--- /dev/null
+%
+% bibliography database
+%
+
+% molecular dynamics: basics / potential
+
+@article{albe_sic_pot,
+ author = {Paul Erhart and Karsten Albe},
+ title = {Analytical potential for atomistic simulations of silicon, carbon,
+ and silicon carbide},
+ publisher = {APS},
+ year = {2005},
+ journal = {Phys. Rev. B},
+ volume = {71},
+ number = {3},
+ eid = {035211},
+ numpages = {14},
+ pages = {035211},
+ notes = {alble reparametrization, analytical bond oder potential (ABOP)},
+ keywords = {silicon; elemental semiconductors; carbon; silicon compounds;
+ wide band gap semiconductors; elasticity; enthalpy;
+ point defects; crystallographic shear; atomic forces},
+ url = {http://link.aps.org/abstract/PRB/v71/e035211},
+ doi = {10.1103/PhysRevB.71.035211}
+}
+
+@Article{albe2002,
+ title = {Modeling the metal-semiconductor interaction:
+ Analytical bond-order potential for platinum-carbon},
+ author = {Albe, Karsten and Nordlund, Kai and Averback, Robert S.},
+ journal = {Phys. Rev. B},
+ volume = {65},
+ number = {19},
+ pages = {195124},
+ numpages = {11},
+ year = {2002},
+ month = {May},
+ doi = {10.1103/PhysRevB.65.195124},
+ publisher = {American Physical Society},
+ notes = {derivation of albe bond order formalism},
+}
+
+@Article{koster2002,
+ title = {Stress relaxation in $a-Si$ induced by ion bombardment},
+ author = {M. Koster, H. M. Urbassek},
+ journal = {Phys. Rev. B},
+ volume = {62},
+ number = {16},
+ pages = {11219--11224},
+ numpages = {5},
+ year = {2000},
+ month = {Oct},
+ doi = {10.1103/PhysRevB.62.11219},
+ publisher = {American Physical Society},
+ notes = {virial derivation for 3-body tersoff potential}
+}
+
+@Article{breadmore99,
+ title = {Direct simulation of ion-beam-induced stressing
+ and amorphization of silicon},
+ author = {K. M. Beardmore, N. Gr\o{}nbech-Jensen},
+ journal = {Phys. Rev. B},
+ volume = {60},
+ number = {18},
+ pages = {12610--12616},
+ numpages = {6},
+ year = {1999},
+ month = {Nov},
+ doi = {10.1103/PhysRevB.60.12610},
+ publisher = {American Physical Society},
+ notes = {virial derivation for 3-body tersoff potential}
+}
+
+@Article{verlet67,
+ title = {Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules},
+ author = {Verlet, Loup },
+ journal = {Phys. Rev.},
+ volume = {159},
+ number = {1},
+ pages = {98},
+ year = {1967},
+ month = {Jul},
+ doi = {10.1103/PhysRev.159.98},
+ publisher = {American Physical Society},
+ notes = {velocity verlet integration algorithm equation of motion}
+}
+
+@article{berendsen:3684,
+ author = {H. J. C. Berendsen and J. P. M. Postma and W. F. van Gunsteren
+ and A. DiNola and J. R. Haak},
+ collaboration = {},
+ title = {Molecular dynamics with coupling to an external bath},
+ publisher = {AIP},
+ year = {1984},
+ journal = {The Journal of Chemical Physics},
+ volume = {81},
+ number = {8},
+ pages = {3684-3690},
+ keywords = {MOLECULAR DYNAMICS CALCULATION; TRANSPORT THEORY;
+ COMPUTERIZED SIMULATION; LIQUIDS; STRUCTURE FACTORS},
+ url = {http://link.aip.org/link/?JCP/81/3684/1},
+ doi = {10.1063/1.448118},
+ notes = {berendsen thermostat barostat}
+}
+
+% molecular dynamics: applications
+
+@Article{batra87,
+ title = {Molecular-dynamics study of self-interstitials in silicon},
+ author = {Inder P. Batra, Farid F. Abraham, S. Ciraci},
+ journal = {Phys. Rev. B},
+ volume = {35},
+ number = {18},
+ pages = {9552--9558},
+ numpages = {6},
+ year = {1987},
+ month = {Jun},
+ doi = {10.1103/PhysRevB.35.9552},
+ publisher = {American Physical Society},
+ notes = {selft-interstitials in silicon, stillinger-weber,
+ calculation of defect formation energy, defect interstitial types}
+}
+
+@Article{schober89,
+ title = {Extended interstitials in silicon and germanium},
+ author = {H. R. Schober},
+ journal = {Phys. Rev. B},
+ volume = {39},
+ number = {17},
+ pages = {13013--13015},
+ numpages = {2},
+ year = {1989},
+ month = {Jun},
+ doi = {10.1103/PhysRevB.39.13013},
+ publisher = {American Physical Society},
+ notes = {stillinger-weber silicon 110 stable and metastable dumbbell
+ configuration}
+}
+
+@Article{gao02,
+ title = {Cascade overlap and amorphization in $3C-SiC:$
+ Defect accumulation, topological features, and disordering},
+ author = {Gao, F. and Weber, W. J.},
+ journal = {Phys. Rev. B},
+ volume = {66},
+ number = {2},
+ pages = {024106},
+ numpages = {10},
+ year = {2002},
+ month = {Jul},
+ doi = {10.1103/PhysRevB.66.024106},
+ publisher = {American Physical Society},
+ note = {sic intro, si cascade in 3c-sic, amorphization, tersoff modified,
+ 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,
+ title = {Intrinsic point defects in crystalline silicon:
+ Tight-binding molecular dynamics studiesof self-diffusion,
+ interstitial-vacancy recombination, and formation volumes},
+ author = {M. Tang, L. Colombo, J. Zhu, T. Diaz de la Rubia},
+ journal = {Phys. Rev. B},
+ volume = {55},
+ number = {21},
+ pages = {14279--14289},
+ numpages = {10},
+ year = {1997},
+ month = {Jun},
+ doi = {10.1103/PhysRevB.55.14279},
+ publisher = {American Physical Society},
+ notes = {si self interstitial, diffusion, tbmd}
+}
+
+@Article{tang97,
+ title = {Tight-binding theory of native point defects in silicon},
+ author = {L. Colombo},
+ journal = {Annu. Rev. Mater. Res.},
+ volume = {32},
+ pages = {271--295},
+ numpages = {25},
+ year = {2002},
+ doi = {10.1146/annurev.matsci.32.111601.103036},
+ publisher = {Annual Reviews},
+ notes = {si self interstitial, tbmd, virial stress}
+}
+
+% mixed
+
+@Article{gao2001,
+ title = {Ab initio and empirical-potential studies of defect properties
+ in $3C-SiC$ },
+ author = {F. Gao, E. J. Bylaska, W. J. Weber, L. R. Corrales},
+ journal = {Phys. Rev. B},
+ volume = {64},
+ number = {24},
+ pages = {245208},
+ numpages = {7},
+ year = {2001},
+ month = {Dec},
+ doi = {10.1103/PhysRevB.64.245208},
+ publisher = {American Physical Society},
+ notes = {defects in 3c-sic}
+}
+
+% ab initio
+
+@Article{leung99,
+ title = {Calculations of Silicon Self-Interstitial Defects},
+ author = {Leung, W.-K. and Needs, R. J. and Rajagopal, G. and
+ Itoh, S. and Ihara, S. },
+ journal = {Phys. Rev. Lett.},
+ volume = {83},
+ number = {12},
+ pages = {2351--2354},
+ numpages = {3},
+ year = {1999},
+ month = {Sep},
+ doi = {10.1103/PhysRevLett.83.2351},
+ publisher = {American Physical Society},
+ notes = {nice images of the defects}
+}
+
+@Article{PhysRevB.50.7439,
+ title = {Identification of the migration path of interstitial carbon
+ in silicon},
+ author = {R. B. Capazd, A Dal Pino, J. D. Joannopoulos},
+ journal = {Phys. Rev. B},
+ volume = {50},
+ number = {11},
+ pages = {7439--7442},
+ numpages = {3},
+ year = {1994},
+ month = {Sep},
+ doi = {10.1103/PhysRevB.50.7439},
+ publisher = {American Physical Society},
+ notes = {carbon interstitial migration path shown, 001 c-si dumbbell}
+}
+
+% experimental stuff - interstitials
+
+@Article{watkins76,
+ title = {EPR Observation of the Isolated Interstitial Carbon Atom in Silicon},
+ author = {G. D. Watkins and K. L. Brower},
+ journal = {Phys. Rev. Lett.},
+ volume = {36},
+ number = {22},
+ pages = {1329--1332},
+ numpages = {3},
+ year = {1976},
+ month = {May},
+ doi = {10.1103/PhysRevLett.36.1329},
+ publisher = {American Physical Society},
+ notes = {epr observations of 100 interstitial carbon atom in silicon}
+}
+
+@Article{song90,
+ title = {EPR identification of the single-acceptor state of interstitial carbon in silicon},
+ author = {L. W. Song, G. D. Watkins},
+ journal = {Phys. Rev. B},
+ volume = {42},
+ number = {9},
+ pages = {5759--5764},
+ numpages = {5},
+ year = {1990},
+ month = {Sep},
+ doi = {10.1103/PhysRevB.42.5759},
+ publisher = {American Physical Society}
+}
+
+% experimental stuff - strained silicon
+
+@Article{strane96,
+ title = {Carbon incorporation into Si at high concentrations
+ by ion implantation and solid phase epitaxy},
+ author = {J. W. Strane and S. R. Lee and H. J. Stein and S. T. Picraux and
+ J. K. Watanabe and J. W. Mayer},
+ journal = {J. Appl. Phys.},
+ volume = {79},
+ pages = {637},
+ year = {1996},
+ month = {January},
+ doi = {10.1063/1.360806},
+ 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,
+ title = {Prospects for device implementation of wide band gap semiconductors},
+ author = {J. H. Edgar},
+ journal = {J. Mater. Res.},
+ volume = {7},
+ pages = {235},
+ year = {1992},
+ month = {January},
+ doi = {10.1557/JMR.1992.0235},
+ notes = {properties wide band gap semiconductor, sic polytypes}
+}
+
+% my own publications
+
+@article{zirkelbach2007,
+ title = {Monte Carlo simulation study of a selforganisation process
+ leading to ordered precipitate structures},
+ author = {F. Zirkelbach, M. H"aberlen, J.K.N. Lindner, B. Stritzker},
+ journal = {Nucl. Instr. and Meth. B},
+ volume = {257},
+ number = {1--2},
+ pages = {75--79},
+ numpages = {5},
+ year = {2007},
+ month = {Apr},
+ doi = {doi:10.1016/j.nimb.2006.12.118},
+ publisher = {ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}
+}
+
+@article{zirkelbach2006,
+ title = {Monte-Carlo simulation study of the self-organization of nanometric
+ amorphous precipitates in regular arrays during ion irradiation},
+ author = {F. Zirkelbach, M. H"aberlen, J.K.N. Lindner, B. Stritzker},
+ journal = {Nucl. Instr. and Meth. B},
+ volume = {242},
+ number = {1--2},
+ pages = {679--682},
+ numpages = {4},
+ year = {2006},
+ month = {Jan},
+ doi = {doi:10.1016/j.nimb.2005.08.162},
+ publisher = {ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}
+}
+
+@article{zirkelbach2005,
+ title = {Modelling of a selforganization process leading to periodic arrays
+ of nanometric amorphous precipitates by ion irradiation},
+ author = {F. Zirkelbach, M. H"aberlen, J.K.N. Lindner, B. Stritzker},
+ journal = {Comp. Mater. Sci.},
+ volume = {33},
+ number = {1--3},
+ pages = {310--316},
+ numpages = {7},
+ year = {2005},
+ month = {Apr},
+ doi = {doi:10.1016/j.commatsci.2004.12.016},
+ publisher = {ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}
+}
+
+% the one of my boss
+
+@Article{lindner02,
+ title = {High-dose carbon implantations into silicon:
+ fundamental studies for new technological tricks},
+ author = {J. K. N. Lindner},
+ journal = {Appl. Phys. A},
+ volume = {77},
+ pages = {27--38},
+ year = {2003},
+ doi = {10.1007/s00339-002-2062-8},
+ notes = {ibs, burried sic layers}
+}
+
+
+++ /dev/null
-%
-% bibliography database
-%
-
-% molecular dynamics: basics / potential
-
-@article{albe_sic_pot,
- author = {Paul Erhart and Karsten Albe},
- title = {Analytical potential for atomistic simulations of silicon, carbon,
- and silicon carbide},
- publisher = {APS},
- year = {2005},
- journal = {Phys. Rev. B},
- volume = {71},
- number = {3},
- eid = {035211},
- numpages = {14},
- pages = {035211},
- notes = {alble reparametrization, analytical bond oder potential (ABOP)}
- keywords = {silicon; elemental semiconductors; carbon; silicon compounds;
- wide band gap semiconductors; elasticity; enthalpy;
- point defects; crystallographic shear; atomic forces},
- url = {http://link.aps.org/abstract/PRB/v71/e035211},
- doi = {10.1103/PhysRevB.71.035211}
-}
-
-@Article{albe2002,
- title = {Modeling the metal-semiconductor interaction:
- Analytical bond-order potential for platinum-carbon},
- author = {Albe, Karsten and Nordlund, Kai and Averback, Robert S.},
- journal = {Phys. Rev. B},
- volume = {65},
- number = {19},
- pages = {195124},
- numpages = {11},
- year = {2002},
- month = {May},
- doi = {10.1103/PhysRevB.65.195124},
- publisher = {American Physical Society}
- notes = {derivation of albe bond order formalism}
-}
-
-@Article{koster2002,
- title = {Stress relaxation in $a-Si$ induced by ion bombardment},
- author = {M. Koster, H. M. Urbassek},
- journal = {Phys. Rev. B},
- volume = {62},
- number = {16},
- pages = {11219--11224},
- numpages = {5},
- year = {2000},
- month = {Oct},
- doi = {10.1103/PhysRevB.62.11219},
- publisher = {American Physical Society}
- notes = {virial derivation for 3-body tersoff potential}
-}
-
-@Article{breadmore99,
- title = {Direct simulation of ion-beam-induced stressing
- and amorphization of silicon},
- author = {K. M. Beardmore, N. Gr\o{}nbech-Jensen},
- journal = {Phys. Rev. B},
- volume = {60},
- number = {18},
- pages = {12610--12616},
- numpages = {6},
- year = {1999},
- month = {Nov},
- doi = {10.1103/PhysRevB.60.12610},
- publisher = {American Physical Society}
- notes = {virial derivation for 3-body tersoff potential}
-}
-
-% molecular dynamics: applications
-
-@Article{batra87,
- title = {Molecular-dynamics study of self-interstitials in silicon},
- author = {Inder P. Batra, Farid F. Abraham, S. Ciraci},
- journal = {Phys. Rev. B},
- volume = {35},
- number = {18},
- pages = {9552--9558},
- numpages = {6},
- year = {1987},
- month = {Jun},
- doi = {10.1103/PhysRevB.35.9552},
- publisher = {American Physical Society}
- notes = {selft-interstitials in silicon, stillinger-weber,
- calculation of defect formation energy, defect interstitial types}
-}
-
-@Article{schober89,
- title = {Extended interstitials in silicon and germanium},
- author = {H. R. Schober},
- journal = {Phys. Rev. B},
- volume = {39},
- number = {17},
- pages = {13013--13015},
- numpages = {2},
- year = {1989},
- month = {Jun},
- doi = {10.1103/PhysRevB.39.13013},
- publisher = {American Physical Society}
- notes = {stillinger-weber silicon 110 stable and metastable dumbbell
- configuration}
-}
-
-% tight binding
-
-@Article{tang97,
- title = {Intrinsic point defects in crystalline silicon:
- Tight-binding molecular dynamics studiesof self-diffusion,
- interstitial-vacancy recombination, and formation volumes},
- author = {M. Tang, L. Colombo, J. Zhu, T. Diaz de la Rubia},
- journal = {Phys. Rev. B},
- volume = {55},
- number = {21},
- pages = {14279--14289},
- numpages = {10},
- year = {1997},
- month = {Jun},
- doi = {10.1103/PhysRevB.55.14279},
- publisher = {American Physical Society}
- notes = {si self interstitial, diffusion, tbmd}
-}
-
-@Article{tang97,
- title = {Tight-binding theory of native point defects in silicon}
- author = {L. Colombo},
- journal = {Annu. Rev. Mater. Res.},
- volume = {32},
- pages = {271--295},
- numpages = {25},
- year = {2002},
- doi = {10.1146/annurev.matsci.32.111601.103036},
- publisher = {Annual Reviews}
- notes = {si self interstitial, tbmd, virial stress}
-}
-
-% mixed
-
-@Article{gao2001,
- title = {Ab initio and empirical-potential studies of defect properties
- in $3C-SiC$ },
- author = {F. Gao, E. J. Bylaska, W. J. Weber, L. R. Corrales},
- journal = {Phys. Rev. B},
- volume = {64},
- number = {24},
- pages = {245208},
- numpages = {7},
- year = {2001},
- month = {Dec},
- doi = {10.1103/PhysRevB.64.245208},
- publisher = {American Physical Society}
- notes = {defects in 3c-sic}
-}
-
-% ab initio
-
-@Article{leung99,
- title = {Calculations of Silicon Self-Interstitial Defects},
- author = {Leung, W.-K. and Needs, R. J. and Rajagopal, G. and
- Itoh, S. and Ihara, S. },
- journal = {Phys. Rev. Lett.},
- volume = {83},
- number = {12},
- pages = {2351--2354},
- numpages = {3},
- year = {1999},
- month = {Sep},
- doi = {10.1103/PhysRevLett.83.2351},
- publisher = {American Physical Society}
- notes = {nice images of the defects}
-}
-
-% experimental stuff
-
-@Article{watkins76,
- title = {EPR Observation of the Isolated Interstitial Carbon Atom in Silicon},
- author = {Watkins, G. D. and Brower, K. L.},
- journal = {Phys. Rev. Lett.},
- volume = {36},
- number = {22},
- pages = {1329--1332},
- numpages = {3},
- year = {1976},
- month = {May},
- doi = {10.1103/PhysRevLett.36.1329},
- publisher = {American Physical Society}
- notes = {epr observations of 100 interstitial carbon atom in silicon}
-}
-
-% my own publications
-
-@article{zirkelbach2007,
- title = {Monte Carlo simulation study of a selforganisation process
- leading to ordered precipitate structures},
- author = {F. Zirkelbach, M. H"aberlen, J.K.N. Lindner, B. Stritzker},
- journal = {Nucl. instr. and Meth. B},
- volume = {257},
- number = {1--2},
- pages = {75--79},
- numpages = {5},
- year = {2007},
- month = {Apr},
- doi = {doi:10.1016/j.nimb.2006.12.118},
- publisher = {ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}
-}
-
-@article{zirkelbach2006,
- title = {Monte-Carlo simulation study of the self-organization of nanometric
- amorphous precipitates in regular arrays during ion irradiation},
- author = {F. Zirkelbach, M. H"aberlen, J.K.N. Lindner, B. Stritzker},
- journal = {Nucl. instr. and Meth. B},
- volume = {242},
- number = {1--2},
- pages = {679--682},
- numpages = {4},
- year = {2006},
- month = {Jan},
- doi = {doi:10.1016/j.nimb.2005.08.162},
- publisher = {ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}
-}
-
-@article{zirkelbach2005,
- title = {Modelling of a selforganization process leading to periodic arrays
- of nanometric amorphous precipitates by ion irradiation},
- author = {F. Zirkelbach, M. H"aberlen, J.K.N. Lindner, B. Stritzker},
- journal = {Comp. Mater. Sci.},
- volume = {33},
- number = {1--3},
- pages = {310--316},
- numpages = {7},
- year = {2005},
- month = {Apr},
- doi = {doi:10.1016/j.commatsci.2004.12.016},
- publisher = {ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS}
-}
-
--- /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}
+
+\renewcommand{\labelenumi}{(\alph{enumi})}
+
+\begin{document}
+
+% header
+\begin{center}
+ {\LARGE {\bf Demo gegen Vorratsdatenspeicherung}\\}
+ \vspace{8pt}
+ Frank Zirkelbach\\
+ 30.10.2007\\
+ \vspace{8pt}
+ {\Large\bf Besprechung}
+\end{center}
+
+\section{Begr"u"sung/Einleitung}
+
+ \subsection{Grund der Zusammenkunft}
+ \subsection{Vorstellung aller Gruppen und Einzelpersonen}
+
+\section{Definition der Probleme/Aufgaben}
+
+ \subsection{Demonstrations/Versammlungs-Voraussetzungen}
+ \subsection{Aktionsm"oglichkeiten}
+
+\section{Ausarbeitung der Demonstration}
+
+ \subsection{Festlegung des Demonstrationsablaufs}
+ \subsection{Aufgabenverteilung}
+ \subsection{Offene Aufgaben}
+ \subsection{Weitere Treffen}
+
+\section{Zusammenfassung}
+
+\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}
+
+\renewcommand{\labelenumi}{(\alph{enumi})}
+
+\begin{document}
+
+% header
+\begin{center}
+ {\LARGE {\bf Gegen Vorratsdatenspeicherung}\\}
+ \vspace{8pt}
+ 6.11.2007\\
+ \vspace{8pt}
+ {\Large\bf Demonstrationsablauf und Reden}
+\end{center}
+
+\begin{itemize}
+ \item {\bf 16.00: Vorbereitungen}
+ \begin{itemize}
+ \item Becher / Kerzen
+ \item Flyer / GG-Auszug / Pavillon / Tisch
+ \item Auto / Anlage / Generator
+ \item Ordneranweisung durch Leiter:\\
+ Edgar, Jessica, Andi, Ingo, Benedikt, Schwester / Muckl
+ \end{itemize}
+ \item {\bf 17.00: Offizielle Er"offnung der Demonstration}\\
+ Herzlich Wilkommen, hiermit er"offne ich unsere Versammlung.\\
+ Zun"achst m"ochte ich noch auf einige Dinge hinweisen:
+ \begin{itemize}
+ \item 12: Inhalt Kungebungsmittel darf nicht versto"sen gegen:
+ Strafgesetz, Rechtsordnung, Gedanken der V"olkerverst"andigung
+ \item 13: gewerbliche Werbung ist nicht zul"assig
+ \item 14: Verkauf von B"uchern, Zeitschriften, Infobrosch"uren nur
+ zum Selbstkostenpreis
+ \item 17: Maskierungen, Verkleidungen zur Verhinderung
+ der Identit"atsfeststellung nicht erlaubt
+ \item 19: keine Tonwiedergabeger"ate f"ur Teilnehmer erlaubt
+ \item 24: Mitf"uhren von Tieren insbesondere Hunden ist untersagt
+ \item 25: Abgabe, Mitnahme und Konsum von Alkohol verboten
+ \item 26: Transparente/Seile kleiner 3m
+ \item 27: Tragstangen nur aus Weichholz < 2m und < 3cm Durchmesser,
+ Oberleitungen beachten!
