Influence of Crucible Support Rod on the Growth Rate and ......Bridgman growih of tin crystal was carried out in a graphite crucible that was fixed on a quartz support rod or a copper

53

Received October 6, 2003 Accepted for Publication November 1 9, 2003 C2003 Soc. Mater. Eng. Resour. Japan

Influence of Crucible Support Rod on

Temperature Gradient in a Bridgman

the Growth Rate and

Growth of Tin Crystal

Yuji IMASHIMIZU, Koji MIURA, Masaki KAMATA and Jir6 WATANAB~'

Department of Materials Science and Engineering, Faculty of Engineering

and Resource Science, Akita University, I - I Tegata-Gakuen-cho, Akita. O I O - 8502, Japan

' Emeritus Professor, Akita University

E-mail .' [email protected]. acjp

Bridgman growih of tin crystal was carried out in a graphite crucible that was fixed on a quartz support

rod or a copper one. The growth rate and axial temperature distribution were examined by recording the

temperature variation with time at each of four prescribed positions in the solid-liquid system during solidification, I ) Actual growth rate of crystal increased with progress of solidification while the furnace

elevated at a constant rate, but the tendency was different depending on the type of support rod used. 2) We

could increase the temperature gradient in the crystal-melt system without varying the interface shape, if

we used a copper support rod in place of a quartz one together with raising the maximum temperature of the fumace. 3) The thermal conductivity of the crucible support rod is thought to be an important factor

affecting the growth rate and temperature gradient in the growih system in the Bridgman process.

Key Words : Bridgman method, temperature gradient, actual growih rate, crucible support rod, temperature-

time curve, tin crystal, solid-Iiquid interface

1 . Introduction

For the growih of high perfection crystal from the melt, it

is necessary to control the temperature distribution near the

solid-liquid interface so that the interface becomes macroscopi-

cally flat. This is because the inhomogeneous temperature

distribution near the interface is accompanied by thermal stress

which is responsible for the production of dislocations into

growing crystal. In crystal growih with the Bridgman method, the

temperature distribution and interface shape in the growih

system have been investigated by solving the partial differential

equation for heat conduction subject to appropriate boundary

conditions.*~') However, the experimental examinations"') have not

been done so much because of the difficulty of the measurement,

and our understanding and control of the Bridgman process for

growing crystal with a flat interface remain unsatisfactory.

On the other hand, the crystal growih rate during the Bridgman

process is often assumed to correspond to the translation rate of

the heater or crucible, and is not measured commonly. However,

it has been shown that the actual growih rate is different from

the translation rate of the heater or crucible in the Bridgman

unidirectional solidification of some materials.'~*') The difference

between the actual growih rate and the translation rate of the

heater or crucible is thought to be accompanied by a variation

of the temperature distribution near the solid-liquid interface,

accordingly that of the macroscopic interface shape. Moreover, it

is known that the formation of microdefects and the segregation of

impurities in melt-grown crystal depends on the growih rate and

axial temperature gradient at the solid-liquid interface. Thus, it is

important for defect control in Bridgman-grown crystal to know

the factors affecting the actual growth rate and temperature

distribution,"*) but sufficient research of these factors has not yet

been done.

In this study, a tin crystal was grown in the crucible which was

fixed on a quartz support rod or a copper one, by the use of a

simple Bridgman apparatus.*') The effect of the type of support

rod on the actual growih rate and axial temperature gradient was

investigated by recording the temperature variation with time at a

given location in the solid-liquid system during solidification.

2. Experlmental procedures

2.1 Measurement of the temperature-time curve

A schematic diagram of the apparatus used for the Bridgman

growih of tin crystal**) is shown in Figure I . A tin ingot I O mm in

diameter and 100 mm long was prepared from 99.999 mass~ tin,

in which the junction of a thermocouple O. I mm in diameter (K1)

was set at the center of an axial position of about 20, 40, 60, or 80

mm distant from the bottom. The graphite crucible containing the

tin ingot was fixed on a support rod made of quartz or copper that

was placed in the vertical evacuated quartz tube (referred to as

ftimace tube in the following) . Another thermocouple 0.65 mm in

diameter (K2) was inserted along the inner wall of the furnace

tube so that the junction located at a given position. The melting

point of tin is 232"C .**) The maximum temperature of a resistance

heater furnace was regulated at 300'C for the use of a quartz

support rod and at 400~C for the use of a copper support rod. The

tin ingot was heated and melted except for the lower end portion

Int. J. Soc. Mater. Eng. Resour. Vol, 1 1 , N0.2, (Sept. 2003)

Akita University

54 Yuj i IMASHIMIZU et. al.

at first by holding the fumace at an initial position for I .8 X I O* s.

