Science in China Ser. E Engineering & Materials Science 2004 Vol.47 No.3 281—292
281
Growth of Czochralski silicon under magnetic
field
XU Yuesheng, LIU Caichi, WANG Haiyun, ZHANG Weilian, YANG Qingxin,
LI Yangxian, REN Binyan & LIU Fugui
Institute of Information Function Materials, Hebei University of Technology, Tianjin 300130, China
Correspondence should be addressed to Xu Yuesheng(email: [email protected])
Received January 22, 2004
Abstract Growth of Czochralski (CZ) silicon crystals under the magnetic field induced
by a cusp-shaped permanent magnet of NdFeB has been investigated. It is found that the
mass transport in silicon melt was controlled by its diffusion while the magnetic intensity
at the edge of a crucible was over 0.15 T. In comparison with the growth of conventional
CZ silicon without magnetic field, the resistivity homogeneity of the CZ silicon under the
magnetic field was improved. Furthermore, the Marangoni convection which has a
significant influence on the control of oxygen concentration was observed on the surface
of silicon melt. It is suggested that the crystal growth mechanism in magnetic field was
similar to that in micro-gravity if a critical value was reached, named the growth of
equivalent micro-gravity. The relationship of the equivalent micro-gravity and the
magnetic intensity was derived as g=(v0/veff)g0. Finally, the orders of the equivalent
micro-gravity corresponding to two crucibles with characteristic sizes were calculated.
Keywords: Magnetic field, equivalent micro-gravity, diffusion-controlled mechanism, Marangoni convection.
DOI: 10.1360/03ye0325
During the growth of CZ silicon, polycrystalline silicon raw materials in quartz
crucibles become heavier and heavier with the increase in the diameter of silicon single
crystal. Therefore, the thermal convection of silicon melt plays more and more important
roles in controlling silicon crystal quality. In general, the driving force of thermal convection can be expressed by the Rayleigh number (R) as
R = g β b3 ∆T / κ V ,
(1)
where β is the bulk expanding coefficient of melt, g the gravity accelerator, ∆T the radial
temperature difference on the free surface of melt, b the characteristic size of melt (the
radius of crucibles), v the dynamic viscosity of melt and κ the thermal diffusion coefficient of melt. It can be known from eq. (1) that R is in direct proportion to b3, but in reverse proportion to v.
Copyright by Science in China Press 2004
282
Science in China Ser. E Engineering & Materials Science 2004 Vol.47 No.3 281—292
There are two ways to restrain the thermal convection of silicon melt. One is to
grow silicon crystal under micro-gravity in the space, where g→0 (in lower-orbit, g→g0
×10−4, and in higher-orbit, g→g0×10−5—10−6) and then R→0. In this case, there is no
macro-convection in melt, the transport of mass in melt is mainly controlled by its diffusion, the so-called diffusion mechanism. Therefore, the integrality and homogeneity of
—
silicon crystal can be improved greatly[1 3]. The other way is to grow silicon crystal in a
—
magnetic field[4 6]. It is well known that the convection of conductive melt in a magnetic
field is affected by the Lorentz’s force[7]. That means that the effective dynamic viscosity
of melt increases. The magnetic dynamic viscosity coefficient of melt can be expressed
as
veff = ( µ i B i b) 2 i σ / ρ ,
(2)
where µ is the magnetoconductivity of melt (µ=1 for silicon melt), B is the intensity of
magnetic field, σ is the conductivity of melt and ρ is the density of melt. It can be found
from eqs. (1) and (2) that the increase in veff and the decrease in g has almost the same
influence on Rayleigh number R.
For the growth of CZ silicon under micro-gravity in the space, the transport of mass
in melt is mainly controlled by diffusion mechanism. However, during the growth of CZ
silicon under magnetic field, if the intensity of magnetic field reaches a critical value (B
≥B0), all the macro-convection in melt can be restrained by the Lorentz’s force. That
means that the transport of mass in melt is also mainly dependent on its diffusion.
Therefore, we considered this growth as crystal growth under equivalent micro-gravity.