+ \item 28: Uniformverbot
+ \item 29: keine pyrotechnischen Gegenst"ande
+ \item 30: Kerzen $\rightarrow$ gen"ugend Sicherheitsabstand
+ \end{itemize}
+ Wenn es Probleme oder Fragen geben sollte,
+ wendet euch bitte an mich oder die ausgezeichneten Ordner.\\
+ \\
+ Wir danken der Stadt Augsburg f"ur die M"oglichkeit
+ und der Polizei f"ur die Unterst"utzung der
+ Durchf"uhrung dieser Demonstration.\\
+ \\
+ Wir warten jetzt noch kurz eine Liedl"ange auf versp"atete Teilnehmer.
+ Ich w"unsche uns schonmal eine friedliche und erfolgreiche Demo
+ und vorallem (sau) viel Spa"s! ;)
+ \item {\bf 17.05: Lied} Browser + Bitte recht freundlich
+ \item {\bf 17.10 Begr"u"sung und Einleitung}\\
+ \begin{itemize}
+ \item Herzlich Wilkommen im Namen des Augsburger Ak gegen VDS
+ \item Wir freuen uns "uber so viele Teilnehmer
+ trotz der kurzen Mobilisierungsphase
+ \end{itemize}
+ \begin{itemize}
+ \item Urspr"unglich: 6. Nov. -> Abstimmung "uber den Gesetzesentwurf
+ zur Neuregelung der Telekommunikations"uberwachung
+ \item Gestern Presse: Auf Grund der anstehenden Proteste will Bundestag
+ neue Bedenkzeit
+ \item Unsere Bem"uhungen zeigen also schon Erfolg!
+ \end{itemize}
+ \begin{itemize}
+ \item Gesetz zur Vorratsdatenspeicherung sieht sechsmonatige Speicherung
+ von Telefon, Handy, E-Mail und Internetverbidungen vor
+ \item Unserer Meinung ist das ein unverh"altnism"a"siger und drastischer
+ Eingriff in die Grundrechte
+ \item Mehr Details von Rednern
+ \item Redner:
+ \begin{itemize}
+ \item Bruno (attac, Augsburg) - Danke au"serdem f"ur materielle
+ und finanzielle Unterst"utzung
+ \item Ingo (Piratenpartei, Augsburg - Vorsicht, lange S"atze)
+ \item Benedikt (CCC, Augsburg) - kurze Erl"auterung zur
+ Unwirksamkeit der VDS
+ \end{itemize}
+ \end{itemize}
+ \begin{itemize}
+ \item Verlauf: (ablesen)
+ \item Route:\\
+ Elias-Holl-Platz, Treppen hoch, warten aufs Auto, Moritzplatz,
+ K"o, warten auf Auto, Annastra"se, Steingasse, Perlachberg,
+ Sterngasse, Elias-Holl-Platz
+ \item Bitte: hinter Auto bleiben, auf Ordner h"oren
+ \item Jetzt viel Spa"s bei erstem Redebeitrag von Bruno ...
+ \end{itemize}
+ \item {\bf 17.15: Rede 1:} Bruno (attac, Augsburg)
+ \item {\bf 17.25: Vorbereitung Demozug}
+ \begin{itemize}
+ \item Ansage Martin:\\
+ Kerze holen und langsam vor Treppe sammeln.
+ Wenn oben, auf Auto warten!
+ \item Lied: Sandb"urger
+ \item Kerzenvergabe
+ \item Auto klar machen
+ \end{itemize}
+ \item {\bf 17.30 - 18.15: Demonstrationszug durch die Innenstadt}\\
+ \begin{itemize}
+ \item Lieder: Bundestag United 1-3 + Browser
+ \item Spr"uche:
+ \begin{itemize}
+ \item Freiheit statt Angst - Stoppt den "Uberwachungswahn"
+ \item Wir sind hier und wir sind laut -
+ weil ihr uns in die Daten schaut!
+ \end{itemize}
+ \end{itemize}
+ \item {\bf 18.15: Lied} Bananenrepublik
+ \item {\bf 18.20: Rede 2:} Ingo (Piratenpartei, Augsburg)
+ \item {\bf 18.27: Lied} TET
+ \item {\bf 18.30: Rede 3:} Benedikt (CCC, Augsburg)
+ \item {\bf 18.35: Mahnwache/GG-Lesung}
+ \item {\bf 18.45: LAUT!}
+ \item {\bf 18.50: Abschlussrede}
+ \begin{itemize}
+ \item Hinweis auf zuk"unftige AK-Vorrat Treffen
+ \item Hinweis auf Sammelklage
+ \item Danksagung
+ \item letztes Lied
+ \end{itemize}
+ \item {\bf 19.00: Ende der Versammlung}\\
+ Vielen Dank, da"s ihr so zahlreich hier ward und mit uns
+ f"ur die Grundrechte und gegen den "Uberwachungswahn demonstriert habt.
+ \\
+ \\
+ Hiermit schlie"se ich die Versammlung und will euch bitten den Platz
+ samt eurer Kungebungsmittel friedlich zu verlassen.
+\end{itemize}
+\ldots und jetzt erstmal 'n Bier! ;)
+
+\end{document}
--- /dev/null
+# Makefile
+LATEX = latex
+DVIPDF = dvipdf
+
+SRC := $(shell ls *.tex)
+PDF = $(SRC:%.tex=%.pdf)
+
+all: $(PDF)
+
+%.dvi: %.tex
+ $(LATEX) $< $@
+ $(LATEX) $< $@
+
+%.pdf: %.dvi
+ $(DVIPDF) $< $@
+
+clean:
+ rm -f *.log *.aux
--- /dev/null
+\documentclass[a3paper]{article}
+\usepackage{epsf,psfig,pstricks,multicol,pst-grad,pst-node,color}
+\usepackage{graphicx,amsmath,amssymb,layout}
+\graphicspath{{./}}
+\usepackage[german]{babel}
+\usepackage[centering,noheadfoot,hmargin={-0.6cm,9.2cm},vmargin={-0.1cm,12.2cm}]{geometry}
+\usepackage{helvet}
+
+\newcommand{\veryHuge}{\fontsize{35.83}{45}\selectfont}
+\newcommand{\VeryHuge}{\fontsize{43}{54}\selectfont}
+\newcommand{\VERYHuge}{\fontsize{51.6}{64}\selectfont}
+
+\pagestyle{empty}
+
+\psset{xunit=\textwidth}
+\psset{yunit=\textheight}
+
+\begin{document}
+\begin{pspicture}[](0,0)(1.\textwidth,1.\textheight)
+
+\linespread{1.3}
+
+\psframe[fillstyle=solid,fillcolor=lightgray](0,0)(1.,1.)
+
+\rput(0.8,0.8){%
+ \includegraphics[width=8cm]{kamera.eps}
+}
+
+\psframe[fillcolor=red,fillstyle=solid,linecolor=red](0,0.43)(1.,0.57)
+\rput(0.5,0.5){\mbox{%
+ {\VERYHuge\bf\sf\color{white}
+ Freiheit statt Angst
+ }
+}}
+
+\rput(0.5,0.38){\mbox{%
+ {\VeryHuge\bf\sf\color{black}
+ F\"ur die Grundrechte
+ }
+}}
+
+\rput(0.8,0.1){%
+ \includegraphics[width=5cm]{logo.eps}
+}
+
+\end{pspicture}
+
+\end{document}
--- /dev/null
+# Makefile
+LATEX = latex
+DVIPS = dvips -tlandscape
+DVIPDF= dvipdf
+PS2PDF = ps2pdf
+PDFLATEX = pdflatex
+
+SRC := $(shell ls *.tex)
+PDF = $(SRC:%.tex=%.pdf)
+
+all: $(PDF)
+
+%.dvi: %.tex
+ $(LATEX) $< $@
+ $(LATEX) $< $@
+
+%.ps: %.dvi
+ $(DVIPS) $<
+
+#%.pdf: %.ps
+# $(PS2PDF) $<
+
+%.pdf: %.dvi
+ $(DVIPDF) $<
+
+#%.dvi: %.tex
+# $(PDFLATEX) $<
+
+clean:
+ rm -f *.log *.aux
--- /dev/null
+\pdfoutput=0
+\documentclass[landscape,semhelv]{seminar}
+
+\usepackage{verbatim}
+\usepackage[german]{babel}
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{amsmath}
+\usepackage{latexsym}
+\usepackage{ae}
+
+\usepackage{calc} % Simple computations with LaTeX variables
+\usepackage{caption} % Improved captions
+\usepackage{fancybox} % To have several backgrounds
+
+\usepackage{fancyhdr} % Headers and footers definitions
+\usepackage{fancyvrb} % Fancy verbatim environments
+\usepackage{pstricks} % PSTricks with the standard color package
+
+\usepackage{pstricks}
+\usepackage{pst-node}
+
+%\usepackage{epic}
+%\usepackage{eepic}
+
+\usepackage{graphicx}
+\graphicspath{{./}}
+
+\usepackage[setpagesize=false]{hyperref}
+
+\usepackage{semcolor}
+\usepackage{semlayer} % Seminar overlays
+\usepackage{slidesec} % Seminar sections and list of slides
+
+\input{seminar.bug} % Official bugs corrections
+\input{seminar.bg2} % Unofficial bugs corrections
+
+\articlemag{1}
+
+\special{landscape}
+
+\begin{document}
+
+\extraslideheight{10in}
+\slideframe{none}
+
+\pagestyle{empty}
+
+% specify width and height
+\slidewidth 27.7cm
+\slideheight 19.1cm
+
+% shift it into visual area properly
+\def\slideleftmargin{3.3cm}
+\def\slidetopmargin{0.6cm}
+
+% itemize level ii
+\renewcommand\labelitemii{{\color{gray}$\bullet$}}
+
+% topic
+
+\begin{slide}
+\begin{center}
+
+ \vspace{16pt}
+
+ {\LARGE\bf
+ Vorstellung des Arbeitskreises Vorratsdatenspeicherung
+ }
+
+ \vspace{18pt}
+
+ \includegraphics[height=2.5cm]{ak-vorrat.eps}
+
+ \vspace{12pt}
+
+ {\LARGE\bf
+ Widerstand gegen das geplante\\
+ bayerische Versammlungsgesetz
+ }
+
+ \vspace{24pt}
+
+ {\small Kontakt: augsburg@vorratsdatenspeicherung.de}
+
+\end{center}
+\end{slide}
+
+% contents
+
+% no contents for such a short talk!
+\begin{slide}
+
+{\large Vorstellung des AK-Vorrat}
+\begin{itemize}
+ \item Das B"undnis
+ \item Neuregelung der Telekommunikations"uberwachung
+ \item Kritik
+ \item Aktionen
+ \item Reaktionen
+\end{itemize}
+\vspace{18pt}
+{\large Das neue geplante BayVersG}
+\begin{itemize}
+ \item Unterschiede zum jetzigen VersG
+ \item Problematik
+ \item B"undnis
+ \item Aktionen
+\end{itemize}
+\end{slide}
+
+% start of contents
+
+\begin{slide}
+
+ {\large\bf
+ AK-VDS - Das B"undnis
+ }
+
+ Bundesweiter Zusammenschluss von B"urgerrechtlern, Datensch"utzern und
+ Internet-Nutzern aus Einzelpersonen und Organisationen zur Koordination
+ eines gemeinsamen Vorgehens gegen die Vorratsdatenspeicherung.
+
+ \vspace{8pt}
+
+ {\bf Einige Fakten:}
+ \begin{itemize}
+ \item Grundsatz:\\
+ Ablehnung der verdachtsunabh"angigen Speicherung von
+ Telekommunikationsdaten
+ \item Aufbau:\\
+ keine konventionelle Struktur, kein Verein, Mailinglisten,
+ Ortsgruppen
+ \item Gr"undung:\\
+ Durch NNM initiertes Treffen beim CCC im Dezember 2005 mit
+ Vertretern von
+ \begin{itemize}
+ \item amtlichen Datenschutzbeauftragten
+ \item attac
+ \item Deutsche Vereinigung f"ur Datenschutz
+ \item FoeBuD, Stop1984
+ \item verschiedensten Providern
+ \end{itemize}
+ \end{itemize}
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ AK-VDS - Neuregelung der Telekommunikations"uberwachung
+ }
+
+ \vspace{4pt}
+
+ Umsetzung der EG Richtlinie 2006/24/EG
+
+ \vspace{4pt}
+
+ Folgende Daten m"ussen sechs Monate lang vom Dienstanbieter gespeichert werden:
+ \begin{itemize}
+ \item {\bf Festnetztelefon:}
+ Telefonnummer eingehender und ausgehender Anrufe, Uhrzeit und Dauer.
+ \item {\bf Mobiltelefon:}
+ Telefonnummer eingehender und ausgehender Anrufe, Uhrzeit, Dauer,
+ IMEI-Nummern und Mobilfunkzellen.
+ \item {\bf e-Mail:}
+ IP- und Mailadressen von Absender,
+ Empf"anger und Zeitpunkte jedes Zugriffs auf das Postfach.
+ \item {\bf Internet:}
+ Zeitpunkt, Dauer und IP-Adresse einer Verbindung ins Internet.
+ \end{itemize}
+
+ \vspace{4pt}
+
+ Zugriff auf diese Daten haben:
+ \begin{itemize}
+ \item {\bf Polizei, Staatsanwaltschaft:}
+ mit richterlichen Beschluss zur Aufkl"arung schwerer Straftaten
+ \item {\bf MAD, BND, Verfassungsschutz:}
+ selbst ohne richterlichen Beschluss
+ \item {\bf zus"atzlich zur EG-Richtlinie:}
+ Verwendung der Daten bei allen mittels TK begangener Straftaten
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ AK-VDS - Kritik
+ }
+
+ \vspace{8pt}
+
+ \begin{itemize}
+ \item {\bf Versto"s gegen den Erforderlichkeitsgrundsatz}\\
+ Anlasslose Speicherung von personenbezogenen Daten
+ \item {\bf Eingriff in die informationelle Selbstbestimmung}
+ \begin{itemize}
+ \item Erm"oglicht vermeintliche Aussagen betreffend
+ sozialer Kontakte, politischem Engagement bis hin zu
+ Krankheiten
+ \item Gefahr der Verhaltensanpassung des Betroffenen
+ \end{itemize}
+ $\Rightarrow$ Diametraler Gegensatz zur freiheitlich demokratischen
+ Grundordnung\\
+ $\Rightarrow$ Eingriff in freie Entfaltung und das
+ Recht auf Meinungs"au"serung (Art. 2/5 GG)
+ \item {\bf Unwirksamkeit}
+ \begin{itemize}
+ \item Speicherung der Daten notwendigerweise vergangenheitsbezogen\\
+ $\Rightarrow$ ausschlie"slich zur Aufkl"arung
+ begangener Straftaten
+ \item Studie BKA: Aufkl"arungsquote um 0.006 Prozentpunkte erh"oht\\
+ $\Rightarrow$ Unverh"altnism"a"sig zum starken Eingriff in die
+ B"urgerrechte
+ \end{itemize}
+ \item {\bf Missbrauchs- und Irrtumspotential}
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ AK-VDS - Aktionen
+ }
+
+ \vspace{12pt}
+
+ Bundesweite Aktionen:
+ \begin{itemize}
+ \item {\bf 22/09/2007:} Demonstration \dq Freiheit statt Angst\dq{} in Berlin
+ (15,000 Teilnehmer).
