30 Melt growth

Prof. P. N. Kotru

 30.1.  Introduction

Growth from molten phase is the best method for growing large crystals of high perfection faster than any other method. Melt growth normally requires that the material melts congruently in the sense that it does not decompose below or near its melting point and has a manageable vapour pressure at its melting point. Melt growth may be divided into four main groups of techniques:

1. Normal Freezing: In this technique the ingot is gradually frozen from one end.
2. Crystal Pulling : In this method the crystal is grown on a seed withdrawn from the melt.
3. Zone Melting : In this technique a molten zone is passed through an ingot

4.    Flame Fusion or Pedestal Growth: In this technique crystal grows below a melt which is fed from above .

Melt growth is essentially a process of controlled solidification. Solidification involves change of state which can be described in terms of two processes and that is nucleation and growth. Nucleation can be achieved from the melt itself or by introducing a seed crystal. In other words, nucleation can be homogeneous or heterogeneous. Material to be grown as single crystal is placed in a suitable container and then heated in a furnace above its melting point. The melt is then cooled from its equilibrium melting point to initiate growth. If seed is used, growth usually begins when the temperature is slightly below the equilibrium melting point. However, in the absence of seed crystal, the melt will generally supercool until a stable nucleus is formed. At the equilibrium state the material is completely molten above the melting point and completely solid below the melting point. As such, the transition of material from its molten state to solid state is quite fast at this equilibrium state. The problem for the crystal grower is, therefore, to control this rate of transition from molten state to solid state in order to ensure that single crystals grow. To achieve this, a small volume of the melt is permitted at a time to pass through this transition temperature in order to achieve crystallization. It is necessary to have a temperature gradient with one part of the system above and the other part below the melting point having a uniform temperature gradient.

In this method of growth crystals usually grow most rapidly in certain crystallographic directions in which thermal conductivities are larger. It is on account of these reasons that growth from melt becomes primarily a problem of controlling temperatures and thermal gradients. There are

various techniques by which this control can be achieved and the prominent ones are:

•    Czochralski and other related techniques.

•    Bridgman-Stockbarger technique

•    Growth by zone melting and

•    Verneuil flame fusion technique

Let us describe some more details of prominent techniques falling in the group of Czochralski and some other related techniques of growth from the molten phase.

30.2        Czochralski Crystal Pulling & Other Related Techniques

30.2.1     The Basic Crystal Pulling Methods.

In this section we describe processes which are often referred to as crystal pulling. Most of them involve relative motion of a seed crystal and the melt so that the crystal is literally pulled from the melt. The process as described by Czochraski in 1918 is the fastest melt growth method. Crystal pulling technique is also the method which can be used to produce the highest quality crystal from the point of view of perfection and homogeneity. Crystal pulling is applicable to materials which melt congruently, i.e., the chemical composition of the solid and the melt in equilibrium cannot differ much. Crystal pulling is much faster as compared to another technique of growth from melt, i.e., Bridgman method. Silicon slowly dissolves fused SiO2 (Silica), but large quantities, more than 2500 tonnes of silicon crystals are pulled each year from silica crucibles. Crystal growth from the molten phase are the Czochralski pulling method, the technique of Kyropoulos ( 1926 , 1930 ) which actually does not involve pulling , dendrite methods , the method invented by Stepnov in 1969 and film-fed edge-defined growth.

While the largest use of the Czochralski method is for the growth of silicon, it has been used for commercial growth of around one hundred materials. Commercially-available materials should be of large size with diameters of more than 50 mm. The largest size of silicon crystal grown by this method is more than 250 mm in diameter. Table 30.1 provides some examples and their growth conditions typical for small size crystals (~ 2cm. dia.)

