Download Solubilities and Equilibrium Distribution Coefficients of Oxygen and

Materials Transactions, Vol. 43, No. 8 (2002) pp. 2120 to 2124
c
2002
The Japan Institute of Metals
Solubilities and Equilibrium Distribution Coefficients of Oxygen and
Carbon in Silicon
Takayuki Narushima, Atsushi Yamashita ∗ , Chiaki Ouchi and Yasutaka Iguchi
Department of Metallurgy, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
Solubilities of oxygen and carbon in solid silicon at 1673 K were determined by using a chemical equilibrium technique. Solid silicon
was heated at 1673 K in an oxygen atmosphere for 1800 ks, and then oxygen content in the solid silicon equilibrated with silica was measured
by the inert gas fusion-IR absorption method. Carbon content in the solid silicon equilibrated with silicon carbide after heating at 1673 K in an
Ar–5%CO atmosphere for 4860 ks was measured by the combustion-IR absorption method. Comparing these solubility values in solid silicon
with those in liquid silicon that were previously reported by the present authors, the equilibrium distribution coefficients of oxygen and carbon
in silicon at the melting point were evaluated to be 0.85 ± 0.08 and 0.30 ± 0.16, respectively.
(Received May 10, 2002; Accepted June 12, 2002)
Keywords: silicon, carbon, oxygen, distribution coefficient, thermodynamics, solubility, segregation
1. Introduction
Oxygen is one of the most important impurity elements in
silicon single crystals grown by the Czochralski (CZ) method.
It is well known that oxygen is introduced to silicon melt due
to dissolution of a silica crucible, and then distributed to the
CZ silicon single crystal at the melting point.1) Oxygen in the
CZ silicon crystal plays an important role for intrinsic gettering or for suppression of dislocation motion in silicon wafers.
Therefore, the homogeneity of oxygen in CZ silicon wafers
has been required for optimization of VLSIs’ characteristics.
Recently, a pyrometallurgical process for manufacturing
solar grade (SOG) silicon from metallurgical grade (MG) silicon has been noted because of its mass-production ability in
low cost. Since the MG silicon is produced by carbon reduction of silica, the total carbon content in the MG silicon is
much higher than 100 mass ppm. The carbon concentration in
the SOG silicon is required to be less than 5 mass ppm,2) and
the decarburization of MG silicon is one of the key technologies in a pyrometallurgical process. Kato et al.3) proposed the
pyrometallurgical process, in which polycrystalline silicon ingots were manufactured by directional solidification after a
decarburization process using plasma for silicon melt. Therefore, the final carbon content in the silicon ingot is determined
by the distribution between crystal and melt.
There have been many studies on the equilibrium distribution of oxygen and carbon between crystal and melt at the
melting point because of their importance in silicon production processes. The reported equilibrium distribution coefficients of oxygen ranged widely from 0.2 to 1.25,4–12) and the
values of the equilibrium distribution coefficient of carbon
were reported to be less than 0.1.13–16) The crystal-growthrelated techniques, such as the zone melting process and the
CZ process, were employed to prepare the specimens for oxygen or carbon analysis in the experimental studies on the
distribution.5–11, 14) The equilibrium distribution of oxygen or
carbon between crystal and melt has been assumed in these
studies.
∗ Graduate
Student, Tohoku University. Present Address: Toyota Industries
Co., Obu 474-8668, Japan.
The present authors have reported the solubilities of oxygen,17) nitrogen18) and carbon19) in liquid silicon equilibrated
with silica, silicon nitride and silicon carbide, respectively,
and clarified the effect of alloying elements on oxygen and
carbon solubilities.20, 21) In the present work, solubilities of
oxygen and carbon in the solid silicon equilibrated with silica
and silicon carbide at 1673 K, respectively, were measured by
using a chemical equilibrium technique and gas fusion-IR absorption methods for oxygen and carbon analyses. The equilibrium distribution coefficients of oxygen and carbon in silicon at the melting point were determined by comparing the
solubility values in solid silicon with those in liquid silicon
previously reported by the present authors.
