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Study of characteristics of the crystal temperature in a Czochralski puller through experiment and simulation
j........ C R Y S T A L
Journal of Crystal Growth 128 (1993) 275-281 North-Holland
G ROW T H
Study of characteristics of the crystal temperature in a Czochralski puller through experiment and simulation T. Fujiwara, S. I n a m i , S. M i y a h a r a , S. K o b a y a s h i , T. K u b o a n d H. F u j i w a r a Advanced Technology Research Labs., Sumitomo Metal Ind., Ltd., 1-8 Fuso-cho, Amagasaki, Hyogo 660, Japan
The characteristics of the temperature of the 2 inch Si crystal in a CZ puller are studied through experiments and simulations. The mechanism determining the temperature is briefly described. The principal results are: (1) the temperature was fundamentally determined by the distance from the surface of the melt, (2) at the same distance, the temperature at the top portion of the crystal was higher than that at other portions, and (3) for a pull-rate of less than 1 mm/min, the temperature was almost the same as that with zero pull-rate.
1. Introduction The demand for the qualities of a Si crystal grown by Czochralski (CZ) method is getting severe as device density in LSI is increasing. Some of the qualities are point defects and oxygen, and are incorporated in a crystal during the growth in the puller. After annealing, the oxygen in a Si crystal precipitates, and the precipitation causes the formation of stacking faults and dislocations, which are needed for the device process. Even though the precipitation is expected to be uniform along the axial direction of the crystal, it depends on the axial position. One of the reasons for the position-dependence of the precipitation is said to be the thermal history of a crystal in the puller. So far, the measurements or analyses concerning the thermal history, however, are few [1-4], and the history has been studied in detail neither experimentally nor analytically. The temperature measurements of a crystal in a puller are not easy, not practical, and limited to point measurements. Conversely, numerical analysis is practical since the change of the pulling conditions is easy and many trials are possible, suitable for a detailed investigation of the temperature distribution, but the accuracy is not clear. Therefore we study the thermal history, especially the characteristics of a crystal temperature in a CZ puller, through not only measurements but also
simulations. We already developed a mathematical model for CZ crystal growth [5]. The model is based on the assumptions of axial symmetry, diffuse-gray radiation, and conduction dominated heat transfer in the melt. The model (1) includes global radiative heat exchange, (2) is a transient model, and (3) requires only physical properties and complete geometry (self-contained). Here, for a 2 inch Si crystal in the puller, temperature is measured and calculated under both static and dynamic conditions. The mechanism determining the temperature is described.
2. Experiment and simulation The characteristics of the temperature of a Si crystal in the puller are studied through the temperature measurements of a crystal and simulations. The study is made under static and dynamic conditions.
2.1. Equipment The configuration of the puller used for the experiment is shown in fig. la. The puller has a resistive heater, a quartz crucible, insulators and a cooling tube which is placed in the inside of a
0022-0248/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
276
T. Fujiwara et al. / Study of characteristics of crystal temperature in CZ puller
assumptions of axial symmetry, diffuse-gray radiation and conduction dominant heat transfer in the melt. The model includes global and multiple radiative heat exchange, and is a transient one. The configuration and dimensions of the puller for the simulation are almost the same as those for the experiment as shown in fig. lb and table 1. The grids for the simulations are shown in fig. lc.
pull-chamber. Their dimensions are shown in table 1. The crystals used for the experiments are shown in fig. 2. The diameter of the crystal is 50 mm. The axial temperature distribution of the crystals was measured by thermocouples ( P t / P t Rh), which were embedded in the crystal through quartz pipes with 5 mm inner diameter and 8 mm outer diameter as shown in fig. 3. The measuring radial position is the axis of the crystal. Ar is supplied to the chamber with the flow rate, 5 I/min, and is vacuum-pumped to maintain a pressure of 10 Torr. Throughout the experiment, the surface position of melt was kept constant.
3. C o n d i t i o n for experiments and s i m u l a t i o n s
3.1. Static problem 2.2. Simulation
The experiments were made under static conditions, in which the pull-rate was zero. The temperature of the crystal was measured when it
The simulation was made by the global heat transfer model [5]. The model is based on the
pull chamber
cooling tube
/
(a)
cr,sta,
(b)
chamber
(C)
\ lO0(mm)
lO0(mm) quartz crucible
graphite crucible
shield
II
I
~edestal
heater
Fig. I. (a) Configuration of a C Z puller used for the experiment, (b) configuration of a model for the simulation and (c) grids for thc simulation.
