\usepackage{graphicx}
\graphicspath{{../img/}}
+\usepackage{miller}
+
\usepackage[setpagesize=false]{hyperref}
\usepackage{semcolor}
}
\begin{itemize}
- \item Fabrication of silicon carbide
- \item Precipitation model
+ \item Polyteps and fabrication of silicon carbide
+ \item Supposed precipitation mechanism of SiC in Si
\item Utilized simulation techniques
\begin{itemize}
\item Molecular dynamics (MD) simulations
\item Density functional theory (DFT) calculations
\end{itemize}
- \item Point defects in silicon
- \item Precipitation simulations
+ \item C and Si self-interstitial point defects in silicon
+ \item Silicon carbide precipitation simulations
+ \item Investigation of a silicon carbide precipitate in silicon
\item Summary / Conclusion / Outlook
\end{itemize}
\begin{slide}
{\large\bf
- Motivation
+ Polytypes of SiC
}
+
+ \vspace{4cm}
+
+ \small
+
+\begin{tabular}{l c c c c c c}
+\hline
+ & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\
+\hline
+Hardness [Mohs] & \multicolumn{3}{c}{------ 9.6 ------}& 6.5 & - & 10 \\
+Band gap [eV] & 2.36 & 3.23 & 3.03 & 1.12 & 3.39 & 5.5 \\
+Break down field [$10^6$ V/cm] & 4 & 3 & 3.2 & 0.6 & 5 & 10 \\
+Saturation drift velocity [$10^7$ cm/s] & 2.5 & 2.0 & 2.0 & 1 & 2.7 & 2.7 \\
+Electron mobility [cm$^2$/Vs] & 800 & 900 & 400 & 1100 & 900 & 2200 \\
+Hole mobility [cm$^2$/Vs] & 320 & 120 & 90 & 420 & 150 & 1600 \\
+Thermal conductivity [W/cmK] & 5.0 & 4.9 & 4.9 & 1.5 & 1.3 & 22 \\
+\hline
+\end{tabular}
+
+{\tiny
+ Values for $T=300$ K
+}
+
+\begin{picture}(0,0)(-160,-155)
+ \includegraphics[width=7cm]{polytypes.eps}
+\end{picture}
+\begin{picture}(0,0)(-10,-185)
+ \includegraphics[width=3.8cm]{cubic_hex.eps}\\
+\end{picture}
+\begin{picture}(0,0)(-10,-175)
+ {\tiny cubic (twist)}
+\end{picture}
+\begin{picture}(0,0)(-60,-175)
+ {\tiny hexagonal (no twist)}
+\end{picture}
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=green](5.7,3.03)(0.4,0.5)
+\end{pspicture}
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=green](5.6,1.68)(0.4,0.2)
+\end{pspicture}
+\begin{pspicture}(0,0)(0,0)
+\psellipse[linecolor=red](10.7,1.13)(0.4,0.2)
+\end{pspicture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Fabrication of silicon carbide
+ }
+
+ \small
\vspace{4pt}
SiC - \emph{Born from the stars, perfected on earth.}
-
+
\vspace{4pt}
- Herstellung d"unner SiC-Filme:
+ Conventional thin film SiC growth:
\begin{itemize}
- \item modifizierter Lely-Prozess
+ \item \underline{Sublimation growth using the modified Lely method}
\begin{itemize}
- \item Impfkristall mit $T=2200 \, ^{\circ} \text{C}$
- \item umgeben von polykristallinen SiC mit
- $T=2400 \, ^{\circ} \text{C}$
+ \item SiC single-crystalline seed at $T=1800 \, ^{\circ} \text{C}$
+ \item Surrounded by polycrystalline SiC in a graphite crucible\\
+ at $T=2100-2400 \, ^{\circ} \text{C}$
+ \item Deposition of supersaturated vapor on cooler seed crystal
