posic/talks/seminar_2010.tex

   1 \pdfoutput=0
   2 \documentclass[landscape,semhelv]{seminar}
   3
   4 \usepackage{verbatim}
   5 \usepackage[greek,german]{babel}
   6 \usepackage[latin1]{inputenc}
   7 \usepackage[T1]{fontenc}
   8 \usepackage{amsmath}
   9 \usepackage{latexsym}
  10 \usepackage{ae}
  11
  12 \usepackage{calc}               % Simple computations with LaTeX variables
  13 \usepackage{caption}            % Improved captions
  14 \usepackage{fancybox}           % To have several backgrounds
  15
  16 \usepackage{fancyhdr}           % Headers and footers definitions
  17 \usepackage{fancyvrb}           % Fancy verbatim environments
  18 \usepackage{pstricks}           % PSTricks with the standard color package
  19
  20 \usepackage{pstricks}
  21 \usepackage{pst-node}
  22
  23 %\usepackage{epic}
  24 %\usepackage{eepic}
  25
  26 \usepackage{graphicx}
  27 \graphicspath{{../img/}}
  28
  29 \usepackage{miller}
  30
  31 \usepackage[setpagesize=false]{hyperref}
  32
  33 \usepackage{semcolor}
  34 \usepackage{semlayer}           % Seminar overlays
  35 \usepackage{slidesec}           % Seminar sections and list of slides
  36
  37 \input{seminar.bug}             % Official bugs corrections
  38 \input{seminar.bg2}             % Unofficial bugs corrections
  39
  40 \articlemag{1}
  41
  42 \special{landscape}
  43
  44 % font
  45 %\usepackage{cmbright}
  46 %\renewcommand{\familydefault}{\sfdefault}
  47 %\usepackage{mathptmx}
  48
  49 \usepackage{upgreek}
  50
  51 \begin{document}
  52
  53 \extraslideheight{10in}
  54 \slideframe{none}
  55
  56 \pagestyle{empty}
  57
  58 % specify width and height
  59 \slidewidth 27.7cm
  60 \slideheight 19.1cm
  61
  62 % shift it into visual area properly
  63 \def\slideleftmargin{3.3cm}
  64 \def\slidetopmargin{0.6cm}
  65
  66 \newcommand{\ham}{\mathcal{H}}
  67 \newcommand{\pot}{\mathcal{V}}
  68 \newcommand{\foo}{\mathcal{U}}
  69 \newcommand{\vir}{\mathcal{W}}
  70
  71 % itemize level ii
  72 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
  73
  74 % colors
  75 \newrgbcolor{si-yellow}{.6 .6 0}
  76 \newrgbcolor{hb}{0.75 0.77 0.89}
  77 \newrgbcolor{lbb}{0.75 0.8 0.88}
  78 \newrgbcolor{hlbb}{0.825 0.88 0.968}
  79 \newrgbcolor{lachs}{1.0 .93 .81}
  80
  81 % topic
  82
  83 \begin{slide}
  84 \begin{center}
  85
  86  \vspace{16pt}
  87
  88  {\LARGE\bf
  89   Atomistic simulation study of the silicon carbide precipitation
  90   in silicon
  91  }
  92
  93  \vspace{48pt}
  94
  95  \textsc{F. Zirkelbach}
  96
  97  \vspace{48pt}
  98
  99  Lehrstuhlseminar
 100
 101  \vspace{08pt}
 102
 103  17. Juni 2010
 104
 105 \end{center}
 106 \end{slide}
 107
 108 % motivation / properties / applications of silicon carbide
 109 \begin{slide}
 110
 111 \small
 112
 113 \begin{pspicture}(0,0)(13.5,5)
 114
 115
 116
 117  \psframe*[linecolor=hb](0,0)(13.5,5)
 118
 119  \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](5.5,1)(7,1)(7,3)(5.5,3)
 120  \pspolygon[linecolor=hlbb,fillcolor=hlbb,fillstyle=solid](6.75,0.5)(8,2)(8,2)(6.75,3.5)
 121
 122  \rput[lt](0.2,4.6){\color{gray}PROPERTIES}
 123
 124  \rput[lt](0.5,4){wide band gap}
 125  \rput[lt](0.5,3.5){high electric breakdown field}
 126  \rput[lt](0.5,3){good electron mobility}
 127  \rput[lt](0.5,2.5){high electron saturation drift velocity}
 128  \rput[lt](0.5,2){high thermal conductivity}
 129
 130  \rput[lt](0.5,1.5){hard and mechanically stable}
 131  \rput[lt](0.5,1){chemically inert}
 132
 133  \rput[lt](0.5,0.5){radiation hardness}
 134
 135  \rput[rt](13.3,4.6){\color{gray}APPLICATIONS}
 136
 137  \rput[rt](13,3.85){high-temperature, high power}
 138  \rput[rt](13,3.5){and high-frequency}
 139  \rput[rt](13,3.15){electronic and optoelectronic devices}
 140
 141  \rput[rt](13,2.35){material suitable for extreme conditions}
 142  \rput[rt](13,2){microelectromechanical systems}
 143  \rput[rt](13,1.65){abrasives, cutting tools, heating elements}
 144
 145  \rput[rt](13,0.85){first wall reactor material, detectors}
 146  \rput[rt](13,0.5){and electronic devices for space}
 147
 148 \end{pspicture}
 149
 150 \begin{picture}(0,0)(-10,68)
 151 \includegraphics[width=2.6cm]{wide_band_gap.eps}
 152 \end{picture}
 153 \begin{picture}(0,0)(-295,-165)
 154 \includegraphics[width=3cm]{sic_led.eps}
 155 \end{picture}
 156 \begin{picture}(0,0)(-215,-165)
 157 \includegraphics[width=2.5cm]{6h-sic_3c-sic.eps}
 158 \end{picture}
 159 \begin{picture}(0,0)(-313,65)
 160 \includegraphics[width=2.2cm]{infineon_schottky.eps}
 161 \end{picture}
 162 \begin{picture}(0,0)(-220,65)
 163 \includegraphics[width=2.9cm]{sic_wechselrichter_ise.eps}
 164 \end{picture}
 165
 166 \end{slide}
 167
 168 % contents
 169
 170 \begin{slide}
 171
 172 {\large\bf
 173  Outline
 174 }
 175
 176  \begin{itemize}
 177   \item Polyteps and fabrication of silicon carbide
 178   \item Supposed precipitation mechanism of SiC in Si
 179   \item Utilized simulation techniques
 180         \begin{itemize}
 181          \item Molecular dynamics (MD) simulations
 182          \item Density functional theory (DFT) calculations
 183         \end{itemize}