30.2.2.   Basic Method

The basic technique is simple as may be summarized below:

1. Raise the temperature of the melt just a few degrees above the melting point. In a well-designed system, temperature differences, both radially as well as vertically, are maintained to the minimum possible.
2. The crystal used as seed which rotates slowly, is brought slowly into contact with the surface of the melt. When it is just in contact with the melt surface, the lowering of the seed crystal is stopped. The seed starts melting slowly and at a decreasing rate .It is ensured that the seed remains in contact with the melt. If the seed does not remain in contact with the melt surface, it means that the melt temperature is too high and is required to be brought to the optimum value. If it is observed that crystal growth has taken place it means that the melt temperature is too low and needs to be increased until all the grown material and a tiny portion of the seed has melted.
3. After waiting for a while, typically say about one to three minutes, pulling is started at a slow rate around half of the final value. New crystals should grow with a diameter that is less than the diameter of the seed.
4. The rates of growth and rotation are increased to their final values. The diameter of the growing crystal should decrease. If it is desired to have dislocation-free crystal, a long narrow neck is grown, the length of which depends on the material and the growth direction .Normally, about 5 to 10 times the seed diameter is an optimum length.
5. On completion of the neck, the melt temperature is lowered slowly. The diameter of the crystal increases. The lowering of the melt temperature is stopped and the crystal starts attaining its final diameter.
6. Growth at a constant diameter is maintained until the growth of crystal of the desired length has taken place.
7. At this point, the growth is terminated. Termination of growth is achieved either by sharply increasing the pulling rate so as to break contact of crystal with the melt, or by increasing the melt temperature so as to bring down the diameter of the crystal slowly to zero. If changes are brought about rapidly, they can cause cracking of the crystal or become cause for dislocation formation in the crystal. After completion of the growth process, the system is cooled slowly.

Constant diameter of the crystal is maintained by increasing or decreasing the power input to the melt. Increasing power decreases the crystal diameter. Increasing either the growth rate or the seed rotation rate produces the same effect. In commercial production, all the stages after step number 3 and the final cooling procedure are carried out by automatic control system.

In modern systems, actual diameter measurements are done directly. One type of system watches the crystal with a television camera and accordingly processes the signal to derive a diameter.

30.2.3   Experimental arrangement for Czochralski growth.

This type of growth falls under a process in which crystal is grown on a seed withdrawn from the melt. The technique was originated by Czochralski in 1918 and so is named after him. Through this method one can produce crystals weighing from several grams to many kilograms. All crystal pulling processes are based upon a technique developed by Czochralski. This technique and its various modifications have become the dominant process used in industry today for the growth of semiconductor and oxide single crystals which include silicon , germanium, GaP, InP, GaAs,Sapphire, LiNbO₃, Gd₃Ga₅O₁₂ , Nd : Y₃Al₅O₁₂ and scores of others. It is, therefore, important to understand the basic principles, the advantages and limitations of this technique.

The basic process is simple. A vertically mounted seed crystal is lowered into contact with the molten material held in a crucible. The bottom of the seed crystal is allowed to melt and when the contact between seed and melt has been established, the seed is slowly raised to pull out a crystal. If suitable precautions are taken, the material withdrawn from the melt solidifies as a large single crystal.

Figure 30.1 gives the details of the apparatus used for the growth of calcium tungstate (Scheelite; chemical composition CaWO4). The crucibles required for carrying out growth by this technique are made up of iridium or rhodium. The reason for the strict use of these crucibles is the high melting point which is even higher than the material to be grown. Since the crucible is heated directly, radio frequency heating is preferred. Electrical power from a generator at 50 kilocycles is fed into a water cooled copper coil surrounding the crucible.

A current of 100 amperes is produced in the crucible which heats it. Platinum rhodium thermocouple records the temperature. The electrical and heat insulation are provided by the alumina powder filling the space between crucible and high frequency coil. This powder also supports the crucible. The crucible is filled with highly purified molten sheelite (in the case of sheelite growth) and a    small seed of sheelite is lowered to just touch the surface of the melt. This seed is fastened by a vertical puller so that it can be rotated and raised. Care has to be taken at the start as the seed crystal may fracture if inserted too suddenly in the melt or it may melt if the temperature is too high. At very low temperatures instead of single crystal a polycrystalline mass containing hundreds of tiny crystals may result. This method has certain advantages such as:

(i) The crystal can be observed during the growth and so temperature and the growth rate can be adjusted

according to the need.

(ii) It is possible to achieve rapid rate of growth .Growth rates as high as four inches per hour are practical.

