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 {\color{cyan}
1038 \framebox{
1039 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1040 }}
1041 \end{minipage}
1042 \begin{minipage}[t]{3.0cm}
1043 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1044 {\color{orange}
1045 \framebox{
1046 \includegraphics[width=2.5cm]{00-1dc/2-39.eps}
1047 }}
1048 \end{minipage}
1049 \begin{minipage}[t]{6.1cm}
1050 \vspace{0.7cm}
1051 \begin{itemize}
1052  \item \ci{} agglomeration energetically favorable
1053  \item Most favorable: strong C-C bond\\
1054        {\color{red}However \ldots}\\
1055         \ldots high migration barrier ($>4\,\text{eV}$)\\
1056         \ldots entropy:
1057         $4\times{\color{cyan}[-2.25]}$ versus
1058         $2\times{\color{orange}[-2.39]}$
1059 \end{itemize}
1060 \begin{center}
1061 {\color{blue}\ci{} agglomeration / no C clustering}
1062 \end{center}
1063 \end{minipage}
1064
1065 \end{slide}
1066
1067 \begin{slide}
1068
1069 \headphd
1070 {\large\bf\boldmath
1071  Defect combinations --- ab inito
1072 }
1073
1074 \footnotesize
1075
1076 \vspace{0.3cm}
1077
1078 \begin{minipage}{9cm}
1079 {\bf
1080  Summary of combinations}\\[0.1cm]
1081 {\scriptsize
1082 \begin{tabular}{l c c c c c c}
1083 \hline
1084  $E_{\text{b}}$ [eV] & 1 & 2 & 3 & 4 & 5 & R\\
1085  \hline
1086  \hkl[0 0 -1] & {\color{red}-0.08} & -1.15 & {\color{red}-0.08} & 0.04 & -1.66 & -0.19\\
1087  \hkl[0 0 1] & 0.34 & 0.004 & -2.05 & 0.26 & -1.53 & -0.19\\
1088  \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}\\
1089  \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}\\
1090  \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}\\
1091  \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}\\
1092  \hline
1093  C$_{\text{sub}}$ & 0.26 & -0.51 & -0.93 & -0.15 & 0.49 & -0.05\\
1094  Vacancy & -5.39 ($\rightarrow$ C$_{\text{sub}}$) & -0.59 & -3.14 & -0.54 & -0.50 & -0.31\\
1095 \hline
1096 \end{tabular}
1097 }
1098 \vspace{0.2cm}
1099 \begin{center}
1100 {\color{blue}
1101  $E_{\text{b}}$ explainable by stress compensation / increase
1102 }
1103 \end{center}
1104 \end{minipage}
1105 \begin{minipage}{3cm}
1106 \includegraphics[width=3.5cm]{comb_pos.eps}
1107 \end{minipage}
1108
1109 \vspace{0.2cm}
1110
1111 {\bf\boldmath Combinations of \hkl<1 0 0>-type interstitials}\\[0.2cm]
1112 \begin{minipage}[t]{3.2cm}
1113 \underline{\hkl[1 0 0] at position 1}\\[0.1cm]
1114 {\color{cyan}
1115 \framebox{
1116 \includegraphics[width=2.8cm]{00-1dc/2-25.eps}
1117 }}
1118 \end{minipage}
1119 \begin{minipage}[t]{3.0cm}
1120 \underline{\hkl[0 -1 0] at position 1}\\[0.1cm]
1121 {\color{orange}
1122 \framebox{
1123 \includegraphics[width=2.5cm]{00-1dc/2-39.eps}
1124 }}
1125 \end{minipage}
1126 \begin{minipage}[t]{6.1cm}
1127 \vspace{0.7cm}
1128 \begin{itemize}
1129  \item \ci{} agglomeration energetically favorable
1130  \item Most favorable: C clustering\\
1131        {\color{red}However \ldots}\\
1132         \ldots high migration barrier ($>4\,\text{eV}$)\\
1133         \ldots entropy:
1134         $4\times{\color{cyan}[-2.25]}$ versus
1135         $2\times{\color{orange}[-2.39]}$
1136 \end{itemize}
1137 \begin{center}
1138 {\color{blue}\ci{} agglomeration / no C clustering}
1139 \end{center}
1140 \end{minipage}
1141
1142 % insert graph ...
1143 \begin{pspicture}(0,0)(0,0)
1144 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1145 \begin{minipage}{14cm}
1146 \hfill
1147 \vspace{12cm}
1148 \end{minipage}
1149 }}
1150 \rput(6.5,5.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1151 \begin{minipage}{8cm}
1152 \begin{center}
1153 \vspace{0.2cm}
1154 \scriptsize
1155 Interaction along \hkl[1 1 0]
1156 \includegraphics[width=7cm]{db_along_110_cc.ps}
1157 \end{center}
1158 \end{minipage}
1159 }}}
1160 \end{pspicture}
1161
1162 \end{slide}
1163
1164 \begin{slide}
1165
1166 \headphd
1167 {\large\bf
1168  Defect combinations of C-Si dimers and vacancies
1169 }
1170 \footnotesize
1171
1172 \vspace{0.2cm}
1173
1174 \begin{minipage}[b]{2.6cm}
1175 \begin{flushleft}
1176 \underline{V at 2: $E_{\text{b}}=-0.59\text{ eV}$}\\[0.1cm]
1177 \includegraphics[width=2.5cm]{00-1dc/0-59.eps}
1178 \end{flushleft}
1179 \end{minipage}
1180 \begin{minipage}[b]{7cm}
1181 \hfill
1182 \end{minipage}
1183 \begin{minipage}[b]{2.6cm}
1184 \begin{flushright}
1185 \underline{V at 3, $E_{\text{b}}=-3.14\text{ eV}$}\\[0.1cm]
1186 \includegraphics[width=2.5cm]{00-1dc/3-14.eps}
1187 \end{flushright}
1188 \end{minipage}\\[0.2cm]
1189
1190 \begin{minipage}{6.5cm}
1191 \includegraphics[width=6.0cm]{059-539.ps}
1192 \end{minipage}
1193 \begin{minipage}{5.7cm}
1194 \includegraphics[width=6.0cm]{314-539.ps}
1195 \end{minipage}
1196
1197 \begin{pspicture}(0,0)(0,0)
1198 \psline[linewidth=0.05cm,linecolor=gray](6.3,9.0)(6.3,0)
1199
1200 \rput(6.3,7.0){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=gray]{
1201 \begin{minipage}{6.5cm}
1202 \begin{center}
1203 IBS: Impinging C creates V \& far away \si\\[0.3cm]
1204 Low migration barrier towards C$_{\text{sub}}$\\
1205 \&\\
1206 High barrier for reverse process\\[0.3cm]
1207 {\color{blue}
1208 High probability of stable C$_{\text{sub}}$ configuration
1209 }
1210 \end{center}
1211 \end{minipage}
1212 }}}
1213 \end{pspicture}
1214
1215 \end{slide}
1216
1217 \begin{slide}
1218
1219 \headphd
1220 {\large\bf
1221  Combinations of substitutional C and Si self-interstitials
1222 }
1223
1224 \scriptsize
1225
1226 \vspace{0.3cm}
1227
1228 \begin{minipage}{6.2cm}
1229 \begin{center}
1230 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1231 \begin{itemize}
1232  \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1233  \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1234  \item Interaction drops quickly to zero\\
1235        $\rightarrow$ low capture radius
1236 \end{itemize}
1237 \end{center}
1238 \end{minipage}
1239 \begin{minipage}{0.2cm}
1240 \hfill
1241 \end{minipage}
1242 \begin{minipage}{6.0cm}
1243 \begin{center}
1244 {\bf Transition from the ground state}
