Influence of Crucible Support Rod on the Growth Rate and ......Bridgman growih of tin crystal was...
Transcript of Influence of Crucible Support Rod on the Growth Rate and ......Bridgman growih of tin crystal was...
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
1 .5
1
0.5
O
(b) 3.5
3
2.5
2
1 .5
0.5
O
E 'o
¥ d~o S J: ~ 2 O
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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' 50 =~=~;'~~;;'~~ ":~":~~=* ~~~*~;~ '~~'+"'== '=~~~ ~:~~i~~=~i~
"~~~~;P/'~f"~;~"~; " ~i~~;~~':~"//It;' ' ;sE~:~;;;'.i/"~~i;~~//~~'~/;'~;~/:;i~;;:~i~~;*~'~~~~~;;'=;~~ ~~:#=*~;~f~~ ~='*i~~~~s '~~~~#:' ~~~ ~~~;~~/~,~~~'~"=' #= ~:!/1'~~':;~~'=:~f/!~~"'~~~"':~~'//:'=!""/fr."/!'i~' ~
~';;,{::i/!~l'i'~;'~~'~!~'~!~'/~::~//:/~"/'~///~i::1:r~/=~!~~;/':/~/~'~//~/;/':~{,~'::'~//~;/~/"~~ti'~~"~~;i/~~:~"(j~~;/;:'~sF"'~'j~!:~~!':,//:(:~~~'~//~~
's;;/;~;;1;:".:~~;~i~;'~'./~~;~~;~~~';;*'~:~ii':~{;r~~:;;~ii:;;:;f/;:(;~';";~:;~;':;~~~:~:.*~~~".~;;i/;~;~;~'<(i~
1 OO '~='#~ '~;**~~'="~~~;'<~'~F'*;~~~ii~~' !~' ==~~~~f' ~/* ~'isi"~';~~~~#~;'~
O 20 40 60 80 100 Coordinate / mm
t2 = 40 min
300 ~~t~'~~=~ ="~=i~,~~;'~~i~~:~{==~~;'~~=,;:/:1:~/;1:i_':~"~',".~j~:i~""~'~~/:・::~F./::~~~<..;~,;~';':"~:/:f'~f;'~~.~~'.~~~i';~~~.~';""~i~j~
'*~/~i==~:+* ~~~~=~** ~;~=*i'i'*~~=~~~~~.*=;'=~'* ~=*~ **.'= =
i~;:~~~
~)~;==~~~~;~~;. ~~;,':*~:~~{:,~~.",'****~*-":'1~:i{;~1~~;:/;*i*"'i'*;**."~~~*#*~;~~~.+~ *~~:
250 +=~'*'*=;*~'i.~.*..~~"/"'~""' =~~*:'1"=~'~~'~~~""'~~*.~~'//"~*"/~~~=~~{""*' ~*'* =*~~'~~~:'*'.
';/"~/'i/~*~;i./r~~;/~"'~~':~~-::~'~i~~;~*;://:~:{{~:~:;:・~))'f(:~~'#~i~;;':'~~.1~;~'~~~~i;~~'t':i::x~(:~/=)/~~:'i~;'~~
;~ *..~: ~!~/*"*~**i'* * **~;~~ 200 ~~~!~= ~ *' *~*~~:"~='i~'**:';~i"'~;;"~'.~~;=~~l==~!'~~~'~~'//"i~:~'t=~~*~:'.~"f~~~)/i~
~~" ~~'~!'~j"';~~'~...",~~;"~~~/:;';'~/:'/:~';'(:;')/=;;~~>:::・~i~=;
1 50 ~~~=/:./(;:'~~.~~ .*.~~{~~;j#:'i""}:.<~*~*~ ~ ...*_ .:-.~~;*_'*"'*'
~ ;f~~'~~'~:://~~~:'~~"i""; '~~)~/"'i~"'/;~.^;:~"~/~f=~;, ~/i~~~,,fi'/(" ~:
O 20 40 60 80 100 Coordinate / mm
t3 = 50 min 300 '~~"":~~"//*~*~;~;'~~"'~";~~
~~~ ~;!"~:~";.~t=1=~:~1~~"'~:>"~"/:~i~i~~/"~1'~~~t~~f"';:~;::~(:".:~/~~~.~//~;~~'~:.~!:;~~~;~;~~~~~;:,i~~i~~"~;'~t't;;/:~::;;'://:ii/~i~;~:~~:~;;~s/~:;,//~'~;'~~~~
'~i~~.~~l!~1.~~~~i~;;~:/i~;',;~;;:i,:~!:;'f~::'~;":~:'~~~;.~~({・;~~;~~;,;{~~~~i;~~/::'i:,;;()':i:,:;~~;;;:;~~:,~:(/i:/'i/;'~'!~i/~{;:;//;/:,;:i~',/';~,i'//;,)~:~'=~~'~:t~~~.
