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2. 3 tf? 2±<D$im................................................. 10

2 . 4 Czfc^TJimm..................................................................................................................... 11

2 . 5 • ###&%..........,............................................................................................. 12

Chapter 2 Outline of the reseach and development results ............................................................ 18

2 . 1 Measurements of thermophysical properties of semiconductors......................... 18

2 . 2 Computer simulations............................................................................................................... 22

2 . 3 Experimental validation of the global simulation code......................................... 23

2 . 4 Model Experiment of Cz Furnace................................................................................. 24

2.5 Outcomes............................................................................................................................ 25

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APPENDIX- 1 iKa## - (t ......................................................334

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(Iflli:#) 1999 ¥ 3 n11) K.Nagata, E.Yamasue, H.Fukuyama, M.Hayashi and M.Susa

“Thermal Conductivity Measurement of Liquid Silicon under Microgravity

0cs i [ufflE-t^'>3 >) ^ os in, 1999 ¥ u ^, #

# (h 7° nt % , 12, [4], 857 (1999)

12) LU ¥ SO, # $, # lij t# ±: ri4 ÊtcS0@#:43 cfc

m 125 im, 1999 ¥

11 ^, 535

13) E.Yamasue, M.Susa, M.Hayashi, H.Fukuyama and K.Nagata: “Contribution from Phonon and

Electron to Thermal Conductivities of Solid and Liquid Silicon 15th European Conference

on Thermophysical Properties, Wuzburg, Germany, Sep. (1999)

14) H.Watanabe, M.Susa, H.Fukuyama and K.Nagata: “Emissivities of Liquid and Solid Silicon at

Melting Point 15th European Conference on Thermophysical Properties, Wuzburg, Germany,

Sep.(1999)

15) : “û n >*©**»*&” . 0*^sfi£S¥^, sg 4i mm

1999 ¥ 5 ft 20 0

( 2 ) '> S n. 1/ - 3 >

1) ill 1*1 , G.Mika, # ¥, Three-dimensional Numerical Simulation of Melt Flow and Its Thermal

Characteristics in Cz Crucible (Further Report), SB36[HlB¥'Ei^:S/^/7^>?rÂ l (1999) p75

2) K.Suzuki, T.Yamauchi, G.Mika and J.Szmyd, Unsteady Three-dimensional Melt Flow

Computation of Czochralski Single Crystal Growth of Super-Conducting Material, PCC99

AMIF European Science Foundation Workshop Phase Change with Convection : Modeling and

Validation. (1999)

3) #, 3 ? B *#

*¥= 1999 = , 1999 ^ 7 fl 29 B

4) S.H.Hahn, 0tt

4-5*2.: -mm&migfficomuizm-fz&mmtff”, 32

%*#%###, B204, 1999.

-13-

5) "Uniaxial strain observed in solid/liquid interface during crystal growth from melted Si : A

molecular dynamics study" by Ken Nishihira, Shinji Munetoh, and Teruaki Motooka 8th Int.

Conf. on Defects-Recognition, Imaging and Physics in Semiconductors, Narita, Japan,

September 15-18, 1999

6) "Molecular dynamics simulations of solid phase epitaxy of Si: Growth mechanism and defect

formation" by T.Motooka and K.Nisihira, S.Munetoh, K.Moriguchi, and A.Shintani Materials

Reasearch Society meeting, Boston, USA, November 29-December 5, 1999

7) ammm, wmmm s >”

2. s. 2

(i)

1) H.Fujii, M.Yamamoto, S.Hara and K.Nogi, “Effect of Gas Evolution at Solid-Liquid Interface

on Contact between Liquid Si and Si02”, J. Mater. Sci., 34 (1999) 3165-3168.

2) K.Mukai, Z.Yuan, K.Nogi and T.Hibiya, “Influence of Oxygen Partial Pressure in Atmosphere

on Temperature Coefficient of Surface Tension of Molten Silicon”, Proc. Twentieth Jpn Symp.

Thermophysical Properties, Tokyo, October (1999) 264-267.

3) K.Nogi, T.Matsumoto and H.Fujii, “Surface Tension Measurements of Molten Silicon in

Microgravity Environment”, 20th Jpn Symp. Thermophysical Properties, (1999) October 20-

22, Tokyo, 268-271.

4) K.Mukai, Z.Yuan, T.Hibiya and K.Nogi, “Effect of Oxygen partial Pressure on Temperature

Coefficient of Surface Tension of Molten Silicon”, Proc. Int. Astronautical Federation, IAF-

99-J1.06, p.1-6, 4-8, Oct. 1999.

5) K.Nogi, T.Nakano, T.Matsumoto and H.Fujii, “Effect of Droplet Distortion on Surface

Tension in Electromagnetic Levitation Method”, ISIJ int. Vol.40 (2000) in press.

6) K.Mukai, Z.Yuan, K.Nogi and T.Hibiya, “Effect of Oxygen Partial Pressure on the Surface

Tension of Molten Silicon and its Temperature Coefficient”, ISIJ int. Vol.40 (2000) in press.

7) Y.Asakuma, S.H.Hahn, Y.Sakai, T.Tsukada, M.Hozawa, T.Matsumoto, H.Fujii and K.Nogi,

—14 —

“Equilibrium Shape of a Molten Silicon Drop in an Electromagnetic Levitator in Microgravity

Environment”, Metall. Trans. A (2000) in press.

8) H.Fujii, T.Matsumoto, N.Hata, T.Nakano, M.Kohno and K.Nogi, “Surface Tension of Molten

Silicon Measured by Electromagnetic Levitation Method under Microgravity”, Metall. Trans.

A (2000) in press

9) H.Fujii, T.Matsumoto, M.Kohno, N.Hata and K.Nogi, “Analysis of Surface Oscillation of

Levitated Droplet in Microgravity”, submitted to Space Forum

10) H.Fujii, T.Matsumoto and K.Nogi, “Analysis of Surface Oscillation of Droplet under

Microgravity for the Determination of its Surface Tension”, submitted to Acta Metall.

11) K.Nogi, A.Shiraki, T.Nakano, T.Matsumoto and H.Fujii, “Surface Tension of Liquid Silicon”,

submitted to Proc. Spacebound 2000.

12) Yuzuru Sato, Takefumi Nishizuka, Ttomohiro Tachikawa, Masayoshi Hoshi, Tsutomu

Yamamura and Yoshio Waseda : Viscosity and Density of Molten Germanium, High Temp.

High Press., 32 (2000),

13) E.Yamasue, M.Susa, H.Fukuyama and K.Nagata “Non-stationary hot wire method with silica

coated probe for measuring thermal conductivities of molten metals” Metallurgical and

Materials Transactions A Vol.30A [8] (1999), p.1971-1979

14) H.Watanabe, M.Susa, H.Fukuyama and K.Nagata “Emissivities of Liquid and Solid Silicon at

the Melting Point” High Temp.-High Press., Vol.31 (1999), p.587-593

15) H.Fukuyama, E.Yamasue, M.Hayashi, M.Susa and K.Nagata : “ Challenge to Thermal

Conductivity Measurement of Liquid Silicon under Microgravity” , B 5/ > ^ V

^ AS 20 [Hi, C, 1999 ¥ 10 , Sg^lro^tS, A216, 280-283

16) H.Watanabe, M.Susa, H.Fukuyama and K.Nagata: “Measurement of Spectral Emissivity for

Metals and Semiconductors Using Cold Crucible” , 20 Ini,

1999 ¥ 10/3, A226, 308-311

17) D.Mitev, M.Saito and Y.Waseda, “Theoretical Estimation of Diffusion Coefficients of

Impurities in Silicon Melt”, High Temp. Mater. Proc., 19 (2000), f=P fiM 41.

