- Email: [email protected]
Containerless crystallization of silicon
Journal of Crystal Growth 237–239 (2002) 1840–1843
Containerless crystallization of silicon K. Kuribayashia,b,*, T. Aoyamaa a
The Institute of Space and Astronautical Science, Yoshinodai, Sagamihara, Kanagawa 229-8510, Japan b CREST, Japan Science and Technology Corporation, Sengen, Tsukuba, Ibaragi 305-00467, Japan
Abstract Crystallization from undercooled melt of silicon was carried out by means of electro-magnetic levitation method under controlled undercooling. The measured growth rate vs. undercooling was categorized into three regions, I, II and III, respectively, from the point of the interface morphology. Thin plate crystals whose interface consisted of both faceted (1 1 1) plane and wavy edge plane like saw-tooth were observed in the region I where the undercooling is less than 100 K. The growth rate of the wavy edge plane was well described by the dendrite growth model. The morphology of growing crystals was abruptly changed to faceted dendrite in the region II, though there was no abrupt change in the growth rate. Seeding at temperatures in the region I changes the drop to a mono-crystalline sphere, if the growth rate along the normal direction of the thin plate crystal is controlled by step-wise growth on the faceted plane. Actually, the sample of 5 mm in diameter seeded at undercooling of 26 K was a quasi-single crystal with large grain, except for a small area where twinning and cracking are observed. The result suggests that the single crystal could be grown, if a smaller sample, 1 or 2 mm in diameter, that is difficult to be levitated by electro-magnetic force were processed with other methods such as free fall in a drop tube. r 2002 Elsevier Science B.V. All rights reserved. Keywords: A1. Morphological stability; A1. Solidification; B2. Semiconducting silicon
1. Introduction Over the past several decades silicon has been one of the most important industrial materials. In this period, electronics industries have strived to increase the size of ingots in order to lower the cost of chip production. The larger the diameter, however, the higher the amount of investments in plants and equipment for processing the substrate has to be. Recently, a challenging idea that will *Corresponding author. The Institute of Space and Astronautical Science, Yoshinodai, Sagamihara, Kanagawa 2298510, Japan. Tel.: +81-42-759-8262; fax: +81-42-759-8461. E-mail address: [email protected] (K. Kuribayashi).
reduce the cost has been proposed; that is to mount integrated circuit on the surface of a small spherical silicon crystal. However, the technique of growing such spherical single crystals needs to be developed. We have in our previous paper [1], carried out in-situ observation of rapid crystallization processes that take place in undercooled drops of silicon. We have reported that the relationship between the growth rate and the undercooling could be categorized into three regions, I, II and III, where a plate-like crystal, coarse faceted dendrite and fine faceted dendrite are observed, respectively, and determined experimentally the critical undercooling from the region I to II as about 100 K.
0022-0248/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 1 ) 0 2 1 0 5 - 4
K. Kuribayashi, T. Aoyama / Journal of Crystal Growth 237–239 (2002) 1840–1843
In the present experiment, crystallography of the plate-like crystal observed at the region I was characterized by in-situ observation of drops crystallizing when they were seeded with single crystals of silicon, and then a trial for growing a spherical single crystal was attempted.
1841
respectively, with the spot size of 1 mm in diameter. The detailed description on the method of temperature measurement is given elsewhere [2]. The growth rates of crystalline Si were measured by a high-speed video camera (HVC) with a maximum sampling rate of 40,500 frames/s for 0.4 s.
2. Experimental procedure 3. Experimental results Fig. 1 shows a photograph of a sample positioned inside the working coil of an electromagnetic levitation furnace and schematics of the present apparatus. The furnace chamber was evacuated to 10 4 Pa by a turbo-molecular pump and then filled with pure argon gas. Then the residual oxygen concentration was less than 2 ppb. A sample, undoped Si, was supported by a quartz holder located several centimeters below from the levitation coil. The sample was preheated by a CO2 laser up to a temperature at which the electrical resistivity is reduced enough for the sample to be levitated by the applied electromagnetic force. After the sample was levitated, the holder was removed outside the coil and a seed crystal was set just below the sample. A peace of silicon wafer having (1 1 1) orientation was used as the seed crystal. The temperature of the specimen was measured with two mono-color pyrometers whose operating wavelengths are 900 and 1550 nm,
Fig. 1. Photograph of levitated pure silicon in the electromagnetic levitation coil and schematic of the apparatus.
