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Diffusion-controlled distribution of solute in Sn-1% Bi specimens solidified by the submerged heater method
950
Journal of Crystal Growth 110 (1991) 950—954 North-Holland
Letter to the Editors
Diffusion-controlled distribution of solute in Sn—i % Bi specimens solidified by the submerged heater method Aleksandar G. Ostrogorsky Mechanical Engineering Department, Columbia University, New York, New York 10027, USA
Frank Mosel Institur für Werkstoffwissenschaften VI, Universität Er/angen-Nurnberg, W-8520 Er/angen, Germany
and Michael T. Schmidt Microelectronics Sciences Laboratories, Columbia University, New York, New York 10027, USA
Received 4 September 1990; manuscript received in final form 24 October 1990
Two 1.35 kg, 5.8 cm diameter Sn—1%Bi specimens were solidified using the submerged heater method (SHM). The distribution of solute was found to be uniform axially, indicating that diffusion-controlled steady-state segregation, though to be unattainable on earth because of the gravity induced interference, was achieved.
In all currently preferred methods for crystal growth from the melt (e.g. Czochralski, Bridgman, zone melting), the solidification process is carried on inside of tube-type furnaces. The heat is supplied to the melt radially inwards, through the crucible wall, inducing radial temperature gradients in the melt and the growing crystal. It is established that radial temperature gradients: (a) promote longitudinal macroscopic segregation, caused by convective mixing in the melt [1]; (b) result in nonplanar solid—liquid interfaces [1,2]; (c) induce thermal stresses and dislocations in the growing crystal [3], and upon exceeding a critical value; (d) drive the unsteady natural convection causing microscopic inhomogeneities in the crystal [1]. Because most of the heat is supplied radially, conservation of energy implies that on average radial and axial temperature gradients in the melt 0022-0248/91/$03.50 © 1991
—
have the same order of magnitude. Reduction of radial temperature gradients results in reduction of the total amount of heat flowing through the melt and the growth interface, weakening the desirable axial temperature gradient normal to the growth interface. Bourret et al. performed an evaluation of a multizone Mellen furnace in a horizontal configuration [4]. A specially designed quartz ampule, with thermocouples located at the center of the ampule, allowed an estimate of temperature gradients in the melt and the crystal during the growth process. Axial temperature gradients, measured just 2 mm above the GaAs melt and crystal were in the range 3 to 7 K/cm. Radial temperature gradients above the melt were between 1.1 to 2.5 K/cm. They observed improvement of crystalline perfection by increasing the axial temperature gradient over the solid and decreasing the radial
Elsevier Science Publishers B.V. (North-Holland)
A. G. Ostrogorsky et al.
/
temperature gradient over the melt. When axial and radial gradients were about equal, single crystallinity could not be sustained: grains of random orientation nucleated on the top of the melt, The recently proposed submerged heater method (SHM) utilizes axial heat supply [5]. Numerical simulations indicated that one-dimensional, close-to-purely axial heat flux can be established within the melt [6]. In this letter we explore a simplified version of the SHM: we used a dummy (i.e. unpowered) submerged heater to solidify specimens of Sn— 1%Bi alloy Utech et al performed solidification of Sn—1%Bi specimens by withdrawing a horizontal boat from a tubular furnace and reported a distribution coefficient, k 0.35 [7]. Unsteady thermal convection controlled the distribution of solute atoms. Niawa et al. performed extensive measurements of the diffusion coefficient of bismuth in tin [8]. A schematic diagram of the experimental setup is shown in fig. 1. The melt of the material to be solidified is held in a bottom seeded crucible. The heat is supplied to the melt axially-downward by the top axial heater. In the interest of simplicity, an unpowered graphite member was used as dummy submerged heater. The submerged heater divides the melt into the top melt located above the heater and the enclosed melt located below the heater. The melt is solidified by lowering the crucible, The heaters (including the submerged dummy heater) and the insulation remain at a fixed position. While the crucible is lowered, the large top melt provides a liquid feed of a constant composition to the small enclosed melt. The melt solidifies at a small constant distance H below the bottom surface of the submerged heater. Assuming a constant axial temperature gradient 0T/3z in the submerged melt, the distance H is equal to H
— —
T~ Tm 3T/3z
~
—
‘
951
Diffusion-controlled distribution of solute in Sn—i %Bi
‘
/
where Tm is the melting point of the charge. For a constant temperature of the submerged heater (i.e.