2. Experimental
The silicon single crystal prepared by the floating zone
(FZ) method was used as a source material for specimens
in the equilibrium experiment. The FZ silicon single crystal was cut into plates. The silicon crystal plate size was
10 mm × 15 mm × 1.5 mm (W × L × T ). Both of initial
oxygen and carbon contents in the specimens were less than
5 mass ppm. The FZ crystal is considered to be suitable for the
equilibrium experiment because of less initial oxygen precipitates in the body than those in CZ crystal. The silicon crystal
plates were heated at 1673 K in an oxygen atmosphere or an
Ar–5%CO atmosphere in order to form silica or silicon carbide film on their surface. The specimen temperature was
maintained at 1673 ± 1 K using a PID controller, and monitored with two Pt-Pt13Rh thermocouples set near the specimen. Since the silica and silicon carbide films on specimens
are expected to be protective,22) the equilibria represented by
eqs. (1) and (2) are established at the SiO2 /Si and SiC/Si interfaces, respectively.
Si(s) + 2O(in solid silicon) = SiO2 (s)
(1)
Si(s) + C(in solid silicon) = SiC(s)
(2)
Oxygen and carbon potentials, i.e., oxygen and carbon concentrations in solid silicon, at the interface are constantly de-
Solubilities and Equilibrium Distribution Coefficients of Oxygen and Carbon in Silicon
2121
Table 1 Analytical conditions for carbon in silicon.
Baking of alumina crucible
1623 K, 600 s
Baking of specimen and metal bath
Size of specimen block
Metal bath
Fe standard sample
923 K, 600 s
1–3 mm (0.1 g)
Cu (501–623, LECO), 3 g
4.2 mass ppm (502–401, LECO)
30 mass ppm (001–050, LECO)
Fig. 2 XRD pattern of silicon heated at 1673 K in an oxygen atmosphere
for 1800 ks.
Fig. 1 Calculated oxygen contents in solid silicon equilibrated with silica
at 1673 K.
termined by eqs. (1) and (2), respectively. In the present
experiment, it was required that the oxygen or carbon concentration was homogeneous in the entire solid silicon at
1673 K. Figure 1 shows the calculated oxygen contents in
solid silicon equilibrated with silica. The oxygen contents
were calculated with the Fick’s second law assuming that
oxygen content at the SiO2 /Si interface was 30 mass ppm and
initial oxygen content in the solid silicon was 5 mass ppm.
The thickness of solid silicon was 1.5 mm and the diffusivity of oxygen in solid silicon at 1673 K was assumed to be
3.5 × 10−9 cm2 ·s−1 .23–25) According to Fig. 1, the establishment of equilibrium in the entire solid silicon is expected after heating for 1800 ks (500 h). On the other hand, the specimen was heated in an Ar–5%CO atmosphere up to 4860 ks
(1350 h), which was longer than that in an oxygen atmosphere
because the carbon diffisivity in solid silicon at 1673 K has
ranged from 10−7 cm2 ·s−1 to 10−10 cm2 ·s−1 .26–29)
After the equilibrium was established, oxygen or carbon
content in the specimen was determined. Oxygen contents
were measured by inert gas fusion-IR absorption method
(TC436, LECO) using the analytical conditions that were
reported elsewhere.17) Carbon contents were measured by
combustion-IR absorption method (CS444LS, LECO). The
analytical conditions for carbon in silicon were shown in
Table 1.
3. Results
Figure 2 demonstrates XRD pattern of the surface of the
solid silicon after heating at 1673 K in an oxygen atmosphere
for 1800 ks. Since silica (cristobalite) was found on the solid
silicon, it was confirmed that the equilibrium reaction can
be represented by eq. (1). The relationship between heating time and the oxygen contents in solid silicon is shown
in Fig. 3. The analytical values of oxygen contents agreed
within 2 mass ppm at each heating time. As shown in the figure, the equilibrium between solid silicon and silica was established and the constant oxygen content was obtained after
1000 ks. According to Fig. 3, the value of oxygen solubility
in solid silicon equilibrated with silica at 1673 K was concluded to be 33 ± 3 mass ppm (2.9 × 1018 atoms·cm−3 ± 2.6 ×
1017 atoms·cm−3 ).