-15-

(2) y 5 a 1/ — is s y

1) Z.Guo, S.Maruyama, A.Komiya, “Rapid yet accurate measurement of mass diffusion

coefficients by phase shifting interferometer”, Journal of Physics. D, Applied Physics, Vol.32,

pp.995-999, 1999.

2) Z.Guo, S.H.Hahn, S.Maruyama and T.Tsukada, “Global Heat Transfer Analysis in Czochralski

Silicon Furnace with Radiation on Curved Specular Surfaces”, Heat and Mass Transfer,

Vol.35, pp.185-190, 1999

3) muaii : “ttwfeufttusoinmitomr’, % 36

BWLmJCM, Vol.n, pp. 467-468, 1999.

4) SJA#-, S.H.Hahn, #0#^, R ill S S , #,

— 615, : “SiCz4p30^#&8lt###T”, B Vol.26, p.18, 1999.

5) S.H.Hahn, T.Tsukada, M.Hozawa, S.Maruyama and N.Imaishi, “Analysis of Radiation Heat

Transfer in CZ Crystal Growth Process”, 1999 JSME Annual Meeting, Vol.3, No.99-1,

pp.000-000, 1999.

6) K.Kakimoto, T.Umehara and H.Ozoe, ’’Molecular dynamics analysis on diffusion of point

defects” J.Crystal Growth, in print.

7) K.Kakimoto, T.Umehara and H.Ozoe, ’’Molecular dynamics analysis of point defects in silicon

near solid-liquid interface”, J.Vacuum Science, in print.

8) K.Kakimoto, Shin Kikuchi and H.Ozoe, ’’Molecular dynamics simulation of oxygen in silicon

melt”, J.Crystal Growth, 198/199 (1999) 114.

9) Y.Asakuma, S.H.Hahn, Y.Sakai, T.Tsukada, M.Hozawa, T.Matsumoto, H.Fujii, K.Nogi and

N.Imaishi : “Equilibrium Shape of a Molten Silicon Drop in an Electromagnetic Levitator in

Microgravity Environment”, Metall. Trans. B, in press.

10) M.Ishimaru and T.Motooka:"Molecular dynamics simulations of crystal growth from melted

silicon: defect formation processes" Mat. Res. Symp. Proc. Vol.538, 247-250 (1999).

11) Ken Nishihira, Shinji Munetoh, and Teruaki Motooka:"Uniaxial Strain Observed in

Solid/Liquid Interface during Crystal Growth from Melted Si: A Molecular Dynamics

Study" J.Crystal Growth, in press (2000)

12) T.Motooka, K.Nisihira, S.Munetoh, K.Moriguchi, and A.Shintani : "Molecular dynamics

—16 —

simulations of solid phase epitaxy of Si: Growth mechanisms" Phys. Rev. B, in press (2000)


simulations of solid phase epitaxy of Si: Growth mechanism and defect formation" Mat. Res.

Symp. Proc. , in press (2000)

-17-

Chapter 2 Outline of the Research and Development of Results

2 . 1 Measurement of Thermophysical Properties of Semiconductors

Kiyoshi Nogi

Joining and Welding Research Institute

Osaka University

The surface tension and density of liquid silicon were measured using the elctromagnetic

method in a high quality microgravity condition which is produced at JAMIC. The main results

are summarised as follows:

(1) The surface tension of liquid silicon was measured with a spherical droplet, the shape of

which was controlled by changing the current ratio between the quadru-pole coil and the

di-pole coil. The values were obtained in a wide temperature range of 1460K (below melting

point) to 1880K, and the temperature dependency are expressed by the following equation:

T =733-0.062 (T-1687)

T : surface tension (mN/m), T : temperature (K)

(2) The measured surface tension values of liquid silicon in purified Ar-H2 atmosphere (Po2 is at

least less than 1.1 x 10'14) and in Ar atmosphere are not significantly different. Therefore, it

is considered that the surface tension value during the actual production process of silicon

crystals can be expressed by the above equation.

(3) When the distortion of a droplet is small (approximately less than 1%), the surface tension

of the liquid can be calculated using Cummings' equation. However, as the distortion is

larger, the error in the surface tension value is also larger. This result indicates that when

the equation is applied to the results obtained in a terrestrial condition, the calculated value

includes a large error.

(4) Only 1% distortion can shift peaks in the frequency spectrum. Accordingly, in order to

obtain an precise surface tension value, it is essential to confirm that five modes exist (at

the same place) even when one peak is obtained.

-18

(5) The density of liquid silicon was precisely measured by obtaining the volume of the droplet

both from the top and side views. The temperature dependency can be expressed by the

following equation:

P =2.39 -2.47 X 10"4 (T-1687)

P : density (Mg/m3), T: temperature (K).

The experiments were carried out to obtain the precise and reliable viscosity and density of

molten semiconductors for improving the industrial crystal growth and studying the

thermophysics of the semiconductors. Viscosity has been measured by using the oscillating

viscometer which was suitable for high temperature melt with low viscosity. Density was

measured by using the pycnometric method which was suitable for oxidizable high temperature

molten metals. For the viscosity measurement of molten silicon, various refractories which have

different wettability with molten silicon were used for the crucible materials to study the effect

on the measurement. Alumina crucible was used for molten germanium. GaSb and InSb were

sealed perfectly in the quartz crucible to avoid the evaporation of Sb. All the results on the

viscosity showed good Arrhenian behavior and no abnormality was found near the melting

temperatures. Most results for molten silicon showed almost same viscosity independently of the

crucible materials. The feature of molten semiconductors on the viscosity are low viscosity, low

activation energy compared with other molten metals. Furthermore, the semiconductors studied

show not so different viscosities. It is very interesting on the viewpoint of the structure of molten

semiconductors. Densities of molten silicon and germanium were measured by using the

pycnometer made of boron nitride showed good linear relationship against the temperature and

the absolute values were intermediate values compared with literature values.

The thermal conductivity and normal spectral emissivity of solid and liquid silicon are

required to develop mathematical models of the heat flow in manufacturing processes for silicon

single crystals. This work aimed at obtaining accurate values for these thermophysical

properties.

The non-stationary hot wire method was used to measure thermal conductivities of solid and

liquid silicon, where hot-wire probes were insulated electrically from silicon samples using silica

films. The thermal conductivity of solid silicon decreased with increasing temperature. In solid

silicon, heat is principally transported by phonon conduction at temperatures below 1000 K, and

above 1000 K electronic conduction also contributes to heat transfer. The thermal conductivities

-19-

(X) in the respective temperature ranges can be expressed as a function of temperature (T) as

follows:

rt < T < 1000 K Xsolidilow tcmp = (1.40x10 2 + 1.90x10 + 2.92X10'5)1 Wm 'K'1

1000 K < T < 1673K Xsolidhigh tcmp = Xsoljd low temp + Xe Wm K

where Xe = 8.28 - 2.35x10 2T + 2.01x10 2 - 4.30x10 3 Wm 'K1

The thermal conductivity of liquid silicon measured under microgravity is 6 to 8 Wm^K"1 at

1698-1737K.

On the other hand, the normal spectral emissivity of silicon was derived as the ratio of the

normal radiation intensity from silicon sample to that from a blackbody at the same temperature

as the sample. The sample and the blackbody were heated up using the cold crucible. Normal

spectral emissivities of liquid and solid silicon were determined at the melting point in the

wavelength ranges of 650-850 nm and 1000-2500 nm. For example, values of emissivities

measured at 650 nm and 1500 nm are as follows:

650 nm: 0.231 for the liquid, 0.377 for the solid,


The emissivity in solid is larger than that in liquid at the wavelength investigated. The emissivity

in liquid decreases slightly with increasing wavelength, which indicates that molten silicon is

metallic. On the contrary, the emissivity in solid increases with increasing wavelength, which

indicates solid silicon is still semiconductor even at high temperature such as the melting point.

