Czochralski process
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[[Image:Czochralski Process.svg|thumb|right|350px|The Czochralski process]]
The '''Czochralski process''' is a method of [[crystal]] growth used to obtain [[single crystal]]s of [[semiconductors]] (e.g. [[silicon]], [[germanium]] and [[gallium arsenide]]), metals (e.g. [[palladium]], [[platinum]], [[silver]], [[gold]]), salts, and synthetic [[gemstone]]s. The process is named after Polish scientist [[Jan Czochralski]], who discovered the method in [[1916]] while investigating the crystallization rates of metals.
The most important application may be the growth of large cylindrical [[ingot]]s, or [[boule (crystal)|boules]], of [[single crystal]] [[silicon]]. Other semiconductors, such as [[gallium arsenide]], can also be grown by this method, although lower defect densities in this case can be obtained using variants of the [[Bridgman-Stockbarger technique]].
==Process==
[[Image:Silicon seed crystal puller rod.jpg|thumb|A puller rod with [[seed crystal]] for growing [[Single crystal|single-crystal]] [[silicon]] by the Czochralski process]]
High-purity, [[semiconductor]]-grade silicon (only a few parts per million of impurities) is melted down in a [[crucible]] , which is usually made of [[quartz]]. Dopant impurity atoms such as [[boron]] or [[phosphorus]] can be added to the molten intrinsic silicon in precise amounts in order to dope the silicon, thus changing it into n-type or p-type extrinsic silicon. This influences the [[electrical conductivity]] of the silicon. A ''[[seed crystal]]'', mounted on a rod, is dipped into the molten silicon. The seed crystal's rod is pulled upwards and rotated at the same time. By precisely controlling the temperature gradients, rate of pulling and speed of rotation, it is possible to extract a large, single-crystal, cylindrical ingot from the melt. Occurrence of unwanted instabilities in the melt can be avoided by investigating and visualizing the temperature and velocity fields during the crystal growth process.<ref>J. Aleksic et al., Ann. of NY Academy of Sci. 972 (2002) 158.</ref> This process is normally performed in an [[inert]] atmosphere, such as [[argon]], and in an inert chamber, such as [[quartz]].
==Size of crystals==
While the largest silicon ingots produced today are 400 [[millimetre|mm]] in diameter and 1 to 2 [[metre]]s in length, 200 mm and 300 mm diameter crystals are standard industrial processes. Thin silicon [[wafer (electronics)|wafer]]s are cut from these ingots (typically about 0.2 - 0.75 mm thick) and can be polished to a very high flatness for making [[integrated circuit]]s, or textured for making [[solar cell]]s.
==Impurity incorporation==
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]] impurities with a typical concentration of <math>10^{18}cm^{-3}</math>. Oxygen impurities can have beneficial effects. Carefully chosen annealing conditions can allow the formation of oxygen [[precipitates]]. These have the effect of trapping unwanted [[transition metal]] impurities in a process known as [[gettering]]. Additionally, oxygen impurities can improve the mechanical strength of silicon wafers by immobilising any [[dislocations]] which may be introduced during device processing. It has experimentally been proved in the 1990s that the high oxygen concentration is also beneficial for [[radiation hardness]] of silicon [[particle detector]]s used in harsh radiation environment ( eg. [[CERN]]'s [[Large Hadron Collider|LHC]]/[[S-LHC]] projects)<ref>Z. Li et al., IEEE Trans Nucl. Sci. 39 (6) (1992) 1730</ref><ref>A. Ruzin et al., IEEE Trans Nucl. Sci. 46 (5) (1999) 1310</ref><ref>G. Lindström et al., Nucl. Instr. and Meth. A 466 (2001) 308 and cited literature therein.</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>J. Härkönen et al., Nucl. Instr. and Meth. A 541 (2005)202.</ref> However, oxygen impurities can react with boron in an illuminated environment, such as 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>Eikelboom, J.A., Jansen, M.J., 2000. Characteristion of PV modules of new generations; results of tests and simulations. Report ECN-C-00-067, 18.</ref>
===Mathematical expression of impurity incorporation from melt===
The impurity concentration in the solid crystal that results from freezing an incremental amount of volume can be obtained from consideration of the segregation coefficient. <ref>James D. Plummer, Michael D. Deal, and Peter B. Griffin, Silicon VLSI Technology, Prentice Hall, 2000, p. 126-27</ref>
:<math>k_O</math>: Segregation coefficient
:<math>V_0</math>: Initial volume
:<math>I_0</math>: Number of impurities
:<math>C_0</math>: Impurity concentration in the melt
:<math>V_L</math>: Volume of the melt
:<math>I_L</math>: Number of impurities in the melt
:<math>C_L</math>: Concentration of impurities in the melt
:<math>V_S</math>: Volume of solid
:<math>C_S</math>: Concentration of impurities in the solid
During the growth process, volume of melt <math>dV</math> freezes, and there are impurities from the melt that are removed.
:<math>dI = -k_O C_L dV\;</math>
:<math>dI = - k_O \frac{I_L}{V_O - V_S} dV</math>
:<math>\int_{I_O}^{I_L} \frac{dI}{I_L} = -k_O \int_{0}^{V_S} \frac{dV}{V_O - V_S}</math>
:<math>\log \left ( \frac{I_L}{I_O} \right ) = \log \left ( 1 - \frac{V_S}{V_O} \right )^{k_O}</math>
:<math>I_L = I_O \left ( 1 - \frac{V_S}{V_O} \right )^{k_O}</math>
:<math>C_S = - \frac{dI_L}{dV_S}</math>
<math>C_S = C_O k_O (1-f)^{k_o - 1}</math>
:<math>f = V_S / V_O\;</math>
==Gallery==
{{commonscat|Czochralski method}}
<gallery>
Image:Czochralski method crucibles.jpg|Crucibles used in Czochralski method
Image: Czochralski method used crucible 1.jpg|Crucible after being used
Image:Monokristalines Silizium für die Waferherstellung.jpg|Silicon ingot
</gallery>
==References==
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==See also==
* [[Bridgman-Stockbarger technique]]
* [[Float-zone silicon]]
==External links==
* [http://www.articleworld.org/index.php/Czochralski_process Czochralski doping process]
[[Category:Industrial processes]]
[[Category:Semiconductor growth]]
[[Category:Science and technology in Poland]]
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