Czochralski method

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Last updated May 09, 2023

The Czochralski method, also Czochralski technique or 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 method 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: instead of dipping his pen into his inkwell, he dipped it in molten tin, and drew a tin filament, which later proved to be a single crystal.^[3] The method is still used in over 90 percent of all electronics in the world that use semiconductors.^[4]

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 method.

The method is not limited to production of metal or metalloid crystals. For example, it is used to manufacture very high-purity crystals of salts, including material with controlled isotopic composition, for use in particle physics experiments, with tight controls (part per billion measurements) on confounding metal ions and water absorbed during manufacture.^[5]

Application

Monocrystalline silicon (mono-Si) grown by the Czochralski method 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.^[6] 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 Monokristalines Silizium fur die Waferherstellung.jpg — Crystal of Czochralski-grown silicon

High-purity, semiconductor-grade silicon (only a few parts per million of impurities) is melted in a crucible at 1,425 °C (2,597 °F; 1,698 K), 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.^[7] This process is normally performed in an inert atmosphere, such as argon, in an inert chamber, such as quartz.

Crystal sizes

Due to efficiencies of scale, the semiconductor industry often uses wafers with standardized dimensions, or common wafer specifications. Early on, boules were small, a few cm wide. With advanced technology, high-end device manufacturers use 200 mm and 300 mm diameter wafers. Width is controlled by precise control of temperature, speeds of rotation, and the speed at which the seed holder is withdrawn. The crystal ingots from which wafers are sliced can be up to 2 metres in length, weighing several hundred kilograms. Larger wafers allow improvements in manufacturing efficiency, as more chips can be fabricated on each wafer, with lower relative loss, so there has been a steady drive to increase silicon wafer sizes. The next step up, 450 mm, was scheduled for introduction in 2018.^[8] 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.

Incorporating impurities

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 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 detectors used in harsh radiation environment (such as CERN's LHC/HL-LHC projects).^[9]^[10] Therefore, radiation detectors made of Czochralski- and magnetic Czochralski-silicon are considered to be promising candidates for many future high-energy physics experiments.^[11]^[12] It has also been shown that the presence of oxygen in silicon increases impurity trapping during post-implantation annealing processes.^[13]

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.^[14]

Mathematical form

Concerning a mathematical expression of impurity incorporation from melt,^[15] consider the following.

The impurity concentration in the solid crystal that results from freezing an amount of volume can be obtained from consideration of the segregation coefficient.

k_{O}

: Segregation coefficient

V_{0}

: Initial volume

I_{0}

: Number of impurities

C_{0}

: Impurity concentration in the melt

V_{L}

: Volume of the melt

I_{L}

: Number of impurities in the melt

C_{L}

: Concentration of impurities in the melt

V_{S}

: Volume of solid

C_{S}

: Concentration of impurities in the solid

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

dI=-k_{O}C_{L}dV\;

dI=-k_{O}{\frac {I_{L}}{V_{O}-V_{S}}}dV

\int _{I_{O}}^{I_{L}}{\frac {dI}{I_{L}}}=-k_{O}\int _{0}^{V_{S}}{\frac {dV}{V_{O}-V_{S}}}

\ln \left({\frac {I_{L}}{I_{O}}}\right)=\ln \left(1-{\frac {V_{S}}{V_{O}}}\right)^{k_{O}}

I_{L}=I_{O}\left(1-{\frac {V_{S}}{V_{O}}}\right)^{k_{O}}

C_{S}=-{\frac {dI_{L}}{dV_{S}}}

C_{S}=C_{O}k_{O}(1-f)^{k_{o}-1}

f=V_{S}/V_{O}\;

Related Research Articles

A semiconductor is a material which has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity falls as its temperature rises; metals behave in the opposite way. Its conducting properties may be altered in useful ways by introducing impurities ("doping") into the crystal structure. When two differently doped regions exist in the same crystal, a semiconductor junction is created. The behavior of charge carriers, which include electrons, ions, and electron holes, at these junctions is the basis of diodes, transistors, and most modern electronics. Some examples of semiconductors are silicon, germanium, gallium arsenide, and elements near the so-called "metalloid staircase" on the periodic table. After silicon, gallium arsenide is the second-most common semiconductor and is used in laser diodes, solar cells, microwave-frequency integrated circuits, and others. Silicon is a critical element for fabricating most electronic circuits.

