--- /dev/null
+\pdfoutput=0
+\documentclass[a4paper,11pt]{article}
+\usepackage[activate]{pdfcprot}
+\usepackage{verbatim}
+\usepackage{a4}
+\usepackage{a4wide}
+\usepackage[german]{babel}
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{amsmath}
+\usepackage{ae}
+\usepackage{aecompl}
+\usepackage[dvips]{graphicx}
+\graphicspath{{./img/}}
+\usepackage{color}
+\usepackage{pstricks}
+\usepackage{pst-node}
+\usepackage{rotating}
+
+\setlength{\headheight}{0mm} \setlength{\headsep}{0mm}
+\setlength{\topskip}{-10mm} \setlength{\textwidth}{17cm}
+\setlength{\oddsidemargin}{-10mm}
+\setlength{\evensidemargin}{-10mm} \setlength{\topmargin}{-1cm}
+\setlength{\textheight}{26cm} \setlength{\headsep}{0cm}
+
+\begin{document}
+
+% header
+\begin{center}
+ {\LARGE {\bf Molecular dynamics simulation study
+ of the silicon carbide precipitation process}\\}
+ \vspace{16pt}
+ \textsc{\Large \underline{F. Zirkelbach}$^1$, J. K. N. Lindner$^1$,
+ K. Nordlund$^2$, B. Stritzker$^1$}\\
+ \vspace{16pt}
+ $^1$ Experimentalphysik IV, Institut f"ur Physik, Universit"at Augsburg,\\
+ Universit"atsstr. 1, D-86135 Augsburg, Germany\\
+ \vspace{16pt}
+ $^2$ Accelerator Laboratory, Department of Physical Sciences,
+ University of Helsinki,\\
+ Pietari Kalmink. 2, 00014 Helsinki, Finland\\
+\end{center}
+
+\vspace{24pt}
+
+\section*{Abstract}
+The precipitation process of silicon carbide in heavily carbon doped silicon is not yet understood for the most part.
+High resolution transmission electron microscopy indicates that in a first step carbon atoms form $C-Si$ dumbbells on regular $Si$ lattice sites which agglomerate into large clusters.
+In a second step, when the cluster size reaches a radius of a few $nm$, the high interfacial energy due to the $SiC$/$Si$ lattice misfit of almost $20 \, \%$ is overcome and the precipitation occurs.
+A molecular dynamics simulation approach is used to gain information of the precipitation process on the atomic level.
+A newly parametrized Tersoff like bond-order potential is used to model the system appropriately.
+The present work discusses the first results gained by the molecular dynamics simulation.
+
+\end{document}
--- /dev/null
+\pdfoutput=0
+\documentclass[a4paper,11pt]{article}
+\usepackage[activate]{pdfcprot}
+\usepackage{verbatim}
+\usepackage{a4}
+\usepackage{a4wide}
+\usepackage[german]{babel}
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{amsmath}
+\usepackage{ae}
+\usepackage{aecompl}
+\usepackage[dvips]{graphicx}
+\graphicspath{{./img/}}
+\usepackage{color}
+\usepackage{pstricks}
+\usepackage{pst-node}
+\usepackage{rotating}
+
+\setlength{\headheight}{0mm} \setlength{\headsep}{0mm}
+\setlength{\topskip}{-10mm} \setlength{\textwidth}{17cm}
+\setlength{\oddsidemargin}{-10mm}
+\setlength{\evensidemargin}{-10mm} \setlength{\topmargin}{-1cm}
+\setlength{\textheight}{26cm} \setlength{\headsep}{0cm}
+
+\begin{document}
+
+% header
+\begin{center}
+ {\LARGE {\bf Molecular dynamics simulation
+ of defect formation and precipitation
+ in heavily carbon doped silicon.
+ }\\}
+ \vspace{16pt}
+ \textsc{\Large \underline{F. Zirkelbach}$^1$, J. K. N. Lindner$^1$,
+ K. Nordlund$^2$, B. Stritzker$^1$}\\
+ \vspace{16pt}
+ $^1$ Experimentalphysik IV, Institut f"ur Physik, Universit"at Augsburg,\\
+ Universit"atsstr. 1, D-86135 Augsburg, Germany\\
+ \vspace{16pt}
+ $^2$ Accelerator Laboratory, Department of Physical Sciences,
+ University of Helsinki,\\
+ Pietari Kalmink. 2, 00014 Helsinki, Finland\\
+\end{center}
+
+\vspace{24pt}
+
+\section*{Abstract}
+The precipitation process of silicon carbide in heavily carbon doped silicon is not yet understood for the most part.