In 1966, the growth of InSb crystal in a magnetic field was first investigated[8]. It
was believed that under a magnetic filed the thermal convection and temperature fluctuation on the interface of crystal/melt was restrained so that growth striation was also
suppressed. However, Witt et al.[9] did not get the same results in 1970. Since the1980s,
due to the control of oxygen concentration and other benefits, the growth of CZ silicon
under a magnetic field has attracted much attention[10]. Nowadays, CZ silicon with a
diameter larger than 200 mm must be grown under a magnetic field in which the magnetic force line is vertical, horizontal or cusp-shape. In common, the magnetic field
could be induced by using electric magnet, low-temperature superconductor magnet and
permanent magnet. Among them, the permanent magnet is believed to be widely used in
future due to its simple equipment and no consumption of cooling water and power.
Furthermore, it is also well accepted that the cusp-shaped magnetic field is beneficial to
control oxygen concentration.
In this work, φ3″CZ silicon ingots were grown under the magnetic field introduced by using an NdFeB permanent magnet. The relation between the magnetic field
intensity and the order of micro-gravity will be discussed below.
Copyright by Science in China Press 2004
Growth of Czochralski silicon under magnetic field
1
283
Experimental apparatus
The furnace with a permanent magnet of NdFeB was used for the growth of CZ
silicon. The charge of polycrystalline silicon was about 10—15 kg. Outside the chamber
of the furnace, three independent permanent magnet rings numbered as A, B and C ring
were set, as shown in fig. 1. Those rings induced a magnet field with the cusp distribution of magnetic force line. By moving the rings B and C along a vertical axis, the distribution and intensity of the magnetic field in melt can be controlled. The intensity of
the magnetic field increased or decreased while rings B and C moved towards or away
from ring A. Meanwhile, the intensity of the magnetic field at the edge of crucibles
could be continuously changed from 0.01 to 0.02 T.
Fig. 1. Sketch map of the NdFeB permanent magnet structure in the furnace.
Fig. 2 is a sketch map of the magnetic field with the cusp-shaped magnetic force
lines, which was induced by the three conjoint magnetic rings. It is noted that on the
level plane of ring A, Bx=B, and Bz=0. Here, Bx and Bz are the intensity of the magnetic
field in x axis and z axis direction, respectively. The plane was named “plane 0”. In this
case, the intensity Bx of the magnetic field on plane 0 as a function of the radius of crucibles is given in fig. 3. Furthermore, Bz and B as a function of the distance away from
plane 0 are given in figs. 4 and 5, respectively.
2
Growth of silicon crystals
φ3", N-type, 〈111〉 oriented CZ silicon with a resistivity of 11—18 Ω·cm was
grown in a furnace. The diameter of the quartz crucible was 8 inches, and the charge 10
kg. During the growth of the crystal, the crystal rotation rate, the crucible rotation rate
and the pulling rate were 2—3 rpm, 1—1.2 rpm, and 1.0—1.2 mm/min, respectively.
2.1
Observation of Marangoni convection
During the growth of silicon crystal, a piece of molybdenum (Mo) as a marker was
put on the surface of the silicon melt in order to observe the Marangoni convection. By
adjusting the three conjoint magnetic rings, the “plane 0” was set up on the free surface
www.scichina.com
284
Science in China Ser. E Engineering & Materials Science 2004 Vol.47 No.3 281—292
of the silicon melt so that the magnetic field in melt reached the maximum value. It
could be observed in the furnace that the marker moved quickly to the center of the crucible due to surface tension gradient, which was so-called the Marangoni convection.
Fig. 2. Sketch map of the magnetic field with the cusp-shaped magnetic force lines, induced by three conjoint
magnetic rings as given in fig. 1.
Fig. 3. Intensity Bx of the magnetic field on plane 0 as a function of the radius of crucibles.