TC 2
TC 1
top heater
•s.
L~!~I
crucible top melt
:
uard ~eater
enclosed melt
~: :
dummy submerged heater
solidified specimen
SUpport pedestal
water cooled shaft Fig. 1. Schematic of directional solidification by the SHM [61 using a dummy submerged heater.
constant TSH Tm), H depends only on the axial temperature gradient in the enclosed melt. The hot zone is insulated radially and from above. A tube-type guard heater is placed around the enclosed melt to control the radial heat flow. When the temperature of the guard heater is higher than the temperature of the enclosed melt, the heat flows radially inwards resulting in convex isotherms [61. For zero radial heat flow, the isotherms are flat, including the isotherm defining the solid liquid interface. The heat is extracted from the growing crystal axially downward, —
through graphite support pedestal, attached to the wateracooled shaft. An annular gap between the crucible wall and the submerged heater interconnects the top and the enclosed melt. We found that a gap of S 0.03 —
952
A. G. Ostrogorsky et aL
/ Diffusion-controlled
cm was sufficient to allow a smooth liquid feed with downward velocity, “feed
=
R Acrystai/A&
—
50J’~,
Growth was induced by withdrawing the crucible at J’~ 4.17 X iO~cm/s (the same rate as in ref. [7]). =
(2)
where l’~is the rate of lowering the crucible, and Acrystai and A
8 are the cross sectional areas of the specimen and the annular gap respectively. Vfeed prevents back diffusion and allows implementation of zone leveling techniques. For example, to pursue the Starting Charge Only procedure [9], al the solute is placed below the submerged heater while the top melt is pure. Two specimens were solidified in the following manner: a 1350 g Sn—1%Bi charge was loaded into a 5.8 cm ID graphite crucible. The crucible tapers down to a 0.5 cm ID seed well. No seed was used. The submerged heater (unpowered) was held above the charge during melting to allow convective mixing yielding uniform distribution of Bi throughout the melt. After melting, the heater was submerged and rapidly up the and top down further enhancemoved mixing between andtothe enclosed melt. This was done in order to prevent zone leveling effects. Finally, the heater was fixed several millimeters above the lowest position in the crucible, The axial temperature gradient in the melt, measured using movable Chromel—Alumel thermocouples, was found to be 8T/0z 10 K/cm. The temperature of the submerged heater was measured using two Chromel—Alumel thermocouples TC1 and TC2, located at the centerline and at the outer edge of the lower heater surface respec-
tively. The temperature of the top heater was slowly reduced to bring the TC1 (i.e. the submerged heater) to 10 K above the solidification point of the tin. Using eq. (1), one can estimate that the height of the enclosed melt decreased to H 1 cm; solidification was initiated in the seed—well region. The temperature of the guard heater was readjusted to minimize the temperature difference between TC1 and TC2. We readily achieved TTC
2 TTCI
distribution of solute in Sn—i %Bi
—
0,5 K. During growth, the temperatures of the top and the guard heater were held constant via PID controllers.
