Box ID:

938

D090A:

19860011072 1986011072.pdf

D090F:

1986011072

D035Z:

86N20543

D088A:

NASA-CR-176606;NAS 1.26:176606;SAPR-1

D245A:

Modelling direction solidification

Center for Aerospace Information
fcjMODELLING DIRECTION SOLIDIFICATION

NAG8-541

First Semi-annual Progress Report

1 September 1985 to 28 February 1986

CLARKSON UNIVERSITY

Potsdam, New York 13676

Principal Investigator: Dr. William R. Wilcox

Professor and Chair

Department of Chemical Engineering

315-268-6650

Graduate Student Research Assistants:

Mr. Greg Neugebauer, M.S. Candidate in Chemical Engineering

Ms. Lorraine Ruggiano, Ph.D. Candidate in Chemical Engineering

(NASA-CR-176606) MODELLIHG DIRECTION N86-20543

SOLIDIFICATION Semiannual Progress Report,

1 Sep. 1885 - 26Feb. 1986 {Clarkson Oniv.)

TV p HC A04/H! A01 CSCi 11F Unclas

G3/26 . 05666
OBJECTIVE

This grant is a continuation of Contract NAS8-34891. The overall

objective of this program is to develop an improved understanding of some

phenomena of importance to directional solidification, to enable us to explain

and predict differences in behavior between solidification on earth and

solidification in space.

RESEARCH COMPLETED

The first six months of the new grant were devoted primarily to

completion of research begun under the previous contract. One paper was

published, three others were accepted for publication, two others were

completed and submitted for publication, and an U.S. thesis completed. These

are listed below.

1. "Thermal fields in the Bridgman-Stockbarger technique," H. Potts and W.R.

Wilcox, J. Crystal Growth H, 350 (1985).

2. "Chaotic asymmetric convection in the Bridgman-Stockbarger technique," H.

Potts and W.R. Wilcox, J. Crystal Growth (in press).

3. "Behavior of a non-wetting melt in free fall: experimental," R. Sen Jayaraj

and W.R. Wilcox, J. Crystal Growth .;(in press). .

4. "Behavior of a non-wetting melt in free fall: theoretical," R., Sen Jayaraj;

and W.R. Wilcox, J. Crystal Growth (submitted). .

5. "Twinning of dodecanedicarboxylic acid," R. Sen Jayaraj and W.R. Wilcox,.

J. Crystal Growth (in press).

6. "Validity of the Burton-Prim-Slichter equation," W.R. Wilcox, J. Crystal

Growth (submitted)

7. "Influence of heater configuration on convection in the

Bridgman-Stockbarger technique," G. Neugebauer, M.S. thesis.
All but one of these papers and the M.S. thesis are included as

appendices in the final report of the previous contract, a draft of which was

recently submitted to NASA MSFC. To avoid duplication, only

the remaining paper (number 6) is attached here. During the last six months

revisions were made in papers 2, 3 and 5. Papers 4 and 6 were written during

this period, along with additional computations and preparation of additional

figures for these papers.

RESEARCH INITIATED

Ms. Lorraine Ruggiano spent the last six months preparing for her

qualifying examination, which consisted of surveying the literature and

preparing a written research proposition, or proposal. She has chosen to

study the influence of convection on the perfection of indium gallium

antimonide. (In a Skylab experiment directed by Wilcox it was found that

processing in space causes significant differences in the resultant ingots.

Some differences were not immediately apparent and so did not appear in the

Skylab proceedings, but only later in the Materials Research Bulletin.) Note

that indium gallium antimonide is representative of the class of III-V, II-VI

and other solid solution semiconductors which are of such great importance for

infrared sensors, opto-electronics, quantum well devices, solar cells, etc.

Examples include lead tin telluride and mercury cadmium telluride. Growth on

earth with natural convection yields polycrystalline ingots with twins and

unacceptable concentration variations. The causes of the twinning and

polycrystallinity are not known. Some of the sources of concentration

variation are known, but the influence of natural convection remains somewhat

uncertain.
RESEARCH PLANS

Ms. Ruggiano will take her Ph.D. qualifying examination. She will

construct the apparatus required for her experiments. She will purchase a

rotating/pulling head, heating wires, ceramic components, silica tubing, high

purity materials, etc. Ampoules will be prepared and slowly solidified with

spin-up/spin-down (accelerated crucible rotation). The solidification will be

perturbed to reveal the solid-liquid interfac.e shape. The twin and grain

structure will be compared in ingots grown with and without stirring.

In the next six months Mr. Neugebauer will defend his M.S. thesis,

prepare his research proposition and take his Ph.D. qualifying examination.

At the moment it appears that he will propose to use a transparent organic

material to study the relationship between the temperature distribution in the

heater, the natural convection currents, and the impurity distribution in

crystals solidified from the melt. This represents an extension of his M.S.

thesis in which he showed that axisymmetric convection is very difficult to

obtain in the Bridgman-Stockbarger technique and that this convection can be

controlled by varying the vertical and azimuthal variation in heater

temperature. (It was even possible to reduce convection near the freezing

interface to near zero by increasing the heater temperature with height.)

A paper on behavior of a melt in a non-wetted ampoule (numbers 3 and 4

above) will be presented at the Metallurgical Society meeting in New Orleans

in March, at a microgravity session. Mr. Neugebauer will present an after

dinner talk on his research to a local section of the American Association for

Crystal Growth in New Jersey in March. At July's International Conference on

Crystal Growth in York, England, 3 papers will be presented: "Validity of the

Burton-Prim-Slichter Equation," "Convection in the Bridgman-Stockbarger

Technique," and "Liquid Behavior in a Non-Wetted Ampoule."
VALIDITY OF THE BURTON-PRIM-SLIGHTER EQUATION

William R. WILCOX

Department of Chemical Engineering and Center for Advanced Materials

Processing, Clarkson University, Potsdam, New York 13676, USA

ABSTRACT

The following must be assumed in order to derive the classic

Burton-Prim-Slichter equation for segregation during crystal growth: isobaric,

isothermal, isopotential or uncharged species, binary, planar interface,

steady state, constant diffusion coefficient in fluid, no diffusion in

crystal, no lateral convection within fluid film at interface with complete

mixing beyond (stagnant film model), and either density, total concentration

or partial molar volumes constant in the fluid phase. In addition, the

effective distribution coefficient and the interfacial distribution

coefficient must be defined properly. The velocity in the equation is the

growth rate times a factor correcting for the difference in volumetric

properties between crystal and fluid. The stagnant film thickness 6 is

usually a function of growth rate, with the precise functionality depending on

the type of convection occurring in the growth fluid. In general 6 varies

much more with laminar forced convection than with free convection or

turbulent forced convection. The Wilson film thickness always varies much

more strongly with growth rate than does the stagnant film thickness.

The results are also applicable to computation of growth and dissolution

rates from solutions and gases.
ORIGINAL PAGE IS

1. Introduction OF POOR QUALfTY

For many years the Burton-Prim-Slichter equation has provided the basis

for interpreting experimental segregation data and for predicting the

influence of stirring and finite freezing rate on the effective distribution

coefficient k [1]. However, many assumptions were made implicitly in its

e 11

derivation. In order to make these assumptions clear, we rederive here the

BPS equation from the most general assumption-free mass transfer equations.

In using the BPS equation it has generally been assumed that the stagnant

film thickness 8 is independent of freezing rate v . In the second part of

this paper we use results from the hydrodynamic literature to show that 8 can

be a strong function of v at even moderate freezing rates.

c

-- Derivation of BPS Equation

In order to make clear all of the assumptions involved in BPS, we start

it$ derivation with the general multicomponent diffusion equations of

Reference [2]. The notation is the same as in Reference 12], and is also

civen here at the end. The subscripts denote first the component (i for

= '•»! t icomponent, A and B for binary), and second the phase (c for cry-stal, f

JOT fluid (either liquid or gas), 0 for interfacial fluid, and <*> for bulk

-Icid far from the interface). The superscript r denotes that a standard

reference system is used, mole centered (m), mass centered (') or volume

•srtered (v). These represent the choices of average fluid velocity that may

-i used. A choice is necessary because each component moves at a different

"-locit y v. in a fluid with mass transfer taking place. The diffusion

r r r «x-£tions are written in terms of the general parameters Z., a., and Y., which

-i- take the values shown in Table 1.
ORIGINAL PAGE IS TART E ,

OF POOR QUALITY

Diffusio n Parameters in Differen t Reference Systems

Referenc e System

Mass centered

(const, o)

Mole centered

(const. C)

Volume centered

(const. V.)

(const. V.)

z

r

i

M 1

M .

1

M .

1

1

1

1

\

V .1

?

i

r

a . .

ij

p

C"M.M./ r

i J

1

C

P

2

/CM.M.

i J

1

1

c

2

v.v.