1: F,tjiwara et aL / Study of characteristics of crystal temperature in CZ puller
277
Table 1 Dimensions of the model for simulation Radius of crystal Position of surface of melt from base of chamber Radius of pedestal Quartz crucible Radius Height Graphite crucible Radius Thickness Heater Radius Length Heat generation length Position from base of chamber Chamber Radius Height Cooling tube Radius Length Position from base of chamber
0.025 m 0.300 m 0.020 m 0.0753/0.0778 m 0.136 m 0.0865 m 0.0087 m
60
0.0965/0.1075 m 0.270 m 0.180 m 0.085 m Fig. 3. Schematic diagram of a thermocouple embedded in a crystal.
0.202 m 0.565 m 0.040/0.060 m 0.230 m 0.535 m
had lengths of 121, 142, 184, 250 and 300 mm. The bottom of the crystal was touching the melt and a stable meniscus was maintained, namely the growth process with zero pull-rate. Crystal A in fig. 2 was used. The length of the crystal was changed by melting the crystal. Initially, the weights of the crystal and the melt were 1.45 and 1.35 kg, respectively.
325
I
l
31
1 200 25
3.2. Dynamic problem (m)
crystal
A
155
The temperature of the crystal was measured for the different gaps between the bottom of the crystal and the surface of the melt when the crystal was apart from the melt and was stationary, namely the cooling process with zero pullrate. The gaps between the bottom of the crystal and the surface of the melt were 0, 50, 100, 150 and 200 mm. Crystal B in fig. 2 was used. The weights of the crystal and the melt were 1.55 and 1.25 kg, respectively. The heater power was controlled higher than that of the growth process by 1 kW to avoid the solidification of the melt surface. The simulations were also made for the growth and cooling processes under static condition as well as the experiments.
304
crystal B Fig. 2. Crystals used for the experiments. Diameters of the crystals are 50 mm.
The experiments were made under dynamic conditions, in which the pull-rate is not zero. The temperature of the crystal was measured for the different gaps between the bottom of the crystal and the surface of the melt when the crystal was apart from the melt and was transient, namely the cooling process with non-zero pull-rate. After the temperature of the crystal was made stable at the initial position at which the gap was 0 mm, the crystal was moved upward by 200 mm. The
278
T. Fujiwara et aL / Study of characteristicsof crystal temperature in CZ puller
pull-rates were 1, 3 and 6 m m / m i n . The conditions were otherwise the same as those of the cooling process with zero pull-rate. The simulations were also made under dynamic condition as well as the experiments.
1400 v
~. I~ ~.~. ~ "~D , ~
1200
oo 1000
3.3. Transient response
growthprocess length .,xperimenLsi~lati0n 1:300 o A !:250 ~ B 1=184 v C 1:152 o D I =1211 <> g
c001ing process gap experimentsimulatioo g: 0 • F g= 50 • G g=100 • H g=lS0 • I g=200 • J
E" N C / B
800 o
The experiments for the transient response of the temperature were made to find the difference between the dynamic and static conditions in the cooling process more clearly. Initially, the bottom of the crystal was touching the surface of the melt. After the stable condition was attained, the crystal was pulled at constant pull-rate by 200 mm. Then it was stopped. The temperature of the crystal had been measured from the stable condition until it became stationary. The pullrates were 1 and 6 m m / m i n . Crystal B in fig. 2 was used.
4. Result
4.1. Static problem T h e relations b e t w e e n the t e m p e r a t u r e of the crystal a n d the distance from the surface of the melt u n d e r static c o n d i t i o n s for growth a n d cooling processes, o b t a i n e d from the e x p e r i m e n t s a n d simulations, are shown in fig. 4. T h e relations show for both processes that the t e m p e r a t u r e (1) f u n d a m e n t a l l y d e p e n d e d o n the distance, (2) was almost i n d e p e n d e n t of the crystal length or the position in the crystal, n a m e l y top, m i d d l e or b o t t o m portion, a n d (3) was i n d e p e n d e n t of the processes. F o r the same distance, however, the t e m p e r a t u r e at the top p o r t i o n was higher t h a n that at other portions by 50°C for the m e a s u r e m e n t s a n d m o r e for the simulations.