Measurements performed using a sensitive 0.5 mm inconel sheath Chromel-Alumel thermocouple confirmed that the temperature field in the melt is steady. During solidification TTc2 TTci remained equal to 0.5 K, corresponding to aT/ar 0.1 to 0.2 K/cm. The ratio between the axial and the radial temperature gradients was equal to —
—
G ratio
aT/az =
=
so
aT/ar
The dimensionless Rayleigh number reveals the relative importance of buoyancy and viscous forces in a melt. Rayleigh number of the enclosed melt, based on the axial temperature gradient 8T/8z 10 K/cm depends strongly on H [cm]: 3g (8T/0z ) H’~Pr 2000H4. Ra axial 1 V2 Because the heat flows axially-downward the enclosed melt is stratified. The Rayleigh number based on the axial temperature gradient opposes the flow in the enclosed melt. In the presence of gravity, horizontal temperature gradients (generated by radial heating or cooling) always produce convective motion in the melt [1]. The Rayleigh number based on the radial temperature gradient (driving the flow) is equal to =
Raradja,
/3g(aT/ar)H4
Raaxia,
Pr~
=40H4. Gratio
During growth, as the crucible was withdrawn away from the top heater, the temperature of the unpowered submerged heater slowly decreased, Based on eq. (1), the height of the enclosed melt must also have decreased, No attempt was made to stop this change by increasing the temperature of the top heater. In experiments performed using a powered submerged heater (not reported here), this change did not develop. Toward the end of the solidification, TTCI approached the solidification temperature Tm. Table 1 shows the values of
A. G. Ostrogorsky et aL
/
Diffusion-controlled distribution of solute in Sn—i %Bi
Table 1 Change of the height H, Raaxiai and Raradial as a function of the heater temperature TTCI, at selected locations x; H estimated based on eq. (1) TTCi — (K)
x (cm)
Tm
10 5
2
—
—0
H
Ra~ai
Raraaiai
(cm)
—
—
2000
40 3.1 0.08
0.5 to 3.5 4.5 5.5
1 0.5 0.2
6to6.5
—
125 3.2 0
953
that of decreasing the gravitational acceleration to iO~of earth gravity. The first-to-freeze 6 cm of both specimens were comprised of several large grains. The last 1.5 cm of the specimens were polycrystalline perhaps, because of a proximity or contact between the specimen and the submerged heater. Fig. 2 shows the concentration of Bi along the axis of specimen 1 and specimen 2 together with the theoretical profiles computed assuming complete mixing [9],
0
k—I
H, Raaxjai and Raradja, as a function of the heater
temperature TTCI, at selected locations x. Without the submerged heater, the height of the melt would have been 7 cm. The submerged heater reduces the active height of the melt for approximately one order of magnitude, compared to configuration without the submerged heater. As a result, both Rayleigh numbers are reduced for a factor of iQ~.Furthermore, due to axial heat supply, radial temperature gradients in the enclosed melt are very low, reducing the horizontal Rayleigh number (which contributes buoyancy forces driving the flow) for another order of magnitude compared the vertical (YB) configuration. Thistoimplies that theBndgman ratio between buoyancy forces and viscous forces is reduced for a factor of io~,a reduction which is compatible to —
—
_______________________________ 10 diffusion controlled
•~ 1
A
D IC
/
~ specimen A specimen 2I
complete mixing
0.1
•
0
2
4
6
0 k(1 g) (3) and assuming diffusion controlled segregation [10], =
—
,
( (4) Co where C0 is the initial concentration of the solute in the melt; C5(g) is the concentration in the solid at the location where a fraction g of the melt is solidified; C5(x) is the concentration in the solid at distance x measured from the beginning of the specimen; k is the equilibrium distribution coefficient, D is the diffusion coefficient of the solute in the melt and R is the growth rate. For Sn—1%Bi 2/s at alloy 571 K k[8]. 0.35 [7] and D 1.6 X 10~ cm The axial concentration in the specimens shown in fig. 2 was measured using the inductively coupled plasma (ICP) method, with an accuracy of 1% of the measured concentration. In both specimens, the axial distribution of the solute follows the line computed assuming pure diffusive transport in the melt, indicating that diffusion-controlled segregation was achieved. Because of the Cs x) =k+ (1 _k)[1 _exp(_k~x)J,