+ \item {\bf 06/11/2007:} Dezentrale bundesweite Demonstrationen.
+ \item {\bf 31/12/2007:} Einreichung der Verfassungsbeschwerde
+ (34,451 Unterschriften).
+ \end{itemize}
+
+ \vspace{12pt}
+
+ Aktionen in Augsburg:
+ \begin{itemize}
+ \item {\bf 06/11/2007:} Demo mit "uber 250 Teilnehmern.
+ \item {\bf 06/03/2008:} Filmpate beim Filmfestival \dq "uber morgen\dq{}.
+ \item {\bf in Zukunft:} Infost"ande, Demo, \ldots
+ \end{itemize}
+\end{slide}
+
+\end{document}
--- /dev/null
+\documentclass[a4paper]{article}
+\usepackage{epsf,psfig,pstricks,multicol,pst-grad,pst-node,color}
+\usepackage{graphicx,amsmath,amssymb,layout}
+\graphicspath{{./img/}}
+\usepackage[german]{babel}
+\usepackage[centering,noheadfoot,hmargin={-0.8in,0mm},vmargin={4mm,-4mm}]{geometry}
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+
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+Augsburger Aktionsb\"undnis\\
+\color{black}
+Rettet die Versammlungsfreiheit
+}}
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+ Versammlungsfreiheit\\[0.3cm]
+ in Bayern
+ }
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+ {\color{white}
+ 04. Juni 2008, 19.30 Uhr
+ }
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+\rput(9cm,5.8cm){\parbox{12cm}{\sf
+{\large\sf\color{gray}
+ Wir brauchen unsere Versammlungsfreiheit\\[0.5cm]
+}%
+{\sf
+ Im Rahmen der F\"oderalismusreform plant die bayerische Staatsregierung
+ die Verabschiedung eines eigenen Versammlungsgesetzes.
+ Dieses sieht erhebliche Einschr\"ankungen der Versammlungsfreiheit vor.\\\\
+ Zusammen mit Herrn Hartmut W\"achtler,
+ Fachanwalt f\"ur Strafrecht in M\"unchen,
+ der sich besonders auch mit B\"urgerrechten befasst
+ und zur Expertenanh\"orung zum
+ neuen Versammlungsgesetz im bayerischen Landtag geladen war,
+ wollen wir an diesem Abend \"uber das neue Gesetz diskutieren.
+}
+}}
+\rput(19cm,5.8cm){\parbox{6cm}{\sf\color{gray}
+Diskussion:\\
+Ort: Filmsaal im Zeughaus, Augsburg\\
+Zeit: 04. Juni 2008, 19.30 h\\
+\\
+Weitere Informationen:\\
+http://demorecht.de/augsburg
+}}
+
+\linespread{1.2}
+
+\rput(9cm,1.3cm){\parbox{12cm}{\sf\scriptsize\color{white}
+Unterst\"utzer des Augsburger Aktionsb\"undnisses:\\
+ATIF, Attac, Arbeitskreis Vorratsdatenspeicherung,
+Augsburger Friedensinitiative, Bund f\"ur Geistesfreiheit,
+B\"undnis 90/Die Gr\"unen, Die Linke,
+Deutsche Friedensgesellschaft-Vereinigte KriegsdienstgegnerInnen,
+Forum solidarisches und friedliches Augsburg,
+Griechische Gemeinde von Augsburg und Umgebung e.V.,
+Gruppe Contra REAL, Internationales Kulturzentrum,
+Junge Liberale, Montagsdemonstration,
+MLPD, Kulturladen in Selbstverwaltung "Die ganze B\"ackerei",
+pax christi,
+Piratenpartei Bayern,
+Rebell Augsburg,
+Vereinigung der Verfolgten des Naziregimes/BdA.
+}}
+\rput(19cm,1.3cm){\parbox{6cm}{\sf\scriptsize\color{white}
+Weitere Aufrufer:\\
+DGB - Region Augsburg, ver.di Bezirk Augsburg,\\
+IG Metall Augsburg,
+Betriebsrat der Hermann-Schmid-Akademie Augsburg\\\\
+{\tiny
+ v.i.S.d.P. Frank Zirkelbach, R\"omerweg 10, 86391 Stadtbergen
+}
+}}
+}
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+4 0 0 50 -1 0 12 0.0000 6 135 1275 6885 3375 dx = +0.014 nm\001
+4 0 0 50 -1 0 12 0.0000 6 135 1260 4950 1440 dz = +0.020 nm\001
+4 0 0 50 -1 0 12 0.0000 6 180 1275 4950 1215 dy = +0.014 nm\001
+4 0 0 50 -1 0 12 0.0000 6 135 1275 4950 990 dx = - 0.014 nm\001
+4 0 0 50 -1 0 12 0.0000 6 135 1260 2610 4095 dz = +0.084 nm\001
+4 0 0 50 -1 0 12 0.0000 6 135 1215 2655 5895 dz = -0.091 nm\001
+4 0 7 45 -1 0 16 0.0000 4 195 180 5310 3330 C\001
+4 0 0 50 -1 0 12 0.0000 4 90 105 2250 2295 x\001
+4 0 0 50 -1 0 12 0.0000 4 90 90 1620 1575 z\001
+4 0 0 50 -1 0 12 0.0000 4 135 105 2070 1800 y\001
+4 0 0 50 -1 0 12 0.0000 4 135 105 5670 6840 1\001
+4 0 0 50 -1 0 12 0.0000 4 135 105 6075 3060 3\001
+4 0 0 50 -1 0 12 0.0000 4 135 765 9495 1530 0.366 nm\001
+4 0 0 50 -1 0 12 0.0000 4 135 765 9495 1260 0.362 nm\001
+4 0 0 50 -1 0 12 0.0000 4 135 765 9495 990 0.340 nm\001
+4 0 0 50 -1 0 12 0.0000 4 135 765 9495 720 0.244 nm\001
+4 0 0 50 -1 0 12 0.0000 4 135 765 9495 1800 0.368 nm\001
+4 0 0 50 -1 0 12 0.0000 4 135 765 9495 2070 0.369 nm\001
+4 0 0 50 -1 0 12 0.0000 4 135 765 9495 2340 0.390 nm\001
+4 0 0 50 -1 0 12 0.0000 4 135 765 9495 2610 0.394 nm\001
+4 0 0 50 -1 0 12 0.0000 4 135 765 9495 2880 0.396 nm\001
+4 0 0 50 -1 0 12 0.0000 4 135 765 9495 3150 0.397 nm\001
+4 0 0 50 -1 0 12 0.0000 4 135 765 9495 3420 0.405 nm\001
+4 0 0 50 -1 0 12 0.0000 4 135 765 9495 3690 0.419 nm\001
+4 0 0 50 -1 0 12 0.0000 4 180 2115 9450 360 More Si-Si' pair distances:\001
+4 0 0 50 -1 0 12 0.0000 4 135 1725 9450 4275 More C-Si' distances:\001
+4 0 0 50 -1 0 12 0.0000 4 135 105 4005 765 4\001
+4 0 0 50 -1 0 12 0.0000 4 135 105 9495 6300 5\001
+4 0 0 50 -1 0 12 0.0000 4 135 105 1260 9045 2\001
+4 0 0 50 -1 0 12 0.0000 4 120 285 9495 3915 etc.\001
+4 0 0 50 -1 0 12 0.0000 4 165 1380 9225 8955 r(3C) = 0.186 nm\001
+4 0 0 50 -1 0 12 0.0000 4 165 1470 9225 8730 r(2C) = 0.329 nm \001
+4 0 0 50 -1 0 12 0.0000 4 165 1425 9225 8505 r(1C) = 0.175 nm \001
+4 0 0 50 -1 0 12 0.0000 4 135 765 9495 4635 0.337 nm\001
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+4 0 0 50 -1 0 12 0.0000 4 135 765 9495 5175 0.386 nm\001
+4 0 0 50 -1 0 12 0.0000 4 135 765 9495 5445 0.393 nm\001
+4 0 0 50 -1 0 12 0.0000 4 135 765 9495 5715 0.431 nm\001
+4 0 0 50 -1 0 12 0.0000 4 120 285 9495 5940 etc.\001
+4 0 0 50 -1 0 12 0.0000 4 135 1455 10755 5940 Si': not visualized\001
+4 0 0 50 -1 0 12 0.0000 6 135 1215 2250 8955 dz = -0.031 nm\001
--- /dev/null
+#FIG 3.2 Produced by xfig version 3.2.5
+Landscape
+Center
+Metric
+A4
+100.00
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+-2
+1200 2
+6 4365 8370 7560 9000
+4 0 0 50 -1 0 12 0.0000 4 165 1395 4365 8505 r(12) = 0.226 nm \001
+4 0 0 50 -1 0 12 0.0000 4 165 1440 4365 8730 r(13) = 0.300 nm \001
+4 0 0 50 -1 0 12 0.0000 4 165 1350 6120 8730 r(25) = 0.425 nm\001
+4 0 0 50 -1 0 12 0.0000 4 165 1350 4365 8955 r(34) = 0.343 nm\001
+4 0 0 50 -1 0 12 0.0000 4 165 1440 6120 8505 r(23) = 0.423 nm \001
+-6
+6 8055 8370 9540 9000
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+4 0 0 50 -1 0 12 0.0000 4 165 1470 8055 8730 r(2C) = 0.329 nm \001
+4 0 0 50 -1 0 12 0.0000 4 165 1425 8055 8505 r(1C) = 0.175 nm \001
+-6
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+4 0 0 50 -1 0 12 0.0000 6 135 1230 4950 990 dx = -0.014 nm\001
--- /dev/null
+#FIG 3.2 Produced by xfig version 3.2.5
+Landscape
+Center
+Metric
+A4
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+-2
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+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 7470 405 101 101 7470 405 7571 405
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 8370 405 101 101 8370 405 8471 405
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 9270 405 101 101 9270 405 9371 405
+-6
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 1800 9000 101 101 1800 9000 1901 9000
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 2700 9000 101 101 2700 9000 2801 9000
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 3600 9000 101 101 3600 9000 3701 9000
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 4500 9000 101 101 4500 9000 4601 9000
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 5400 9000 101 101 5400 9000 5501 9000
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 6300 9000 101 101 6300 9000 6401 9000
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 7200 9000 101 101 7200 9000 7301 9000
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 8100 9000 101 101 8100 9000 8201 9000
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 9000 9000 101 101 9000 9000 9101 9000
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 1800 7965 101 101 1800 7965 1901 7965
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+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 3600 7965 101 101 3600 7965 3701 7965
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 4500 7965 101 101 4500 7965 4601 7965
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 5400 7965 101 101 5400 7965 5501 7965
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+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 7200 7965 101 101 7200 7965 7301 7965
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 8100 7965 101 101 8100 7965 8201 7965
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 9000 7965 101 101 9000 7965 9101 7965
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 1800 6930 101 101 1800 6930 1901 6930
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+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 3600 6930 101 101 3600 6930 3701 6930
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 4500 6930 101 101 4500 6930 4601 6930
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 5400 6930 101 101 5400 6930 5501 6930
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 6300 6930 101 101 6300 6930 6401 6930
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 7200 6930 101 101 7200 6930 7301 6930
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 8100 6930 101 101 8100 6930 8201 6930
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 9000 6930 101 101 9000 6930 9101 6930
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 1800 4905 101 101 1800 4905 1901 4905
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+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 4500 4905 101 101 4500 4905 4601 4905
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 5400 4905 101 101 5400 4905 5501 4905
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 6300 4905 101 101 6300 4905 6401 4905
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 7200 4905 101 101 7200 4905 7301 4905
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 8100 4905 101 101 8100 4905 8201 4905
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 9000 4905 101 101 9000 4905 9101 4905
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 1800 5895 101 101 1800 5895 1901 5895
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+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 3600 5895 101 101 3600 5895 3701 5895
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 4500 5895 101 101 4500 5895 4601 5895
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+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 6300 5895 101 101 6300 5895 6401 5895
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+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 8100 5895 101 101 8100 5895 8201 5895
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 9000 5895 101 101 9000 5895 9101 5895
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 1800 3870 101 101 1800 3870 1901 3870
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+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 3600 3870 101 101 3600 3870 3701 3870
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 4500 3870 101 101 4500 3870 4601 3870
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 5400 3870 101 101 5400 3870 5501 3870
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 6300 3870 101 101 6300 3870 6401 3870
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 7200 3870 101 101 7200 3870 7301 3870
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 8100 3870 101 101 8100 3870 8201 3870
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 9000 3870 101 101 9000 3870 9101 3870
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 1800 2835 101 101 1800 2835 1901 2835
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+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 3600 2835 101 101 3600 2835 3701 2835
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 4500 2835 101 101 4500 2835 4601 2835
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 5400 2835 101 101 5400 2835 5501 2835
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 6300 2835 101 101 6300 2835 6401 2835
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 7200 2835 101 101 7200 2835 7301 2835
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 8100 2835 101 101 8100 2835 8201 2835
+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 9000 2835 101 101 9000 2835 9101 2835
Single
-2
1200 2
-6 2430 2700 2970 2970
-1 3 0 1 4 4 50 -1 20 0.000 1 0.0000 2835 2835 101 101 2835 2835 2936 2835
-1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 2565 2835 101 101 2565 2835 2666 2835
--6
-6 3330 6795 3870 7065
-1 3 0 1 4 4 50 -1 20 0.000 1 0.0000 3735 6930 101 101 3735 6930 3836 6930
-1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 3465 6930 101 101 3465 6930 3566 6930
--6
-6 7830 7830 8370 8100
-1 3 0 1 4 4 50 -1 20 0.000 1 0.0000 8235 7965 101 101 8235 7965 8336 7965
-1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 7965 7965 101 101 7965 7965 8066 7965
--6
-6 6930 5760 7470 6030
-1 3 0 1 4 4 50 -1 20 0.000 1 0.0000 7335 5895 101 101 7335 5895 7436 5895
-1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 7065 5895 101 101 7065 5895 7166 5895
--6
-6 7830 2700 8370 2970
-1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 8235 2835 101 101 8235 2835 8336 2835
-1 3 0 1 4 4 50 -1 20 0.000 1 0.0000 7965 2835 101 101 7965 2835 8066 2835
--6
-6 5130 3735 5670 4005
-1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 5535 3870 101 101 5535 3870 5636 3870
-1 3 0 1 4 4 50 -1 20 0.000 1 0.0000 5265 3870 101 101 5265 3870 5366 3870
--6
-6 2430 4770 2970 5040
-1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 2835 4905 101 101 2835 4905 2936 4905
-1 3 0 1 4 4 50 -1 20 0.000 1 0.0000 2565 4905 101 101 2565 4905 2666 4905
--6
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 1800 9000 101 101 1800 9000 1901 9000
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 2700 9000 101 101 2700 9000 2801 9000
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 3600 9000 101 101 3600 9000 3701 9000
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 5400 7965 101 101 5400 7965 5501 7965
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 6300 7965 101 101 6300 7965 6401 7965
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 7200 7965 101 101 7200 7965 7301 7965
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1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 9000 7965 101 101 9000 7965 9101 7965
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 1800 6930 101 101 1800 6930 1901 6930
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 2700 6930 101 101 2700 6930 2801 6930
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1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 4500 6930 101 101 4500 6930 4601 6930
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 5400 6930 101 101 5400 6930 5501 6930
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 6300 6930 101 101 6300 6930 6401 6930
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 8100 6930 101 101 8100 6930 8201 6930
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 9000 6930 101 101 9000 6930 9101 6930
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 1800 4905 101 101 1800 4905 1901 4905
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1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 3600 4905 101 101 3600 4905 3701 4905
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 4500 4905 101 101 4500 4905 4601 4905
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 5400 4905 101 101 5400 4905 5501 4905
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 6300 4905 101 101 6300 4905 6401 4905
-1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 7200 4905 101 101 7200 4905 7301 4905
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 8100 4905 101 101 8100 4905 8201 4905
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 9000 4905 101 101 9000 4905 9101 4905
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 1800 5895 101 101 1800 5895 1901 5895
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 4500 5895 101 101 4500 5895 4601 5895
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 5400 5895 101 101 5400 5895 5501 5895
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 6300 5895 101 101 6300 5895 6401 5895
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1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 8100 5895 101 101 8100 5895 8201 5895
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 9000 5895 101 101 9000 5895 9101 5895
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 1800 3870 101 101 1800 3870 1901 3870
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1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 3600 3870 101 101 3600 3870 3701 3870
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 4500 3870 101 101 4500 3870 4601 3870
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1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 6300 3870 101 101 6300 3870 6401 3870
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 7200 3870 101 101 7200 3870 7301 3870
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 8100 3870 101 101 8100 3870 8201 3870
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 5400 2835 101 101 5400 2835 5501 2835
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 6300 2835 101 101 6300 2835 6401 2835
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 7200 2835 101 101 7200 2835 7301 2835
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1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 9000 2835 101 101 9000 2835 9101 2835
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1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 1800 1800 101 101 1800 1800 1901 1800
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 2700 1800 101 101 2700 1800 2801 1800
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 3600 1800 101 101 3600 1800 3701 1800
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 7200 1800 101 101 7200 1800 7301 1800
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 8100 1800 101 101 8100 1800 8201 1800
1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 9000 1800 101 101 9000 1800 9101 1800
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+1 3 0 1 0 0 50 -1 20 0.000 1 0.0000 4680 6615 101 101 4680 6615 4781 6615
--- /dev/null
+#FIG 3.2 Produced by xfig version 3.2.5
+Landscape
+Center
+Metric
+A4
+100.00
+Single
+-2
+1200 2
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--- /dev/null
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--- /dev/null
+#FIG 3.2 Produced by xfig version 3.2.5
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--- /dev/null
+ \begin{pspicture}(0,0)(12,8)
+ % nodes
+ \rput(4.5,6.5){\rnode{init}{\psframebox{\parbox{7cm}{
+ \begin{itemize}
+ \item Initial configuration: $31\times31\times31$ unit cells Si
+ \item Periodic boundary conditions
+ \item $T=450\, ^{\circ}C$
+ \item Equilibration of $E_{kin}$ and $E_{pot}$ for $600\, fs$
+ \end{itemize}
+ }}}}
+ \rput(4.5,4.5){\rnode{tc1}{\psframebox[fillstyle=solid,fillcolor=red]{
+ $T=450\pm 1\, ^{\circ}C$}}}
+ \rput(7,3.5){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{
+ \parbox{3cm}{
+ Insertion of 10 atoms\\
+ at random positions}}}}
+ \rput(2,3.5){\rnode{adj1}{\psframebox[fillstyle=solid,fillcolor=red]{
+ \parbox{3.5cm}{
+ Adjusting temperature\\
+ for another $100\, fs$}}}}
+ \rput(7,2.5){\rnode{nc}{\psframebox[fillstyle=solid,fillcolor=red]{
+ $N_{atoms}=6000$}}}
+ \rput(4.5,2){\rnode{tc2}{\psframebox[fillstyle=solid,fillcolor=cyan]{
+ $T=T_{set}$}}}
+ \rput(7,1){\rnode{td}{\psframebox[fillstyle=solid,fillcolor=cyan]{
+ $T_{set}:=T_{set}-1\, ^{\circ}C$}}}
+ \rput(2,1){\rnode{adj2}{\psframebox[fillstyle=solid,fillcolor=cyan]{
+ \parbox{3.5cm}{
+ Adjusting temperature\\
+ for another $50\, fs$}}}}
+ \rput(7,0){\rnode{tc3}{\psframebox[fillstyle=solid,fillcolor=cyan]{
+ $T_{set}=20\, ^{\circ}C$}}}
+ \rput(10,0){\rnode{end}{\psframebox{End}}}
+ % help nodes
+ \rput(7,4.5){\pnode{tc1-h}}
+ \rput(2,4.5){\pnode{tc1-hh}}
+ \rput(4.5,2.5){\pnode{nc-h}}
+ \rput(9,2.5){\pnode{nc-hh}}
+ \rput(9,2){\pnode{tc2-h}}
+ \rput(2,2){\pnode{tc2-hh}}
+ \rput(4.5,0){\pnode{tc3-h}}
+ % direct lines
+ \ncline[]{->}{init}{tc1}
+ \ncline[]{->}{adj1}{tc1}
+ \ncline[]{->}{insert}{nc}
+ \ncline[]{->}{adj2}{tc2}
+ \ncline[]{->}{tc2}{td}
+ \lput*{0}{yes}
+ \ncline[]{->}{td}{tc3}
+ \ncline[]{->}{tc3}{end}
+ \lput*{0}{yes}
+ % lines using help nodes
+ \ncline[]{tc1}{tc1-h}
+ \lput*{0}{yes}
+ \ncline[]{->}{tc1-h}{insert}
+ \ncline[]{tc1}{tc1-hh}
+ \lput*{0}{no}
+ \ncline[]{->}{tc1-hh}{adj1}
+ \ncline[]{nc}{nc-h}
+ \lput*{0}{no}
+ \ncline[]{->}{nc-h}{tc1}
+ \ncline[]{nc}{nc-hh}
+ \ncline[]{-}{nc-hh}{tc2-h}
+ \ncline[]{->}{tc2-h}{tc2}
+ \lput*{0}{yes, {\footnotesize $T_{set}:=450\, ^{\circ}C$}}
+ \ncline[]{tc2}{tc2-hh}
+ \lput*{0}{no}
+ \ncline[]{->}{tc2-hh}{adj2}
+ \ncline[]{tc3}{tc3-h}
+ \lput*{0}{no}
+ \ncline[]{->}{tc3-h}{tc2}
+ % insertion volumes
+ \psframe[fillstyle=solid,fillcolor=white](9.5,1.3)(13.5,5.3)
+ \psframe[fillstyle=solid,fillcolor=lightgray](10,1.8)(13,4.8)
+ \psframe[fillstyle=solid,fillcolor=gray](10.5,2.3)(12.5,4.3)
+ \rput(9.75,3){\pnode{ins1}}
+ \rput(10.25,3.3){\pnode{ins2}}
+ \rput(10.75,3.6){\pnode{ins3}}
+ \ncline[]{-}{insert}{ins1}
+ \ncline[]{-}{insert}{ins2}
+ \ncline[]{-}{insert}{ins3}
+ \psframe[fillstyle=solid,fillcolor=white](9.5,7.6)(13.5,8.1)
+ \psframe[fillstyle=solid,fillcolor=lightgray](9.5,6.8)(13.5,7.3)
+ \psframe[fillstyle=solid,fillcolor=gray](9.5,6)(13.5,6.5)
+ \rput(11.5,7.85){{\tiny Simulation volume:
+ $31\times31\times31\, a^3_{Si}$}}
+ \rput(11.5,7.05){{\tiny Volume of minimal SiC precipitation}}
+ \rput(11.5,6.25){{\tiny Volume of necessary amount of Si}}
+ \end{pspicture}
--- /dev/null
+#FIG 3.2 Produced by xfig version 3.2.5
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--- /dev/null
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--- /dev/null
+#!/usr/bin/gnuplot -persist
+#
+#
+# G N U P L O T
+# Version 4.2 patchlevel 2
+# last modified 31 Aug 2007
+# System: Linux 2.6.22-2-686
+#
+# Copyright (C) 1986 - 1993, 1998, 2004, 2007
+# Thomas Williams, Colin Kelley and many others
+#
+# Type `help` to access the on-line reference manual.