+High resolution transmission electron microscopy indicates that in a first step carbon atoms form $C-Si$ dumbbells on regular $Si$ lattice sites which agglomerate into large clusters.
+In a second step, when the cluster size reaches a radius of a few $nm$, the high interfacial energy due to the $SiC$/$Si$ lattice misfit of almost $20 \, \%$ is overcome and the precipitation occurs.
+By simulation details of the precipitation process can be obtained on the atomic level.
+A newly parametrized Tersoff like bond-order potential is used to model the system appropriately.
+First results gained by molecular dynamics simulations using this potential are presented.
+The influence of the amount and placement of inserted carbon atoms on the defect formation and structural changes is discussed.
+Furthermore a minimal carbon concentration necessary for precipitation is examined by simulation.
+
+\end{document}
--- /dev/null
+\pdfoutput=0
+\documentclass[a4paper,11pt]{article}
+\usepackage[activate]{pdfcprot}
+\usepackage{verbatim}
+\usepackage{a4}
+\usepackage{a4wide}
+\usepackage[german]{babel}
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{amsmath}
+\usepackage{ae}
+\usepackage{aecompl}
+\usepackage[dvips]{graphicx}
+\graphicspath{{./img/}}
+\usepackage{color}
+\usepackage{pstricks}
+\usepackage{pst-node}
+\usepackage{rotating}
+
+\setlength{\headheight}{0mm} \setlength{\headsep}{0mm}
+\setlength{\topskip}{-10mm} \setlength{\textwidth}{17cm}
+\setlength{\oddsidemargin}{-10mm}
+\setlength{\evensidemargin}{-10mm} \setlength{\topmargin}{-1cm}
+\setlength{\textheight}{26cm} \setlength{\headsep}{0cm}
+
+\begin{document}
+
+% header
+\begin{center}
+ {\LARGE {\bf Molecular dynamics simulation
+ of defect formation and precipitation
+ in heavily carbon doped silicon
+ }\\}
+ \vspace{16pt}
+ \textsc{\Large F. Zirkelbach$^1$, J. K. N. Lindner$^1$,
+ K. Nordlund$^2$, B. Stritzker$^1$}\\
+ \vspace{16pt}
+ $^1$ Experimentalphysik IV, Institut f"ur Physik, Universit"at Augsburg,\\
+ Universit"atsstr. 1, D-86135 Augsburg, Germany\\
+ \vspace{16pt}
+ $^2$ Accelerator Laboratory, Department of Physical Sciences,
+ University of Helsinki,\\
+ Pietari Kalmink. 2, 00014 Helsinki, Finland\\
+ \vspace{16pt}
+ {\scriptsize Corresponding author: Frank Zirkelbach
+ <frank.zirkelbach@physik.uni-augsburg.de>}
+\end{center}
+
+\vspace{24pt}
+
+\section*{Abstract}
+The precipitation process of silicon carbide in heavily carbon doped silicon is not yet understood for the most part.
+High resolution transmission electron microscopy indicates that in a first step carbon atoms form $C-Si$ dumbbells on regular $Si$ lattice sites which agglomerate into large clusters.
+In a second step, when the cluster size reaches a radius of a few $nm$, the high interfacial energy due to the $SiC$/$Si$ lattice misfit of almost $20 \, \%$ is overcome and the precipitation occurs.
+By simulation details of the precipitation process can be obtained on the atomic level.
+A newly parametrized Tersoff like bond-order potential is used to model the system appropriately.
+First results gained by molecular dynamics simulations using this potential are presented.
+The influence of the amount and placement of inserted carbon atoms on the defect formation and structural changes is discussed.
+Furthermore a minimal carbon concentration necessary for precipitation is examined by simulation.
+\\\\
+{\bf Keywords:} Silicon carbide, Nucleation, Molecular dynamics simulation.
+
+\section*{Introduction}
+Understanding the precipitation process of cubic silicon carbide (3C-SiC) in heavily carbon doped silicon (Si) will enable significant technological progress in thin film formation of an important wide band gap semiconductor material.