=
=
is reached rapidly. The effective distribution coef-
£
___________
U
C~(g)/C
8
Distance [cm] Fig. 2. Axial concentration of Bi in two Sn—1%Bi specimens plotted versus solidification distance. The theoretical curves are computed assuming complete 2/smixing, [5]; k —and 0.35diffusion [4]. control. D = 1.6X 10 cm
ficient low diffusion computed coefficient, using eq. (4), steady-state is keff = Csegregation 0.9 at x = 0,2, This explains the achievement of steady-state segregation in the 0.5 cm 5/C0 long =seed well, During growth in the conical region (0.5
954
/ Diffusion-controlled distribution
A. G. Ostrogorsky et aL
2
of solute in Sn—i %Bi
crystals. Our experiments performed using a dummy submerged heater indicate that: for the first time in the presence of gravity, diffusion-controlled steady-state segregation was achieved in large specimens; radial and axial temperature gradients are uncoupled, i.e. can be adjusted independently; aT/ar 0,1 K/cm and aT/az 10 K/cm is readily achieved; the temperature field in the melt is steady; the desired shape of the growth interface is obtained by setting the temperature of the guard heater; the control strategy is simple: the heaters can be kept at a constant temperature during growth. Because of keff = 1, SHM can be effective for growth of ternary compounds and alloys with large separation between solidus and liquidus lines. For systems having k << 1, the Starting Charge Only procedure can be used to reduce the initial transient time. To ensure diffusion-controlled segregation, the growth interface should be kept 0,2 to 0.8 cm below the submerged heater. —
i
.
~
~‘
—
—
U
ft
I
,~
~
,,
~
Radial distance r[cm] Fig. 3. Radial concentration of Bi, 2.0 cm from the beginning of specimen 2.
by relatively large melt height and volume (Ra radjal 40). The nonuniform radial distribution of Bi at x = 2 cm, shown in fig. 3, provides further evidence of convective interference. The radial distribution of Bi was measured by Auger spectroscopy with a peak-to-peak accuracy of ±10% of the measured concentration. At x 4.5 cm, the height of the enclosed melt decreased to H = 0.5 cm yielding Raradlal = 3.1. As a result, kett = 1, while the radial distribution of solute, 4,0 cm from the beginning of specimen 2, is uniform (fig. 4). For x > 4.5 cm, keff remains exactly one in both specimens, For H = 0.4 cm, Raradja, is reduced for six orders of magnitudes. SHM offers a unique, axial heat transfer environment suitable for growth of large single
—
—
The authors wish to express their appreciation to Dipl. Ing. D. Hofmann of the University of Erlangen—Nurnberg for valuable discussions and for suggesting the use of the unpowered submerged heater.
References [1] D.E. Holmes and H.C. Gatos, J. Electrochemical Soc. 128
2. ______________________________
(1981) 429. [2] C.J. Chang and R.A. Brown, J. Crystal Growth 63 (1983) 343. [3] A.S. Jordan, A.R. Von Neida and R. Caruso, Growth 76 (1986) 243.
J.
Crystal
[4] E.D. Bourret, J.B. Guitron and E.E. Haller, J. Crystal ‘~
1
-
.
Growth 85 (1987) 124. [5] AG. Ostrogorsky, US Patent Application S.N. 397,741
.
1~
C
C)
o’
_______________________________
-2.8
0.0
2.8
Radial distance r[cm] Fig. 4. Radial concentration of Bi, 4.0 cm from the beginning of specimen 2.
(1989). [6] A.G. Ostrogorsky, J. Crystal Growth 104 (1990) 233. [7] H.P. Utech, W.S. Brower and J.G. Early, in: Crystal Growth, Ed. H.S. Peiser (Pergamon, Oxford,1967). [8] K. Niwa, M. Shimoji, S. Kado, Y. Watanabe and T. Yokokawa, Trans. AIME 209 (1957) 96.
[9] W.G. Pfann, Zone Melting (Wiley, New York, 1966). [10] W.A. Tiller, K.A. Jackson, J.W. Rutter and B. Chalmers, Acta Met. 1 (1953) 428.
