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Imaging of convection in a Czochralski crucible under ultrasound waves
ARTICLE IN PRESS
Journal of Crystal Growth 257 (2003) 237–244
Imaging of convection in a Czochralski crucible under ultrasound waves G.N. Kozhemyakin* Laboratory of Crystal Growth, Department of Applied Materials The V. Dal Eastern Ukrainian National University, Bl. Molodezhniy, 20A, Lugansk 91034, Ukraine Received 31 March 2003; accepted 28 May 2003 Communicated by M. Schieber
Abstract The influence of ultrasound on natural and forced convection in a Czochralski crucible was investigated experimentally. We present a method for simulation of ultrasound influence on convection in the melt during Czochralski growth. Distilled water is used as model fluid contained in a stainless-steel crucible with two glass windows. An aluminum cylinder is used to simulate the growing crystal. Flow and standing waves visualization and flow velocity measurements were performed. We report the flow patterns observed under ultrasound influence at frequencies of 0.6 and 1.25 MHz in the fluid for different conditions: temperature difference, cylinder rotation and fluid depth. r 2003 Elsevier B.V. All rights reserved. PACS: 47.27.T; 81.10; 61.72; 43.35; 43.20.K Keywords: A1. Convection; A1. Fluid flows; A1. Growth models; A2. Czochralski method; A2. Seed crystals; B2. Semiconducting III–V materials
1. Introduction The application of ultrasound to Czochralski process is a useful tool to decrease the components inhomogeneity in semiconductors single crystals. There have been reports on impurity segregation in Czochralski crystal growth in ultrasound field such as doping striations in the grown crystals. Detailed investigations of the effect of ultrasound with a frequency of 10 kHz and power of 120 W on the growth morphology in InSb and InxGa1xSb *Tel.: +38-0642-517-924; fax: +380-642-461-364. E-mail address: [email protected] (G.N. Kozhemyakin).
single crystals were conducted by Hayakawa et al. [1–7]. The introduction of ultrasonic vibrations into the melt through the carbon crucible during growth changed the crystal diameter, the width of the facet region and appearance of large voids, with an increase of the output power to 120 W. The effect of the striations, which decrease in number and disappear in the central part of InSb, GaAs and BiSb alloys pulled single crystals, was studied and reported in a few publications of our group [8–11]. Only in these experiments ultrasonic waves at frequencies of 0.15, 0.25, 0.6, 1.2, 2.5, 5 and 10 MHz were introduced into the melt through a quartz waveguide, fused to the bottom
0022-0248/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0022-0248(03)01459-3
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of the quartz crucible. We supposed that ultrasonic standing waves might influence the flow patterns in the melts and reduce the striations in the growing crystals [9]. However, this model of ultrasound influence on the disappearance of the striations is not a clear evidence. It is known that the occurrence of dopant inhomogeneities is affected by the flow patterns in the melt during the crystal growth process [12–15]. Many papers have discussed the decrease in dopant inhomogeneity by the application of magnetic fields to Czochralski process and liquidphase epitaxy [16–20]. The influence of magnetic field on the convection was investigated experimentally and numerically [21,22]. However, the observation of the flow patterns under the influence of ultrasonic vibrations in the fluid was studied only at a frequency of 10 kHz [23]. Therefore, the present work is part of a series of experimental studies of the behavior of convective flow in the fluid and the ultrasound influence in a Czochralski configuration. In this paper, the effect of temperature gradient, seed rotation and different shapes of the solid/liquid (S/L) interface on the flow patterns in an ultrasound field is discussed.
2. Experimental procedure The experimental configuration is represented schematically in Fig. 1. The model fluid is distilled water, which has properties similar to the InSb melt. The relevant physical properties and dimensionless numbers of distilled water and InSb melt are given in Table 1. The distilled water is contained in the stainlesssteel crucible with 200 mm diameter and 150 mm height, and two glass windows for light beam and flow observation. The cylindrical aluminum disk with 60 mm diameter serves as a crystal dummy. Ultrasound at frequencies of 0.6 and 1.25 MHz was introduced into the water from a piezotransducer through a fused silica waveguide, with 20 mm diameter and 100 mm length. The direction of the ultrasonic waves was parallel to the disk axis. Polymer heater of 200 mm external diameter, 30 mm inside diameter and 1 mm thickness was used to set the temperatures of the crucible
Fig. 1. Sketch of the experimental apparatus for the observation of ultrasound influence on the convection in the fluids.