+# The gnuplot FAQ is available from http://www.gnuplot.info/faq/
+#
+# Send bug reports and suggestions to <http://sourceforge.net/projects/gnuplot>
+#
+set terminal epslatex color solid standalone
+set output 'sic_pc.tex'
+unset clip points
+set clip one
+unset clip two
+set bar 1.000000
+set border 31 front linetype -1 linewidth 1.000
+set xdata
+set ydata
+set zdata
+set x2data
+set y2data
+set timefmt x "%d/%m/%y,%H:%M"
+set timefmt y "%d/%m/%y,%H:%M"
+set timefmt z "%d/%m/%y,%H:%M"
+set timefmt x2 "%d/%m/%y,%H:%M"
+set timefmt y2 "%d/%m/%y,%H:%M"
+set timefmt cb "%d/%m/%y,%H:%M"
+set boxwidth
+set style fill empty border
+set style rectangle back fc lt -3 fillstyle solid 1.00 border -1
+set dummy x,y
+set format x "% g"
+set format y "% g"
+set format x2 "% g"
+set format y2 "% g"
+set format z "% g"
+set format cb "% g"
+set angles radians
+unset grid
+set key title ""
+set key inside right top vertical Right noreverse enhanced autotitles nobox
+set key noinvert samplen 4 spacing 1 width 0 height 0
+unset label
+set label 1 "1" at 2, 350, 0 left norotate back nopoint offset character 0, 0, 0
+set label 2 "2" at 3.7, 200, 0 left norotate back nopoint offset character 0, 0, 0
+set label 3 "3" at 4.8, 100, 0 left norotate back nopoint offset character 0, 0, 0
+set label 4 "4" at 5.66, 50, 0 left norotate back nopoint offset character 0, 0, 0
+unset arrow
+set style increment default
+unset style line
+unset style arrow
+set style histogram clustered gap 2 title offset character 0, 0, 0
+unset logscale
+set offsets 0, 0, 0, 0
+set pointsize 1
+set encoding default
+unset polar
+unset parametric
+unset decimalsign
+set view 60, 30, 1, 1
+set samples 100, 100
+set isosamples 10, 10
+set surface
+unset contour
+set clabel '%8.3g'
+set mapping cartesian
+set datafile separator whitespace
+unset hidden3d
+set cntrparam order 4
+set cntrparam linear
+set cntrparam levels auto 5
+set cntrparam points 5
+set size ratio 0 1,1
+set origin 0,0
+set style data points
+set style function lines
+set xzeroaxis linetype -2 linewidth 1.000
+set yzeroaxis linetype -2 linewidth 1.000
+set zzeroaxis linetype -2 linewidth 1.000
+set x2zeroaxis linetype -2 linewidth 1.000
+set y2zeroaxis linetype -2 linewidth 1.000
+set ticslevel 0.5
+set mxtics default
+set mytics default
+set mztics default
+set mx2tics default
+set my2tics default
+set mcbtics default
+set xtics border in scale 1,0.5 mirror norotate offset character 0, 0, 0
+set xtics autofreq
+set noytics
+set ztics border in scale 1,0.5 nomirror norotate offset character 0, 0, 0
+set ztics autofreq
+set nox2tics
+set noy2tics
+set cbtics border in scale 1,0.5 mirror norotate offset character 0, 0, 0
+set cbtics autofreq
+set title "Reference pair (Si-C) correlation function of ideal 3C-SiC"
+set title offset character 0, 0, 0 font "" norotate
+set timestamp bottom
+set timestamp ""
+set timestamp offset character 0, 0, 0 font "" norotate
+set rrange [ * : * ] noreverse nowriteback # (currently [0.00000:10.0000] )
+set trange [ * : * ] noreverse nowriteback # (currently [-5.00000:5.00000] )
+set urange [ * : * ] noreverse nowriteback # (currently [-5.00000:5.00000] )
+set vrange [ * : * ] noreverse nowriteback # (currently [-5.00000:5.00000] )
+set xlabel "$r\\, [\\AA]$"
+set xlabel offset character 0, 0, 0 font "" textcolor lt -1 norotate
+set x2label ""
+set x2label offset character 0, 0, 0 font "" textcolor lt -1 norotate
+set xrange [ * : * ] noreverse nowriteback # (currently [-10.0000:10.0000] )
+set x2range [ * : * ] noreverse nowriteback # (currently [-10.0000:10.0000] )
+set ylabel "$g(r)$"
+set ylabel offset character 0, 0, 0 font "" textcolor lt -1 rotate by 90
+set y2label ""
+set y2label offset character 0, 0, 0 font "" textcolor lt -1 rotate by 90
+set yrange [ * : * ] noreverse nowriteback # (currently [-10.0000:10.0000] )
+set y2range [ * : * ] noreverse nowriteback # (currently [-10.0000:10.0000] )
+set zlabel ""
+set zlabel offset character 0, 0, 0 font "" textcolor lt -1 norotate
+set zrange [ * : * ] noreverse nowriteback # (currently [-10.0000:10.0000] )
+set cblabel ""
+set cblabel offset character 0, 0, 0 font "" textcolor lt -1 norotate
+set cbrange [ * : * ] noreverse nowriteback # (currently [-10.0000:10.0000] )
+set zero 1e-08
+set lmargin -1
+set bmargin -1
+set rmargin -1
+set tmargin -1
+set locale "C"
+set pm3d explicit at s
+set pm3d scansautomatic
+set pm3d interpolate 1,1 flush begin noftriangles nohidden3d corners2color mean
+set palette positive nops_allcF maxcolors 0 gamma 1.5 color model RGB
+set palette rgbformulae 7, 5, 15
+set colorbox default
+set colorbox vertical origin screen 0.9, 0.2, 0 size screen 0.05, 0.6, 0 bdefault
+set loadpath
+set fontpath
+set fit noerrorvariables
+GNUTERM = "wxt"
+plot [1.5:6] "sic_pc_20.txt" w l t "$20\\, ^{\\circ}$C", "sic_pc_450.txt" w l t "$450\\, ^{\\circ}$C"
+# EOF
--- /dev/null
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--- /dev/null
+\documentclass[portrait,a0b,final]{a0poster}
+\usepackage{epsf,psfig,pstricks,multicol,pst-grad,pst-node,color}
+\usepackage{graphicx,amsmath,amssymb}
+\graphicspath{{../img/}}
+\usepackage[english,german]{babel}
+
+\input{a0poster-kh}
+
+\selectlanguage{english}
+
+\renewcommand\labelitemii{{\color{black}$\bullet$}}
+
+\begin{document}
+
+% Fliessenden Hintergrund von RGB-Farbe 1. .98 .98 nach 1. .85 .85
+% und wieder nach 1. .98 .98 (1. .85 .85 wird nach 0.1=10% des Hinter-
+% grunds angenommen)
+% Achtung Werte unter .8 verbrauchen zu viel Tinte!!!
+
+%\background{.95 .95 1.}{.78 .78 1.}{0.05}
+%\background{.50 .50 .50}{.85 .85 .85}{0.5}
+\background{.40 .48 .71}{.99 .99 .99}{0.5}
+
+\newrgbcolor{si-yellow}{.6 .6 0}
+\newrgbcolor{hb}{0.75 0.77 0.89}
+\newrgbcolor{lbb}{0.75 0.8 0.88}
+\newrgbcolor{lachs}{1.0 .93 .81}
+
+% Groesse der einzelnen Spalten als Anteil der Gesamt-Textbreite
+\renewcommand{\columnfrac}{.31}
+
+% potential
+\newcommand{\pot}{\mathcal{V}}
+
+% header
+\vspace{-18.5cm}
+\begin{header}
+ \centerline{{\Huge \bfseries Molecular dynamics simulation
+ of defect formation and precipitation}}
+ \vspace*{0.5cm}
+ \centerline{{\Huge \bfseries in heavily carbon doped silicon}}
+ \vspace*{1cm}
+ \centerline{\huge\textsc {\underline{F.~Zirkelbach}$^1$,
+ J.~K.~N.~Lindner$^1$,
+ K.~Nordlund$^2$, B.~Stritzker$^1$}}
+ \vspace*{1cm}
+ \begin{center}
+ \begin{minipage}{.065\textwidth}
+ \includegraphics[height=5.5cm]{uni-logo.eps}
+ \end{minipage}
+ \begin{minipage}{.57\textwidth}
+ \centerline{\Large $^1$ Experimentalphysik IV, Institut f\"ur Physik,
+ Universit\"at Augsburg,}
+ \centerline{\Large Universit\"atsstr. 1, D-86135 Augsburg, Germany}
+ \end{minipage}
+ \begin{minipage} {.065\textwidth}
+ \includegraphics[height=5cm]{Lehrstuhl-Logo.eps}
+ \end{minipage}
+ \end{center}
+ \begin{center}
+ \begin{minipage}{.20\textwidth}
+ \includegraphics[height=5.5cm]{logo_eng.eps}
+ \end{minipage}
+ \begin{minipage}{.50\textwidth}
+ \centerline{\Large $^2$ Accelerator Laboratory,
+ Department of Physical Sciences,
+ University of Helsinki,}
+ \centerline{\Large Pietari Kalmink. 2, 00014 Helsinki, Finland}
+ \end{minipage}
+ \end{center}
+\end{header}
+
+\begin{poster}
+
+\vspace{-1cm}
+\begin{pcolumn}
+ \begin{pbox}
+ \section*{Motivation}
+ {\bf Importance of the 3C-SiC precipitation process in silicon}
+ \begin{itemize}
+ \item SiC is a promising wide band gap material for high-temperature,
+ high-power, high-frequency semiconductor devices [1].
+ \item 3C-SiC epitaxial thin film formation on Si requires detailed
+ knowledge of SiC nucleation.
+ \item Fabrication of high carbon doped, strained pseudomorphic
+ $\text{Si}_{1-y}\text{C}_y$ layers requires suppression of
+ 3C-SiC nucleation [2].
+ \end{itemize}
+ {\tiny
+ [1] J. H. Edgar, J. Mater. Res. 7 (1992) 235.}\\
+ {\tiny
+ [2] J. W. Strane, S. R. Lee, H. J. Stein, S. T. Picraux,
+ J. K. Watanabe, J. W. Mayer, J. Appl. Phys. 79 (1996) 637.}
+ \end{pbox}
+ \vspace{-0.45cm}
+ \begin{pbox}
+ \section*{Crystalline silicon and cubic silicon carbide}
+ {\bf Lattice types and unit cells:}
+ \begin{itemize}
+ \item Crystalline silicon (c-Si) has diamond structure\\
+ $\Rightarrow {\color{si-yellow}\bullet}$ and
+ ${\color{gray}\bullet}$ are Si atoms
+ \item Cubic silicon carbide (3C-SiC) has zincblende structure\\
+ $\Rightarrow {\color{si-yellow}\bullet}$ are Si atoms,
+ ${\color{gray}\bullet}$ are C atoms
+ \end{itemize}
+ \begin{minipage}{15cm}
+ {\bf Lattice constants:}
+ \[
+ 4a_{\text{c-Si}}\approx5a_{\text{3C-SiC}}
+ \]
+ {\bf Silicon density:}
+ \[
+ \frac{n_{\text{3C-SiC}}}{n_{\text{c-Si}}}=97,66\,\%
+ \]
+ \end{minipage}
+ \begin{minipage}{10cm}
+ \includegraphics[width=10cm]{sic_unit_cell.eps}
+ \end{minipage}
+ \end{pbox}
+ \vspace{-0.45cm}
+ \begin{pbox}
+ \section*{Supposed Si to 3C-SiC conversion}
+ {\bf Schematic of the conversion mechanism}\\\\
+ \begin{minipage}[c]{8.8cm}
+ \includegraphics[width=8.0cm]{sic_prec_seq_01.eps}
+ \end{minipage}
+ \begin{minipage}[c]{8.8cm}
+ \includegraphics[width=8.0cm]{sic_prec_seq_02.eps}
+ \end{minipage}
+ \begin{minipage}[c]{8.1cm}
+ \includegraphics[width=8.0cm]{sic_prec_seq_03.eps}
+ \end{minipage}
+ \vspace{1cm}
+ \begin{enumerate}
+ \item Formation of C-Si dumbbells on regular c-Si lattice sites
+ \item Agglomeration into large clusters (embryos)
+ \item Precipitation of 3C-SiC + Creation of interstitials
+ \end{enumerate}
+ \vspace{1cm}
+ {\bf Experimental observations} [3]
+ \begin{itemize}
+ \item Minimal radius of precipitates: 2 - 4 nm
+ \item Equal orientation of c-Si and 3C-SiC (hkl)-planes
+ \end{itemize}
+ {\tiny
+ [3] J. K. N. Lindner, Appl. Phys. A 77 (2003) 27.