We have previously reported [1] that the growth rates at the regions I and II are expressed qualitatively by the non-parametric dendrite growth model proposed by Lipton et al. [3] incorporating the term of kinetic undercooling DTk : The critical undercooling DT for transition from the region I to II is identified as 100 K. At the region I, anisotropic plate-like crystal was observed, while a coarse faceted dendrite was observed at the region II. Fig. 2 shows the high-speed video image of the levitated sample, the bottom of which was seeded at undercooling of 45 K. The crystallization front is shown in advance in parallel and epitaxial with the seed crystal and to form a circumference on the surface of the sample. Note that this circumference
Fig. 2. Video image of the surface of the levitated sample seeded at undercooling of 45 K and schematic illustration of external seeding by a single crystal of silicon wafer of (1 1 1) orientation with the edge in the /1 1 0S direction. The circumference of the thin plate crystal is discontinuous, indicating that the morphology of the crystallization front is wavy.
1842
K. Kuribayashi, T. Aoyama / Journal of Crystal Growth 237–239 (2002) 1840–1843
is discontinuous. This may indicate that the plate-like crystal observed at the region I is a thin plate having a (1 1 1) planar interface with a wavy edge plane as shown schematically in this figure.
4. Discussions The growth rates at the region I and the region II could be well described by the dendrite growth model with the same kinetic coefficient. This result suggests that the tip of the wavy edge plane and the faceted dendrite tip consists of rough interfaces, and they have paraboloidal shapes like those of metallic materials. One hypothesis can be deduced here, that is, the transition from the thin plate crystal to the faceted dendrite is ascribed to the morphological instability of the rough interface. According to this hypothesis it is suspected that the stability of the thin plate crystal is controlled by the ratio of the thickness of the thin plate crystal L to the tip radius of the wavy edge plane R: If the ratio is larger than the critical value, typically two, that occurs at the critical undercooking, the thin plate crystal is destabilized and changed to faceted dendrite. Fig. 3 shows schematically this instability criterion. Fig. 4 shows an optical micrograph of the cross section of a sample seeded at undercooling of 26 K in the region I. The sample was a quasi-single crystal with a large grain, except a small area where twinning and a cracking are observed, which are ascribed mainly to the dilatational strain due to crystallization and secondarily to the fluid convection induced thermally and also by electromagnetic stirring. Those imperfections could be successfully suppressed, if a smaller sample, for instance, 1 or 2 mm in diameter that is difficult to be levitated by electro-magnetic force, were processed with other methods such as free fall in a drop tube. Microgravity condition provides the additional benefit of using substantially less electromagnetic force for sample positioning than in the normal gravity condition. This may enable us to process samples of different sizes using moderate electromagnetic force that will in turn substantially reduce the convective flows generated by the electromagnetic induction.
Fig. 3. Schematic presentation of stability criterion of thin plate crystal. The spherical nucleus, whose diameter is dn ; grows to an ellipsoidal shape due to the anisotropy of the growth rate and subsequently forms a thin plate crystal. The edge plane of the thin plate crystal is destabilized when L; the thickness of the thin plate crystal, becomes larger than twice R; the tip radius of the edge plane.
Fig. 4. Optical micrograph of the cross section of the sample seeded at undercooling of 26 K.
K. Kuribayashi, T. Aoyama / Journal of Crystal Growth 237–239 (2002) 1840–1843
5. Summary The undercooled drop of silicon was containerlessly solidified into the spherical crystal using the technique of electro-magnetic levitation under the controlled undercooling. The growth rate vs. undercooling was categorized into three regions, I, II and III, respectively, from the point of the interface morphology. A thin plate crystal whose interface consisted of both faceted (1 1 1) plane and wavy edge plane like saw-tooth was observed in the region I where the undercooling is less than 100 K. The dendrite growth model that incorporates the kinetic undercooling could well describe the growth rates of not only the edge plane observed at the region I but also the tip of the faceted dendrite at the region II. This result suggests that the morphological transition from the thin plate crystal to the faceted dendrite is ascribed to the destabilization of the edge plane and then the drop can be solidified into a monocrystalline sphere under the controlled undercooling at the region I. The sample, the diameter of which is around 5 mm, seeded at undercooling of 26 K was actually a quasi-single crystal including a small amount of deformation twinning that was
1843
induced for releasing the dilatational elastic strain due to solidification. A single crystal could be successfully grown, if a smaller sample, for instance, 1 or 2 mm in diameter that is difficult to be levitated by electro-magnetic force, were processed.
Acknowledgements This work has been supported mainly by a Grant-in Aid for Scientific Research from The Ministry of Education, Science, Sports and Culture, and partly by the New Energy and Industrial Technology Development Organization for the R&D of Industrial Science and Technology Frontier Program.
References [1] T. Aoyama, K. Kuribayashi, Acta Mater. 48 (2000) 3739. [2] T. Aoyama, Y. Takamura, K. Kuribayashi, Metall. Mater. Trans. 30A (1999) 3013. [3] J. Lipton, W. Kurz, R. Trivedi, Acta Metall. 35 (1987) 957.