bottom. The temperature in the water under aluminum disk and over the bottom of the crucible is measured using the two Cr/Al thermocouples. Al and Al2O3 particles are suspended in the fluid, and the light cut technique is used for flow visualization. The flows are observed in a vertical axial plane. Al particles were in the disk form with 100 mm diameter and 5 mm thickness. Al2O3 round particles were 50 mm in diameter. CCD camera is installed such that the flow in the water can be viewed and recorded on video. Flow velocities were calculated by determining the position coordinates of Al particles in consecutive video images. The influence of ultrasound on changing Al and Al2O3 particles motion in the central flows between the disk and waveguide in video images is observed. Characteristic digital image processing software Ulead VideoStudio 4 is used for this purpose. In the model experiment several parameters are varied independently: the temperature difference
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Table 1 Physical properties and non-dimensional numbers Constants and numbers
H2O
InSb melt
Gravity, g (m/s2) Thermal coefficient of volume expansion, a (K1) Radial temperature difference in fluid, DTr (K) Height of fluid, h (m) Thermal diffusivity, w (m2/s) Kinematic viscosity, n (m2/s) Diameter of crucible, d (m) Rotation rate, n (rpm) Angular velocity, o (c1) Characteristic length, l (m) h=d Rayleigh number (Raw ) n=o Reynolds number (RO )
9.8 2 104 0.1 0.06/0.12 0.015 105 1 106 0.2 1/15 0.105/1.57 0.03 0.3 17 104 1/0.105 94.5
9.8 5.2 105 5 0.012/0.024 1.65 105 0.34 106 0.04 1/15 0.105/1.57 0.005 0.3 0.5 103 1/0.105 7.7
0.6 271 104 15/1.57 1413
0.6 7.5 103 15/1.57 115
DT; the crystal dummy rotation rate n, different shape of the S/L interface, the fluid depth h; the amplitude A and frequency f of ultrasound on the piezotransducer.
3. Experimental results and discussion The convective flows are supervised in video clips, which can be viewed on TV and PC in AVI (720 480, 29.97 fps, DV NTSC) format. The images of flow patterns and standing waves are observed without the distortions owing to flat glass windows in the stainless-steel crucible. 3.1. Convective flows without ultrasound The first flows are observed in the water at a low value of DT ¼ 0:1 K. Fig. 2 shows the features of the flows at DT ¼0.4 and 4 K. Axisymmetric flows are spread in all the volume of the fluid without the crystal dummy rotation. The cooling of the crystal dummy for DT ¼ 4 K generated axisymmetric flow patterns from top to the bottom of the crucible (Fig. 2b). In this case the maximum flow velocity is 6 mm/s and is obtained by digital image processing. The rotation of the crystal dummy at DT ¼ 0 forms the symmetric flows upwards along the crucible axis (Fig. 3a), which makes a 90 turn
Fig. 2. Convection in the distilled water: (a) DT ¼ 0:4 K; (b) DT ¼ 4 K.
and then flows along the growth interface. Such behavior of the flow has been reported in Ref. [24]. The flow in the ‘‘exit region’’ under the growth interface leads to the formation of an opposite rotating vortex by making a 20 turn at this region. Further the flow departs from the growth interface and makes a 70 turn at the wall, next
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eliminate all periodicity in the melt motion and to eliminate striations produced by unsteady melt motions. An important advantage of ultrasound is the influence on convective flows of the melt in the vicinity of the crystallization front. We suppose that ultrasound standing waves can stabilize the flux in the melt. It is known that the force Fr acting on incompressible particle in running wave can be obtained [25]: Fr ¼ 2=9pR2 ðkRÞ4 rv2 ða21 þ a1 a2 þ 34a22 Þ;
Fig. 3. Flow patterns at (a) o ¼ 1 rpm and (b) o ¼ 15 rpm.