+ }
+ \end{pbox}
+ \vspace{-0.45cm}
+ \begin{pbox}
+ \section*{Simulation details}
+ {\bf MD basics:}
+ \begin{itemize}
+ \item Microscopic description of N particles
+ \item Analytical interaction potential
+ \item Propagation rule in 6N-dim. phase space:
+ Hamilton's equations of motion
+ \item Observables obtained by time or ensemble averages
+ \end{itemize}
+ {\bf Application details:}\\[0.5cm]
+ \begin{minipage}{17cm}
+ \begin{itemize}
+ \item Integrator: Velocity Verlet, timestep: 1 fs
+ \item Ensemble: isothermal-isobaric NPT [4]
+ \begin{itemize}
+ \item Berendsen thermostat:
+ $\tau_{\text{T}}=100\text{ fs}$
+ \item Brendsen barostat:\\
+ $\tau_{\text{P}}=100\text{ fs}$,
+ $\beta^{-1}=100\text{ GPa}$
+ \end{itemize}
+ \item Potential: Tersoff-like bond order potential [5]
+ \[
+ E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
+ \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
+ \]
+ \end{itemize}
+ \end{minipage}
+ \begin{minipage}{9cm}
+ \includegraphics[width=9cm]{tersoff_angle.eps}
+ \end{minipage}\\[1cm]
+ {\tiny
+ [4] L. Verlet, Phys. Rev. 159 (1967) 98.}\\
+ {\tiny
+ [5] P. Erhart and K. Albe, Phys. Rev. B 71 (2005) 35211.}
+ \end{pbox}
+
+\end{pcolumn}
+\begin{pcolumn}
+
+ \begin{pbox}
+ \section*{Interstitial configurations}
+ {\bf Simulation sequence:}\\
+
+\begin{minipage}{15cm}
+{\small
+ \begin{pspicture}(0,0)(14,14)
+ \rput(7,12.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+ \parbox{14cm}{
+ \begin{itemize}
+ \item Initial configuration: $9\times9\times9$ unit cells Si
+ \item Periodic boundary conditions
+ \item $T=0\text{ K}$, $p=0\text{ bar}$
+ \end{itemize}
+ }}}}
+\rput(7,6){\rnode{insert}{\psframebox{
+ \parbox{14cm}{
+ Insertion of C / Si atom:
+ \begin{itemize}
+ \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
+ (${\color{red}\triangleleft}$)
+ \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
+ (${\color{green}\triangleright}$)
+ \item $(-1/8,-1/8,-1/4)$, $(-3/8,-3/8,-1/4)$\\
+ $\rightarrow$ {\color{magenta}110 dumbbell}
+ (${\color{magenta}\Box}$,$\circ$)
+ \item random positions (critical distance check)
+ \end{itemize}
+ }}}}
+ \rput(7,1.5){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
+ \parbox{7cm}{
+ Relaxation time: 2 ps
+ }}}}
+ \ncline[]{->}{init}{insert}
+ \ncline[]{->}{insert}{cool}
+ \end{pspicture}
+}
+\end{minipage}
+\begin{minipage}{10cm}
+ \includegraphics[width=11cm]{unit_cell_s.eps}
+\end{minipage}
+
+ {\bf Si self-interstitial results:}\\
+
+{\small
+ \begin{minipage}[t]{8.5cm}
+ \underline{Tetrahedral}\\
+ $E_f=3.41$ eV\\
+ \includegraphics[width=8cm]{si_self_int_tetra_0.eps}
+ \end{minipage}
+ \begin{minipage}[t]{8.5cm}
+ \underline{110 dumbbell}\\
+ $E_f=4.39$ eV\\
+ \includegraphics[width=8cm]{si_self_int_dumbbell_0.eps}
+ \end{minipage}
+ \begin{minipage}[t]{8.5cm}
+ \underline{Hexagonal}\\
+ $E_f^{\star}\approx4.48$ eV (unstable!)\\
+ \includegraphics[width=8cm]{si_self_int_hexa_0.eps}
+ \end{minipage}\\[1cm]
+
+ \underline{Random insertion}\\
+
+ \begin{minipage}{8.5cm}
+ $E_f=3.97$ eV\\
+ \includegraphics[width=8cm]{si_self_int_rand_397_0.eps}
+ \end{minipage}
+ \begin{minipage}{8.5cm}
+ $E_f=3.75$ eV\\
+ \includegraphics[width=8cm]{si_self_int_rand_375_0.eps}
+ \end{minipage}
+ \begin{minipage}{8.5cm}
+ $E_f=3.56$ eV\\
+ \includegraphics[width=8cm]{si_self_int_rand_356_0.eps}
+ \end{minipage}\\[1cm]
+}
+
+ {\bf C in Si interstitial results:}\\
+
+{\small
+ \begin{minipage}[t]{8.5cm}
+ \underline{Tetrahedral}\\
+ $E_f=2.67$ eV\\
+ \includegraphics[width=8cm]{c_in_si_int_tetra_0.eps}
+ \end{minipage}
+ \begin{minipage}[t]{8.5cm}
+ \underline{110 dumbbell}\\
+ $E_f=1.76$ eV\\
+ \includegraphics[width=8cm]{c_in_si_int_dumbbell_0.eps}
+ \end{minipage}
+ \begin{minipage}[t]{8.5cm}
+ \underline{Hexagonal}\\
+ $E_f^{\star}\approx5.6$ eV (unstable!)\\
+ \includegraphics[width=8cm]{c_in_si_int_hexa_0.eps}
+ \end{minipage}\\[1cm]
+}
+\begin{minipage}{17cm}
+\underline{\flq100\frq{} dumbbell configuration}
+\begin{itemize}
+ \item $E_f=0.47$ eV
+ \item Very often observed
+ \item Most energetically favorable configuration
+ \item Experimental evidence [6]
+\end{itemize}
+\end{minipage}
+\begin{minipage}{8cm}
+\includegraphics[width=8cm]{c_in_si_int_001db_0.eps}
+\end{minipage}\\[1cm]
+\begin{center}
+\includegraphics[width=26cm]{100-c-si-db_s.eps}\\[0.35cm]
+\end{center}
+{\tiny
+ [6] G. D. Watkins and K. L. Brower, Phys. Rev. Lett. 36 (1976) 1329.}
+
+ \end{pbox}
+
+\end{pcolumn}
+\begin{pcolumn}
+
+ \begin{pbox}
+ \section*{High C concentration simulations}
+
+ {\bf Simulation sequence:}\\
+
+{\small
+ \begin{pspicture}(0,0)(30,13)
+ % nodes
+ \rput(7.5,11){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=hb]{
+ \parbox{15cm}{
+ \begin{itemize}
+ \item Initial configuration: $31\times31\times31$ unit cells Si
+ \item Periodic boundary conditions
+ \item $T=450\, ^{\circ}\textrm{C}$, $p=0\text{ bar}$
+ \item Equilibration of $E_{kin}$ and $E_{pot}$
+ \end{itemize}
+ }}}}
+ \rput(7.5,5){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=lachs]{
+ \parbox{15cm}{
+ Insertion of 6000 carbon atoms at constant\\
+ temperature into $V_1$ or $V_2$ or $V_3$:
+ \begin{itemize}
+ \item Total simulation volume $V_1$
+ \item Volume of minimal 3C-SiC precipitation $V_2$
+ \item Volume of necessary amount of Si $V_3$
+ \end{itemize}
+ }}}}
+ \rput(7.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=lbb]{
+ \parbox{8cm}{
+ Cooling down to $20\, ^{\circ}\textrm{C}$
+ }}}}
+ \ncline[]{->}{init}{insert}
+ \ncline[]{->}{insert}{cool}
+ \psframe[fillstyle=solid,fillcolor=white](16,2.6)(26,12.6)
+ \psframe[fillstyle=solid,fillcolor=lightgray](18,4.6)(24,10.6)
+ \psframe[fillstyle=solid,fillcolor=gray](18.5,5.1)(23.5,10.1)
+ \rput(9,5.4){\pnode{in1}}
+ \rput(15,5.4){\pnode{in-1}}
+ \rput(17,7.2){\pnode{ins1}}
+ \rput(14,4.2){\pnode{in2}}
+ \rput(15,4.2){\pnode{in-2}}
+ \rput(18.25,6.88){\pnode{ins2}}
+ \rput(12,3.0){\pnode{in3}}
+ \rput(15,3.0){\pnode{in-3}}
+ \rput(21,7.6){\pnode{ins3}}
+ \ncline[linewidth=0.05]{->}{in-1}{ins1}
+ \ncline[linewidth=0.05]{->}{in-2}{ins2}
+ \ncline[linewidth=0.05]{->}{in-3}{ins3}
+ \ncline[linewidth=0.05]{-}{in1}{in-1}
+ \ncline[linewidth=0.05]{-}{in2}{in-2}
+ \ncline[linewidth=0.05]{-}{in3}{in-3}
+ \end{pspicture}
+}
+ {\bf Results:}\\
+ Si-C and C-C pair correlation function:\\
+ \hspace*{1.3cm} \includegraphics[width=22cm]{pc_si-c_c-c.eps}
+ \begin{center}
+ {\tiny
+ {\bf Dashed vertical lines:} Further calculated C-Si distances
+ in the \flq100\frq{} C-Si dumbbell interstitial configuration}\\[0.5cm]
+ \end{center}
+ Si-Si pair correlation function:\\
+ \hspace*{1.3cm} \includegraphics[width=22cm]{pc_si-si.eps}\\
+ {\bf Interpretation:}
+ {\small
+ \begin{itemize}
+ \item C-C peak at 0.15 nm similar to next neighbour distance of graphite
+ or diamond\\
+ $\Rightarrow$ Formation of strong C-C bonds
+ (almost only for high C concentrations)
+ \item Si-C peak at 0.19 nm similar to next neighbour distance in 3C-SiC
+ \item C-C peak at 0.31 nm equals C-C distance in 3C-SiC\\
+ (due to concatenated, differently oriented
+ \flq100\frq{} dumbbell interstitials)
+ \item Si-Si shows non-zero g(r) values around 0.31 nm like in 3C-SiC\\
+ and a decrease at regular distances\\
+ (no clear peak,
+ interval of enhanced g(r) corresponds to C-C peak width)
+ \item Low C concentration (i.e. $V_1$):
+ The \flq100\frq{} dumbbell configuration
+ \begin{itemize}
+ \item is identified to stretch the Si-Si next neighbour distance
+ to 0.3 nm
+ \item is identified to contribute to the Si-C peak at 0.19 nm
+ \item explains further C-Si peaks (dashed vertical lines)
+ \end{itemize}
+ $\Rightarrow$ C atoms are first elements arranged at distances
+ expected for 3C-SiC\\
+ $\Rightarrow$ C atoms pull the Si atoms into the right
+ configuration at a later stage
+ \item High C concentration (i.e. $V_2$ and $V_3$):
+ \begin{itemize}
+ \item High amount of damage introduced into the system
+ \item Short range order observed but almost no long range order
+ \end{itemize}
+ $\Rightarrow$ Start of amorphous SiC-like phase formation\\
+ $\Rightarrow$ Higher temperatures required for proper SiC formation
+ \end{itemize}
+ }
+
+ \end{pbox}
+ \vspace{-2cm}
+ \begin{pbox}
+ \section*{Conclusion}
+ \begin{itemize}
+ \item \flq100\frq{} C-Si dumbbell interstitial configuration is observed
+ to be the energetically most favorable configuration
+ \item For low C concentrations C atoms introduced as differently
+ oriented C-Si dumbbells in c-Si are properly arranged
+ for 3C-SiC formation
+ \item For high C concentrations an amorphous SiC-like phase is observed
+ which suggests higher temperature simulation runs for proper
+ 3C-SiC formation
+ \end{itemize}
+ \end{pbox}
+ \vspace{-2cm}
+ \begin{pbox}
+ One of us (F. Z.) wants to acknowledge financial support by the\\
+ {\bf Bayerische Forschungsstiftung} (DPA-61/05).
+ \end{pbox}
+
+\end{pcolumn}
+\end{poster}
+\end{document}
+
--- /dev/null
+# Makefile
+LATEX = latex
+DVIPDF = dvipdf
+BIBTEX = bibtex
+
+SRC := $(shell ls *.tex)
+PDF = $(SRC:%.tex=%.pdf)
+
+all: $(PDF)
+
+%.dvi: %.tex
+ $(LATEX) $< $@
+ $(BIBTEX) `basename $< .tex`
+ $(LATEX) $< $@
+ $(LATEX) $< $@
+
+%.pdf: %.dvi
+ $(DVIPDF) $< $@
+
+clean:
+ rm -f *.log *.aux *.bbl *.blg
--- /dev/null
+\pdfoutput=0
+\documentclass[a4paper,11pt]{article}
+\usepackage[activate]{pdfcprot}
+\usepackage{verbatim}
+\usepackage{a4}
+\usepackage{a4wide}
+\usepackage[german]{babel}
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{amsmath}
+\usepackage{ae}
+\usepackage{aecompl}
+\usepackage[dvips]{graphicx}
+\graphicspath{{./img/}}
+\usepackage{color}
+\usepackage{pstricks}
+\usepackage{pst-node}
+\usepackage{rotating}
+
+\setlength{\headheight}{0mm} \setlength{\headsep}{0mm}
+\setlength{\topskip}{-10mm} \setlength{\textwidth}{17cm}
+\setlength{\oddsidemargin}{-10mm}
+\setlength{\evensidemargin}{-10mm} \setlength{\topmargin}{-1cm}
+\setlength{\textheight}{26cm} \setlength{\headsep}{0cm}
+
+\begin{document}
+
+% header
+\begin{center}
+ {\LARGE {\bf Molecular dynamics simulation study
+ of the silicon carbide precipitation process}\\}
+ \vspace{16pt}
+ \textsc{\Large \underline{F. Zirkelbach}$^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[doublespacing]{elsart}
+\documentclass[]{elsart}
+%\usepackage[activate]{pdfcprot}
+\usepackage{verbatim}
+%\usepackage{a4}
+%\usepackage{a4wide}
+\usepackage[english]{babel}
+\usepackage[latin1]{inputenc}
+\usepackage[T1]{fontenc}
+\usepackage{amsmath}
+\usepackage{latexsym}
+\usepackage{ae}
+\usepackage{aecompl}
+\usepackage[dvips]{graphicx}
+\graphicspath{{./}}
+\usepackage{color}
+\usepackage{pstricks}
+\usepackage{pst-node}
+\usepackage{rotating}
+
+\selectlanguage{english}
+
+\begin{document}
+
+\begin{frontmatter}
+
+\title{Molecular dynamics simulation of defect formation and precipitation
+ in heavily carbon doped silicon}
+
+\author[augsburg]{F. Zirkelbach\corauthref{cor}}
+\author[augsburg]{J. K. N. Lindner}
+\author[helsinki]{K. Nordlund}
+\author[augsburg]{B. Stritzker}
+
+\address[augsburg]{Experimentalphysik IV, Institut f\"ur Physik,
+ Universit\"at Augsburg,\\
+ Universit\"atsstr. 1, D-86135 Augsburg, Germany}
+\address[helsinki]{Accelerator Laboratory, Department of Physical Sciences,
+ University of Helsinki,\\
+ Pietari Kalmink. 2, 00014 Helsinki, Finland}
+
+\corauth[cor]{Corresponding author.\\
+ Tel.: +49-821-5983008; fax: +49-821-5983425.\\
+ E-mail address: frank.zirkelbach@physik.uni-augsburg.de
+ (Frank Zirkelbach)}
+
+\begin{abstract}
+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.
+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.
+\end{abstract}
+
+\begin{keyword}
+Silicon, carbon, silicon carbide, nucleation, defect formation,
+molecular dynamics simulations
+\end{keyword}
+
+\end{frontmatter}
+
+\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 the important wide band gap semiconductor material SiC \cite{1}.
+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{2}.
+
+Epitaxial growth of 3C-SiC films is achieved either by ion beam synthesis (IBS) \cite{3}, chemical vapour deposition (CVD) or molecular beam epitaxy (MBE) techniques.
+While in CVD and MBE surface effects need to be taken into account, SiC formation during IBS takes place in the bulk of the Si crystal.
+In the present work the simulation assumes conditions similar to those of the ion implantation process.
+
+First of all a picture of the supposed precipitation event is presented.
+Then the applied simulation sequences are introduced.
+Finally first simulation results are presented.
+
+\section{Supposed Si to 3C-SiC conversion mechanism}
+Crystalline silicon (c-Si) 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 one out of which is occupied by Si and the other by C atoms.
+The length of four lattice constants of c-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 c-Si.
+
+There is a supposed conversion mechanism of heavily carbon doped c-Si into 3C-SiC \cite{4}.
+As concluded from high resolution transmission electron microscopy (HREM) carbon atoms introduced into c-Si 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/c-Si lattice misfit is overcome and precipitation occurs.
+In HREM this transformation manifests itself by the disappearance of patches with dark background in favour of high resolution Moir\'e fringes due to 3C-SiC precipitates embedded in c-Si \cite{3,4}.
+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 c-Si 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 3C-SiC in heavily C doped c-Si.
+
+\section{Simulation sequences}
+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 \cite{5} with a timestep of 1 fs is adopted.
+The interaction of the silicon and carbon atoms is realized by a newly parametrized Tersoff-like bond order potential \cite{6}.
+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 \cite{7} with a time constant of 100 fs.
+The pressure is controlled by the Berendsen barostat \cite{7} again using a time constant of 100 fs and a bulk modulus of 100 GPa for silicon.
+To exclude surface effects periodic boundary conditions are applied.
+In order to study the behaviour of carbon in c-Si, two different simulation sequences are used.
+
+To investigate the interstitial configurations of C and Si atoms in c-Si, a simulation volume of $9\times9\times9$ silicon unit cells is used.
+The temperature is set to 0 K.
+In separated simulation runs a carbon or a silicon atom is inserted in the central unit cell at the tetrahedral (0,0,0) (${\color{red}\triangleleft}$), a hexagonal (-1/8,-1/8,1/8) (${\color{green}\triangleright}$), a nearly dumbbell (-1/8,-1/8,-1/4) (${\color{magenta}\Box}$) or at a random position (in units of the silicon lattice constant) where the origin is located in the centre of the unit cell (Fig. 1).
+In order to avoid too high potential energies in the case of the dumbbell configuration the nearest silicon neighbour atom is manually shifted to (-3/8,-3/8,-1/4) ($\circ$).
+The energy introduced into the system by the insertion of atoms is scaled out within a relaxation phase of 2 ps.
+
+For the simulations aiming to reproduce a precipitation process the simulation volume is 31 silicon lattice constants in each direction.
+The system temperature is set to $450\, ^{\circ} \textrm{C}$ like in IBS \cite{3}.
+$6000$ carbon atoms (the number necessary to form a 3C-SiC precipitate with a radius of $\sim 3$ nm) are consecutively inserted in a way to keep the system temperature constant.
+Carbon is inserted statistically distributed over either the whole simulation volume (insertion volume $V_1$), an insertion volume $V_2$ corresponding to the minimum size of a 3C-SiC precipitate or the volume $V_3$ containing the number of Si atoms necessary for the formation of such a minimum precipitate.
+The two latter insertion volumes are considered since no diffusion of carbon atoms is observed at this temperature.
+Following the insertion procedure the system is cooled down to $20\, ^{\circ} \textrm{C}$.
+
+\section{Results}
+The insertion of individual Si atoms leads to stable tetrahedral and <110> dumbbell self-interstitial configurations as observed earlier in \cite{6}.
+The formation energies are 3.4 eV and 4.4 eV, respectively.
+However, the hexagonal dumbbell configuration is not stable opposed to results in \cite{6}.
+The Si interstitial atom moves towards an energetically more favorable position very close to the tetrahedral one but slightly displaced along the three coordinate axes.
+The formation energy of 4.0 eV for this type of interstitials equals the result obtained in \cite{6} for the hexagonal one.
+The same type of interstitial arises using random insertions.
+In addition, variations exist in which the displacement is only along two <100> axes ($E_f=3.8\, \text{eV}$) or along a single <100> axis ($E_f=3.6\, \text{eV}$) succesively approximating the tetrahedral configuration and formation energy.
+
+In carbon insertion simulations the tetrahedral and <110> dumbbell carbon interstitial configurations are observed to be stable.
+The formation energies are 2.7 eV and 1.8 eV, respectively.
+Again, the hexagonal configuration is found to be unstable.
+The carbon interstitial atom moves to the more favorable <100> dumbbell position which has a formation energy of 0.5 eV.
+This interstitial configuration is shown in Fig. 2.
+There is experimental evidence \cite{8} of the existence of this configuration.
+It is frequently generated and has the lowest formation energy of all the defects observed in all the simulation runs in which carbon is inserted at random positions.
+Fig. 3 schematically displays the <100> dumbbell configuration including the atomic displacements relative to the atoms initial positions together with resulting new Si-Si and C-Si pair distances.