Journal of Crystal Growth 110 (1991) 950—954 North-Holland
Letter to the Editors
Diffusion-controlled distribution of solute in Sn—i % Bi specimens solidified by the submerged heater method Aleksandar G. Ostrogorsky Mechanical Engineering Department, Columbia University, New York, New York 10027, USA
Frank Mosel Institur für Werkstoffwissenschaften VI, Universität Er/angen-Nurnberg, W-8520 Er/angen, Germany
and Michael T. Schmidt Microelectronics Sciences Laboratories, Columbia University, New York, New York 10027, USA
Received 4 September 1990; manuscript received in final form 24 October 1990
Two 1.35 kg, 5.8 cm diameter Sn—1%Bi specimens were solidified using the submerged heater method (SHM). The distribution of solute was found to be uniform axially, indicating that diffusion-controlled steady-state segregation, though to be unattainable on earth because of the gravity induced interference, was achieved.
In all currently preferred methods for crystal growth from the melt (e.g. Czochralski, Bridgman, zone melting), the solidification process is carried on inside of tube-type furnaces. The heat is supplied to the melt radially inwards, through the crucible wall, inducing radial temperature gradients in the melt and the growing crystal. It is established that radial temperature gradients: (a) promote longitudinal macroscopic segregation, caused by convective mixing in the melt [1]; (b) result in nonplanar solid—liquid interfaces [1,2]; (c) induce thermal stresses and dislocations in the growing crystal [3], and upon exceeding a critical value; (d) drive the unsteady natural convection causing microscopic inhomogeneities in the crystal [1]. Because most of the heat is supplied radially, conservation of energy implies that on average radial and axial temperature gradients in the melt 0022-0248/91/$03.50 © 1991
—
have the same order of magnitude. Reduction of radial temperature gradients results in reduction of the total amount of heat flowing through the melt and the growth interface, weakening the desirable axial temperature gradient normal to the growth interface. Bourret et al. performed an evaluation of a multizone Mellen furnace in a horizontal configuration [4]. A specially designed quartz ampule, with thermocouples located at the center of the ampule, allowed an estimate of temperature gradients in the melt and the crystal during the growth process. Axial temperature gradients, measured just 2 mm above the GaAs melt and crystal were in the range 3 to 7 K/cm. Radial temperature gradients above the melt were between 1.1 to 2.5 K/cm. They observed improvement of crystalline perfection by increasing the axial temperature gradient over the solid and decreasing the radial
Elsevier Science Publishers B.V. (North-Holland)
A. G. Ostrogorsky et al.
/
temperature gradient over the melt. When axial and radial gradients were about equal, single crystallinity could not be sustained: grains of random orientation nucleated on the top of the melt, The recently proposed submerged heater method (SHM) utilizes axial heat supply [5]. Numerical simulations indicated that one-dimensional, close-to-purely axial heat flux can be established within the melt [6]. In this letter we explore a simplified version of the SHM: we used a dummy (i.e. unpowered) submerged heater to solidify specimens of Sn— 1%Bi alloy Utech et al performed solidification of Sn—1%Bi specimens by withdrawing a horizontal boat from a tubular furnace and reported a distribution coefficient, k 0.35 [7]. Unsteady thermal convection controlled the distribution of solute atoms. Niawa et al. performed extensive measurements of the diffusion coefficient of bismuth in tin [8]. A schematic diagram of the experimental setup is shown in fig. 1. The melt of the material to be solidified is held in a bottom seeded crucible. The heat is supplied to the melt axially-downward by the top axial heater. In the interest of simplicity, an unpowered graphite member was used as dummy submerged heater. The submerged heater divides the melt into the top melt located above the heater and the enclosed melt located below the heater. The melt is solidified by lowering the crucible, The heaters (including the submerged dummy heater) and the insulation remain at a fixed position. While the crucible is lowered, the large top melt provides a liquid feed of a constant composition to the small enclosed melt. The melt solidifies at a small constant distance H below the bottom surface of the submerged heater. Assuming a constant axial temperature gradient 0T/3z in the submerged melt, the distance H is equal to H
— —
T~ Tm 3T/3z
~
—
‘
951
Diffusion-controlled distribution of solute in Sn—i %Bi
‘
/
where Tm is the melting point of the charge. For a constant temperature of the submerged heater (i.e.