P

2 V.V./M.M .

i J 1 J

Y. Average Velocity F.Z . ('. .

W./M .

i i

X . /M . i i

C. = P./M .

X.

i

w.

1

C. = CX.

1 1

C.

1

x./v .

w./v .

1 1

v ' = IW v o i i

v

m

 = ZX.v . C i i

v

V

 = IF.v. 1 i i ,

In the absence of chemical reactions, the multicomponent mass transfer

equation is given by [2]:

_ r

V

'

J

if

(1)

The most common phenomenological expression used for the diffusion flux J"if in

an isobaric, isothermal, isopotential (or non-electrolyte) system is:

n-1

^

 = " J-l

a

r. Dr. VYr

(2)

Note that the flux of component i depends not only on its own concentration

gradient X. but on the gradients of the other constituents as well.

To derive EPS. Equation (1) must be greatly simplified via the following:

(a) Binary, with J = -ct D VY.. Not e that D is independent of

reference system, whereas D.. is not.
(b) One dimensional problem, so V = 3/3y. This is true only if the interface

is planar and if there is no convection parallel to the interface (no

stirring).

(c) D is constant, enabling us to move D.^ out of the differential.

(d) Steady state, so 9C /3t = 0.

At

(e) ZZf C and Z1. f are constant. This causes V-vf = 0, thereby eliminating

the C.-V-V* term.

Af f

Note that the conditions in (e) correspond to constant density p for the mass

centered system, constant total concentration C for the mole centered system,

and constant partial molar volumes V. and VR for the volume centered

system. A constant density is approximated by some organic mixtures and by

very dilute systems (C.«C ). Constant Cf is found for ideal gas mixtures,

while constant V. is fairly good for most liquid and gas mixtures. Thus the

Ax

volume-centered system is the one of most general applicability. However, as

pointed out later the average velocity appearing in the hydrodynamic equations

is the mass-average velocity v' .

With assumptions (a) through (e), Equation 1 becomes:

D Al _ r

_

9y2 f 3y

At this point we don't yet know what is the fluid velocity v . The condition

7«v = 0 and absence of lateral convection insure that it is constant. (If

£zffC. and zff are not both constant, vf is likewise not constant.)

Intuitively one feels that v must be related to the crystal growth rate v .

The relationship is found by a material balance at the freezing interface,

taking the interface to be fixed at y = 0 and assuming no diffusion in the

solid [2,3]:
,nN

v = v (0) = -v = -v

ZAfCAC + ZBf°BC

'f

 vivw

 cf c 7r yr

^Af^Af Bf'Bf

The negative sign comes from the fact that v. is directed out of the interface

into the fluid (positive y), while v and v are traditionally taken to be in

ci c

the opposite direction. Equation (4) gives (v ./v ) = p /p. for the

C I C C I

mass-centered system, C /C. for the mole centered system, and V.-C.- + VB,

for the volume centered system. For C..«C_, all are equivalent.

To solve Equation (3) with vf = -v . we need the boundary conditions:

at y = 0 (interface): C^ = CAQ

at y = 6r: C^ = C^

Note that this is equivalent to assuming the stagnant film model, in which it

is imagined that there is no lateral convection within a layer of thickness 6

at the freezing interface, with complete mixing beyond this giving a uniform

concentration C. . Note that the value of 6 depends on the reference system.

A

00

The solution of Equations (3) and (5) is

CAf-CAO , l-e*P(-yVcf/V (6)

To obtain the EPS equation we need a material balance for the impurity A

across the interface. Assuming no diffusion in the solid this is, at y = 0:

Af r

V

c

C

AC =

 DAB IT + CAOVcf

If we differentiate Equation (6) and substitute into Equation (7) we get the

BPS equation only if we define the distribution coefficients as follows:

. r CAC _ , r CAC

V = - ; k
The correct form of EPS is thereby:

k

r

 = _ 2 _ . (9)

ko +

Note that k is not the equilibrium distribution coefficient, but is the

interfacial distribution coefficient. While these distribution coefficients

may be identical at low freezing rates, they certainly are not equal at high

freezing rates. It is also worth noting that Eqs. (8) actually correspond to

common usage, because concentrations have been based on analyses of solids

rather than on concentrations in the liquid at the melting point. Since the

liquid has a density different from that of the solid, when one melts a solid

the impurity concentration (in atoms/volume) changes.

3. Variation of Stagnant Film Thickness

There is no such thing as a stagnant film in convective mass transfer,

even if it is erroneously called by the sophisticated sounding name ''boundary

layer.1' In actuality the lateral velocity parallel to a solid surface (such

as a freezing interface) only approaches zero as one approaches the surface.

In mass transfer problems, the fictitious film thickness 6 is defined as that

giving the correct answer. In that sense, within the validity of the other

assumptions made, the EPS equation is correct because 6 is defined as having

that value required to make it correct. In practice, therefore, 6 must be

obtained from experiments, from solutions of the real boundary-layer

equations, or solutions of the exact hydrodynamic and mass transfer

equations. It turns out that 6 is a function of DAO» ^e kinematic viscosity

v, and the freezing rate v .

In correlating segregation data, a convenient technique is to rearrange

BPS into the form:
(

1 \ / 1 \ / c cf c \

~ -

 1 }=

 \~ -

 : eXP ( D I (10)

k

r

,, / \kn / \ AB / eff / > 0 ' x '

so that one plots experimental values of ln(l/k *~~D vs. growth rate v to

e 11 c

obtain 6 from the slope and k from the intercept. However, this is an

o

accurate procedure only if 6 is not a function of v .

c

In predicting segregation from theory, values of 5 are by far most

available for v = 0. (We denote these as 8* .) But does 6=6 * =

c

constant? We can answer this for only some mass transfer situations, using

experimental data and theoretical results in the existing literature. Most of

the results are actually for heat transfer,"requiring substitution of Sherwood

number Sh for Nusselt number Nu, concentration gradient for temperature

gradient, and Schmidt number Sc for Prandtl number Pr.

The methods used to convert the literature results to a form useful and

familiar to us were outlined in Reference [4] and are based on Equations (6)

and (7). The equations used are:

Sh

Sh^ (12)

where the interfacial velocity parameter e is defined as

and

(14)
Note that for constant p, in the mass-centered system, e' = (W. -!»«)/!. -W..J

f v A<*> AO Ac AO

while for constant Cf , eTM = (X. -XAQ) / (XAc~XAO*'

 The neSative of e

v

 is the

same as A used by Wilson [5], which she equated to 6 v /D. Here we have used

W C

the subscript w to denote the Wilson film thickness. This would be the

stagnant film thickness if the concentration profile were linear in the film.

However as we see in Eq. (6), the fluid flow feeding the crystal growth would

cause the concentration profile to be exponential in a stagnant film. That

*

is, if we had a real stagnant film, 6 and 6 both would equal 6 at very low

growth rates, both only 6 would remain constant as v is increased. We now

c

see that exact theories predict that both 6 and 5 vary with v , but 6 more

* W * C W

so than 6. Thus one is most likely to obtain correct results by using 6.

Before discussing the literature results, we note that 5 is also useful

in calculating growth rates and dissolution rates for solutions and vapors.

The concentration in the equations now refers to solute concentration rather

than impurity concentration,

a. Rotating disk

Figure 1 shows results for laminar flow caused by an infinite rotating

disk. The theoretical curves are the same as those presented in 1969 [4],

For gases (Sc=l), 5 is independent of v . For liquids (high Sc), the

''exact'' results of Burton, Prim and Slichter [1], the results of the

hydrodyaamicists [5,6], and the results of Wilson [5] all agree. The others

considered an infinite body of liquid, while Wilson used an infinite

non-rotating plane parallel to the rotating disk. Consequently Wilson's 8*

values are about 15% larger than obtained by the others. That is, the

non-rotating parallel surface reduced the mass transfer. In addition, Wilson

summarized her results in a simple equation, which becomes in the present

notation:
U _ ,- , -s

-5* " 1 + 0.0699 6'v' /D,_ • ^

cr AB

Also shown on Figure 1 are data for segregation of Sb in Czochralski

growth of Ge, published as a companion article [8] to the EPS theoretical

paper. The scatter is considerable. A statistical treatment of the data

revealed the predicted dependence of 6' on rotation rate and no dependence of

5'/8* on freezing rate. That is, within experimental accuracy the data agree

with the theory.

On the other hand, the data on dissolution of EBr and sucrose in water

[9] do not agree with theory. This was attributed to variable properties. In

such concentrated solutions, viscosity, density and diffusion coefficient are

all functions of composition, while the simple theory assumes that all of

these properties are constant.