4.2. D y n a m i c problem T h e relations b e t w e e n the t e m p e r a t u r e of the crystal a n d the distance from the surface of the melt u n d e r the d y n a m i c conditions for the cooling process, o b t a i n e d from the e x p e r i m e n t s a n d simulations, are shown in fig. 5. T h e relations show in b o t h e x p e r i m e n t s a n d simulations that (1)
600
400 E
200 0
i
I
,
I
,
I
0 0.2 0.4 0.6 d i s t a n c e from s u r f a c e of melL (m) Fig. 4. Relation between the temperature of the 2 inch crystal and the distance from the surface of the melt in the growth and cooling processes under static conditions (v = 0); v is the pull-rate. Symbols represent the experimental results and curves represent the calculated results. The radial position of the crystal temperature is the axis of the crystal.
the temperature under the dynamic conditions was higher than that under the static conditions for the same distance, and (2) for a pull-rate of 1400v 1200
gap stalk lmm/mi~3mm/min6mm/min •
~ I \
1000
,
expermen~
'
g=lO0
o
• g=200 B C .... g=lO0 A ~ , D smuJauoo g 200 E
A
m
O
•
•
•
B F
C G
D H
800 O
600-
400E
2000
m
I
m
i
m
I
0.2 0.4 0.6 0 d i s t a n c e from s u r f a c e of m e l t (m)
Fig. 5. Relation between the temperature of the 2 inch crystal and the distance from the surface of the melt in the cooling process under the dynamic (v 4=0) and static (v = 0) conditions at the gaps of 100 and 200 mm. v is the pull-rate. The length of the crystal is 345 mm. Symbolsrepresent the experimental results and curves represent the calculated results. The radial position of the crystal temperature is the axis of the crystal.
T. Fujiwara et al. / Study of characteristics of crystal temperature in CZ puller
less than 1 m m / m i n , the difference in the temperature between both conditions was small, but that the difference became larger as the pull-rate was increased.
1400~
(a)
-~ 10001"- -~'---. I
4.3. Transient response The measured t e m p e r a t u r e response is shown in fig. 6. In the case of 6 m m / m i n , it took about 10 min to become stationary after being stopped and the drop of the t e m p e r a t u r e was about 50°C at the top portion of the crystal. When the pullrate was 1 m m / m i n , there was almost no change in the t e m p e r a t u r e before and after being stopped. This result coincided with that found for the dynamic condition in fig. 5.
279
~
stopping
40
---
2o I
0 20 40 60 80 100 120 140 160 180 200 220 240 time (min)
~!
o aa
A C D
el * •
crystal B
5. D i s c u s s i o n
5.1. Characteristics of the temperature of a crystal in the puller The results of experiments and simulations are summarized in table 2 and discussed below. The
0 20 40 60 80 i00 time(mia) Fig. 6. Transient response of the temperature of the 2 inch crystal by stopping of the moving crystal in the cooling process. The pull-rates are (a) 1 mm/min and (b) 6 mm/min. The length of the crystal is 345 mm.
Table 2 Results of experiments and simulations concerning the temperature of the 2 inch crystal in the puller (v is the pull rate) Process
Static conditions (v = 0)
Growth process
Temperature is determined by distance from surface of melt and independent of length in experiments and simulations (fig. 4)
Cooling process
Temperature is determined by distance from surface of melt and independent of position in crystal in experiments and simulations (fig. 4)
Temperature is determined by distance from surface of melt and independent of position in crystal in experiments and simulations (fig. 5)
Temperature at top portion is higher than that at other portions at the same distance in experiments and simulations (fig. 4)
Temperature at top portion is higher than that at other portions at the same distance in experiments and simulations (fig. 5)
Both processes
Dynamic conditions (c ~ 0)
Difference between static and dynamic conditions is negligible for pull-rate of less than 1 mm/min in experiments and simulations (fig. 5) Temperature is independent of processes in experiments and simulations (fig. 4)
T. Fujiwara et al. / Study of characteristics of crystal temperature in CZ puller
280
results of both were the same. The following three points are discussed in more detail below: (1) The temperature of the crystal depends fundamentally on the distance from the melt surface and is independent of the position in the crystal or the length of the crystal. (2) At the same distance, the temperature at the top portion of the crystal is higher than that at other portions when the top of the crystal is located more than 300 mm from the melt surface in the measurement. This effect is more intense in the simulation, since it has a whole axial temperature distribution. (3) At the same distance, the temperature at the bottom portion of the crystal in the cooling process is almost the same as that at other portions, although the bottom of the crystal is partially facing the high-temperature melt. The characteristic length scale for the temperature [6] in the crystal with temperatures higher than 700°C is about 10-50 mm, which is shorter than the crystal length. Therefore the temperature or axial heat flux at the top and bottom surfaces of the crystal cannot determine the temperature in the middle portion of the crystal. This means that the temperature is fundamentally determined by the radiation from the surroundings toward the side surface of the crystal. In fig. 7 the radiation heat flux from the surroundings is shown. The net heat flux at the surface of the
v
0.25 O
,~ 0 . 2 0
fr0mtop surface f heat shield(C)
1 kl'
0 ¢,.)