90 turn at the bottom and the water centerline. The increase of the crystal dummy rotation to 15 rpm causes two vigorous rotating vortices (Fig. 3b). Switching off the crystal dummy rotation changed the flows to the opposite direction and to the cooling off direction. We observed the solute boundary layer forming between the crystal dummy rotation and the tangential flows in the fluid under the S/L interface. Al and Al2O3 particles motion was not present in this layer. The thickness of the solute boundary layer was less than 1.4 mm for the crystal dummy rotation of 15 rpm. Under the solute boundary layer high-rate flows in radial direction changed the velocity values from 0.3 to 2 mm/s with increases of the crystal dummy rotation. The maximum velocity value in the flux moving upward along the crucible axis was 1.4 mm/s. 3.2. Convective flows in ultrasonic field An ultrasonic field directed to the S/L interface can be used to stabilize the melt in order to
ð1Þ
where R is the radius of the particle, k is the wavenumber, r is the density of the fluid, n is the sound particle velocity in ultrasound wave, a1 ¼ 1 rx2 =rp x2p and a2 ¼ 2ðrp r=2rp þ rÞ; rp is the density of the particle, x and xp are the sound velocity of the fluid and the particle, respectively, at the motion direction of the wave. When ultrasound wave has the flat barrier, for example, the S/L interface can form ultrasonic standing waves in the melt. Then the force Fs acting on the particle in ultrasound standing wave can be written as [25] Fs ¼ pR2 ðkRÞrv2 " # rp þ 23ðrp rÞ rx2 : 2rp þ r 3rp x2p
ð2Þ
Since the radius of the atoms or molecules in the melt is less than RE1 nm, Fs > Fr by 104 times. Therefore, ultrasound standing waves can reduce the buoyant convection owing to the particles oscillation in the wave antinodes. As the semiconductor melts are not transparent for a direct visual observation of the influence of standing waves on the flow patterns by the light cut technique, we used distilled water. In our experiments the waveguide had the diameter less than three times the diameter of the crystal dummy. Therefore, standing waves can be formed in the water volume between higher waveguide flat and the S/L interface. This is observed in our experiments in the water during the introduction of ultrasound. White channel without Al particles formed in ultrasound standing waves is shown in Fig. 4d. Standing waves create the illusion that the Al particles are vanishing. This may be the well-known result of
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Fig. 4. Effect of the appearance of the standing waves canal in the moment of switching on ultrasound at a frequency of 1.25 MHz, n¼ 5 rpm and DT ¼ 3 K: (a) 1 s before switching on ultrasound; (b) 1 s (c) 4 s and (d) 9 s after switching on ultrasound.
the phenomenon of Raleigh disk, which turns the plane perpendicular to the ultrasound waves direction. Indeed Al particles having the disk form with 5 mm thickness after turning in standing waves were not seen in the ultrasound direction perpendicular to the observation direction of the Al particles. Fig. 4 shows the beginning time moment of switching on the ultrasound waves during 9 s when standing waves channel appears between the waveguide and the crystal dummy. The formation time of standing waves was 5–7 s after switching on the ultrasound. Also the disappearance of the standing waves was not instantaneous but it occurred during 4–9 s after switching off the ultrasound in the modeling experiments. Besides, the renewal time of the appearance of the flow patterns after switching off ultrasound is reduced to 3–2 s, which is caused by the increase of h=d ratio from 0.3 to 0.6 and the crystal dummy rotation rate n from 1 to 15 rpm. This may be due to the fact that the increase of these parameters causes further unsteady convection. The mode of natural and forced convection can be described in terms of non-dimensional numbers such as
Rayleigh number Raw and Reynolds number RO [26], which consider h=d and o parameters. The Rayleigh number for thermal convection Raw is defined as Raw ¼ ga2 DTr h4 =wnd;
ð3Þ
where g is the gravity, a is the thermal coefficient of volume expansion, DTr is the radial temperature differences in the fluid, h is the height of the fluid, d is the diameter of the crucible, w is the thermal diffusivity and n is the kinematic viscosity. In rotating flows, the Reynolds number is determined by the influence of the rotation of the crystal: RO ¼ ol 2 =n;
ð4Þ
where o is the angular velocity and l is the characteristic length equal to the crystal dummy radius. In our experiments, with the increase of h=d and o; non-dimensional numbers Raw and RO (Table 1) rise by a factor of 15 or 16 times that can influence the reduction of the flows renewal time. One of the other advantages of using Al2O3 particles is the possibility to observe their
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Fig. 5. Distribution of Al2O3 particles in standing waves of ultrasound at a frequency of 1.25 MHz.
distribution in standing waves as these particles have a spherical form. Fig. 5 shows the pictures of the particles fixed in the standing waves antinodes. The distance between the layers with maximum concentration of the particles is equal to 0.6 mm and conforms to half wavelength of the ultrasound wave in the water at a frequency of 1.25 MHz. The oscillations of Al2O3 particles in the antinodes of the standing waves prevent the motion of convective flows in the region of these waves. It is the convincing evidence of the influence of the ultrasound standing waves on the convection in the fluids. The observed influence of the interface shape for the cases of convex and concave shapes was conducted on the aluminum disk with 40 mm diameter and 25 mm sphere radius. In these experiments we have also seen the formation of ultrasound standing waves but the channel diameter is reduced by 10%. Only this difference does influence the ultrasound affect on convective flows in water for the cases of rotating and non-rotating disk, which has spherical and flat shapes. A given modeling experiment in water was conducted with ultrasound at frequencies of 0.6 and 1.25 MHz. Using these frequencies equally influenced the formation of standing waves and convection, but the distances between the standing waves antinodes correspond to half wavelength, and were 1.25 and 0.6 mm, respectively. The calculated wavelengths of ultrasound for these frequencies in distilled water at 23 C equal 2.49
Table 2 Intensity of ultrasound I (W/cm2) in distilled water Frequency of ultrasound (f ) (MHz)
Effective volume on a piezotransducer (U) (V) 5
0.6 1.25
10 3
7 10 3 102
15 2
3 10 0.12
30 2
7 10 0.3
0.25 —
and 1.2 mm, which are in good agreement with the observed values. Experimentally, it is difficult to measure the intensity of ultrasound at a high frequency. Therefore, we calculated the intensity I (Table 2) according to the relationship [27] I¼
ð0:9 1:44Þ 102 f 2 U 2 105 ; rc
ð5Þ
where f is the frequency of ultrasound in MHz, U is the effective volume on a piezotransducer, r is the density of the distilled water and c is the velocity of sound in the distilled water at 23 C. We investigated the increase of the ultrasound intensity to a maximum value of 0.3 W/cm2 and we have not seen the influence of ultrasound power on standing waves and the flow patterns around them in water. The given values of ultrasound intensity were smaller than the cavitation threshold. However, these results indicate that standing waves are appearing at the threshold intensity Is =7 103 W/cm2.