A semiconductor device is an electronic component that relies on the electronic properties of a semiconductor material for its function. Its conductivity lies between conductors and insulators. Semiconductor devices have replaced vacuum tubes in most applications. They conduct electric current in the solid state, rather than as free electrons across a vacuum or as free electrons and ions through an ionized gas.

<span class="mw-page-title-main">Wafer (electronics)</span> Thin slice of semiconductor used for the fabrication of integrated circuits

In electronics, a wafer is a thin slice of semiconductor, such as a crystalline silicon (c-Si), used for the fabrication of integrated circuits and, in photovoltaics, to manufacture solar cells. The wafer serves as the substrate for microelectronic devices built in and upon the wafer. It undergoes many microfabrication processes, such as doping, ion implantation, etching, thin-film deposition of various materials, and photolithographic patterning. Finally, the individual microcircuits are separated by wafer dicing and packaged as an integrated circuit.

Zone melting is a group of similar methods of purifying crystals, in which a narrow region of a crystal is melted, and this molten zone is moved along the crystal. The molten region melts impure solid at its forward edge and leaves a wake of purer material solidified behind it as it moves through the ingot. The impurities concentrate in the melt, and are moved to one end of the ingot. Zone refining was invented by John Desmond Bernal and further developed by William G. Pfann in Bell Labs as a method to prepare high-purity materials, mainly semiconductors, for manufacturing transistors. Its first commercial use was in germanium, refined to one atom of impurity per ten billion, but the process can be extended to virtually any solute–solvent system having an appreciable concentration difference between solid and liquid phases at equilibrium. This process is also known as the float zone process, particularly in semiconductor materials processing.

<span class="mw-page-title-main">Epitaxy</span> Crystal growth process relative to the substrate

Epitaxy refers to a type of crystal growth or material deposition in which new crystalline layers are formed with one or more well-defined orientations with respect to the crystalline seed layer. The deposited crystalline film is called an epitaxial film or epitaxial layer. The relative orientation(s) of the epitaxial layer to the seed layer is defined in terms of the orientation of the crystal lattice of each material. For most epitaxial growths, the new layer is usually crystalline and each crystallographic domain of the overlayer must have a well-defined orientation relative to the substrate crystal structure. Epitaxy can involve single-crystal structures, although grain-to-grain epitaxy has been observed in granular films. For most technological applications, single domain epitaxy, which is the growth of an overlayer crystal with one well-defined orientation with respect to the substrate crystal, is preferred. Epitaxy can also play an important role while growing superlattice structures.

In solid-state physics, the electron mobility characterises how quickly an electron can move through a metal or semiconductor when pulled by an electric field. There is an analogous quantity for holes, called hole mobility. The term carrier mobility refers in general to both electron and hole mobility.

In semiconductor production, doping is the intentional introduction of impurities into an intrinsic semiconductor for the purpose of modulating its electrical, optical and structural properties. The doped material is referred to as an extrinsic semiconductor.

<span class="mw-page-title-main">Boule (crystal)</span> Synthetic ingot of crystal

A boule is a single-crystal ingot produced by synthetic means.

An epitaxial wafer is a wafer of semiconducting material made by epitaxial growth (epitaxy) for use in photonics, microelectronics, spintronics, or photovoltaics. The epi layer may be the same material as the substrate, typically monocrystaline silicon, or it may be a silicon dioxide (SoI) or a more exotic material with specific desirable qualities. The purpose of epitaxy is to perfect the crystal structure over the bare substrate below and to improve electrical characteristics of the wafer surface, making it suitable for highly complex microprocessors and memory devices.