Then, the tin melt in the crucible was unidirectionally solidified

by elevating the fhrnace at a constant rate of 1.3 x lO~=m/s. The

variation of temperature with time at a given position in the

crystal-melt system and that at another position near the furnace

tube were simultaneously recorded during solidification. After the

measurement of the temperature-time curve, the length of the

unmelted lower end portion of the ingot was measured by

inspecting the state of the flaws on the side surface of the portion

which were scratched before the Bridgman growth experiment. It

should be noted that the length of the unmelted portion tended to

decrease slowly while the furnace was held at the initial position

and each time we measured the length scattered especially for

the case where the copper support rod was used. The above

measurement was repeated two or three times for every ingot with

a thermocouple junction at one of the four prescribed positions.

In the experiment using the quartz support rod, a similar meas-

urement was carried out under the following conditions.*') The

whole of the tin ingot was melted at first by setting the ftlrnace at

a lower level and regulating the maximum temperature at about

Fumac

Gra phit

crucible

Tin

ingot

Quartz

tube

Support rod

Cooling w8ter

'1

300'C or 400'C . The temperature-time curves were simultaneously

recorded at an axial position in the partly supercooled melt and at

the position level with the former near the furnace tube. The axial

temperature profile in the partly supercooled melt and the vertical

one along the furnace tube during elevation of the ftlmace were

examined by combining the temperature-time curves recorded at

the four given positions 20, 40, 60, and 80mm distant from the

bottom. Thus, the effect of the maximum temperature of the

furnace on the temperature distribution in the growih system was

investigated.

2.2 EStimation of actual growth rate

Figure 2 shows a tracing of the temperature-time curves in

which the curve S ' L represents a variation of temperature with

elevating time at a given position in the coexisting state of solid

and liquid and the curve F that at another position near the

surrounding furnace tube. The times t , , t * and t , indicated by

arrows s , m and " e , respectively, were examined on the

former curve. That is, the furnace started in elevating at t ~ = O,

the temperature at the distance I ~ from the bottom where

therrnocouple junction was set reduced to the melting temperature

of tin T* at t~ and the melt solidified completely at t., which is

known from an abrupt increase in gradient of the S 'L curve shown

at the arrow "e

In order to estimate the growth rate, we assume that the

solidification of tin proceeded as shown in Figure 3 . That is, the

solid-liquid interface was frrstly at a position which is given by

the coordinate I*/mm (corresponding to the length of unmelted

p ¥ 3~~ "L; a E ho

25Q

200

150

~

S･L m ~

sr

F

e ~---- rm

Figure 2

e

1 .Q 2.0 3.0 Time 1 IO' s

4.Q

An example of the temperature-time curves at given positions

during elevation of the fumace. The curve S ･ L represents the

variation of temperature with time at a position in the solid-

liquid system and the curve F that at another position near the

furnace tube.

Time t.=0 ~

t~ l

~

K2 Position l, Im

le

Figure I Schematic drawjng of the apparatus for the Bridgman growih of

tin crystal. K1 and K2 are chron]el/alurnel thennocouples for

the measurement of temperature variation and R is a Pt/Pt-

13010Rh thennocouple for regulating the ftimace ternperature.

Figure

o 20 40 80 1 OO 60

Coordinate / mm

3 A schematic illustration of the relationship between reference

positions and the times when the interface reaches the posi-

tions.