1245 \begin{itemize}
1246  \item Low transition barrier
1247  \item Barrier smaller than \ci{} migration barrier
1248  \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1249        $\rightarrow$ Separation of \cs{} \& \si{} most probable
1250 \end{itemize}
1251 \end{center}
1252 \end{minipage}\\[0.3cm]
1253
1254 \begin{minipage}{6.0cm}
1255 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1256 \end{minipage}
1257 \begin{minipage}{0.4cm}
1258 \hfill
1259 \end{minipage}
1260 \begin{minipage}{6.0cm}
1261 \begin{flushright}
1262 \includegraphics[width=6.0cm]{162-097.ps}
1263 \end{flushright}
1264 \end{minipage}
1265
1266 \begin{pspicture}(0,0)(0,0)
1267 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1268 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1269 \begin{minipage}{8cm}
1270 \begin{center}
1271 \vspace{0.1cm}
1272 {\color{black}
1273 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1274 IBS --- process far from equilibrium\\
1275 }
1276 \end{center}
1277 \end{minipage}
1278 }}}
1279 \end{pspicture}
1280
1281 \end{slide}
1282
1283 \begin{slide}
1284
1285 \headphd
1286 {\large\bf
1287  Combinations of substitutional C and Si self-interstitials
1288 }
1289
1290 \scriptsize
1291
1292 \vspace{0.3cm}
1293
1294 \begin{minipage}{6.2cm}
1295 \begin{center}
1296 {\bf\boldmath C$_{\text{sub}}$ - \si{} \hkl<1 1 0> interaction}
1297 \begin{itemize}
1298  \item Most favorable: \cs{} along \hkl<1 1 0> chain of \si{}
1299  \item Less favorable than ground-state \ci{} \hkl<1 0 0> DB
1300  \item Interaction drops quickly to zero\\
1301        $\rightarrow$ low capture radius
1302 \end{itemize}
1303 \end{center}
1304 \end{minipage}
1305 \begin{minipage}{0.2cm}
1306 \hfill
1307 \end{minipage}
1308 \begin{minipage}{6.0cm}
1309 \begin{center}
1310 {\bf Transition from the ground state}
1311 \begin{itemize}
1312  \item Low transition barrier
1313  \item Barrier smaller than \ci{} migration barrier
1314  \item Low \si{} migration barrier (\unit[0.67]{eV})\\
1315        $\rightarrow$ Separation of \cs{} \& \si{} most probable
1316 \end{itemize}
1317 \end{center}
1318 \end{minipage}\\[0.3cm]
1319
1320 \begin{minipage}{6.0cm}
1321 \includegraphics[width=6.0cm]{c_sub_si110.ps}
1322 \end{minipage}
1323 \begin{minipage}{0.4cm}
1324 \hfill
1325 \end{minipage}
1326 \begin{minipage}{6.0cm}
1327 \begin{flushright}
1328 \includegraphics[width=6.0cm]{162-097.ps}
1329 \end{flushright}
1330 \end{minipage}
1331
1332 \begin{pspicture}(0,0)(0,0)
1333 \psline[linewidth=0.05cm,linecolor=gray](6.5,0)(6.5,7.5)
1334 \rput(6.5,-0.7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.05cm,linecolor=blue]{
1335 \begin{minipage}{8cm}
1336 \begin{center}
1337 \vspace{0.1cm}
1338 {\color{black}
1339 \cs{} \& \si{} instead of thermodynamic ground state\\[0.1cm]
1340 IBS --- process far from equilibrium\\
1341 }
1342 \end{center}
1343 \end{minipage}
1344 }}}
1345 \end{pspicture}
1346
1347 % md support
1348 \begin{pspicture}(0,0)(0,0)
1349 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1350 \begin{minipage}{14cm}
1351 \hfill
1352 \vspace{14cm}
1353 \end{minipage}
1354 }}
1355 \rput(6.5,4.3){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1356 \begin{minipage}{11cm}
1357 \begin{center}
1358 \vspace{0.2cm}
1359 \scriptsize
1360 Ab initio MD at \degc{900}\\[0.4cm]
1361 \begin{minipage}{5.4cm}
1362 \centering
1363 \includegraphics[width=4.3cm]{md01_bonds.eps}\\
1364 $t=\unit[2230]{fs}$
1365 \end{minipage}
1366 \begin{minipage}{5.4cm}
1367 \centering
1368 \includegraphics[width=4.3cm]{md02_bonds.eps}\\
1369 $t=\unit[2900]{fs}$
1370 \end{minipage}\\[0.5cm]
1371 {\color{blue}
1372 Contribution of entropy to structural formation\\[0.1cm]
1373 }
1374 \end{center}
1375 \end{minipage}
1376 }}}
1377 \end{pspicture}
1378
1379 \end{slide}
1380
1381 \begin{slide}
1382
1383 \headphd
1384 {\large\bf
1385  Silicon carbide precipitation simulations
1386 }
1387
1388 \small
1389
1390 \vspace{0.2cm}
1391
1392 {\bf Procedure}
1393
1394 {\scriptsize
1395  \begin{pspicture}(0,0)(12,6.5)
1396   % nodes
1397   \rput(3.5,5.2){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
1398    \parbox{7cm}{
1399    \begin{itemize}
1400     \item Create c-Si volume
1401     \item Periodc boundary conditions
1402     \item Set requested $T$ and $p=0\text{ bar}$
1403     \item Equilibration of $E_{\text{kin}}$ and $E_{\text{pot}}$
1404    \end{itemize}
1405   }}}}
1406   \rput(3.5,2.7){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
1407    \parbox{7cm}{
1408    Insertion of C atoms at constant T
1409    \begin{itemize}
1410     \item total simulation volume {\pnode{in1}}
1411     \item volume of minimal SiC precipitate size {\pnode{in2}}
1412     %\item volume consisting of Si atoms to form a minimal {\pnode{in3}}\\
1413     \item volume containing Si atoms to form a minimal {\pnode{in3}}\\
1414           precipitate
1415    \end{itemize}
1416   }}}}
1417   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
1418    \parbox{7.0cm}{
1419    Run for 100 ps followed by cooling down to $20\, ^{\circ}\textrm{C}$
1420   }}}}
1421   \ncline[]{->}{init}{insert}
1422   \ncline[]{->}{insert}{cool}
1423   \psframe[fillstyle=solid,fillcolor=white](7.3,0.7)(12.8,6.3)
1424   \rput(7.6,6){\footnotesize $V_1$}
1425   \psframe[fillstyle=solid,fillcolor=lightgray](8.7,2)(11.6,5)
1426   \rput(8.9,4.85){\tiny $V_2$}
1427   \psframe[fillstyle=solid,fillcolor=gray](8.95,2.25)(11.35,4.75)
1428   \rput(9.25,4.45){\footnotesize $V_3$}
1429   \rput(7.9,3.2){\pnode{ins1}}
1430   \rput(8.92,2.8){\pnode{ins2}}
1431   \rput(10.8,2.4){\pnode{ins3}}
1432   \ncline[]{->}{in1}{ins1}
1433   \ncline[]{->}{in2}{ins2}
1434   \ncline[]{->}{in3}{ins3}
1435  \end{pspicture}
1436 }
1437
1438 \vspace{-0.5cm}
1439
1440 {\bf Note}
1441
1442 \footnotesize
1443
1444 \begin{minipage}{5.7cm}
1445 \begin{itemize}
1446  \item Amount of C atoms: 6000\\
1447        ($r_{\text{prec}}\approx 3.1\text{ nm}$, IBS: \unit[2--4]{nm})
1448  \item Simulation volume: $31^3$ Si unit cells\\