Containerless crystallization of silicon K. Kuribayashia,b,*, T. Aoyamaa a
The Institute of Space and Astronautical Science, Yoshinodai, Sagamihara, Kanagawa 229-8510, Japan b CREST, Japan Science and Technology Corporation, Sengen, Tsukuba, Ibaragi 305-00467, Japan
Abstract Crystallization from undercooled melt of silicon was carried out by means of electro-magnetic levitation method under controlled undercooling. The measured growth rate vs. undercooling was categorized into three regions, I, II and III, respectively, from the point of the interface morphology. Thin plate crystals whose interface consisted of both faceted (1 1 1) plane and wavy edge plane like saw-tooth were observed in the region I where the undercooling is less than 100 K. The growth rate of the wavy edge plane was well described by the dendrite growth model. The morphology of growing crystals was abruptly changed to faceted dendrite in the region II, though there was no abrupt change in the growth rate. Seeding at temperatures in the region I changes the drop to a mono-crystalline sphere, if the growth rate along the normal direction of the thin plate crystal is controlled by step-wise growth on the faceted plane. Actually, the sample of 5 mm in diameter seeded at undercooling of 26 K was a quasi-single crystal with large grain, except for a small area where twinning and cracking are observed. The result suggests that the single crystal could be grown, if a smaller sample, 1 or 2 mm in diameter, that is difficult to be levitated by electro-magnetic force were processed with other methods such as free fall in a drop tube. r 2002 Elsevier Science B.V. All rights reserved. Keywords: A1. Morphological stability; A1. Solidification; B2. Semiconducting silicon
1. Introduction Over the past several decades silicon has been one of the most important industrial materials. In this period, electronics industries have strived to increase the size of ingots in order to lower the cost of chip production. The larger the diameter, however, the higher the amount of investments in plants and equipment for processing the substrate has to be. Recently, a challenging idea that will *Corresponding author. The Institute of Space and Astronautical Science, Yoshinodai, Sagamihara, Kanagawa 2298510, Japan. Tel.: +81-42-759-8262; fax: +81-42-759-8461. E-mail address: [email protected] (K. Kuribayashi).
reduce the cost has been proposed; that is to mount integrated circuit on the surface of a small spherical silicon crystal. However, the technique of growing such spherical single crystals needs to be developed. We have in our previous paper [1], carried out in-situ observation of rapid crystallization processes that take place in undercooled drops of silicon. We have reported that the relationship between the growth rate and the undercooling could be categorized into three regions, I, II and III, where a plate-like crystal, coarse faceted dendrite and fine faceted dendrite are observed, respectively, and determined experimentally the critical undercooling from the region I to II as about 100 K.
0022-0248/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 1 ) 0 2 1 0 5 - 4
K. Kuribayashi, T. Aoyama / Journal of Crystal Growth 237–239 (2002) 1840–1843
In the present experiment, crystallography of the plate-like crystal observed at the region I was characterized by in-situ observation of drops crystallizing when they were seeded with single crystals of silicon, and then a trial for growing a spherical single crystal was attempted.
1841
respectively, with the spot size of 1 mm in diameter. The detailed description on the method of temperature measurement is given elsewhere [2]. The growth rates of crystalline Si were measured by a high-speed video camera (HVC) with a maximum sampling rate of 40,500 frames/s for 0.4 s.
2. Experimental procedure 3. Experimental results Fig. 1 shows a photograph of a sample positioned inside the working coil of an electromagnetic levitation furnace and schematics of the present apparatus. The furnace chamber was evacuated to 10 4 Pa by a turbo-molecular pump and then filled with pure argon gas. Then the residual oxygen concentration was less than 2 ppb. A sample, undoped Si, was supported by a quartz holder located several centimeters below from the levitation coil. The sample was preheated by a CO2 laser up to a temperature at which the electrical resistivity is reduced enough for the sample to be levitated by the applied electromagnetic force. After the sample was levitated, the holder was removed outside the coil and a seed crystal was set just below the sample. A peace of silicon wafer having (1 1 1) orientation was used as the seed crystal. The temperature of the specimen was measured with two mono-color pyrometers whose operating wavelengths are 900 and 1550 nm,
Fig. 1. Photograph of levitated pure silicon in the electromagnetic levitation coil and schematic of the apparatus.
