# Czochralski process

The Czochralski process is a method of crystal growth used to obtain single crystals of semiconductors (e.g. silicon, germanium and gallium arsenide), metals (e.g. palladium, platinum, silver, gold), salts and synthetic gemstones. The process is named after Polish scientist Jan Czochralski,[1] who invented the method in 1915 while investigating the crystallization rates of metals.[2] He made this discovery by accident, while studying the crystallization rate of metals when, instead of dipping his pen into the ink, he did so in molten tin and drew a tin filament, that later proved to be a single crystal.[3]

The most important application may be the growth of large cylindrical ingots, or boules, of single crystal silicon used in the electronics industry to make semiconductor devices like integrated circuits. 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.

## Application

Monocrystalline silicon (mono-Si) grown by the Czochralski process is often referred to as monocrystalline Czochralski silicon (Cz-Si). It is the basic material in the production of integrated circuits used in computers, TVs, mobile phones and all types of electronic equipment and semiconductor devices.[4] Monocrystalline silicon is also used in large quantities by the photovoltaic industry for the production of conventional mono-Si solar cells. The almost perfect crystal structure yields the highest light-to-electricity conversion efficiency for silicon.

## Production of Czochralski silicon

Crystal of Czochralski grown silicon.

High-purity, semiconductor-grade silicon (only a few parts per million of impurities) is melted in a crucible at 1425 degree Celsius, usually made of quartz. Dopant impurity atoms such as boron or phosphorus can be added to the molten silicon in precise amounts to dope the silicon, thus changing it into p-type or n-type silicon, with different electronic properties. A precisely oriented rod-mounted seed crystal is dipped into the molten silicon. The seed crystal's rod is slowly pulled upwards and rotated simultaneously. 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.[5] This process is normally performed in an inert atmosphere, such as argon, in an inert chamber, such as quartz.

## Crystal sizes

Silicon crystal being grown by Czochralski process at Raytheon, 1956. The induction heating coil is visible, and the end of the crystal just emerging from the melt. The technician is measuring the temperature with an optical pyrometer. One of the earliest Si plants, the crystals produced by this early apparatus were only one inch in diameter.

Due to the efficiencies of common wafer specifications, the semiconductor industry has used wafers with standardized dimensions. In the early days, the boules were smaller, only a few inches wide. With advanced technology, high-end device manufacturers use 200 mm and 300 mm diameter wafers. The width is controlled by precise control of the temperature, the speeds of rotation and the speed the seed holder is withdrawn. The crystal ingots from which these wafers are sliced can be up to 2 metres in length, weighing several hundred kilogrammes. Larger wafers allow improvements in manufacturing efficiency, as more chips can be fabricated on each wafer, so there has been a steady drive to increase silicon wafer sizes. The next step up, 450 mm, is currently scheduled for introduction in 2018.[6] Silicon wafers are typically about 0.2–0.75 mm thick, and can be polished to great flatness for making integrated circuits or textured for making solar cells.

The process begins when the chamber is heated to approximately 1500 degrees Celsius, melting the silicon. When the silicon is fully melted, a small seed crystal mounted on the end of a rotating shaft is slowly lowered until it just dips below the surface of the molten silicon. The shaft rotates counterclockwise and the crucible rotates clockwise. The rotating rod is then drawn upwards very slowly—about 25mm per hour when making a crystal of ruby[7]—allowing a roughly cylindrical boule to be formed. The boule can be from one to two metres, depending on the amount of silicon in the crucible.

The electrical characteristics of the silicon are controlled by adding material like phosphorus or boron to the silicon before it is melted. The added material is called dopant and the process is called doping. This method is also used with semiconductor materials other than silicon, such as gallium arsenide.

## Incorporating impurities

A puller rod with seed crystal for growing single-crystal silicon by the Czochralski process.

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 1018
cm−3
. 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 was experimentally shown in the 1990s that the high oxygen concentration is also beneficial for the radiation hardness of silicon particle detectors used in harsh radiation environment (such as CERN's LHC/HL-LHC projects).[8][9] Therefore, radiation detectors made of Czochralski- and Magnetic Czochralski-silicon are considered to be promising candidates for many future high-energy physics experiments.[10][11] It has also been shown that the presence of oxygen in silicon increases impurity trapping during post-implantation annealing processes.[12]

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.[13]

### Mathematical expression of impurity incorporation from melt[citation needed]

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.[14]

${\displaystyle k_{O}}$: Segregation coefficient
${\displaystyle V_{0}}$: Initial volume
${\displaystyle I_{0}}$: Number of impurities
${\displaystyle C_{0}}$: Impurity concentration in the melt
${\displaystyle V_{L}}$: Volume of the melt
${\displaystyle I_{L}}$: Number of impurities in the melt
${\displaystyle C_{L}}$: Concentration of impurities in the melt
${\displaystyle V_{S}}$: Volume of solid
${\displaystyle C_{S}}$: Concentration of impurities in the solid

During the growth process, volume of melt ${\displaystyle dV}$ freezes, and there are impurities from the melt that are removed.