ARTICLE IN PRESS G.N. Kozhemyakin / Journal of Crystal Growth 257 (2003) 237–244
4. Discussions and conclusions In order to determine special growth conditions for striation-free single crystals the convection, the temperature gradient, the fluid depth, the crystal rotation rate and ultrasound field in a model Czochralski experiment were studied using the light cut method and digital image processing. The flow velocity in distilled water was measured experimentally using buoyant tracer particles. The maximum flow velocity was observed to be equal to 6 mm/s for cooling the crystal dummy at DT ¼ 4 K. In this case the axisymmetric flow patterns were formed. Convective flows were observed for different crystal dummy rotations and were found to be strongly correlated with the flow velocity during the rotation. We have shown experimentally that ultrasound at a high frequency can be used for reducing the convection in the melt during the crystal growth by Czochralski method. The strong reduction of the flow oscillations is connected with formatting standing waves between the S/L interface and a waveguide. It was found that ultrasound standing waves turn the flat Al particles in the water perpendicular to the ultrasound waves direction and create the illusion of their vanishing in digital images. These results are in accord with the well-known phenomenon of Raleigh disk and are direct evidence of the formatting of standing waves. Another version of clear evidence of standing waves in our model experiment is the distribution of Al2O3 particles with maximum concentration in standing waves antinodes. For a given system, appearing time and disappearing time of the standing waves were 5–7 and 4–9 s, respectively. The increase of h=d ratio from 0.3 to 0.6 and the crystal dummy rotation rate n to 15 rpm has reduced the flows renewal time to 2–3 s after switching off the ultrasound. In these cases the Rayleigh number Raw and Reynolds number RO rise by a factor of 16 and 15 times, respectively. The formatting of standing waves, reducing only the waves channel diameter by 10%, insignificantly influences convex and concave shapes of the S/L interface. The effect of standing waves is noted at the threshold intensity Is larger than 7 103 W/cm2.
243
The increase of ultrasound intensity to maximum value 0.3 W/cm2 does not change the conformation of standing waves and their influence on the convective patterns. These values of ultrasound intensity were smaller than that of the cavitation threshold.
Acknowledgements The author thanks Mr. N.V. Komarov for technical assistance.
References [1] Y. Hayakawa, Y. Sone, K. Tatsumi, M. Kumagawa, Japan J. Appl. Phys. 21 (1982) 1273. [2] Y. Hayakawa, Y. Sone, K. Tatsumi, M. Kumagawa, Japan J. Appl. Phys. 22 (1983) 206. [3] Y. Hayakawa, M. Kumagawa, Cryst. Res. Technol. 20 (1983) 3. [4] T. Tsuruta, Y. Hayakawa, M. Kumagawa, Japan J. Appl. Phys. 27 (1988) 47. [5] T. Tsuruta, Y. Hayakawa, M. Kumagawa, Japan J. Appl. Phys. 28 (1989) 36. [6] T. Tsuruta, K. Yamashita, S. Adachi, Y. Hayakawa, M. Kumagawa, Japan J. Appl. Phys. 31 (1992) 23. [7] M. Kumagawa, T. Tsuruta, N. Nishida, J. Ohtsuki, K. Takashi, S. Adachi, Y. Hayakawa, Cryst. Res. Technol. 29 (1994) 1037. [8] G.N. Kozhemyakin, V.G. Kosushkin, S.U. Kurochkin, J. Crystal Growth 121 (1992) 240. [9] G.N. Kozhemyakin, L.G. Kolodyazhnaya, J. Crystal Growth 147 (1995) 200. [10] G.N. Kozhemyakin, J. Crystal Growth 149 (1995) 266. [11] G.N. Kozhemyakin, Ultrasonics 35 (1998) 599. [12] K.M. Kim, P. Smetana, J. Appl. Phys. 58 (1985) 2731. [13] K.M. Kim, P. Smetana, J. Electrochem. Soc. 133 (1986) 1682. [14] G. Muller, . A. Ostrogorsky, in: D.T.J. Hurle (Ed.), Handbook of Crystal Growth 2b, North-Holland, Amsterdam, 1994, p. 709. [15] A. Lipchin, R.A. Brown, J. Crystal Growth 205 (1999) 71. [16] D.T.J. Hurle, in: H.S. Peiser (Ed.), Crystal Growth, Pergamon, Oxford, 1967, p. 659. [17] H.P. Utech, M.C. Flemmings, J. Appl. Phys. 37 (1966) 2021. [18] K. Hoshikawa, Japan J. Appl. Phys. 21 (9) (1982) L545. [19] V.S. Zemskov, M.R. Raukhman, Y.M. Mgaloblishvili, Phys. Chem. Obrab. Mater. 5 (1985) 50. [20] A.N. Danilewsky, P. Dold, K.W. Benz, J. Crystal Growth 121 (1992) 305.
