Editing Czochralski method (section)

==Incorporating impurities==
[[Image:Silicon seed crystal puller rod.jpg|thumb|240px|A puller rod with [[seed crystal]] for growing [[single-crystal silicon]] by the Czochralski method]]
[[Image:Czochralski method crucibles.jpg|thumb|240px|Crucibles used in Czochralski method]]
[[Image:Czochralski method used crucible 1.jpg|thumb|240px|Crucible after being used]]

When silicon is grown by the Czochralski method, the melt is contained in a [[silica]] ([[quartz]]) crucible. During growth, the walls of the crucible dissolve into the melt and Czochralski silicon therefore contains [[oxygen]] at a typical concentration of 10{{su|p=18}}&nbsp;cm{{su|p=−3}}. Oxygen impurities can have beneficial or detrimental effects. Carefully chosen annealing conditions can give rise to the formation of oxygen [[precipitates]]. These have the effect of trapping unwanted [[transition metal]] impurities in a process known as [[gettering]], improving the purity of surrounding silicon. However, formation of oxygen [[precipitates]] at unintended locations can also destroy electrical structures. Additionally, oxygen impurities can improve the mechanical strength of silicon wafers by immobilising any [[dislocations]] which may be introduced during device processing. It was experimentally shown in the 1990s that the high oxygen concentration is also beneficial for the [[radiation hardness]] of silicon [[particle detector]]s used in harsh radiation environment (such as [[CERN]]'s [[Large Hadron Collider|LHC]]/[[High Luminosity Large Hadron Collider|HL-LHC]] projects).<ref>{{cite journal|doi=10.1109/23.211360 |title=Investigation of the oxygen-vacancy (A-center) defect complex profile in neutron irradiated high resistivity silicon junction particle detectors|year=1992|last1=Li|first1=Z.|last2=Kraner|first2=H.W.|last3=Verbitskaya|first3=E.|last4=Eremin|first4=V.|last5=Ivanov|first5=A.|last6=Rattaggi|first6=M.|last7=Rancoita|first7=P.G.|last8=Rubinelli|first8=F.A.|last9=Fonash|first9=S.J.|journal=IEEE Transactions on Nuclear Science|volume=39|issue=6|pages=1730|bibcode = 1992ITNS...39.1730L |display-authors=9 |last10=Dale |first10=C. |last11=Marshall |first11=P. |url=https://digital.library.unt.edu/ark:/67531/metadc1059922/}}</ref><ref>{{cite journal|doi=10.1016/S0168-9002(01)00560-5|title=Radiation hard silicon detectors—developments by the RD48 (ROSE) collaboration|year=2001|last1=Lindström|first1=G|journal=Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment|volume=466|issue=2|pages=308|bibcode = 2001NIMPA.466..308L |last2=Ahmed|first2=M|last3=Albergo|first3=S|last4=Allport|first4=P|last5=Anderson|first5=D|last6=Andricek|first6=L|last7=Angarano|first7=M.M|last8=Augelli|first8=V|last9=Bacchetta|first9=N|last10=Bartalini|first10=P|last11=Bates|first11=R|last12=Biggeri|first12=U|last13=Bilei|first13=G.M|last14=Bisello|first14=D|last15=Boemi|first15=D|last16=Borchi|first16=E|last17=Botila|first17=T|last18=Brodbeck|first18=T.J|last19=Bruzzi|first19=M|last20=Budzynski|first20=T|last21=Burger|first21=P|last22=Campabadal|first22=F|last23=Casse|first23=G|last24=Catacchini|first24=E|last25=Chilingarov|first25=A|last26=Ciampolini|first26=P|last27=Cindro|first27=V|last28=Costa|first28=M.J|last29=Creanza|first29=D|last30=Clauws|first30=P|display-authors=29|hdl=11568/67464|hdl-access=free}}</ref> Therefore, radiation detectors made of Czochralski- and magnetic Czochralski-silicon are considered to be promising candidates for many future [[high-energy physics]] experiments.<ref>CERN RD50 Status Report 2004, CERN-LHCC-2004-031 and LHCC-RD-005 and cited literature therein</ref><ref>{{cite journal|doi=10.1016/j.nima.2005.01.057|title=Particle detectors made of high-resistivity Czochralski silicon|year=2005|last1=Harkonen|first1=J|last2=Tuovinen|first2=E|last3=Luukka|first3=P|last4=Tuominen|first4=E|last5=Li|first5=Z|last6=Ivanov|first6=A|last7=Verbitskaya|first7=E|last8=Eremin|first8=V|last9=Pirojenko|first9=A|journal=Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment|volume=541|issue=1–2|pages=202–207|bibcode = 2005NIMPA.541..202H |last10=Riihimaki|first10=I.|last11=Virtanen|first11=A.|citeseerx=10.1.1.506.2366}}</ref> It has also been shown that the presence of oxygen in silicon increases impurity trapping during post-implantation annealing processes.<ref>{{cite journal|doi=10.1063/1.356173|title=Erbium in crystal silicon: Segregation and trapping during solid phase epitaxy of amorphous silicon|year=1994|last1=Custer|first1=J. S.|last2=Polman|first2=A.|last3=Van Pinxteren|first3=H. M.|journal=Journal of Applied Physics|volume=75|issue=6|pages=2809|bibcode = 1994JAP....75.2809C }}</ref>

However, oxygen impurities can react with boron in an illuminated environment, such as that experienced by solar cells. This results in the formation of an electrically active boron–oxygen complex that detracts from cell performance. Module output drops by approximately 3% during the first few hours of light exposure.<ref>{{Citation |last1=Eikelboom |first1=J.A. |last2=Jansen |first2=M.J. |year=2000 |url=https://publications.tno.nl/publication/34628019/z869hR/c00067.pdf |title=Characterisation of PV modules of new generations; results of tests and simulations |work=Report ECN-C-00-067, 18}}</ref>

===Mathematical form===
Impurity concentration in the final solid is given by <math display=block>\frac{C}{C_0} = k\left(1-\frac{V}{V_0}\right)^{k-1}\text{,}</math> where {{mvar|C}} and {{math|''C''<sub>0</sub>}} are (respectively) the initial and final concentration, {{mvar|V}} and {{math|''V''<sub>0</sub>}} the initial and final volume, and {{mvar|k}} the [[segregation coefficient]] associated with impurities at the melting phase transition.  This follows from the fact that <math display=block>dI = -k_O C_L dV</math> impurities are removed from the melt when an infinitesimal volume {{math|d''V''}} freezes.<ref>James D. Plummer, Michael D. Deal, and Peter B. Griffin, ''Silicon VLSI Technology,'' Prentice Hall, 2000, {{ISBN|0-13-085037-3}} pp. 126–27</ref>
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