Int. J. Soc. Mater. Eng. Resour, Vol.1 1 , N0.2, (Sept. 2003)

Akita University

Influence of Crucible Support Rod on the Growlh Rate and

Temperature Gradient in a Bridgman Growih of Tin Crystal

55

lower end portion) where the origin of the coordinate consists

with the bottom of the ingot. It began to advance at t,= O, passed

the coordinate l*/mm at t~ and reached the upper end of the ingot,

the coordinate /. (the total length of ingot) /mm at t,. Then, an

average growth rate Rl between the distances lo and l* is given by

(l~ - l*)/(t~ - t,) and the rate R, between the distances l~ and

l, is given by (1, - l*)/(t. - t~).*')

2.3 Estimation of temperature distribution

The variation of axial temperature profile in the crystal-melt

system with elevation of the ftimace was investigated by examin-

ing the temperatures of four given positions at any time from a

series of the temperature-time curves. As mentioned above,

however, the length of the unmelted lower end portion of the ingot

lo Was different in each growih experiment, resulting in some large

scatter particularly in the case of the use of a copper support

rod. Taking account of this, we have estimated the relationship

between axial temperature profile and the interface position in the

solid-1i-quid system during growih in the following way.

The growth rate is thought to vary with the growth of crystal

during the Bridgman process because the temperature distribution

near the solid-liquid interface generally changes as the solidifica-

tion proceeds with an increase in relative displacement between

the crucible with a finite length and the surrounding furnace.

In order to identify the position of advancing solid-liquid interface

during growth, we assume that the growth rate, that is the

advancing rate ofthe interface R, varies linearly with the elevating

time of the furnace t as,

R=2at + b (1) Then, the coordinate of the interface !/mm at any time t is given

by

l=at' + bt + c (2) where a, b and c = /o are constants. Hence the average growth rate

R* defined in prescribed section 2.2 is expressed from eq. (2) as

l~ - l* (3) = t~ + b R*=

t~- t,

where t*= O, and the R, is written as

I. - l~

= (t~ + t.) + b (4) R,= t.- t~

Thus, estimating R * and R , from the temperature-time curve

measured at a given position during growth, we can determine a

and b by eqs. (3) and (4). Subsequently, by calculating the time

t when the advancing interface reaches any coordinate / from

eq. (2) we can determine the relationship between the tempera-

ture T of the given position where the thermocouple junction

was set and the coordinate of the interface during the growth

from the temperature-time curve. The scatter of the temperature T

detenuined in this manner is comparably small. Therefore, the

analysis seems reasonable.

Thus, we determined the temperatures of four given positions

T, , T,, T, and T+ at the time when the advancing interface reaches

any coordinate I from the temperaure-time curves at the four

axial positions, and examined the relationship between the axial

temperature profiles and the solid-liquid interface positions in the

crystal-melt system during growth.

The vertical temperature distribution along the surrounding

furnace tube at the time when the interface reaches any position

was estimated together with that. It was made from a combination

of the temperature measured at a given position near the furnace

tube during elevation of the furnace and the stationary vertical

temperature distribution which was independently measured fixing

the furnace at some proper position.

3 Results and discussion

3.1 Actual growth rate of tin crystal

In this Bridgman growih of tin crystal, the growih rates R * and

R, are plotted as a function of mean interface positions l* and /,,

respectively, with solid marks in Figure 4, where the mean

interface positions l* and l, are defmed as (l~ + l~) /2 and (l~ +

/.) /2, respectively. Graph (a) is in the case of growth with use of

the quartz support rod while holding the maximum temperature of

the furnace at 300'C, showing that the actual growth rate increases

with advance ofthe interface. Graph (b) is in the case of growth

with use of the copper support rod while regulating the furnace

temperature at 400~C. This also shows that the growth rate tends

to increase with progress of solidification. However, the data

scatters because of the difi'erence in length of the unmelted lower

end portion ofthe ingot in each growth experiment. The reason for

this is probably that the solid-liquid interface did not attain a

thermal steady state in the crucible fixed on the copper support rod

with high thermal conductivity while the heated furnace was held

at an initial position.