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[21] B. Fisher, J. Friedrich, H. Weimann, G. Muller, J. Crystal Growth 198/199 (1999) 170. [22] J.L. Morton, N. Ma, D.F. Bliss, G.G. Bryant, J. Crystal Growth 242 (2002) 471. [23] Y. Hayakawa, Y. Sone, F. Ishino, M. Kumagawa, Japan J. Appl. Phys. 22 (1983) No.1. [24] A.G. Ostrogorsky, G. Muller, . J. Crystal Growth 121 (1992) 587.
[25] B.A. Agranat, M.N. Dubrovin, N.N. Havskiy, G.I. Eskin, Based of Physics and Technique of Ultrasound, High School, Moscow, 1987. [26] G. Muller, . Crystal Growth, Properties and Applications, Vol. 12, Springer, Berlin, 1988. [27] D.A. Gershgal, V.M. Fridman, Ultrasonic Technological Equipment, Energy, Moscow, 1976.
Journal of Crystal Growth 257 (2003) 237–244
Imaging of convection in a Czochralski crucible under ultrasound waves G.N. Kozhemyakin* Laboratory of Crystal Growth, Department of Applied Materials The V. Dal Eastern Ukrainian National University, Bl. Molodezhniy, 20A, Lugansk 91034, Ukraine Received 31 March 2003; accepted 28 May 2003 Communicated by M. Schieber
Abstract The influence of ultrasound on natural and forced convection in a Czochralski crucible was investigated experimentally. We present a method for simulation of ultrasound influence on convection in the melt during Czochralski growth. Distilled water is used as model fluid contained in a stainless-steel crucible with two glass windows. An aluminum cylinder is used to simulate the growing crystal. Flow and standing waves visualization and flow velocity measurements were performed. We report the flow patterns observed under ultrasound influence at frequencies of 0.6 and 1.25 MHz in the fluid for different conditions: temperature difference, cylinder rotation and fluid depth. r 2003 Elsevier B.V. All rights reserved. PACS: 47.27.T; 81.10; 61.72; 43.35; 43.20.K Keywords: A1. Convection; A1. Fluid flows; A1. Growth models; A2. Czochralski method; A2. Seed crystals; B2. Semiconducting III–V materials
1. Introduction The application of ultrasound to Czochralski process is a useful tool to decrease the components inhomogeneity in semiconductors single crystals. There have been reports on impurity segregation in Czochralski crystal growth in ultrasound field such as doping striations in the grown crystals. Detailed investigations of the effect of ultrasound with a frequency of 10 kHz and power of 120 W on the growth morphology in InSb and InxGa1xSb *Tel.: +38-0642-517-924; fax: +380-642-461-364. E-mail address: [email protected] (G.N. Kozhemyakin).
single crystals were conducted by Hayakawa et al. [1–7]. The introduction of ultrasonic vibrations into the melt through the carbon crucible during growth changed the crystal diameter, the width of the facet region and appearance of large voids, with an increase of the output power to 120 W. The effect of the striations, which decrease in number and disappear in the central part of InSb, GaAs and BiSb alloys pulled single crystals, was studied and reported in a few publications of our group [8–11]. Only in these experiments ultrasonic waves at frequencies of 0.15, 0.25, 0.6, 1.2, 2.5, 5 and 10 MHz were introduced into the melt through a quartz waveguide, fused to the bottom
0022-0248/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0022-0248(03)01459-3
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of the quartz crucible. We supposed that ultrasonic standing waves might influence the flow patterns in the melts and reduce the striations in the growing crystals [9]. However, this model of ultrasound influence on the disappearance of the striations is not a clear evidence. It is known that the occurrence of dopant inhomogeneities is affected by the flow patterns in the melt during the crystal growth process [12–15]. Many papers have discussed the decrease in dopant inhomogeneity by the application of magnetic fields to Czochralski process and liquidphase epitaxy [16–20]. The influence of magnetic field on the convection was investigated experimentally and numerically [21,22]. However, the observation of the flow patterns under the influence of ultrasonic vibrations in the fluid was studied only at a frequency of 10 kHz [23]. Therefore, the present work is part of a series of experimental studies of the behavior of convective flow in the fluid and the ultrasound influence in a Czochralski configuration. In this paper, the effect of temperature gradient, seed rotation and different shapes of the solid/liquid (S/L) interface on the flow patterns in an ultrasound field is discussed.