It is of interest to determine the error caused by neglecting the

freezing rate dependence of 6' in the EPS equation. From Equation (9),

% error = 100%

k

Q

+

- 1 (16)

Figure 2 shows that for typical Czochralski growth rates (6*v f/D^ ~ 1), the

error never exceeds 10*. Similarly for 0.2<. kQ the error is 10% or less at

all freezing rates. However for k 1 0.1 and moderate freezing rates the

error becomes sizeable, and increasingly so as k.. decreases. At very large

freezing rates the error again decreases. As v f increases the mass transfer

becomes increasingly determined by diffusion and by the crystallization flow,

and less and less by convective mixing; k .. -*• 1, corresponding to steady

state in the absence of mixing.
The influence of a magnetic field on segregation with a rotating disk was

calculated by Hurle and Series [10]. Figure 3 shows their results for i\ •*• 0

i i i 1/2 -1/4

converted to (6 v ./D^) vs. 9.where i\ = (v f/D) (W<o) Sc and 0 is a

magnetic interaction parameter. As expected, increasing the magnetic field

increases 6. Figure 4 shows the change of 5 with increasing growth rate vs.

magnetic field. Note that 8 becomes significantly more sensitive to growth

rate as the magnetic field increases.

Figure 5 compares the variation in Wilson film thickness with the

variation in stagnant film thickness, with and without a magnetic field. The

variation in Wilson thickness is significantly larger, especially without a

magnetic field applied. This is true for all available data for all types of

convection,

b. Forced convection

Figure 6 shows theoretical results from several authors for laminar

forced convection parallel to a flat plate [11-27]. The negative values of

* ,

6 v /D correspond to melting or dissolution, or as the hydrodynamicists

express it, blowing rather than suction. Note that for Sc=0.7 the variation

in 6 depends strongly on the boundary condition assumed at the surface of the

crystal. Unlike the results for a rotating disk, 6 varies much more for gases

than for liquids (large Sc).

Generally theorists assume constant density and viscosity in the fluid,

because this greatly simplifies their task. In practice, however, these

properties vary, sometimes considerably. Figure 7 shows the effect of a 10

fold change in density in going from the crystal surface to the bulk fluid,

for forced convection over a flat plate. For gases, a variation in density

has no effect, while for liquids the effect is large. Thus in solidification

with large segregation and large differences in density of the constituents,

one might expect significant deviations from constant density results.

10
At high fluid velocities the flow becomes turbulent. Figure 8 shows

results for air on a flat plate for v" independent of length along the

plate. Figure 9 shows results for a variety of other boundary conditions.

Note that there is considerable scatter in the experimental data. For

constant v' along the plate it would seem reasonable to take 5 as constant,

C I

while with v1, decreasing with distance down the plate 6 seems to increase

cf

with increasing 6 v' /D.

Figure 10 shows results for laminar flow around the front of a blunt

object. While 5 varies more with gases, the difference between gases and

liquids in small, particularly for growth (suction). Figure 11 shows the

correlation of numerical computations for laminar flow of gases around a

sphere with uniform v' . Note that 6 does not vary strongly and reaches a

ct

minimum at about 5 v',/D = 0.6.

cf

c. Natural convection

Now we consider convection driven by buoyancy. While the results are for

density changes caused entirely by variations in concentration, similar

results are expected for situations in which the variations in density are

driven predominantly by variations in temperature.

Figure 12 shows the theoretical results for free convection of gases on a

vertical flat plate with different boundary conditions at the crystal

surface. The wide variation in predicted behavior provides little guidance

and one may conclude that one might as well assume 6* independent of v' .

Figure 13 shows experimental and theoretical results for free convection

of liquids over a vertical flat plate. The theoretical results predict little

variation in 6* with v' , while the experimental data for dissolution

ct

(blowing) show 6 increasing as the amount of dissolution decreases. This is

the reverse trend from those for forced convection.

11
Figure 14 shows theoretical results for free convection around the

leading portion of bodies. For both gases and liquids little change in &' is

predicted for growth (suction).

Figure 15 shows that significantly different results are predicted for

liquid metals when a portion of the density change in the fluid results for

temperature variations.

NOMENCLATURE

C Total molar concentration (=EC.) (mol/m ).

i

C. Molar concentration of component i (mol/m ).

D.. Multicomponent diffusion coefficient in reference system

r (m /s).

2

D Binary diffusion coefficient (m /s).

AD

F. Volume fraction of i (=C.VJ.

i 11

r r r

J. Diffusion flux relative to r-average velocity v (= C.(v.-v ))

(mol/m •s).

K Mass transfer coefficient (= DSh/L)(m/s).

k Distribution coefficient (See Eq. 8).

L Characteristic dimension or length (m).

M. Molecular weight of i (g/mol).

*•

Pr Prandtl number (V/K).

Re Reynolds number, D^x/v .

Sc Schmidt number (v/D.R).

Sh Sherwood number (O(W -W. )/Wk. -W. ))/ 3(y/D).

A A°° AO A°>

D Free stream velocity of fluid (m/s).

12
V Partial molar volume of i (m /mol).

v Average velocity in y direction in r reference system (m/s).

v Crystal growth velocity (m/s).

c

v. Velocity in y direction of component i (m/s).

v Crystallization flow velocity in negative y direction taking

interface as fixed at y=0 (m/s). Same as V in figures.

W. Weight fraction of i in mixture.

X. Mole fraction of i.

i

x Distance along surface in flow direction (m).

Y. Composition variable (see Table 1).

y Distance from interface into fluid (m).

Z

r Weighting factor (See Table 1).

o

r. Weighting factor (See Table 1).

A 6' v' /D = -e*.

w cf v

5 Fictitious stagnant film thickness (m).

e Interfacial velocity parameter (See Eq. 13).

v

(V

ct

2

K Thermal ciffusivity (m /s).

p Viscosity (g/m s).

2

v Kinematic viscosity (= (i/p)(m /s).

to Rotation rate (s ).

9 Magnetic interaction parameter [10].

13
p Total density (g/m ).

Subscripts

A Solute in binary mixture.

B Solvent in binary.

c Crystal.

eff Effective value.

f Fluid (liquid or gas).

i Component i in multicomponent mixture.

j Component j.

0 Value at interface.

w Wilson value, based on linear concentration profile through film.

(Ref. [5]).

00 Value in bulk fluid.

Superscripts

m Mole centered (based on mole-average velocity) .

v Volume centered (based on volume-average velocity) .

' Mass centered (based on mass-centered velocity).

* Value for zero interfacial velocity (v = 0, v = 0, e = 0) .

cf c v

This work was supported by NASA via grantjNAG 8-480. I am grateful to

A

Professors Taylor and Subramanian for their encouragement.

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14
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[30]. K. Torii, N. Nishiwaki and M. Hirata. Proc. Third International Heat

Transfer Conference, The Science Press, Inc. (1966).

[31]. T. Cebeci and G. J. Mosinskis, J. Heat Transfer 93. (1971) 271.

[32]. R. J. Moffat and W. M. Kays, Int. J. Heat Mass Transfer 11. (1968) 1547.

[33]. V. M. K. Sastri and J. P. Hartnett, FC8.6 in "Heat Transfer," Vol.

III. eds. D. Grigull and E. Hahne, Elsevier, Amsterdam (1970).

[34], W. H. Thielbahr, W. M. Kays and R. J. Moffat, "The Turbulent Boundary

Layer on a Porous Plate. Experimental Heat Transfer with Uniform

Blowing and Suction, with Moderately Strong Acceleration.'' Stanford

University, Report HMT-11 (1970).

[35], W. P. Manos and D. E. Taylor, Int. Dev. Heat Transfer, ASME, NY (1963)

731.

[36], P. Chuchottaworm, A..Fujinami and K. Asano, J. Chem. Eng. Jap. 17

(1984) 1.

[37]. J. F. Clarke. J. Fluid Mech. 57. (1973) 45.

[38], W. N. Gill. E. Del Casal and D. W. Zeh, Int. J. Heat Mass Transfer 8.

(1965) 1135.

[39]. D. V. Gardner, Ph.D. Dissertation, Rice University, Houston (1963).

[40]. J. H. Merkin, Int. J. Heat Mass Transfer lj> (1972) 989.

[41]. R. Eichhorn, J. Heat Transfer 82 (1960) 260.

[42]. G. B. Lewis, J. L. Novotny and K. T. Yang, J. Heat Transfer ££ (1977)

446.

[43]. J. H. Merkin. Int. J. Heat Mass Transfer 18. (1975) 237.

[44]. W. E. Stewart, Int. J. Heat Mass Transfer 14 (1971) 1013.

[45]. D. V. Gardner and J. D. Heliums, I PEG Fund. 6. (1967) 376.