+
+Fig. 4 shows resulting pair correlation functions of the simulation runs targeting the observation of precipitation events.
+The contributions of Si-C and C-C pairs are presented separately.
+The three curves represent results for the insertion of 6000 C atoms into the three different volumes $V_1$, $V_2$ and $V_3$, as explained above.
+There is no significant difference between carbon insertions into $V_2$ and $V_3$.
+
+The number of C-C bonds for $V_1$ is much smaller than for $V_2$ and $V_3$ since carbon atoms are spread over the total simulation volume, which means that there is only 0.2 carbon atoms per silicon unit cell on average.
+The first C-C peak appears at about 0.15 nm.
+This is comparable to the nearest neighbour distance of graphite or diamond.
+It is assumed that these carbon atoms form strong C-C bonds which is supported by a decrease of the total energy during carbon insertion for the $V_2$ and $V_3$ in contrast to the $V_1$ simulation.
+
+The C-C peak at $\sim 0.31$ nm perfectly matches the distance of two carbon atoms in the 3C-SiC lattice. In 3C-SiC the same distance is also expected for Si-Si bonds.
+The Si-Si portion of the pair correlation function for the case of 3000 C atoms inserted into $V_2$ is displayed in Fig. 5, together with a reference function for pure c-Si.
+After insertion of C atoms the Si-Si pair correlation function in fact shows non-zero g(r) values around distance values of 0.31 nm while the amount of Si pairs at the regular distances of 0.24 and 0.38 nm decreases.
+However, no clear peak is observed but the interval of enhanced g(r) values corresponds to the width of the C-C g(r) peak.
+Analyses of randomly chosen configurations in which distances around 0.3 nm appear, identify <100> C-Si dumbbells to be responsible for stretching the Si-Si next neighbour distance for low C concentrations, i.e. for the $V_1$ and early stages of $V_2$ and $V_3$ simulation runs.
+This excellently agrees with the calculation for a single <100> dumbbell (r(13) in Fig. 3).
+For higher C concentrations the defect concentration is likewise increased and a considerable amount of damage is introduced into the insertion volume.
+Damage and superposition of defects generate new displacement arrangements which become hard to categorize and trace and obviously lead to a broader distribution of pair distances.
+The step-like increase of Si-Si pairs at 0.29 nm is probably due to the Si-Si cut-off radius of 0.296 nm in the used bond order potential \cite{6}.
+The cut-off function causes artificial forces pushing the Si atoms out of the cut-off region.
+By visualizing the C-C atom pairs with distances of 0.31 nm, concatenated, differently oriented <100> dumbbell interstitials are frequently observed.
+This leads to the assumption that C atoms introduced in that way are the first elements arranged at distances expected for 3C-SiC which at a later stage pull the Si atoms into the right configuration.
+
+The Si-C pair correlation (Fig. 4) shows the formation of Si-C atom pairs displaced approximately by 0.187 nm.
+This corresponds quite well to the expected next neighbour distance of 0.189 nm for Si and C atoms in 3C-SiC.
+For low concentrations again <100> dumbbell configurations can be identified to contribute to this pair distance (r(3C) in Fig. 3).
+Further more, the bump at 0.175 (r(1C) in Fig. 3) and the peaks at about 0.333, 0.374, 0.386, 0.431 and 0.464 nm are comprehensible by comparing with calculated values in Fig. 3 and the dashed vertical lines in Fig. 4.
+The dashed lines mark further calculated C-Si atom pair distances appearing in the <100> C-Si dumbbell interstitial configuration which are not displayed in Fig. 3.
+The distinct peak at 0.26 nm, which exactly matches the cut-off radius of Si-C interaction, is again a potential artefact.
+For high carbon concentrations again superposition of defects and high amounts of damage characterize the pair distances.
+Short range order indeed is observed but only hardly visible is the long range order.
+This suggests to use higher temperatures particularly with regard to $V_2$ and $V_3$ simulations, i.e. simulations with high carbon concentrations, so that the system is able to get over an energy barrier escaping a local minimum configuration.
+An increase of the simulation temperature should not be in conflict with experimental conditions since the target temperature of $450\, ^{\circ} \textrm{C}$ measured during the IBS of 3C-SiC \cite{3} at the substrat holder is most certainly lower than the temperature predominating near the target surface, where 3C-SiC formation takes place.
+
+\section{Summary}
+The conversion of heavily C doped c-Si into 3C-SiC precipitates is investigated.
+Molecular dynamics simulation sequences to analyze interstitial configurations and the precipitation of 3C-SiC are introduced.
+The <100> C-Si dumbbel reproduced by simulation is observed the energetically most favorable configuration and explained in detail.
+First results of the simulations suggest that in the precipitation process C atoms introduced as differently oriented C-Si dumbbells into the c-Si matrix are the first elements properly arranged for the 3C-SiC formation.
+Furthermore, the observation of high amounts of damage particularly for high carbon concentrations demands for elevated system temperatures to achieve the precipitation event.
+
+\begin{thebibliography}{8}
+ \bibitem{1} J. H. Edgar, J. Mater. Res. 7 (1992) 235.
+ \bibitem{2} J. W. Strane, S. R. Lee, H. J. Stein, S. T. Picraux,
+ J. K. Watanabe, J. W. Mayer, J. Appl. Phys. 79 (1996) 637.
+ \bibitem{3} J. K. N. Lindner, Appl. Phys. A 77 (2003) 27.
+ \bibitem{4} P. Werner, R. Koegler, W. Skorupa, and D. Eichler:
+ in Proc. 11th Int. Conf. on Ion Implantation Technology,
+ ed. by E. Ishidida, S. Banerjee, S. Mehta, T. C. Smith,
+ M. Current, L. Larson, A. Tasch, T. Romig
+ (Austin, TX, USA, June 16-21, 1996) pp. 675
+ \bibitem{5} L. Verlet, Phys. Rev. 159 (1967) 98.
+ \bibitem{6} P. Erhart and K. Albe, Phys. Rev. B 71 (2005) 35211.
+ \bibitem{7} H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren,
+ A. DiNola, J. R. Haak, J. Chem. Phys. 81 (1984) 3684.
+ \bibitem{8} G. D. Watkins and K. L. Brower, Phys. Rev. Lett. 36 (1976) 1329.
+ \end{thebibliography}
+
+\newpage
+\section*{Figures}
+
+\begin{figure}[!h]
+ \begin{center}
+ \includegraphics[width=8cm]{fig1.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}
+
+\begin{figure}[!h]
+ \begin{center}
+ \includegraphics[width=6cm]{fig2.eps}
+ \caption{Position of a <100> dumbbell carbon interstitial in silicon.
+ Only bonds of the carbon interstitial atom are shown.}
+ \end{center}
+\end{figure}
+
+\begin{figure}[!h]
+ \begin{center}
+ \includegraphics[width=15cm]{fig3.eps}
+ \caption{Schematic of the <100> C-Si dumbbell configuration.
+ Displacements of the atoms relative to their initial position are given.
+ The displacement of the carbon atom is relative to the initial position of atom 1.
+ New resulting Si-Si and C-Si pair distances r(ij) for the atoms (ij) shown in the schematic are recorded.}
+ \end{center}
+\end{figure}
+
+\begin{figure}[!h]
+ \begin{center}
+ \includegraphics[]{fig4.eps}
+ \caption{Pair correlation functions for Si-C and C-C bonds.
+ The three curves represent results for the three different insertion volumes $V_1$, $V_2$ and $V_3$, as explained in the text.
+ The dashed vertical lines mark further calculated C-Si atom pair distances appearing in the <100> C-Si dumbbell interstitial configuration, which are not displayed in Fig. 3.}
+ \end{center}
+\end{figure}
+
+\begin{figure}[!h]
+ \begin{center}
+ \includegraphics[]{fig5.eps}
+ \caption{Si-Si pair correlation function for pure Si and Si with 3000 inserted C atoms.
+ The inset shows a magnified region between 0.28 and 0.36 nm.}
+ \end{center}
+\end{figure}
+
+\end{document}
--- /dev/null
+\pdfoutput=0
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+\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}
$RSYNC -e "ssh -p 3389" $SRC/img/ ./img/
$RSYNC -e "ssh -p 3389" $SRC/figs/ ./figs/
+$RSYNC -e "ssh -p 3389" $SRC/plot/ ./plot/
$RSYNC -e "ssh -p 3389" $SRC/talks/*.pdf ./talks/
# Makefile
LATEX = latex
DVIPS = dvips -tlandscape
+DVIPDF= dvipdf
PS2PDF = ps2pdf
+PDFLATEX = pdflatex
SRC := $(shell ls *.tex)
PDF = $(SRC:%.tex=%.pdf)
%.ps: %.dvi
$(DVIPS) $<
-%.pdf: %.ps
- $(PS2PDF) $<
+#%.pdf: %.ps
+# $(PS2PDF) $<
+
+%.pdf: %.dvi
+ $(DVIPDF) $<
+
+#%.dvi: %.tex
+# $(PDFLATEX) $<
clean:
rm -f *.log *.aux
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
+\usepackage{latexsym}
\usepackage{ae}
\usepackage{calc} % Simple computations with LaTeX variables
\usepackage{fancyvrb} % Fancy verbatim environments
\usepackage{pstricks} % PSTricks with the standard color package
+\usepackage{pstricks}
+\usepackage{pst-node}
+
+%\usepackage{epic}
+%\usepackage{eepic}
+
\usepackage{graphicx}
\graphicspath{{../img/}}
+\usepackage[setpagesize=false]{hyperref}
+
\usepackage{semcolor}
\usepackage{semlayer} % Seminar overlays
\usepackage{slidesec} % Seminar sections and list of slides
\articlemag{1}
+\special{landscape}
+
\begin{document}
\extraslideheight{10in}
-\slideframe{plain}
+\slideframe{none}
+
+\pagestyle{empty}
% specify width and height
\slidewidth 27.7cm
% shift it into visual area properly
\def\slideleftmargin{3.3cm}
-\def\slidetopmargin{0.0cm}
+\def\slidetopmargin{0.6cm}
\newcommand{\ham}{\mathcal{H}}
\newcommand{\pot}{\mathcal{V}}
\newcommand{\foo}{\mathcal{U}}
\newcommand{\vir}{\mathcal{W}}
+% itemize level ii
+\renewcommand\labelitemii{{\color{gray}$\bullet$}}
+
% topic
\begin{slide}
% contents
+% no contents for such a short talk!
+
+% start of contents
+
\begin{slide}
- \begin{center}
- {\bf
- Molecular dynamics simulation study\\
- of the silicon carbide precipitation process
+ {\large\bf
+ Motivation / Introduction
}
- \end{center}
\vspace{16pt}
- {\large\bf
- Outline
- }
+ Reasons for understanding the SiC precipitation process:
+
+ \begin{itemize}
+ \item 3C-SiC wide band gap semiconductor formation
+ \item Strained Si (no precipitation wanted!)
+ \end{itemize}
\vspace{16pt}
+ Si / 3C-SiC facts:
+
+ \begin{minipage}{8cm}
\begin{itemize}
- \item Motivation / Introduction
- \item Molecular dynamics simulation details
+ \item Unit cell:
\begin{itemize}
- \item Integrator, potential, ensemble control
- \item Simulation sequence
+ \item {\color{orange}fcc} $+$
+ \item {\color{gray}fcc shifted $1/4$ of volume diagonal}
\end{itemize}
- \item Results gained by simulation
- \begin{itemize}
- \item Carbon interstitials in silicon
- \item Existence of $SiC$-precipitates
- \end{itemize}
- \item Conclusion / Outlook
+ \item Lattice constants:
+ \[
+ 4a_{Si}\approx5a_{SiC}
+ \]
+ \item Silicon density:
+ \[
+ \frac{n_{SiC}}{n_{Si}}=97,66\,\%
+ \]
\end{itemize}
+ \end{minipage}
+ \hspace{8pt}
+ \begin{minipage}{4cm}
+ \includegraphics[width=4cm]{sic_unit_cell.eps}
+ \end{minipage}
+
\end{slide}
-% start of contents
+ \small
+\begin{slide}
+
+ {\large\bf
+ Motivation / Introduction
+ }
+
+ \small
+ \vspace{6pt}
+
+ Supposed conversion mechanism of heavily carbon doped Si into SiC:
+
+ \vspace{8pt}
+
+ \begin{minipage}{3.8cm}
+ \includegraphics[width=3.7cm]{sic_prec_seq_01.eps}
+ \end{minipage}
+ \hspace{0.6cm}
+ \begin{minipage}{3.8cm}
+ \includegraphics[width=3.7cm]{sic_prec_seq_02.eps}
+ \end{minipage}
+ \hspace{0.6cm}
+ \begin{minipage}{3.8cm}
+ \includegraphics[width=3.7cm]{sic_prec_seq_03.eps}
+ \end{minipage}
+
+ \vspace{8pt}
+
+ \begin{minipage}{3.8cm}
+ Formation of C-Si dumbbells on regular c-Si lattice sites
+ \end{minipage}
+ \hspace{0.6cm}
+ \begin{minipage}{3.8cm}
+ Agglomeration into large clusters (embryos)\\
+ \end{minipage}
+ \hspace{0.6cm}
+ \begin{minipage}{3.8cm}
+ Precipitation of 3C-SiC + Creation of interstitials\\
+ \end{minipage}
+
+ \vspace{12pt}
+
+ Experimentally observed:
+ \begin{itemize}
+ \item Minimal diameter of precipitation: 4 - 5 nm
+ \item Equal orientation of Si and SiC (hkl)-planes
+ \end{itemize}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Simulation details
+ }
+
+ \vspace{12pt}
+
+ MD basics:
+ \begin{itemize}
+ \item Microscopic description of N particle system
+ \item Analytical interaction potential
+ \item Hamilton's equations of motion as propagation rule\\
+ in 6N-dimensional phase space
+ \item Observables obtained by time average
+ \end{itemize}
+
+ \vspace{12pt}
+
+ Application details:
+ \begin{itemize}
+ \item Integrator: Velocity Verlet, timestep: $1\, fs$
+ \item Ensemble: NVT, Berendsen thermostat, $\tau=100.0$
+ \item Potential: Tersoff-like bond order potential\\
+ \[
+ E = \frac{1}{2} \sum_{i \neq j} \pot_{ij}, \quad
+ \pot_{ij} = f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right]
+ \]
+ \begin{center}
+ {\scriptsize P. Erhart and K. Albe. Phys. Rev. B 71 (2005) 035211}
+ \end{center}
+ \end{itemize}
+
+ \begin{picture}(0,0)(-240,-70)
+ \includegraphics[width=5cm]{tersoff_angle.eps}
+ \end{picture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Simulation details
+ }
+
+ \vspace{8pt}
+
+ Interstitial simulations:
+
+ \vspace{8pt}
+
+ \begin{pspicture}(0,0)(7,8)
+ \rput(3.5,7){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
+ \parbox{7cm}{
+ \begin{itemize}
+ \item Initial configuration: $9\times9\times9$ unit cells Si
+ \item Periodic boundary conditions
+ \item $T=0 \, K$
+ \end{itemize}
+ }}}}
+\rput(3.5,3.5){\rnode{insert}{\psframebox{
+ \parbox{7cm}{
+ Insertion of C / Si atom:
+ \begin{itemize}
+ \item $(0,0,0)$ $\rightarrow$ {\color{red}tetrahedral}
+ \item $(-1/8,-1/8,1/8)$ $\rightarrow$ {\color{green}hexagonal}
+ \item $(-1/8,-1/8,-1/4)$, $(-1/4,-1/4,-1/4)$\\
+ $\rightarrow$ {\color{magenta}110 dumbbell}
+ \item random positions (critical distance check)
+ \end{itemize}
+ }}}}
+ \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
+ \parbox{3.5cm}{
+ Relaxation time: $2\, ps$
+ }}}}
+ \ncline[]{->}{init}{insert}
+ \ncline[]{->}{insert}{cool}
+ \end{pspicture}
+
+ \begin{picture}(0,0)(-210,-45)
+ \includegraphics[width=6cm]{unit_cell.eps}
+ \end{picture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Results
+ } - Si self-interstitial runs
+
+ \small
+
+ \begin{minipage}[t]{4.3cm}
+ \underline{Tetrahedral}\\
+ $E_f=3.41\, eV$\\
+ \includegraphics[width=3.8cm]{si_self_int_tetra_0.eps}
+ \end{minipage}
+ \begin{minipage}[t]{4.3cm}
+ \underline{110 dumbbell}\\
+ $E_f=4.39\, eV$\\
+ \includegraphics[width=3.8cm]{si_self_int_dumbbell_0.eps}
+ \end{minipage}
+ \begin{minipage}[t]{4.3cm}
+ \underline{Hexagonal} \hspace{4pt}
+ \href{../video/si_self_int_hexa.avi}{$\rhd$}\\
+ $E_f^{\star}\approx4.48\, eV$ (unstable!)\\
+ \includegraphics[width=3.8cm]{si_self_int_hexa_0.eps}
+ \end{minipage}
+
+ \underline{Random insertion}
+
+ \begin{minipage}{4.3cm}
+ $E_f=3.97\, eV$\\
+ \includegraphics[width=3.8cm]{si_self_int_rand_397_0.eps}
+ \end{minipage}
+ \begin{minipage}{4.3cm}
+ $E_f=3.75\, eV$\\
+ \includegraphics[width=3.8cm]{si_self_int_rand_375_0.eps}
+ \end{minipage}
+ \begin{minipage}{4.3cm}
+ $E_f=3.56\, eV$\\
+ \includegraphics[width=3.8cm]{si_self_int_rand_356_0.eps}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Results
+ } - Carbon interstitial runs
+
+ \small
+
+ \begin{minipage}[t]{4.3cm}
+ \underline{Tetrahedral}\\
+ $E_f=2.67\, eV$\\
+ \includegraphics[width=3.8cm]{c_in_si_int_tetra_0.eps}
+ \end{minipage}
+ \begin{minipage}[t]{4.3cm}
+ \underline{110 dumbbell}\\
+ $E_f=1.76\, eV$\\
+ \includegraphics[width=3.8cm]{c_in_si_int_dumbbell_0.eps}
+ \end{minipage}
+ \begin{minipage}[t]{4.3cm}
+ \underline{Hexagonal} \hspace{4pt}
+ \href{../video/c_in_si_int_hexa.avi}{$\rhd$}\\
+ $E_f^{\star}\approx5.6\, eV$ (unstable!)\\
+ \includegraphics[width=3.8cm]{c_in_si_int_hexa_0.eps}
+ \end{minipage}
+
+ \underline{Random insertion}
+
+ \footnotesize
+
+\begin{minipage}[t]{3.3cm}
+ $E_f=0.47\, eV$\\
+ \includegraphics[width=3.3cm]{c_in_si_int_001db_0.eps}
+ \begin{picture}(0,0)(-15,-3)
+ 001 dumbbell
+ \end{picture}
+\end{minipage}
+\begin{minipage}[t]{3.3cm}
+ $E_f=1.62\, eV$\\
+ \includegraphics[width=3.2cm]{c_in_si_int_rand_162_0.eps}
+\end{minipage}
+\begin{minipage}[t]{3.3cm}
+ $E_f=2.39\, eV$\\
+ \includegraphics[width=3.1cm]{c_in_si_int_rand_239_0.eps}
+\end{minipage}
+\begin{minipage}[t]{3.0cm}
+ $E_f=3.41\, eV$\\
+ \includegraphics[width=3.3cm]{c_in_si_int_rand_341_0.eps}
+\end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Simulation details
+ }
+
+ \small
+
+ \vspace{8pt}
+
+ SiC precipitation simulations:
+
+ \vspace{8pt}
+
+ \begin{pspicture}(0,0)(12,8)
+ % nodes
+ \rput(3.5,6.5){\rnode{init}{\psframebox[fillstyle=solid,fillcolor=green]{
+ \parbox{7cm}{
+ \begin{itemize}
+ \item Initial configuration: $31\times31\times31$ unit cells Si
+ \item Periodic boundary conditions
+ \item $T=450\, ^{\circ}C$
+ \item Equilibration of $E_{kin}$ and $E_{pot}$ for $600\, fs$
+ \end{itemize}
+ }}}}
+ \rput(3.5,3.2){\rnode{insert}{\psframebox[fillstyle=solid,fillcolor=red]{
+ \parbox{7cm}{
+ Insertion of $6000$ carbon atoms at constant\\
+ temperature into:
+ \begin{itemize}
+ \item Total simulation volume {\pnode{in1}}
+ \item Volume of minimal SiC precipitation {\pnode{in2}}
+ \item Volume of necessary amount of Si {\pnode{in3}}
+ \end{itemize}
+ }}}}
+ \rput(3.5,1){\rnode{cool}{\psframebox[fillstyle=solid,fillcolor=cyan]{
+ \parbox{3.5cm}{
+ Cooling down to $20\, ^{\circ}C$
+ }}}}
+ \ncline[]{->}{init}{insert}
+ \ncline[]{->}{insert}{cool}
+ \psframe[fillstyle=solid,fillcolor=white](7.5,1.8)(13.5,7.8)
+ \psframe[fillstyle=solid,fillcolor=lightgray](9,3.3)(12,6.3)
+ \psframe[fillstyle=solid,fillcolor=gray](9.25,3.55)(11.75,6.05)
+ \rput(7.9,4.8){\pnode{ins1}}
+ \rput(9.22,4.4){\pnode{ins2}}
+ \rput(10.5,4.8){\pnode{ins3}}
+ \ncline[]{->}{in1}{ins1}
+ \ncline[]{->}{in2}{ins2}
+ \ncline[]{->}{in3}{ins3}
+ \end{pspicture}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Very first results of the SiC precipitation runs
+ }
+
+ \footnotesize
+
+ \begin{minipage}[b]{6.9cm}
+ \includegraphics[width=6.3cm]{../plot/sic_prec_energy.ps}
+ \includegraphics[width=6.3cm]{../plot/sic_prec_temp.ps}
+ \end{minipage}
+ \begin{minipage}[b]{5.5cm}
+ \begin{itemize}
+ \item {\color{red} Total simulation volume}
+ \item {\color{green} Volume of minimal SiC precipitation}
+ \item {\color{blue} Volume of necessary amount of Si}
+ \end{itemize}
+ \vspace{40pt}
+ \includegraphics[width=6.3cm]{../plot/foo150.ps}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Very first results of the SiC precipitation runs
+ }
+
+ \begin{minipage}[t]{6.9cm}
+ \includegraphics[width=6.3cm]{../plot/sic_pc.ps}
+ \includegraphics[width=6.3cm]{../plot/foo_end.ps}
+ \hspace{12pt}
+ \end{minipage}
+ \begin{minipage}[c]{5.5cm}
+ \includegraphics[width=6.0cm]{sic_si-c-n.eps}
+ \end{minipage}
+
+\end{slide}
+
+\begin{slide}
+
+ {\large\bf
+ Summary / Outlook
+ }
+
+\vspace{24pt}
+
+\begin{itemize}
+ \item Importance of understanding the SiC precipitation mechanism
+ \item Interstitial configurations in silicon using the Albe potential
+ \item Indication of SiC precipitation
+\end{itemize}
+
+\vspace{24pt}
+
+\begin{itemize}
+ \item Displacement and stress calculations
+ \item Refinement of simulation sequence to create 3C-SiC
+ \item Analyzing self-designed Si/SiC interface
+\end{itemize}
+
+\end{slide}
\end{document}
--- /dev/null
+#!/bin/bash
+
+#
+# copy to /usr/bin
+#
+# enhance: if $1 is a url ... start firefox not mplayer!