The solubilities of oxygen, nitrogen and carbon in liquid silicon equilibrated with silica,

silicon nitride and silicon carbide, respectively, were measured. The melting and analytical

methods were developed and accurate data on the solubilities were obtained. The standard Gibbs

free energy changes for dissolution of oxygen, nitrogen and carbon in liquid silicon were

determined. The effect of alloying elements on oxygen and carbon solubilities was clarified.

The relationship between SiO partial pressure in gas phase and oxygen contents in liquid

silicon was discussed thermodynamically, which is an important factor for removing of the

dissolved oxygen from liquid silicon. The maximum SiO partial pressure was calculated to be

around 0.01 atm at 1685 K. The SiO partial pressure was graphically shown as a function of the

dissolved oxygen contents.

Oxygen solubility in solid silicon at the melting point of silicon (Cs) was measured by a

chemical equilibrium method. The value of oxygen equilibrium distribution coefficient

(segregation coefficient, Cs / CL) was evaluated to be from 0.7 to 0.9 by using Cs and oxygen

-20-

solubility in liquid silicon at the melting point (CL) which has been reported by the authors.

The self-diffusion coefficient in pure silicon melt and diffusion coefficients of O, Al, B and

P impurities in silicon melt have been calculated on the basis of the Enskog theory implemented

with a pair-correlation function at contact between dissimilar atoms. The activation energies for

diffusion were also estimated by taking in account the temperature dependence of packing

fraction of silicon melt. Although only limited experimental data are available for comparison,

the present theoretical approach appears to work well and to be useful for predicting diffusion

coefficients of impurities in silicon melts.

-21-

2 . 2 Computer Simulations

Nobuyuki Imaishi

Institute of Advanced Material Study

Kyushu University

Numerical simulation codes have been developed during these 5 years. The most important

simulation codes are such as the gas phase transport phenomena code (flow, heat transfer and

mass transfer in the gas phase), melt phase transport phenomena code, heat transfer in the solid

phases together with radiative heat transfer between partially specular diffuse gray surfaces, 2

and 3 dimensional melt flow analysis codes based on a k-e turbulent model, 3 dimensional

unsteady melt phase transport phenomena codes and a main program which enables the global

simulation by combining the whole set of program codes to determine the pseudo steady state of a

Cz furnace under a given geometry and heat input. As of the end of January 2000, this global

analysis code has been developed and confirmed its validity for a small scale Cz furnace.

However, the code is subjected to some difficulties for application to a large scale Cz furnaces,

since the 3-D unsteady simulation of melt flow in a large crucible requires very long CPU time on

the conventional computers. More powerful Computer and/or a further development of a reliable

turbulent model, which is applicable to such a weak turbulent flow accompanied by rotating flow.

In addition to these macro-scale simulations, micro-scale simulations, such as the Molecular

Dynamics (MD) simulation and the Monte Carlo (MC) simulation, have been conducted in order

to investigate fundamental aspect of crystal growth from atomistic viewpoints. The results of

these micro-scale simulations must be explained and connected with the realistic crystal growth

phenomena via some, yet unknown, scaling laws. MD simulations investigated on 1) behavior of

silicon crystal under highly compressive or tensile forces, 2) diffusion of point defects in crystal

and 3) diffusion of oxygen atom in silicon melt.

-22-

2 . 3 Experimental validation of the global simulation code

Nobuyuki Imaishi


Kyushu University

It is necessary to place some experimental works to confirm the validity of the developed

global simulation code. This research project could not expect the cooperation from industry.

Then we decided to conduct some cold model experiments by using silicone oil and low

temperature liquid alloys. But these experiments provide only information on flow velocity and

temperature distribution in the model fluids. These do not represent the complex phenomena in

silicon Cz furnaces. Then, we asked Prof. Hoshikawa of Shinshu University and the Fundamental

Research Laboratories of NEC Corporation to conduct some crystal growth experiments and

provide the results for the sake of validity check. Prof. Hoshikawa has provided us temperature

distribution in his Cz furnace (crucible diameter: 168mm) with and without a funnel shaped gas

guide. His experiments confirmed the simulation’s results that the gas guide would reduce power

consumption and also provide easier control of temperature gradient in the growing crystal. Prof.

Hoshikawa is going to install a power supply meter to his furnace and will provide us more

detailed data.

The Cz furnace at NEC was operated and a 35mm diameter crystal was grown from a crucible

(diameter: 75mm). An X ray radiographic observation of the melt-crystal interface was conducted

and the results were provided. The melt-crystal interface shape was well simulated by the global

simulation code. Further, a simulated oxygen concentration is compared with an experimental

result that was reported by the NEC researchers using the same furnace, although the

experimental condition was slightly different from the present experiment. The simulated oxygen

concentration falls very close to their experimental result. The present simulation requires no

adjustable parameters on oxygen mass transfer. These results suggest the validity of the global

analysis code developed by this research project.

-23-

2 . 4 Model Experiment of Cz Furnace

Kimihisa Itoh

Department of Science & technology,

Waseda University

The precise experimental data are important to develop and verify a computer simulation

program of the unsteady convection flow of melt. The following experiments were conducted to

establish the database of the melt flow in a cold model using water, silicone oil and Wood's metal

as model materials.

(1) Temperature profile measurement in the melt: The temperatures in Wood's metal which is a

low Pr melt as silicon were continuously measured using telemeter system. The obtained results

were arranged in a visible form and stored as a database.

(2) Velocity profile measurement in the model crucible: The larger single crystal was employed

and the experimental furnace was modified to rotate at very low rate. This modification made the

model experiments more close to the actual operating conditions of Cz furnace. Time change of

melt flow was measured by LDV and the flow profile was measured by PIV. The obtained results

were arranged and stored as a database.

— 24 —

2 . 5 Outcomes

2 . 5 . 1 Symposiums

( 1 ) Measurements of Physical Properties

1) mm m, uhxdsm:*?, es

SJ S^ 30 (NCCG-30) * /t ;i/ ^7 fiKS ^ 5/ ^7 A , 1999 ¥

7 /! 22 0

2) m#^#, ew m, si

m 89 1999 ¥ 11 ^ 26 0

3) BÊsE, m, LU# f] : HD*6$ ; SB 124 00*Am

(1999), 110. (1999 ¥ 3 £ 29 0), Mm.

4) &B I : '> U 3 ; 0 **§B(S 30 HI £S B S ffl ft £

S) , 26 (1999), 14. (1999 ¥ 7 ^ 22 0), # 0 .

5) Yuzuru Sato, Takefumi Nishizuka, Tomohiro Tachikawa, Masayoshi Hoshi, Tsutomu

Yamamuraand Yoshio Waseda : Viscosity and Density of Molten Germanium ; 15th Europian

Conference on Thermophysical Properties Abstract, (1999), 165. (1999 ¥ 9 ^ 8 0), H -T

V * Wurzburg.

6) &m m, m a#, m# am

; m 31 (1999) , 1.

(1998 ¥ 11 ft 11 0), Mii?.

7) &m m, am * : ^s* insb <d*ss ■, m 125 00^^!^

(1999), 540. (1998 ¥ 11 £ 21 0), A2R.

