introduction to single crystals
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Introduction to single crystals
A single crystal or mono crystalline solid 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 mono crystals uniqueproperties, particularly mechanical, optical and electrical, which can also be anisotropic,
depending on the type of crystallographic structure. These properties, in addition to making
them precious in some gems, are industrially used in technological applications, especially in
optics and electronics.
Because entropic effects favour the presence of some imperfections in the microstructure
of solids, such as impurities, inhomogeneous strain and crystallographic defects such as
dislocations, perfect single crystals of meaningful size are exceedingly rare in nature, and
are also difficult to produce in the laboratory, though they can be made under controlled
conditions. On the other hand, imperfect single crystals can reach enormous sizes in nature:
several mineral species such as beryl, gypsum and feldspars are known to have produced
crystals several metres across.
Fig. 1: Single crystal quartz drawn by hydrothermal synthesis
1.1 Uses of single crystals
Their various uses are as follows:
1.1.1 Semiconductor industry: Single crystal silicon is used in the fabrication of
semiconductors. On the quantum scale that microprocessors operate on, the
presence of grain boundaries would have a significant impact on the functionality of
field effect transistors by altering local electrical properties. Therefore,
microprocessor fabricators have invested heavily in facilities to produce large single
crystals of silicon.
1.1.2 Optics:
Monocrystals of sapphire and other materials are used for lasers and
nonlinear optics.
Monocrystals of fluorite are sometimes used in the objective lenses of
apochromatic refracting telescopes.
1.1.3 Materials engineering: Another application of single crystal solids is in materials
science in the production of high strength materials with low thermal creep, such as
turbine blades. Here, the absence of grain boundaries actually gives a decrease in
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yield strength, but more importantly decreases the amount of creep which is critical
for high temperature, close tolerance part applications.
1.1.4 Electrical conductors: Single crystal copper has better conductivity than
polycrystalline copper. As of 2009, no single crystal copper is manufactured on a
large scale industrially, but methods of producing very large individual crystal sizesfor copper conductors are exploited for high performance electrical applications.
These can be considered meta-single crystals with only a few crystals per metre of
length.
1.1.5 In research: Single crystals are essential in research especially condensed-matter
physics, materials science etc. The detailed study of the crystal structure of a
material by techniques such as Bragg diffraction and helium atom scattering is much
easier with monocrystals. Only in single crystals it is possible to study directional
dependence of various properties. In superconductivity there have been cases of
materials where superconductivity is only seen in single crystalline specimen. They
may be grown for this purpose, even when the material is otherwise only needed in
polycrystalline form.
1.2 Thermodynamics related to process:
The nature of a crystallization process is governed by both thermodynamic and kinetic
factors, which can make it highly variable and difficult to control. Factors such as
impurity level, mixing regime, vessel design, and cooling profile can have a major
impact on the size, number, and shape of crystals produced.( )
This rule suffers no exception when the temperature is lowering. On cooling back the
melt, Crystallization occurs. The entropy decrease due to the ordering of molecules
within the system is overcompensated by the thermal randomization of the
surroundings, due to the release of the heat of fusion; the entropy of the universe
increases. The nucleation and growth of a crystal are under kinetic, rather than
thermodynamic, control.
Crystallization or Nucleation can be of two types either homogeneous or
heterogeneous.
Homogeneous Nucleation can occur anywhere in the liquid without any
preferences i.e. possibility of it is same everywhere.
Heterogeneous Nucleation can occur certain sites i.e. probability of nucleation is
more at certain sites.
Critical radius values for homogenous and heterogeneous nucleation are
and
respectively where is surface energy of liquid solid interface.
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Fig. 2: Critical radius for Homogenous Nucleation
Fig. 3: Energy barrier difference between homogeneous and heterogeneous crystallization.
Once the first small crystal, the nucleus, forms it acts as a convergence point (if unstable
due to super saturation) for molecules of solute touching – or adjacent to – the crystal
so that it increases its own dimension in successive layers. The pattern of growth
resembles the rings of an onion, as shown in the picture, where each colour indicates
the same mass of solute; this mass creates increasingly thin layers due to the increasingsurface area of the growing crystal. The supersaturated solute mass the original nucleus
may capture in a time unit is called the growth rate which is a constant specific to the
process. Growth rate is influenced by several physical factors, such as surface tension of
solution, pressure, temperature, relative crystal velocity in the solution, Reynolds
number, and so forth.