*~' =-~~~:=";#'~~~~-~~~'="i';*~)('~'~ '~~'i/~'~~~':~~~f~'.~~~~/:.:~:;~//~{;;~
=~.r./"'~i~~;~/~:f~~~;i~;~~~'_'/';'/~/'.()~;~:;~~"/i/~~~!~'~a~~~~."~"~.;'.'.'j~'=~;..=;"~~"~;#~~'~~'.. ~~~=
*'~~"*=*"~'!~:~~~~*~~*/"'+~'*"I~~~~;~~;~~*;"~'~<i*~~~*'.~ * ... ~ = ~ ='~ ~'!~~~=:'===~~~:i~=~:= ~~"~~~;"~~'~'==~;~' ~' ~~~
..*'~='::~;~~;;': '~'*"~;:'*~~~;'~~' ~'*~~~'~{~/~~s=~i!/i'~i'f'/'~~~/'~*'~~'2;~~~/'1;'"~~~~~~~'~~;.'~~ "'
200 " " i~"~~~~,~~~~:',..=~=i/~~~;~t~;'~~~~i;'~'(~:~i~~~~;~/i/'i'~~'~s~'~;'~//~~:/~/i::/~/~~/;~j:~~~~~/~';'"~~';~~'
'
*'*** ~~:'=*~";~!~;++~~"~""~~'~'~ =*=' ~:':~~{';~/;~
* *=~'*" ~'*'*;=* '~~ ~=~~~*";i~=~~{~;~~.*~~'*~=~~'~rsi~~'+;:+ :='#:~~~"I;;;~;~:://:/si~'."/~~~i"/'~~~~;/'r;,~~~~~;~~~~'~~~/~~f'~~~/~~~:~i~~~'~"'i';~/~:=~~{{~/~;.;~;";;(;~~;~~.:'/'~;~'=:(!';;;/:;~"'~/';~~i/;;;/=~~{'~~~~
1 50 i'/~;~:~;'~;;j~:#:";ti':~i~・~i~;/;:r.':=~:'t~i~,;~~~i':;~'i';:;/'~~~;j':~;・・~:::".'+'~~~f~'~{~;f~!i"i~.:i;~(:;~/ft~;,~~:~~~".~//~1('~{;:~~:";(!/.~,~~~~'~:~
**+ ~~i;+i.i*~~:~~'~~~:*=~*~;*.~;~~~".,ii".'~~l,~~~'~.;~;'*~**~;=ii~~*f~:*~*~
~7/~~~/~"~;~f~~~~/:'~/:/~i:L'~;;"'~.".:=~~~;f/"~'~~'.~ ~;./~si:;~i..'~- '~i:"=~i~~! "'~;"= i
;~~;~;;~~.i:;i~~i~~~e~;f~" " '.~~~~'~~';~;~~~;;//i~~~~:'!"~~:"~;.~~;(/)~~i~';~"";./~:./f'~~:'.~~:)~"i"!~;~~~
~~~ ;~~"~#.~i~~',.'//~'~//~'/~~~!'"t//~~"'~~'.'1//'~~s/'#~;';;~".'~~""~~~;~i~;//~/~~//~'~i(;~~:~~/"'~;/~~'!'j/1~;~~:'(/"{~~f"'~~'f'/~/';
100 ~~*~~~=i~~~*'=~~;~~"~'~*""~"= ' ^ = '*
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
~~:"~;/'~~';~//~^!~~~/':"i.'~-'~'m~j~f~i~=*~'~*=~='~/'~~~!~~'/~"~~.~~*~:~=~":#~*~~~'=~~~/"~~== ~{~i ~~~ ~'~i~:{:~'<~'=<==~~i~=-~:' " ---'^ ' '#S~{ '"~;~~!~'=:"":~':~'~~~:*'*'{~~">~:"'""~'~===> ~*'*'+!"i'~~ ~ '~ *== '~='~'i* :'==i '~~ =:~i~==~i*':~*~ '~~~- ~i~=~_**==*=i"='~~'<~===:*~~*~~*~~~~ ":",;;~j~'{:~~i~~;;:::i;i;f~;{l~ii;;._1;I~'!:1,'1・"I~~;=~~"~';"'~i~'~{~~~~~;i~="/"~'i~~=~~i'~i~f~~"';'~~~'~'~"'~.(.'i~"""', 'l~"""i~:".~~",~~.~t~:~;.~~~;~~'~~~'/~;~;'~~~'!';~:~/.:/':~')~:1/'~/'~~'~'!;~~"f!~~~==;=~~;t~;~~i'~/'~:~~;'='~'~;Is ~~i