8) , S£ES, # #, is Lilith, TkfflfnS : f&{£'> U n ><D BASSOS

gi^j , ^ 1999 ¥ 3 ^

9) tmsx, m&m®, miumz, 3d m

j , (m^%#±#) 1999 ¥

3 n

10) WfflSX, 3I£E®, : ryij3>-^fJK-7A0

-25-

(iMli^f) 1999 ¥ 3 B


Conductivity Measurement of Liquid Silicon under Microgravity”, B¥l^$£J ft X > ^ V

AS 20 HI, 1999 ¥ 10 ^ A216, 280-283

12) H.Watanabe, M.Susa, H.Fukuyama and K.Nagata : “Measurement of Spectral Emissivity for

Metals and Semiconductors Using Cold Crucible”, B ^ ft S/ > # v ^ A S 20 HI, $

1999 ¥ 10 ^ A226, 308-311

13) K.Nagata, E.Yamasue, H.Fukuyama, M.Hayashi and M.Susa “ Thermal Conductivity

Measurement of Liquid Silicon under Microgravity” B (S 1 HI @1 IE

-k y '> 3 >) S 138 HI, 1999 ¥ 11 £ , yntx, 12, [4], 857(1999)

14) OJ^SI, M&m®, # $, tg Lilith, : ri4 #70^00#:^ j; a'##: I:

s 125hi, 1999¥ 11 n, 535

15) E.Yamasue, M.Susa, M.Hayashi, H.Fukuyama and K.Nagata : “Contribution from Phonon and

Electron to Thermal Conductivities of Solid and Liquid Silicon” 15th European Conference on

Thermophysical Properties, Wilzburg, Germany, Sep. (1999)

16) H.Watanabe, M.Susa, H.Fukuyama and K.Nagata : “Emissivities of Liquid and Solid Silicon

at Melting Point” 15th European Conference on Thermophysical Properties, Wuzburg,

Germany, Sep. (1999)

i?) : “vun i 41 mi

1999 ¥ 5 20 B

( 2 ) Computer Simulations

1) ill 1*1, G.Mika, In Tfc, Three-dimensional Numerical Simulation of Melt Flow and Its Thermal

Characteristics in Cz Crucible (Further Report), S 36 HlB^fc;#&S/>3^;/Â \ (1999)

P75



-26-


Validation.(1999)

3) ** «t, ff : “^3 » B*«

1999 # 1999 # 7 fl 29 H

4) «###. TfflStil, S.H.Hahn, «B|S£*, SiRÊ, $**¥, *#£*, »» ».

: “»ESili$#©S«iCier-5.»<*)R#r", 32

%*!*#$ WS, B204, 1999.

5) "Uniaxial strain observed in solid/liquid interface during crystal growth from melted Si : A

molecular dynamics study" by Ken Nishihira, Shinji Munetoh, and Teruaki Motooka 8th Int.






?> ammm, mmmm )iuzs a

>” 1999 B

2 . 5 . 2 Submitted Papers

( 1 ) Measurements of Physical Properties


on Contact between Liquid Si and Si02”, J. Mater. Sci., 34 (1999) 3165-3168.





Microgravity Environment”, 20th Jpn Symp. Thermophysical Properties, (1999)October 20-22,

Tokyo, 268-271.


-27-


99-J1.06, p.1-6, 4-8, Oct. 1999.

5) K.Nogi, T.Nakano, T.Matsumoto and H.Fujii, “Effect of Droplet Distortion on Surface

Tension in Electromagnetic Levitation Method”, ISIJ int. Vol.40 (2000) in press.








A (2000) in press







12) Yuzuru Sato, Takefumi Nishizuka, Ttomohiro Tachikawa, Masayoshi Hoshi, Tsutomu

Yamamura and Yoshio Waseda : Viscosity and Density of Molten Germanium, High Temp.

High Press., 32 (2000),

13) E.Yamasue, M.Susa, H.Fukuyama and K.Nagata “Non-stationary hot wire method with silica

coated probe for measuring thermal conductivities of molten metals Metallurgical and

Materials Transactions A Vol.30A [8] (1999), p.1971-1979

14) H.Watanabe, M.Susa, H.Fukuyama and K.Nagata “Emissivities of Liquid and Solid Silicon at

the Melting Point” High Temp.-High Press., Vol.31 (1999), p.587-593

15) D.Mitev, M.Saito and Y.Waseda, “Theoretical Estimation of Diffusion Coefficients of

Impurities in Silicon Melt”, High Temp. Mater. Proc., 19 (2000), EP MW 41.

-28-

( 2 ) Computer Simulations

1) Z.Guo, S.Maruyama, A.Komiya, “Rapid yet accurate measurement of mass diffusion

coefficients by phase shifting interferometer”, Journal of Physics. D, Applied Physics, Vol.32,

pp.995-999, 1999.


Silicon Furnace with Radiation on Curved Specular Surfaces”, Heat and Mass Transfer, Vol.35,

pp.185-190, 1999.

3) ff 36

M&mlCM, Vol.H, pp. 467-468, 1999.

4) S.H.Hahn, HOlSS, ## #,

— 615, MiWMM : “SiCz B Vol.26, p.18, 1999.



pp.000-000, 1999.


defects” J.Crystal Growth, in print.


near solid-liquid interface”, J.Vacuum Science, in print.

8) K.Kakimoto, Shin Kikuchi and H.Ozoe, "Molecular dynamics simulation of oxygen in silicon

melt”, J.Crystal Growth, 198/199 (1999) 114.


N.Imaishi : “Equilibrium Shape of a Molten Silicon Drop in an Electromagnetic Levitator in

Microgravity Environment”, Metall. Trans. B, in press.

10) M.Ishimaru and T.Motooka : "Molecular dynamics simulations of crystal growth from melted

silicon: defect formation processes" Mat. Res. Symp. Proc. Vol.538, 247-250 (1999).

11) Ken Nishihira, Shinji Munetoh, and Teruaki Motooka: "Uniaxial Strain Observed in

Solid/Liquid Interface during Crystal Growth from Melted Si: A Molecular Dynamics Study"

J.Crystal Growth, in press (2000)

-29-


simulations of solid phase epitaxy of Si : Growth mechanisms" Phys. Rev. B, in press (2000)




-30-

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Precise measurements for surface tension, density

Kiyoshi Nogi, Hidetoshi Fujii and Taihei Matsumoto

Joining and Welding Research Institute,

Osaka University

Abstract:

The surface tension and density of liquid silicon were measured using the elctromagnetic

method in a high quality microgravity condition which is produced at JAMIC. The main results

are summarised as follows:

(1) The surface tension of liquid silicon was measured with a spherical droplet, the shape of

which was controlled by changing the current ratio between the quadru-pole coil and the di

pole coil. The values were obtained in a wide temperature range of 1460K (below melting

point) to 1880K, and the temperature dependency are expressed by the following equation:

T =733-0.062 (T-1687)

T : surface tension (mN/m), T : temperature (K)

(2) The measured surface tension values of liquid silicon in purified Ar-H2 atmosphere (Po2 is at

least less than 1.1 x 10'14) and in Ar atmosphere are not significantly different. Therefore, it

is considered that the surface tension value during the actual production process of silicon

crystals can be expressed by the above equation.

(3) No effect of the addition of 20ppm antimony to silicon was observed.

-32-

(4) When the distortion of a droplet is small (approximately less than 1%), the surface tension

of the liquid can be calculated using Cummings’ equation. However, as the distortion is

larger, the error in the surface tension value is also larger. This result indicates that when the

equation is applied to the results obtained in a terrestrial condition, the calculated value

includes a large error.

(5) Only 1 % distortion can shift peaks in the frequency spectrum. Accordingly, in order to

obtain an precise surface tension value, it is essential to confirm that five modes exisit (at

the same place) even when one peak is obtained.