Thus, we have approximately estimated the relationship

between growth rate R and interface position I in each growth

e Measured O Estimated

(a)

g 'o

¥ tf~Lo J: ~ Lo O

3.5

3

2.5

2

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1

0.5

O

(b) 3.5

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2.5

2

1 .5

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O

E 'o

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Figure 4

o

20 40 60 80 1 oo

o

20 40 60

Coordinate of interf:aGe / mm

80 1 OO

Plots of the growih rate against interface position. Solid marks

are the values obtained from a simple experimental relation and

open marks the ones estimated by assuming an expression for

a variation of growth rate with time. The latter represents an

average growih rate. Graphs (a) and (b) are the results from

the experiments performed with use of a quartz support rod and

a copper one, respectively.

Int. J. Soc. Mater. Eng. Resour. Vol.1 1 , N0.2, (Sept. 2003)

Akita University

56 Yuji IMASHIMIZU et al.

experiment by applying a and b that are determined from R * and

R, with use ofeqs. (3) and (4) and c=]~ to eqs. (1) and (2).

An average of the growth rates estimated in this way was plotted

as a function of interface position l. It is shown with open marks

in Figures 4 (a) and (b) for the growth processes with use of

the quartz and copper support rods, respectively. They roughly

agree with the values (solid marks) determined from a simple

experimental relation described above, where the appreciable

difference is owing to the inaccuracies in determination of the

mean interface position from the simple experimental relation.

Comparison of Figures 4 (a) and (b) indicate that the

dependence of actual growth rate on the growth distance is

different between growth processes using two types of support

rods. Overall average growih rate through the solidification from

start to finish is estimated to be 1.8 X 10~5m/s for the use of the

quartz support rod and to be 1.4 x lO~'m/s for the use of copper

one. The former is about one and a half times of the elevating rate

of the ftlmace I .3 X I 0~5m/s, while tbc latter is nearly equal to that.

These results are probably due to the fact that the thermal

conductivities of the quartz and copper making up the support rods

are I .67 and 394 W/Km,~") respectively, and that the difference

between them is considerably large. On the other hand, the above

tendency of the growth rate disagrees with that in the Bridgman

growth of Cd-Tes) and Pb*_.Ba.Nb,O**') where the growih rate

decreased with progress of solidification. This seems due to the

difference in the thermal properties of the growth systems,**) but

needs to be discussed') in more detail.

3.2 Temperature distribution in the growih system

3.2.1 Effect of maximum temperature of the furnace

Figure 5 shows the axial temperature profiles in the partly

supercooled melt in the crucible fixed on the quartz support rod

and the vertical temperature ones along the surrounding tube at

three times, t*, t, and t, after the furnace started to elevate. Graphs

(a) and (b) show the profiles in cases where the maximum

temperatures of the fumace were regulated at about 300'C and

400'C, respectively. The profiles (a) and (b) in Figure 6 show

the estimated temperature distributions along the surrounding

furnace tube in a range of crucible length, which correspond to the

profiles at the times t, shown in Figures 5 (a) and (b), respec-

tively.

The coordinate of the melting temperature of tin T* in the

supercooled melt is roughly consistent with that along the furnace

tube when the maximum temperature of the furnace was regulated

at about 300 'C , as shown in Figure 5 (a) . Average temperature

gradients in the melt and along the furnace tube are GM=0.25 X

1 03 'C/m and G* = 2.0 X I 03 'C/m, respectively. On the other hand,

in case (b) where the maximum temperature of the furnace was

regulated at 400'C. GM=0.38 x lO* 'C/m and G*= 3.6 X 103 'C/m

(from the profile (b) in Figure 6) are obtained, which are

somewhat larger than those in case (a) . However, the difference

between the vertical coordinate of T~ in the supercooled melt and

that along the surrounding tube becomes considerably larger,

which is estimated to be = 53 mm (minus means the coordinate of

the former is smaller than that of the latter) from Figures 5 (b)

(a)

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O 20 40 60 80 100 Coordinate / mm

Figure 5 Temperature profiles in the partly supercooled melt of tin in the crucible that was fixed on a quartz support rod and vertical ones

along the surrounding fumace tube at the times t*, t, and t, after the furnace began to elevate. Graphs (a) and (b) are in cases

where the maximum temperatures of the ftimace were regulated at about 300~~ and 400~, respectively.