TC 2
TC 1
top heater
•s.
L~!~I
crucible top melt
:
uard ~eater
enclosed melt
~: :
dummy submerged heater
solidified specimen
SUpport pedestal
water cooled shaft Fig. 1. Schematic of directional solidification by the SHM [61 using a dummy submerged heater.
constant TSH Tm), H depends only on the axial temperature gradient in the enclosed melt. The hot zone is insulated radially and from above. A tube-type guard heater is placed around the enclosed melt to control the radial heat flow. When the temperature of the guard heater is higher than the temperature of the enclosed melt, the heat flows radially inwards resulting in convex isotherms [61. For zero radial heat flow, the isotherms are flat, including the isotherm defining the solid liquid interface. The heat is extracted from the growing crystal axially downward, —
through graphite support pedestal, attached to the wateracooled shaft. An annular gap between the crucible wall and the submerged heater interconnects the top and the enclosed melt. We found that a gap of S 0.03 —
952
A. G. Ostrogorsky et aL
/ Diffusion-controlled
cm was sufficient to allow a smooth liquid feed with downward velocity, “feed
=
R Acrystai/A&
—
50J’~,
Growth was induced by withdrawing the crucible at J’~ 4.17 X iO~cm/s (the same rate as in ref. [7]). =
(2)
where l’~is the rate of lowering the crucible, and Acrystai and A
8 are the cross sectional areas of the specimen and the annular gap respectively. Vfeed prevents back diffusion and allows implementation of zone leveling techniques. For example, to pursue the Starting Charge Only procedure [9], al the solute is placed below the submerged heater while the top melt is pure. Two specimens were solidified in the following manner: a 1350 g Sn—1%Bi charge was loaded into a 5.8 cm ID graphite crucible. The crucible tapers down to a 0.5 cm ID seed well. No seed was used. The submerged heater (unpowered) was held above the charge during melting to allow convective mixing yielding uniform distribution of Bi throughout the melt. After melting, the heater was submerged and rapidly up the and top down further enhancemoved mixing between andtothe enclosed melt. This was done in order to prevent zone leveling effects. Finally, the heater was fixed several millimeters above the lowest position in the crucible, The axial temperature gradient in the melt, measured using movable Chromel—Alumel thermocouples, was found to be 8T/0z 10 K/cm. The temperature of the submerged heater was measured using two Chromel—Alumel thermocouples TC1 and TC2, located at the centerline and at the outer edge of the lower heater surface respec-
tively. The temperature of the top heater was slowly reduced to bring the TC1 (i.e. the submerged heater) to 10 K above the solidification point of the tin. Using eq. (1), one can estimate that the height of the enclosed melt decreased to H 1 cm; solidification was initiated in the seed—well region. The temperature of the guard heater was readjusted to minimize the temperature difference between TC1 and TC2. We readily achieved TTC
2 TTCI
distribution of solute in Sn—i %Bi
—
0,5 K. During growth, the temperatures of the top and the guard heater were held constant via PID controllers.