(6) The density of liquid silicon was precisely measured by obtaining the volume of the droplet

both from the top and side views. The temperature dependency can be expressed by the

following equation:

P =2.39 -2.47X10-4 (T-1687)

P : density (Mg/m3), T: temperature (K).

(2)

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— 44 —

(6)


on Contact between Liquid Si and Si02”, J.Mater. Sci., 34 (1999) 3165-3168.





Microgravity Environment”, 20th Jpn Symp. Thermophysical Properties, (1999) October 20-22,

Tokyo, 268-271.



99-J1.06, p.1-6, 4-8, Oct. 1999.

5) K.Nogi, T.Nakano, T.Matsumoto and H.Fujii, “Effect of Droplet Distortion on Surface Tension

in Electromagnetic Levitation Method”, ISIJ int. Vol.40 (2000) in press.








A (2000) in press.







-45

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( 7 ) *#X«

1) B.J.Keen, Surface Inteface, Annal., 10 (1987), 367.

2) R.C.Murarka, W.K.Lu and A.E.Hamielec, Metall. Trans., 2B (1971), 2949.

3) K.Nogi, K.Ogino, A.Mclean and W.A.Miller, Metall. Trans., 17B (1986), 163.

4) A.Kasama, A.McLean, W.A.Miller, Z.Morita and M.J.Ward, Canad. Metall. Q., 22 (1983), 9.

5) I.Egry, G.Lohoefer and G.Jacobs, Phys. Rev. Lett., 75 (1995), 4043.

6) D.Cummings and D.Blackburn, J. Fluid Mech., 224 (1991), 395.

7) P.V.R.Suryanarayana and Y.Bayazitoglu, Phy. Fluids, A3 (1991), 967.

8) I.Egry, S.Sauerland, and G.Jacobs, High Temp. High Press., 26 (1994), 217.

9) K.C.Mills and R.F.Brooks, Mat. Sci. Eng., A178 (1994), 77.

10) M.Langen, T.Hibiya, M.Eguchi and I.Egry, J.Crystal Growth, 186 (1998) 550.

11) Load Rayleigh, Proc. Roy. Soc. London 29 (1879), 71.

12) Iron and Steel institute of Japan, Database for physical values of Moten iron and slags, 1972,

1.

13) K.Eckler, I.Egry and D.M.Herlach, Mater. Sci. Eng., A133, (1991) 718.

14) S.Krishnan, G.P.Hansen, R.H.Hauge and J.L.Margrave, High Temp. Sci., 26, (1990) 143.

15) H.Lamb, Hydrodynamics, 6th Edition, (1932).

16) * ]EP!!, 05 Bit##:#, /MU1EA,

23 (1996), 374.

17) JANAF Thermochemical Tables, Second Ed., by D.R.Stull and H.Prophet (1971).

18) M.Przyborowski, T.Hibiya, M.Eguchi and I.Egry, J.Crystal Growth, 151 (1995) 60.

— 46 —

gas inlet

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— 56 —

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57-

Measurement of Viscosity of Molten Silicon, Germanium, GaSb and InSb,

and Density of Molten Silicon and Germanium

* Yuzuru Sato and **Yoshio Waseda

* Graduate School of Engineering, Tohoku University

** Institute for Advanced Materials Processing, Tohoku University

Abstract:

The experiments were carried out to obtain the precise and reliable viscosity and density of

molten semiconductors for improving the industrial crystal growth and studying the thermophys

ics of the semiconductors. Viscosity has been measured by using the oscillating viscometer which

was suitable for high temperature melt with low viscosity. Density was measured by using the

pycnometric method which was suitable for oxidizable high temperature molten metals. For the

viscosity measurement of molten silicon, various refractories which have different wettability

with molten silicon were used for the crucible materials to study the effect on the measurement.

Alumina crucible was used for molten germanium. GaSb and InSb were sealed perfectly in the

quartz crucible to avoid the evaporation of Sb. All the results on the viscosity showed good Ar-

rhenian behavior and no abnormality was found near the melting temperatures. Most results for

molten silicon showed almost same viscosity independently of the crucible materials. The feature

of molten semiconductors on the viscosity are low viscosity, low activation energy compared

with other molten metals. Furthermore, the semiconductors studied show not so different vis

cosities. It is very interesting on the viewpoint of the structure of molten semiconductors. Densi

ties of molten silicon and germanium were measured by using the pycnometer made of boron

nitride showed good linear relationship against the temperature and the absolute values were

intermediate values compared with literature values.

-58-

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(6) *3t«W

1) Yuzuru Sato, Hongmin Zhu, Yuichi Kameda, Takeshi Nagasawa and Tsutomu Yamamura :

Viscosity Measurement of Molten Fe base Si Alloy ;

S 17 @&t#ltt->>7it>'>.ftS#S5ii!5t* (1996), 119-122 (1996 11 fl 29 B ) , O < tt.

2) ft* e, lu# *, * as, j$s s* is, mm*-, m = >u 3 >m

«©fflStiSEie ; S 120 @H*6S¥S#IS«tE, (1997), 331. (19973 fl 27 B),

3) Yuzuru Sato, Shinpei Moriguchi and Tsutomu Yamamura : Viscosity of Molten Iron *,

# 18 0%##>>Ai>')ftMiK#3t# (1997), 149. (1997 ¥ 10 fl 24 B), $6

4) ftS m. Hi# ft : SStS# ©®tt ; S#XÊ%0r» 6 @E%M

ms, (1997 ¥ 11 Ji 13 H), Ml6

5) feS E, 111# ft : *##:m#:0#*IC3HT ; (1998),

14. (1998 ¥ 7 fl 25 B), ftE.

6) Yuzuru Sato, Yuichi Kameda, Toru Nagasawa, Takeshi Sakamoto, Shinpei Moriguchi and

-69-

Tsutomu Yamamura : Viscosity of Molten Silicon and its Temperature Dependence ; Proceed

ings of the 5th Asian Thermophysical Properties Conference (ATPC’98) (1998), 511. (1998 ¥

9 ft 2 0), 1 Seoul.

7) m, ti: mm-v'DKomm.; % 123 @8*##

(1998), 181. (1998 ^9^ 28 0), Yk Ol.

8) Yuzuru Sato, Takeshi Sakamoto, Shinpei Moriguchi, Tsutomu Yamamura and Yoshio

Waseda : Viscosity Measurement of Molten Silicon and its Behavior near the Melting Point ;

(1998), 119. (1998 ¥ 10 £ 22 0 ), IB3.

9) m, m, m m#, ti:; m 30 (1998), 57. (1998 ¥ 11 n 12 B),

;kE.

10) *jhm, m 124 mi8$A

(1999), 110. (1999 ¥ 3 ft 29 8 ), 3EM.

u) &jm m : v u n ; b^sssu&s^ss ob 30

, 26 (1999), 14. (1999 ¥ 1 ft 22 0), #0.

12) Yuzuru Sato, Takefumi Nishizuka, Tomohiro Tachikawa, Masayoshi Hoshi, Tsutomu Yama-

muraand Yoshio Waseda : Viscosity and Density of Molten Germanium ; 15th Europian Con

ference on Thermophysical Properties Abstract, (1999), 165. (1999 ¥ 9 ft 8 0), Y ¥ V m

Wurzburg.

13) &# m, b#pm®, m re, m# ts, subs* :

^31 imgmmfk#####;#### (1999), 1.

(1998 ¥ 11 fl 11 0), fill#.

14) HSHis, &m m, m# * = mm insb ©tss ; s 125 @0*#*

(1999), 540. (1998 ¥ 11 J? 21 0), AiR.