Silicon carbide (β type) was found on the surface of the
solid silicon after heating at 1673 K in an Ar–5%CO atmosphere for 1800 ks as shown in Fig. 4. It was confirmed
that the solid silicon coexisted with silicon carbide. Figure
5 shows the change of carbon contents in the solid silicon
with heating time at 1673 K. The uncertainty in the analytical values of carbon contents increased with the increase
of heating time. However, it is considered that the equilibrium between solid silicon and silicon carbide was established after 3000 ks because the average value of carbon
contents appeared to be constant. Therefore, the value of
carbon solubility in solid silicon equilibrated with silicon
2122
T. Narushima, A. Yamashita, C. Ouchi and Y. Iguchi
Fig. 3 Change of oxygen contents in solid silicon with heating time at
1673 K.
Fig. 5 Change of carbon contents in solid silicon with heating time at
1673 K.
Fig. 4 XRD pattern of silicon heated at 1673 K in an Ar–5%CO atmosphere for 1800 ks.
carbide at 1673 K was determined to be 24 ± 13 mass ppm
(2.8 ± 1018 atoms·cm−3 ± 1.5 × 1018 atoms·cm−3 ) by considering the uncertainty of analytical values of carbon contents.
4. Discussion
4.1 Solubility of oxygen in solid silicon
The comparison of the reported5, 11, 24, 30–34) and present
oxygen solubilities in solid silicon equilibrated with silica is
shown in Fig. 6. Several research groups24, 32–34) evaluated
the oxygen solubility by measuring the oxygen concentration profiles in the solid silicon after heating in various atmospheres. Yatsurugi et al.5) and Huang et al.11) measured
the oxygen contents in the solid silicon crystals grown by a
zone melting method in an oxygen atmosphere and a vertical
freezing method in a silica ampoule, respectively. Hrostowski
and Kaiser,30) and Bean and Newman31) annealed the CZ solid
Fig. 6 Comparison of the reported and present oxygen solubilities in solid
silicon equilibrated with silica.
silicon crystals containing 1.4–1.6 × 1018 atoms·cm−3 as initial oxygen, and then measured the concentrations of soluble
oxygen in the solid silicon using IR absorption method. The
different principles and analytical techniques were employed
in the experiments to determine the oxygen solubility. Nevertheless, almost all reported and extrapolated oxygen solubility in solid silicon at the melting point including the present
data agreed in the range between 20 and 33 mass ppm. The
solubility values reported by Mikkelsen, Jr.33) are lower than
those reported by other research groups. It is suggested that
the equilibrium between solid silicon and silica was not established by annealing in an inert gas atmosphere.33)
Solubilities and Equilibrium Distribution Coefficients of Oxygen and Carbon in Silicon
2123
Table 2 Equilibrium Distribution coefficients of oxygen and carbon in silicon at the melting point.
Oxygen
Carbon
Authors
(year) [Ref. No.]
Distribution
coefficients
Authors
(year) [Ref.No.]
Distribution
coefficients
Trumbore
(1960) [4)]
0.5
Haas et al.
(1969) [13)]
0.1
Yatsurugi et al.
(1973) [5)]
1.25 ± 0.17
Nozaki et al.
(1970) [14)]
0.07 ± 0.01
Murgai et al.
>1
Kolbesen
and Mühlbauer
(1982) [15)]
0.058 ± 0.005
Lin et al.
(1983) [7)]
(1985) [8)]
0.25–0.3
Durand and Duby
(1999) [16)]
0.034
Iino et al.
(1993) [9)]
0.2–0.4
Present work
0.30 ± 0.16
Kakimoto
and Ozoe
(1998) [10)]
0.35–0.8
Huang et al.