2. Experimental procedure The experimental configuration is represented schematically in Fig. 1. The model fluid is distilled water, which has properties similar to the InSb melt. The relevant physical properties and dimensionless numbers of distilled water and InSb melt are given in Table 1. The distilled water is contained in the stainlesssteel crucible with 200 mm diameter and 150 mm height, and two glass windows for light beam and flow observation. The cylindrical aluminum disk with 60 mm diameter serves as a crystal dummy. Ultrasound at frequencies of 0.6 and 1.25 MHz was introduced into the water from a piezotransducer through a fused silica waveguide, with 20 mm diameter and 100 mm length. The direction of the ultrasonic waves was parallel to the disk axis. Polymer heater of 200 mm external diameter, 30 mm inside diameter and 1 mm thickness was used to set the temperatures of the crucible
Fig. 1. Sketch of the experimental apparatus for the observation of ultrasound influence on the convection in the fluids.
bottom. The temperature in the water under aluminum disk and over the bottom of the crucible is measured using the two Cr/Al thermocouples. Al and Al2O3 particles are suspended in the fluid, and the light cut technique is used for flow visualization. The flows are observed in a vertical axial plane. Al particles were in the disk form with 100 mm diameter and 5 mm thickness. Al2O3 round particles were 50 mm in diameter. CCD camera is installed such that the flow in the water can be viewed and recorded on video. Flow velocities were calculated by determining the position coordinates of Al particles in consecutive video images. The influence of ultrasound on changing Al and Al2O3 particles motion in the central flows between the disk and waveguide in video images is observed. Characteristic digital image processing software Ulead VideoStudio 4 is used for this purpose. In the model experiment several parameters are varied independently: the temperature difference
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Table 1 Physical properties and non-dimensional numbers Constants and numbers
H2O
InSb melt
Gravity, g (m/s2) Thermal coefficient of volume expansion, a (K1) Radial temperature difference in fluid, DTr (K) Height of fluid, h (m) Thermal diffusivity, w (m2/s) Kinematic viscosity, n (m2/s) Diameter of crucible, d (m) Rotation rate, n (rpm) Angular velocity, o (c1) Characteristic length, l (m) h=d Rayleigh number (Raw ) n=o Reynolds number (RO )
9.8 2 104 0.1 0.06/0.12 0.015 105 1 106 0.2 1/15 0.105/1.57 0.03 0.3 17 104 1/0.105 94.5
9.8 5.2 105 5 0.012/0.024 1.65 105 0.34 106 0.04 1/15 0.105/1.57 0.005 0.3 0.5 103 1/0.105 7.7
0.6 271 104 15/1.57 1413
0.6 7.5 103 15/1.57 115
DT; the crystal dummy rotation rate n, different shape of the S/L interface, the fluid depth h; the amplitude A and frequency f of ultrasound on the piezotransducer.
3. Experimental results and discussion The convective flows are supervised in video clips, which can be viewed on TV and PC in AVI (720 480, 29.97 fps, DV NTSC) format. The images of flow patterns and standing waves are observed without the distortions owing to flat glass windows in the stainless-steel crucible. 3.1. Convective flows without ultrasound The first flows are observed in the water at a low value of DT ¼ 0:1 K. Fig. 2 shows the features of the flows at DT ¼0.4 and 4 K. Axisymmetric flows are spread in all the volume of the fluid without the crystal dummy rotation. The cooling of the crystal dummy for DT ¼ 4 K generated axisymmetric flow patterns from top to the bottom of the crucible (Fig. 2b). In this case the maximum flow velocity is 6 mm/s and is obtained by digital image processing. The rotation of the crystal dummy at DT ¼ 0 forms the symmetric flows upwards along the crucible axis (Fig. 3a), which makes a 90 turn
Fig. 2. Convection in the distilled water: (a) DT ¼ 0:4 K; (b) DT ¼ 4 K.
and then flows along the growth interface. Such behavior of the flow has been reported in Ref. [24]. The flow in the ‘‘exit region’’ under the growth interface leads to the formation of an opposite rotating vortex by making a 20 turn at this region. Further the flow departs from the growth interface and makes a 70 turn at the wall, next
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eliminate all periodicity in the melt motion and to eliminate striations produced by unsteady melt motions. An important advantage of ultrasound is the influence on convective flows of the melt in the vicinity of the crystallization front. We suppose that ultrasound standing waves can stabilize the flux in the melt. It is known that the force Fr acting on incompressible particle in running wave can be obtained [25]: Fr ¼ 2=9pR2 ðkRÞ4 rv2 ða21 þ a1 a2 þ 34a22 Þ;
Fig. 3. Flow patterns at (a) o ¼ 1 rpm and (b) o ¼ 15 rpm.