<span class="mw-page-title-main">Single crystal</span> Material with a continuous, unbroken crystal lattice

In materials science, a single crystal is a material in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample, with no grain boundaries. The absence of the defects associated with grain boundaries can give monocrystals unique properties, particularly mechanical, optical and electrical, which can also be anisotropic, depending on the type of crystallographic structure. These properties, in addition to making some gems precious, are industrially used in technological applications, especially in optics and electronics.

Float-zone silicon is very pure silicon obtained by vertical zone melting. The process was developed at Bell Labs by Henry Theuerer in 1955 as a modification of a method developed by William Gardner Pfann for germanium. In the vertical configuration molten silicon has sufficient surface tension to keep the charge from separating. The major advantages is crucibleless growth that prevents contamination of the silicon from the vessel itself and therefore an inherently high-purity alternative to boule crystals grown by the Czochralski method.

<span class="mw-page-title-main">Verneuil method</span> Manufacturing process of synthetic gemstones

The Verneuil method, also called flame fusion, was the first commercially successful method of manufacturing synthetic gemstones, developed in the late 1883 by the French chemist Auguste Verneuil. It is primarily used to produce the ruby, sapphire and padparadscha varieties of corundum, as well as the diamond simulants rutile, strontium titanate and spinel. The principle of the process involves melting a finely powdered substance using an oxyhydrogen flame, and crystallising the melted droplets into a boule. The process is considered to be the founding step of modern industrial crystal growth technology, and remains in wide use to this day.

In microfabrication, thermal oxidation is a way to produce a thin layer of oxide on the surface of a wafer. The technique forces an oxidizing agent to diffuse into the wafer at high temperature and react with it. The rate of oxide growth is often predicted by the Deal–Grove model. Thermal oxidation may be applied to different materials, but most commonly involves the oxidation of silicon substrates to produce silicon dioxide.

The Deal–Grove model mathematically describes the growth of an oxide layer on the surface of a material. In particular, it is used to predict and interpret thermal oxidation of silicon in semiconductor device fabrication. The model was first published in 1965 by Bruce Deal and Andrew Grove of Fairchild Semiconductor, building on Mohamed M. Atalla's work on silicon surface passivation by thermal oxidation at Bell Labs in the late 1950s. This served as a step in the development of CMOS devices and the fabrication of integrated circuits.

Monocrystalline silicon, more often called single-crystal silicon, in short mono c-Si or mono-Si, is the base material for silicon-based discrete components and integrated circuits used in virtually all modern electronic equipment. Mono-Si also serves as a photovoltaic, light-absorbing material in the manufacture of solar cells.

Crystalline silicon or (c-Si) Is the crystalline forms of silicon, either polycrystalline silicon, or monocrystalline silicon. Crystalline silicon is the dominant semiconducting material used in photovoltaic technology for the production of solar cells. These cells are assembled into solar panels as part of a photovoltaic system to generate solar power from sunlight.

The Monte Carlo method for electron transport is a semiclassical Monte Carlo (MC) approach of modeling semiconductor transport. Assuming the carrier motion consists of free flights interrupted by scattering mechanisms, a computer is utilized to simulate the trajectories of particles as they move across the device under the influence of an electric field using classical mechanics. The scattering events and the duration of particle flight is determined through the use of random numbers.

Polycrystalline silicon, or multicrystalline silicon, also called polysilicon, poly-Si, or mc-Si, is a high purity, polycrystalline form of silicon, used as a raw material by the solar photovoltaic and electronics industry.

Two-photon photovoltaic effect is an energy collection method based on two-photon absorption (TPA). The TPP effect can be thought of as the nonlinear equivalent of the traditional photovoltaic effect involving high optical intensities. This effect occurs when two photons are absorbed at the same time resulting in an electron-hole pair.

<span class="mw-page-title-main">Kyropoulos method</span> Method of bulk crystal growth used to obtain single crystals

The Kyropoulos method, KY method, or Kyropoulos technique, is a method of bulk crystal growth used to obtain single crystals.