2.2
Oxygen concentration
Six CZ silicon ingots numbered as ingot A, B, C, D, E and F were grown respectively in the furnace with different intensities of magnetic field, which could be adjusted
by changing the distance between the “plane 0” and the surface of silicon melt. After
Copyright by Science in China Press 2004
Growth of Czochralski silicon under magnetic field
285
growing, the interstitial oxygen concentration of the ingots was measured by Fourier
transform infrared spectroscopy (FTIR) at room temperature. The relationship between
oxygen concentrations and magnetic field intensity was analyzed. It is assumed that Bz
keeps unchanged, while the distance between the “plane 0” and the free surface of silicon melt is in the range of 0—10 mm.
Fig. 4. Bz as a function of the distance away from the plane 0.
Fig. 5. B as a function of the distance away from plane 0.
2.3
Resistivity
The radial and vertical resistivity of the silicon ingots was measured by means of
four-probe method, and then was converted into carrier concentration. The relation between carrier concentration and magnetic field intensity was investigated.
www.scichina.com
286
Science in China Ser. E Engineering & Materials Science 2004 Vol.47 No.3 281—292
Table 1 Oxygen concentration in silicon vs. intensity of magnetic field
Magnetic field intensity（T）at the edge of
Oxygen concentration ([Oi])
φ200 mm crucible
No.
A
B
C
3
BX
BZ
B
0
0.1023
0.1570
0
0
0
0
0.1023
0.1570
head
14.9
9.1
7.2
1017cm−3
middle
14.7
7.5
6.36
tail
13.1
5.9
/
Results
3.1
The interstitial oxygen concentrations in ingots A, B and C
The interstitial oxygen concentrations in the wafers cut from ingots A, B and C,
which were grown under 0, 0.1, 0.15 T magnetic field, are shown in table 1. It can be
seen that the oxygen concentration was related to the intensity of the magnetic field.
3.2
Influence of Marangoni convection on interstitial oxygen concentrations
Ingots D, E and F ingots were grown while the distance between the free surface of
silicon melt and the “plane 0” was set at 20, 30 and 40 mm, respectively. With the increasing distance, Bz increased. Because the direction of Bz is vertical to the direction of
the Marangoni convection, Marangoni convection is restrained so that the oxygen concentrations in CZ silicon are affected. The oxygen concentrations in silicon vs. the distance between the free surface of silicon melt and the “plane 0” are listed in table 2. The
oxygen concentration in silicon vs. Bz is shown in fig. 6.
No.
C
D
E
F
3.3
Table 2 Oxygen concentration in silicon vs. the distance away from the plane 0
Magnetic field intensity/T at the edge
Interstitional oxygen
Distance away from
concentration
of φ 200 mm crucible
“plane 0”/mm
BX
By
B
ppma
1017cm−3
0.1570
0
0.1570
0
7.2
14.4
0.1491
0.1590
20
8.27
16.6
−0.0557
0.1406
0.1672
30
9.3
18.6
−0.0904
0.1291
0.1786
40
11.7
23.4
−0.1234
Solidified
percent
g (%)
20
20
20
20
Resistivity of ingots B, E, and F
Our resistivities of ingot B, E, and F which were grown under the 0.1, 0.16, 0.18T
magnetic field are shown in table 3. The axial resistivities of ingots E and F are converted into carrier concentration, as shown in fig. 7.
4
4.1
Discussion
Marangoni convection and oxygen concentration
The experimental results show that the oxygen concentration in CZ silicon grown
under magnetic field is related not only to magnetic field intensity, but also to the Marangoni convection on the surface of melt. When B reaches a critical value,
macro-convection in melt is restrained, and then the Marangoni convection driven by the
Copyright by Science in China Press 2004
Growth of Czochralski silicon under magnetic field
287
Fig. 6. Oxygen concentration vs. Bz and the distance between the free surface of silicon melt and the plane 0.
No.