 184   \item C and Si self-interstitial point defects in silicon
 185   \item Silicon carbide precipitation simulations
 186   \item Investigation of a silicon carbide precipitate in silicon
 187   \item Summary / Conclusion / Outlook
 188  \end{itemize}
 189
 190 \end{slide}
 191
 192 % start of contents
 193
 194 \begin{slide}
 195
 196  {\large\bf
 197   Polytypes of SiC
 198  }
 199
 200  \vspace{4cm}
 201
 202  \small
 203
 204 \begin{tabular}{l c c c c c c}
 205 \hline
 206  & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
 207 \hline
 208 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
 209 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
 210 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
 211 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
 212 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
 213 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
 214 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
 215 \hline
 216 \end{tabular}
 217
 218 {\tiny
 219  Values for $T=300$ K
 220 }
 221
 222 \begin{picture}(0,0)(-160,-155)
 223  \includegraphics[width=7cm]{polytypes.eps}
 224 \end{picture}
 225 \begin{picture}(0,0)(-10,-185)
 226  \includegraphics[width=3.8cm]{cubic_hex.eps}\\
 227 \end{picture}
 228 \begin{picture}(0,0)(-10,-175)
 229  {\tiny cubic (twist)}
 230 \end{picture}
 231 \begin{picture}(0,0)(-60,-175)
 232  {\tiny hexagonal (no twist)}
 233 \end{picture}
 234 \begin{pspicture}(0,0)(0,0)
 235 \psellipse[linecolor=green](5.7,3.03)(0.4,0.5)
 236 \end{pspicture}
 237 \begin{pspicture}(0,0)(0,0)
 238 \psellipse[linecolor=green](5.6,1.68)(0.4,0.2)
 239 \end{pspicture}
 240 \begin{pspicture}(0,0)(0,0)
 241 \psellipse[linecolor=red](10.7,1.13)(0.4,0.2)
 242 \end{pspicture}
 243
 244 \end{slide}
 245
 246 \begin{slide}
 247
 248  {\large\bf
 249   Fabrication of silicon carbide
 250  }
 251
 252  \small
 253
 254  \vspace{4pt}
 255
 256  SiC - \emph{Born from the stars, perfected on earth.}
 257
 258  \vspace{4pt}
 259
 260  Conventional thin film SiC growth:
 261  \begin{itemize}
 262   \item \underline{Sublimation growth using the modified Lely method}
 263         \begin{itemize}
 264          \item SiC single-crystalline seed at $T=1800 \, ^{\circ} \text{C}$
 265          \item Surrounded by polycrystalline SiC in a graphite crucible\\
 266                at $T=2100-2400 \, ^{\circ} \text{C}$
 267          \item Deposition of supersaturated vapor on cooler seed crystal
 268         \end{itemize}
 269   \item \underline{Homoepitaxial growth using CVD}
 270         \begin{itemize}
 271          \item Step-controlled epitaxy on off-oriented 6H-SiC substrates
 272          \item C$_3$H$_8$/SiH$_4$/H$_2$ at $1100-1500 \, ^{\circ} \text{C}$
 273          \item Angle, temperature $\rightarrow$ 3C/6H/4H-SiC
 274          \item High quality but limited in size of substrates
 275         \end{itemize}
 276   \item \underline{Heteroepitaxial growth of 3C-SiC on Si using CVD/MBE}
 277         \begin{itemize}
 278          \item Two steps: carbonization and growth
 279          \item $T=650-1050 \, ^{\circ} \text{C}$
 280          \item Quality and size not yet sufficient
 281         \end{itemize}
 282  \end{itemize}
 283
 284  \begin{picture}(0,0)(-280,-65)
 285   \includegraphics[width=3.8cm]{6h-sic_3c-sic.eps}
 286  \end{picture}
 287  \begin{picture}(0,0)(-280,-55)
 288   \begin{minipage}{5cm}
 289   {\tiny
 290    NASA: 6H-SiC and 3C-SiC LED\\[-7pt]
 291    on 6H-SiC substrate
 292   }
 293   \end{minipage}
 294  \end{picture}
 295  \begin{picture}(0,0)(-265,-150)
 296   \includegraphics[width=2.4cm]{m_lely.eps}
 297  \end{picture}
 298  \begin{picture}(0,0)(-333,-175)
 299   \begin{minipage}{5cm}
 300   {\tiny
 301    1. Lid\\[-7pt]
 302    2. Heating\\[-7pt]
 303    3. Source\\[-7pt]
 304    4. Crucible\\[-7pt]
 305    5. Insulation\\[-7pt]
 306    6. Seed crystal
 307   }
 308   \end{minipage}
 309  \end{picture}
 310
 311 \end{slide}
 312
 313 \begin{slide}
 314
 315  {\large\bf
 316   Fabrication of silicon carbide
 317  }
 318
 319  \small
 320
 321  Alternative approach:
 322  Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
 323  \begin{itemize}
 324   \item \underline{Implantation step 1}\\
 325         180 keV C$^+$, $D=7.9\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=500\,^{\circ}\mathrm{C}$\\
 326         $\Rightarrow$ box-like distribution of equally sized
 327                        and epitactically oriented SiC precipitates
 328
 329   \item \underline{Implantation step 2}\\
 330         180 keV C$^+$, $D=0.6\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=250\,^{\circ}\mathrm{C}$\\
 331         $\Rightarrow$ destruction of SiC nanocrystals
 332                       in growing amorphous interface layers
 333   \item \underline{Annealing}\\
 334         $T=1250\,^{\circ}\mathrm{C}$, $t=10\,\text{h}$\\
 335         $\Rightarrow$ homogeneous, stoichiometric SiC layer
 336                       with sharp interfaces
 337  \end{itemize}
 338
 339  \begin{minipage}{6.3cm}
 340  \includegraphics[width=6cm]{ibs_3c-sic.eps}\\[-0.2cm]