\end{itemize}
- \item CVD Homoepitaxie
+ \item \underline{Homoepitaxial growth using CVD}
\begin{itemize}
- \item 'step controlled epitaxy' auf 6H-SiC-Substrat
- \item C$_3$H$_8$/SiH$_4$/H$_2$ bei $1500 \, ^{\circ} \text{C}$
- \item Winkel $\rightarrow$ 3C/6H/4H-SiC
- \item hohe Qualit"at aber limitiert durch\\
- Substratgr"o"se
+ \item Step-controlled epitaxy on off-oriented 6H-SiC substrates
+ \item C$_3$H$_8$/SiH$_4$/H$_2$ at $1100-1500 \, ^{\circ} \text{C}$
+ \item Angle, temperature $\rightarrow$ 3C/6H/4H-SiC
+ \item High quality but limited in size of substrates
\end{itemize}
- \item CVD/MBE Heteroepitaxie von 3C-SiC auf Si
+ \item \underline{Heteroepitaxial growth of 3C-SiC on Si using CVD/MBE}
\begin{itemize}
- \item 2 Schritte: Karbonisierung und Wachstum
+ \item Two steps: carbonization and growth
\item $T=650-1050 \, ^{\circ} \text{C}$
- \item Qualit"at/Gr"o"se noch nicht ausreichend
+ \item Quality and size not yet sufficient
\end{itemize}
\end{itemize}
- \begin{picture}(0,0)(-245,-50)
- \includegraphics[width=5cm]{6h-sic_3c-sic.eps}
+ \begin{picture}(0,0)(-280,-65)
+ \includegraphics[width=3.8cm]{6h-sic_3c-sic.eps}
\end{picture}
- \begin{picture}(0,0)(-240,-35)
+ \begin{picture}(0,0)(-280,-55)
\begin{minipage}{5cm}
- {\scriptsize
- NASA: 6H-SiC LED und 3C-SiC LED\\[-6pt]
- nebeneinander auf 6H-SiC-Substrat
+ {\tiny
+ NASA: 6H-SiC and 3C-SiC LED\\[-7pt]
+ on 6H-SiC substrate
+ }
+ \end{minipage}
+ \end{picture}
+ \begin{picture}(0,0)(-265,-150)
+ \includegraphics[width=2.4cm]{m_lely.eps}
+ \end{picture}
+ \begin{picture}(0,0)(-333,-175)
+ \begin{minipage}{5cm}
+ {\tiny
+ 1. Lid\\[-7pt]
+ 2. Heating\\[-7pt]
+ 3. Source\\[-7pt]
+ 4. Crucible\\[-7pt]
+ 5. Insulation\\[-7pt]
+ 6. Seed crystal
}
\end{minipage}
\end{picture}
\end{slide}
+\begin{slide}
+
+ {\large\bf
+ Fabrication of silicon carbide
+ }
+
+ \small
+
+ Alternative approach:
+ Ion beam synthesis (IBS) of burried 3C-SiC layers in Si\hkl(1 0 0)
+ \begin{itemize}
+ \item \underline{Implantation step 1}\\
+ 180 keV C$^+$, $D=7.9\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=500\,^{\circ}\mathrm{C}$\\
+ $\Rightarrow$ box-like distribution of equally sized
+ and epitactically oriented SiC precipitates
+
+ \item \underline{Implantation step 2}\\
+ 180 keV C$^+$, $D=0.6\times 10^{17}$ cm$^{-2}$, $T_{\text{i}}=250\,^{\circ}\mathrm{C}$\\
+ $\Rightarrow$ destruction of SiC nanocrystals
+ in growing amorphous interface layers
+ \item \underline{Annealing}\\
+ $T=1250\,^{\circ}\mathrm{C}$, $t=10\,\text{h}$\\
+ $\Rightarrow$ homogeneous, stoichiometric SiC layer
+ with sharp interfaces
+ \end{itemize}
+
+ \begin{minipage}{6.3cm}
+ \includegraphics[width=6cm]{ibs_3c-sic.eps}\\[-0.2cm]
+ {\tiny
+ XTEM micrograph of single crystalline 3C-SiC in Si\hkl(1 0 0)
+ }
+ \end{minipage}
+ \begin{minipage}{6.3cm}
+ \begin{center}
+ {\color{blue}
+ Precipitation mechanism not yet fully understood!