1449        (238328 Si atoms)
1450 \end{itemize}
1451 \end{minipage}
1452 \begin{minipage}{0.3cm}
1453 \hfill
1454 \end{minipage}
1455 \framebox{
1456 \begin{minipage}{6.0cm}
1457 Restricted to classical potential caclulations\\
1458 $\rightarrow$ Low C diffusion / overestimated barrier\\
1459 $\rightarrow$ Consider $V_2$ and $V_3$
1460 %\begin{itemize}
1461 % \item $V_2$ and $V_3$ considered due to expected low C diffusion
1462 %\end{itemize}
1463 \end{minipage}
1464 }
1465
1466 \end{slide}
1467
1468 \begin{slide}
1469
1470 \headphd
1471 {\large\bf\boldmath
1472  Silicon carbide precipitation simulations at \degc{450} as in IBS
1473 }
1474
1475 \small
1476
1477 \begin{minipage}{6.3cm}
1478 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1479 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1480 \hfill
1481 \end{minipage}
1482 \begin{minipage}{6.1cm}
1483 \scriptsize
1484 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1485 \ci{} \hkl<1 0 0> dumbbell dominated structure
1486 \begin{itemize}
1487  \item Si-C bumbs around \unit[0.19]{nm}
1488  \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1489        concatenated differently oriented \ci{} DBs
1490  \item Si-Si NN distance stretched to \unit[0.3]{nm}
1491 \end{itemize}
1492 \begin{pspicture}(0,0)(6.0,1.0)
1493 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1494 \begin{minipage}{6cm}
1495 \centering
1496 Formation of \ci{} dumbbells\\
1497 C atoms separated as expected in 3C-SiC
1498 \end{minipage}
1499 }}
1500 \end{pspicture}\\[0.1cm]
1501 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1502 \begin{itemize}
1503 \item High amount of strongly bound C-C bonds
1504 \item Increased defect \& damage density\\
1505       $\rightarrow$ Arrangements hard to categorize and trace
1506 \item Only short range order observable
1507 \end{itemize}
1508 \begin{pspicture}(0,0)(6.0,0.8)
1509 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1510 \begin{minipage}{6cm}
1511 \centering
1512 Amorphous SiC-like phase
1513 \end{minipage}
1514 }}
1515 \end{pspicture}\\[0.3cm]
1516 \begin{pspicture}(0,0)(6.0,2.0)
1517 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=white]{
1518 \begin{minipage}{6cm}
1519 \hfill
1520 \vspace{2.5cm}
1521 \end{minipage}
1522 }}
1523 \end{pspicture}
1524 \end{minipage}
1525
1526 \end{slide}
1527
1528 \begin{slide}
1529
1530 \headphd
1531 {\large\bf\boldmath
1532  Silicon carbide precipitation simulations at \degc{450} as in IBS
1533 }
1534
1535 \small
1536
1537 \begin{minipage}{6.3cm}
1538 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-c.ps}\\
1539 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{sic_prec_450_si-si_c-c.ps}
1540 \hfill
1541 \end{minipage}
1542 \begin{minipage}{6.1cm}
1543 \scriptsize
1544 \underline{Low C concentration --- {\color{red}$V_1$}}\\[0.1cm]
1545 \ci{} \hkl<1 0 0> dumbbell dominated structure
1546 \begin{itemize}
1547  \item Si-C bumbs around \unit[0.19]{nm}
1548  \item C-C peak at \unit[0.31]{nm} (expected in 3C-SiC):\\
1549        concatenated differently oriented \ci{} DBs
1550  \item Si-Si NN distance stretched to \unit[0.3]{nm}
1551 \end{itemize}
1552 \begin{pspicture}(0,0)(6.0,1.0)
1553 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1554 \begin{minipage}{6cm}
1555 \centering
1556 Formation of \ci{} dumbbells\\
1557 C atoms separated as expected in 3C-SiC
1558 \end{minipage}
1559 }}
1560 \end{pspicture}\\[0.1cm]
1561 \underline{High C concentration --- {\color{green}$V_2$}/{\color{blue}$V_3$}}
1562 \begin{itemize}
1563 \item High amount of strongly bound C-C bonds
1564 \item Increased defect \& damage density\\
1565       $\rightarrow$ Arrangements hard to categorize and trace
1566 \item Only short range order observable
1567 \end{itemize}
1568 \begin{pspicture}(0,0)(6.0,0.8)
1569 \rput(3.2,0.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1570 \begin{minipage}{6cm}
1571 \centering
1572 Amorphous SiC-like phase
1573 \end{minipage}
1574 }}
1575 \end{pspicture}\\[0.3cm]
1576 \begin{pspicture}(0,0)(6.0,2.0)
1577 \rput(3.2,1.0){\psframebox[linewidth=0.05cm,linecolor=black]{
1578 \begin{minipage}{6cm}
1579 \vspace{0.1cm}
1580 \centering
1581 {\bf\color{red}Formation of 3C-SiC fails to appear}\\[0.3cm]
1582 \begin{minipage}{0.8cm}
1583 {\bf\boldmath $V_1$:}
1584 \end{minipage}
1585 \begin{minipage}{5.1cm}
1586 Formation of \ci{} indeed occurs\\
1587 Agllomeration not observed
1588 \end{minipage}\\[0.3cm]
1589 \begin{minipage}{0.8cm}
1590 {\bf\boldmath $V_{2,3}$:}
1591 \end{minipage}
1592 \begin{minipage}{5.1cm}
1593 Amorphous SiC-like structure\\
1594 (not expected at \degc{450})\\[0.05cm]
1595 No rearrangement/transition into 3C-SiC
1596 \end{minipage}\\[0.1cm]
1597 \end{minipage}
1598 }}
1599 \end{pspicture}
1600 \end{minipage}
1601
1602 \end{slide}
1603
1604 \begin{slide}
1605
1606 \headphd
1607 {\large\bf
1608  Limitations of MD and short range potentials
1609 }
1610
1611 \small
1612
1613 \vspace{0.2cm}
1614
1615 {\bf Time scale problem of MD}\\[0.2cm]
1616 Minimize integration error \& precise thermodynamic sampling\\
1617 $\Rightarrow$ $\Delta t \ll \left( \max{\omega} \right)^{-1}$,
1618               $\omega$: vibrational mode\\
1619 $\Rightarrow$ {\color{red}\underline{Slow}} phase space propagation\\[0.2cm]
1620 Several local minima separated by large energy barriers\\
1621 $\Rightarrow$ Transition event corresponds to a multiple
1622               of vibrational periods\\
1623 $\Rightarrow$ Phase transition consists of {\color{red}\underline{many}}
1624               infrequent transition events\\[0.2cm]
1625 {\color{blue}Accelerated methods:}
1626 \underline{Temperature accelerated} MD (TAD), self-guided MD \ldots
1627
1628 \vspace{0.2cm}
1629
1630 {\bf Limitations related to the short range potential}\\[0.2cm]
1631 Cut-off function limits interaction to next neighbours\\
1632 $\Rightarrow$ Overestimated diffusion barrier (factor: 2.4--3.4)
1633
1634 \vspace{1.4cm}
1635
1636 {\bf Approach to the (twofold) problem}\\[0.2cm]