While considering the growth of crystals by using crystal pulling technique, one has to take into account special requirements and restrictions regarding materials which have to be used for growth. So, one has to find suitable solutions to the following questions:

1. Compatibility of the material to be grown as single crystal with the restrictions placed upon it by the crystal pulling technique.
2. Are crucible materials available which meet the requirements demanded by the crystal growth by this technique?
3. Is a heat source available which is consistent with the crucible selection and growth conditions? For a material to be considered for growth by pulling technique, one is required to look for suitable solutions to the following as may be summarized below:

1. The material is required to have a congruent melting point, i.e., the material should not decompose upon

or before melting.

2. It should have a relatively low vapour pressure.

3. It should not have first order solid-solid phase transitions or reconstructive phase transitions.

4. Crucible material has to be non-reactive with the material above its melting point.

Figure 30.1: Schematic diagram showing the apparatus for the Czochralski growth of Calcium Tungstate crystals

Before one takes up crystal pulling technique for the growth of a crystal, it is necessary to understand phase equilibrium between a solid and its liquid so that the results of a crystal pulling experiments are positive.

The successful growth of  a crystal by pulling technique  depends  on factors that include manipulation of the pulling rate, rotation rate, thermal geometry and atmosphere to achieve as perfect crystal as possible.  In melt growth it  is  important  to consider distribution or  segregation coefficient ‘σ’  (generally, represented by ‘k’  by most  of the authors). It  is  defined as  the ratio of  the  solid concentration CS  to the  liquid concentration Cl. The more  ‘σ’ differs  from unity, the  greater is  the separation of the solid and liquid states and the process of crystal pulling process become more difficult. At equilibrium, the concentration in the solid is given by:

CS = σ C0 (1─ g )σ─1,

Where C0 is the initial concentration of the impurity ions and g is the fraction of melt that has been crystallized. All these factors have to be considered before experiments on crystal pulling technique are performed.

Most impurities have segregation coefficient (σ) less than unity means that at a growth face they are rejected. Therefore, in growth from melt we have a situation when the melts are not pure; there  is a high concentration of  impurities near the growth face. These diffuse  across the boundary layer into the bulk of the melt. So, an impurity concentration gets created away from the growth face for solutes with σ < 1 (In the event of σ > 1, the gradient is reversed). A gradient of melting point is created away from the growth face (Impurities with σ < 1 decrease the melting point. However, those with σ > 1 increase the melting point.). The melting point increases across the boundary layer towards the bulk melt. Let the melting point of pure melt be Tmp, the actual melting point can be written as Tmp ─ mi  ci  , where ci is the concentration of impurity  i which decreases the melting point by mi per mole . mi for an ideal solution of a solute having segregation coefficient σi is given by :

mi = RT ( 1─ σi ) /si

Where  si is change in entropy.

30.3    Kyropoulos Growth.

The Czochralski growth method produces crystals with length-to-diameter ratios which greatly exceeds unity, and the diameters of the crystals rarely exceed half the crucible diameter. It is very difficult to hold a constant diameter of the crystal. However, there are applications in which the crystal should have a large diameter rather than large length. These applications include lenses, prisms, windows and other optical components. For such requirements, it is the Kyropoulos method which is widely used.

Figure 30.2: Schematic illustration of Kyropoulos growth process (i) seed crystal is brought in contact with the melt. A small part of seed is melted and then cooling is started to give the situations (ii) & (iii).

The basic system is almost the same as that of Czochralski system. However, the difference lies in the fact that in Kyropoulos method, the seed is brought into contact with the melt as in the Czochralski method but is not raised much during growth. After the seed contacts the melt, part of the seed is allowed to melt and a short narrow neck is grown. The vertical motion of the seed is stopped after that and growth is allowed to proceed by decreasing the power input of the melt. Figure 30.2 shows sequentially the stages of operation which may be described as follows:

1.  In step no.1, the pointed seed crystal is brought into contact with the melt as shown in (i) of figure 30.2.

2. The above process melts a small part of the seed.

3. The cooling is started which leads to situations as shown in (ii) and (iii) of figure 30.2.

In such a system a simple control system is required, but it is necessary that the crucible has a suitable temperature distribution. The shape of the crystal grown depends strongly on the temperature distribution and the relative densities of the melt and crystal. In a typical case of the growth of alkali halides, the crystal has a greater density than the metal, so that as growth proceeds the melt level falls, and the desired temperature distribution is one in which the crucible temperature rises slowly and uniformly towards the bottom of the crucible The method is economically attractive. However, the method has technical deficiencies. The isothermal surfaces in the system are curved, often spherical in shape, with radii almost equal to the diameter of the crystal. This leads to large dislocation densities and the growth interface is composed of many different crystal faces, so that the crystal is composed of many zones with different impurity and vacancy concentrations. The crystals are imperfect, inhomogeneous and strained.

