pair correlation of amorphous sic, md result analyze}
}
+@Article{batra87,
+ title = {SiC/Si heteroepitaxial growth},
+ author = {M. Kitabatake},
+ journal = {Thin Solid Films},
+ volume = {369},
+ pages = {257--264},
+ numpages = {8},
+ year = {2000},
+ notes = {md simulation, sic si heteroepitaxy, mbe}
+}
+
% tight binding
@Article{tang97,
notes = {strained silicon, carbon supersaturation}
}
+% sic formation mechanism
+
+@article{werner97,
+ author = {P. Werner and S. Eichler and G. Mariani and R. K\"{o}gler and W. Skorupa},
+ title = {Investigation of C[sub x]Si defects in C implanted silicon by transmission electron microscopy},
+ publisher = {AIP},
+ year = {1997},
+ journal = {Applied Physics Letters},
+ volume = {70},
+ number = {2},
+ pages = {252-254},
+ keywords = {silicon; ion implantation; carbon; crystal defects;
+ transmission electron microscopy; annealing;
+ positron annihilation; secondary ion mass spectroscopy;
+ buried layers; precipitation},
+ url = {http://link.aip.org/link/?APL/70/252/1},
+ doi = {10.1063/1.118381},
+ notes = {si-c complexes, agglomerate, sic in si matrix, sic precipitate}
+}
+
+@article{strane94,
+ author = {J. W. Strane and H. J. Stein and S. R. Lee and S. T. Picraux and
+ J. K. Watanabe and J. W. Mayer},
+ collaboration = {},
+ title = {Precipitation and relaxation in strained
+ Si[sub 1 - y]C[sub y]/Si heterostructures},
+ publisher = {AIP},
+ year = {1994},
+ journal = {Journal of Applied Physics},
+ volume = {76},
+ number = {6},
+ pages = {3656-3668},
+ keywords = {SILICON CARBIDES; SILICON; PRECIPITATION; STRAINS},
+ url = {http://link.aip.org/link/?JAP/76/3656/1},
+ doi = {10.1063/1.357429},
+ notes = {strained si-c to 3c-sic, carbon nucleation + refs}
+}
+
% properties sic
@Article{edgar92,
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
+\usepackage{latexsym}
\usepackage{ae}
\usepackage{aecompl}
\usepackage[dvips]{graphicx}
\setlength{\evensidemargin}{-10mm} \setlength{\topmargin}{-1cm}
\setlength{\textheight}{26cm} \setlength{\headsep}{0cm}
+%\linespread{2.0}
+
\selectlanguage{english}
\begin{document}
The precipitation process of silicon carbide in heavily carbon doped silicon is not yet fully understood.
High resolution transmission electron microscopy observations suggest 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.
+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.
\\\\
-{\bf Keywords:} Silicon, Carbon, Silicon carbide, Nucleation, Diffusion, Defect formation.
+{\bf Keywords:} Silicon, carbon, silicon carbide, nucleation, defect formation,
+ molecular dynamics simulations
\section*{Introduction}
-Understanding the precipitation process of cubic silicon carbide (3C-SiC) in heavily carbon doped silicon 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 events, e.g. the fabrication of strained silicon.
+Understanding the precipitation process of cubic silicon carbide (3C-SiC) in heavily carbon doped silicon will enable significant technological progress in thin film formation of the important wide band gap semiconductor material SiC \cite{edgar92}.
+On the other hand it will likewise offer perspectives for processes which rely upon prevention of precipitation events, e.g. the fabrication of strained, pseudomorphic $\text{Si}_{1-y}\text{C}_y$ heterostructures \cite{}.
-Epitaxial growth of 3C-SiC films is achieved either by ion implantation or chemical vapour deposition (CVD) techniques.
-While CVD is governed by surface effects carbon is directly introduced into bulk silicon for the implantation process.
-In the present work the simulation runs try to realize conditions which hold for the ion implantation process.
+Epitaxial growth of 3C-SiC films is achieved either by ion beam synthesis (IBS) \cite{lindner02} and chemical vapour deposition (CVD) or molecular beam epitaxy (MBE) techniques.
+While in CVD and MBE surface effects need to be takein into account, SiC formation during IBS takes place in the bulk of the Si crystal.
+In the present work the simulation tries to realize conditions which hold for the ion implantation process.
First of all a picture of the supposed precipitation event is presented.
Afterwards the applied simulation sequences are discussed.
Finally first results gained by simulation are presented.
\section*{Supposed conversion mechanism}
-Silicon nucleates in diamond structure.
-This structure is composed of two fcc lattices which are displaced by one quarter of the volume diagonal.
-3C-SiC nucleates in zincblende structure in which atoms of one fcc lattice are substituted by carbon atoms.