0.15 0.1{3 0 q~
o
0.05
0
o.oo
1 2 3 4 radiation Loward crystal ( xl06W/m z ) Fig. 7. Radiation heat flux from the surroundings toward the crystal.
f2
(a) f3=fl+fz
(b) f3'=fl
Fig. 8. Flow of the heat near (a) middle and (b) top portions of the crystals at the same distance from the surface of the melt. d: distance from surface of melt; f~: heat flux across top surface; f2: heat flux across side surface; f3, f~, axial heat flux in crystal at distance d.
crystal, the difference between the radiation heat flux toward and that from the surface, is small and usually less than 1% of the radiation heat flux toward the crystal when its temperature is higher than 700°C. Therefore it is said that the temperature of the crystal is balanced with the radiation from the surroundings, which can be thought to be a stable radiation source. Namely, the shortness of the characteristic length and the large radiation heat flux toward the crystal lead to result (1). Fundamentally, the temperature of the crystal is determined by distance, but the temperature of the top portion of the crystal is not determined only by distance because the characteristic length, which becomes longer as the temperature becomes lower, is not negligible. Especially for a distance larger than 300 mm, the length is longer than 70 mm, which is comparable with the crystal length, and then the conduction effect appears. As shown in fig. 8, the axial heat flux at point B, f~, is less than that at point A, f3, due to the heat flux across the side surface, f2. Here, since the cooling tube is located at higher than 235 mm, the effect of the flux f2 is exaggerated for a distance of larger than 235 mm. When the distance is the same, the temperature near the bottom of the crystal is almost the same as that at other portions. One reason for the difference between the bottom and top portions is that the characteristic length is short
T. Fujiwara et al. / Study of characteristics of crystal temperature in CZ puller
enough at the bottom portion, so that there the temperature is determined by the radiation toward the side surface. We have to consider the influence of the radiation toward the bottom surface from the surface of the melt, but it is still under study.
281
1 m m / m i n , the temperature was almost the same as that with zero pull-rate. We plan to investigate the characteristics of the temperature of a crystal with a larger diameter.
References 6. Conclusion
The characteristics of the temperature of a 2 inch Si crystal in a puller were investigated through experiments and simulations, and some knowledge of the mechanism which determines the temperature of the crystal was described. The principal results are: (1) the temperature was fundamentally determined by the distance from the surface of the melt, independent of the crystal length or the position in the crystal, (2) at the same distance, the temperature at the top portion in the crystal was higher than that at other portions, and (3) for a pull-rate of less than
[1] Y. Shimanuki, H. Furuya, I. Suzuki and K. Murai, Japan. J. Appl. Phys. 24 (1985) 1594. [2] S. Shinoyama, M. Hasebe and T. Yamauchi, Oyo Buturi 60 (1991) 766. [3] S. Miyahara, S. Kobayashi, T. Fujiwara, T. Kubo and H. Fujiwara, in: Semiconductor Silicon 1990, Eds. H.R. Huff, K.G. Barraclough and J. Chikawa (Electrochem. Soc., Pennington, NJ, 1990) p. 94. [4] S. Miyahara, S. Kobayashi, T. Fujiwara, T. Kubo and H. Fujiwara, in: Computer Aided Innovation Materials (1991) p. 561. [5] S. Miyahara, S. Kobayashi, T. Fujiwara, T. Kubo and H. Fujiwara, J. Crystal Growth 99 (1990) 696 [6] S. Miyahara, S. Kobayashi, T. Fujiwara, T. Kubo, H. Fujiwara and S. Inami, in: Thermal Engineering '91 (1991) p. 105.