90 turn at the bottom and the water centerline. The increase of the crystal dummy rotation to 15 rpm causes two vigorous rotating vortices (Fig. 3b). Switching off the crystal dummy rotation changed the flows to the opposite direction and to the cooling off direction. We observed the solute boundary layer forming between the crystal dummy rotation and the tangential flows in the fluid under the S/L interface. Al and Al2O3 particles motion was not present in this layer. The thickness of the solute boundary layer was less than 1.4 mm for the crystal dummy rotation of 15 rpm. Under the solute boundary layer high-rate flows in radial direction changed the velocity values from 0.3 to 2 mm/s with increases of the crystal dummy rotation. The maximum velocity value in the flux moving upward along the crucible axis was 1.4 mm/s. 3.2. Convective flows in ultrasonic field An ultrasonic field directed to the S/L interface can be used to stabilize the melt in order to
ð1Þ
where R is the radius of the particle, k is the wavenumber, r is the density of the fluid, n is the sound particle velocity in ultrasound wave, a1 ¼ 1 rx2 =rp x2p and a2 ¼ 2ðrp r=2rp þ rÞ; rp is the density of the particle, x and xp are the sound velocity of the fluid and the particle, respectively, at the motion direction of the wave. When ultrasound wave has the flat barrier, for example, the S/L interface can form ultrasonic standing waves in the melt. Then the force Fs acting on the particle in ultrasound standing wave can be written as [25] Fs ¼ pR2 ðkRÞrv2 " # rp þ 23ðrp rÞ rx2 : 2rp þ r 3rp x2p
ð2Þ
Since the radius of the atoms or molecules in the melt is less than RE1 nm, Fs > Fr by 104 times. Therefore, ultrasound standing waves can reduce the buoyant convection owing to the particles oscillation in the wave antinodes. As the semiconductor melts are not transparent for a direct visual observation of the influence of standing waves on the flow patterns by the light cut technique, we used distilled water. In our experiments the waveguide had the diameter less than three times the diameter of the crystal dummy. Therefore, standing waves can be formed in the water volume between higher waveguide flat and the S/L interface. This is observed in our experiments in the water during the introduction of ultrasound. White channel without Al particles formed in ultrasound standing waves is shown in Fig. 4d. Standing waves create the illusion that the Al particles are vanishing. This may be the well-known result of
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Fig. 4. Effect of the appearance of the standing waves canal in the moment of switching on ultrasound at a frequency of 1.25 MHz, n¼ 5 rpm and DT ¼ 3 K: (a) 1 s before switching on ultrasound; (b) 1 s (c) 4 s and (d) 9 s after switching on ultrasound.
the phenomenon of Raleigh disk, which turns the plane perpendicular to the ultrasound waves direction. Indeed Al particles having the disk form with 5 mm thickness after turning in standing waves were not seen in the ultrasound direction perpendicular to the observation direction of the Al particles. Fig. 4 shows the beginning time moment of switching on the ultrasound waves during 9 s when standing waves channel appears between the waveguide and the crystal dummy. The formation time of standing waves was 5–7 s after switching on the ultrasound. Also the disappearance of the standing waves was not instantaneous but it occurred during 4–9 s after switching off the ultrasound in the modeling experiments. Besides, the renewal time of the appearance of the flow patterns after switching off ultrasound is reduced to 3–2 s, which is caused by the increase of h=d ratio from 0.3 to 0.6 and the crystal dummy rotation rate n from 1 to 15 rpm. This may be due to the fact that the increase of these parameters causes further unsteady convection. The mode of natural and forced convection can be described in terms of non-dimensional numbers such as
Rayleigh number Raw and Reynolds number RO [26], which consider h=d and o parameters. The Rayleigh number for thermal convection Raw is defined as Raw ¼ ga2 DTr h4 =wnd;
ð3Þ
where g is the gravity, a is the thermal coefficient of volume expansion, DTr is the radial temperature differences in the fluid, h is the height of the fluid, d is the diameter of the crucible, w is the thermal diffusivity and n is the kinematic viscosity. In rotating flows, the Reynolds number is determined by the influence of the rotation of the crystal: RO ¼ ol 2 =n;
ð4Þ
where o is the angular velocity and l is the characteristic length equal to the crystal dummy radius. In our experiments, with the increase of h=d and o; non-dimensional numbers Raw and RO (Table 1) rise by a factor of 15 or 16 times that can influence the reduction of the flows renewal time. One of the other advantages of using Al2O3 particles is the possibility to observe their
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Fig. 5. Distribution of Al2O3 particles in standing waves of ultrasound at a frequency of 1.25 MHz.