1637 Increased temperature simulations without TAD corrections\\
1638 Accelerated methods or higher time scales exclusively not sufficient!
1639
1640 \begin{pspicture}(0,0)(0,0)
1641 \rput(4.0,2.8){\psframebox[linewidth=0.07cm,linecolor=red]{
1642 \begin{minipage}{7.5cm}
1643 \centering
1644 \vspace{0.05cm}
1645 Potential enhanced slow phase space propagation
1646 \end{minipage}
1647 }}
1648 \rput(11.3,7.5){\psframebox[linewidth=0.03cm,linecolor=blue]{
1649 \begin{minipage}{2.7cm}
1650 \tiny
1651 \centering
1652 retain proper\\
1653 thermodynamic sampling
1654 \end{minipage}
1655 }}
1656 \psline[linewidth=0.03cm,linecolor=blue]{<-}(11.3,7.0)(11.0,5.7)
1657 \rput(10.85,2.6){\psframebox[linewidth=0.03cm,linecolor=blue]{
1658 \begin{minipage}{3.6cm}
1659 \tiny
1660 \centering
1661 \underline{IBS}\\[0.1cm]
1662 3C-SiC also observed for higher T\\[0.1cm]
1663 Higher T inside sample\\[0.1cm]
1664 Structural evolution vs.\\
1665 equilibrium properties
1666 \end{minipage}
1667 }}
1668 \psline[linewidth=0.03cm,linecolor=blue]{->}(10.85,1.75)(9.0,1.0)
1669 \end{pspicture}
1670
1671 \end{slide}
1672
1673 \begin{slide}
1674
1675 \headphd
1676 {\large\bf\boldmath
1677  Increased temperature simulations --- $V_1$
1678 }
1679
1680 \small
1681
1682 \begin{minipage}{6.2cm}
1683 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
1684 \hfill
1685 \end{minipage}
1686 \begin{minipage}{6.2cm}
1687 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
1688 \end{minipage}
1689
1690 \begin{minipage}{6.2cm}
1691 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
1692 \hfill
1693 \end{minipage}
1694 \begin{minipage}{6.3cm}
1695 \scriptsize
1696  \underline{Si-C bonds:}
1697  \begin{itemize}
1698   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
1699   \item Structural change: \ci{} \hkl<1 0 0> DB $\rightarrow$
1700         {\color{blue}\cs{}}
1701  \end{itemize}
1702  \underline{Si-Si bonds:}
1703  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
1704  ($\rightarrow$ 0.325 nm)\\[0.1cm]
1705  \underline{C-C bonds:}
1706  \begin{itemize}
1707   \item C-C next neighbour pairs reduced (mandatory)
1708   \item Peak at 0.3 nm slightly shifted\\[0.05cm]
1709         $\searrow$ \ci{} combinations (dashed arrows)\\
1710         $\nearrow$ \ci{} \hkl<1 0 0> \& {\color{blue}\cs{} combinations} (|)\\
1711         $\nearrow$ \ci{} pure \cs{} combinations ($\downarrow$)\\[0.05cm]
1712         Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si}
1713  \end{itemize}
1714 \end{minipage}
1715
1716 \end{slide}
1717
1718 \begin{slide}
1719
1720 \headphd
1721 {\large\bf\boldmath
1722  Increased temperature simulations --- $V_1$
1723 }
1724
1725 \small
1726
1727 \begin{minipage}{6.2cm}
1728 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc_thesis.ps}
1729 \hfill
1730 \end{minipage}
1731 \begin{minipage}{6.2cm}
1732 \includegraphics[width=6.5cm]{tot_pc3_thesis.ps}
1733 \end{minipage}
1734
1735 \begin{minipage}{6.2cm}
1736 \hspace*{-0.4cm}\includegraphics[width=6.5cm]{tot_pc2_thesis.ps}
1737 \hfill
1738 \end{minipage}
1739 \begin{minipage}{6.3cm}
1740 \scriptsize
1741  \underline{Si-C bonds:}
1742  \begin{itemize}
1743   \item Vanishing cut-off artifact (above $1650\,^{\circ}\mathrm{C}$)
1744   \item Structural change: \ci{} \hkl<1 0 0> DB $\rightarrow$
1745         {\color{blue}\cs{}}
1746  \end{itemize}
1747  \underline{Si-Si bonds:}
1748  {\color{blue}Si-C$_{\text{sub}}$-Si} along \hkl<1 1 0>
1749  ($\rightarrow$ 0.325 nm)\\[0.1cm]
1750  \underline{C-C bonds:}
1751  \begin{itemize}
1752   \item C-C next neighbour pairs reduced (mandatory)
1753   \item Peak at 0.3 nm slightly shifted\\[0.05cm]
1754         $\searrow$ \ci{} combinations (dashed arrows)\\
1755         $\nearrow$ \ci{} \hkl<1 0 0> \& {\color{blue}\cs{} combinations} (|)\\
1756         $\nearrow$ \ci{} pure \cs{} combinations ($\downarrow$)\\[0.05cm]
1757         Range [|-$\downarrow$]: {\color{blue}\cs{} \& \cs{} with nearby \si}
1758  \end{itemize}
1759 \end{minipage}
1760
1761 % conclusions
1762 \begin{pspicture}(0,0)(0,0)
1763 \rput(6.5,5.0){\psframebox[fillstyle=solid,opacity=0.5,fillcolor=black]{
1764 \begin{minipage}{14cm}
1765 \hfill
1766 \vspace{14cm}
1767 \end{minipage}
1768 }}
1769 \rput(6.5,5.0){\psframebox[fillstyle=solid,fillcolor=white,linewidth=0.1cm]{
1770 \begin{minipage}{9cm}
1771 \vspace{0.2cm}
1772 \small
1773 \begin{center}
1774 {\color{gray}\bf Conclusions on SiC precipitation}\\[0.1cm]
1775 {\Huge$\lightning$} {\color{red}\ci{}} --- vs --- {\color{blue}\cs{}} {\Huge$\lightning$}\\
1776 \end{center}
1777 \begin{itemize}
1778 \item Stretched coherent SiC structures directly observed\\
1779 \psframebox[linecolor=blue,linewidth=0.05cm]{
1780 \begin{minipage}{7cm}
1781 \centering
1782 \cs{} involved in the precipitation mechanism\\
1783 \end{minipage}
1784 }
1785 \item Emission of \si{} serves several needs:
1786       \begin{itemize}
1787        \item Vehicle to rearrange \cs --- [\cs{} \& \si{} $\leftrightarrow$ \ci]
1788        \item Building block for surrounding Si host \& further SiC
1789        \item Strain compensation \ldots\\
1790              \ldots Si/SiC interface\\
1791              \ldots within stretched coherent SiC structure
1792       \end{itemize}
1793 \item Explains annealing behavior of high/low T C implantations
1794       \begin{itemize}
1795        \item Low T: highly mobile {\color{red}\ci}
1796        \item High T: stable configurations of {\color{blue}\cs}
1797       \end{itemize}
1798 \psframebox[linecolor=blue,linewidth=0.05cm]{
1799 \begin{minipage}{7cm}
1800 \centering
1801 High T $\leftrightarrow$ IBS conditions far from equilibrium\\
1802 \end{minipage}
1803 }
1804 \end{itemize}
1805 \end{minipage}
1806 \vspace{0.2cm}
1807 }}
1808 \end{pspicture}
1809
1810 \end{slide}
1811
1812 \begin{slide}
1813
1814 \headphd
1815 {\large\bf
1816  Summary and Conclusions
1817 }