<'__' '~' = ~~~{~==;~~1:~~;"= ,...=~#~~~~==~~~~' =;~/fl//;,. ,.~~i~= ~~i~'~~~'~<~=~=~--==~=:='~='~~=i~:=='~=-' ~i ~~i~i~'"-
~'~;~{i'*/t'~;~!"/~~/ ~~~~i ~;'
S~~ ~'///~;'~~!~/~;~i"'~:f;;~~~'i~:~~~~c: : ' = *'_~".~i"=~~i=!~ :~~~j/=1~~~~~~r~./;~i.~~fl!i':"~'_~"' ~'=:;~/~~~'~~~~'~/!"jr~~'1;~~/'~/'&~:~~~"".~'..~:;~~:~;::" ' ;1~~~~/"';~/'~_~'/~~'{{~;f"~:;<= "~~ ~~;i:,
~:~~:/~~t~'~i'~~'.~~:/;~~;;;; ;';~~~.~:#~~;;/i'~;"~'~'~ ' ~~!~~~~'~!:'!~"~~'~~"~~!~/~' ~.~;~~."."'~~;.:;'~=" ~~= ~=-=' ~'~'~== ~:#'~~=-=> ""'~~"'
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. ~ ~ . ._ '
'~.***/;~.=~~/;~'**'"~**~="!"i"~~-~if'~~~i"'**. ~~~*r'i~**~~F/""~~* '~i~:':;~~*'~:/;~~;'~*~"/~~;) "~/~:~/;;~~~~~";~~~/~;;'*/'~~*~i'~~*'~~~;!;{~~~**~i"'
~/~i~i : ~i ~= '~~;"=~~/"i~~'# ~='==""~~~ '~"~~~~; ~'/'*~i"~~" ~~~#:'~~'~~'~i '~i"'~i::#::'~-' --*-""~~= ' ~ * ______r_[_______~___ ~;~~='~i~~~i'=*;ii~:;~~~f*~~s;r~~/*~~~_=~~~~~*.'~~~'+~:~*=i~=*i'(f~~*~:t~*i~!i/~;~~/"~~~'r~:";r/~"'~**/~i*
'""'/;~~' ~"~' ~~: ~ ~i ~{~ ~~~-'~:;'*~:~_~=:~~~"i*~*/' =~i: ~=! - ' -~---'= ' =-'~~~~~={ '~ - ' ~- #' ' ----'"-~~-' --- -#~ ' ~~'~ ~"~. " '='=-~ i;='" ='~ ~: ri/~~l'~!;/;~'~i~# ~~~~; ~; ~"!*'~i~~j
~r~'~~:'*=**'!/'*'~- "'*"~'~'~!"'; ~' :# =~i*~' ""'; ~"s/~*/~~i+;.~*'i';~~~~~~{_"'"/'~:i~- ~~_ i*~::"~~*~~~:';r~'*~~~:'.:f*~~*~~"~~'":",~*~=~< ~~:~~ =" :~ '*~i'=+ *< = >~'~:~~~{~~/'i~~~/~:/~'/~'/~~"~~""~~~~~_~ ...;~i**:;;?~i~~/~~~~.;,~~(/~.'~~~'~~~~ "'"'"'" '=' ~"' '=" '""" ' ~~i #~/'~:~';"~(~i~"~;~~~;'~~~~i..'~~F~~;#~~~~"'/~"r~.."~~#~# ~"~~"'~~'~;" "~i'~~~"~~ ~
=~ '~~=':'; =~~; ~~=='~'=':;~'~> -- . ' '=_.<.~='=~~ :* _ '~~; = ~=~; ~i~ ~~:~:=~:={F~~;;~=~1~~~~~;~=~i~S~;