16
1.8

1.6

1.4

1.2

0.8

0.6

a

a

S*V . LV

Sh*D K*

Figure 1. Laninar convection on an infinite rotating disk. Here V = v1 is

the crystallization flow in the mass centered system. Solid

corves represent theoretical results of References [1.5-7] for

liquids (Sc _> 10) and of Reference [7] for gases (Sc = 1).

O " Experimental data of Ref. [8] on segregation of Sb in

Czochxalski gro-wth of Ge.

D- Experimental data of Ref. [9] for dissolution of KBr

in water.

A - Sucrose dissolution in water [9],
Figure 2. Error in calculating effective distribution coefficient by

assuming 81 = 8 for liquid on rotating disk. From Eq. (16) and

curve for Sc £ 10 in Figure 1.
EFFECT OF MAG. FIELD ON FILM THICKNES

O

\

hi

Q

100

90-

80-

70-

50

40

30

20-

10

0

UMTTWG DELTA V/D ETA AT SHALL ETA

246 8

THET A (MAOCTK FIELD PARAMETER)

10

Figure 3. 5 v' /Ehi vs. 9 for a rotating disk with a magnetic field applied

(calculated from [10]).
FILM THICKNESS FOR ROT.DISK w MAG.F1EL

1

UJ

o

UJ

o

0.9 -

0.8 -

0.7-

0.6 -

0.5-

0.4-

0.3-

0.2

4 6

DELTA * V/ D

8

Figure 4. 6/6* vs. 5% /D with a magnetic field applied of interaction

strength 3 (calculated from [10]).
*

<

u

a

LJ

o

TRUE THICKNESS VS. WILSON THICKNESS

ROTATING DISK W/WO MAG. FIELD

ORIGINAL PAGE IS

POOR QUALfTY

+ WILSON, THETA-0

0 -

6

DELTA * V/ D

o SF, THETA-10

8

WILSON,

• * 1* 1

Figure 5. 5/6 and 6^/6^/vcf/D for a rotating disk (calculated from Eq. (15)

without a magnetic field and from ref. [10] with a magnetic

field).

O ~ Stagnant film with no magnetic field.

^> - Stagnant film with magnetic field, 9=10.

4" - Wilson film with no magnetic field.

A - Wilson film with magnetic field, 8=10.
1.8

1.6

1.4

1.2

_8_,

8*

0.8

0.6

-5 -4 -3 -2 0 I 2

8*V LV V

D

 = Sh'D = ~K*~

Figure 6. Theoretical results for laminar forced convection over a flat

plate.

Constant concentration in crystal and in fluid at surface of

flat plate, independent of distance z; v' a 1//I.

Values for Sc » 1 from references [11-16], for Sc - 15 from

[17], 10 from [18], 2 from [12,19,20], 1 from [11,14,16-19,

21-25], 0.7 from [18,20,25-27], and Sc = 0.6 from

[12,19,201.

Concentration in crystal varying with /x, v" with l//z. and

constant product of v' and concentration in crystal.

For Sc = 0.7 [27],

Constant v' with Sc = 0.7 [26,27].
1.6

1.4

1.2

0.8

0.6

-3 -2 -I 0

LV

D Sh* D K'

Figure 7. Laminar forced convection over a flat plate with variable density

[16].
1.6

1.4

1.2

0.8

0.6

cP

-6 -5 -4 -3

K*

Figure 8. Tnrbnlent flow of air over a flat plate with constant v'cf.

Theoretical treatments

X - Ref. [28]

ol - Ref. [29]

oP - Ref. [30]

oZ - Ref. [31]

O - Experiments [32]

• - Experiments [19],
ORIGINAL PAGE «S

OF POOR QUALITY

1.6

1-4

1.2

0.8

0.6

~4

o

o

o

o

8

-3 -2

S*V LV

Sh*D

V

K*

Theoretical treetrert s for nc growth fcr initial cistare e

x , with free stream velocity independent of x [33],

o

a - x/x = 1.15, Re = 10.4 x 105

o

b - x/x = 1.77, Re = 7 x 10'

o

0.2

- Experimental for v' a 1/x, U a 1/x * , C. constant [34]

cf AO

O ~ Experimental for v . constant after laminar region, with

cf

v a 1/x , C.n approximately constant, U^ constant [19]

CI AU

X - Experimental for v , constant after laminar region with

cf

v a II x [19].
Figure 10. Laminar forced convection at stagnation point. Sc = 10 results

from reference [18], Sc = 1 from [18,21,22,25], and Sc = 0.71 from

[18.25,35].
*

<

o

\

<

H

_l

UJ

Q

1.08

SPHERE WITH FORCED CONVECTION

J.CH.E.JAP. 17(1984)1

1.07 -

1.06 -

1.05 -

1.04-

1.03 -

1.02 -

1.01 -

1.00 -

0.99

-2.0 •1.0

DELT A

0.0

V / D

1.0

Figure 11. Laminar forced convection around sphere with uniform snction or

blowing, for Re = 5 to 150 and Sc = 0.5 to 2 [36],
1.4

1.3

1.2

I.I

8*

0.9

U

.W

W

0.8

-5 -4 -3 -2 0

S*V LV

D

 = Sh*D K*

Figure 12. Theoretical resnlts for free convection on a vertical flat plate.

, , 0.25

Sc = 1. C... constant, YC{. a 1/x

I - Ref. [37]; D - Ref. [21]; 3 - Ref. [11];

Q - Ref. [38]; 5 - Ref. [39].

Sc = 1, v' constant; J - Ref. [40],

cf

. . 0.25

•••• Sc = 0.71, C constant. V . a 1/x ;

W - Ref. [41]; Q - Ref. [38].
0.9

o o

x*• > • # • * * « 5 "^..a

0.8

0.7

0

0

0.6

o°

 Oo

1 1

-7 -6 -5 -4 -3 -2 -I 0

8S/_ LV . V

D " Sh*D " K*

Figure 13. Free convection of liquids on a vertical flat plate.

Theory for Sc » 1 with C . constant, v' o l/i

0.25

AO cf

Theory for Sc = 10 with C constant, v' a 1/x

0.25

AO

[11].

[21]

•• • Theory for Sc = 5 [39].

O Experiments for Sc about 610 with v , constant [42]. ^*** ci
.4

.3

.2

8*

0.9

\

\

\

\

\

\

-5-4-3- 2

S'V

D

0

LV

Sh*D

234 5

V

K*

Figure 14. Theoretical results for free convection on the leading portion of

a body.

F Sc above about 2000 for three-dimensional flow

without separation [43].

E Sc = 1. forward part of horizontal cylinder [44].
Gr =IOG r

mass heat

Figure 15. Theoretical results for free convection on a vertical flat plate

with Pr = 0.2 and Sc = 5 [39,45]. Gr /Gr, . equals the ratio

mass heat

of density change caused by the concentration difference to that

caused by the temperature variation in the fluid.
CLARKSOH UNIVERSITY

Department of Chemical Engineering

THE EFFECT OF SPIN-UP/SPIN-DOWN ON TOINNING IN In Ga, Sb

2k X ^ A

A Doctoral

Research Proposal

by

L. Ruggiano

March , 1986
TABLE OF CONTENTS

Chapter Title Page

1. Introduction 1

2. Literature Review 10

3. Experimental Procedure 31

References 34
CHAPTER 1

Introduction

I. .III-V Compounds

III V Solid solutions of A 3 semiconducting systems are important

for many electronic devices. They offer advantages of

composition-dependent band structures and properties different from

simple binary compounds. By varying cotr.postion, these properties can

be altered to suit different purposes. Because of its band

structure, In Ga. _ Sb is promising for optoelectronic instruments

jC X *TMX

such as photodetectors, light-emitting diodes and lasers (1,2,3).

Optimum device characteristics occur at a composition of about 80%

GaSb. However, in this composition range, In Ga1 Sb does not meet

x i *~x

the electrical property requirements. The material is p-type with a

high acceptor concentration whereas a low concentration (less than

15 3

10 electrons/cm ) n-type material with a high electron mobility is

required (1,2,3).

For these applications, damage and inhomogeneity fr.ee crystals

of high quality with low dislocation densities are required. Many

different methods of growing these crystals in bulk have been

published, but the end products were usually polycrystalline and/or

compositionally inhomogeneous. Consequently, for the most part, bulk

growth III-V alloys have been limited to scientific investigations.

Extensive segregation occurs when bulk alloy melts are solidified,

resulting in very inhoniogeneous solids which are not suitable for any
devices

A review of the pertinent literature exhibits the difficulties

that previous experimenters have found in growing bulk crystals of

In__Ga1 _Sb by taany different crystallization techniques. These will

*C i. 1C

be discussed in more detail later. Although films of this and other

alloys have been produced by liquid phase epitaxy and chemical vapor

deposition, bulk crystals are important because of their application

as substrates for film growth and the need of bulk material for

fabrication of many devices.