(1998) [11)]
0.8 ± 0.1
Xu
(1999) [12)]
0.998
Present work
0.85 ± 0.08
(1979) [6)]
Fig. 7 Comparison of the reported and present carbon solubilities in solid
silicon equilibrated with silicon carbide.
4.2 Solubility of carbon in solid silicon
Nozaki et al.14) zone-melted silicon rods on which carbon in aqueous suspension was painted. The zone melting
was carried out in a vacuum. After a single zone pass, carbon contents in the silicon rod were determined as a function of the distance from top by CPAA (charged particle activation analysis) method. The carbon content just prior to
the appearance of silicon carbide on the surface of silicon
rods was concluded as the solubility of carbon in solid silicon at the melting point. Bean and Newman,31) and Endo
et al.35) annealed the carbon-rich silicon at various temperatures, and then the concentrations of soluble carbon were
measured by IR absorption method. The value of carbon solubility obtained in the present work was higher than those
reported by other research groups as shown in Fig. 7. Bean
and Newman31) estimated the carbon solubility at the melting point (4.5 × 1017 atoms·cm−3 ) from their temperature dependence of carbon solubility. They stated, however, that the
higher value than 4.5 × 1017 atoms·cm−3 appeared to be more
reasonable at the melting point because it was reported36, 37)
that carbon can be soluble in as-grown silicon crystals up to
2–3 × 1018 atoms·cm−3 . Recently, Newman38) suggested that
carbon solubility was enhanced by the presence of oxygen
atoms in silicon crystal, which expanded the lattice of the silicon crystal. In the present work, oxygen contents in the solid
silicon after heating in an Ar–5%CO atmosphere have not
been analyzed. Further research on the interaction between
oxygen and carbon in solid silicon is needed.
4.3 Equilibrium distribution coefficient of oxygen and
carbon
The present authors have reported the oxygen and carbon solubilities in liquid silicon using a chemical equilibrium technique.17, 19) The temperature dependence of oxy-
gen and carbon solubilities in liquid silicon is represented as
follows.17, 19)
log(C o /mass%) = −4620/T + 0.332(T : 1693–1823 K)
(3)
log(C c /mass%) = −9660/T + 3.63(T : 1723–1873 K)
(4)
According to eqs. (3) and (4), the oxygen (C Ol ) and carbon
(C Cl ) solubilities in liquid silicon at the melting point were
calculated to be 38.9 and 79.1 mass ppm, respectively.
In the present work, the oxygen and carbon solubilities
were measured at 1673 K. There have been several investigations on temperature dependence of oxygen and carbon
solubilities in solid silicon as shown in Figs. 6 and 7. The
relative difference in the values of oxygen and carbon solubilities between at 1673 K and at the melting point of silicon (1685 K) were no more than 5% and 10%, respectively.
Therefore, the solubility values of oxygen (C Os ) and carbon
(C Cs ) in solid silicon at the melting point can be assumed to be
the same as those at 1673 K. Using the solubilities at the melting point of silicon, the equilibrium distribution coefficients
of oxygen (kO = C Os /C Ol ) and carbon (kC = C Cs /C Cl ) were
determined to be 0.85 ± 0.08 and 0.30 ± 0.16, respectively.
The equilibrium distribution coefficients of oxygen and carbon in silicon reported in the past are summarized in Table 2.
In the experimental studies by other research groups,5–11) the
specimens for oxygen analysis were prepared by the crystalgrowth-related techniques. Kakimoto and Ozoe,39) however,
clarified that surface-tension-driven flow affected the oxygen
2124
T. Narushima, A. Yamashita, C. Ouchi and Y. Iguchi
distribution at the interface between crystal and melt. It is
suggested that the achievement of equilibrium distribution between crystal and melt is difficult in the crystal-growth-related
processes. They reported kO = 0.35–0.8 in the silicon crystal
growth under vertical magnetic fields at 0.3 T to prevent melt
flow in radial directions. Huang et al.11) determined the value
of kO , 0.8±0.1, at the melting point by comparing the oxygen
solubility in the silicon crystal with that in the silicon melt.40)
The value of kO in the present work agreed well with that reported by Huang et al.,11) who used a small silica ampoule to
ensure the equilibrium in the SiO2 (s)–Si(s,l)–SiO(g) system.