 341  {\tiny
 342   XTEM micrograph of single crystalline 3C-SiC in Si\hkl(1 0 0)
 343  }
 344  \end{minipage}
 345 \framebox{
 346  \begin{minipage}{6.3cm}
 347  \begin{center}
 348  {\color{blue}
 349   Precipitation mechanism not yet fully understood!
 350  }
 351  \renewcommand\labelitemi{$\Rightarrow$}
 352  \small
 353  \underline{Understanding the SiC precipitation}
 354  \begin{itemize}
 355   \item significant technological progress in SiC thin film formation
 356   \item perspectives for processes relying upon prevention of SiC precipitation
 357  \end{itemize}
 358  \end{center}
 359  \end{minipage}
 360 }
 361
 362 \end{slide}
 363
 364 \begin{slide}
 365
 366  {\large\bf
 367   Supposed precipitation mechanism of SiC in Si
 368  }
 369
 370  \scriptsize
 371
 372  \vspace{0.1cm}
 373
 374  \begin{minipage}{3.8cm}
 375  Si \& SiC lattice structure\\[0.2cm]
 376  \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
 377  \hrule
 378  \end{minipage}
 379  \hspace{0.6cm}
 380  \begin{minipage}{3.8cm}
 381  \begin{center}
 382  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 383  \end{center}
 384  \end{minipage}
 385  \hspace{0.6cm}
 386  \begin{minipage}{3.8cm}
 387  \begin{center}
 388  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 389  \end{center}
 390  \end{minipage}
 391
 392  \begin{minipage}{4cm}
 393  \begin{center}
 394  C-Si dimers (dumbbells)\\[-0.1cm]
 395  on Si interstitial sites
 396  \end{center}
 397  \end{minipage}
 398  \hspace{0.2cm}
 399  \begin{minipage}{4.2cm}
 400  \begin{center}
 401  Agglomeration of C-Si dumbbells\\[-0.1cm]
 402  $\Rightarrow$ dark contrasts
 403  \end{center}
 404  \end{minipage}
 405  \hspace{0.2cm}
 406  \begin{minipage}{4cm}
 407  \begin{center}
 408  Precipitation of 3C-SiC in Si\\[-0.1cm]
 409  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 410  \& release of Si self-interstitials
 411  \end{center}
 412  \end{minipage}
 413
 414  \begin{minipage}{3.8cm}
 415  \begin{center}
 416  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 417  \end{center}
 418  \end{minipage}
 419  \hspace{0.6cm}
 420  \begin{minipage}{3.8cm}
 421  \begin{center}
 422  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 423  \end{center}
 424  \end{minipage}
 425  \hspace{0.6cm}
 426  \begin{minipage}{3.8cm}
 427  \begin{center}
 428  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 429  \end{center}
 430  \end{minipage}
 431
 432 \begin{pspicture}(0,0)(0,0)
 433 \psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
 434 \psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
 435 \rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
 436 \psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
 437 \end{pspicture}
 438
 439 \end{slide}
 440
 441 \begin{slide}
 442
 443  {\large\bf
 444   Molecular dynamics (MD) simulations
 445  }
 446
 447  \vspace{12pt}
 448
 449  \small
 450
 451  {\bf MD basics:}
 452  \begin{itemize}
 453   \item Microscopic description of N particle system
 454   \item Analytical interaction potential
 455   \item Numerical integration using Newtons equation of motion\\
 456         as a propagation rule in 6N-dimensional phase space
 457   \item Observables obtained by time and/or ensemble averages
 458  \end{itemize}
 459  {\bf Details of the simulation:}
 460  \begin{itemize}
 461   \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
 462   \item Ensemble: NpT (isothermal-isobaric)
 463         \begin{itemize}
 464          \item Berendsen thermostat:
 465                $\tau_{\text{T}}=100\text{ fs}$
 466          \item Berendsen barostat:\\
 467                $\tau_{\text{P}}=100\text{ fs}$,
 468                $\beta^{-1}=100\text{ GPa}$
 469         \end{itemize}
 470   \item Erhart/Albe potential: Tersoff-like bond order potential
 471   \vspace*{12pt}
 472         \[
 473         E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
 474         \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
 475         \]
 476  \end{itemize}
 477
 478  \begin{picture}(0,0)(-230,-30)
 479   \includegraphics[width=5cm]{tersoff_angle.eps}
 480  \end{picture}
 481
 482 \end{slide}
 483
 484 \begin{slide}
 485
 486  {\large\bf
 487   Density functional theory (DFT) calculations
 488  }
 489
 490  \small
 491
 492  Basic ingredients necessary for DFT
 493
 494  \begin{itemize}
 495   \item \underline{Hohenberg-Kohn theorem} - ground state density $n_0(r)$ ...