30.4. Dendrite Method.

The word dendrite literary means “tree like”. We have already talked about defects in crystals in previous sections. Planar defect known as twinning has been described. Twinning can be formed by rotation or reflection. Presence of a twin plane provides a permanent ledge on a growth face which becomes a source for rapid growth. Figure 30.3 shows dendrite structures for crystals exhibiting diamond and zinc blende lattices. On a growth face as illustrated in this figure, the growth rate is directly proportional to the melt supercooling ΔT.

where KL is the thermal conductivity of the melt,

w is the thickness of the dendrite and

A is nearly 0.7 if no heat is conducted by the dendrite.

In practice, values of A are about 0.9. A typical growth rate for a dendrite 0.5 mm thick with TB (supercooling of the bulk of the melt) is 3mm s─1. In both theory and practice the thickness depends on the rate of growth, which is the rate at which the seed is withdrawn.

The general, procedure is to lower a dendrite seed so that it just touches the surface of a melt which is just above the melting point. The seed is left to attain equilibrium and the melt is then cooled rapidly by about 20 ⁰C. After waiting for a while pulling is started. Taking the example of a typical case, a pulling rate of 100mm s─ 1 gives dendrites 0.2 to 0.4 mm thick. The dendrite surfaces are almost perfect and as such the thin dendrites can be rolled on to a drum of about 0.5 m in diameter.Germanium dendrites having thickness of about 0.5 mm can be wrapped around drums of 10 cm. dia without breaking, provided that their surfaces are scratchless.

Dermatis and Faust in 1962 modified the process by using two dendrite seeds to grow a pair of dendrites which support a thin sheet of crystal between them as illustrated in figure 30.4. With the help of this procedure wider sheets can be grown.

This technique is also known as web technique. Through this technique, it is possible to produce crystals with dislocation densities of more than 103 cm─2. However, by controlling the temperature gradients, stable growth with dislocation densities of about 100 cm─2 was achieved by Barnett et al (1971). The high rate of growth in dendrite technique appears to be quite attractive but purity of the material grown is an issue which raises some concern. Most impurities will have effective segregation coefficients nearing unity when grown from unstirred melts at the rates used in dendrite growth.

Figure 30.3: Schematic illustration of dendrite structures (a) shows a stable multi-twinned dendrite and (b) shows an unstable single twinned dendrite.

Figure 30.4: Schematic diagram showing the use of two dendrites to support a web of untwinned growth

30.5     The Stepanov Method

In this method the crystal is pulled from a crucible which has an aperture in the shape of the crystal. The idea is that the melt and crystal may have the same shape on either side of the growth face as shown in a schematic diagram of figure 30.5. For a given material, this technique is considered as faster than the growth achieved in Bridgman method (another method of growth from the molten phase, to be described later) but slower than in case of Czochralski growth. This method is not yet put to any commercial use for the growth of single crystals. The method finds its use in making shaped polycrystalline metal rods. Stepanov has reviewed work on the subject in 1969.

Figure 30.5: Schematic diagram illustrating Stepanov technique in which crystal is pulled through an aperture which controls its shape.

30.6.  Edge-defined Film–fed Growth (EDFFG)

A tube, made of a material which is wetted by a liquid, is placed in a way as to cut the liquid–vapour interface, the liquid rises in the tube to a height given by the following expression:

hr=   2γ/ ρgr    …………………………………….30.1

Where γ is the surface tension,

ρ is the density,

r is the radius of the tube and

g is acceleration due to gravity.

One can find similar expressions for differently shaped apertures like inclined plates or parallel plates and so on .γ is also an important factor which is different for different interfaces.