II. Obi ectives

The objective of the present investigation is to grow bulk

single crystals of In Ga1_ Sb and to learn about the processes

X i^X

causing polycrystallinity and the influence of operating variables on

grain and twin generation and propagation. Twinning often occurs

during crystal growth from vapor, melt and solution. In this

research we are only concerned with growth from the taelt. Many

factors play a role in twin formation. The most extensively studied

is mechanical stress. Twin formation and movement is a mechanism for

plastic deformation in some materials. The other factors that may

cause twin formation have not been thoroughly studied. Some of these

that I propose to investigate are:

(a.) growth rate.

(b.) thermal stress.

(c.) feed composition.

(d.) foreign particles.
(e.) soluble impurities.

(f. ) interface breakdown due to constitutional supercooling.

The crystals will be grown by the vertical B rid smart-Stockbarger

technique with and without spin-up/spin-down applied to the ampoule.

III. Constitutional Supercooling

The primary difficulty in producing homogeneous single crystals

of mixed III-V compounds from the melt can be seen upon examination

of a typical temperature-composition phase diagram (Figure 1). If

the lower melting component (InSb) is designated as the solute, its

distribution coefficient is always less than unity and this component

will be concentrated in the last segment to freeze. The melt

adjacent to the interface becomes enriched in InSb. This extensive

segregation generally leads to an inhomogeneous solid and can result

in constitutional supercooling and interface breakdown.

Tiller at al. (5) first formulated the idea of constitutional

supercooling to explain the breakdown of a planar interface to that

of a cellular interface during alloy solidification. Only the

concepts and results are presented here. For a more in-depth

discussion of this topic the reader is referred to the original

paper. A much more rigorous theory of stability criterion for the

planar to cellular interface transition has been developed by Mullins

and Sekerka (6), but physical insight can still be obtained from the

classical concepts of constitutional supercooling.
700k

u

o

600h

500

Figure 1: The InGa-GaSb psueciobinary phase diagrav. (37)

is mole fraction of GaSb.
Consider a melt of binary alloy of composition x . It is

undergoing directional solidification at a constant freezing rate V

under an imposed temperature gradient G = dt/dx. The solid is

composed of more of the higher melting component (e.g. GaSb) than the

liquid from which it solidifies. Consequently the higher melting

component becomes depleted in the liquid adjacent to the solid/liquid

interface. There will then exist a melting point gradient in the

melt since the melting point T is composition dependent. When

in

conditions of low temperature gradient and/or high freezing rate are

imposed, the melting point can actually exceed the imposed

temperature in melt adjacent to the interface. This can be seen in

Figure 2. The region of constitutionally supercooled liquid is the

shaded area between the imposed temperature T and the equilibrium

melting temperature T . The condition for the occurrence of

constitutional supercooling is given mathematically by:

G/V > (x - x.) (m C /DC,) . (1)

s i s 1

where

x = composition of solid in mole fraction

s

x. = composition of liquid in mole fraction

m = slope of liquidus at the interfacial liquid composition x.

C = Total molar concentration of the crystal

C. = total molar concentration of the melt

D = Binary diffusion coefficient

From equation (1) it is seen that avoidance of constitutional

supercooling can be attained by maintaining a high interfacial melt
LJ

o:

<r

UJ

CL

2

LJ

X= 0

DISTANCE (x)

(b)

Figure 2: Constitutional Supercooling - The shaded region

between the equilibrium melting temperature T ,

m

and the imposed temperature T, represents

the region of constitutionally supercooled

liauid.
temperature gradient G and low growth rate V.

Constitutional supercooling is responsible for the transition of

planar solid/liquid interfaces to cellular and eventually dendritic

interfaces. Under cellular interfacial conditions less solute is

swept along with the moving interface than under planar interfacial

conditions. Instead, much of the solute laterally segregates into

cell boundaries. Dendritic interfacial conditions produce trapping,

v?ith most of the solute incorporated in the interdendritic regions.

As can be deduced from the above discussion, interface breakdown has

a very detrimental effect on crystal homogeneity and perfection. It

leads to crystal defects such as inclusions, dislocations and

possibly twins.

Free convection is a result of density variations arising from

compositional and/or temperature variations in a gravitational or

acceleration field. Uniform and time independent (steady state)

flows can be useful since they decrease the buildup of compositional

variations at the interface due to segregation, causing the growth to

be less sensitive to small fluctuations in growth rate. However,

time-dependent (transient, oscillatory and turbulent) flows are

undesireable, because they generate variations in local temperature

and flow velocity, resulting in growth rate variations and

fluctuations in mass transfer causing the growing crystal to develop

inhomogeneous compositional distributions and compositional

striations parallel to the growth interface. Transients such as

temperature fluctuations due to convection cause nucleation of twins

and grains before interface breakdown has time to occur. If growth
conditions are such that the interface is near constitutional

supercooling, then a momentary drop in temperature could cause a

supercooled region in front of the interface and perhaps cause

nucleation. Close to constitutional supercooling a sudden

temperature drop can cause lattice mismatch by attachment of ordered

groups of atoms in the melt adjacent to interface. A twin

configuration is more likely for small perturbations, because it

requires very little energy compared with grain boundary formation.

For the InSb-GaSb system Sen (7,0) plotted the critical G/V

ratio versus the mole fraction of GaSb in the melt. For this purpose

the binary diffusion coefficient B was assumed to be equal to 2 x

-5 2 10 cm /sec. It can be observed from Figure 3 that a very large

region of instability is encountered, resulting in a very small range

of experimental conditions that will avoid constitutional

supercooling. Sen (6) found that a temperature gradient greater than

40 C/cm produced thermal stresses in the In_Ga1 Sb ingots that

*"fc JL'" A

resulted in microcracks and other defects. On the other hand, smooth

translation rates can be difficult to achieve experimentally when the

rates are very low. This is due to the mechanical nature of such

apparatus.
2000

i i t i i

0 0,2 0.4 0.6 0.8 1.0

MOLE FRACTION GaSb IN MELT

Figure 3: Critical G/V for constitutional supercooling in

In__Ga1 ..Sb calculated from equation (1) ascmai

~"
CHAPTER 2.

Literature Review

I.Twinning

Two joined single crystals are twins when the crytallographic

orientation between them corresponds to low Miller indices and this

orientation occurs frequently in growth or plastic deformation of the

material. They require very little energy of formation and so are

generally not considered grain boundaries, but a kind of crystal

defect. Crystallographers believe that twin formation takes place

when a crystal is unable to make an energetic distinction between the

twinned and the untwinned extension. It is thought that twins occur

randomly when the twin plane has a low energy (9). Twinning is not a

random accidental phenomenon. Some materials frequently twin under

particular conditions and not at all under other conditions. Twin

planes are frequently utilized to obtain rapid crystal growth rates

along a crystallographic direction parallel to the growth plane.

They are one of the most common defects that occur during crystal

growth, but their origin is not well understood. Twinning is a

serious problem with the melt growth of group IV, III-V and II-VI

alloy semiconductors. Compounds with the zinc-blende structure, such

o

as In Ga1 Sb, exhibit twinning with a geometry corresponding to 180

2C X "^X

rotation about the (111) twin plane.

The definition of a twin can be quite ambiguous, because there

are so many different types. Friedel (10) said a twin may be defined

10
as a polycrystalline edifice, built up of two or more homogeneous

portions of the sama crystal species in juxtaposition, and oriented

with respect to each other according to xjell defined laws. Here

homogeneous means that each portion can be referred to a single

continuous lattice and that the constituent atoms are everywhere

related in the same way to their nearest lattice points, i.e., each

portion is a single crystal (11). Juxtaposition implies that the

parts are in such intimate contact with each other over part of their

boundary surfaces that they cohere, this cohesion being often, though

not always, as strong as the internal cohesion of a single crystal

(11). The requirement that the orientations be related according to

well-defined laws is the most ambiguous part of the definition and

has frequently given rise to dissension as to whether a particular

specimen should be considered twinned. The components of a twin are

£"•-.; : rtly related to one another in one of ths '" "'.'-.- •'. '-'-'. •

1.) ]jy ro:;^.-. ;•: . . " ;. ne which is common to

both parts.

2.) By rotation of one part by ISO about an axis common to both

parts.

3.) By both of the above operations taking place

siniulataneously.