 496         \begin{itemize}
 497          \item ... uniquely determines the ground state potential
 498                / wavefunctions
 499          \item ... minimizes the systems total energy
 500         \end{itemize}
 501   \item \underline{Born-Oppenheimer}
 502         - $N$ moving electrons in an external potential of static nuclei
 503 \[
 504 H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
 505               +\sum_i^N V_{\text{ext}}(r_i)
 506               +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
 507 \]
 508   \item \underline{Effective potential}
 509         - averaged electrostatic potential \& exchange and correlation
 510 \[
 511 V_{\text{eff}}(r)=V_{\text{ext}}(r)+\int\frac{e^2 n(r')}{|r-r'|}d^3r'
 512                  +V_{\text{XC}}[n(r)]
 513 \]
 514   \item \underline{Kohn-Sham system}
 515         - Schr\"odinger equation of N non-interacting particles
 516 \[
 517 \left[ -\frac{\hbar^2}{2m}\nabla^2 + V_{\text{eff}}(r) \right] \Phi_i(r)
 518 =\epsilon_i\Phi_i(r)
 519 \quad
 520 \Rightarrow
 521 \quad
 522 n(r)=\sum_i^N|\Phi_i(r)|^2
 523 \]
 524   \item \underline{Self-consistent solution}\\
 525 $n(r)$ depends on $\Phi_i$, which depends on $V_{\text{eff}}$,
 526 which in turn depends on $n(r)$
 527   \item \underline{Variational principle}
 528         - minimize total energy with respect to $n(r)$
 529  \end{itemize}
 530
 531 \end{slide}
 532
 533 \begin{slide}
 534
 535  {\large\bf
 536   Density functional theory (DFT) calculations
 537  }
 538
 539  \small
 540
 541  \vspace*{0.2cm}
 542
 543  Details of applied DFT calculations in this work
 544
 545  \begin{itemize}
 546   \item \underline{Exchange correlation functional}
 547         - approximations for the inhomogeneous electron gas
 548         \begin{itemize}
 549          \item LDA: $E_{\text{XC}}^{\text{LDA}}[n]=\int \epsilon_{\text{XC}}(n)n(r)d^3r$
 550          \item GGA: $E_{\text{XC}}^{\text{GGA}}[n]=\int \epsilon_{\text{XC}}(n,\nabla n)n(r)d^3r$
 551         \end{itemize}
 552   \item \underline{Plane wave basis set}
 553         - approximation of the wavefunction $\Phi_i$ by plane waves $\phi_j$
 554 \[
 555 \rightarrow
 556 \text{Fourier series: } \Phi_i=\sum_{|G+k|<G_{\text{cut}}} c_j^i \phi_j(r), \quad E_{\text{cut}}=\frac{\hbar^2}{2m}G^2_{\text{cut}}
 557 \]
 558   \item \underline{$k$-point sampling} - $\Gamma$-point only calculations
 559   \item \underline{Pseudo potential}
 560         - consider only the valence electrons
 561   \item \underline{Code} - VASP 4.6
 562  \end{itemize}
 563
 564  \vspace*{0.2cm}
 565
 566  MD and structural optimization
 567
 568  \begin{itemize}
 569   \item MD integration: Gear predictor corrector algorithm
 570   \item Pressure control: Parrinello-Rahman pressure control
 571   \item Structural optimization: Conjugate gradient method
 572  \end{itemize}
 573
 574 \end{slide}
 575
 576 \begin{slide}
 577
 578  {\large\bf
 579   C and Si self-interstitial point defects in silicon
 580  }
 581
 582  \small
 583
 584  \vspace*{0.3cm}
 585
 586 \begin{minipage}{8cm}
 587 Procedure:\\[0.3cm]
 588   \begin{pspicture}(0,0)(7,5)
 589   \rput(3.5,4){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
 590    \parbox{7cm}{
 591    \begin{itemize}
 592     \item Creation of c-Si simulation volume
 593     \item Periodic boundary conditions
 594     \item $T=0\text{ K}$, $p=0\text{ bar}$
 595    \end{itemize}
 596   }}}}
 597 \rput(3.5,2.1){\rnode{insert}{\psframebox{
 598  \parbox{7cm}{
 599   \begin{center}
 600   Insertion of interstitial C/Si atoms
 601   \end{center}
 602   }}}}
 603   \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
 604    \parbox{7cm}{
 605    \begin{center}
 606    Relaxation / structural energy minimization
 607    \end{center}
 608   }}}}
 609   \ncline[]{->}{init}{insert}
 610   \ncline[]{->}{insert}{cool}
 611  \end{pspicture}
 612 \end{minipage}
 613 \begin{minipage}{5cm}
 614   \includegraphics[width=5cm]{unit_cell_e.eps}\\
 615 \end{minipage}
 616
 617 \begin{minipage}{9cm}
 618  \begin{tabular}{l c c}
 619  \hline
 620  & size [unit cells] & \# atoms\\
 621 \hline
 622 VASP & $3\times 3\times 3$ & $216\pm 1$ \\
 623 Erhart/Albe & $9\times 9\times 9$ & $5832\pm 1$\\
 624 \hline
 625  \end{tabular}
 626 \end{minipage}
 627 \begin{minipage}{4cm}
 628 {\color{red}$\bullet$} Tetrahedral\\
 629 {\color{green}$\bullet$} Hexagonal\\
 630 {\color{yellow}$\bullet$} \hkl<1 0 0> dumbbell\\
 631 {\color{magenta}$\bullet$} \hkl<1 1 0> dumbbell\\
 632 {\color{cyan}$\bullet$} Bond-centered\\
 633 {\color{black}$\bullet$} Vacancy / Substitutional
 634 \end{minipage}
 635
 636 \end{slide}
 637
 638 \begin{slide}
 639
 640  \footnotesize
 641
 642 \begin{minipage}{9.5cm}
 643
 644  {\large\bf
 645   Si self-interstitial point defects in silicon\\
 646  }
 647
 648 \begin{tabular}{l c c c c c}
 649 \hline
 650  $E_{\text{f}}$ [eV] & \hkl<1 1 0> DB & H & T & \hkl<1 0 0> DB & V \\
 651 \hline
 652  VASP & \underline{3.39} & 3.42 & 3.77 & 4.41 & 3.63 \\
 653  Erhart/Albe & 4.39 & 4.48$^*$ & \underline{3.40} & 5.42 & 3.13 \\
 654 \hline
 655 \end{tabular}\\[0.2cm]
 656
 657 \begin{minipage}{4.7cm}
 658 \includegraphics[width=4.7cm]{e_kin_si_hex.ps}