15) Yuzuru Sato, Takefumi Nishizuka, Ttomohiro Tachikawa, Masayoshi Hoshi, Tsutomu Yama

mura and Yoshio Waseda : Viscosity and Density of Molten Germanium, High Temp. High

Press., 32 (2000),

-70-

( 7) ####

1) V.M.Glazov, S.N.Chizhevskaya and N.N.Glagoleva : Liquid Semiconductors (1969), Plenum

Press, NY.

2) K.Kakimoto, M.Egichi, H.Watanabe and T.Hibiya : J.Cryst.Growth, 94 (1989), 412-420.

3) H.Sasaki, E.Tokizaki, X.M.Huang, K.Terashima and S.Kimura : Jpn.J.Appl.Phys., 34 (1995),

3432-3436.

(1997), 59-88.

5) H.Sasaki, E.Tokizaki, K.Terashima and S.Kimura : Jpn.J.Appl.Phys., 33 (1994), 3803-3807, 34

(1995), 6078-6081.

6) L.-D.Lucas : Mem.Sci.Rev.Metal., 61, 1 (1964), 1-24.

7) W.K.Rhim, S.K.Chung, A.J.Rulison and R.E.Spjut : Int.J.Thermophys., 18 (1997), 459-469.

8) Yu.N.Taran-Zhovnir, N.M.Kochegura, S.P.Kazachkov, V.R.Pilipchuk, E.A.Markovskii, V.Z.

Kutsova and K.V.Uzlov : Sov.Phys.Dokl., 34 (1989), 282-284.

9) N.P.Mokrovski and A.R.Regel : J.Phys.Tech., 22 (1952), 1281.[Ref.l3 K)

10) % m 14

5:S, (1993), 319-322.

11) L.Martin-Garin, M.Gomez, P.Bedon and P.Desre : J.Less-Common Metal.. 41 (1975), 65-76.

12) W.Klemm et.al : Monatsch.Chem., 83 (1952), 629. [Ref.ll 0 31 ]

13) & mm, m, a:

14) R.Roscoe : Proc. Phys.Soc., 72 (1958), 576.

15) ebjes, s, afinite, *s m,

51(1987), 328-337.

16) Y.Sato, T.Yamamura, H-M.Zhu, M.Endo, T.Yamazaki, H.Kato, T.Ejima and G.J.Janz :

Proc.Third Intern.Sympo.Carbonate Fuel Cell Tech., (1993), 416-428.

(1998), 50-69.

18) K.Yanaba, M.Akasaka, M.Takeuchi, M.Watanabe, T.Narushima and Y.Iguchi : Mater. Trans.

JIM, 38 (1997), 990.

-71-

Data processing

Wire(Pt-13%Rh)TimeCounter

Phototransistor

Inertia diskLaser light

Colimator lens Oscillationinitiator

Convex lens —i Tungsten rod

CrucibleHe-Ne laser

m 3.1.2-1

‘ e1 *""1 1 , , , ' ' 1

§8

1 i8...... «... ....a......

■

■ ■ ■ ■ ■ ■ , . , . . ,) —i—i—i—i—i—i .-I —i—i—i ,—>—i—, i—i—0.0 2.0 4.0 6.0 8.0 10.0

ratio, h/r

m 3.1.2-2awt 4-a. a 26m

(molten Sn, Temp.=573K, radius=8mm)

3.1.2-1 tHEIEibEBSIHc

Substance TempVK Obtained /mPa s

Literature /mPa s

Deviation(%)

289.5 1.095 1.101 -0.5

Water 293.6 1.010 0.933 +1.7296.6 0.927 0.925 +0.2

Mercury 288.4 1.578 1.583 -0.3

305.0 1.497 1.489 +0.5

-72-

11: Head Com 2: Gas Inlet 3: Torsion Wire 4: Water Circulation Pipe 5: Reflection Mirror 6: Window 7: Inertia Disk 8: Oscillation Initiator 9: Water Jacket

10: WRod 11: Mo plate 12: Crucible13: Three divided Furnace 14: Zr sponge 15: Thermocouple

9

m 3.i.2-3

60

55

E 5001 45

3

5 40

8 35

5G 30

251600 1650 1700 1750 1800 1850 1900

7VK

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i * :* :

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i _ _ _ _ _ _ _ _ _ _ i_ _ _ _ _ _ _ _ _

5 4 3

CoolingWater

1: Alumina outer tube 2: Water jacket 3: Gas inlet4: Alumina tube for pushing 5: Thermocouple 6: Tungsten rod 7: Molybdenum plate 8: Pycnometer 9: Zirconium sponge

10: MoSi2 Furnace 11: Alumina support tube 12: Graphite rod

___ CoolingWater

H3.1.2-5

push4

4pull down

0 3.1.2-6

-73-

-0.18

Boron Nitride-0.22

-0.24

-0.26

-0.28

-0.32

1000/Tm 3.1.2-7

v u n

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-0.22

^ -0.24

pr -0.26

-0.28

-0.30

-0.320.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61

1000/Tm 3.1.2-8

-0.18

-0.20

-0.22

-0.24

-0.28

-0.30

-0.320.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61

1000/T

m 3.1.2-9 u u >

-0.18

-0.20■*— Silicon Nitride

-0.22

cd -0.24

-0.26

-0.28

-0.30

-0.320.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61

1000/Tb 3.1.2-10 sfctisoatcj;-5

-74-

Graphite - Run 1

Graphite - Run 2-0.18

-0.20

-0.22

-0.24

-0.26

-0.28

-0.30

-0.320.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61

-0.18 -

Silicon Carbide-0.20 —

Cd -0.22

P: -0.24

-0.26

-0.28

-0.300.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61

looo/r0 3.1.2-11 jcaisa*

> u 3

1000/Tm 3.1.2-12

'>u 3

-0.18

-0.20

8mol% YSZ-0.22

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-0.26

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1000/T

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3.1.2-16(r 1656k)

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c2

O

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Average : log r| =-0.758 + 874/Ti----- 1----- 1----- 1----- 1----- 1----- r -i----- 1----- r i r

-0.32

Average (Limited Temp.)Boron NitrideSilicon NitrideAluminaQuartz8mol% YSZ

-0.28 -

—0.30 —........-*4

0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61

1000/T

m 3.1.2-17 u 3

-77-

log (

r) /

mPa

s )

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— Present work

x Glazov

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1000/T

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—78 —

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log (

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-79-

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1000/T

m 3.1.2-21 Six Gex GaSb £ InSb 0 & 14 ¥ Ml ^ ^ £Glazov 0 # o' # £: 0 .fcfct£

-80-

Den

sity

/g cm

3

2.70

2.65 ™~

2.60 -

2.55 -

2.50 -

2.45 -

2.40

Present work *— Mukai *— Mukai

Glazov *— Lucas

Taran-Inc.Temp. Tar an-Dec. Temp. Sasaki-Quartz Sasaki-SiC

1650 1700 1750 1800 1850 1900 1950 2000 2050 2100

Temperature / K

m 3.1.2-22 ^|y'j3 >©?g&0«|j£J|g£:i3<k

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Temperature / K

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Thermal Conductivity and Normal Spectral Emmisivity of Molten and Crystal Silicon

Kazuhiro Nagata, Masahiro Susa*, Hiroyuki Fukuyama and Miyuki Hayashi

Department of Chemistry and Materials Science

*Department of Metallurgy and Ceramics Science

Tokyo Institute of Technology

Abstract:

The thermal conductivity and normal spectral emissivity of solid and liquid silicon are

required to develop mathematical models of the heat flow in manufacturing processes for silicon

single crystals. This work aimed at obtaining accurate values for these thermophysical properties.

