X-Git-Url: https://hackdaworld.org/gitweb/?a=blobdiff_plain;f=posic%2Ftalks%2Fseminar_2010.tex;h=58369fab1c5fee4dc78b2bd011e7b56cbddb7798;hb=f9465130d3e796c6cf3a381b62285c281704b7ab;hp=9743c73ee45884f6093fb3505590642112b2590a;hpb=6923081bcd4d77d0516bce5fb8ab29bd5ec467fd;p=lectures%2Flatex.git diff --git a/posic/talks/seminar_2010.tex b/posic/talks/seminar_2010.tex index 9743c73..58369fa 100644 --- a/posic/talks/seminar_2010.tex +++ b/posic/talks/seminar_2010.tex @@ -26,6 +26,8 @@ \usepackage{graphicx} \graphicspath{{../img/}} +\usepackage{miller} + \usepackage[setpagesize=false]{hyperref} \usepackage{semcolor} @@ -172,15 +174,16 @@ } \begin{itemize} - \item Fabrication of silicon carbide and different polytypes - \item Precipitation model of 3C-SiC in Si + \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 C and Si self-interstitial point defects in silicon - \item Precipitation simulations + \item Silicon carbide precipitation simulations + \item Investigation of a silicon carbide precipitate in silicon \item Summary / Conclusion / Outlook \end{itemize} @@ -198,23 +201,45 @@ \small -\begin{tabular}{l | c c c c c c} +\begin{tabular}{l c c c c c c} \hline & 3C-SiC & 4H-SiC & 6H-SiC & Si & GaN & Diamond\\ \hline -Hardness [Mohs] & 9.6 & & & 6.5 & & 10 \\ +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] & & & & & & \\ -Saturation drift velocity [] & & & & & & \\ -Electron mobility [] & & & & & & \\ -Hole mobility [] & & & & & & \\ -Thermal conductivity [] & & & & & & \\ +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} @@ -285,4 +310,205 @@ Thermal conductivity [] & & & & & & \\ \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