posic/talks/seminar_2010.tex

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  31 \usepackage[setpagesize=false]{hyperref}
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  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}
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  44 % font
  45 %\usepackage{cmbright}
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  47 %\usepackage{mathptmx}
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  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
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  68 \newcommand{\foo}{\mathcal{U}}
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  70
  71 % itemize level ii
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  73
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  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)
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 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}
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 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  \begin{minipage}{6.3cm}
 346  \begin{center}
 347  {\color{blue}
 348   Precipitation mechanism not yet fully understood!
 349  }
 350  \renewcommand\labelitemi{$\Rightarrow$}
 351  \small
 352  \underline{Understanding the SiC precipitation}
 353  \begin{itemize}
 354   \item significant technological progress in SiC thin film formation
 355   \item perspectives for processes relying upon prevention of SiC precipitation
 356  \end{itemize}
 357  \end{center}
 358  \end{minipage}
 359
 360 \end{slide}
 361
 362 \begin{slide}
 363
 364  {\large\bf
 365   Supposed precipitation mechanism of SiC in Si
 366  }
 367
 368  \scriptsize
 369
 370  \vspace{0.1cm}
 371
 372  \begin{minipage}{3.8cm}
 373  Si \& SiC lattice structure\\[0.2cm]
 374  \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
 375  \hrule
 376  \end{minipage}
 377  \hspace{0.6cm}
 378  \begin{minipage}{3.8cm}
 379  \begin{center}
 380  \includegraphics[width=3.3cm]{tem_c-si-db.eps}
 381  \end{center}
 382  \end{minipage}
 383  \hspace{0.6cm}
 384  \begin{minipage}{3.8cm}
 385  \begin{center}
 386  \includegraphics[width=3.3cm]{tem_3c-sic.eps}
 387  \end{center}
 388  \end{minipage}
 389
 390  \begin{minipage}{4cm}
 391  \begin{center}
 392  C-Si dimers (dumbbells)\\[-0.1cm]
 393  on Si interstitial sites
 394  \end{center}
 395  \end{minipage}
 396  \hspace{0.2cm}
 397  \begin{minipage}{4.2cm}
 398  \begin{center}
 399  Agglomeration of C-Si dumbbells\\[-0.1cm]
 400  $\Rightarrow$ dark contrasts
 401  \end{center}
 402  \end{minipage}
 403  \hspace{0.2cm}
 404  \begin{minipage}{4cm}
 405  \begin{center}
 406  Precipitation of 3C-SiC in Si\\[-0.1cm]
 407  $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
 408  \& release of Si self-interstitials
 409  \end{center}
 410  \end{minipage}
 411
 412  \begin{minipage}{3.8cm}
 413  \begin{center}
 414  \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
 415  \end{center}
 416  \end{minipage}
 417  \hspace{0.6cm}
 418  \begin{minipage}{3.8cm}
 419  \begin{center}
 420  \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
 421  \end{center}
 422  \end{minipage}
 423  \hspace{0.6cm}
 424  \begin{minipage}{3.8cm}
 425  \begin{center}
 426  \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
 427  \end{center}
 428  \end{minipage}
 429
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 435 \end{pspicture}
 436
 437 \end{slide}
 438
 439 \begin{slide}
 440
 441  {\large\bf
 442   Basics of molecular dynamics (MD) simulations
 443  }
 444
 445  \vspace{12pt}
 446
 447  \small
 448
 449  {\bf MD basics:}
 450  \begin{itemize}
 451   \item Microscopic description of N particle system
 452   \item Analytical interaction potential
 453   \item Numerical integration using Newtons equation of motion\\
 454         as a propagation rule in 6N-dimensional phase space
 455   \item Observables obtained by time and/or ensemble averages
 456  \end{itemize}
 457  {\bf Details of the simulation:}
 458  \begin{itemize}
 459   \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
 460   \item Ensemble: NpT (isothermal-isobaric)
 461         \begin{itemize}
 462          \item Berendsen thermostat:
 463                $\tau_{\text{T}}=100\text{ fs}$
 464          \item Berendsen barostat:\\
 465                $\tau_{\text{P}}=100\text{ fs}$,
 466                $\beta^{-1}=100\text{ GPa}$
 467         \end{itemize}
 468   \item Potential: Tersoff-like bond order potential
 469   \vspace*{12pt}
 470         \[
 471         E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
 472         \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
 473         \]
 474  \end{itemize}
 475
 476  \begin{picture}(0,0)(-230,-30)
 477   \includegraphics[width=5cm]{tersoff_angle.eps}
 478  \end{picture}
 479
 480 \end{slide}
 481
 482 \begin{slide}
 483
 484  {\large\bf
 485   Basics of density functional theory (DFT) calculations
 486  }
 487
 488  \small
 489
 490  Ingredients
 491  \begin{itemize}
 492   \item Hohenberg-Kohn (HK) theorem
 493   \item \underline{Born-Oppenheimer}
 494         - $N$ moving electrons in an external potential of static nuclei\\
 495 \[
 496 H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
 497               +\sum_i^N V_{\text{ext}}(r_i)
 498               +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
 499 \]
 500   \item \underline{Effective potential}
 501         - replace electrostatic potential by an average over e$^-$ positions\\
 502 \[
 503 V_{\text{eff}}=...
 504 \]
 505   \item Exchange correlation (EC) LDA / GGA
 506   \item Self-consistent solution
 507   \item Plane wave basis set
 508   \item Pseudo potential
 509  \end{itemize}
 510
 511 \end{slide}
 512
 513
 514 \end{document}