The main values to control are therefore:
Super saturation value, as an index of the quantity of solute available for the growth
of the crystal;
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Total crystal surface in unit fluid mass, as an index of the capability of the solute to
fix onto the crystal;
Retention time, as an index of the probability of a molecule of solute to come into
contact with an existing crystal;
Flow pattern, again as an index of the probability of a molecule of solute to come
into contact with an existing crystal (higher in laminar flow, lower in turbulent flow, but
the reverse applies to the probability of contact).
The first value is a consequence of the physical characteristics of the solution, while the
others define a difference between a well- and poorly designed crystallizer.
Fig.4: Crystal Growth
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2.1 Production processes of single crystals
2.1.1 Czochralski Process:
Introduction
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 who invented the method in 1916 while investigating the
crystallization rates of metals.
The most important application may be the growth of large cylindrical ingots, or 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.
Procedure
High-purity, semiconductor-grade silicon (only a few parts per million of impurities) is
melted in a crucible, 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,
Production of SingleCrystals
Czochralski Process
Bridgeman Technique
HydrothermalSynthesis
Sublimation Technique
Float Zone Technique
Recrystallization
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cylindrical ingot from the melt. Occurrence of unwanted instabilities in the melt can be
avoided by investigating and visualising the temperature and velocity fields during the
crystal growth process. This process is normally performed in an inert atmosphere, such as
argon, in an inert chamber, such as quartz.
Fig. 5: The Czochralski process
Here, a seed crystal is a small piece of single crystal / polycrystal material from which a large
crystal of the same material typically is to be grown.
The theory behind this effect is thought to derive from the physical intermolecularinteraction that occurs between compounds in a supersaturated solution (or possibly
vapor). In solution, liberated (soluble) molecules (solute) are free to move about in random
flow. This random flow permits for the possibility of two or more molecular compounds to
interact. This interaction can potentiate intermolecular forces between the separate
molecules and form a basis for a crystal lattice. The placement of a seed crystal into solution
allows the recrystallization process to expedite by eliminating the need for random
molecular collision / interaction. By introducing an already pre-formed basis of the target
crystal to act upon, the intermolecular interactions are formed much more easily / readily
than relying on random flow. Often, this phase transition from solute in a solution to acrystal lattice will be referred to as nucleation. Seeding is therefore said to decrease the
necessary amount of time needed for nucleation to occur in a recrystallization process.
2.1.2 Bridgman –Stockbarger technique:
Introduction
The Bridgman –Stockbarger technique is named after Harvard physicist Percy Williams
Bridgman and MIT physicist Donald C. Stockbarger. They are two similar methods primarily
used for growing single crystal ingots (boules), but which can be used for solidifying
polycrystalline ingots as well.
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Procedure
The methods involve heating polycrystalline material above its melting point and slowly
cooling it from one end of its container, where a seed crystal is located. A single crystal of
the same crystallographic orientation as the seed material is grown on the seed and is
progressively formed along the length of the container. The process can be carried out in a
horizontal or vertical geometry.
Fig.6: Bridgman –Stockbarger Furnace
The Bridgman method is a popular way of producing certain semiconductor crystals such as
gallium arsenide, for which the Czochralski process is more difficult.
2.1.3 Hydrothermal Synthesis
Introduction
Hydrothermal synthesis includes the various techniques of crystallizing substances from
high-temperature aqueous solutions at high vapour pressures.
Hydrothermal synthesis can be defined as a method of synthesis of single crystals that
depends on the solubility of minerals in hot water under high pressure. The crystal growth is
performed in an apparatus consisting of a steel pressure vessel called autoclave, in which a
nutrient is supplied along with water. A gradient of temperature is maintained at the
opposite ends of the growth chamber so that the hotter end dissolves the nutrient and thecooler end causes seeds to take additional growth.
Possible advantages of the hydrothermal method over other types of crystal growth include
the ability to create crystalline phases which are not stable at the melting point. Also,
materials which have a high vapour pressure near their melting points can also be grown by
the hydrothermal method. The method is also particularly suitable for the growth of large
good-quality crystals while maintaining good control over their composition. Disadvantages
of the method include the need of expensive autoclaves, and the impossibility of observing
the crystal as it grows.
Procedure:
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Temperature difference method
The most extensively used method in hydrothermal synthesis and crystal growing. The
supersaturation is achieved by reducing the temperature in the crystal growth zone. The
nutrient is placed in the lower part of the autoclave filled with a specific amount of solvent.
The autoclave is heated in order to create two temperature zones. The nutrient dissolves inthe hotter zone and the saturated aqueous solution in the lower part is transported to the
upper part by convective motion of the solution. The cooler and denser solution in the
upper part of the autoclave descends while the counterflow of solution ascends. The
solution becomes supersaturated in the upper part as the result of the reduction in
temperature and crystallization sets in.