B
E
F
Table 3 Resistivity distribution of silicon
Intensity of magnetic
Radial inhomogeneSolidified percent
ity of resistivity(%) field at the edge of φ200
g(%)
C
D
mm crucible/T
13.5
13.60
3.34
0.1023
10
10.6
10.15
8.4
50
6.15
6.60
7
90
18.37
18.63
4.6
0.1672
10
18.14
18.38
1.3
50
17.98
17.06
5.5
85
10.64
10.40
3.8
0.1786
10
9.96
9.90
1
25
9.30
9.40
2.1
55
8.60
8.55
2.3
85
Resistivity/Ωcm
A
B
13.15
9.75
6.55
18.8
18.33
17.03
10.8
9.95
9.5
8.70
13.55
9.95
6.40
19.23
18.15
17.04
10.50
10.0
9.46
8.50
Fig. 7.
Axial distribution of carrier concentration in silicon ingots E and F.
www.scichina.com
288
Science in China Ser. E Engineering & Materials Science 2004 Vol.47 No.3 281—292
gradient of surface tension becomes a dominant factor. The driving force can be expressed by the Marangoni number as
Ma= − ( ∆Tb / κ v)(∂r / ∂T ),
(3)
where ∂r / ∂T is the variation of surface tension with temperatures.
It is well known that silicon melt interacts with quartz crucibles to form SiO during
the growth of silicon ingots. The reaction is as follows:
SiO2+Si=2SiO.
(4)
In normal, SiO in silicon melt is saturated because of the strong thermal convection.
However, on the free surface, more than 99% of SiO evaporates out of the melt, and only
less than 1% of SiO gets into silicon crystal[7,11]. Therefore, oxygen concentration in
silicon crystal depends on the evaporation of SiO from the surface. Because the Marangoni convection is beneficial to the evaporation of SiO, oxygen concentration on the
melt surface is much lower; thus lower oxygen concentration in silicon crystals can be
obtained. It is clear that the oxygen concentration in silicon can be controlled by the
Marangoni convection. Fig. 8 shows the Marangoni convection and the evaporation of
SiO from silicon melt.
Fig. 8. Sketch map of the Marangoni convection and the evaporation of SiO from the silicon melt.
It was reported that the lines of magnetic force are always parallel to the Marangoni
convection in the cusp-shaped magnetic field[12, 13], as shown in fig. 9. The cusp-shaped
magnetic field has no influence on the Marangoni convection if the distance between the
free surface of melting silicon and “plane 0” is 0—10 mm, which is beneficial to the
evaporation of SiO from silicon melt.
In our experiments, while the distance between the plane 0 and the melt surface
was about 0—10 mm, the Marangoni convection was observed and then interstitial
Copyright by Science in China Press 2004
Growth of Czochralski silicon under magnetic field
289
oxygen concentration of 7×1017cm-3 in CZ silicon was obtained, which means that the
Marangoni convection could decrease oxygen concentration in silicon ingot. If the distance between the free surface and the plane 0 was 20, 30 and 40 mm respectively, the Bz
on the free surface increased so that the Marangoni convection was weakened. It is disadvantageous to the evaporation of SiO out of the melt, thus increasing the oxygen concentration in silicon crystals (table 2). Therefore, it is considered that the Marangoni
convection and oxygen concentration can be controlled by the distance between the
plane 0 and the melt surface. Because the distance can be continuously and precisely
regulated, the oxygen concentration in silicon crystals may be controlled in 5×1016cm−3
order(fig. 6).
Fig. 9. Sketch map of cusp-shaped magnetic field and Marangoni convection.