The non-stationary hot wire method was used to measure thermal conductivities of solid and

liquid silicon, where hot-wire probes were insulated electrically from silicon samples using silica

films. The thermal conductivity of solid silicon decreased with increasing temperature. In solid

silicon, heat is principally transported by phonon conduction at temperatures below 1000 K, and

above 1000 K electronic conduction also contributes to heat transfer. The thermal conductivities

(X) in the respective temperature ranges can be expressed as a function of temperature (T) as

follows:

rt < T < 1000 K Xsoli<Uow temp = (1.40xl0'8r 2 + 1.90x10 5T + 2.92x10 ") ' Wm ’K1

1000 K < T < 1673K Xsolid high temp = Xsolid low temp + Xe Wm 1K 1

where Xe = 8.28 - 2.35xl0 2T + 2.01x10 "T 2 - 4.30xl0"9r 3 Wm 'K1

The thermal conductivity of liquid silicon measured under microgravity is 6 to 8 Wm^K1 at

1698-1737K.

— 84 —

On the other hand, the normal spectral emissivity of silicon was derived as the ratio of the

normal radiation intensity from silicon sample to that from a blackbody at the same temperature

as the sample. The sample and the blackbody were heated up using the cold crucible. Normal

spectral emissivities of liquid and solid silicon were determined at the melting point in the

wavelength ranges of 650-850 nm and 1000-2500 nm. For example, values of emissivities

measured at 650 nm and 1500 nm are as follows:



The emissivity in solid is larger than that in liquid at the wavelength investigated. The

emissivity in liquid decreases slightly with increasing wavelength, which indicates that molten

silicon is metallic. On the contrary, the emissivity in solid increases with increasing wavelength,

which indicates solid silicon is still semiconductor even at high temperature such as the melting

point.

(2)

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(6)

a.

1) M.Susa, H.Watanabe, H.Fukuyama and K.Nagata : “Emissivity measurement on liquid metals

using cold crucible technique” , Proceedings of The 5th Asian Thermophysical Properties

Conference, (1998), p.479

2) H.Watanabe, M.Susa, H.Fukuyama and K.Nagata: “Measurement and Theoretical modeling for

emissivities of liquid noble metals in the infrared region” Proceedings of The 5th Asian

Thermophysical Properties Conference, (1998), p.483

3) Lii^so, m&m®, Isanti, *ea*n;£ : rFz n >¥rB<DB

SSJ, B p.184, 1998 ¥ 9 /!

4) maitm, wmm*K, m&m®, : ri*,&t:;mta#ft#ztmft

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9 %

5) m&m®, # #, fmiiiit±, ^cbb^p^ : rEftyij □ ><Dmfc^&<Dmm

m mM 1999*3 ft

6) Eiaitii, nmmiK, m&m®, mmit^, 3d m

Bft&M M S* (^Mll^) 1999 ¥ 3 £

7) ̂ j21#jI, ttfflSX, tsiiilt;*., : r~>un> • >r ;i/ ~ r7 a <D 5>

M 3C* OK

5KXM±¥) 1999 ¥ 3 £


—104 —

Conductivity Measurement of Liquid Silicon under, Microgravity” 0 ^ v > ^ v ^7

A B 20 IhJ, 1999 ¥ 10 A216, 280-283

9) H.Watanabe, M.Susa, H.Fukuyama and K.Nagata : “Measurement of Spectral Emissivity for

Metals and Semiconductors Using Cold, Crucible” 0 >" > V ^ A ^ 20 IhJ, 3fEM ,

1999 ¥ 10 £ , SSElm^S, A226, 308-311

10) K.Nagata, E.Yamasue, H.Fukuyama, M.Hayashi and M.Susa : “ Thermal Conductivity

Measurement of Liquid Silicon under Microgravity”, 0 (SB 1 ©HI

IE "tl y '> 3 >) S 138 HI, 1999 ¥ 11 ^ 12, [4], 857 (1999)

11) # #, : ri4 # O @ ## # I: &

m 125@, 1999 ¥ n^, 535

12) E.Yamasue, M.Susa, M.Hayashi, H.Fukuyama and K.Nagata : “Contribution from Phonon and

Electron to Thermal Conductivities of Solid and,Liquid Silicon” 15th European Conference

on Thermophysical Properties,Wurzburg, Germany, Sep. (1999)

13) H.Watanabe, M.Susa, H.Fukuyama and K.Nagata: “Emissivities of Liquid and Solid Silicon at

Melting Point ” 15th European, Conference on Thermophysical Properties, Wurzburg,

Germany, Sep. (1999)

b . Ws3C

1) E.Yamasue, M.Susa, H.Fukuyama and K.Nagata : “Non-stationary hot wire method with silica

coated probe for measuring thermal, conductivities of molten metals” Metallurgical and

Materials Transactions A, Vol.30 A [8] (1999), p.1971-1979

2) H.Watanabe, M.Susa, H.Fukuyama and K.Nagata : “Emissivities of Liquid and Solid Silicon at

the Melting Point” , High Temp. - High Press., Vol.31 (1999), p.587-593

(7)

(3)-l Y.S.Touloukian, R.W.Powell, C.Y.Ho, P.G.Klemens, : Thermophysical Properties of

Matter :Vol.l Thermal conductivity of metallic elements and alloys, Publ. IFI/Plenum Press,

New York (1970)

-105-

(3)-2 K.Yamamoto, T.Abe and S.Takasu : Jpn. J. App. Phys. Vol.30, No.10, Oct. (1991),

pp.2423-2426

(3)-3 S.Kimura, K.Terashima, H.Sasaki, E.Tokizaki, Y.Anzai, S.Kawanishi, E.Takasuka, A.Ikari,

X.Huang, S.Togawa, S.Chung and K.Izunome : Proc. 4th Asian Thermophys. Properties

Conference (Tokyo Sep. 1995), Alai

(3)-4 Y.Nagasaka and A.Nagashima : Trans. J. Soc. Mech. Eng., Vol.47 (1981), pp.1323-31.

(3)-5 S.Konno. Sci. Repts., Tohoku Imp. Univ., (1919)

(3)-6 W.B.Brown, Phys. Rev., Vol.22, (1923), pp.171-179

(3)-7 L.P.Filippov, High Temp. Vol.3, (1965), pp.291-292

(3)-8 B.P.Pashaev, Soviet Phys. -Solid State., Vol.3, No.2, (1961), pp.303-305

(3)-9 R.P.Yurchak and L.P.Filippov. High Temp. Vol.3, (1965), pp.290-291

(3)-10 N.A.Nikolskii, N.A.Kalakutskaya, I.M.Pchelkin, T.V.Klassen and V.A.Veltishchea.