-The length of four lattice constants of Si is approximately equal to the length of five 3C-SiC lattice constants ($4a_{\text{Si}}\approx 5a_{\text{3C-SiC}}$) resultings in a lattice misfit of almost 20\%.
-Due to this the silicon density of 3C-SiC is slightly lower than the one of Si.
-
-\begin{figure}[!h]
- \begin{center}
- \begin{minipage}{5.5cm}
- \includegraphics[width=5cm]{sic_prec_seq_01.eps}
- \end{minipage}
- \begin{minipage}{5.5cm}
- \includegraphics[width=5cm]{sic_prec_seq_02.eps}
- \end{minipage}
- \begin{minipage}{5.5cm}
- \includegraphics[width=5cm]{sic_prec_seq_03.eps}
- \end{minipage}
- \caption{Schematic of the supposed conversion mechanism of highly C (${\color{red}\bullet}$) doped Si (${\color{black}\bullet}$) into SiC ($_{\color{black}\bullet}^{{\color{red}\bullet}}$) and residual Si atoms ($\circ$). The figure shows the dumbbell formation (left), the agglomeration into clusters (middle) and the situation after precipitation (right).}
- \end{center}
-\end{figure}
-There is a supposed conversion mechanism of heavily carbon doped Si into SiC \cite{}.
-Fig. 1 schematically displays the mechanism.
-As indicated by high resolution transmission microscopy \cite{} introduced carbon atoms (${\color{red}\bullet}$) form C-Si (${\color{black}\bullet}\,{\color{red}\bullet}$) dumbbells on regular Si (${\color{black}\bullet}$) 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 ($_{\color{black}\bullet}^{{\color{red}\bullet}}$) residual silicon atoms ($\circ$) 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.
+Silicon has diamond structure and thus is composed of two fcc lattices which are displaced by one quarter of the volume diagonal.
+3C-SiC grows in zincblende structure, i.e. is also composed of two fcc lattices out of which one is occupied by Si the other by C atoms.
+The length of four lattice constants of Si is approximately equal to the length of five 3C-SiC lattice constants ($4a_{\text{Si}}\approx 5a_{\text{3C-SiC}}$) resulting in a lattice misfit of almost 20\%.
+Due to this the silicon atomic density of 3C-SiC is slightly lower than the one of pure Si.
+
+%\begin{figure}[!h]
+% \begin{center}
+% \begin{minipage}{5.5cm}
+% \includegraphics[width=5cm]{sic_prec_seq_01_s.eps}
+% \end{minipage}
+% \begin{minipage}{5.5cm}
+% \includegraphics[width=5cm]{sic_prec_seq_02_s.eps}
+% \end{minipage}
+% \begin{minipage}{5.5cm}
+% \includegraphics[width=5cm]{sic_prec_seq_03_s.eps}
+% \end{minipage}
+% \caption{Schematic of the supposed conversion mechanism of highly C (${\color{red}\Box}$) doped Si (${\color{black}\bullet}$) into SiC ($_{\color{black}\bullet}^{{\color{red}\Box}}$) and residual Si atoms ($\circ$). The figure shows the dumbbell formation (left), the agglomeration into clusters (middle) and the situation after precipitation (right).}
+% \end{center}
+%\end{figure}
+There is a supposed conversion mechanism of heavily carbon doped Si into SiC \cite{werner97}.
+As concluded by high resolution transmission electron microscopy \cite{werber97,} introduced carbon atoms form C-Si dumbbells on regular Si lattice sites.
+The dumbbells agglomerate into large clusters, called embryos.
+Finally, when the cluster size reaches a critical radius of 2 to 4 nm, the high interfacial energy due to the 3C-SiC/Si lattice misfit is overcome and precipitation occurs.
+Due to the slightly lower silicon density of 3C-SiC excessive silicon atoms exist which will most probably end up as self-interstitials in the silicon matrix since there is more space than in 3C-SiC.
+
+Thus, in addition to the precipitation event itself, knowledge of C and Si interstitials in Si are of great interest in order to investigate the precipitation of heavily C doped Si into SiC.
+%Additionaly the influence of interstitials on atomic diffusion is investigated.
\section*{Simulation sequences}
A molecular dynamics simulation approach is used to examine the steps involved in the precipitation process.
\begin{figure}[!h]
\begin{center}
- \includegraphics[width=8cm]{unit_cell.eps}
- \caption{Insertion positions for the tetrahedral (${\color{red}\bullet}$), hexagonal (${\color{green}\bullet}$) and <110> dumbbell (${\color{magenta}\bullet}$) interstitial configuration.}
+ \includegraphics[width=8cm]{unit_cell_s.eps}
+ \caption{Insertion positions for the tetrahedral (${\color{red}\triangleleft}$), hexagonal (${\color{green}\triangleright}$) and <110> dumbbell (${\color{magenta}\Box}$) interstitial configuration.}
\end{center}
\end{figure}
-To investigate the intesrtitial configurations of C and Si in Si, a simulation volume of 9 silicon unit cells in each direction is used.