We have previously reported [1] that the growth rates at the regions I and II are expressed qualitatively by the non-parametric dendrite growth model proposed by Lipton et al. [3] incorporating the term of kinetic undercooling DTk : The critical undercooling DT for transition from the region I to II is identified as 100 K. At the region I, anisotropic plate-like crystal was observed, while a coarse faceted dendrite was observed at the region II. Fig. 2 shows the high-speed video image of the levitated sample, the bottom of which was seeded at undercooling of 45 K. The crystallization front is shown in advance in parallel and epitaxial with the seed crystal and to form a circumference on the surface of the sample. Note that this circumference
Fig. 2. Video image of the surface of the levitated sample seeded at undercooling of 45 K and schematic illustration of external seeding by a single crystal of silicon wafer of (1 1 1) orientation with the edge in the /1 1 0S direction. The circumference of the thin plate crystal is discontinuous, indicating that the morphology of the crystallization front is wavy.
1842
K. Kuribayashi, T. Aoyama / Journal of Crystal Growth 237–239 (2002) 1840–1843
is discontinuous. This may indicate that the plate-like crystal observed at the region I is a thin plate having a (1 1 1) planar interface with a wavy edge plane as shown schematically in this figure.
4. Discussions The growth rates at the region I and the region II could be well described by the dendrite growth model with the same kinetic coefficient. This result suggests that the tip of the wavy edge plane and the faceted dendrite tip consists of rough interfaces, and they have paraboloidal shapes like those of metallic materials. One hypothesis can be deduced here, that is, the transition from the thin plate crystal to the faceted dendrite is ascribed to the morphological instability of the rough interface. According to this hypothesis it is suspected that the stability of the thin plate crystal is controlled by the ratio of the thickness of the thin plate crystal L to the tip radius of the wavy edge plane R: If the ratio is larger than the critical value, typically two, that occurs at the critical undercooking, the thin plate crystal is destabilized and changed to faceted dendrite. Fig. 3 shows schematically this instability criterion. Fig. 4 shows an optical micrograph of the cross section of a sample seeded at undercooling of 26 K in the region I. The sample was a quasi-single crystal with a large grain, except a small area where twinning and a cracking are observed, which are ascribed mainly to the dilatational strain due to crystallization and secondarily to the fluid convection induced thermally and also by electromagnetic stirring. Those imperfections could be successfully suppressed, if a smaller sample, for instance, 1 or 2 mm in diameter that is difficult to be levitated by electro-magnetic force, were processed with other methods such as free fall in a drop tube. Microgravity condition provides the additional benefit of using substantially less electromagnetic force for sample positioning than in the normal gravity condition. This may enable us to process samples of different sizes using moderate electromagnetic force that will in turn substantially reduce the convective flows generated by the electromagnetic induction.
Fig. 3. Schematic presentation of stability criterion of thin plate crystal. The spherical nucleus, whose diameter is dn ; grows to an ellipsoidal shape due to the anisotropy of the growth rate and subsequently forms a thin plate crystal. The edge plane of the thin plate crystal is destabilized when L; the thickness of the thin plate crystal, becomes larger than twice R; the tip radius of the edge plane.
Fig. 4. Optical micrograph of the cross section of the sample seeded at undercooling of 26 K.
K. Kuribayashi, T. Aoyama / Journal of Crystal Growth 237–239 (2002) 1840–1843
5. Summary The undercooled drop of silicon was containerlessly solidified into the spherical crystal using the technique of electro-magnetic levitation under the controlled undercooling. The growth rate vs. undercooling was categorized into three regions, I, II and III, respectively, from the point of the interface morphology. A thin plate crystal whose interface consisted of both faceted (1 1 1) plane and wavy edge plane like saw-tooth was observed in the region I where the undercooling is less than 100 K. The dendrite growth model that incorporates the kinetic undercooling could well describe the growth rates of not only the edge plane observed at the region I but also the tip of the faceted dendrite at the region II. This result suggests that the morphological transition from the thin plate crystal to the faceted dendrite is ascribed to the destabilization of the edge plane and then the drop can be solidified into a monocrystalline sphere under the controlled undercooling at the region I. The sample, the diameter of which is around 5 mm, seeded at undercooling of 26 K was actually a quasi-single crystal including a small amount of deformation twinning that was
1843
induced for releasing the dilatational elastic strain due to solidification. A single crystal could be successfully grown, if a smaller sample, for instance, 1 or 2 mm in diameter that is difficult to be levitated by electro-magnetic force, were processed.
Acknowledgements This work has been supported mainly by a Grant-in Aid for Scientific Research from The Ministry of Education, Science, Sports and Culture, and partly by the New Energy and Industrial Technology Development Organization for the R&D of Industrial Science and Technology Frontier Program.
References [1] T. Aoyama, K. Kuribayashi, Acta Mater. 48 (2000) 3739. [2] T. Aoyama, Y. Takamura, K. Kuribayashi, Metall. Mater. Trans. 30A (1999) 3013. [3] J. Lipton, W. Kurz, R. Trivedi, Acta Metall. 35 (1987) 957.