Int. J, Soc. Mater. Eng. Resour. Vol.1 1 , N0.2, (Sept. 2003)

Akita University

Influence of Crucible Support Rod on the Growih Rate and

Temperature Gradient in a Bridgman Growth of Tin Crystal

57

Table 1 The coordinate of the melting temperature T* and axial tempera-

ture gradient in the partly supercooled melt of tin or the solid-

liquid system and those near the furnace tube, and vertical

difference between the coordinates of T~ in the former and the

latter. The origin of the coordinate is positioned at the bottom of

charged tin ingot

and 6. These values are summarised in Table I .

The temperature distribution in the supercooled state which

resulted from melting the whole ingot in the crucible at first should

be different from that in the coexisting state of solid and liquid

during crystal growth, but the difference between them seems

to be small, as discussed later. Therefore, when a steady

solidification proceeded, the solid-liquid interface would become

relatively flat under the conditon of (a) , but concave to the melt

under that of (b) because the surrounding temperature at the

solid-liquid interface position was considerably lower than T**) for

the latter. Thus, it is thought not to be able to raise the temperature

' <300~C JL 4000c

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O I OO 1 50 200 50

Distance / mm

gradient at the solid-liquid interface without any change of

interface shape only by changing the maximum temperature of the

furnace. This means that to make a flat interface it is necessary to

control the maximum temperature of the furnace at a proper one

when we grow a crystal with a Bridgman growih apparatus.

.O

¥ e ~ ~ q, a E o H

400

350

3 oo

250

200

1 50

1 OO

Figure 6 Vertical temperature distribution along the furnace tube that

was approximated from a combination of the temperature

measured at a given position during elevation of the furnace

and a stationary temperature distribution. The plots (a) and

(b) are the profiles where the maximum temperature of the

furnace were regulated at about 300'C and 400'C, correspond-

ing to the profiles at t, in Figure 5 (a) and (b) , respectively.

The abscissa is the distance from the lower end of the cucible

and the white region designates the position of the partly

supercooled melt of tin.

3.2.2 Effect of the type of crucible support rod

(1) The temperature gradient in the growih system

Figure 7 shows the axial temperature profiles in the tin crystal-

melt system and the vertical ones along the furnace tube while the

furnace elevates at a constant rate. They show the profiles at the

times when the interface reached three positions which are at the

distances /* = 40, l, = 60 and l, = 80 mm from the bottom of the tin

ingot.

Graph (a) is in the case where the crystal growth proceeds

in the crucible fixed on the quartz support rod, showing that the

coordinates of the melting point of tin T~ in the axial profiles

well agree with the estimated interface positions. An average

temperature gradient in the solid-liquid system is estimated to be

G** = 0.28 x I O"C/m. This approximately agrees with the gradient

obtained from the temperature distributions in Figure 5 (a) which

were measured in the supercooled melt, as shown in Table I . The

difference between temperature distributions in the supercooled

state and the coexisting state of solid and liquid during crystal

growth is small.

On the other hand, Graph (b), where tin crystal grew in

the crucible fixed on the copper support rod, shows that the

coordinates of the melting point T* in the axial temperature

profiles approximately agree with the interface positions. An

average temperature gradient in the crystal-melt system is

estimated to be G**=0.67 x lO* 'C/m. It is about two times larger

than the gradient in the supercooled melt shown in Figure 5 (b)

using the quartz support rod where the maximum temperature of

the fhrnace was regulated at 400~~, as shown in Table I . The

difference in the temperature gradients may be attributed to that in

the thermal conductivity between the quartz and copper making up

the support rods. This shows that the use ofthe copper support rod

with a high thermal conductivity together with holding the fumace

at a higher temperature increases the temperature gradient at the

interface effectively.

(2) The correlation of the interface position and vertical

temperature distribution in the furnace

In the growth with use of the quartz support rod where the

maximum temperature of the furnace is regulated at 300'C , as

shown in Figure 7 (a) , the surrounding temperature at the

coordinate of the solid-liquid interface is lower than T* when the

interface is at the coordinate of 40, but becomes nearly equal to

T* when at 60 and higher than T* when at 80. This suggests that

the interface shape changes from concave to convex to the melt as

the interface advances in a range from 40 mrn to 80mm distant

from the bottom.