distribution in standing waves as these particles have a spherical form. Fig. 5 shows the pictures of the particles fixed in the standing waves antinodes. The distance between the layers with maximum concentration of the particles is equal to 0.6 mm and conforms to half wavelength of the ultrasound wave in the water at a frequency of 1.25 MHz. The oscillations of Al2O3 particles in the antinodes of the standing waves prevent the motion of convective flows in the region of these waves. It is the convincing evidence of the influence of the ultrasound standing waves on the convection in the fluids. The observed influence of the interface shape for the cases of convex and concave shapes was conducted on the aluminum disk with 40 mm diameter and 25 mm sphere radius. In these experiments we have also seen the formation of ultrasound standing waves but the channel diameter is reduced by 10%. Only this difference does influence the ultrasound affect on convective flows in water for the cases of rotating and non-rotating disk, which has spherical and flat shapes. A given modeling experiment in water was conducted with ultrasound at frequencies of 0.6 and 1.25 MHz. Using these frequencies equally influenced the formation of standing waves and convection, but the distances between the standing waves antinodes correspond to half wavelength, and were 1.25 and 0.6 mm, respectively. The calculated wavelengths of ultrasound for these frequencies in distilled water at 23 C equal 2.49
Table 2 Intensity of ultrasound I (W/cm2) in distilled water Frequency of ultrasound (f ) (MHz)
Effective volume on a piezotransducer (U) (V) 5
0.6 1.25
10 3
7 10 3 102
15 2
3 10 0.12
30 2
7 10 0.3
0.25 —
and 1.2 mm, which are in good agreement with the observed values. Experimentally, it is difficult to measure the intensity of ultrasound at a high frequency. Therefore, we calculated the intensity I (Table 2) according to the relationship [27] I¼
ð0:9 1:44Þ 102 f 2 U 2 105 ; rc
ð5Þ
where f is the frequency of ultrasound in MHz, U is the effective volume on a piezotransducer, r is the density of the distilled water and c is the velocity of sound in the distilled water at 23 C. We investigated the increase of the ultrasound intensity to a maximum value of 0.3 W/cm2 and we have not seen the influence of ultrasound power on standing waves and the flow patterns around them in water. The given values of ultrasound intensity were smaller than the cavitation threshold. However, these results indicate that standing waves are appearing at the threshold intensity Is =7 103 W/cm2.
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4. Discussions and conclusions In order to determine special growth conditions for striation-free single crystals the convection, the temperature gradient, the fluid depth, the crystal rotation rate and ultrasound field in a model Czochralski experiment were studied using the light cut method and digital image processing. The flow velocity in distilled water was measured experimentally using buoyant tracer particles. The maximum flow velocity was observed to be equal to 6 mm/s for cooling the crystal dummy at DT ¼ 4 K. In this case the axisymmetric flow patterns were formed. Convective flows were observed for different crystal dummy rotations and were found to be strongly correlated with the flow velocity during the rotation. We have shown experimentally that ultrasound at a high frequency can be used for reducing the convection in the melt during the crystal growth by Czochralski method. The strong reduction of the flow oscillations is connected with formatting standing waves between the S/L interface and a waveguide. It was found that ultrasound standing waves turn the flat Al particles in the water perpendicular to the ultrasound waves direction and create the illusion of their vanishing in digital images. These results are in accord with the well-known phenomenon of Raleigh disk and are direct evidence of the formatting of standing waves. Another version of clear evidence of standing waves in our model experiment is the distribution of Al2O3 particles with maximum concentration in standing waves antinodes. For a given system, appearing time and disappearing time of the standing waves were 5–7 and 4–9 s, respectively. The increase of h=d ratio from 0.3 to 0.6 and the crystal dummy rotation rate n to 15 rpm has reduced the flows renewal time to 2–3 s after switching off the ultrasound. In these cases the Rayleigh number Raw and Reynolds number RO rise by a factor of 16 and 15 times, respectively. The formatting of standing waves, reducing only the waves channel diameter by 10%, insignificantly influences convex and concave shapes of the S/L interface. The effect of standing waves is noted at the threshold intensity Is larger than 7 103 W/cm2.
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The increase of ultrasound intensity to maximum value 0.3 W/cm2 does not change the conformation of standing waves and their influence on the convective patterns. These values of ultrasound intensity were smaller than that of the cavitation threshold.
Acknowledgements The author thanks Mr. N.V. Komarov for technical assistance.
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