm}
2015
2016 \footnotesize
2017
2018 \begin{tabular}{l c c c c c c}
2019 \hline
2020  & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
2021 \hline
2022 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
2023 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
2024 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
2025 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
2026 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
2027 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
2028 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
2029 \hline
2030 \end{tabular}
2031
2032 \begin{pspicture}(0,0)(0,0)
2033 \psellipse[linecolor=green](5.7,2.05)(0.4,0.50)
2034 \end{pspicture}
2035 \begin{pspicture}(0,0)(0,0)
2036 \psellipse[linecolor=green](5.6,0.89)(0.4,0.20)
2037 \end{pspicture}
2038 \begin{pspicture}(0,0)(0,0)
2039 \psellipse[linecolor=red](10.45,0.42)(0.4,0.20)
2040 \end{pspicture}
2041
2042 \end{slide}
2043
2044 \begin{slide}
2045
2046 \footnotesize
2047
2048 \headphd
2049 {\large\bf
2050  Si self-interstitial point defects in silicon\\[0.1cm]
2051 }
2052
2053 \begin{center}
2054 \begin{tabular}{l c c c c c}
2055 \hline
2056  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
2057 \hline
2058  \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
2059  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
2060 \hline
2061 \end{tabular}\\[0.4cm]
2062 \end{center}
2063
2064 \begin{minipage}{3cm}
2065 \begin{center}
2066 \underline{Vacancy}\\
2067 \includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
2068 \end{center}
2069 \end{minipage}
2070 \begin{minipage}{3cm}
2071 \begin{center}
2072 \underline{\hkl<1 1 0> DB}\\
2073 \includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
2074 \end{center}
2075 \end{minipage}
2076 \begin{minipage}{3cm}
2077 \begin{center}
2078 \underline{\hkl<1 0 0> DB}\\
2079 \includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
2080 \end{center}
2081 \end{minipage}
2082 \begin{minipage}{3cm}
2083 \begin{center}
2084 \underline{Tetrahedral}\\
2085 \includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
2086 \end{center}
2087 \end{minipage}\\
2088
2089 \underline{Hexagonal} \hspace{2pt}
2090 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
2091 \framebox{
2092 \begin{minipage}{2.7cm}
2093 $E_{\text{f}}^*=4.48\text{ eV}$\\
2094 \includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
2095 \end{minipage}
2096 \begin{minipage}{0.4cm}
2097 \begin{center}
2098 $\Rightarrow$
2099 \end{center}
2100 \end{minipage}
2101 \begin{minipage}{2.7cm}
2102 $E_{\text{f}}=3.96\text{ eV}$\\
2103 \includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps}
2104 \end{minipage}
2105 }
2106 \begin{minipage}{5.5cm}
2107 \begin{center}
2108 {\tiny nearly T $\rightarrow$ T}\\
2109 \end{center}
2110 \includegraphics[width=6.0cm]{nhex_tet.ps}
2111 \end{minipage}
2112
2113 \end{slide}
2114
2115 \begin{slide}
2116
2117 \headphd
2118 {\large\bf\boldmath
2119  C-Si dimer \& bond-centered interstitial configuration
2120 }
2121
2122 \footnotesize
2123
2124 \vspace{0.1cm}
2125
2126 \begin{minipage}[t]{4.1cm}
2127 {\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
2128 \begin{minipage}{2.0cm}
2129 \begin{center}
2130 \underline{Erhart/Albe}
2131 \includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
2132 \end{center}
2133 \end{minipage}
2134 \begin{minipage}{2.0cm}
2135 \begin{center}
2136 \underline{\textsc{vasp}}
2137 \includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
2138 \end{center}
2139 \end{minipage}\\[0.2cm]
2140 Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
2141 $\Rightarrow$ $sp$ hybridization\\[0.1cm]
2142 Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
2143 $\Rightarrow$ $sp^2$ hybridization
2144 \begin{center}
2145 \includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
2146 {\tiny Charge density isosurface}
2147 \end{center}
2148 \end{minipage}
2149 \begin{minipage}{0.2cm}
2150 \hfill
2151 \end{minipage}
2152 \begin{minipage}[t]{8.1cm}
2153 \begin{flushright}
2154 {\bf Bond-centered interstitial}\\[0.1cm]