+#
+
+file=`echo $1 | awk -F: '{ print $2 }'`
+
+echo "playing $file ..."
+
+mplayer -fs $file
+
+echo "done"
+
--- /dev/null
+# copy / add to ~/.xpdfrc
+
+urlCommand "/usr/bin/xpdfplayer %s"
+
--- /dev/null
+# Makefile
+LATEX = latex
+DVIPS = dvips -tlandscape
+DVIPDF= dvipdf
+PS2PDF = ps2pdf
+PDFLATEX = pdflatex
+
+SRC = thesis.tex
+PDF = $(SRC:%.tex=%.pdf)
+
+all: $(PDF)
+
+%.dvi: %.tex
+ $(PDFLATEX) $< $@
+ $(PDFLATEX) $< $@
+
+%.ps: %.dvi
+ $(DVIPS) $<
+
+%.pdf: %.dvi
+ $(DVIPDF) $<
+
+clean:
+ rm -f *.log *.aux
-\chapter{Derivative of the three body Tersoff potential}
+\chapter{Force evaluation for the three body Tersoff potential}
\label{app:d_tersoff}
\section{Form of the Tersoff potential and its derivative}
\begin{eqnarray}
\nabla_{{\bf r}_i} V_{jk} & = & f_C(r_{jk}) f_A(r_{jk}) \nabla_{{\bf r}_i} b_{jk} \\
\nabla_{{\bf r}_i} b_{jk} & = & - \frac{\chi_{jk}}{2} (1+\beta^{n_j} \zeta_{jk}^{n_j})^{-\frac{1}{2n_j}-1} \beta^{n_j} \zeta_{jk}^{n_j-1} \nabla_{{\bf r}_i} \zeta_{jk} \\
-\nabla_{{\bf r}_i} \zeta_{jk} & = & \sum_{l \neq j,k} \big( g(\theta_{jkl}) \nabla_{{\bf r}_i} f_C(r_{jl}) + f_C(r_{jl}) \nabla_{{\bf r}_i} g(\theta_{jkp}) \big) \nonumber \\
+\nabla_{{\bf r}_i} \zeta_{jk} & = & \sum_{l \neq j,k} \big( g(\theta_{jkl}) \nabla_{{\bf r}_i} f_C(r_{jl}) + f_C(r_{jl}) \nabla_{{\bf r}_i} g(\theta_{jkl}) \big) \nonumber \\
& = & f_C(r_{ji}) \nabla_{{\bf r}_i} g(\theta_{jki}) + g(\theta_{jki}) \nabla_{{\bf r}_i} f_C(r_{ji}) \\
\nabla_{{\bf r}_i} g(\theta_{jki}) & = & - \frac{2(h_j-\cos\theta_{jki})c_j^2}{\big[d_j^2 + (h_j - \cos\theta_{jki})^2\big]^2} \nabla_{{\bf r}_i} (\cos\theta_{jki}) \\
\nabla_{{\bf r}_i} \cos \theta_{jki} & = & \nabla_{{\bf r}_i} \Big( \frac{{\bf r}_{jk} {\bf r}_{ji}}{r_{jk} r_{ji}} \Big) \nonumber \\
& = & \frac{1}{r_{jk} r_{ji}} {\bf r}_{jk} - \frac{\cos\theta_{jki}}{r_{ji}^2} {\bf r}_{ji}
\end{eqnarray}
+
+ \section{Implementation issues}
+
+As seen in the last sections the derivatives of $V_{ij}$, $V_{ji}$ and $V_{jk}$
+with respect to ${\bf r}_i$ are necessary to compute the forces for atom $i$.
+According to this, for every triple $(ijk)$ the derivatives of the three
+potential contributions, denoted by $V_{ijk}$, $V_{jik}$ and $V_{jki}$
+have to be computed.
+In simulation, however, it is not practical to evaluate all three potential
+derivatives for each $(ijk)$ triple.
+The $V_{jik}$ and $V_{jki}$ potential and its derivatives will be calculated
+in subsequent loops anyways.
+To avoid multiple computation of the same potential derivatives
+the force contributions for atom $j$ and $k$ due to the $V_{ijk}$ contribution
+have to be considered by calculating the derivatives of $V_{ijk}$
+with respect to ${\bf r}_j$ and ${\bf r}_k$
+inside the loop of the $(ijk)$ triple
+in addition to the derivative with respect to ${\bf r}_i$.
+This poses a more convenient method to obtain the forces
+keeping in mind that all the necessary force contributions for atom $i$
+are calculated and added in subsequent loops.
+
+The following symmetry considerations help to obtain the
+
+ \subsection{Derivative of $V_{ij}$ with respect to ${\bf r}_j$}
+
+\begin{eqnarray}
+ \nabla_{{\bf r}_j} V_{ij} & = &
+ \nabla_{{\bf r}_j} f_C(r_{ij}) \big[ f_R(r_{ij}) +
+ b_{ij} f_A(r_{ij}) \big] + \nonumber \\
+ & & + f_C(r_{ij}) \big[ \nabla_{{\bf r}_j} f_R(r_{ij}) +
+ b_{ij} \nabla_{{\bf r}_j} f_A(r_{ij}) +
+ f_A(r_{ij}) \nabla_{{\bf r}_j} b_{ij} \big]
+\end{eqnarray}
+Using the equality $\nabla_{{\bf r}_i} r_{ij}=-\nabla_{{\bf r}_j} r_{ij}$
+the following relations are valid:
+\begin{eqnarray}
+ \nabla_{{\bf r}_j} f_R(r_{ij}) &=& - \nabla_{{\bf r}_i} f_R(r_{ij}) \\
+ \nabla_{{\bf r}_j} f_A(r_{ij}) &=& - \nabla_{{\bf r}_i} f_A(r_{ij}) \\
+ \nabla_{{\bf r}_j} f_C(r_{ij}) &=& - \nabla_{{\bf r}_i} f_C(r_{ij})
+\end{eqnarray}
+The pair contributions .... easy.
+Now having a look at $b_{ij}$.
+\begin{eqnarray}
+ \nabla_{{\bf r}_j}\cos\theta_{ijk} &=&
+ \nabla_{{\bf r}_j}\Big(\frac{{\bf r}_{ij}{\bf }r_{ik}}{r_{ij}r_{ik}}\Big)
+ \nonumber \\
+ &=& \frac{1}{r_{ij}r_{ik}}{\bf r}_{ik} -
+ \frac{\cos\theta_{ijk}}{r_{ij}^2}{\bf r}_{ij}
+\end{eqnarray}
+
+ \subsection{Derivative of $V_{ij}$ with respect to ${\bf r}_k$}
+
+The derivative of $V_{ij}$ with respect to ${\bf r}_k$ just consists of the
+single term
+\begin{eqnarray}
+ \nabla_{{\bf r}_k} V_{ij} & = &
+ f_C(r_{ij})f_A(r_{ij})\nabla_{{\bf r}_{k}}b_{ij}
+\end{eqnarray}
+since the derivatives of the functions only depending on atom $i$ and $j$
+vanish.
+\begin{eqnarray}
+ \nabla_{{\bf r}_k} f_R(r_{ij}) &=& 0 \\
+ \nabla_{{\bf r}_k} f_A(r_{ij}) &=& 0 \\
+ \nabla_{{\bf r}_k} f_C(r_{ij}) &=& 0
+\end{eqnarray}
+Now look at $b_{ij}$, not only angle important here!
+\begin{eqnarray}
+ \nabla_{{\bf r}_k}\zeta_{ij} &=&
+ g(\theta_{ijk})\nabla_{{\bf r}_k}f_C(r_{ik}) +
+ f_C(r_{ik})\nabla_{{\bf r}_k}g(\theta_{ijk}) \\
+ \nabla_{{\bf r}_k}f_C(r_{ik}) &=& - \nabla_{{\bf r}_i}f_C(r_{ik}) \\
+ \nabla_{{\bf r}_k}\cos\theta_{ijk} &=&
+ \nabla_{{\bf r}_k}\Big(\frac{{\bf r}_{ij}{\bf }r_{ik}}{r_{ij}r_{ik}}\Big)
+ \nonumber \\
+ &=&\frac{1}{r_{ij}r_{ik}}{\bf r}_{ij} -
+ \frac{\cos\theta_{ijk}}{r_{ik}^2}{\bf r}_{ik}
+\end{eqnarray}
+
+ \subsection{Code realization}
+
+The implementation of the force evaluation shown in the following
+is applied to the potential designed by Erhard and Albe.
+There are slight differences comparted to the original potential by Tersoff:
+\begin{itemize}
+ \item Difference in sign of the attractive part.
+ \item $c$, $d$ and $h$ values depend on atom $k$ in addition to atom $i$.
+ \item Difference in sign of the $\cos\theta_{ijk}$ term.
+ \item There are no parameters $\beta$ and $\chi$.
+ \item The exponent of the $b$ term is constantly $-\frac{1}{2}$.
+\end{itemize}
+These differences actually slightly ease code realization.
+
+\begin{figure}
+\renewcommand\labelitemi{}
+\renewcommand\labelitemii{}
+\renewcommand\labelitemiii{}
+LOOP i \{
+\begin{itemize}
+ \item // nop (only used in orig. Tersoff)
+ \item LOOP j \{
+ \begin{itemize}
+ \item // nop (only used in orig. Tersoff)
+ \end{itemize}
+ \item \}
+ \item LOOP j \{
+ \begin{itemize}
+ \item $\zeta_{ij}=0$
+ \item set $S_{ij}$ (cutoff)
+ \item calculate: $r_{ij}$, $r_{ij}^2$
+ \item IF $r_{ij} > S_{ij}$ THEN CONTINUE
+ \item
+ \item LOOP k \{
+ \begin{itemize}
+ \item set $ik$-depending values
+ \item calculate: $r_{ik}$, $r_{ik}^2$
+ \item IF $r_{ik} > S_{ik}$ THEN CONTINUE
+ \item calculate: $\theta_{ijk}$, $\cos(\theta_{ijk})$,
+ $dg(\theta_{ijk})$, $g(\theta)$,
+ $f_C(r_{ik})$, $df_C(r_{ik})$
+ \item $\zeta_{ij}=\zeta_{ij}+f_C(r_{ik})g(\theta)$
+ \end{itemize}
+ \item \}
+ \item
+ \item calculate: $f_C(r_{ij})$, $df_C(r_{ij})$, $f_A(r_{ij})$,
+ $df_A(r_{ij})$, $f_R(r_{ij})$, $df_R(r_{ij})$,
+ $b_{ij}$, $db_{ij}$
+ \item calculate:
+$
+F=-\frac{1}{2}\big(
+\nabla_{{\bf r}_i} f_C(r_{ij}) \big[ f_R(r_{ij}) - b_{ij} f_A(r_{ij}) \big] +
+f_C(r_{ij}) \big[ \nabla_{{\bf r}_i} f_R(r_{ij}) -
+ b_{ij} \nabla_{{\bf r}_i} f_A(r_{ij}) \big]\big)
+$
+ \item $F_{Atom\, i} = F_{Atom\, i} + F$
+ \item $F_{Atom\, j} = F_{Atom\, j} - F$
+ \item $E=E+\frac{1}{2}f_C(r_{ij})[f_R(r_{ij})-b_{ij}f_A(r_{ij})]$
+ \item $d\zeta_{ij}=\frac{1}{2}f_A(r_{ij})f_C(r_{ij})db_{ij}$
+ \item
+ \item LOOP k \{
+ \begin{itemize}
+ \item calculate: $\nabla_{{\bf r}_i}\cos\theta_{ijk}$,
+ $\nabla_{{\bf r}_j}\cos\theta_{ijk}$,
+ $\nabla_{{\bf r}_k}\cos\theta_{ijk}$
+ \item $
+F_{Atom\, i}+= d\zeta_{ij}\big(
+g(\theta_{ijk})\nabla_{{\bf r}_i}f_C(r_{ik}) +
+f_C(r_{ik})dg(\theta_{ijk})\nabla_{{\bf r}_i}\cos\theta_{ijk}\big)$
+ \item $
+F_{Atom\, j}+= d\zeta_{ij}
+f_C(r_{ik})dg(\theta_{ijk})\nabla_{{\bf r}_j}\cos\theta_{ijk}$
+ \item $
+F_{Atom\, k}+= d\zeta_{ij}\big(
+g(\theta_{ijk})\nabla_{{\bf r}_k}f_C(r_{ik}) +
+f_C(r_{ik})dg(\theta_{ijk})\nabla_{{\bf r}_k}\cos\theta_{ijk}\big)$
+ \end{itemize}
+ \item \}
+ \end{itemize}
+ \item \}
+\end{itemize}
+\}
+\caption{Implementation of the force evaluation for Tersoff like bond-order
+ potentials using pseudocode.}
+\end{figure}
+
\chapter{Simulation}
-\newpage
+\section{Cohesive energies}
\begin{figure}[!h]
\begin{center}
\label{img:ec_vs_lc}
\end{center}
\end{figure}
+
+
+\section{Silicon self-interstitials}
+
+\begin{itemize}
+ \item Tetrahedral:
+ \begin{itemize}
+ \item Cohesive energy: $3.405 \, eV$
+ \end{itemize}
+ \item Hexagonal:
+ \begin{itemize}
+ \item Cohesive energy: $4.480 \, eV$
+ \end{itemize}
+ \item 110 dumbbell:
+ \begin{itemize}
+ \item Cohesive energy: $4.392 \, eV$
+ \end{itemize}
+\end{itemize}
--- /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}
+
+\renewcommand{\labelenumi}{(\alph{enumi})}
+\renewcommand{\labelenumii}{\arabic{enumii})}
+\renewcommand{\labelenumiii}{\roman{enumiii})}
+
+\begin{document}
+
+% header
+\begin{center}
+ {\LARGE {\bf Materials Physics II}\\}
+ \vspace{8pt}
+ Prof. B. Stritzker\\
+ SS 2008\\
+ \vspace{8pt}
+ {\Large\bf Tutorial 1}
+\end{center}
+
+\section{Diamagnetism}
+There is a linear relationship of the magnetic field ${\bf B}$ and
+the magnetization ${\bf M}$ of some material.
+The factor of proportionality is called the magnetic suscebtibility $\chi$.
+\[
+ \chi=\frac{\mu_0 {\bf M}}{{\bf B}}
+\]
+For negative values of $\chi$ the induced magnetization aligns opposite
+to the applied magnetic field.
+This behaviour is called diamagnetism.
+\\\\
+Develop an expression for the diamagnetic contribution to $\chi$ for some
+atom or ion.
+
+\begin{enumerate}
+ \item {\bf Classical approach:}\\
+ Consider the outer electrons of an atom or ion orbiting
+ the core with a radius $r$.