The plane normal to the axis of rotation or the plane across

which reflection is imagined to have taken place is called the

twinning plane and the axis as the twinning axis. The composition

plane is the common plane of contact between two individuals of a

twinned crystal. Optical examinations have revealed, however, that a

true plane of contact does not exist in the case of interpenetrant

11
twins. The composition plane is often the same as the twinning

plane, but not always. I-.'hen not coincident, they are often at right

angles to each other. Figures 4.1 to 4.6 show typical twinned

crystals. Contact twins are joined at a face with atoms conuion to

both parts (Figures 4.1 to 4.4). Interpenetration twins are shown in

Figures 4.5 and 4.6. In this type the interface follows a number of

different planes or may be quite irregular. The individual parts of

interpenetration twinned crystals follow the same rules as for

contact twins. They also have a common axis of rotation or common

reflection plane existing as in the case of contact twins. Lamellar

twinning is said to occur if individuals related in this way occur

alternately. The twinned crystals of Figures 4.1 and 4.3 are as if

one part of the crystal has been rotated 180 with respect to the

other about an axis normal to the twinning plane. One part is the

mirror image of the other about the twinning plane. In these two

crystals the twinning plane and the twinning axis bear the same

relation to the two parts of the twins. Figure 4.4 depicts a twinned

crystal with composition plane parallel to (010), but the disposition

of the parts can be only described by supposing the twinning .axis to

be either normal to (100) or parallel to their vertical axis.

Therefore the twinning plane is (100) whereas the composition plane

is (010), which is perpendicular to the twinning plane.

12
V

- -t

of T\;ins (16)

A.I Spinel twins with (111) twinning plane.

4.2 Hexagonal prism twinned on a pyramid face.

4.3 Arrowhead twin of gypsum.

4.4 Orthoclase twin (monoclinic) .

4.5 Flourite interpcnetration twin.

4.6 Interpenetration twin of potassiur. sulphate.

each one comprising opposite sej-nents.

Three individuals

13
Sometimes more than two individuals are twinned together. In

this case, when the twinning plane is parallel to a pinacoid, every

alternate member of the series is similarly oriented. Uhereas when

the twinning plane is inclined, as is the case of a prism or pyramid

face, a cyclic grouping results. Twinning involving more than too

individuals is known as multiple or inimeiaic twinning. If this kind

of twinning is repeated several times, so that each part is of

microscopic thickness, then the outer surface of such a crystal

appears to be striated. This is known as polysynthetic twinning.

Twin formation takes place either when the material is

mechanically stressed (by applying a load on it) or during its growth

from solution, melt or vapor. Mechanical twins are formed when the

stress causes the crystal to dislocate through a distance which is

not a multiple of the unit cell dimension (i.e., via a partial

dislocation). In this work we are only interested in growth twins.

There are too views on the origin of growth twins (11):

(1.) Growth accidents at the interface, because of high growth

rates (13), impurities (14, 15) and interfacial perturbations leading

to dislocations acting as sites for twin formation. The implication

here is that twinning might occur directly as the crystal grows from

the melt, i.e., during deposition of individual atomic layers.

Twinning in the diamond or zinc-blend crystal structure is always

observed with one of the {111} family of lattice planes acting as a

twin plane (111). In the diamond lattice there are four types of

such octahedral planes belonging to the same family inclined at

14
70°32' to each other. Twinning about a '(111) plane is a simple

stacking fault. It gives a perfect fit of the lattices on either

side. Therefore it leaves all distances between nearest neighbors

and all bond angles undisturbed. Consequently, very little energy is

required, only that due to interaction between second nearest

neighbors, to initiate such twinning. Therefore a single crystal

growing with a certain crystallographic orientation can readily swing

over to one of four other orientations by this mechanism.

Temperature fluctuations in the melt may be sufficient to initiate

such twinning.

Quite often the consequence of twinning on the growth mechanism

and kinetics can be explained by the reentrant corner effect. The

concept is based on the premise that a pair of twins form a reentrant

corner at the growth interface which acts as a favorable nucleation

site for new steps. The reason for the formation of favorable

nucleation sites at the reentrant corner has been explained by Sen

(16) in the following way. The twins considered are depicted in

Figure 5. These twins come into contact at corner A. If a growth

layer is started on face B or C due possibly to a screw dislocation

or to two dimensional nucleation, then the growth layer spreads on

surface B. This growth layer will then reach corner A where it acts

as a nucleation site for atoms on surface C. Growth proceeds on

surface C once a layer of atoms nucleates at corner A. Because the

twins are at an angle to each other, the growth layers on surface B

and C do not match, leaving a ledge at position A. This ledge (step)

now provides nucleation sites for growth on surface B. Similarly the

15
Figure 5: Reentrant corner effect. The twins form an open

figure v;ith faces B and C. Face C provides a

source of steps for B and vice versa. The

numbers denote the sequence of-layer formation

(16).
growth layer on surface B forms a ledge at A which provides favorable

nucleation sites for growth on surface C. Growth then proceeds in

this fashion with the help of ledges and corner A. Uagner and Brown

(17) postulated the conditions for crystal growth using the twin

plane reentrant corner effect:

(a.) Growth form of the material should be faceted.

(b.) Twin boundaries should be present, caused by a fault

in the layer sequence during growth by plastic deformation or by an

accidental meeting of crystals at the twin angle.

(c.) Twins should form a reentrant step where the twin

boundary terminates at the faceted growth interface.

It is also thought that twins might be caused by local

disturbances such as the presence of foreign particles. Such

particles may appea: £nywhere on the growing front and a twin can

thus start within an ingot (15). On earth the particles with a

density higher than the melt will tend to settle down near the

solid/liquid interface due to gravity. If convection is present

particles will move along the connective flow path and bounce

repeatedly on the solid/liquid interface. Twins might be generated

when they come in contact with the interface. When the convection is

suppressed, as by the imposition of a magnetic field, the particle

motion is suppressed inside the melt. Due to gravity they will tend

to settle down at the interface. Therefore it would be expected that

under gravity conditions the twins would all emerge at the beginning

of growth and then their number would gradually decrease as

solidification progresses. In the Skylab (19.20,21) grown samples of

17
In Ga, Sb there was a 70% reduction of straight twin boundaries as

:c 1-s

compared to earth grown samples. Due to the lack of gravity any

particles present inside the melt in the Skylab would have remained

dispersed in the melt and would have contacted the surface only when

the interface reached them, preventing the particles from settling on

the interface unless surface driven convection was significant.

(2.) The second view proposes that growth twins are sometimes or

even always of mechanical origin (18) . Thermal stresses in

solidified crystals that are near the melting point can cause crystal

defects. Ge and Si (15), which are known to plastically deform, are

thought to fault during constrained growth (growth in a crucible) .

The twins Sen (7) saw in grown ingots of In Ga, Sb were believed to

X J. "X

have been generated after solidification when the solid was still hot

and capable of plastic deformation due to the thermal stresses

internally and within the crucible. More; twins were formed when a

magnetic field was not applied or partially applied compared to

ingots where the field was applied for the entire growth period.

Since the magnetic field did not completely suppress formation of

twins, both factors (free convection and thermal stress) were

probably responsible for the generation of twins.

II. Literatur ^_^«B_^_^^W«_B__^B«^_^^»^Bi^B«_«^ e Review On» I Xn Ga .L^J 1_,Sk b

Sen (7,8,21,23) produced bulk ingots of In Ga., Sb by the

X 1"~X

vertical Bridgman-Stockbarger technique. Ampoule travel rates were

4.0 and 8.0 mm/day. Electron inicroprobe analysis performed on the

grown ingots showed no significant radial composition gradients. The

18
average number of grain boundaries increased approximately 30% when

the mole fraction of InSb in the feed was increased from 0.1 to 0.5.

Sen explains this as an increase in the segregation of solute which

causes the development of a solute rich layer adjacent to the

solid/liquid interface. As can be seen from the temperature -

composition phase diagram of Figure 1, a decrease in the melting

point is associated with an increase in the concentration of InSb.

This causes an acceleration in growth and more rapid nucleation. The

average number of twin boundaries was found to be less composition

dependent. Lower G/V ratios produced more twins and grain boundaries

than higher. Increasing the temperature gradient to 40 - 50 C/cm

did not yield single crystals. This increase resulted in a fine

grain structure due to increased thermal stress with cracking and

dislocations, perhaps leading to new grains and twins. Increasing

the temperature gradient probably also generated irregular turbulent

convection in the melt giving rise to larger growth rate

fluctuations.

The total number of twins and grains were much less in the case

of an applied magnetic field of 2 KG than otherwise, and when twins

were generated it was to a much lesser extent in the presence of a .

field. The magnetic field reduced formation of twins probably by

inhibiting convection and therefore reducing temperature fluctuations

in the melt. The magnetic field did not completely inhibit the

formation of grain and twin boundaries indicating that their

formation was also caused by compositional or thermal stresses.

19
Sen also found that when twins nucleated, sometimes new grains

were seen shortly thereafter, but in smaller quantities. Twins grew

out quickly, because they are geometry dominated rather than

interface (shape or position) dominated. Grains grew out slowly

suggesting an only.slightly favorable curvature of the interface.