Temperature reduction method
In this technique crystallization takes place without a temperature gradient between the
growth and dissolution zones. The supersaturation is achieved by a gradual reduction intemperature of the solution in the autoclave. The disadvantage of this technique is the
difficulty in controlling the growth process and introducing seed crystals. For these reasons,
this technique is very seldom used.
Metastable phase method
This technique is based on the difference in solubility between the phase to be grown and
that serving as the starting material. The nutrient consists of compounds that are
thermodynamically unstable under the growth conditions. The solubility of the metastable
phase exceeds that of the stable phase, and the latter crystallize due to the dissolution of the metastable phase. This technique is usually combined with one of the other two
techniques above.
2.1.4 Sublimation
Introduction
Sublimation is the transition of a substance directly from the solid to the gas phase without
passing through an intermediate liquid phase. Sublimation is an endothermic phase
transition that occurs at temperatures and pressures below a substance's triple point in itsphase diagram. The reverse process of sublimation is desublimation, or deposition.
At normal pressures, most chemical compounds and elements possess three different states
at different temperatures. In these cases, the transition from the solid to the gaseous state
requires an intermediate liquid state. Note, however, that the pressure referred to here is
the partial pressure of the substance, not the total (e.g., atmospheric) pressure of the entire
system. So, all solids that possess an appreciable vapor pressure at a certain temperature
usually can sublime in air (e.g., water ice just below 0 °C). For some substances, such as
carbon and arsenic, sublimation is much easier than evaporation from the melt, because the
pressure of their triple point is very high, and it is difficult to obtain them as liquids.
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Sublimation requires additional energy and is an endothermic change. The enthalpy of
sublimation (also called heat of sublimation) can be calculated as the enthalpy of fusion plus
the enthalpy of vaporization.
Procedure
Using the sublimation method, AlN single crystal was grown on SiC substrate. Figure 1 shows
a schematic of the crystal growth furnace used. By placing AlN raw material in the growth
vessel, heating the vessel by high frequency induction heating and keeping the raw material
at a high temperature from 1900°C to 2250°C, the raw material was sublimed (Equation 1).
In addition, by placing a SiC substrate in the area whose temperature was lower than that in
the raw-material area inside the growth vessel (ΔT = 100°C to 500°C), AlN was grown on the
SiC substrate (Equation 2).
2 AlN (s) 2 Al (g) + N2 (g) (Equation 1)
2 Al (g) + N2(g) 2 AlN (s) (Equation 2)
Fig. 7: Schematic of Sublimation Furnace
Fig. 8: Photograph of 3-μm thick AlN crystal
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2.1.5 Float zone technique
Introduction
It is generally used for production of monocrystal of Silicon. 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. Avoidance of the necessity of a containment vessel
prevents contamination of the silicon.
Procedure
A schematic setup of the process is shown in Fig. 9. The production takes place under
vacuum or in an inert gaseous atmosphere. The process starts with a high-purity
polycrystalline rod and a monocrystalline seed crystal that is held face to face in a vertical
position and both are rotated.
Fig.9: Float zone Process
With a radio frequency field both are partially melted. The seed is brought up from below to
make contact with the drop of melt formed at the tip of the poly rod. A necking process is
carried out to establish a dislocation free crystal before the neck is allowed to increase in
diameter to form a taper and reach the desired diameter for steady-state growth. As the
molten zone is moved along the polysilicon rod, the molten silicon solidifies into a single
Crystal and, simultaneously, the material is purified.
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2.1.6 Recrystallization method
In chemistry, recrystallization is a technique used to purify chemicals. By dissolving both
impurities and a compound in an appropriate solvent, either the desired compound or
impurities can be coaxed out of solution, leaving the other behind. It is named for the
crystals often formed when the compound precipitates out.
References:
1. www.wikipedia.com
2. Research Paper by Jan Czochralski
3. A guide to Man-made Gemstones by O'Donoghue, M.
4. Single Crystal Growth of AlN by Sublimation Method by Michimasa MIYANAGA,
Naho MIZUHARA, Shinsuke FUJIWARA, Mitsuru SHIMAZU,Hideaki NAKAHATA and
Tomohiro KAWASE
5. Techniques for Nuclear and Particle Physics Experiments by W. R. Leo
6. Preparation of Single Crystals by W.D. Lawson and S. Neilsen
7. www.images.google.com
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