2 \documentclass[landscape,semhelv]{seminar}
5 \usepackage[greek,german]{babel}
6 \usepackage[latin1]{inputenc}
7 \usepackage[T1]{fontenc}
12 \usepackage{calc} % Simple computations with LaTeX variables
13 \usepackage{caption} % Improved captions
14 \usepackage{fancybox} % To have several backgrounds
16 \usepackage{fancyhdr} % Headers and footers definitions
17 \usepackage{fancyvrb} % Fancy verbatim environments
18 \usepackage{pstricks} % PSTricks with the standard color package
27 \graphicspath{{../img/}}
31 \usepackage[setpagesize=false]{hyperref}
34 \usepackage{semlayer} % Seminar overlays
35 \usepackage{slidesec} % Seminar sections and list of slides
37 \input{seminar.bug} % Official bugs corrections
38 \input{seminar.bg2} % Unofficial bugs corrections
45 %\usepackage{cmbright}
46 %\renewcommand{\familydefault}{\sfdefault}
47 %\usepackage{mathptmx}
53 \extraslideheight{10in}
58 % specify width and height
62 % shift it into visual area properly
63 \def\slideleftmargin{3.3cm}
64 \def\slidetopmargin{0.6cm}
66 \newcommand{\ham}{\mathcal{H}}
67 \newcommand{\pot}{\mathcal{V}}
68 \newcommand{\foo}{\mathcal{U}}
69 \newcommand{\vir}{\mathcal{W}}
72 \renewcommand\labelitemii{{\color{gray}$\bullet$}}
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}
89 Atomistic simulation study of the silicon carbide precipitation
95 \textsc{F. Zirkelbach}
108 % motivation / properties / applications of silicon carbide
113 \begin{pspicture}(0,0)(13.5,5)
117 \psframe*[linecolor=hb](0,0)(13.5,5)
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)
122 \rput[lt](0.2,4.6){\color{gray}PROPERTIES}
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}
130 \rput[lt](0.5,1.5){hard and mechanically stable}
131 \rput[lt](0.5,1){chemically inert}
133 \rput[lt](0.5,0.5){radiation hardness}
135 \rput[rt](13.3,4.6){\color{gray}APPLICATIONS}
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}
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}
145 \rput[rt](13,0.85){first wall reactor material, detectors}
146 \rput[rt](13,0.5){and electronic devices for space}
150 \begin{picture}(0,0)(-10,68)
151 \includegraphics[width=2.6cm]{wide_band_gap.eps}
153 \begin{picture}(0,0)(-295,-165)
154 \includegraphics[width=3cm]{sic_led.eps}
156 \begin{picture}(0,0)(-215,-165)
157 \includegraphics[width=2.5cm]{6h-sic_3c-sic.eps}
159 \begin{picture}(0,0)(-313,65)
160 \includegraphics[width=2.2cm]{infineon_schottky.eps}
162 \begin{picture}(0,0)(-220,65)
163 \includegraphics[width=2.9cm]{sic_wechselrichter_ise.eps}
177 \item Polyteps and fabrication of silicon carbide
178 \item Supposed precipitation mechanism of SiC in Si
179 \item Utilized simulation techniques
181 \item Molecular dynamics (MD) simulations
182 \item Density functional theory (DFT) calculations
184 \item C and Si self-interstitial point defects in silicon
185 \item Precipitation simulations
186 \item Summary / Conclusion / Outlook
203 \begin{tabular}{l c c c c c c}
205 & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
207 Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
208 Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
209 Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
210 Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
211 Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
212 Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
213 Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
221 \begin{picture}(0,0)(-160,-155)
222 \includegraphics[width=7cm]{polytypes.eps}
224 \begin{picture}(0,0)(-10,-185)
225 \includegraphics[width=3.8cm]{cubic_hex.eps}\\
227 \begin{picture}(0,0)(-10,-175)
228 {\tiny cubic (twist)}
230 \begin{picture}(0,0)(-60,-175)
231 {\tiny hexagonal (no twist)}
233 \begin{pspicture}(0,0)(0,0)
234 \psellipse[linecolor=green](5.7,3.03)(0.4,0.5)
236 \begin{pspicture}(0,0)(0,0)
237 \psellipse[linecolor=green](5.6,1.68)(0.4,0.2)
239 \begin{pspicture}(0,0)(0,0)
240 \psellipse[linecolor=red](10.7,1.13)(0.4,0.2)