The values of kC reported by other research groups are
less than the present data as shown in Table 2. Durand and
Duby16) selected the carbon solubilities in solid and liquid silicon from the literatures, and the value of kC was evaluated to
be 0.034 at the melting point of silicon. Other three research
groups13–15) experimentally measured the carbon contents in
the silicon after zone melting, and the values of kC were reported in the range between 0.058 and 0.1. Since the zone
melting is a dynamic process, it may be difficult to achieve
the equilibrium distribution between crystal and melt especially at high temperatures, even if the zone traveling velocity
is extrapolated to zero.14, 15) In addition, it was reported that
carbon content in silicon was affected by the ambient atmosphere during the zone melting process.34) The accuracy of
the kC value obtained in the present work depends on that
of the carbon solubility in solid silicon. The equilibrium between solid silicon and silicon carbide was confirmed, but as
described in 4.2, the effect of oxygen atoms in solid silicon on
the carbon solubility should be clarified in order to evaluate
the accuracy of the present kC value in detail.
5. Conclusions
The oxygen and carbon contents in the solid silicon crystals after heating at 1673 K in an oxygen atmosphere and an
Ar–5%CO atmosphere, respectively, were measured and the
following results were obtained.
(1) The solubility values of oxygen and carbon in
solid silicon at 1673 K were 33 ± 3 mass ppm (2.9 ×
1018 atoms·cm−3 ± 2.6 × 1017 atoms·cm−3 ) and 24 ±
13 mass ppm (2.8×1018 atoms·cm−3 ±1.5×1018 atoms·cm−3 ),
respectively.
(2) The equilibrium distribution coefficients of oxygen
and carbon in silicon at the melting point were concluded to
be 0.85 ± 0.08 and 0.30 ± 0.16, respectively, by comparing
the solubilities at 1673 K with those in liquid silicon that were
previously reported by the present authors.
Acknowledgments
This work was partly supported by KAWASAKI STEEL
21st Century Foundation and the New Energy and Industrial
Technology Development Organization (NEDO) through the
Japan Space Utilization Promotion Center (JSUP).
REFERENCES
1) X. Huang and K. Hoshikawa: J. Crystal Growth Soc. Jpn. 26 [5] (1999)
226–234.
2) J. Fally, E. Fabre and B. Chabot: Rev. Phys. Appl. 22 (1987) 529–534.
3) Y. Kato, K. Hanazawa, H. Baba, N. Nakamura, N. Yuge, Y. Sakaguchi,
S. Hiwasa and F. Aratani: Tetsu-to-Nagaé, 86 [11] (2000) 717–724.
4) F. A. Trumbore: Bell. Syst. Tech. J., 39 (1960) 205–233.
5) Y. Yatsurugi, N. Akiyama, Y. Endo and T. Nozaki: J. Electrochem. Soc.
120 (1973) 975–979.
6) A. Murgai, H. C. Gatos and W. A. Westdorp: J. Electrochem. Soc. 120
(1979) 2240–2245.
7) W. Lin and D. W. Hill: J. Appl. Phys. 54 (1983) 1082–1094.
8) W. Lin and M. Stavola: J. Electrochem. Soc. 132 (1985) 1412–1416.
9) E. Iino, I. Fusegawa and H. Yamagishi: J. Jpn. Assoc. Crystal Growth
20 (1993) 37–44.
10) K. Kakimoto and H. Ozoe: J. Electrochem. Soc. 145 (1998) 1692–1695
11) X. Huang, T. Nakazawa, K. Terashima and K. Hoshikawa: Jpn. J. Appl.