+To investigate the interstitial configurations of C and Si in Si, a simulation volume of 9 silicon unit cells in each direction is 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 $(0,0,0)$ (${\color{red}\bullet}$), hexagonal $(-1/8,-1/8,1/8)$ (${\color{green}\bullet}$), supposed dumbbell $(-1/8,-1/8,-1/4)$ (${\color{magenta}\bullet}$) and at random positions (in units of the silicon lattice constant) where the origin is located in the middle of the unit cell.
+In separated simulation runs a carbon and a silicon atom respectively is inserted at the tetrahedral $(0,0,0)$ (${\color{red}\triangleleft}$), hexagonal $(-1/8,-1/8,1/8)$ (${\color{green}\triangleright}$), supposed dumbbell $(-1/8,-1/8,-1/4)$ (${\color{magenta}\bullet}$) and at random positions (in units of the silicon lattice constant) where the origin is located in the centre of the unit cell.
In order to avoid too high potential energies in the case of the dumbbell configuration the nearest silicon neighbour atom is shifted to $(-3/8,-3/8,-1/4)$ ($\circ$).
The energy introduced into the system is scaled out within a relaxation phase of $2\, ps$.
The same volume is used to investigate diffusion.
Different amounts of silicon atoms are inserted at random positions within a centered region of $11 \,\textrm{\AA}$ in each direction.
-Insertion events are carried out step by step maintaining a constant system temeprature.
+Insertion events are carried out step by step maintaining a constant system temperature of $450\, ^{\circ} \textrm{C}$.
Finally a single carbon atom is inserted at a random position within the unit cell located in the middle of the simulation volume.
The simulation is proceeded for another $30\, ps$.
For the simulations aiming to reproduce a precipitation process the volume is 31 silicon lattice constants in each direction.
The system temperature is set to $450\, ^{\circ} \textrm{C}$.
-$6000$ carbon atoms (the amount necessary to form a minimal 3C-SiC precipitate) are consecutively inserted in a way to keep constant the system temperature.
+$6000$ carbon atoms (the amount necessary to form a 3C-SiC precipitate with a radius of 3 nm) are consecutively inserted in a way to keep constant the system temperature.
Precipitation is examined for three insertion volumes which differ in size.
The whole simulation volume, the volume corresponding to the size of a minimal SiC precipitate and the volume containing the amount of silicon necessary for the formation of such a minimal precipitate.
Following the insertion procedure the system is cooled down to $20\, ^{\circ} \textrm{C}$.
\section*{Results}
-The tetrahedral and the <110> dumbbell self interstitial configurations can be reproduced as observed in \cite{albe_sic_pot}.
+The tetrahedral and the <110> dumbbell self-interstitial configurations can be reproduced as observed in \cite{albe_sic_pot}.
The formation energies are $3.4\, eV$ and $4.4\, eV$ respectively.
However the hexagonal one is not stable opposed to what is presented in \cite{albe_sic_pot}.
The atom moves towards an energetically more favorable position very close to the tetrahedral one but slightly displaced along the three coordinate axes.
\caption{Diffusion coefficients of a single carbon atom for different amount of Si selft interstitials}
\end{center}
\end{figure}
-The influence of Si self interstitials on the diffusion of a single carbon atom is displayed in Fig. 3.
-Diffusion coefficients for different amount of Si self interstitials are shown.
+The influence of Si self-interstitials on the diffusion of a single carbon atom is displayed in Fig. 3.
+Diffusion coefficients for different amount of Si self-interstitials are shown.
A slight increase is first observed in the case of 30 interstitial atoms.
Further increasing the amount of interstitials leads to a tremendous decay of the diffusion coeeficient.
Generally there is no long range diffusion of the carbon atom for a temperature of $450\, ^{\circ} \textrm{C}$.
The supposed conversion mechanism of heavily carbon doped silicon into silicon carbide is presented.
Molecular dynamics simulation sequences to investigate interstitial configurations, the influence of interstitials on the atomic diffusion and the precipitation of SiC are proposed.
The <100> C-Si dumbbel is reproducable by simulation and is the energetically most favorable configuration.
-The influence of silicon self interstitials on the diffusion of a single carbon atom is demonstrated.
+The influence of silicon self-interstitials on the diffusion of a single carbon atom is demonstrated.
Two competing bond formations, either Si-C or C-C, seem to coexist, where the strength of either of them depends on the size of the region in which carbon is introduced.
\bibliography{../../bibdb/bibdb}
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