4.2
Improvement of resistivity homogeneity of silicon
The axial homogeneity of resistivity is generally controlled by impurity segregation
and convection effect during silicon crystal growth. As mentioned above, when the intensity of magnetic field reaches a critical value, the macro-convection in melt is inhibited so that the transportation of mass only depends on its diffusion. In this case, the
crystal growth is similar to that in the space. Thus, the effective segregation coefficient
of impurities is expressed as
keff =
k0
⎛ υ ⎞
k0 + (1 − k0 ) exp ⎜ − δ ⎟
⎝ D ⎠
,
(5)
where k0 is the equilibrium segregation coefficient of impurity in melt, δ is the thickness
of diffusion boundary layer, and D is diffusion coefficient of impurity in melt. In diffusion mechanism, the thickness of diffusion boundary layer δ →∞; therefore, keff=1,
meaning that the impurity concentration and resistivity along with the axial direction of
crystal are homogeneous. As is well known, the impurity concentration in crystals can be
www.scichina.com
290
Science in China Ser. E Engineering & Materials Science 2004 Vol.47 No.3 281—292
expressed as
⎡
⎛ k
CS ( z ) = CL ⎢1 − (1 − k0 ) exp ⎜ − 0
⎝ l
⎣
⎞⎤
z ⎟⎥ ,
⎠⎦
(6)
where z is solidified percentage of crystal. Using eq.(6) we calculated impurity concentration distribution along with the axial direction of crystal, as shown in fig. 7. It can be
seen that the distribution of the calculated impurity concentration is the same as the experimental. In this case, the intensity of magnetic field at the edge of crucible was higher
than 0.15 T, for example the growth of ingots E and F. Furthermore, the radial inhomogeneity of resistivity (∆ρ) of ingots E and F is also small. ∆ρ<5.5% for E, and ∆ρ≤
3.8% for F. However, if the intensity of magnetic field at the edge of crucible is less than
1 T (such as ingot B), the calculated data of impurity concentration distribution is greatly
different from the experimental. In this case, the radial inhomogeneity of resistivity (∆ρ)
is also bigger. For example, ∆ρ is less than 8.4% for ingot B.
4.3
The order of micro-gravity corresponding to magnetic field
In our experiments, oxygen concentration was controlled well and resistivity uniformity was improved when the magnetic field intensity at the edge of quartz crucibles
was higher than 0.15 T. To understand the influence of magnetic field intensity on the
control of oxygen concentration and resistivity uniformity, equivalent micro-gravity order should be derived. By eqs. (1) and (2), it can be derived as
g=
v0
g0 ,
veff
(7)
where g is the corresponding order of the equivalent micro-gravity, g0 the standard gravity accelerator and v0 the dynamic viscosity without magnetic field.
For Si melt, ρ =2530 Kg/m3, v0 =7.0×10−4 Kg/ms, and σ =1.2×106 s/m[14]. If the
influence of magnetic field on the β, κ, σ and ρ is neglected, the corresponding relation
between B and g could be calculated for b=0.15 m which is used in our experiments, as
listed in table 4. It can be seen from the table that the order of equivalent micro-gravity
is 3×10−3g0—1×10−3g0 , which is the gravity value of low orbit, when B at the edge of
quartz crucible is over 0.15 T.
5
Conclusion
(1) On the basis of Einstein’s equivalent principle, the increase in effective dynamic
viscosity of the melt is equivalent to the decrease in the order of gravity during crystal
growth. The liquid behaves as secondary class effect of micro-gravity in the case without
first class effect of micro-gravity[2,12,14]. In secondary class effect of micro-gravity, those
inferior forces concealed by gravity are unfolded evidently. In our experiment, the Marangoni convection became a dominant form of convection; therefore, δ →∞ and Keff
→1.
Copyright by Science in China Press 2004
Growth of Czochralski silicon under magnetic field
291
Table 4 Corresponding order of micro-gravity to magnetic field intensity
Intensity of magnetic field /T
0.06
Equivalent micro-gravity order
b=0.15 m(φ 8″ crucible)
b=0.25 m(φ16″ crucible)
1.82×10−2 g 0
6.56×10−3 g 0
1.02×10−2 g 0
6.58×10−3 g 0
3.68×10−3 g 0
2.37×10−3 g 0
4.58×10−3 g 0
2.92×10−3 g 0
1.65×10−3 g 0
1.05×10−3 g 0
0.25
1.64×10−3 g 0
1.05×10−3 g 0
5.92×10−4 g 0
3.79×10−4 g 0
0.3
7.29×10−4 g 0
2.62×10−4 g 0
0.08
0.1
0.12
0.15
0.2
The secondary class effect of micro-gravity shows that the mass transportation in
melt depends mainly on its diffusion, as in the situation of crystal growth in the space.
Therefore, crystal growth in equivalent micro-gravity can be realized on the ground.