On the other hand, when the tin crystal was grown with use of

the quartz support rod holding the maximum temperature of the

furnace at 400'C , the vertical difference between the coordinates

ofthe melting temperature T~ in the crystal-melt system and along

the surrounding furnace tube would become considerably large to

be about - 50mm, as shown in Table I . The interface shape is

thought to be concave to the melt,*) as described in 3.2.1.

However, the difference became small to be about I O mm in the

case of growih with use of the copper support rod, as shown in

Int. J. Soc. Mater. Eng. Resour. Vol.1 1 , N0.2, (Sept. 2003)

Akita University

58 Yuji IMASHIMIZU et. af

Figure 7 (b) and Table I , so that the interface shape may become

flat or convex.*) The surrounding temperature at the interface

is appreciably higher than the melting temperature T~, and the

difference tended to increase slowly with an increase in the

coordinate of the interface. This suggests that convexity of the

interface shape') increases as the crystal growth proceeds. The

correlation of the axial temperature profile in the crystal-melt

system and the vertical one along the surrounding furnace tube

depends on the type of crucible support rod in the Bridgman

growih of tin crystal.

Thus, we could not increase the temperature gradient at the

solid-Iiquid interface without change of the interface shape, only

by changing the temperature profile of the furnace, as mentioned

in 3 .2.1. However, it would be possible if a support rod of high

thermal conductivity material such as copper was used in place of

a quartz support rod at the same time. The thermal conductivity

of the crucible support rod is thought to be an important factor

affecting the actual growth rate and the axial temperature gradient

in the crystal-melt system in the Bridgman growih of crystal.

4. Conclusions

Bridgman growth of tin crystal in the graphite crucible fixed on

the quartz support rod or the copper one was performed, and the

growth rate and temperature distributioyl were examined by

recording the temperature-time curves during growih. The results

are summarized as follows. I ) Actual crystal growth rate

increased with procession of solidification while the furnace

elevated at a constant rate, in which the tendency was different

depending on the type of support rod. 2) The temperature gradient

at the solid-liquid interface could be increased without changing

the interface shape, if a copper support rod with a high conductiv-

ity is used in place of a quartz one together with raising the

furnace temperature. 3) The thermal conductivity of the crucible

support rod is thought to be an important factor affecting the

growth rate and temperature gradient in the growth system in the

Bridgman process.

ReferenceS

l) C E Chang and W R Wilcox (1974), Control of Interface

Shape in the Vertical Bridgman-Stockbarger Technique, J. Cryst.

. Solid-liquid o Fumace (a)

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O 20 40 /1 = 40 mm

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Figure 7 Axial temperature profiles in the solid-liquid system and vertical ones along the surrounding furnace tube at the times when the

interface reached the positions l,, l, and l, during the growih of tin crystal. The type of support rod and the maximum tempera-

ture of the furnace are (a) quartz and 300"C and (b) copper and 400'C, respectively.

Int. J. Soc. Mater. Eng. Resour. Vol. 1 1 , N0.2, (Sept. 2003)

Akita University

Influence of Crucible Support Rod on the Growth Rate and

Temperature Gradient in a Bridgman Growih of Tin Crystal 59

Growth, 21 , pp.135-140.

2) T-W. Fu and W.R. Wilcox (1980), Influence oflnsulation on

Stability of Interface Shape and Position in the Vertical Bridgman-

Stockbarger Technique, J. Cryst. Growih, 48, pp.416-424.

3) R.J.Naumann (1982), An Analytical Approach to Thermal

Modeling of Bridgman-Type Crystal Growth, J. Cryst. Growth,

58, pp.554-568.

4) C.E.Huang, D.El.Well and R.S.Feigelson (1983), Influence of

Thermal Conductivity on Interface Shape during Bridgman

Growth, J. Cryst. Growth, 64, pp.441-447.

5) T.Jasinski and A.F.Witt (1985), On Control of the Crystal-

Melt Interface Shape During Growth in a Vertical Bridgman

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Int. J. Soc. Mater. Eng. Resour. Vol. 1 1 , N0.2, (Sept. 2003)

Akita University