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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