' ~~~"'P'~~i~:~~~';~;~~;i~~'...,f)~/'~'~/"~;~'~!~:'~ ' "~ ~, ~~~:'~"'{~~//;~- ,~:~~~';'"~l';~~/~:~'~~~'~r.~:~i~'/";;~~/~~~~~i/~!~i";/'~:.~';;:/"'~~~//;'/;~'/'/~{~~//""~:~~t,~~./"~~~".~f~~; " ~ ~~!_~~fT'i~j/i'/;~~~';'~ii~ ! ~r+~'~~~i'+*"'=~'~~~*~~~~*~~~~~*ri!/;~~'+'~~~'/~' **<= '=;>'~ *= <~i'~i~~* ~~~= =~'.~'1~:: ==t==* ~~= ' *==<*{~= ~ ~i==;+=~;=~"=~;~;;
'~~~~-<'~~:":~'~=~-~~~i~~'~r:/~;!1;~~~~_~~~:;~~'~;=
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~ *~' r'~;~:~~*~/~/1
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)
280
.o 260
¥ c'
~ 240 ,g
* o a Eo 220 h
(b)
200
1 80
280
.O 260
¥ o * ::
~,9 240 * o ~L E a, ~ 220
200
1 80
/~ = 40 mm
:;~*i~~~~~:
/*~!i:~~~~.,".~;..~~.~f=;"/'"~;~~~~~;;*~+;・;;
*~ ***'"**~.~=~~<#**~;~;'
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=~~;~~;~~i:=::=;::~:~~+~~~1i~:**~'~'i;;~~=:=':
O 20 40 /1 = 40 mm
~~==:~#:=".~~:/=;~i*
;・・=i:・;~*・=~・,~~~'.';~.;:;:~;~
280
260
240
220
/2 :: 60 mm
200 ~~.~~E:*
,',+**=
1 80 ""
60 80 1 oo o 20 40 60 80
~~~*~: ~~::~~~~~}:1::~~~:~~~i,~~:::~::i ~i~:::::+s:isf~.~, ~~:!#'~/~~s'ft;~'.:#(;/~;.:~~:~ ~:~~,~:;i~':::i~~.}~#;r(/~,~~:;~:~~:~:;'~~ ~/~r~:~;/~~~
~~:s*:+++';~:;:'~*.~.*~E~,*r~..:i;c/~:1://~~~!i~~::~~;"::+L{~~;~~~~,:;i~i
~;:t~~:#:~:~~~;::~:*~:'~~:~~:"s~t:::~~;=:#~:~:' ~~#i~;~t:'~~':~~~'~~'~~#::=:~~:':#''~~
~;i/i~~{ ~~~~~'~~:,・:~!~~/~~~~~;::;;~~i;'~~i:~::~~:~~:'~~~i:~'i~:~'i(~:~:i~~j~.~'~t::
~~;~;i~~~~{~:~~'= ~~~~:"~:;~~~~j~~:isj~!~:~~'~,~~~
~~~ ~
O 20 40 60 80 Coordinate / mm
2 80
260
240
220
/2 :: 60 mm
{ '~ ~ ~・.~,
=~j~ .,;~~*~
~
,'..*
1 oo
~
~"i
2 80
260
240
/3 :: 80 mm
220 .
s{
~,=~~~~~ *
200 i~"・,*= **~",/#i!;~~!;.~;~~ ~ ~~,.・~~.・!.=~,・~::
1 80
280
260
240
220
o
~
~~~;.
~~:~~~~;
";=~"i~::~:~'~:~..',~~~~;,~.~.i=1_~,・,~i~.~ rrs
:~~;~:/~
~=~/+.~i(~~**'*~;1/'~i=~:+~=:~i~=.=**i;~;i/.~;~'i
;:~:=:~~=='#'~=~
~.=';;~~~'"t/'~~'~;::'~/~~/;'.;'=~=:=~:~~.