${\displaystyle dI=-k_{O}C_{L}dV\;}$
${\displaystyle dI=-k_{O}{\frac {I_{L}}{V_{O}-V_{S}}}dV}$
${\displaystyle \int _{I_{O}}^{I_{L}}{\frac {dI}{I_{L}}}=-k_{O}\int _{0}^{V_{S}}{\frac {dV}{V_{O}-V_{S}}}}$
${\displaystyle \ln \left({\frac {I_{L}}{I_{O}}}\right)=\ln \left(1-{\frac {V_{S}}{V_{O}}}\right)^{k_{O}}}$
${\displaystyle I_{L}=I_{O}\left(1-{\frac {V_{S}}{V_{O}}}\right)^{k_{O}}}$
${\displaystyle C_{S}=-{\frac {dI_{L}}{dV_{S}}}}$
${\displaystyle C_{S}=C_{O}k_{O}(1-f)^{k_{o}-1}}$
${\displaystyle f=V_{S}/V_{O}\;}$

## References

1. ^ (Polish), (English), Paweł Tomaszewski, ""Jan Czochralski i jego metoda" (ang.Jan Czochralski and his method), Oficyna Wydawnicza ATUT, Wrocław–Kcynia 2003, ISBN 83-89247-27-5
2. ^ J. Czochralski (1918) "Ein neues Verfahren zur Messung der Kristallisationsgeschwindigkeit der Metalle" [A new method for the measurement of the crystallization rate of metals], Zeitschrift für Physikalische Chemie, 92 : 219–221.
3. ^ Nishinaga, Tatau (2015). Handbook of Crystal Growth: Fundamentals (Second ed.). Amsterdam, the Netherlands: Elsevier B.V. p. 21. ISBN 978-0-444-56369-9.
4. ^ Czochralski Crystal Growth Method. Bbc.co.uk. 30 January 2003. Retrieved on 2011-12-06.
5. ^ Aleksic, Jalena; Zielke, Paul; Szymczyk, Janusz A.; et al. (2002). "Temperature and Flow Visualization in a Simulation of the Czochralski Process Using Temperature-Sensitive Liquid Crystals". Ann. N.Y. Acad. Sci. 972: 158. Bibcode:2002NYASA.972..158A. doi:10.1111/j.1749-6632.2002.tb04567.x.
6. ^ Doubts over 450mm and EUV. Electronicsweekly.com. December 30, 2013. Retrieved on 2014-01-09.
7. ^ "Czochralski Process". www.theimage.com. Retrieved 2016-02-25.
8. ^ Li, Z.; Kraner, H.W.; Verbitskaya, E.; Eremin, V.; Ivanov, A.; Rattaggi, M.; Rancoita, P.G.; Rubinelli, F.A.; Fonash, S.J.; et al. (1992). "Investigation of the oxygen-vacancy (A-center) defect complex profile in neutron irradiated high resistivity silicon junction particle detectors". IEEE Transactions on Nuclear Science. 39 (6): 1730. Bibcode:1992ITNS...39.1730L. doi:10.1109/23.211360.
9. ^ Lindström, G; Ahmed, M; Albergo, S; Allport, P; Anderson, D; Andricek, L; Angarano, M.M; Augelli, V; Bacchetta, N; Bartalini, P; Bates, R; Biggeri, U; Bilei, G.M; Bisello, D; Boemi, D; Borchi, E; Botila, T; Brodbeck, T.J; Bruzzi, M; Budzynski, T; Burger, P; Campabadal, F; Casse, G; Catacchini, E; Chilingarov, A; Ciampolini, P; Cindro, V; Costa, M.J; Creanza, D; Clauws, P (2001). "Radiation hard silicon detectors—developments by the RD48 (ROSE) collaboration". Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. 466 (2): 308. Bibcode:2001NIMPA.466..308L. doi:10.1016/S0168-9002(01)00560-5.
10. ^ CERN RD50 Status Report 2004, CERN-LHCC-2004-031 and LHCC-RD-005 and cited literature therein
11. ^ Harkonen, J; Tuovinen, E; Luukka, P; Tuominen, E; Li, Z; Ivanov, A; Verbitskaya, E; Eremin, V; Pirojenko, A; Riihimaki, I.; Virtanen, A. (2005). "Particle detectors made of high-resistivity Czochralski silicon". Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. 541: 202. Bibcode:2005NIMPA.541..202H. doi:10.1016/j.nima.2005.01.057.
12. ^ Custer, J. S.; Polman, A.; Van Pinxteren, H. M. (1994). "Erbium in crystal silicon: Segregation and trapping during solid phase epitaxy of amorphous silicon". Journal of Applied Physics. 75 (6): 2809. Bibcode:1994JAP....75.2809C. doi:10.1063/1.356173.
13. ^ Eikelboom, J.A., Jansen, M.J., 2000. Characterisation of PV modules of new generations; results of tests and simulations. Report ECN-C-00-067, 18.
14. ^ James D. Plummer, Michael D. Deal, and Peter B. Griffin, Silicon VLSI Technology, Prentice Hall, 2000, ISBN 0-13-085037-3 pp. 126–27