+ Apply a magnetic field $B$ perpendicular to the orbit plane.
+ According to Lenz's law the induced current creates a magnetic
+ field that tends to keep the magnetic flux unchanged.
+ \begin{enumerate}
+ \item Calculate the induced voltage $U$ due to the change in flux.
+ What is the related electric field $E$ along the orbit track?
+ Calculate the corresponding change of the electron velocity
+ due to the change of the magnetic field.
+ What is the resulting angular frequency $\omega_L$
+ (Larmor frequency, named after Joseph Larmor)?
+ \item Determine the magnetic momentum $\mu$ caused by the
+ Larmor precession of $Z$ electrons which have a mean square
+ distance $<r^2>$ to the core.
+ {\bf Hint:}
+ The magnetic momentum of a current loop is the product of
+ the current and the area of the loop.
+ The average square of the loop radius $<\rho^2>$ is the average
+ square distance of the electrons perpendicular to the direction
+ of the applied magnetic field ($<\rho^2>=<x^2>+<y^2>$).
+ The average square distance of the electrons to the core is
+ $<r^2>=<x^2>+<y^2>+<z^2>$.
+ Assuming a spherically symmetric charge distribution
+ the equality $<x^2>=<y^2>=<z^2>$ holds.
+ \item Write down the magnetic suscebtibility $\chi$.
+ {\bf Hint:} By definition the magnetization is given by $N\mu$,
+ where $N$ is the amount of atoms per unit volume.
+ \end{enumerate}
+ \item {\bf Quantum mechanical theory:}\\
+ In the presence of a magnetic field ${\bf B}=\nabla\times{\bf A}$
+ the kinetic part of the Hamiltonian is extended to read
+ \[
+ H_{kin}=\frac{1}{2m}(-i\hbar\nabla_{r}-e{\bf A})^2
+ =H_{kin}^0 + H_{kin}'
+ \]
+ where ${\bf A}$ is the vector potential and $H_{kin}^0$ is
+ the kinetic part of the Hamiltonian without apllied magnetic field.
+ \begin{enumerate}
+ \item Write down the additional terms $H_{kin}'$ of the kinetic part
+ of the Hamiltonian.
+ \item Choose a reasonable vector potential ${\bf A}$ to get a constant
+ magnetic field ${\bf B}$ in $z$-direction.
+ \item Rewrite the Hamiltonian
+ using the definition of the angular momentum operator
+ $L_z=x\frac{\partial}{\partial y}-y\frac{\partial}{\partial x}$.
+ \item Calculate the magnetic suscebtibility in a state $\phi$.
+ What term is responsible for the diamagnetic contribution?
+ {\bf Hint:} The magnetic suscebtibility is defined as
+ $\chi=-\frac{1}{V}\mu_0\frac{\partial^2 E}{\partial B^2}$.
+ \item Assuming a spherically symmetric charge distribution the equality
+ $<\phi|x^2|\phi>=<\phi|y^2|\phi>=\frac{1}{3}<\phi|r^2|\phi>$
+ is valid. Rewrite the diamagnetic part of the suscebtibility
+ and compare the result to the one obtained
+ by the classical approach.
+ \end{enumerate}
+\end{enumerate}
+
+\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}
+
+\renewcommand{\labelenumi}{(\alph{enumi})}
+\renewcommand{\labelenumii}{\arabic{enumii})}
+\renewcommand{\labelenumiii}{\roman{enumiii})}
+
+\begin{document}
+
+% header
+\begin{center}
+ {\LARGE {\bf Materials Physics II}\\}
+ \vspace{8pt}
+ Prof. B. Stritzker\\
+ SS 2008\\
+ \vspace{8pt}
+ {\Large\bf Tutorial 1 - proposed solutions}
+\end{center}
+
+\section{Diamagnetism}
+\begin{itemize}
+ \item Magnetic field ${\bf B}$
+ \item Magnetization ${\bf M}$
+ \item Suscebtibility $\chi=\frac{\mu_0 {\bf M}}{{\bf B}}$
+\end{itemize}
+
+\begin{enumerate}
+ \item {\bf Classical approach:}
+ \begin{enumerate}
+ \item Maxwell: $\oint_{\partial A} E \, ds
+ = -\frac{d}{dt}(\int_A B \, dA)
+ \stackrel{B(r)=B}{=}-\frac{d}{dt}(BA)$\\
+ $-\frac{d(BA)}{dt}=-\pi r^2 \dot{B}=U_{ind}$\\
+ $U_{ind}=\oint_{\partial A} E \, ds
+ \stackrel{E(s)=E}{\Rightarrow}
+ E=-\frac{\pi r^2}{2\pi r}\dot{B}$\\
+ $\dot{v}=a=\frac{e}{m}E=-\frac{e}{2m}r\dot{B}
+ \Rightarrow v=-\frac{e}{2m}rB$\\
+ $\omega_L=\frac{v}{r}=-\frac{e}{2m}B$
+ \item $I = (\textrm{charge}) \cdot (\textrm{loops per time})
+ \stackrel{1/T=\omega_L/2\pi}{=}
+ (Ze)(\frac{1}{2\pi}\frac{-e}{2m}B)$\\
+ $\mu=IA=I2\pi<\rho^2>=-\frac{Ze^2B}{4m}<\rho^2>$\\
+ $<x^2>=<y^2>=<z^2> \Rightarrow <r^2>=3<x^2>=3<y^2>$\\
+ $<\rho^2>=<x^2>+<y^2>=\frac{2}{3}<r^2>$\\
+ $\mu=-\frac{Ze^2B}{6m}$
+ \item $\chi=\frac{\mu_0N\mu}{B}=-\frac{\mu_0NZe^2}{6m}<r^2>$
+ \end{enumerate}
+ \item {\bf Quantum mechanical theory:}
+ \begin{itemize}
+ \item vector potential ${\bf A}$
+ \item ${\bf B}=\nabla\times{\bf A}$
+ \item $
+ H_{kin}=\frac{1}{2m}(-i\hbar\nabla_{r}-e{\bf A})^2
+ =H_{kin}^0 + H_{kin}'
+ $
+ \end{itemize}
+ \begin{enumerate}
+ \item \begin{eqnarray}
+ H_{kin}&=&\frac{1}{2m}(-\hbar^2\nabla_{r}^2+e^2{\bf A}^2
+ +i\hbar \nabla_{r}e{\bf A}
+ +e{\bf A}i\hbar \nabla_{r})\nonumber\\
+ H_{kin}^0&=&\frac{-\hbar^2}{2m}\nabla_r^2\nonumber\\
+ H_{kin}'&=&\frac{i\hbar e}{2m}(\nabla_r{\bf A}+{\bf A}\nabla_r)+
+ \frac{e^2{\bf A}^2}{2m}\nonumber
+ \end{eqnarray}
+ Terms in $H_{kin}'$ can be treated as small perturbation.
+ \item ${\bf A}=\left(-\frac{1}{2}yB,\frac{1}{2}xB,0\right)$, since:
+ $\nabla_r\times{\bf A}=\left(0,0,\frac{1}{2}B+\frac{1}{2}B\right)=
+ \left(0,0,B\right)$\\
+ Note: $\nabla_r{\bf A}=0$
+ \item $
+ H_{kin}'=\frac{i\hbar e}{2m}\left(
+ x\frac{\partial}{\partial y}-y\frac{\partial}{\partial x}
+ \right)+\frac{e^2B^2}{8m}(x^2+y^2)
+ $\\
+ $
+ L_z=x\frac{\partial}{\partial y}-y\frac{\partial}{\partial x}
+ \Rightarrow H_{kin}'=\frac{i\hbar e}{2m}L_z+
+ \frac{e^2B^2}{8m}(x^2+y^2)
+ $
+ \item $\chi=-\frac{1}{V}\mu_0\frac{\partial^2 E}{\partial B^2}
+ \Rightarrow$
+ only second term contributes to $\chi$!\\
+ $\chi=-\frac{1}{V}\mu_0\frac{e^2}{4m}<\phi|(x^2+y^2)|\phi>$
+ \item $<\phi|x^2|\phi>=<\phi|y^2|\phi>=\frac{1}{3}<\phi|r^2|\phi>$\\
+ $\Rightarrow \chi=-\frac{1}{V}\mu_0\frac{e^2}{6m}
+ <\phi|r^2|\phi>$\\
+ Consider all $Z$ electrons and all atoms per volume:\\
+ $\chi=-\frac{\mu_0NZe^2}{6m}<\phi|r^2|\phi>$
+ \end{enumerate}
+\end{enumerate}
+
+\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}
+
+\renewcommand{\labelenumi}{(\alph{enumi})}
+\renewcommand{\labelenumii}{\arabic{enumii})}
+\renewcommand{\labelenumiii}{\roman{enumiii})}
+
+\begin{document}
+
+% header
+\begin{center}
+ {\LARGE {\bf Materials Physics II}\\}
+ \vspace{8pt}
+ Prof. B. Stritzker\\
+ SS 2008\\
+ \vspace{8pt}
+ {\Large\bf Tutorial 2}
+\end{center}
+
+\section{Critical current in the surface region of a type 1 superconductor}
+There is an exponential decay of the current in the surface region of
+a superconductor.
+For a cylindric wire the equation
+\[
+ j_s(r)=j_s(R)\exp\left(\frac{-(R-r)}{\lambda}\right)
+\]
+is given.
+$R$ is the radius of the wire, $r$ is the distance from the cylinder axis
+and $\lambda$ is the London penetration depth.
+
+\begin{enumerate}
+ \item Derive an expression for the critical current density at the
+ surface of the wire with subject to the critical current $I_c$
+ of the wire. Assume, that the penetration depth $\lambda$ is much
+ smaller than the radius $R$ of the cylinder.
+ {\bf Hint:}
+ Use the relation $I_c=\int_0^R dr \int_0^{2\pi} d\phi \, j_c(r) r$
+ and integration by parts.
+ \item Calculate $j_c(R,T=0K)$ for a wire of Sn with a radius of 1 mm at $T=0K$.
+ The critical current and penetration depth at $T=0K$ are
+ $I_c=75\, A$ and $\lambda =300\cdot 10^{-10}\, m$.
+\end{enumerate}
+
+\section{Penetration of the magnetic field into a type 1 superconductor}
+In the following, the behaviour of the magnetic field ${\bf B}_s({\bf r})$
+in the surface layer of a superconductor is calculated.
+Inside the superconductor the magnetic field is given by
+\[
+ {\bf B}_s=\mu_0 \left({\bf H}_a + {\bf M}_s\right)
+\]
+in which ${\bf H}_a$ is the strength of the applied magnetic field and
+${\bf M}_s$ is the magnetization of the superconductor.
+
+\begin{enumerate}
+ \item Set up the differential equation for ${\bf B}_s$.
+ {\bf Hint:}
+ Use the appropriate Maxwell equation to connect the magnetic field
+ to the generating current densities.
+ What is the value of the current density responsible for the external
+ magnetic field inside the superconductor?
+ Apply the second London equation
+ $\nabla \times {\bf j}_s=-{\bf B}_s/\Lambda$
+ with $\lambda=\sqrt{\Lambda/\mu_0}$
+ relating the supercurrent to the magnetic field.
+
+ \item Consider a superconducting half space. The interface of the
+ superconductor ($x>0$) and the vacuum ($x<0$) is located at $x=0$.
+ A magnetic field ${\bf B}_a=\mu_0 H_a {\bf e}_z$
+ parallel to the surface is applied.
+ Calculate and sketch the decay of
+ ${\bf B}_s=B_{s_z}(x) {\bf e}_x$
+ in the superconductor.
+ Introduce the London penetration depth $\lambda$.
+ \item Out of this, calculate the screening current density ${\bf j}_s$.
+ What is the direction of the current?
+ Calculate the value of ${\bf j}_s$ at the interface?
+\end{enumerate}
+
+\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}
+
+\renewcommand{\labelenumi}{(\alph{enumi})}
+\renewcommand{\labelenumii}{\arabic{enumii})}
+\renewcommand{\labelenumiii}{\roman{enumiii})}
+
+\begin{document}
+
+% header
+\begin{center}
+ {\LARGE {\bf Materials Physics II}\\}
+ \vspace{8pt}
+ Prof. B. Stritzker\\
+ SS 2008\\
+ \vspace{8pt}
+ {\Large\bf Tutorial 3}
+\end{center}
+
+\vspace{8pt}
+
+The specific heat (capacity) is the measure of the energy
+required to increase the temperature of a unit quantity of a substance
+by a certain temperature interval.
+Thus, the specific heat at constant volume $V$ is given by
+\[
+c_V = \frac{\partial w}{\partial T}
+\]
+in which $w$ is the internal energy density of the system.
+In the following the contribution to the specific heat due to the
+degrees of freedom of the lattice ions is calculated.
+
+\section{Specific heat in the classical theory of the harmonic crystal -\\
+ The law of Dulong and Petit}
+
+In the classical theory of the harmonic crystal equilibrium properties
+can no longer be evaluated by simply assuming that each ion sits quietly at
+its Bravais lattice site {\bf R}.
+From now on expectation values have to be claculated by
+integrating over all possible ionic configurations weighted by
+$\exp(-E/k_{\text{B}}T)$, where $E$ is the energy of the configuration.
+Thus, the energy density $w$ is given by
+\[
+w=\frac{1}{V} \frac{\int d\Gamma\exp(-\beta H)H}{\int d\Gamma\exp(-\beta H)},
+\qquad \beta=\frac{1}{k_{\text{B}}T}
+\]
+in which $d\Gamma=\Pi_{\bf R} d{\bf u}({\bf R})d{\bf P}({\bf R})$
+is the volume elemnt in crystal phase space.
+${\bf u}({\bf R})$ and ${\bf P}({\bf R})$ are the 3N canonical coordinates
+(here: deviations from equlibrium sites)
+and 3N canonical momenta
+of the ions whose equlibrium sites are ${\bf R}$.
+\begin{enumerate}
+ \item Show that the energy density can be rewritten to read:
+ \[
+ w=-\frac{1}{V}\frac{\partial}{\partial \beta} ln \int d\Gamma \exp(-\beta H).
+ \]
+ \item Show that the potential contribution to the energy
+ in the harmonic approximation is given by
+ \begin{eqnarray}
+ U&=&U_{\text{eq}}+U_{\text{harm}} \nonumber \\
+ U_{\text{eq}}&=&\frac{1}{2}\sum_{{\bf R R'}} \Phi({\bf R}-{\bf R'})
+ \nonumber \\
+ U_{\text{harm}}&=&\frac{1}{4}\sum_{\stackrel{{\bf R R'}}{\mu,v=x,y,z}}
+ [u_{\mu}({\bf R})-u_{\mu}({\bf R'})]\Phi_{\mu v}({\bf R}-{\bf R'})
+ [u_v({\bf R})-u_v({\bf R'})] \nonumber
+ \end{eqnarray}
+ in which
+$\Phi_{\mu v}({\bf r})=
+ \frac{\partial^2 \Phi({\bf r})}{\partial r_{\mu}\partial r_v}$
+ and $\Phi({\bf r})$ is the potential contribution of two atoms
+ separated by ${\bf r}$.
+ {\bf Hint:}
+ Write down the potential energy for the instantaneous positions
+ ${\bf r}({\bf R})$, with ${\bf u}({\bf R})={\bf r}({\bf R})-{\bf R}$.
+ Apply Taylor approximation to $\Phi({\bf r}+{\bf a})$ with
+ ${\bf r}={\bf R}-{\bf R'}$ and
+ ${\bf a}={\bf u}({\bf R})-{\bf u}({\bf R'})$
+ and only retain terms quadratic in $u$.
+ \item Use the evaluated potential to calculate the energy density
+ (do not forget the kinetic energy contribution) and
+ the specific heat $c_{\text{V}}$.
+ {\bf Hint:}
+ Use the following change of variables
+ \[
+ {\bf u}({\bf R})=\beta^{-1/2}\bar{{\bf u}}({\bf R}), \qquad
+ {\bf P}({\bf R})=\beta^{-1/2}\bar{{\bf P}}({\bf R})
+ \]
+ to extract the temperature dependence of the integral.
+ Does this also work for anharmonic terms?
+ Which parts of the integral do not contribute to $w$ and why?
+\end{enumerate}
+
+\section{Specific heat in the quantum theory of the harmonic crystal -\\
+ The Debye model}
+
+As found in exercise 1, the specific heat of a classical harmonic crystal
+is not depending on temeprature.
+However, as temperature drops below room temperature
+the specific heat of all solids is decreasing as $T^3$ in insulators
+and $AT+BT^3$ in metals.
+This can be explained in a quantum theory of the specific heat of
+a harmonic crystal, in which the energy density $w$ is given by
+\[
+w=\frac{1}{V}\frac{\sum_i E_i \exp(-\beta E_i)}{\sum_i \exp(-\beta E_i)}.
+\]
+\begin{enumerate}
+ \item Show that the energy density can be rewritten to read:
+ \[
+ w=-\frac{1}{V}\frac{\partial}{\partial \beta} ln \sum_i \exp(-\beta E_i).
+ \]
+ \item Evaluate the expression of the energy density.
+ {\bf Hint:}
+ The energy levels of a harmonic crystal of N ions
+ can be regarded as 3N independent oscillators,
+ whose frequencies are those of the 3N classical normal modes.
+ The contribution to the total energy of a particular normal mode
+ with angular frequency $\omega_s({\bf k})$
+ ($s$: branch, ${\bf k}$: wave vector) is given by
+ $(n_{{\bf k}s} + \frac{1}{2})\hbar\omega_s({\bf k})$ with the
+ excitation number $n_{{\bf k}s}$ being restricted to integers greater
+ or equal zero.
+ The total energy is given by the sum over the energies of the individual
+ normal modes.
+ Use the totals formula of the geometric series to expcitly calculate
+ the sum of the exponential functions.
+ \item Separate the above result into a term vanishing as $T$ goes to zero and
+ a second term giving the energy of the zero-point vibrations of the
+ normal modes.
+ \item Write down an expression for the specific heat.
+ Consider a large crystal and thus replace the sum over the discrete
+ wave vectors with an integral.
+ \item Debye replaced all branches of the vibrational spectrum with three
+ branches, each of them obeying the dispersion relation
+ $w=ck$.
+ Additionally the integral is cut-off at a radius $k_{\text{D}}$
+ to have a total amount of N allowed wave vectors.
+ Determine $k_{\text{D}}$.
+ Evaluate the simplified integral and introduce the
+ Debye frequency $\omega_{\text{D}}=k_{\text{D}}c$
+ and the Debye temperature $\Theta_{\text{D}}$ which is given by
+ $\Theta_{\text{D}}=\hbar\omega_{\text{D}}$.
+ Write down the resulting expression for the specific heat.
+\end{enumerate}
+
+\end{document}
LATEX = latex
DVIPDF = dvipdf
-SRC := $(shell ls 1_0*.tex)
+SRC := $(shell ls [12]_0*.tex)
PDF = $(SRC:%.tex=%.pdf)
all: $(PDF)
projects / lectures / latex.git / commitdiff