+ }
+ \renewcommand\labelitemi{$\Rightarrow$}
+ \small
+ \underline{Understanding the SiC precipitation}
+ \begin{itemize}
+ \item significant technological progress in SiC thin film formation
+ \item perspectives for processes relying upon prevention of SiC precipitation
+ \end{itemize}
+ \end{center}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Supposed precipitation mechanism of SiC in Si
+ }
+
+ \scriptsize
+
+ \vspace{0.1cm}
+
+ \begin{minipage}{3.8cm}
+ Si \& SiC lattice structure\\[0.2cm]
+ \includegraphics[width=3.5cm]{sic_unit_cell.eps}\\[-0.3cm]
+ \hrule
+ \end{minipage}
+ \hspace{0.6cm}
+ \begin{minipage}{3.8cm}
+ \begin{center}
+ \includegraphics[width=3.3cm]{tem_c-si-db.eps}
+ \end{center}
+ \end{minipage}
+ \hspace{0.6cm}
+ \begin{minipage}{3.8cm}
+ \begin{center}
+ \includegraphics[width=3.3cm]{tem_3c-sic.eps}
+ \end{center}
+ \end{minipage}
+
+ \begin{minipage}{4cm}
+ \begin{center}
+ C-Si dimers (dumbbells)\\[-0.1cm]
+ on Si interstitial sites
+ \end{center}
+ \end{minipage}
+ \hspace{0.2cm}
+ \begin{minipage}{4.2cm}
+ \begin{center}
+ Agglomeration of C-Si dumbbells\\[-0.1cm]
+ $\Rightarrow$ dark contrasts
+ \end{center}
+ \end{minipage}
+ \hspace{0.2cm}
+ \begin{minipage}{4cm}
+ \begin{center}
+ Precipitation of 3C-SiC in Si\\[-0.1cm]
+ $\Rightarrow$ Moir\'e fringes\\[-0.1cm]
+ \& release of Si self-interstitials
+ \end{center}
+ \end{minipage}
+
+ \begin{minipage}{3.8cm}
+ \begin{center}
+ \includegraphics[width=3.3cm]{sic_prec_seq_01.eps}
+ \end{center}
+ \end{minipage}
+ \hspace{0.6cm}
+ \begin{minipage}{3.8cm}
+ \begin{center}
+ \includegraphics[width=3.3cm]{sic_prec_seq_02.eps}
+ \end{center}
+ \end{minipage}
+ \hspace{0.6cm}
+ \begin{minipage}{3.8cm}
+ \begin{center}
+ \includegraphics[width=3.3cm]{sic_prec_seq_03.eps}
+ \end{center}
+ \end{minipage}
+
+\begin{pspicture}(0,0)(0,0)
+\psline[linewidth=4pt]{->}(8.5,2)(9.0,2)
+\psellipse[linecolor=blue](11.5,5.8)(0.3,0.5)
+\rput{-20}{\psellipse[linecolor=blue](3.3,8.1)(0.3,0.5)}
+\psline[linewidth=4pt]{->}(4.0,2)(4.5,2)
+\end{pspicture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Basics of molecular dynamics (MD) simulations
+ }
+
+ \vspace{12pt}
+
+ \small
+
+ {\bf MD basics:}
+ \begin{itemize}
+ \item Microscopic description of N particle system
+ \item Analytical interaction potential
+ \item Numerical integration using Newtons equation of motion\\
+ as a propagation rule in 6N-dimensional phase space
+ \item Observables obtained by time and/or ensemble averages
+ \end{itemize}
+ {\bf Details of the simulation:}
+ \begin{itemize}
+ \item Integration: Velocity Verlet, timestep: $1\text{ fs}$
+ \item Ensemble: NpT (isothermal-isobaric)
+ \begin{itemize}
+ \item Berendsen thermostat:
+ $\tau_{\text{T}}=100\text{ fs}$
+ \item Berendsen barostat:\\
+ $\tau_{\text{P}}=100\text{ fs}$,
+ $\beta^{-1}=100\text{ GPa}$
+ \end{itemize}
+ \item Potential: Tersoff-like bond order potential
+ \vspace*{12pt}
+ \[
+ E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
+ \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
+ \]
+ \end{itemize}
+
+ \begin{picture}(0,0)(-230,-30)
+ \includegraphics[width=5cm]{tersoff_angle.eps}
+ \end{picture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Basics of density functional theory (DFT) calculations
+ }
+
+ \small
+
+ Ingredients
+ \begin{itemize}
+ \item Hohenberg-Kohn (HK) theorem
+ \item \underline{Born-Oppenheimer}
+ - $N$ moving electrons in an external potential of static nuclei\\
+\[
+H\Psi = \left[-\sum_i^N \frac{\hbar^2}{2m}\nabla_i^2
+ +\sum_i^N V_{\text{ext}}(r_i)
+ +\sum_{i<j}^N V_{e-e}(r_i,r_j)\right]\Psi=E\Psi
+\]
+ \item \underline{Effective potential}
+ - replace electrostatic potential by an average over e$^-$ positions\\
+\[
+V_{\text{eff}}=...
+\]
+ \item Exchange correlation (EC) LDA / GGA
+ \item Self-consistent solution
+ \item Plane wave basis set
+ \item Pseudo potential
+ \end{itemize}
+
+\end{slide}
+
+
\end{document}
projects / lectures / latex.git / blobdiff