248 Fabrication of silicon carbide
255 SiC - \emph{Born from the stars, perfected on earth.}
259 Conventional thin film SiC growth:
261 \item \underline{Sublimation growth using the modified Lely method}
263 \item SiC single-crystalline seed at $T=1800 \, ^{\circ} \text{C}$
264 \item Surrounded by polycrystalline SiC in a graphite crucible\\
265 at $T=2100-2400 \, ^{\circ} \text{C}$
266 \item Deposition of supersaturated vapor on cooler seed crystal
268 \item \underline{Homoepitaxial growth using CVD}
270 \item Step-controlled epitaxy on off-oriented 6H-SiC substrates
271 \item C$_3$H$_8$/SiH$_4$/H$_2$ at $1100-1500 \, ^{\circ} \text{C}$
272 \item Angle, temperature $\rightarrow$ 3C/6H/4H-SiC
273 \item High quality but limited in size of substrates
275 \item \underline{Heteroepitaxial growth of 3C-SiC on Si using CVD/MBE}
277 \item Two steps: carbonization and growth
278 \item $T=650-1050 \, ^{\circ} \text{C}$
279 \item Quality and size not yet sufficient
283 \begin{picture}(0,0)(-280,-65)
284 \includegraphics[width=3.8cm]{6h-sic_3c-sic.eps}
286 \begin{picture}(0,0)(-280,-55)
287 \begin{minipage}{5cm}
289 NASA: 6H-SiC and 3C-SiC LED\\[-7pt]
294 \begin{picture}(0,0)(-265,-150)
295 \includegraphics[width=2.4cm]{m_lely.eps}
297 \begin{picture}(0,0)(-333,-175)
298 \begin{minipage}{5cm}
304 5. Insulation\\[-7pt]
315 Fabrication of silicon carbide
320 Alternative approach:
321 Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
323 \item \underline{Implantation step 1}\\
324 180 keV C$^+$, $D=7.9\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=500\,^{\circ}\mathrm{C}$\\
325 $\Rightarrow$ box-like distribution of equally sized
326 and epitactically oriented SiC precipitates
328 \item \underline{Implantation step 2}\\
329 180 keV C$^+$, $D=0.6\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=250\,^{\circ}\mathrm{C}$\\
330 $\Rightarrow$ destruction of SiC nanocrystals
331 in growing amorphous interface layers
332 \item \underline{Annealing}\\
333 $T=1250\,^{\circ}\mathrm{C}$, $t=10\,\text{h}$\\
334 $\Rightarrow$ homogeneous, stoichiometric SiC layer
335 with sharp interfaces
338 \begin{minipage}{6.3cm}
339 \includegraphics[width=6cm]{ibs_3c-sic.eps}\\[-0.2cm]
341 XTEM micrograph of single crystalline 3C-SiC in Si\hkl(1 0 0)
344 \begin{minipage}{6.3cm}
346 {\color{blue}\bf\normalsize
347 Precipitation mechanism not yet fully understood!
349 \renewcommand\labelitemi{$\Rightarrow$}
351 \underline{Understanding the SiC precipitation}
353 \item significant technological progress in SiC thin film formation
354 \item perspectives for processes relying upon prevention of SiC precipitation
364 Supposed precipitation mechanism of SiC in Si
371 \begin{minipage}{3.8cm}
372 Si \& SiC lattice structure\\[0.2cm]
373 \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
377 \begin{minipage}{3.8cm}
379 \includegraphics[width=3.3cm]{tem_c-si-db.eps}
383 \begin{minipage}{3.8cm}
385 \includegraphics[width=3.3cm]{tem_3c-sic.eps}
389 \begin{minipage}{4cm}
391 C-Si dimers (dumbbells)\\[-0.1cm]
392 on Si interstitial sites
396 \begin{minipage}{4.2cm}
398 Agglomeration of C-Si dumbbells\\[-0.1cm]
399 $\Rightarrow$ dark contrasts
403 \begin{minipage}{4cm}
405 Precipitation of 3C-SiC in Si\\[-0.1cm]
406 $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
407 \& release of Si self-interstitials
411 \begin{minipage}{3.8cm}
413 \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
417 \begin{minipage}{3.8cm}
419 \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
423 \begin{minipage}{3.8cm}
425 \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
429 \begin{pspicture}(0,0)(0,0)
430 \psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
431 \psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
432 \rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
433 %\rput{-20}{\psellipse[linecolor=blue](6,6.5)(0.3,0.5)}
434 \psline[linewidth=4pt]{->}(4.0,2)(4.5,2)