 659 \end{minipage}
 660 \begin{minipage}{4.7cm}
 661 \begin{center}
 662 {\tiny nearly T $\rightarrow$ T}\\
 663 \end{center}
 664 \includegraphics[width=4.7cm]{nhex_tet.ps}
 665 \end{minipage}\\
 666
 667 \underline{Hexagonal} \hspace{2pt}
 668 \href{../video/si_self_int_hexa.avi}{$\rhd$}\\[0.1cm]
 669 \framebox{
 670 \begin{minipage}{2.7cm}
 671 $E_{\text{f}}^*=4.48\text{ eV}$\\
 672 \includegraphics[width=2.7cm]{si_pd_albe/hex_a.eps}
 673 \end{minipage}
 674 \begin{minipage}{0.4cm}
 675 \begin{center}
 676 $\Rightarrow$
 677 \end{center}
 678 \end{minipage}
 679 \begin{minipage}{2.7cm}
 680 $E_{\text{f}}=3.96\text{ eV}$\\
 681 \includegraphics[width=2.8cm]{si_pd_albe/hex.eps}
 682 \end{minipage}
 683 }
 684 \begin{minipage}{2.9cm}
 685 \begin{flushright}
 686 \underline{Vacancy}\\
 687 \includegraphics[width=3.0cm]{si_pd_albe/vac.eps}
 688 \end{flushright}
 689 \end{minipage}
 690
 691 \end{minipage}
 692 \begin{minipage}{3.5cm}
 693
 694 \begin{flushright}
 695 \underline{\hkl<1 1 0> dumbbell}\\
 696 \includegraphics[width=3.0cm]{si_pd_albe/110.eps}\\
 697 \underline{Tetrahedral}\\
 698 \includegraphics[width=3.0cm]{si_pd_albe/tet.eps}\\
 699 \underline{\hkl<1 0 0> dumbbell}\\
 700 \includegraphics[width=3.0cm]{si_pd_albe/100.eps}
 701 \end{flushright}
 702
 703 \end{minipage}
 704
 705 \end{slide}
 706
 707 \begin{slide}
 708
 709 \footnotesize
 710
 711  {\large\bf
 712   C interstitial point defects in silicon\\[-0.1cm]
 713  }
 714
 715 \begin{tabular}{l c c c c c c}
 716 \hline
 717  $E_{\text{f}}$ & T & H & \hkl<1 0 0> DB & \hkl<1 1 0> DB & S & B \\
 718 \hline
 719  VASP & unstable & unstable & \underline{3.72} & 4.16 & 1.95 & 4.66 \\
 720  Erhart/Albe MD & 6.09 & 9.05$^*$ & \underline{3.88} & 5.18 & 0.75 & 5.59$^*$ \\
 721 \hline
 722 \end{tabular}\\[0.1cm]
 723
 724 \framebox{
 725 \begin{minipage}{2.7cm}
 726 \underline{Hexagonal} \hspace{2pt}
 727 \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
 728 $E_{\text{f}}^*=9.05\text{ eV}$\\
 729 \includegraphics[width=2.7cm]{c_pd_albe/hex.eps}
 730 \end{minipage}
 731 \begin{minipage}{0.4cm}
 732 \begin{center}
 733 $\Rightarrow$
 734 \end{center}
 735 \end{minipage}
 736 \begin{minipage}{2.7cm}
 737 \underline{\hkl<1 0 0>}\\
 738 $E_{\text{f}}=3.88\text{ eV}$\\
 739 \includegraphics[width=2.7cm]{c_pd_albe/100.eps}
 740 \end{minipage}
 741 }
 742 \begin{minipage}{2cm}
 743 \hfill
 744 \end{minipage}
 745 \begin{minipage}{3cm}
 746 \begin{flushright}
 747 \underline{Tetrahedral}\\
 748 \includegraphics[width=3.0cm]{c_pd_albe/tet.eps}
 749 \end{flushright}
 750 \end{minipage}
 751
 752 \framebox{
 753 \begin{minipage}{2.7cm}
 754 \underline{Bond-centered}\\
 755 $E_{\text{f}}^*=5.59\text{ eV}$\\
 756 \includegraphics[width=2.7cm]{c_pd_albe/bc.eps}
 757 \end{minipage}
 758 \begin{minipage}{0.4cm}
 759 \begin{center}
 760 $\Rightarrow$
 761 \end{center}
 762 \end{minipage}
 763 \begin{minipage}{2.7cm}
 764 \underline{\hkl<1 1 0> dumbbell}\\
 765 $E_{\text{f}}=5.18\text{ eV}$\\
 766 \includegraphics[width=2.7cm]{c_pd_albe/110.eps}
 767 \end{minipage}
 768 }
 769 \begin{minipage}{2cm}
 770 \hfill
 771 \end{minipage}
 772 \begin{minipage}{3cm}
 773 \begin{flushright}
 774 \underline{Substitutional}\\
 775 \includegraphics[width=3.0cm]{c_pd_albe/sub.eps}
 776 \end{flushright}
 777 \end{minipage}
 778
 779 \end{slide}
 780
 781 \begin{slide}
 782
 783 \footnotesize
 784
 785  {\large\bf\boldmath
 786   C \hkl<1 0 0> dumbbell interstitial configuration\\
 787  }
 788
 789 {\tiny
 790 \begin{tabular}{l c c c c c c c c}
 791 \hline
 792  Distances [nm] & $r(1C)$ & $r(2C)$ & $r(3C)$ & $r(12)$ & $r(13)$ & $r(34)$ & $r(23)$ & $r(25)$ \\
 793 \hline
 794 Erhart/Albe & 0.175 & 0.329 & 0.186 & 0.226 & 0.300 & 0.343 & 0.423 & 0.425 \\
 795 VASP & 0.174 & 0.341 & 0.182 & 0.229 & 0.286 & 0.347 & 0.422 & 0.417 \\
 796 \hline
 797 \end{tabular}\\[0.2cm]
 798 \begin{tabular}{l c c c c }
 799 \hline
 800  Angles [$^{\circ}$] & $\theta_1$ & $\theta_2$ & $\theta_3$ & $\theta_4$ \\
 801 \hline
 802 Erhart/Albe & 140.2 & 109.9 & 134.4 & 112.8 \\
 803 VASP & 130.7 & 114.4 & 146.0 & 107.0 \\
 804 \hline
 805 \end{tabular}\\[0.2cm]
 806 \begin{tabular}{l c c c}
 807 \hline
 808  Displacements [nm]& $a$ & $b$ & $|a|+|b|$ \\
 809 \hline
 810 Erhart/Albe & 0.084 & -0.091 & 0.175 \\
 811 VASP & 0.109 & -0.065 & 0.174 \\
 812 \hline
 813 \end{tabular}\\[0.6cm]
 814 }
 815
 816 \begin{minipage}{3.0cm}
 817 \begin{center}
 818 \underline{Erhart/Albe}
 819 \includegraphics[width=3.0cm]{c_pd_albe/100_cmp.eps}
 820 \end{center}
 821 \end{minipage}
 822 \begin{minipage}{3.0cm}
 823 \begin{center}
 824 \underline{VASP}
 825 \includegraphics[width=3.0cm]{c_pd_vasp/100_cmp.eps}
 826 \end{center}
 827 \end{minipage}\\
 828
 829 \begin{picture}(0,0)(-185,10)
 830 \includegraphics[width=6.8cm]{100-c-si-db_cmp.eps}
 831 \end{picture}
 832 \begin{picture}(0,0)(-280,-150)
 833 \includegraphics[width=3.3cm]{c_pd_vasp/eden.eps}
 834 \end{picture}
 835
 836 \begin{pspicture}(0,0)(0,0)
 837 \psellipse[linecolor=green](5.18,5.92)(0.5,0.3)
 838 \psellipse[linecolor=red](3.45,5.92)(1.0,0.4)
 839 \psellipse[linecolor=blue](2.7,6.92)(0.9,0.2)
 840 \psellipse[linecolor=blue](4.65,6.92)(0.9,0.2)