References

↑ Paweł Tomaszewski, "Jan Czochralski i jego metoda. Jan Czochralski and his method" (in Polish and English), Oficyna Wydawnicza ATUT, Wrocław–Kcynia 2003, ISBN 83-89247-27-5
↑ 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.
↑ Nishinaga, Tatau (2015). Handbook of Crystal Growth: Fundamentals (Second ed.). Amsterdam, the Netherlands: Elsevier B.V. p. 21. ISBN 978-0-444-56369-9.
↑ Stuart Dowell. "Scientist who laid the foundations for Silicon Valley honoured at long last". thefirstnews.com. Retrieved 3 May 2023.
↑ Son, JK (2020-05-14). "Growth and development of pure Li2MoO4 crystals for rare event experiment at CUP". Journal of Instrumentation. 15 (7): C07035. arXiv: 2005.06797 . Bibcode:2020JInst..15C7035S. doi:10.1088/1748-0221/15/07/C07035. S2CID 218630318.
↑ Czochralski Crystal Growth Method. Bbc.co.uk. 30 January 2003. Retrieved on 2011-12-06.
↑ 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 (1): 158–163. Bibcode:2002NYASA.972..158A. doi:10.1111/j.1749-6632.2002.tb04567.x. PMID 12496012. S2CID 2212684.
↑ Doubts over 450mm and EUV. Electronicsweekly.com. December 30, 2013. Retrieved on 2014-01-09.
↑ 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.
↑ 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; et al. (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. hdl: 11568/67464 .
↑ CERN RD50 Status Report 2004, CERN-LHCC-2004-031 and LHCC-RD-005 and cited literature therein
↑ 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 (1–2): 202–207. Bibcode:2005NIMPA.541..202H. CiteSeerX 10.1.1.506.2366 . doi:10.1016/j.nima.2005.01.057.
↑ 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.
↑ Eikelboom, J.A., Jansen, M.J., 2000. Characterisation of PV modules of new generations; results of tests and simulations Archived 2012-04-24 at the Wayback Machine . Report ECN-C-00-067, 18.
↑ James D. Plummer, Michael D. Deal, and Peter B. Griffin, Silicon VLSI Technology, Prentice Hall, 2000, ISBN 0-13-085037-3 pp. 126–27

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[1] Paweł Tomaszewski, "Jan Czochralski i jego metoda. Jan Czochralski and his method" (in Polish and English), 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] Stuart Dowell. "Scientist who laid the foundations for Silicon Valley honoured at long last". thefirstnews.com. Retrieved 3 May 2023.

[5] Son, JK (2020-05-14). "Growth and development of pure Li2MoO4 crystals for rare event experiment at CUP". Journal of Instrumentation. 15 (7): C07035. arXiv: 2005.06797 . Bibcode:2020JInst..15C7035S. doi:10.1088/1748-0221/15/07/C07035. S2CID 218630318.

[6] Czochralski Crystal Growth Method. Bbc.co.uk. 30 January 2003. Retrieved on 2011-12-06.

[7] 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 (1): 158–163. Bibcode:2002NYASA.972..158A. doi:10.1111/j.1749-6632.2002.tb04567.x. PMID 12496012. S2CID 2212684.

[8] Doubts over 450mm and EUV. Electronicsweekly.com. December 30, 2013. Retrieved on 2014-01-09.

[9] 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.

[10] 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; et al. (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. hdl: 11568/67464 .

[11] CERN RD50 Status Report 2004, CERN-LHCC-2004-031 and LHCC-RD-005 and cited literature therein

[12] 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 (1–2): 202–207. Bibcode:2005NIMPA.541..202H. CiteSeerX 10.1.1.506.2366 . doi:10.1016/j.nima.2005.01.057.

[13] 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.

[14] Eikelboom, J.A., Jansen, M.J., 2000. Characterisation of PV modules of new generations; results of tests and simulations Archived 2012-04-24 at the Wayback Machine . Report ECN-C-00-067, 18.

[15] James D. Plummer, Michael D. Deal, and Peter B. Griffin, Silicon VLSI Technology, Prentice Hall, 2000, ISBN 0-13-085037-3 pp. 126–27

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