Phys. 37 (1998) L1504–L1507.
12) L. B. Xu: J. Crystal Growth 200 (1999) 414–420.
13) E. Haas, W. Brandt and J. Martin: Solid-State Electron. 12 (1969) 915–
921.
14) T. Nozaki, Y. Yatsurugi and N. Akiyama: J. Electrochem. Soc. 117
(1970) 1566–1568.
15) B. O. Kolbesen and A. Mühlbauer: Solid-State Electron. 25 (1982) 759–
775.
16) F. Durand and J. C. Duby: J. Phase Equilibria 20 (1999) 61–63.
17) T. Narushima, K. Matsuzawa, Y. Mukai and Y. Iguchi: Mater. Trans.,
JIM 35 (1994) 522–528.
18) T. Narushima, N. Ueda, M. Takeuchi, F. Ishii and Y. Iguchi: Mater.
Trans., JIM 35 (1994) 821–826.
19) K. Yanaba, M. Akasaka, M. Takeuchi, M. Watanabe, T. Narushima and
Y. Iguchi: Mater. Trans., JIM 38 (1997) 990–994.
20) T. Narushima, K. Matsuzawa, M. Mamiya and Y. Iguchi: Mater. Trans.,
JIM 36 (1995) 763–769.
21) K. Yanaba, Y. Matsumura, T. Narushima and Y. Iguchi: Mater. Trans.,
JIM 39 (1998) 819–823.
22) B. E. Deal and A. S. Grove: J. Appl. Phys. 36 (1965) 3770–3778.
23) S.-T. Lee and D. Nichols: Appl. Phys. Lett. 47 (1985) 1001–1003.
24) R. A. Logan and A. J. Peters: J. Appl. Phys. 30 (1959) 1627–1630.
25) M. J. Binns, C. A. Londos, S. A. McQuaid, R. C. Newman, N. G.
Semaltianos and J. H. Tucker: J. Mat. Sci.: Mater. Electron. 7 (1996)
47–353.
26) P. A. Stolk, H.-J. Gossmann, D. J. Eaglesham and J. M. Poate: Mat. Sci.
Eng. B36 (1996) 275–281.
27) R. F. Scholz, P. Werner, U. Gösele and T. Y. Tan: Appl. Phys. Lett. 74
(1999) 392–394.
28) F. Rollert, N. A. Stolwijk and H. Mehrer: Mater. Sci. Forum 38–41
(1989) 753–758.
29) Science of Silicon, Surface Science Technology Series 3, ed. by T. Ohmi
and T. Nitta (Realize Inc., Tokyo, 1996) p. 1015.
30) H. J. Hrostowski and R. H. Kaiser: J. Phys. Chem. Solids 9 (1959) 214–
216.
31) A. R. Bean and R. C. Newman: J. Phys. Chem. Solids 32 (1971) 1211–
1219.
32) J. Gass, H. H. Müller, H. Stussi and S. Schweitzer: J. Appl. Phys. 51
(1980) 2030–2037.
33) J. C. Mikkelsen, Jr.: Appl. Phys. Lett. 41 (1982) 871–873.
34) Y. Itoh and T. Nozaki: Jpn. J. Appl. Phys. 24 (1985) 279–284.
35) Y. Endo, Y. Yatsurugi and N. Akiyama: Anal. Chem. 44 (1972) 2258–
2262.
36) F. V. Vook and H. J. Stein: Appl. Phys. Lett. 13 (1968) 343–346.
37) R. C. Newman and R. S. Smith: J. Phys. Chem. Solids 30 (1969) 1493–
1505.
38) R. C. Newman: Mater. Sci. Eng.J. Phys. Chem. Solids B36 (1996) 1–12.
39) K. Kakimoto and H. Ozoe: J. Crystal Growth 212 (2000) 429–437.
40) X. Huang, K. Terashima, H. Sasaki, E. Tokizaki and S. Kimura: Jpn. J.
Appl. Phys. 32 (1993) 3671–3674.