For example:

γSG  > γGL + γLS…………………………………….30..2

The surface tensions of the solid-gas ( γSG), gas–liquid ( γGL ) and liquid–solid ( γLS ) are different and if the surface tensions are in accordance with equation 30.2, a thin film of the liquid will eventually cover the entire solid . As for example, if we have molten bismuth oxide in a platinum crucible in air it creeps up the crucible walls and down the outside of the crucible.

Figure 30.6: Schematic diagram illustrating Edge-defined Film–fed Growth. Pictorial description of the sequential situations in the process of growth is given.

Figure 30.6 shows the process involved in edge-defined film-fed growth. In figure 30.6 (I) the melt which wets the die is drawn up in the central capillary, which should have a radius < 2γ/ρgh , ρ being density of melt and h the length of the capillary and γ is the surface tension of melt. Figure 30.6 (II) shows that when the pointed seed is brought into contact with the melt , it is pulled up and the melt is cooled slightly to permit the size of the crystal to increase and figure 30.6 (III) shows a stage when finally the crystal reaches the size of the die. The process of edge-defined film-fed growth proceeds as shown in figure 30.6. In order that the operation of the system works satisfactorily, the holes in the die should have the lengths (h) and radii (r) such that: h < hr , where hr should be defined by equation no. 30.1.

The process involved in EDEFG is schematically described by figure 30.6. The process relies on creep to cover  the top surface  of the  die. The melt  from which the  crystal grows flows  up the capillary and then horizontally in the thicker layer between the top of the die and the growth face.

The method has advantages only when the crystals have at least one small dimension, i.e., it can be used to grow sheets and tubes. On account of the fact that the growth is rapid, it does not yield high quality crystals.

In this method the die has to be wetted by the melt which indicates that some dissolution will take place. There is also absence of stirring and the growth rate is quite high; the typical growth rate being 20 to 40 mm min.─1 in case of Al2O3… These factors act against the purity of the material.

30.7 Liquid Encaptulation Czochralski (LEC) Growth.

When crystals having volatile components are to be grown, a different set of problems come up. LEC is a technique which falls under the category of crystal pulling techniques which has been developed to overcome one of the main material limitations of crystal pulling namely that the material to be grown is required to have a relatively low vapour pressure. It is widely used for the growth of III-V semiconductor compounds such as GaAs, InP and GaP. Consider growth of gallium arsenide. The solid with the maximum melting point to the tune of 1238⁰C is in equilibrium with arsenic vapour with a partial pressure of about 1 atmosphere. The arsenic vapour needed is mostly As2. Arsenic vapour at a partial pressure of one atmosphere can be provided by an arsenic source maintained at a temperature of 612⁰C and the system should not contain any region cooler than the arsenic source. Different type of pulling systems have been used which allow the provision of partial vapour pressure.

These include sealed systems with magnetic coupling to have pulling and rotation as required, systems with liquid seals e.g., boric oxide or close-fitting piston type seals. However, the only method used on a large scale is liquid encapsulation. The apparatus for liquid-encapsulation Czochralski (LEC) growth is available commercially.

Figure 30.7: Schematic diagram illustrating Liquid Encapsulation Czochralski (LEC) Growth.

The basic requirement of the method is to have no vapour phase; the crystal and the melt surface are covered with a liquid film as shown in figures 30.7 and 30.8. The growth chamber is filled with an inert gas at a pressure in excess of the sum of the maximum partial pressures of the volatile components. The encapsulant is required to have some specific properties which include the following:

a)  It should be inert with respect to the melt, crystal and crucible.

b)  It should have sufficient viscosity so that it adheres to the growing crystal but at the growth temperature

it should be sufficiently fluid so that the crystal can be rotated with respect to the melt.

c)   On cooling the crystal, the encapsulant should not damage the crystal and the encapsulant should be

such as to be easily removable from the grown crystal without damaging the crystal.

Figure 30.8: Schematic diagram illustrating typical arrangement for Liquid Encapsulated crystal growth of gallium arsenide.

The most frequently used encapsulant is boric oxide. Molten B2O2 freezes to yield a crystalline solid at about 450⁰C, but could be supercooled to nearly 300⁰C where it solidifies as a vitreous solid.

The following steps describe the process as illustrated in figure 30.7:

•  The material to be grown and the encapsulant are placed in the crucible which is heated by an r.f. field.

•  The encapsulant melts first and a layer of encapsulant separates the melt from the crucible as illustrated in

figure 30.7(a).