 841 \end{pspicture}
 842
 843 \end{slide}
 844
 845 \begin{slide}
 846
 847 \small
 848
 849 \begin{minipage}{8.5cm}
 850
 851  {\large\bf
 852   Bond-centered interstitial configuration\\[-0.1cm]
 853  }
 854
 855 \begin{minipage}{3.0cm}
 856 \includegraphics[width=2.8cm]{c_pd_vasp/bc_2333.eps}\\
 857 \end{minipage}
 858 \begin{minipage}{5.2cm}
 859 \begin{itemize}
 860  \item Linear Si-C-Si bond
 861  \item Si: one C \& 3 Si neighbours
 862  \item Spin polarized calculations
 863  \item No saddle point!\\
 864        Real local minimum!
 865 \end{itemize}
 866 \end{minipage}
 867
 868 \framebox{
 869  \tiny
 870  \begin{minipage}[t]{6.5cm}
 871   \begin{minipage}[t]{1.2cm}
 872   {\color{red}Si}\\
 873   {\tiny sp$^3$}\\[0.8cm]
 874   \underline{${\color{black}\uparrow}$}
 875   \underline{${\color{black}\uparrow}$}
 876   \underline{${\color{black}\uparrow}$}
 877   \underline{${\color{red}\uparrow}$}\\
 878   sp$^3$
 879   \end{minipage}
 880   \begin{minipage}[t]{1.4cm}
 881   \begin{center}
 882   {\color{red}M}{\color{blue}O}\\[0.8cm]
 883   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
 884   $\sigma_{\text{ab}}$\\[0.5cm]
 885   \underline{${\color{red}\uparrow}{\color{blue}\downarrow}$}\\
 886   $\sigma_{\text{b}}$
 887   \end{center}
 888   \end{minipage}
 889   \begin{minipage}[t]{1.0cm}
 890   \begin{center}
 891   {\color{blue}C}\\
 892   {\tiny sp}\\[0.2cm]
 893   \underline{${\color{white}\uparrow\uparrow}$}
 894   \underline{${\color{white}\uparrow\uparrow}$}\\
 895   2p\\[0.4cm]
 896   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}
 897   \underline{${\color{blue}\uparrow}{\color{blue}\downarrow}$}\\
 898   sp
 899   \end{center}
 900   \end{minipage}
 901   \begin{minipage}[t]{1.4cm}
 902   \begin{center}
 903   {\color{blue}M}{\color{green}O}\\[0.8cm]
 904   \underline{${\color{blue}\uparrow}{\color{white}\downarrow}$}\\
 905   $\sigma_{\text{ab}}$\\[0.5cm]
 906   \underline{${\color{green}\uparrow}{\color{blue}\downarrow}$}\\
 907   $\sigma_{\text{b}}$
 908   \end{center}
 909   \end{minipage}
 910   \begin{minipage}[t]{1.2cm}
 911   \begin{flushright}
 912   {\color{green}Si}\\
 913   {\tiny sp$^3$}\\[0.8cm]
 914   \underline{${\color{green}\uparrow}$}
 915   \underline{${\color{black}\uparrow}$}
 916   \underline{${\color{black}\uparrow}$}
 917   \underline{${\color{black}\uparrow}$}\\
 918   sp$^3$
 919   \end{flushright}
 920   \end{minipage}
 921  \end{minipage}
 922 }\\[0.1cm]
 923
 924 \framebox{
 925 \begin{minipage}{4.5cm}
 926 \includegraphics[width=4cm]{c_100_mig_vasp/im_spin_diff.eps}
 927 \end{minipage}
 928 \begin{minipage}{3.5cm}
 929 {\color{gray}$\bullet$} Spin up\\
 930 {\color{green}$\bullet$} Spin down\\
 931 {\color{blue}$\bullet$} Resulting spin up\\
 932 {\color{yellow}$\bullet$} Si atoms\\
 933 {\color{red}$\bullet$} C atom
 934 \end{minipage}
 935 }
 936
 937 \end{minipage}
 938 \begin{minipage}{4.2cm}
 939 \begin{flushright}
 940 \includegraphics[width=4.3cm]{c_pd_vasp/bc_2333_ksl.ps}\\
 941 {\color{green}$\Box$} {\tiny unoccupied}\\
 942 {\color{red}$\bullet$} {\tiny occupied}
 943 \end{flushright}
 944 \end{minipage}
 945
 946 \end{slide}
 947
 948 \begin{slide}
 949
 950  {\large\bf\boldmath
 951   Migration of the C \hkl<1 0 0> dumbbell interstitial
 952  }
 953
 954 \scriptsize
 955
 956  {\small Investigated pathways}
 957
 958 \begin{minipage}{8.5cm}
 959 \begin{minipage}{8.3cm}
 960 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 0 1>}\\
 961 \begin{minipage}{2.4cm}
 962 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
 963 \end{minipage}
 964 \begin{minipage}{0.4cm}
 965 $\rightarrow$
 966 \end{minipage}
 967 \begin{minipage}{2.4cm}
 968 \includegraphics[width=2.4cm]{c_pd_vasp/bc_2333.eps}
 969 \end{minipage}
 970 \begin{minipage}{0.4cm}
 971 $\rightarrow$
 972 \end{minipage}
 973 \begin{minipage}{2.4cm}
 974 \includegraphics[width=2.4cm]{c_pd_vasp/100_next_2333.eps}
 975 \end{minipage}
 976 \end{minipage}\\
 977 \begin{minipage}{8.3cm}
 978 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0>}\\
 979 \begin{minipage}{2.4cm}
 980 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
 981 \end{minipage}
 982 \begin{minipage}{0.4cm}
 983 $\rightarrow$
 984 \end{minipage}
 985 \begin{minipage}{2.4cm}
 986 \includegraphics[width=2.4cm]{c_pd_vasp/00-1-0-10_2333.eps}
 987 \end{minipage}
 988 \begin{minipage}{0.4cm}