Annealing (23) of the grown ingots at a temperature of 500 C

(80% of the melting point) with a load of 66 grams (0.45 x 10

2

dynes/cm ) on top of the ingots for a period of ten days resulted in

a 40 to 80% decrease in the number of curved boundaries and a 30 to

60% increase in the number of straight twin boundaries for all feed

compositions of alloy. No apparent changes in grain structure were

observed when annealed with no load and the only single crystal grown

during this research showed no change even with load. The reduction

of the number of grain boundaries can be the result of grain boundary

movement at high temperatures and under plastic deformation or grain

growth. There could be some annealing twins also generated,

associated with grain growth under stress. Results of annealing

experiments suggest that the generation of twins during growth

occurred immediately after solidification when the solid was still

hot and plastic. Since it is known that the shear stress required

for twinning at high temperature is very low, the mechanical stress

arising from solidification in a crucible might be sufficient to

generate the observed twins' (23) .

Sen (7) also grew In Ga- Sb by the Gradient Freeze Method (7).

3C L"~X

Grain selection was poor and many more twins were generated in this

method than by the vertical Bridgman-Stockbarger technique.

20
Therefore no quantitative studies were made. The composition of the

grown ingots was fairly homogeneous both radially and axially up to a

point where compositional fluctuations started to develop. This is

because as the interface advanced upwards the effect of the cooler

was less and less felt, thereby reducing the temperature gradient at

the solid/liquid interface, favoring constitutional supercooling.

In order to provide information regarding the theory that free

convection induced compositional fluctuations cause grain generation

directional solidification of In Ga. Sb alloys in a "gravity-free"

X J.—X

environment was undertaken. Three different compositions (x = 0.5,

0.7 and 0.9) of the alloy were directionally solidified by the

Gradient Freeze technique in Skylab missions SL3 and SL4 and for

comparison on earth in horizontal and vertical orientations (19-22).

-4

The average acceleration was about 10 of the earth1s gravity g ,

-3

with occasional fluctuations as high as 10 , which should have been

sufficiently low that free convection was negligible. The objective

was to see if space processing (where natural convection due to

gravity is practically zero) offers any advantages for single crystal

growth of concentrated alloys by melt techniques.

Microstructures of space-processed ingots were superior to those

of vertically and horizontally earth-processed ingots with the

vertically processed being slightly better than the horizontally

processed. Straight twin boundaries were 70% less in the six Skylab

ingots than in the six earth processed ones. The number of grain

boundaries and irregular twin boundaries (exclusive of straight twin

21
boundaries) were approximately 13% less in the Skylab ingots. On

earth, new grains and twins nucleated during growth while in space

almost all grains and twins propagated from the unmelted portion of

the extremely dendritic feed rod. The x-ray 'and electron diffraction

studies revealed that the twin planes were {111} and preferred

orientations xjere <211>, <110>, and <321> (in decreasing order of

frequency). This and twinning in dendrites in the initial cast

material led Sarma to believe that the growth mechanism in this case

may be similar to that of dendritic growth in Ge, Si and InSb (15).

This is a self perpetuating reentrant angle associated with multiple

twinning. In the slowly refrozen regions of the space processed

ingots, the twin boundaries appeared to jog sideways in an attempt to

realign themselves perpendicular to the solid/liquid interface. The

curvature of these twin boundaries suggests energy minimization by

alignment perpendicular to the solid/liquid interface during

solidification in a manner commonly observed for grain boundaries.

On earth, the number of twins initially increased and then decreased

with time. On earth and in space, twinning decreased as the feed

composition of InSb increased (19,20,21,22).

Joullie (2) prepared bulk ingots of In Ga,_ Sb alloys by the

vertical Bridgman-Stockbarger technique. Ampoule travel rates were

1, 0.45 and 0.25 mm/hr. At Imm/hr a second phase arises, generally in

the form of inclusions in the nearly homogeneous matrix. At the two

lower rates, the ingots grown are of one phase which provide radially

homogeneous samples. Uoolley et al. (24) produced solid solutions of

various compositions of InSb-GaSb. The resulting crystals were

inhoraogeneous and polycrystalline. The authors attributed this to

22
the effects of constitutional supercooling. Coderre and Woolley (25)

produced ingots of InSb-GaSb by the vertical Bridgman-Stockbarger

technique. Due to constitutional supercooling the ingots were

polycrystalline, but homogeneous in cross-section at all points.

III. General Literature Review

Skylab 3 and 4 missions also included the growth of undoped,

tellurium and tin-doped InSb in the "Multipurpose Furnace" on earth

and in space (12,26). The Te-doped space-grown crystals will be now

described. The surface of the regrown crystals in the vicinity of

the seed exhibited several bands of differing width oriented normal

to growth direction. These were identified as external boundaries of

(211) rotational twins which are frequently encountered in InSb grown

in the <111> direction. Each band is the result of two consecutive

rotations by 60 of the (111) plane normal to the growth direction.

Etched segments of (211) surface orientation show that some twins

propagated across the entire crystal and some terminated in the

crystal and others deteriorated to grain boundaries. Because of a

concave interface, nucleation during growth was essentially

restricted to the outermost peripheral part of the growth interface.

Rotational twin formation initiated by a nucleus having a 60

misorientation was explained as a result of inisoriented nucleation at

the crystal periphery. Crystals grown in space exhibited a

dislocation density 40% smaller than those in the earth-grown

segment. It was concluded that steady-state segregation and

homogeneous dopant distribution was achieved under zero gravity

conditions. In ground-based identical experiments the dopant profile

23
indicated a steadily increasing dopant concentration which reflects

the presence of slow convection caused by unavoidable lateral thermal

gradients (12,26).

Walter (27) describes the defect properties of InSb single

crystals prepared by a containerless technique on Skylab. Defect

properties of space-grown crystals were compared with

Czochralski-grown crystals that were used as seeds. Undoped and

selenium-doped crystals of InSb were grown in this study. In Skylab,

Czochralski grown crystals were partially backmelted in a gradient

furnace so that large drops of uncontained melt were formed at the

end of the seed crystals. These drops were directionally solidified

during controlled cool-down of the furnace after a one hour soak

period.

2 3 3

Walter's (27) earth-grown InSb exhibited 10 -10 /::.. ..creign

particle inclusions. The larger " •':...•.-•.::••. '. •.••.-. £ r;era frequou"../

.,;,. . ••';••;•• : </.t.:ns and served as nucleation sites for grains and

twins. The dislocations in the Czochralski-grown crystals were

randomly oriented and curvilinear. The InSb crystals grown in space

were very different. Walter (27) describes them as remarkably

homogeneous. The density of inclusions was greatly reduced,

presumably because foreign particles accumulated during soak at the

remelt boundary and at the melt surface. Dislocations originating

from particles at the seed boundary were thought to be the cause of a

sudden increase of dislocation density in the first part of regrown

material. Rectilinear dislocations (pure edge and 60 type) were

observed exclusively in the bulk of the space-grown crystals. Since

24
larger inclusions were absent, few defects vjere generated and the

density of dislocations decreased along the axis of the samples due

to the outgrowing of rectilinear dislocations that were inclined to

the growth a::is. Increasing radial thermal gradients v;ere thought to

have caused the increase of dislocation density in the crystal

section solidified last. (Generation and multiplication of

dislocations due to radial thermal gradients becomes appreciable at

gradients of about 10-15°C/cra (27)).

Te-doped and undoped InSb crystals were grown by the Czochralski

method on earth (28) . These crjrstals were renelted in space on board

the Salyut-6 using the multipurpose apparatus Crystal. Part of the

sample remained unmelted and served as a seed. In this way

directional solidification of the melt was maintained. The

structural perfection of the crystals grown in space was

substantially superior to that of crystals grown on earth. The

experimenters failed to obtain Te-doped InSb single crystals on

earth. Generally all ingots had the structure of small blocks.

These blocks did not retain the growth direction and on their crystal

boundaries were often observed accoraodation bands suggesting high

stresses had been near the boundaries. Typical defects included

shallow etch pits, dislocation nets decorated by impurity,

microtwins, and large inclusions at the seed part of the crystals.

fi 9

Dislocation densities of these crystals were greater than 10 /cm .

The crystals grown in space had large single blocks stretched along

the growth direction given by the seed with a <211> orientation.

Conjugation boundaries of the blocks were usually twin boundaries.

The absence of dislocation arrays near the conjugation boundaries

25
indicated that they were coherent, i.e., during its growth the

crystal didn't experience themoeiastic stresses. The dislocation

5 2 densities did not exceed 2 :: 10 /cm and some blocks had densities as.

3 2 low as 10 /cm . Large inclusions were not found.