1818
1819 \footnotesize
1820
1821 \vspace{0.1cm}
1822
1823 \framebox{
1824 \begin{minipage}{12.3cm}
1825  \underline{Defects}
1826  \begin{itemize}
1827    \item DFT / EA
1828         \begin{itemize}
1829          \item Point defects excellently / fairly well described
1830                by DFT / EA
1831          \item Identified \ci{} migration path
1832          \item EA drastically overestimates the diffusion barrier
1833         \end{itemize}
1834    \item Combinations of defects (DFT)
1835          \begin{itemize}
1836           \item Agglomeration of point defects energetically favorable
1837           \item C$_{\text{sub}}$ favored conditions (conceivable in IBS)
1838           \item \ci{} \hkl<1 0 0> $\leftrightarrow$ \cs{} \& \si{} \hkl<1 1 0>\\
1839                 Low barrier (\unit[0.77]{eV}) \& low capture radius
1840         \end{itemize}
1841  \end{itemize}
1842 \end{minipage}
1843 }
1844
1845 \framebox{
1846 \begin{minipage}[t]{12.3cm}
1847  \underline{Pecipitation simulations}
1848  \begin{itemize}
1849   \item Problem of potential enhanced slow phase space propagation
1850   \item High T necessary to simulate IBS conditions (far from equilibrium)
1851   \item Low T $\rightarrow$ C-Si \hkl<1 0 0> dumbbell dominated structure
1852   \item High T $\rightarrow$ C$_{\text{sub}}$ dominated structure
1853         / Structures of stretched SiC\\
1854         $\Rightarrow$
1855         \cs{} involved in the precipitation process at elevated temperatures
1856   \item \si{}: vehicle to form \cs{} \& supply of Si \& stress compensation
1857         (stretched SiC, interface)
1858  \end{itemize}
1859 \end{minipage}
1860 }
1861
1862 \begin{center}
1863 {\color{blue}\bf
1864 \framebox{IBS: 3C-SiC precipitation occurs by successive agglomeration of \cs{}}
1865 }
1866 \end{center}
1867
1868 \end{slide}
1869
1870 \begin{slide}
1871
1872 \headphd
1873 {\large\bf
1874  Acknowledgements
1875 }
1876
1877  \vspace{0.1cm}
1878
1879  \small
1880
1881  Thanks to \ldots
1882
1883 \begin{minipage}[t]{6cm}
1884  \underline{Augsburg}
1885  \begin{itemize}
1886   \item Prof. B. Stritzker
1887   \item Ralf Utermann
1888   \item EP \RM{4}
1889  \end{itemize}
1890
1891  \underline{Helsinki}
1892  \begin{itemize}
1893   \item Prof. K. Nordlund
1894  \end{itemize}
1895
1896  \underline{Munich}
1897  \begin{itemize}
1898   \item Bayerische Forschungsstiftung
1899  \end{itemize}
1900
1901  \underline{Paderborn}
1902  \begin{itemize}
1903   \item Prof. J. Lindner
1904   \item Prof. G. Schmidt
1905   \item Dr. E. Rauls
1906  \end{itemize}
1907 \end{minipage}
1908 \begin{minipage}[t]{6cm}
1909 \underline{Referees}
1910  \begin{itemize}
1911   \item PD V. Eyert
1912   \item Prof. F. Haider
1913  \end{itemize}
1914 \end{minipage}
1915
1916 \vspace{0.5cm}
1917 \begin{center}
1918 \framebox{
1919 \Large\bf Thank you for your attention!
1920 }
1921 \end{center}
1922
1923 \end{slide}
1924
1925
1926
1927
1928
1929
1930
1931 \begin{slide}
1932
1933 \headphd
1934  {\large\bf
1935   Polytypes of SiC\\[0.6cm]
1936  }
1937
1938 \vspace{0.6cm}
1939
1940 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
1941 \begin{minipage}{1.9cm}
1942 {\tiny cubic (twist)}
1943 \end{minipage}
1944 \begin{minipage}{2.9cm}
1945 {\tiny hexagonal (no twist)}
1946 \end{minipage}
1947
1948 \begin{picture}(0,0)(-150,0)
1949  \includegraphics[width=7cm]{polytypes.eps}
1950 \end{picture}
1951
1952 \vspace{0.6cm}
1953
1954 \footnotesize
1955
1956 \begin{tabular}{l c c c c c c}
1957 \hline
1958  & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
1959 \hline
1960 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
1961 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
1962 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
1963 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
1964 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
1965 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
1966 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
1967 \hline
1968 \end{tabular}
1969
1970 \begin{pspicture}(0,0)(0,0)
1971 \psellipse[linecolor=green](5.7,2.05)(0.4,0.50)
1972 \end{pspicture}
1973 \begin{pspicture}(0,0)(0,0)
1974 \psellipse[linecolor=green](5.6,0.89)(0.4,0.20)
1975 \end{pspicture}
1976 \begin{pspicture}(0,0)(0,0)
1977 \psellipse[linecolor=red](10.45,0.42)(0.4,0.20)
1978 \end{pspicture}
1979
1980 \end{slide}
1981
1982 \begin{slide}
1983
1984 \footnotesize
1985
1986 \headphd
1987 {\large\bf
1988  Si self-interstitial point defects in silicon\\[0.1cm]
1989 }
1990
1991 \begin{center}
1992 \begin{tabular}{l c c c c c}
1993 \hline
1994  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
1995 \hline
1996  \textsc{vasp} & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
1997  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
1998 \hline
1999 \end{tabular}\\[0.4cm]
2000 \end{center}
2001
2002 \begin{minipage}{3cm}
2003 \begin{center}
2004 \underline{Vacancy}\\
2005 \includegraphics[width=2.8cm]{si_pd_albe/vac.eps}
2006 \end{center}
2007 \end{minipage}
2008 \begin{minipage}{3cm}
2009 \begin{center}
2010 \underline{\hkl<1 1 0> DB}\\
2011 \includegraphics[width=2.8cm]{si_pd_albe/110_bonds.eps}
2012 \end{center}
2013 \end{minipage}
2014 \begin{minipage}{3cm}
2015 \begin{center}
2016 \underline{\hkl<1 0 0> DB}\\
2017 \includegraphics[width=2.8cm]{si_pd_albe/100_bonds.eps}
2018 \end{center}
2019 \end{minipage}
2020 \begin{minipage}{3cm}
2021 \begin{center}
2022 \underline{Tetrahedral}\\
2023 \includegraphics[width=2.8cm]{si_pd_albe/tet_bonds.eps}
2024 \end{center}
2025 \end{minipage}\\
2026
2027 \underline{Hexagonal} \hspace{2pt}
2028 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
2029 \framebox{
2030 \begin{minipage}{2.7cm}
2031 $E_{\text{f}}^*=4.48\text{ eV}$\\
2032 \includegraphics[width=2.7cm]{si_pd_albe/hex_a_bonds.eps}
2033 \end{minipage}
2034 \begin{minipage}{0.4cm}