=~..,~!".~~i~:i~:~..'+/~,':~ ~ii~::~~!"';~~
,.;'=';~ 's;~~~;*+~+;
~i~~
20 40 60 80 Ioo
l3 = 80 mm :{'+',<+';;',~=(~:~~~ ':~~#i ~~~#~~~~~:~~;
ii::~i: ~~+~~":
~f::~:~!~'~:~~* ~:' ~~;~ *S~~*~~:
;(;:=/~~~
~='~s~*':i/!~i;;f/'~=";~;:i:~:=i:,-~~*.~.~=.";i~~/"~~:".~*/' ~;*;~i~)i'~;/~,i~:,i'=~/:/:j):/'(::::~i;::;'/9~"~='~~'='~i~,~~..~~~~'/7/:';/'=:=/~'~~'~,.;~~ '/~~;~~~/::,i:'~l~~;~
**~~i~~;
""+~;"=;~'~~~;~' ~~ *"'~$/!~~"""~~~~ ':/'L~"":#'~~* *'~~:"* ~;f;~;!;='={
.. ~~i=;/'i'=.~~'. ,'*'.".'/*}1~* ".'~ '~" ~ ~ *"~' . ,^ ,+ 1 80 ~~ ""~;~'*~(i"~'~9:.**:~1i・~. ~~;=..'~~~/***"':.~~i/i"**~~'~~i:'~l~!~~~~;+'..=:=~:~i" =*"':'~~=!=:~=:=;~: 1 80
O 20 40 60 80 1 OO Coordinate / mm
200 200
**==~/+i~~..*i;;~・=・1・,~!/**."/.f~ *!+5
~~~.~.~=・~;"・==~/;~・=;tS2=~~
~ +*
~i
~~~r;,~~~;;~.;#~.i;~~i
・・+~i:ij;~:.~:
20 40 60 80 Coordinate / mm
, .'=;j
*t~'//~'~:;';~>.:!;i~;
=~~~~=~ ~;'~;;1;=:~~i'.=.:i=
t OO
Tm
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
Configulation, J. Cryst. Growth, 71, pp.295-304.
6) P.S. Dutta, H.L.Bhat, Vikram Kumar (1995), Numerical
Analysis of Melt-Solid Interface Shapes and Growih Rates of
Gallium Antimonide in a Single-Zone Vertical Bridgman Furnace,
J. Cryst. Growth, 154, pp.213-222.
7) I.Nicoar~, A.Pusztai and M.Nicolov ( 1 997), On the Interface
Shape of Semitransparent Crystals Obtained by the Bridgnlan
Method, Cryst. Res. Technol., 32, pp.413-422.
8) R.S.Feigelson and R.K.Route (1980), Vertical Bridgman
Growth of CdGeAs2 With Control of Interface Shape and
Orientation, J. Cryst. Growth, 49, pp.261-273.
9) R.K.Route, M.Wolf and R.S.Feigelson (1984), Interface
Studies during Vertical Bridgman CdTe Crystal Growih, J. Cryst.
Growih, 70, pp.379-385.
lO) T.W.Clyne (1980), Heat Flow in Controlled Directional
Solidification of Metals, J. Cryst. Growih, 50, pp.684-690.
1 1) T.1.Ejiin W.A.Jesser and A.L.Fripp (1984), Solidification
Behavior of Low and High Thermal Conduct. ivity Materials in a
Bridgnlan-Stockbarger Furnace, J. Cryst. Growih, 69, pp.509-5 14.
12) C.A.Wang, A.F.Witt and J.R.Carruthers (1984), Analysis of
Crystal Growth Characteristics in a Conventional Vertical
Bridgman Configuration, J. Cryst. Growth, 66, pp.299-308.
13) Y.Imashimizu, T.Takahashi, Y.Rikiyama, Y.Wakatsuki and
J.Watanab6 (2002), Estimation of Actual Growth Rate in the
Bridgman Growth of Tin Crystal by Recording the Temeperature-
Time Curves, J. Soc. Mater. Eng. Resour.Jap., 15, pp.21-27.
14) Japan Institute of Metal, Kinzoku D~ta Bukku 3 rd Ed.,
(Maruzen, 1993), pp.1 1, 14, 80.
15) H.S. Lee, J.P. Wilde, R.S. Feigelson(1998), Bridgman
Growih of Strontium Barium Niobate Single Crystals, J. Cryst.
Growth, 187, pp.89-lO1 .
Int. J. Soc. Mater. Eng. Resour. Vol. 1 1 , N0.2, (Sept. 2003)
Akita University