 989 $\rightarrow$
 990 \end{minipage}
 991 \begin{minipage}{2.4cm}
 992 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_2333.eps}
 993 \end{minipage}
 994 \end{minipage}\\
 995 \begin{minipage}{8.3cm}
 996 \underline{\hkl<0 0 -1> $\rightarrow$ \hkl<0 -1 0> (in place)}\\
 997 \begin{minipage}{2.4cm}
 998 \includegraphics[width=2.4cm]{c_pd_vasp/100_2333.eps}
 999 \end{minipage}
1000 \begin{minipage}{0.4cm}
1001 $\rightarrow$
1002 \end{minipage}
1003 \begin{minipage}{2.4cm}
1004 \includegraphics[width=2.4cm]{c_pd_vasp/00-1_ip0-10_2333.eps}
1005 \end{minipage}
1006 \begin{minipage}{0.4cm}
1007 $\rightarrow$
1008 \end{minipage}
1009 \begin{minipage}{2.4cm}
1010 \includegraphics[width=2.4cm]{c_pd_vasp/0-10_ip_2333.eps}
1011 \end{minipage}
1012 \end{minipage}
1013 \end{minipage}
1014 \framebox{
1015 \begin{minipage}{4.2cm}
1016  {\small Constrained relaxation\\
1017          technique (CRT) method}\\
1018 \includegraphics[width=4cm]{crt_orig.eps}
1019 \begin{itemize}
1020  \item Constrain diffusing atom
1021  \item Static constraints
1022 \end{itemize}
1023 \vspace*{0.3cm}
1024  {\small Modifications}\\
1025 \includegraphics[width=4cm]{crt_mod.eps}
1026 \begin{itemize}
1027  \item Constrain all atoms
1028  \item Update individual\\
1029        constraints
1030 \end{itemize}
1031 \end{minipage}
1032 }
1033
1034 \end{slide}
1035
1036 \begin{slide}
1037
1038  {\large\bf\boldmath
1039   Migration of the C \hkl<1 0 0> dumbbell interstitial
1040  }
1041
1042 \scriptsize
1043
1044 \framebox{
1045 \begin{minipage}{5.9cm}
1046 \begin{flushleft}
1047 \includegraphics[width=5.8cm]{im_00-1_nosym_sp_fullct_thesis.ps}\\[0.45cm]
1048 \end{flushleft}
1049 \begin{center}
1050 \begin{picture}(0,0)(60,0)
1051 \includegraphics[width=1cm]{vasp_mig/00-1.eps}
1052 \end{picture}
1053 \begin{picture}(0,0)(-5,0)
1054 \includegraphics[width=1cm]{vasp_mig/bc_00-1_sp.eps}
1055 \end{picture}
1056 \begin{picture}(0,0)(-55,0)
1057 \includegraphics[width=1cm]{vasp_mig/bc.eps}
1058 \end{picture}
1059 \begin{picture}(0,0)(12.5,10)
1060 \includegraphics[width=1cm]{110_arrow.eps}
1061 \end{picture}
1062 \begin{picture}(0,0)(90,0)
1063 \includegraphics[height=0.9cm]{001_arrow.eps}
1064 \end{picture}
1065 \end{center}
1066 \vspace*{0.35cm}
1067 \end{minipage}
1068 }
1069 \begin{minipage}{0.3cm}
1070 \hfill
1071 \end{minipage}
1072 \framebox{
1073 \begin{minipage}{5.9cm}
1074 \begin{flushright}
1075 \includegraphics[width=5.9cm]{vasp_mig/00-1_0-10_nosym_sp_fullct.ps}\\[0.5cm]
1076 \end{flushright}
1077 \begin{center}
1078 \begin{picture}(0,0)(60,0)
1079 \includegraphics[width=1cm]{vasp_mig/00-1_a.eps}
1080 \end{picture}
1081 \begin{picture}(0,0)(5,0)
1082 \includegraphics[width=1cm]{vasp_mig/00-1_0-10_sp.eps}
1083 \end{picture}
1084 \begin{picture}(0,0)(-55,0)
1085 \includegraphics[width=1cm]{vasp_mig/0-10.eps}
1086 \end{picture}
1087 \begin{picture}(0,0)(12.5,10)
1088 \includegraphics[width=1cm]{100_arrow.eps}
1089 \end{picture}
1090 \begin{picture}(0,0)(90,0)
1091 \includegraphics[height=0.9cm]{001_arrow.eps}
1092 \end{picture}
1093 \end{center}
1094 \vspace*{0.3cm}
1095 \end{minipage}\\
1096 }
1097
1098 \vspace*{0.05cm}
1099
1100 \framebox{
1101 \begin{minipage}{5.9cm}
1102 \begin{flushleft}
1103 \includegraphics[width=5.9cm]{vasp_mig/00-1_ip0-10_nosym_sp_fullct.ps}\\[0.6cm]
1104 \end{flushleft}
1105 \begin{center}
1106 \begin{picture}(0,0)(60,0)
1107 \includegraphics[width=0.9cm]{vasp_mig/00-1_b.eps}
1108 \end{picture}
1109 \begin{picture}(0,0)(10,0)
1110 \includegraphics[width=0.9cm]{vasp_mig/00-1_ip0-10_sp.eps}
1111 \end{picture}
1112 \begin{picture}(0,0)(-60,0)
1113 \includegraphics[width=0.9cm]{vasp_mig/0-10_b.eps}
1114 \end{picture}
1115 \begin{picture}(0,0)(12.5,10)
1116 \includegraphics[width=1cm]{100_arrow.eps}
1117 \end{picture}
1118 \begin{picture}(0,0)(90,0)
1119 \includegraphics[height=0.9cm]{001_arrow.eps}
1120 \end{picture}
1121 \end{center}
1122 \vspace*{0.3cm}
1123 \end{minipage}
1124 }
1125 \begin{minipage}{0.3cm}
1126 \hfill
1127 \end{minipage}
1128 \begin{minipage}{6.5cm}
1129 VASP results
1130 \begin{itemize}
1131  \item Energetically most favorable path
1132        \begin{itemize}
1133         \item Path 2
1134         \item Activation energy: $\approx$ 0.9 eV
1135         \item Experimental values: 0.73 ... 0.87 eV
1136        \end{itemize}
1137        $\Rightarrow$ {\color{blue}Diffusion} path identified!