(2) Marangoni convection can be observed on the melt surface when B is higher
than 0.15 T. The Marangoni convection is controlled by adjusting the distance between
the plane 0 and the melt surface. Furthermore, Marangoni convection affects effectively
SiO evaporation from silicon melt, hence oxygen concentration in silicon.
(3) The order of equivalent micro-gravity corresponding to magnetic field (B) is
expressed by
g=
v0
g0 .
veff
When B at the edge of crucible is higher than 0.15T, the order of equivalent micro-gravity is 3×10−3g0—1×10−3g0, corresponding to the gravity value of low-orbit satellite. If the magnetic field intensity at the edge of crucible is kept unchanged, the order of
equivalent micro-gravity increases with an increase in crucible diameter.
(4) Crystal growth under micro-gravity in the space seems unlikely to be industrialized. But the crystal growth under equivalent micro-gravity can be realized on the
ground. In our experiment, a stronger cusp-shaped magnetic field introduced by a permanent magnet brings an equivalent micro-gravity environment for growing CZ silicon
crystal, which is a new technique of crystal growth and can be widely used in industry.
Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No.
59972007) and the Ministry of National Science and Technology and the Natural Science Foundation of Hebei
Province (No.599033).
References
1.
Benz, K. W., Cröll, A, Melt growth of semiconductor crystals in micro-gravity conditions, Materials Science
Forum, 1998, 276-277: 109—118.
2. Hu Wenrui, The application and science of micro-gravity, Physics(in Chinese), 1978, 18: 11—14.
www.scichina.com
292
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
Science in China Ser. E Engineering & Materials Science 2004 Vol.47 No.3 281—292
Chen Wanchun, Study on the crystal growth in micro-gravity in the space, J. of Chinese Ceramic Society (in
Chinese) 1995, 23: 420—429.
Liang Xin’an, Jin Weiqing and Pan Zhilei, Progress of magnetic field application in crystal growth, Journal of
Inorganic Materials(in Chinese), 1999, 14: 833—839.
Han Yujie, Sun Tongnian, Introduction of crystal growth in magnetic field, Semiconductor Information(in
Chinese), 1989, 24: 25—30.
Masahito Watanobe, Minoru Eguchi, Wang Wei et al., Controlling oxygen concentration and distribution in
200mm diameter silicon crystals using the electromagnetic Czochralski (EMCZ) method, J. Crystal Growth,
2002, 237-239: 1657—1662. [DOI]
Khine, Y.Y., Walke, J.S., Buoyant convection during Czochralski silicon growth with a strong non-uniform,
axisymmetric magnetic field, J. Crystal Growth, 1995, 147: 313—319. [DOI]
Utech, H.F., Flemings, M., Elimination of solute banding in indium antimonide crystals growth in a magnetic
field, J. Appl. Phys., 1966, 37: 2021—2023.
Hurle, D. T. J., Hydrodynamics, convection and crystal growth, J. Crystal Growth, 1972, 13-14: 39—43.
Langlois, W.E., Lee Ki-Jun, Czochralski crystal growth in an axial magnetic field: effects of joule heating, J.
Crystal Growth, 1983, 62: 481—484 [DOI]
W hicks, T., Organ, A.E., Rileg, N., Oxygen transport in magnetic Czochralski growth of silicon with a
non-uniform magnetic field, J. Crystal Growth, 1989, 94: 213—228. [DOI]
Hiroshi Hirata, Keigo Hoshikana, Three-dimensional numerical analysis of the effects of a cusp magnetic
field on the flows, oxygen transport and heat transfer in a Czochralski Silicon melt, J. Crystal Growth, 1992,
125: 181—207. [DOI]
Hiroshi Hirata, Keigo Hosshikana, Silicon crystal growth in a cusp magnetic field, J. Crystal Growth,1989, 96:
747—755. [DOI]
Sabhapathy, P., Salcudean, M. E., Numerical study of Czochralski growth of silicon in an axisymmetric field,
J. Crystal Growth, 1991, 113: 164—180. [DOI]
Copyright by Science in China Press 2004