Measurements performed using a sensitive 0.5 mm inconel sheath Chromel-Alumel thermocouple confirmed that the temperature field in the melt is steady. During solidification TTc2 TTci remained equal to 0.5 K, corresponding to aT/ar 0.1 to 0.2 K/cm. The ratio between the axial and the radial temperature gradients was equal to —
—
G ratio
aT/az =
=
so
aT/ar
The dimensionless Rayleigh number reveals the relative importance of buoyancy and viscous forces in a melt. Rayleigh number of the enclosed melt, based on the axial temperature gradient 8T/8z 10 K/cm depends strongly on H [cm]: 3g (8T/0z ) H’~Pr 2000H4. Ra axial 1 V2 Because the heat flows axially-downward the enclosed melt is stratified. The Rayleigh number based on the axial temperature gradient opposes the flow in the enclosed melt. In the presence of gravity, horizontal temperature gradients (generated by radial heating or cooling) always produce convective motion in the melt [1]. The Rayleigh number based on the radial temperature gradient (driving the flow) is equal to =
Raradja,
/3g(aT/ar)H4
Raaxia,
Pr~
=40H4. Gratio
During growth, as the crucible was withdrawn away from the top heater, the temperature of the unpowered submerged heater slowly decreased, Based on eq. (1), the height of the enclosed melt must also have decreased, No attempt was made to stop this change by increasing the temperature of the top heater. In experiments performed using a powered submerged heater (not reported here), this change did not develop. Toward the end of the solidification, TTCI approached the solidification temperature Tm. Table 1 shows the values of
A. G. Ostrogorsky et aL
/
Diffusion-controlled distribution of solute in Sn—i %Bi
Table 1 Change of the height H, Raaxiai and Raradial as a function of the heater temperature TTCI, at selected locations x; H estimated based on eq. (1) TTCi — (K)
x (cm)
Tm
10 5
2
—
—0
H
Ra~ai
Raraaiai
(cm)
—
—
2000
40 3.1 0.08
0.5 to 3.5 4.5 5.5
1 0.5 0.2
6to6.5
—
125 3.2 0
953
that of decreasing the gravitational acceleration to iO~of earth gravity. The first-to-freeze 6 cm of both specimens were comprised of several large grains. The last 1.5 cm of the specimens were polycrystalline perhaps, because of a proximity or contact between the specimen and the submerged heater. Fig. 2 shows the concentration of Bi along the axis of specimen 1 and specimen 2 together with the theoretical profiles computed assuming complete mixing [9],
0
k—I
H, Raaxjai and Raradja, as a function of the heater
temperature TTCI, at selected locations x. Without the submerged heater, the height of the melt would have been 7 cm. The submerged heater reduces the active height of the melt for approximately one order of magnitude, compared to configuration without the submerged heater. As a result, both Rayleigh numbers are reduced for a factor of iQ~.Furthermore, due to axial heat supply, radial temperature gradients in the enclosed melt are very low, reducing the horizontal Rayleigh number (which contributes buoyancy forces driving the flow) for another order of magnitude compared the vertical (YB) configuration. Thistoimplies that theBndgman ratio between buoyancy forces and viscous forces is reduced for a factor of io~,a reduction which is compatible to —
—
_______________________________ 10 diffusion controlled
•~ 1
A
D IC
/
~ specimen A specimen 2I
complete mixing
0.1
•
0
2
4
6
0 k(1 g) (3) and assuming diffusion controlled segregation [10], =
—
,
( (4) Co where C0 is the initial concentration of the solute in the melt; C5(g) is the concentration in the solid at the location where a fraction g of the melt is solidified; C5(x) is the concentration in the solid at distance x measured from the beginning of the specimen; k is the equilibrium distribution coefficient, D is the diffusion coefficient of the solute in the melt and R is the growth rate. For Sn—1%Bi 2/s at alloy 571 K k[8]. 0.35 [7] and D 1.6 X 10~ cm The axial concentration in the specimens shown in fig. 2 was measured using the inductively coupled plasma (ICP) method, with an accuracy of 1% of the measured concentration. In both specimens, the axial distribution of the solute follows the line computed assuming pure diffusive transport in the melt, indicating that diffusion-controlled segregation was achieved. Because of the Cs x) =k+ (1 _k)[1 _exp(_k~x)J,