For the undoped InSb crystals grown on earth and in space, the

following characteristics were observed. The earth-grown undoped

InSb crystals exhibited a dislocation' density greater than 5 x

3 2

10 /cni near the seed end of the crystal. With crystal growth the

dislocation density increased by too or more orders of magnitude and

a cell dislocation structure was generated. TV/in lamellae stretched

along the ingot growth direction as well as accomodation bands. The

dislocation density in the undoped crystal investigated both in the

1 2

seed and the space-recrystallized regions was 2.5 x 10 /cm . This

was considered to be an essentially dislocation-free crystal. This

density remained constant along the length of the whole ingot.

Unfortunately, growth conditions were such that a great number of

growth twins were generated. The twinning occurred along the (111)

plane at an angle of 71 to the <211> growth axis and it began at 2.5

mm from the seeding boundary. At the seed end of the ingot the

distance between the twins was 2 mm, but as the ingot grew it reduced

to 0.2 mm. Dislocation arrays were absent near the twins, thus it

was concluded that coherent twinning took place. Kashimov (28)

stated that the generation of twins is known to be connected with

preliminary atom association, the extent of melt supercooling and the

extent of chemical content deviation from stoichiometry. He

attributed twin formation in this study to high supercooling and

deviations from stoichiometry. The deviations from stoichiometry
were evident from the taonotonic increase in the lattice parameter

from the beginning to- the end of the recrystallized region

(28,29,30).

According to Antonov et al (31) , the twin boundary energy in

InSb is one-half the stacking fault energy. They propose that twins

form mechanically as a stress relief during crystal growth or also

that they form at the crystallization front by atomic packing

errors. Statistical analyses were performed on the number of twins

formed in zone raelting and Czochralski growth. From this information

the authors suggested that twin formation was probably due to packing

fault errors. They also found that the frequency of twinning

increased sharply with increases in supercooling, presumably caused

by increasing growth rates. Again, these conclusions are premature.

The cause and effect relationships of these situations have not been

fully explored.

Many different methods of growing GaSb have been attempted, but

the crystals usually contained macro- and niicrodef ects such as twins

and niacrofacets (32, 33). A high quality GaSb bicrystal was grown in

a Bridgman type.apparatus under raicrogravity conditions on board of

Salyut-6 (34,35). The space grown crystal exhibited good surface

quality. There were ridges on the surface similar to those found in

InSb during the Skylab program (12). The majority of these ridges

were oriented. Part of them encompassed the ingot perpendicular to

the growth direction and others made zigzags in different places,

o

oranching at angles which were odd multiples of 15 . Several

intergrowths of twin crystals were noted. Growth began on several

27
seed crystals and then decreased to two. Because interaction of the

solidified material with the ampoule wall apparently was at a

minimum, heat removal was thought to have occurred primarily along

the axis. The authors believed that this condition led to a uniform

defect distribution.

The earth-grown sample grown under the same conditions contained

many more fine grained crystallites than the space sample. The

extensive formation of crystallites and twins on the ingot periphery

was attributed to the deforming effect of the ampoule. This effect

was observed along the entire length of the ingot. In moving from

the ingot surface to the middle, the dislocation density and the

number of large angle grain boundarii increased.

Sen (16) performed an investigation of the effect of different

paramaters on twin formation in dodecanedicarboxylic acid (DBA)

during directional solidification in thin cells. Foreign particles

increased twinning when the difference in the coefficient of thermal

expansion was large. The number of twin boundaries increased

slightly with growth rate, but decreased drastically with temperature

gradient. Twin boundaries started at polycrystals formed at the

growth interface and terminated upon meeting another twin or grain

boundary. Zone refining significantly reduced twin formation.

However, twin formation was restarted in zone refined DBA by adding

soluble impurities with similar molecular structure and size.

23
IV. Spin-Up/Spin-Down

Spin-up/spin-down is the process of adjustment of an initially

uniformly-rotating fluid of angular velocity w to an imposed change

in the rotation rate of its container to w (38). It is a means of

mixing a melt. This method has evolved in crystal growth, because

direct agitation may be difficult. This may be due to corrosion

concerns or because the ampoule may have to be sealed from the

environment to prevent volatiles from escaping or reacting with the

surrounding atmosphere. Spin-up/spin-down is also known as

Accelerated Crucible Rotation Technique (ACRT) when referring to

crystal growth.

Uniform crucible rotation does not lead to adequate mixing of a

melt, because the crucible and the melt rotate at the same angular

velocity, although it will tend to decrease temperature differences

due to a thermally asymmetric furnace. Conversely, bringing a

crucible from rest to rotation will bring about effective stirring of

the liquid. Fluid near the crucible wall will follow any changes in

the motion with little delay. Fluid which is closer to the interior

will tend to continue its previous motion due to inertia. The

resulting pattern of motion is one of slippage and shear around the

rotation axis (39).

ACRT was applied to the Bridgman growth of incongruently melting

Rb 1-lnCl from nonstoichiometric melts. The maximum growth rate of

inclusion free crystals was increased by more than a factor of four

over growth without spin-up/spin-down (40). Bridgman growth of

29
Cd Hg Te using ACRT resulted in a much greater degree of axial and

X X ~TMX

radial homogeneity and an improvement in crystallinity (41,42,43).

In the first documented application of ACRT, GdAlO- grew from a

*

PbO-PbF - 3 0 solution one thousand times larger than any previous

attempts (44). ACRT has also been successfully applied to the

Czochralski growth of silicon crystals (45).

30
CHAPTER 3

Experimental Procedure

Measured amounts of high purity (99.9999J5') gallium, indium and

antimony corresponding to one of three dirrferent compositions

(In Ga, Sb, x =0.5, 0.3, 0.1) will/be placed in a 9 mm ID and 11 mm

x 1-x /

/ -—^

OD fused silica ("quartz") tube. The tubes will be carbonized to \v\ prevent sticking of the melt and subsequent cracking of the ampoule y.

during solidification. The silica tubes containing the elements will

be evacuated to 5 to 10 Torr pressure and sealed to a total.len

about 16 ca with a torch. 5 Wr^w- ^nf^Mib°?*

Sen (7) encountered some difficulty in introducing the desired

amount of liquid gallium into the tube, because gallium in the liquid

form readily sticks to fused silica. To overcome this, liquid

gallium droplets of different sizes and weights were first placed on

clean glossy weighing paper. They were then cooled slightly and

solidified and were then much easier to handle. Formation of a thin

layer of oxide on the gallium droplets could not be avoided in this'

process. Sen (7) found that this did not cause much of a problem,

because after introducing the feed elements and evacuating, the

gallium melted and a thin layer of oxide either came to the surface

or adhered to the silica wall leaving clear gallium inside. Oxide

formation was minimized when the gallium droplets were left in a

dessicator prior to weighing; and loading in the quartz ampoule. Sen

31
(7) also found that it was possible to remove oxide fron the indium

and antimony shot by placing then for 10 to 15 minutes in 1 HC1:2 H-O

(by volume) and then rinsing in methanol prior to weighing. This . A

treatment produced clean and shiny shot.

The contents of the ampoule will then be melted and

directionally solidified in a Bridgman-Stockbarger apparatus. This

apparatus consists of a heating section at the top and a cooling

section at the bottom with a layer of insulation between the too.

The layer of insulation ensures a more planar interface: To obtain a

single crystal it is necessary to maintain the interface either

planar or convex, which tends to prevent nuclei formed at the walls

from growing inward. An ampoule containing the melt is translated

from the heater into the cooler at a specific rate and the melt is

solidified. The rate of solidification is equal to the translation

rate except near the ends of the ampoule. The Bridgman-Stockbarger

apparatus has the advantage of permitting independent control of

interface shape, interfacial temperature gradient and growth rate.

The ampoule will be placed inside the furnace. The voltage

required to produce the desired heater temperature will be turned on Jtf \>^

along with the cold water circulator. The ampoule will be left >y r^^^if

\^n\ A . I °_-u]

stationary for 24 hours to permit temperature equlibrium and melt

homogenization. The lowering operation will then be started at rates

of up to 4 mm/day so that 20 days will be required to grow an ingot

of 8 cm long. In the trials where spin-up/spin-down is to be

employed, the ampoule will be rotated from rest for a period of a few

seconds, stopped and then rotated in the other direction. After the

32 \
growth period the heater power and cold water circulation will be

turned off successively. Uhen the heater cools down to room

temperature, the ampoule will be taken from the furnace and placed in

concentrated hydroflouric acid overnight so as to dissolve the

ampoule. The entire ingot should be extracted clean and intact by

this method.

The ingots will then be cut longitudinally^ sandblasted and then &

chemically etched to show contained microstructures more clearly.

These-~57xrir~rhen be examined using polarized incident light for the ^ ^.

number of grain and twin boundar-ie^TA scanning electron microscope

/with an energy disspersive spectrometer will also be used to view the

longitudinal and transverse sections of the alloy for radial and

longitudinal homogeneity.

ORIGINAL OS

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- , i j ^__JLs

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33

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37