Journal of Crystal Growth 128 (1993) 275-281 North-Holland
G ROW T H
Study of characteristics of the crystal temperature in a Czochralski puller through experiment and simulation T. Fujiwara, S. I n a m i , S. M i y a h a r a , S. K o b a y a s h i , T. K u b o a n d H. F u j i w a r a Advanced Technology Research Labs., Sumitomo Metal Ind., Ltd., 1-8 Fuso-cho, Amagasaki, Hyogo 660, Japan
The characteristics of the temperature of the 2 inch Si crystal in a CZ puller are studied through experiments and simulations. The mechanism determining the temperature is briefly described. The principal results are: (1) the temperature was fundamentally determined by the distance from the surface of the melt, (2) at the same distance, the temperature at the top portion of the crystal was higher than that at other portions, and (3) for a pull-rate of less than 1 mm/min, the temperature was almost the same as that with zero pull-rate.
1. Introduction The demand for the qualities of a Si crystal grown by Czochralski (CZ) method is getting severe as device density in LSI is increasing. Some of the qualities are point defects and oxygen, and are incorporated in a crystal during the growth in the puller. After annealing, the oxygen in a Si crystal precipitates, and the precipitation causes the formation of stacking faults and dislocations, which are needed for the device process. Even though the precipitation is expected to be uniform along the axial direction of the crystal, it depends on the axial position. One of the reasons for the position-dependence of the precipitation is said to be the thermal history of a crystal in the puller. So far, the measurements or analyses concerning the thermal history, however, are few [1-4], and the history has been studied in detail neither experimentally nor analytically. The temperature measurements of a crystal in a puller are not easy, not practical, and limited to point measurements. Conversely, numerical analysis is practical since the change of the pulling conditions is easy and many trials are possible, suitable for a detailed investigation of the temperature distribution, but the accuracy is not clear. Therefore we study the thermal history, especially the characteristics of a crystal temperature in a CZ puller, through not only measurements but also
simulations. We already developed a mathematical model for CZ crystal growth [5]. The model is based on the assumptions of axial symmetry, diffuse-gray radiation, and conduction dominated heat transfer in the melt. The model (1) includes global radiative heat exchange, (2) is a transient model, and (3) requires only physical properties and complete geometry (self-contained). Here, for a 2 inch Si crystal in the puller, temperature is measured and calculated under both static and dynamic conditions. The mechanism determining the temperature is described.
2. Experiment and simulation The characteristics of the temperature of a Si crystal in the puller are studied through the temperature measurements of a crystal and simulations. The study is made under static and dynamic conditions.
2.1. Equipment The configuration of the puller used for the experiment is shown in fig. la. The puller has a resistive heater, a quartz crucible, insulators and a cooling tube which is placed in the inside of a
0022-0248/93/$06.00 © 1993 - Elsevier Science Publishers B.V. All rights reserved
276
T. Fujiwara et al. / Study of characteristics of crystal temperature in CZ puller
assumptions of axial symmetry, diffuse-gray radiation and conduction dominant heat transfer in the melt. The model includes global and multiple radiative heat exchange, and is a transient one. The configuration and dimensions of the puller for the simulation are almost the same as those for the experiment as shown in fig. lb and table 1. The grids for the simulations are shown in fig. lc.
pull-chamber. Their dimensions are shown in table 1. The crystals used for the experiments are shown in fig. 2. The diameter of the crystal is 50 mm. The axial temperature distribution of the crystals was measured by thermocouples ( P t / P t Rh), which were embedded in the crystal through quartz pipes with 5 mm inner diameter and 8 mm outer diameter as shown in fig. 3. The measuring radial position is the axis of the crystal. Ar is supplied to the chamber with the flow rate, 5 I/min, and is vacuum-pumped to maintain a pressure of 10 Torr. Throughout the experiment, the surface position of melt was kept constant.
3. C o n d i t i o n for experiments and s i m u l a t i o n s
3.1. Static problem 2.2. Simulation
The experiments were made under static conditions, in which the pull-rate was zero. The temperature of the crystal was measured when it
The simulation was made by the global heat transfer model [5]. The model is based on the
pull chamber
cooling tube
/
(a)
cr,sta,
(b)
chamber
(C)
\ lO0(mm)
lO0(mm) quartz crucible
graphite crucible
shield
II
I
~edestal
heater
Fig. I. (a) Configuration of a C Z puller used for the experiment, (b) configuration of a model for the simulation and (c) grids for thc simulation.