2035 \begin{center}
2036 $\Rightarrow$
2037 \end{center}
2038 \end{minipage}
2039 \begin{minipage}{2.7cm}
2040 $E_{\text{f}}=3.96\text{ eV}$\\
2041 \includegraphics[width=2.8cm]{si_pd_albe/hex_bonds.eps}
2042 \end{minipage}
2043 }
2044 \begin{minipage}{5.5cm}
2045 \begin{center}
2046 {\tiny nearly T $\rightarrow$ T}\\
2047 \end{center}
2048 \includegraphics[width=6.0cm]{nhex_tet.ps}
2049 \end{minipage}
2050
2051 \end{slide}
2052
2053 \begin{slide}
2054
2055 \headphd
2056 {\large\bf\boldmath
2057  C-Si dimer \& bond-centered interstitial configuration
2058 }
2059
2060 \footnotesize
2061
2062 \vspace{0.1cm}
2063
2064 \begin{minipage}[t]{4.1cm}
2065 {\bf\boldmath C \hkl<1 0 0> DB interstitial}\\[0.1cm]
2066 \begin{minipage}{2.0cm}
2067 \begin{center}
2068 \underline{Erhart/Albe}
2069 \includegraphics[width=2.0cm]{c_pd_albe/100_cmp.eps}
2070 \end{center}
2071 \end{minipage}
2072 \begin{minipage}{2.0cm}
2073 \begin{center}
2074 \underline{\textsc{vasp}}
2075 \includegraphics[width=2.0cm]{c_pd_vasp/100_cmp.eps}
2076 \end{center}
2077 \end{minipage}\\[0.2cm]
2078 Si-C-Si bond angle $\rightarrow$ \unit[180]{$^{\circ}$}\\
2079 $\Rightarrow$ $sp$ hybridization\\[0.1cm]
2080 Si-Si-Si bond angle $\rightarrow$ \unit[120]{$^{\circ}$}\\
2081 $\Rightarrow$ $sp^2$ hybridization
2082 \begin{center}
2083 \includegraphics[width=3.4cm]{c_pd_vasp/eden.eps}\\[-0.1cm]
2084 {\tiny Charge density isosurface}
2085 \end{center}
2086 \end{minipage}
2087 \begin{minipage}{0.2cm}
2088 \hfill
2089 \end{minipage}
2090 \begin{minipage}[t]{8.1cm}
2091 \begin{flushright}
2092 {\bf Bond-centered interstitial}\\[0.1cm]
2093 \begin{minipage}{4.4cm}
2094 %\scriptsize
2095 \begin{itemize}
2096  \item Linear Si-C-Si bond
2097  \item Si: one C \& 3 Si neighbours
2098  \item Spin polarized calculations
2099  \item No saddle point!\\
2100        Real local minimum!
2101 \end{itemize}
2102 \end{minipage}
2103 \begin{minipage}{2.7cm}
2104 %\includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
2105 \vspace{0.2cm}
2106 \includegraphics[width=2.8cm]{c_pd_albe/bc_bonds.eps}\\
2107 \end{minipage}
2108
2109 \framebox{
2110  \tiny
2111  \begin{minipage}[t]{6.5cm}
2112   \begin{minipage}[t]{1.2cm}
2113   {\color{red}Si}\\
2114   {\tiny sp$^3$}\\[0.8cm]
2115   \underline{${\color{black}\uparrow}$}
2116   \underline{${\color{black}\uparrow}$}
2117   \underline{${\color{black}\uparrow}$}
2118   \underline{${\color{red}\uparrow}$}\\
2119   sp$^3$
2120   \end{minipage}
2121   \begin{minipage}[t]{1.4cm}
2122   \begin{center}
2123   {\color{red}M}{\color{blue}O}\\[0.8cm]
2124   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
2125   $\sigma_{\text{ab}}$\\[0.5cm]
2126   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
2127   $\sigma_{\text{b}}$
2128   \end{center}
2129   \end{minipage}
2130   \begin{minipage}[t]{1.0cm}
2131   \begin{center}
2132   {\color{blue}C}\\
2133   {\tiny sp}\\[0.2cm]
2134   \underline{${\color{white}\uparrow\uparrow}$}
2135   \underline{${\color{white}\uparrow\uparrow}$}\\
2136   2p\\[0.4cm]
2137   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
2138   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
2139   sp
2140   \end{center}
2141   \end{minipage}
2142   \begin{minipage}[t]{1.4cm}
2143   \begin{center}
2144   {\color{blue}M}{\color{green}O}\\[0.8cm]
2145   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
2146   $\sigma_{\text{ab}}$\\[0.5cm]
2147   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
2148   $\sigma_{\text{b}}$
2149   \end{center}
2150   \end{minipage}
2151   \begin{minipage}[t]{1.2cm}
2152   \begin{flushright}
2153   {\color{green}Si}\\
2154   {\tiny sp$^3$}\\[0.8cm]
2155   \underline{${\color{green}\uparrow}$}
2156   \underline{${\color{black}\uparrow}$}
2157   \underline{${\color{black}\uparrow}$}
2158   \underline{${\color{black}\uparrow}$}\\
2159   sp$^3$
2160   \end{flushright}
2161   \end{minipage}
2162  \end{minipage}
2163 }\\[0.4cm]
2164
2165 %\framebox{
2166 \begin{minipage}{3.0cm}
2167 %\scriptsize
2168 \underline{Charge density}\\
2169 {\color{gray}$\bullet$} Spin up\\
2170 {\color{green}$\bullet$} Spin down\\
2171 {\color{blue}$\bullet$} Resulting spin up\\
2172 {\color{yellow}$\bullet$} Si atoms\\
2173 {\color{red}$\bullet$} C atom
2174 \end{minipage}
2175 \begin{minipage}{3.6cm}
2176 \includegraphics[width=3.8cm]{c_100_mig_vasp/im_spin_diff.eps}
2177 \end{minipage}
2178 %}
2179
2180 \end{flushright}
2181
2182 \end{minipage}
2183 \begin{pspicture}(0,0)(0,0)
2184 \psline[linecolor=gray,linewidth=0.05cm](-7.8,-8.7)(-7.8,0)
2185 \end{pspicture}
2186
2187 \end{slide}
2188
2189 \begin{slide}
2190
2191  {\large\bf
2192   Increased temperature simulations at high C concentration
2193  }
2194
2195 \footnotesize
2196
2197 \begin{minipage}{6.0cm}
2198 \includegraphics[width=6.4cm]{12_pc_thesis.ps}
2199 \end{minipage}
2200 \begin{minipage}{6.0cm}
2201 \includegraphics[width=6.4cm]{12_pc_c_thesis.ps}
2202 \end{minipage}
2203
2204 \vspace{0.1cm}
2205
2206 \scriptsize
2207
2208 \framebox{
2209 \begin{minipage}[t]{5.5cm}
2210 0.186 nm: Si-C pairs $\uparrow$\\
2211 (as expected in 3C-SiC)\\[0.2cm]
2212 0.282 nm: Si-C-C\\[0.2cm]
2213 $\approx$0.35 nm: C-Si-Si
2214 \end{minipage}
2215 }
2216 \begin{minipage}{0.1cm}
2217 \hfill
2218 \end{minipage}
2219 \framebox{
2220 \begin{minipage}[t]{5.9cm}
2221 0.15 nm: C-C pairs $\uparrow$\\
2222 (as expected in graphite/diamond)\\[0.2cm]
2223 0.252 nm: C-C-C (2$^{\text{nd}}$ NN for diamond)\\[0.2cm]
2224 0.31 nm: shifted towards 0.317 nm $\rightarrow$ C-Si-C
2225 \end{minipage}
2226 }
2227
2228 \begin{itemize}
2229 \item Decreasing cut-off artifact
2230 \item {\color{red}Amorphous} SiC-like phase remains
2231 \item High amount of {\color{red}damage} \& alignement to c-Si host matrix lost
2232 \item Slightly sharper peaks $\Rightarrow$ indicate slight {\color{blue}acceleration of dynamics} due to temperature