1138  \item Reorientation (path 3)
1139        \begin{itemize}
1140         \item More likely composed of two consecutive steps of type 2
1141         \item Experimental values: 0.77 ... 0.88 eV
1142        \end{itemize}
1143        $\Rightarrow$ {\color{blue}Reorientation} transition identified!
1144 \end{itemize}
1145 \end{minipage}
1146
1147 \end{slide}
1148
1149 \begin{slide}
1150
1151  {\large\bf\boldmath
1152   Migration of the C \hkl<1 0 0> dumbbell interstitial
1153  }
1154
1155 \scriptsize
1156
1157 \begin{minipage}{6.5cm}
1158
1159 \framebox{
1160 \begin{minipage}{5.9cm}
1161 \begin{flushleft}
1162 \includegraphics[width=5.9cm]{bc_00-1.ps}\\[2.35cm]
1163 \end{flushleft}
1164 \begin{center}
1165 \begin{pspicture}(0,0)(0,0)
1166 \psframe[linecolor=red,fillstyle=none](-2.8,1.35)(3.3,2.7)
1167 \end{pspicture}
1168 \begin{picture}(0,0)(60,-50)
1169 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_00.eps}
1170 \end{picture}
1171 \begin{picture}(0,0)(5,-50)
1172 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_01.eps}
1173 \end{picture}
1174 \begin{picture}(0,0)(-55,-50)
1175 \includegraphics[width=1cm]{albe_mig/bc_00-1_red_02.eps}
1176 \end{picture}
1177 \begin{picture}(0,0)(12.5,-40)
1178 \includegraphics[width=1cm]{110_arrow.eps}
1179 \end{picture}
1180 \begin{picture}(0,0)(90,-45)
1181 \includegraphics[height=0.9cm]{001_arrow.eps}
1182 \end{picture}\\
1183 \begin{pspicture}(0,0)(0,0)
1184 \psframe[linecolor=blue,fillstyle=none](-2.8,0)(3.3,1.6)
1185 \end{pspicture}
1186 \begin{picture}(0,0)(60,-15)
1187 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_01.eps}
1188 \end{picture}
1189 \begin{picture}(0,0)(35,-15)
1190 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_02.eps}
1191 \end{picture}
1192 \begin{picture}(0,0)(-5,-15)
1193 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_03.eps}
1194 \end{picture}
1195 \begin{picture}(0,0)(-55,-15)
1196 \includegraphics[width=0.9cm]{albe_mig/bc_00-1_04.eps}
1197 \end{picture}
1198 \begin{picture}(0,0)(12.5,-5)
1199 \includegraphics[width=1cm]{100_arrow.eps}
1200 \end{picture}
1201 \begin{picture}(0,0)(90,-15)
1202 \includegraphics[height=0.9cm]{010_arrow.eps}
1203 \end{picture}
1204 \end{center}
1205 \end{minipage}
1206 }\\[0.1cm]
1207
1208 \begin{minipage}{5.9cm}
1209 Erhart/Albe results
1210 \begin{itemize}
1211  \item Lowest activation energy: $\approx$ 2.2 eV
1212  \item 2.4 times higher than VASP
1213  \item Different pathway
1214  \item Transition minima ($\rightarrow$ \hkl<1 1 0> dumbbell)
1215 \end{itemize}
1216 \end{minipage}
1217
1218 \end{minipage}
1219 \begin{minipage}{6.5cm}
1220
1221 \framebox{
1222 \begin{minipage}{5.9cm}
1223 \begin{flushright}
1224 \includegraphics[width=5.9cm]{00-1_0-10.ps}\\[0.75cm]
1225 \end{flushright}
1226 \begin{center}
1227 \begin{pspicture}(0,0)(0,0)
1228 \psframe[linecolor=red,fillstyle=none](-2.8,-0.25)(3.3,1.1)
1229 \end{pspicture}
1230 \begin{picture}(0,0)(60,-5)
1231 \includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_00.eps}
1232 \end{picture}
1233 \begin{picture}(0,0)(0,-5)
1234 \includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_min.eps}
1235 \end{picture}
1236 \begin{picture}(0,0)(-55,-5)
1237 \includegraphics[width=0.9cm]{albe_mig/00-1_0-10_red_03.eps}
1238 \end{picture}
1239 \begin{picture}(0,0)(12.5,5)
1240 \includegraphics[width=1cm]{100_arrow.eps}
1241 \end{picture}
1242 \begin{picture}(0,0)(90,0)
1243 \includegraphics[height=0.9cm]{001_arrow.eps}
1244 \end{picture}
1245 \end{center}
1246 \vspace{0.2cm}
1247 \end{minipage}
1248 }\\[0.2cm]
1249
1250 \framebox{
1251 \begin{minipage}{5.9cm}
1252 \includegraphics[width=5.9cm]{00-1_ip0-10.ps}
1253 \end{minipage}
1254 }
1255
1256 \end{minipage}
1257
1258 \end{slide}
1259
1260 \begin{slide}
1261
1262  {\large\bf\boldmath
1263   Migration involving the C \hkl<1 1 0> dumbbell interstitial
1264  }
1265
1266 \scriptsize
1267
1268
1269 \end{slide}
1270
1271 \begin{slide}
1272
1273  {\large\bf\boldmath
1274   Combinations of point defects
1275  }
1276
1277 \scriptsize
1278
1279
1280 \end{slide}
1281
1282 \begin{slide}
1283
1284  {\large\bf
1285   Silicon carbide precipitation simulations
1286  }
1287
1288  \small
1289
1290 \end{slide}
1291
1292 \begin{slide}
1293
1294  {\large\bf
1295   Investigation of a silicon carbide precipitate in silicon
1296  }
1297
1298  \small
1299
1300 \end{slide}
1301
1302 \end{document}