1: F,tjiwara et aL / Study of characteristics of crystal temperature in CZ puller
277
Table 1 Dimensions of the model for simulation Radius of crystal Position of surface of melt from base of chamber Radius of pedestal Quartz crucible Radius Height Graphite crucible Radius Thickness Heater Radius Length Heat generation length Position from base of chamber Chamber Radius Height Cooling tube Radius Length Position from base of chamber
0.025 m 0.300 m 0.020 m 0.0753/0.0778 m 0.136 m 0.0865 m 0.0087 m
60
0.0965/0.1075 m 0.270 m 0.180 m 0.085 m Fig. 3. Schematic diagram of a thermocouple embedded in a crystal.
0.202 m 0.565 m 0.040/0.060 m 0.230 m 0.535 m
had lengths of 121, 142, 184, 250 and 300 mm. The bottom of the crystal was touching the melt and a stable meniscus was maintained, namely the growth process with zero pull-rate. Crystal A in fig. 2 was used. The length of the crystal was changed by melting the crystal. Initially, the weights of the crystal and the melt were 1.45 and 1.35 kg, respectively.
325
I
l
31
1 200 25
3.2. Dynamic problem (m)
crystal
A
155
The temperature of the crystal was measured for the different gaps between the bottom of the crystal and the surface of the melt when the crystal was apart from the melt and was stationary, namely the cooling process with zero pullrate. The gaps between the bottom of the crystal and the surface of the melt were 0, 50, 100, 150 and 200 mm. Crystal B in fig. 2 was used. The weights of the crystal and the melt were 1.55 and 1.25 kg, respectively. The heater power was controlled higher than that of the growth process by 1 kW to avoid the solidification of the melt surface. The simulations were also made for the growth and cooling processes under static condition as well as the experiments.
304
crystal B Fig. 2. Crystals used for the experiments. Diameters of the crystals are 50 mm.
The experiments were made under dynamic conditions, in which the pull-rate is not zero. The temperature of the crystal was measured for the different gaps between the bottom of the crystal and the surface of the melt when the crystal was apart from the melt and was transient, namely the cooling process with non-zero pull-rate. After the temperature of the crystal was made stable at the initial position at which the gap was 0 mm, the crystal was moved upward by 200 mm. The
278
T. Fujiwara et aL / Study of characteristicsof crystal temperature in CZ puller
pull-rates were 1, 3 and 6 m m / m i n . The conditions were otherwise the same as those of the cooling process with zero pull-rate. The simulations were also made under dynamic condition as well as the experiments.
1400 v
~. I~ ~.~. ~ "~D , ~
1200
oo 1000
3.3. Transient response
growthprocess length .,xperimenLsi~lati0n 1:300 o A !:250 ~ B 1=184 v C 1:152 o D I =1211 <> g
c001ing process gap experimentsimulatioo g: 0 • F g= 50 • G g=100 • H g=lS0 • I g=200 • J
E" N C / B
800 o
The experiments for the transient response of the temperature were made to find the difference between the dynamic and static conditions in the cooling process more clearly. Initially, the bottom of the crystal was touching the surface of the melt. After the stable condition was attained, the crystal was pulled at constant pull-rate by 200 mm. Then it was stopped. The temperature of the crystal had been measured from the stable condition until it became stationary. The pullrates were 1 and 6 m m / m i n . Crystal B in fig. 2 was used.
4. Result
4.1. Static problem T h e relations b e t w e e n the t e m p e r a t u r e of the crystal a n d the distance from the surface of the melt u n d e r static c o n d i t i o n s for growth a n d cooling processes, o b t a i n e d from the e x p e r i m e n t s a n d simulations, are shown in fig. 4. T h e relations show for both processes that the t e m p e r a t u r e (1) f u n d a m e n t a l l y d e p e n d e d o n the distance, (2) was almost i n d e p e n d e n t of the crystal length or the position in the crystal, n a m e l y top, m i d d l e or b o t t o m portion, a n d (3) was i n d e p e n d e n t of the processes. F o r the same distance, however, the t e m p e r a t u r e at the top p o r t i o n was higher t h a n that at other portions by 50°C for the m e a s u r e m e n t s a n d m o r e for the simulations.