=
=
is reached rapidly. The effective distribution coef-
£
___________
U
C~(g)/C
8
Distance [cm] Fig. 2. Axial concentration of Bi in two Sn—1%Bi specimens plotted versus solidification distance. The theoretical curves are computed assuming complete 2/smixing, [5]; k —and 0.35diffusion [4]. control. D = 1.6X 10 cm
ficient low diffusion computed coefficient, using eq. (4), steady-state is keff = Csegregation 0.9 at x = 0,2, This explains the achievement of steady-state segregation in the 0.5 cm 5/C0 long =seed well, During growth in the conical region (0.5
954
/ Diffusion-controlled distribution
A. G. Ostrogorsky et aL
2
of solute in Sn—i %Bi
crystals. Our experiments performed using a dummy submerged heater indicate that: for the first time in the presence of gravity, diffusion-controlled steady-state segregation was achieved in large specimens; radial and axial temperature gradients are uncoupled, i.e. can be adjusted independently; aT/ar 0,1 K/cm and aT/az 10 K/cm is readily achieved; the temperature field in the melt is steady; the desired shape of the growth interface is obtained by setting the temperature of the guard heater; the control strategy is simple: the heaters can be kept at a constant temperature during growth. Because of keff = 1, SHM can be effective for growth of ternary compounds and alloys with large separation between solidus and liquidus lines. For systems having k << 1, the Starting Charge Only procedure can be used to reduce the initial transient time. To ensure diffusion-controlled segregation, the growth interface should be kept 0,2 to 0.8 cm below the submerged heater. —
i
.
~
~‘
—
—
U
ft
I
,~
~
,,
~
Radial distance r[cm] Fig. 3. Radial concentration of Bi, 2.0 cm from the beginning of specimen 2.
by relatively large melt height and volume (Ra radjal 40). The nonuniform radial distribution of Bi at x = 2 cm, shown in fig. 3, provides further evidence of convective interference. The radial distribution of Bi was measured by Auger spectroscopy with a peak-to-peak accuracy of ±10% of the measured concentration. At x 4.5 cm, the height of the enclosed melt decreased to H = 0.5 cm yielding Raradlal = 3.1. As a result, kett = 1, while the radial distribution of solute, 4,0 cm from the beginning of specimen 2, is uniform (fig. 4). For x > 4.5 cm, keff remains exactly one in both specimens, For H = 0.4 cm, Raradja, is reduced for six orders of magnitudes. SHM offers a unique, axial heat transfer environment suitable for growth of large single
—
—
The authors wish to express their appreciation to Dipl. Ing. D. Hofmann of the University of Erlangen—Nurnberg for valuable discussions and for suggesting the use of the unpowered submerged heater.
References [1] D.E. Holmes and H.C. Gatos, J. Electrochemical Soc. 128
2. ______________________________
(1981) 429. [2] C.J. Chang and R.A. Brown, J. Crystal Growth 63 (1983) 343. [3] A.S. Jordan, A.R. Von Neida and R. Caruso, Growth 76 (1986) 243.
J.
Crystal
[4] E.D. Bourret, J.B. Guitron and E.E. Haller, J. Crystal ‘~
1
-
.
Growth 85 (1987) 124. [5] AG. Ostrogorsky, US Patent Application S.N. 397,741
.
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-2.8
0.0
2.8
Radial distance r[cm] Fig. 4. Radial concentration of Bi, 4.0 cm from the beginning of specimen 2.
(1989). [6] A.G. Ostrogorsky, J. Crystal Growth 104 (1990) 233. [7] H.P. Utech, W.S. Brower and J.G. Early, in: Crystal Growth, Ed. H.S. Peiser (Pergamon, Oxford,1967). [8] K. Niwa, M. Shimoji, S. Kado, Y. Watanabe and T. Yokokawa, Trans. AIME 209 (1957) 96.
[9] W.G. Pfann, Zone Melting (Wiley, New York, 1966). [10] W.A. Tiller, K.A. Jackson, J.W. Rutter and B. Chalmers, Acta Met. 1 (1953) 428.