2233 \end{itemize}
2234
2235 \begin{center}
2236 {\color{blue}
2237 \framebox{
2238 {\color{black}
2239 High C \& small $V$ \& short $t$
2240 $\Rightarrow$
2241 }
2242 \begin{minipage}{4cm}
2243 \begin{center}
2244 Slow structural evolution due to strong C-C bonds
2245 \end{center}
2246 \end{minipage}
2247 {\color{black}
2248 $\Leftarrow$
2249 High C \& low T implants
2250 }
2251 }
2252 }
2253 \end{center}
2254
2255 \end{slide}
2256
2257
2258
2259 \begin{slide}
2260
2261  {\large\bf
2262   Valuation of a practicable temperature limit
2263  }
2264
2265  \small
2266
2267 \vspace{0.1cm}
2268
2269 \begin{center}
2270 \framebox{
2271 {\color{blue}
2272 Recrystallization is a hard task!
2273 $\Rightarrow$ Avoid melting!
2274 }
2275 }
2276 \end{center}
2277
2278 \vspace{0.1cm}
2279
2280 \footnotesize
2281
2282 \begin{minipage}{6.4cm}
2283 \includegraphics[width=6.4cm]{fe_and_t.ps}
2284 \end{minipage}
2285 \begin{minipage}{5.7cm}
2286 \underline{Melting does not occur instantly after}\\
2287 \underline{exceeding the melting point $T_{\text{m}}=2450\text{ K}$}
2288 \begin{itemize}
2289 \item required transition enthalpy
2290 \item hysterisis behaviour
2291 \end{itemize}
2292 \underline{Heating up c-Si by 1 K/ps}
2293 \begin{itemize}
2294 \item transition occurs at $\approx$ 3125 K
2295 \item $\Delta E=0.58\text{ eV/atom}=55.7\text{ kJ/mole}$\\
2296       (literature: 50.2 kJ/mole)
2297 \end{itemize}
2298 \end{minipage}
2299
2300 \vspace{0.1cm}
2301
2302 \framebox{
2303 \begin{minipage}{4cm}
2304 Initially chosen temperatures:\\
2305 $1.0 - 1.2 \cdot T_{\text{m}}$
2306 \end{minipage}
2307 }
2308 \begin{minipage}{2cm}
2309 \begin{center}
2310 $\Longrightarrow$
2311 \end{center}
2312 \end{minipage}
2313 \framebox{
2314 \begin{minipage}{5cm}
2315 Introduced C (defects)\\
2316 $\rightarrow$ reduction of transition point\\
2317 $\rightarrow$ melting already at $T_{\text{m}}$
2318 \end{minipage}
2319 }
2320
2321 \vspace{0.4cm}
2322
2323 \begin{center}
2324 \framebox{
2325 {\color{blue}
2326 Maximum temperature used: $0.95\cdot T_{\text{m}}$
2327 }
2328 }
2329 \end{center}
2330
2331 \end{slide}
2332
2333 \begin{slide}
2334
2335  {\large\bf
2336   Long time scale simulations at maximum temperature
2337  }
2338
2339 \small
2340
2341 \vspace{0.1cm}
2342
2343 \underline{Differences}
2344 \begin{itemize}
2345  \item Temperature set to $0.95 \cdot T_{\text{m}}$
2346  \item Cubic insertion volume $\Rightarrow$ spherical insertion volume
2347  \item Amount of C atoms: 6000 $\rightarrow$ 5500
2348        $\Leftrightarrow r_{\text{prec}}=0.3\text{ nm}$
2349  \item Simulation volume: 21 unit cells of c-Si in each direction
2350 \end{itemize}
2351
2352 \footnotesize
2353
2354 \vspace{0.3cm}
2355
2356 \begin{minipage}[t]{4.3cm}
2357 \begin{center}
2358 \underline{Low C concentration, Si-C}
2359 \includegraphics[width=4.3cm]{c_in_si_95_v1_si-c.ps}\\
2360 Sharper peaks!
2361 \end{center}
2362 \end{minipage}
2363 \begin{minipage}[t]{4.3cm}
2364 \begin{center}
2365 \underline{Low C concentration, C-C}
2366 \includegraphics[width=4.3cm]{c_in_si_95_v1_c-c.ps}\\
2367 Sharper peaks!\\
2368 No C agglomeration!
2369 \end{center}
2370 \end{minipage}
2371 \begin{minipage}[t]{3.4cm}
2372 \begin{center}
2373 \underline{High C concentration}
2374 \includegraphics[width=4.3cm]{c_in_si_95_v2.ps}\\
2375 No significant changes\\
2376 iC-Si-Si $\uparrow$\\
2377 C-Si-C $\downarrow$
2378 \end{center}
2379 \end{minipage}
2380
2381 \begin{center}
2382 \framebox{
2383 Long time scales and high temperatures most probably not sufficient enough!
2384 }
2385 \end{center}
2386
2387 \end{slide}
2388
2389 \begin{slide}
2390
2391  {\large\bf
2392   Investigation of a silicon carbide precipitate in silicon
2393  }
2394
2395  \scriptsize
2396
2397 \vspace{0.2cm}
2398
2399 \framebox{
2400 \scriptsize
2401 \begin{minipage}{5.3cm}
2402 \[
2403 \frac{8}{a_{\text{Si}}^3}(
2404 \underbrace{21^3 a_{\text{Si}}^3}_{=V}
2405 -\frac{4}{3}\pi x^3)+
2406 \underbrace{\frac{4}{y^3}\frac{4}{3}\pi x^3}_{\stackrel{!}{=}5500}
2407 =21^3\cdot 8
2408 \]
2409 \[
2410 \Downarrow
2411 \]
2412 \[
2413 \frac{8}{a_{\text{Si}}^3}\frac{4}{3}\pi x^3=5500
2414 \Rightarrow x = \left(\frac{5500 \cdot 3}{32 \pi} \right)^{1/3}a_{\text{Si}}
2415 \]
2416 \[
2417 y=\left(\frac{1}{2} \right)^{1/3}a_{\text{Si}}
2418 \]
2419 \end{minipage}
2420 }
2421 \begin{minipage}{0.1cm}
2422 \hfill
2423 \end{minipage}
2424 \begin{minipage}{6.3cm}
2425 \underline{Construction}
2426 \begin{itemize}
2427  \item Simulation volume: 21$^3$ unit cells of c-Si
2428  \item Spherical topotactically aligned precipitate\\
2429        $r=3.0\text{ nm}$ $\Leftrightarrow$ $\approx$ 5500 C atoms
2430  \item Create c-Si but skipped inside sphere\\
2431        of radius $x$
2432  \item Create 3C-SiC inside sphere of radius $x$\\
2433        and lattice constant $y$
2434  \item Strong coupling to heat bath ($T=20\,^{\circ}\mathrm{C}$)
2435 \end{itemize}
2436 \end{minipage}
2437
2438 \vspace{0.3cm}
2439
2440 \begin{minipage}{6.0cm}
2441 \includegraphics[width=6cm]{pc_0.ps}
2442 \end{minipage}
2443 \begin{minipage}{6.1cm}
2444 \underline{Results}
2445 \begin{itemize}
2446  \item Slight increase of c-Si lattice constant!