4.2. D y n a m i c problem T h e relations b e t w e e n the t e m p e r a t u r e of the crystal a n d the distance from the surface of the melt u n d e r the d y n a m i c conditions for the cooling process, o b t a i n e d from the e x p e r i m e n t s a n d simulations, are shown in fig. 5. T h e relations show in b o t h e x p e r i m e n t s a n d simulations that (1)
600
400 E
200 0
i
I
,
I
,
I
0 0.2 0.4 0.6 d i s t a n c e from s u r f a c e of melL (m) Fig. 4. Relation between the temperature of the 2 inch crystal and the distance from the surface of the melt in the growth and cooling processes under static conditions (v = 0); v is the pull-rate. Symbols represent the experimental results and curves represent the calculated results. The radial position of the crystal temperature is the axis of the crystal.
the temperature under the dynamic conditions was higher than that under the static conditions for the same distance, and (2) for a pull-rate of 1400v 1200
gap stalk lmm/mi~3mm/min6mm/min •
~ I \
1000
,
expermen~
'
g=lO0
o
• g=200 B C .... g=lO0 A ~ , D smuJauoo g 200 E
A
m
O
•
•
•
B F
C G
D H
800 O
600-
400E
2000
m
I
m
i
m
I
0.2 0.4 0.6 0 d i s t a n c e from s u r f a c e of m e l t (m)
Fig. 5. Relation between the temperature of the 2 inch crystal and the distance from the surface of the melt in the cooling process under the dynamic (v 4=0) and static (v = 0) conditions at the gaps of 100 and 200 mm. v is the pull-rate. The length of the crystal is 345 mm. Symbolsrepresent the experimental results and curves represent the calculated results. The radial position of the crystal temperature is the axis of the crystal.
T. Fujiwara et al. / Study of characteristics of crystal temperature in CZ puller
less than 1 m m / m i n , the difference in the temperature between both conditions was small, but that the difference became larger as the pull-rate was increased.
1400~
(a)
-~ 10001"- -~'---. I
4.3. Transient response The measured t e m p e r a t u r e response is shown in fig. 6. In the case of 6 m m / m i n , it took about 10 min to become stationary after being stopped and the drop of the t e m p e r a t u r e was about 50°C at the top portion of the crystal. When the pullrate was 1 m m / m i n , there was almost no change in the t e m p e r a t u r e before and after being stopped. This result coincided with that found for the dynamic condition in fig. 5.
279
~
stopping
40
---
2o I
0 20 40 60 80 100 120 140 160 180 200 220 240 time (min)
~!
o aa
A C D
el * •
crystal B
5. D i s c u s s i o n
5.1. Characteristics of the temperature of a crystal in the puller The results of experiments and simulations are summarized in table 2 and discussed below. The
0 20 40 60 80 i00 time(mia) Fig. 6. Transient response of the temperature of the 2 inch crystal by stopping of the moving crystal in the cooling process. The pull-rates are (a) 1 mm/min and (b) 6 mm/min. The length of the crystal is 345 mm.
Table 2 Results of experiments and simulations concerning the temperature of the 2 inch crystal in the puller (v is the pull rate) Process
Static conditions (v = 0)
Growth process
Temperature is determined by distance from surface of melt and independent of length in experiments and simulations (fig. 4)
Cooling process
Temperature is determined by distance from surface of melt and independent of position in crystal in experiments and simulations (fig. 4)
Temperature is determined by distance from surface of melt and independent of position in crystal in experiments and simulations (fig. 5)
Temperature at top portion is higher than that at other portions at the same distance in experiments and simulations (fig. 4)
Temperature at top portion is higher than that at other portions at the same distance in experiments and simulations (fig. 5)
Both processes
Dynamic conditions (c ~ 0)
Difference between static and dynamic conditions is negligible for pull-rate of less than 1 mm/min in experiments and simulations (fig. 5) Temperature is independent of processes in experiments and simulations (fig. 4)
T. Fujiwara et al. / Study of characteristics of crystal temperature in CZ puller
280
results of both were the same. The following three points are discussed in more detail below: (1) The temperature of the crystal depends fundamentally on the distance from the melt surface and is independent of the position in the crystal or the length of the crystal. (2) At the same distance, the temperature at the top portion of the crystal is higher than that at other portions when the top of the crystal is located more than 300 mm from the melt surface in the measurement. This effect is more intense in the simulation, since it has a whole axial temperature distribution. (3) At the same distance, the temperature at the bottom portion of the crystal in the cooling process is almost the same as that at other portions, although the bottom of the crystal is partially facing the high-temperature melt. The characteristic length scale for the temperature [6] in the crystal with temperatures higher than 700°C is about 10-50 mm, which is shorter than the crystal length. Therefore the temperature or axial heat flux at the top and bottom surfaces of the crystal cannot determine the temperature in the middle portion of the crystal. This means that the temperature is fundamentally determined by the radiation from the surroundings toward the side surface of the crystal. In fig. 7 the radiation heat flux from the surroundings is shown. The net heat flux at the surface of the
v
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,~ 0 . 2 0
fr0mtop surface f heat shield(C)
1 kl'
0 ¢,.)