2155 \begin{minipage}{4.4cm}
2156 %\scriptsize
2157 \begin{itemize}
2158  \item Linear Si-C-Si bond
2159  \item Si: one C \& 3 Si neighbours
2160  \item Spin polarized calculations
2161  \item No saddle point!\\
2162        Real local minimum!
2163 \end{itemize}
2164 \end{minipage}
2165 \begin{minipage}{2.7cm}
2166 %\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
2167 \vspace{0.2cm}
2168 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\
2169 \end{minipage}
2170
2171 \framebox{
2172  \tiny
2173  \begin{minipage}[t]{6.5cm}
2174   \begin{minipage}[t]{1.2cm}
2175   {\color{red}Si}\\
2176   {\tiny sp$^3$}\\[0.8cm]
2177   \underline{${\color{black}\uparrow}$}
2178   \underline{${\color{black}\uparrow}$}
2179   \underline{${\color{black}\uparrow}$}
2180   \underline{${\color{red}\uparrow}$}\\
2181   sp$^3$
2182   \end{minipage}
2183   \begin{minipage}[t]{1.4cm}
2184   \begin{center}
2185   {\color{red}M}{\color{blue}O}\\[0.8cm]
2186   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
2187   $\sigma_{\text{ab}}$\\[0.5cm]
2188   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
2189   $\sigma_{\text{b}}$
2190   \end{center}
2191   \end{minipage}
2192   \begin{minipage}[t]{1.0cm}
2193   \begin{center}
2194   {\color{blue}C}\\
2195   {\tiny sp}\\[0.2cm]
2196   \underline{${\color{white}\uparrow\uparrow}$}
2197   \underline{${\color{white}\uparrow\uparrow}$}\\
2198   2p\\[0.4cm]
2199   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
2200   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
2201   sp
2202   \end{center}
2203   \end{minipage}
2204   \begin{minipage}[t]{1.4cm}
2205   \begin{center}
2206   {\color{blue}M}{\color{green}O}\\[0.8cm]
2207   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
2208   $\sigma_{\text{ab}}$\\[0.5cm]
2209   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
2210   $\sigma_{\text{b}}$
2211   \end{center}
2212   \end{minipage}
2213   \begin{minipage}[t]{1.2cm}
2214   \begin{flushright}
2215   {\color{green}Si}\\
2216   {\tiny sp$^3$}\\[0.8cm]
2217   \underline{${\color{green}\uparrow}$}
2218   \underline{${\color{black}\uparrow}$}
2219   \underline{${\color{black}\uparrow}$}
2220   \underline{${\color{black}\uparrow}$}\\
2221   sp$^3$
2222   \end{flushright}
2223   \end{minipage}
2224  \end{minipage}
2225 }\\[0.4cm]
2226
2227 %\framebox{
2228 \begin{minipage}{3.0cm}
2229 %\scriptsize
2230 \underline{Charge density}\\
2231 {\color{gray}$\bullet$} Spin up\\
2232 {\color{green}$\bullet$} Spin down\\
2233 {\color{blue}$\bullet$} Resulting spin up\\
2234 {\color{yellow}$\bullet$} Si atoms\\
2235 {\color{red}$\bullet$} C atom
2236 \end{minipage}
2237 \begin{minipage}{3.6cm}
2238 \includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
2239 \end{minipage}
2240 %}
2241
2242 \end{flushright}
2243
2244 \end{minipage}
2245 \begin{pspicture}(0,0)(0,0)
2246 \psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0)
2247 \end{pspicture}
2248
2249 \end{slide}
2250
2251 \end{document}
2252