+On the other hand it will likewise offer perspectives for processes which rely upon prevention of precipitation processes, e.g. for the fabrication of strained silicon.
+
+Epitaxial growth of 3C-SiC films is achieved either by ion implantation or chemical vapour deposition techniques.
+Surface effects dominate the CVD process while for the implantation process carbon is introduced into bulk silicon.
+This work tries to realize conditions which hold for the ion implantation process.
+
+First of all a suitable model is considered.
+After that the realization by simulation is discussed.
+First results gained by simulation are presented in a next step.
+Finally these results are outlined and conclusions are infered.
+
+\section*{Supposed conversion mechanism}
+Silicon (Si) nucleates in diamond structure.
+Contains of two fcc lattices, on displaced one quarter of volume diagonal compared to the first.
+3C-SiC nucleates in zincblende structure where the shifted fcc lattice sites are composed of carbon atoms.
+The length of four lattice constants of Si is approximately equal to the length of five 3C-SiC lattice constants ($4a_{Si}\approx 5a_{3C-SiC}$), which means that there is a lattice misfit of almost 20\%.
+Due to this the silicon density of 3C-SiC is slightly lower than the one of silicon.
+
+There is a supposed conversion mechanism of heavily carbon doped Si into SiC.
+Fig. 1 schematically displays the mechanism.
+As indicated by high resolution transmission microscopy \ref{hrem_ind} introduced carbon atoms (red dots) form C-Si dumbbells on regular Si (black dots) lattice sites.
+The dumbbells agglomerate int large clusters, so called embryos.
+Finally, when the cluster size reaches a critical radius of 2 to 4 nm, the high interfacial energy due to the lattice misfit is overcome and the precipitation occurs.
+Due to the slightly lower silicon density of 3C-SiC residual silicon atoms exist.
+The residual atoms will most probably end up as self interstitials in the silicon matrix since there is more space than in 3C-SiC.
+
+Taking this into account, it is important to understand both, the configuration and dynamics of carbon interstitials in silicon and silicon self interstitials.
+Additionaly the influence of interstitials on atomic diffusion is investigated.
+
+\section*{Simulation}
+A molecular dynamics simulation approach is used to examine the steps involved in the precipitation process.
+For integrating the equations of motion the velocity verlet algorithm \ref{} with a timestep of 1 fs is deployed.
+The interaction of the silicon and carbon atoms is realized by a newly parametrized Tersoff like bond order potential \ref{}.
+Since temperature and pressure of the system is kept constant in experiment the isothermal-isobaric NPT ensemble is chosen for the simulation.
+Coupling to the heat bath is achieved by the Berendsen thermostat \ref{} with a time constant $\tau_T=100\, fs$.
+The pressure is scaled by the Berendsen barostat \ref{} again using a timeconstant of $\tau_P=100\, fs$ and a bulk modulus of $100\, GPa$ for silicon.
+To exclude surface effects periodic boundary conditions are applied.
+\\\\
+To investigate the intesrtitial configurations of C and Si in Si, a simulation volume of 9 silicon unit cells is each direction used.
+The temperature is set to $T=0\, K$.
+The insertion positions are illustrated in Fig 2.
+In separated simulation runs a carbon and a silicon atom respectively is inserted at the tetrahedral $(0,0,0)$ (red), hexagonal $(-1/8,-1/8,1/8)$ (green), supposed dumbbell $(-1/8,-1/8)$ (purple) and at random positions (in units of the silicon lattice constant) where the origin is located in the middle of the unit cell.
+In order to avoid too high kinetic energies in the case of the dumbbell configuration the nearest silicon neighbour atom is shifted to $(-1/4,-1/4,-1/4)$ (dashed border).
+The introduced kinetic energy is scaled out by a relaxation time of $2\, ps$.
+\\\\
+The same volume is used to investigate diffusion.
+A certain amount of silicon atoms are inserted at random positions in a centered region of $11 \, \AA$ in each direction.
+The insertion is taking place step by step in order to maintain a constant system temeprature.
+Finally a carbon atom is inserted at a random position in the unit cell located in the middle of the simulation volume.
+The simulation continues for another $30\, ps$.
+\\\\
+Simulation runs /unt
+
+
+
+\section*{Results}
+
+\section*{Conclusion}
+
+\end{document}
projects / lectures / latex.git / commitdiff