0.15 0.1{3 0 q~
o
0.05
0
o.oo
1 2 3 4 radiation Loward crystal ( xl06W/m z ) Fig. 7. Radiation heat flux from the surroundings toward the crystal.
f2
(a) f3=fl+fz
(b) f3'=fl
Fig. 8. Flow of the heat near (a) middle and (b) top portions of the crystals at the same distance from the surface of the melt. d: distance from surface of melt; f~: heat flux across top surface; f2: heat flux across side surface; f3, f~, axial heat flux in crystal at distance d.
crystal, the difference between the radiation heat flux toward and that from the surface, is small and usually less than 1% of the radiation heat flux toward the crystal when its temperature is higher than 700°C. Therefore it is said that the temperature of the crystal is balanced with the radiation from the surroundings, which can be thought to be a stable radiation source. Namely, the shortness of the characteristic length and the large radiation heat flux toward the crystal lead to result (1). Fundamentally, the temperature of the crystal is determined by distance, but the temperature of the top portion of the crystal is not determined only by distance because the characteristic length, which becomes longer as the temperature becomes lower, is not negligible. Especially for a distance larger than 300 mm, the length is longer than 70 mm, which is comparable with the crystal length, and then the conduction effect appears. As shown in fig. 8, the axial heat flux at point B, f~, is less than that at point A, f3, due to the heat flux across the side surface, f2. Here, since the cooling tube is located at higher than 235 mm, the effect of the flux f2 is exaggerated for a distance of larger than 235 mm. When the distance is the same, the temperature near the bottom of the crystal is almost the same as that at other portions. One reason for the difference between the bottom and top portions is that the characteristic length is short
T. Fujiwara et al. / Study of characteristics of crystal temperature in CZ puller
enough at the bottom portion, so that there the temperature is determined by the radiation toward the side surface. We have to consider the influence of the radiation toward the bottom surface from the surface of the melt, but it is still under study.
281
1 m m / m i n , the temperature was almost the same as that with zero pull-rate. We plan to investigate the characteristics of the temperature of a crystal with a larger diameter.
References 6. Conclusion
The characteristics of the temperature of a 2 inch Si crystal in a puller were investigated through experiments and simulations, and some knowledge of the mechanism which determines the temperature of the crystal was described. The principal results are: (1) the temperature was fundamentally determined by the distance from the surface of the melt, independent of the crystal length or the position in the crystal, (2) at the same distance, the temperature at the top portion in the crystal was higher than that at other portions, and (3) for a pull-rate of less than
[1] Y. Shimanuki, H. Furuya, I. Suzuki and K. Murai, Japan. J. Appl. Phys. 24 (1985) 1594. [2] S. Shinoyama, M. Hasebe and T. Yamauchi, Oyo Buturi 60 (1991) 766. [3] S. Miyahara, S. Kobayashi, T. Fujiwara, T. Kubo and H. Fujiwara, in: Semiconductor Silicon 1990, Eds. H.R. Huff, K.G. Barraclough and J. Chikawa (Electrochem. Soc., Pennington, NJ, 1990) p. 94. [4] S. Miyahara, S. Kobayashi, T. Fujiwara, T. Kubo and H. Fujiwara, in: Computer Aided Innovation Materials (1991) p. 561. [5] S. Miyahara, S. Kobayashi, T. Fujiwara, T. Kubo and H. Fujiwara, J. Crystal Growth 99 (1990) 696 [6] S. Miyahara, S. Kobayashi, T. Fujiwara, T. Kubo, H. Fujiwara and S. Inami, in: Thermal Engineering '91 (1991) p. 105.