•  The seed crystal is brought to the melt surface as shown in figure 30.7(b).

•The growth then proceeds as usual (see fig. 30.7(c)), but the crystal is covered by a layer of encapsulant

which prevents it from decomposition.

•The crucible and r.f. coils are placed in pressure vessel. The pressure is required to be more than the sum of

the maximum partial pressures of volatile components. However, this pressure should also not exceed

beyond a particular limit. Heat transfer by convection increases with pressure, and at high pressures the rate of transfer is time-dependent.

Figure 30.8 shows experimental arrangement for the growth of GaAs by liquid-encapsulation technique. The assembly is enclosed in a pressure chamber containing argon at nearly three atmospheres pressure. In this set up very large amount of thermal screening is done in order to reduce and decrease the effect of thermal oscillations due to unsteady convection between this growth assembly and the water-cooled pressure chamber walls. This technique overcomes a primary deficiency in crystal pulling and extends the usefulness of this technique to other materials. It, however, introduces several additional problems. One of the main problems is the addition of a second liquid layer above the first. If the encapsulant is too thick, it will act as a thermal blanket thereby making growth more difficult. If it is too thin, it will not be able to hold in the volatile component which is likely to result in the melt stoichiometry problems. In this technique the crystal has to be pulled through the encapsulant layer. There is every danger of improper draining of the encapsulant from the crystal thus causing cracking during cool down. There is also a problem which is associated with the encapsulant and this is contamination. Small particles in the melt have a tendency to get trapped within the encapsulating layer which impairs visibility. Conversely, some of the encapsulant may get dissolved into the melt and act as an impurity ion. Inspite of these problems, GaP can be grown in weight ranges of 2-5 Kg by this technique and has acquired the status of being commercial production process.

References.

1.  Brice,J.C.: “Crystal Growth Processes”, Blackie & Sons Ltd.,Glasgow,1986.

2.  Pamplin,B.R.: “ Crystal Growth “ II edition,Pergamon Press,Oxford,1980.

3.  Gilman ,J.J. : “ The Art & Science of Growing Crystals”,Wiley,N.Y.,1963.

4.  McKelvey,John,P.:” Solid State & Semiconductor Physics”,Harper&Row,N.Y./John Weather Hill

Inc.,Tokyo,1966.

5.Knight,C.A.: “ The Freezing of SupercooledLiquids”,Van Nostrand,!967.

Suggested Reading For More Information On Theoretical & Experimental Aspects Of Melt Growth.

1. Jackson,J.A.: “ Theory Of Melt Growth” in “Crystal Growth &Characterization”ed.Ueda,R and

Mullin,J.B.,North-Holland,Amsterdam,1974.

2. Mullin,J.B. : “ Crystal Growth From Melt-I(General)”in Crystal Growth &Characterization”ed.Ueda R  and

Mullin,J.B.,North-Holland,Amsterdam,1974.

3.  Mullin,J.B.: “ Crystal Growth From Melt-II(Dissociable Compounds)” in “Crystal Growth &Charac-

terization”,ed.Ueda,R and Mullin,J.B.,North-Holland,Amsterdam,1974.

4. Cockayne,B.:”” Crystal Growth From Melt-III Oxides” in “Crystal Growth &Characterization”ed.

Ueda,R. and Mullin,J.B.,North-Holland ,Amsterdam,1974.

5. Hurle,D.T.J.: “ Mechanism of Growth of Metal Single Crystals From The Melt”,Prog.in Mat.

Sci.,vol.10,Pergamon Press, Oxford, 1963.

6.  Brice, J.C.: “ The Growth of Crystals From The Melt”,North Holland Amsterdam,1965.

7.  Laudise,R.A.:” The Growth Of Crystals ,Prentice-Hall, Englewood cliffs,N,J,,1970.

8.  Lefever,R.A.(ed.)”Aspects of Crystal Growth”,Dekker,N.Y.,1971.

9.Goodman,C.H.L.(ed):” Crystal Growth-theory &Technique”,Vol.1(1975) & Vol.2(1978), Plenum Press,N.Y.

10. Brice,J.C.:” The Growth Of Crystals From Liquids”,North-Holland/Elsevier,N.Y.,1973