2447  \item C-C peaks\\
2448        (imply same distanced Si-Si peaks)
2449        \begin{itemize}
2450         \item New peak at 0.307 nm: 2$^{\text{nd}}$ NN in 3C-SiC
2451         \item Bumps ({\color{green}$\downarrow$}):
2452               4$^{\text{th}}$ and 6$^{\text{th}}$ NN
2453        \end{itemize}
2454  \item 3C-SiC lattice constant: 4.34 \AA (bulk: 4.36 \AA)\\
2455        $\rightarrow$ compressed precipitate
2456  \item Interface tension:\\
2457        20.15 eV/nm$^2$ or $3.23 \times 10^{-4}$ J/cm$^2$\\
2458        (literature: $2 - 8 \times 10^{-4}$ J/cm$^2$)
2459 \end{itemize}
2460 \end{minipage}
2461
2462 \end{slide}
2463
2464 \begin{slide}
2465
2466  {\large\bf
2467   Investigation of a silicon carbide precipitate in silicon
2468  }
2469
2470  \footnotesize
2471
2472 \begin{minipage}{7cm}
2473 \underline{Appended annealing steps}
2474 \begin{itemize}
2475  \item artificially constructed interface\\
2476        $\rightarrow$ allow for rearrangement of interface atoms
2477  \item check SiC stability
2478 \end{itemize}
2479 \underline{Temperature schedule}
2480 \begin{itemize}
2481  \item rapidly heat up structure up to $2050\,^{\circ}\mathrm{C}$\\
2482        (75 K/ps)
2483  \item slow heating up to $1.2\cdot T_{\text{m}}=2940\text{ K}$
2484        by 1 K/ps\\
2485        $\rightarrow$ melting at around 2840 K
2486        (\href{../video/sic_prec_120.avi}{$\rhd$})
2487  \item cooling down structure at 100 \% $T_{\text{m}}$ (1 K/ps)\\
2488        $\rightarrow$ no energetically more favorable struture
2489 \end{itemize}
2490 \end{minipage}
2491 \begin{minipage}{5cm}
2492 \includegraphics[width=5.5cm]{fe_and_t_sic.ps}
2493 \end{minipage}
2494
2495 \begin{minipage}{4cm}
2496 \includegraphics[width=4cm]{sic_prec/melt_01.eps}
2497 \end{minipage}
2498 \begin{minipage}{0.2cm}
2499 $\rightarrow$
2500 \end{minipage}
2501 \begin{minipage}{4cm}
2502 \includegraphics[width=4cm]{sic_prec/melt_02.eps}
2503 \end{minipage}
2504 \begin{minipage}{0.2cm}
2505 $\rightarrow$
2506 \end{minipage}
2507 \begin{minipage}{3.7cm}
2508 \includegraphics[width=4cm]{sic_prec/melt_03.eps}
2509 \end{minipage}
2510
2511 \end{slide}
2512
2513 \begin{slide}
2514
2515  {\large\bf
2516   DFT parameters
2517  }
2518
2519 \scriptsize
2520
2521 \vspace{0.1cm}
2522
2523 Equilibrium lattice constants and cohesive energies
2524
2525 \begin{tabular}{l r c c c c c}
2526 \hline
2527 \hline
2528  & & USPP, LDA & USPP, GGA & PAW, LDA & PAW, GGA & Exp. \\
2529 \hline
2530 Si (dia) & $a$ [\AA] & 5.389 & 5.455 & - & - & 5.429 \\
2531          & $\Delta_a$ [\%] & \unit[{\color{green}0.7}]{\%} & \unit[{\color{green}0.5}]{\%} & - & - & - \\
2532        & $E_{\text{coh}}$ [eV] & -5.277 & -4.591 & - & - & -4.63 \\
2533        & $\Delta_E$ [\%] & \unit[{\color{red}14.0}]{\%} & \unit[{\color{green}0.8}]{\%} & - & - & - \\
2534 \hline
2535 C (dia) & $a$ [\AA] & 3.527 & 3.567 & - & - & 3.567 \\
2536          & $\Delta_a$ [\%] & \unit[{\color{green}1.1}]{\%} & \unit[{\color{green}0.01}]{\%} & - & - & - \\
2537        & $E_{\text{coh}}$ [eV] & -8.812 & -7.703 & - & - & -7.374 \\
2538        & $\Delta_E$ [\%] & \unit[{\color{red}19.5}]{\%} & \unit[{\color{orange}4.5}]{\%} & - & - & - \\
2539 \hline
2540 3C-SiC & $a$ [\AA] & 4.319 & 4.370 & 4.330 & 4.379 & 4.359 \\
2541          & $\Delta_a$ [\%] & \unit[{\color{green}0.9}]{\%} & \unit[{\color{green}0.3}]{\%} & \unit[{\color{green}0.7}]{\%} & \unit[{\color{green}0.5}]{\%} & - \\
2542        & $E_{\text{coh}}$ [eV] & -7.318 & -6.426 &  -7.371 & -6.491 & -6.340 \\
2543        & $\Delta_E$ [\%] & \unit[{\color{red}15.4}]{\%} & \unit[{\color{green}1.4}]{\%} & \unit[{\color{red}16.3}]{\%} & \unit[{\color{orange}2.4}]{\%} & - \\
2544 \hline
2545 \hline
2546 \end{tabular}
2547
2548 \vspace{0.3cm}
2549
2550 \begin{minipage}{7cm}
2551 \begin{center}
2552 \begin{tabular}{l c c c}
2553 \hline
2554 \hline
2555  & Si (dia) & C (dia) & 3C-SiC \\
2556 \hline
2557 $a$ [\AA] & 5.458 & 3.562 & 4.365 \\
2558 $\Delta_a$ [\%] & 0.5 & 0.1 & 0.1 \\
2559 \hline
2560 $E_{\text{coh}}$ [eV] & -4.577 & -7.695 & -6.419 \\
2561 $\Delta_E$ [\%] & 1.1 & 4.4 & 1.2 \\
2562 \hline
2563 \hline
2564 \end{tabular}
2565 \end{center}
2566 \end{minipage}
2567 \begin{minipage}{5cm}
2568 $\leftarrow$ entire parameter set
2569 \end{minipage}
2570
2571 \end{slide}
2572
2573 \begin{slide}
2574
2575  {\large\bf
2576   DFT parameters\\
2577  }
2578
2579 \footnotesize
2580
2581 \begin{minipage}{6cm}
2582 \begin{center}
2583 \includegraphics[width=6cm]{sic_32pc_gamma_cutoff_lc.ps}
2584 \end{center}
2585 \end{minipage}
2586 \begin{minipage}{6cm}
2587 \begin{center}
2588 Lattice constants with respect to the PW cut-off energy
2589 \end{center}
2590 \end{minipage}
2591
2592 \begin{minipage}{6cm}
2593 \begin{center}
2594 \includegraphics[width=6cm]{si_self_int_thesis.ps}
2595 \end{center}
2596 \end{minipage}
2597 \begin{minipage}{6cm}
2598 \begin{center}
2599 Defect formation energy with respect to the size of the supercell\\[0.1cm]
2600 \end{center}
2601
2602 \end{minipage}
2603
2604 \end{slide}
2605
2606 \end{document}
2607