From 26d5ef35681908ed195444714706dddb3d26c7ac Mon Sep 17 00:00:00 2001 From: hackbard Date: Thu, 21 Apr 2011 15:50:16 +0200 Subject: [PATCH] more properties of c in si --- bibdb/bibdb.bib | 98 ++++++++++++++++++++++++++++++++++++++++++++ posic/thesis/sic.tex | 37 +++++++++++++---- 2 files changed, 128 insertions(+), 7 deletions(-) diff --git a/bibdb/bibdb.bib b/bibdb/bibdb.bib index c55a0e1..fdea406 100644 --- a/bibdb/bibdb.bib +++ b/bibdb/bibdb.bib @@ -40,6 +40,37 @@ notes = "derivation of albe bond order formalism", } +@Article{newman65, + title = "Vibrational absorption of carbon in silicon", + journal = "Journal of Physics and Chemistry of Solids", + volume = "26", + number = "2", + pages = "373--379", + year = "1965", + note = "", + ISSN = "0022-3697", + doi = "DOI: 10.1016/0022-3697(65)90166-6", + URL = "http://www.sciencedirect.com/science/article/B6TXR-46RVGM8-1C/2/d50c4df37065a75517d63a04af18d667", + author = "R. C. Newman and J. B. Willis", + notes = "c impurity dissolved as substitutional c in si", +} + +@Article{baker68, + author = "J. A. Baker and T. N. Tucker and N. E. Moyer and R. C. + Buschert", + collaboration = "", + title = "Effect of Carbon on the Lattice Parameter of Silicon", + publisher = "AIP", + year = "1968", + journal = "Journal of Applied Physics", + volume = "39", + number = "9", + pages = "4365--4368", + URL = "http://link.aip.org/link/?JAP/39/4365/1", + doi = "10.1063/1.1656977", + notes = "lattice contraction due to subst c", +} + @Article{bean71, title = "The solubility of carbon in pulled silicon crystals", journal = "Journal of Physics and Chemistry of Solids", @@ -981,6 +1012,39 @@ stress, avoid sic precipitation", } +@Article{foell77, + title = "The formation of swirl defects in silicon by + agglomeration of self-interstitials", + journal = "Journal of Crystal Growth", + volume = "40", + number = "1", + pages = "90--108", + year = "1977", + note = "", + ISSN = "0022-0248", + doi = "DOI: 10.1016/0022-0248(77)90034-3", + URL = "http://www.sciencedirect.com/science/article/B6TJ6-46BWB4Y-44/2/bddfd69e99369473feebcdc41692dddb", + author = "H. Föll and U. Gösele and B. O. Kolbesen", + notes = "b-swirl: si + c interstitial agglomerates, c-si + agglomerate", +} + +@Article{foell81, + title = "Microdefects in silicon and their relation to point + defects", + journal = "Journal of Crystal Growth", + volume = "52", + number = "Part 2", + pages = "907--916", + year = "1981", + note = "", + ISSN = "0022-0248", + doi = "DOI: 10.1016/0022-0248(81)90397-3", + URL = "http://www.sciencedirect.com/science/article/B6TJ6-46MD42X-90/2/a482c31bf9e2faeed71b7109be601078", + author = "H. Föll and U. Gösele and B. O. Kolbesen", + notes = "swirl review", +} + @Article{werner97, author = "P. Werner and S. Eichler and G. Mariani and R. K{\"{o}}gler and W. Skorupa", @@ -1039,6 +1103,25 @@ notes = "c diffusion in si, kick out mechnism", } +@Article{kalejs84, + author = "J. P. Kalejs and L. A. Ladd and U. G{\"{o}}sele", + collaboration = "", + title = "Self-interstitial enhanced carbon diffusion in + silicon", + publisher = "AIP", + year = "1984", + journal = "Applied Physics Letters", + volume = "45", + number = "3", + pages = "268--269", + keywords = "PHOSPHORUS; INTERSTITIALS; SILICON; PHOSPHORUS; + CARBON; DIFFUSION; ANNEALING; ATOM TRANSPORT; VERY HIGH + TEMPERATURE; IMPURITIES", + URL = "http://link.aip.org/link/?APL/45/268/1", + doi = "10.1063/1.95167", + notes = "c diffusion due to si self-interstitials", +} + @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", @@ -4113,6 +4196,21 @@ eprint = "http://journals.cambridge.org/article_S194642740054367X", } +@Article{newman61, + title = "The diffusivity of carbon in silicon", + journal = "Journal of Physics and Chemistry of Solids", + volume = "19", + number = "3-4", + pages = "230--234", + year = "1961", + note = "", + ISSN = "0022-3697", + doi = "DOI: 10.1016/0022-3697(61)90032-4", + URL = "http://www.sciencedirect.com/science/article/B6TXR-46M72R1-4D/2/9235472e4c0a95bf7b995769474f5fbd", + author = "R. C. Newman and J. Wakefield", + notes = "diffusivity of substitutional c in si", +} + @Article{goesele85, author = "U. Gösele", title = "The Role of Carbon and Point Defects in Silicon", diff --git a/posic/thesis/sic.tex b/posic/thesis/sic.tex index 9926ccd..a55b216 100644 --- a/posic/thesis/sic.tex +++ b/posic/thesis/sic.tex @@ -280,17 +280,40 @@ This enables the synthesis of large area SiC films. \section{Substoichiometric concentrations of carbon in crystalline silicon} -The C solid solubility in bulk Si is quite low -% carbon as an impurity / solubility / lattice distortion / diffusion -% agglomeration phenomena -% suppression of transient enhanced diffusion of dopant species -% strained silicon / heterostructures +In the following some basic properties of C in crystalline Si are reviewed. +A lot of work has been done contributing to the understanding of C in Si either as an isovalent impurity as well as at concentrations exceeding the solid solubility limit. +A comprehensive survey on C-mediated effects in Si has been published by Skorupa and Yankov \cite{skorupa96}. + +\subsection{Carbon as an impurity in silicon} + +Below the solid solubility, C mainly occupies substitutionally Si lattice sites in Si \cite{newman65}. +Due to the much smaller covalent radius of C compared to Si every incorporated C atom leads to a decrease in the lattice constant corresponding to a lattice contraction of about one atomic volume \cite{baker68}. +The induced strain is assumed to be responsible for the low solid solubility of C in Si, which was determined \cite{bean71} to be +\begin{equation} +c_{\text{s}}=\unit[4\times10^{24}]{cm^{-3}} +\cdot\exp(\unit[-2.3]{eV/k_{\text{B}}T}) +\text{ .} \text{{\color{red}k recursive!}} +\end{equation} +The barrier of diffusion of substitutional C has been determined to be around \unit[3]{eV} \cite{newman61}. +However, as suspected due to the substitutional position, the diffusion of C requires intrinsic point defects, i.e. Si self-interstitials and vacancies. +Similar to phosphorous and boron, which exclusively use self-interstitials as a diffusion vehicle, the diffusion of C atoms is expected to obey the same mechanism. +Indeed, enhanced C diffusion was observed in the presence of self-interstitial supersaturation \cite{kalejs84} indicating an appreciable diffusion component involving self-interstitials and only a negligible contribution by vacancies. +Substitutional C and interstitial Si react into a C-Si complex forming a dumbbell structure oriented along a crystallographic \hkl<1 0 0> direction on a regular Si lattice site. +This structure, the so called C-Si \hkl<1 0 0> dumbbell structure, was initially suspected by local vibrational mode absorption \cite{bean70} and finally verified by electron paramegnetic resonance \cite{watkins76} studies on irradiated Si substrates at low temperatures. +Measuring the annealing rate of the defect as a function of temperature reveals barriers for migration ranging from \unit[0.73]{eV} \cite{song90} to \unit[0.87]{eV} \cite{tipping87}. +% diffusion pathway? + +%\subsection{Agglomeration phenomena} +% c-si agglomerattion as an alternative to sic precipitation (due to strain) +% -> maybe this fits better in prec model in next chapter + +\subsection{Suppression of transient enhanced diffusion of dopant species} + +\subsection{Strained silicon and silicon heterostructures} % -> skorupa 3.2: c sub vs sic prec % -> my own links: strane etc ... % -> skorupa 3.5: heterostructures -% hmm ... extra section needed? - \section{Assumed cubic silicon carbide conversion mechanisms} \label{section:assumed_prec} -- 2.20.1