Voprosy teploobmena, Akad Nauk. SSR Energet 1st., (1959)

(3)-ll L.P.Filippov. Int. J. Heat Mass Trans., Vol.9, No.7, (1966), pp.681-691

(3)-12 Y.I.Dutchak and P.V.Panasynk, Soviet Phys. -Solid State, Vol.8, No.9, (1967), pp.2244-

2246

(3)-13 R.W.Powell and R.P.Tye. Proc. Conf. of Thermodynamic and Transport Properties of

Fluids., Inst. Mech. Engr. (London), (1958), pp.132-187

(3)-14 R.Berman and D.K.C.MacDonald. Proc. Roy. Soc. (London), Vol.A209, (1951), pp.368-

375

(3)15 R.P.Yurchak and L.P.Filippov. High Temp. Vol.3, (1965), pp.290-291

(3)-16 S.Nakamura, T.Hibiya, F.Yamamoto and T.Yokota. Int. J. Thermophys., Vol.12, No.5,

(1991), pp.783-790

(3)-17 M.J.Duggin. J. Phys., Vol.F2, (1971), p.433

(3)-18 R.Bobone, L.F.Kendall and R.H.Vought. TCREC Tech. Rept., (1961), pp.1-31

(3)-19 D.S.Beers, G.D.Cody and B.Abeles, Proceedings of the International Conference on the

Physics of Semiconductors. Inst, of Phys. and the Physical. Soc., London, (1962)

(3)-20 G.Glassbrenner and G.A.Slack. Phys. Rev., Vol.134, No.4A, (1964), pp.1058-1069

(3)-21 W.Fulkerson, J.P.Moore, R.K.Williams, R.S.Graves and D.L.McElroy. Phys. Rev., Vol.167,

No.3, (1968), pp.765-782

—106 —

(3)-22 Private communication with T.Okutani

(3)-23 F.J.Morin and J.P.Maita, Phys. Rev. Vol.96, (1954), p.28

(3)-24 N.B.Hannay, Semiconductors (Reinhold Publishing Corporation, New York, 1959), p.332

(3) -25 W.Fulkerson, J.P.Moore, R.K.Williams, R.S.Graves, and D.L.McElroy, Phys. Rev. Vol.167,

No.3, (1968), pp.765-782

(4) -l F.G.Allen, J. Appl. Phys., 28, 1510 (1957).

(4)-2 V.K.Lange and H.Schenck, Arch. Eisenhlittenw., 39, 611 (1968).

(4)-3 K.M.Shvarev, B.A.Baum and P.V.Gel’d, Sov. Phys. Solid State, 16, 2111 (1975).

(4)-4 M.O.Lampert, J.M.Koebel and P.Siffert, J. Appl. Phys., 52, 4975 (1981).

(4)-5 D.V.Linde and N.Fabricius, Appl. Phys. Lett., 41, 991 (1982).

(4)-6 G.E.Jellison, Jr and D.H.Lowndes, Appl. Phys. Lett., 47, 718 (1985).

(4)-7 G.E.Jellison, Jr and D.H.Lowndes, Appl. Phys. Lett., 51, 352 (1987).

(4)-8 K.D.Li and P.M.Fauchet, Solid State Commun., 61, 207 (1987).

(4)-9 S.Krishnan, J.K.R.Weber, P.C.Nordine, R.A.Schiffman, R.H.Hauge and J.L.Margrave, High

Temp. Sci., 30, 137 (1991).

(4)-10 E.Takasuka, E.Tokizaki, K.Terashima and S.Kimura, Appl. Phys. Lett., 67, 152 (1995).

(4)-ll E.Takasuka, E.Tokizaki, K.Terashima and S.Kimura, J. Appl. Phys., 81, 6384 (1997).

(4)-12 T.Aoyama, Y.Takamura and K.Kuribayashi, Jpn. J. Appl. Phys., 37, L687 (1998).

(4)-13 H.Watanabe, M.Susa and H.Fukuyama, Metall. Mater. Trans., 28A, 2507 (1997).

(4)-14 H.Sasaki, A.Ikari, K.Terashima and S.Kimura, Jpn. J. Appl. Phys., 34, 3426 (1995).

(4)-15 Y.Sato, Y.Kameda, T.Nagasawa, T.Sakamoto, S.Moriguchi, T.Yamamura and Y.Waseda,

Proc. 5th Asian Thirmophys. Properties Conference, edited by M.S.Kim and S.T.Ro,

(Seoul, 1998), pp.621-624.

(4)-16 H.J.Stein, Defects in Semiconductors, edited by L.C.Kimmerling et al. (Metallurgical Soc.

AIME, 1984), p.839.

(4)-17 P.J.Timans, J. Appl. Phys., 74, 6353 (1993).

107 —

3.1.3-1 Experimental conditions for thermal conductivity measurement od liquid silicon

## mam) JUJf (jUm) ISSlA) S«(K) 11*

A-1 JUG 180 1.998 1698 6.10A-2 JUG 180 1.998 1699 4.31A-3 JUG 350 1.998 1737 7.60A-4 JUG 350 2.003 1719 6.75 •B-1 JUG 350 1.998 1724C-1 1G 350 1.498 1695C-2 1G 350 1.498 1695C-3 1G 350 1.249 1695C-4 1G 350 1.249 1695C-5 1G 350 2.253 1695 ?Q-;/|'©E**ttA<ES.;h,fcA'bfcD-1 1G 350 2.000 1735D-2 1G 350 2.000 1735 «*IC***t**tiLfcD-3 1G 350 1.743 1735D-4 1G 350 1.743 1735D-5 1G 350 2.498 1735E-1 1G 180 2.000 1716E-2 1G 180 2.500 1716 â-yKDE»tt*<»c>h.»6'ofcE-3 1G 180 2.500 ' 1716 ^□•yh(DE6ii14A<EP)tL»A'-ofcE-4 1G 180 1.498 1716 ^□-yKDEEttA<E5>n<?6'-ofc

3.1.3-2 Physical property data used for the calculation of the electronic component in thermal conductivity of silicon at temperatures between 1000 and 1673K

r/K 6(3)-= Eg /eV3)"24 cr/Q'W1^"251000 0.43 0.85 21031200 0.43 0.78 64611400 0.43 0.71 144021600 0.43 0.55 262721673 0.43 0.52 31416

-109-

3.1.3-3 Results of emissivity for Si at melting point.

LiquidWavelengt Run 1 Run 2 Run 3 Average values

500 0.203 0.187 0.197 0.196550 0.194 0.191 0.196 0.194600 0.225 0.214 0.217 0.219650 0.231 0.230 0.231 0.231700 0.236 0.234 0.229 0.233750 0.231 0.234 0.226 0.230800 0.227 0.229 0.222 0.226

1000 0.190 0.197 0.194 0.1941100 0.191 0.192 0.189 0.1911200 0.186 0.187 0.184 0.1861300 0.182 0.180 0.182 0.1811400 0.177 0.176 0.1771500 0.172 0.176 0.1741600 0.180 0.180 0.1801700 0.164 0.164 0.1641800 0.166 0.170 0.1681900 0.160 0.164 0.1622000 0.161 0.164 0.1632100 0.155 0.159 0.1572200 0.157 0.163 0.1602300 0.148 0.152 0.1502400 0.154 0.156 0.1552500 0.161 0.167 0.164

Solid500 0.274 0.286 0.264 0.275550 0.278 0.305 0.289 0.291600 0.343 0.359 0348 0350650 0.369 0.400 0362 0377700 0.389 0.439 0385 0.404750 0.415 0.462 0.432 0.436800 0.406 0.456 0.422 0.428

1000 0.404 0.453 0.460 0.4391100 0.443 0.428 0.449 0.4401200 0.457 0.459 0.470 0.4621300 0.465 0.460 0.475 0.4671400 0.474 0.463 0.4681500 0.484 0.477 0.4801600 0.485 0.515 0.5001700 0.488 0.496 0.4921800 0.514 0.515 0.5141900 0.491 0.518 0.5042000 0.512 0.519 0.5162100 0.526 0.514 0.5202200 0.523 0.532 0.5272300 0.505 0.526 0.5162400 0.539 0.531 0.5352500 0.551 0.570 0.560

-no-

THER

MA

L CO

ND

UCT

IVIT

Y, W

all cm

'

IH 3.1.3-1 Thermal conductivity for solid silicon as a function of temperature.

-Ill-

(f (B In

f + C

))/(ln

t +A

) X10

0 /%

Time/s

0 3.1.3-2 Relation between the deviation from Eq.(3)-2 and time.

0 3.1.3-3 Instrumental setup of the nonstationary hot wire method in this study.

-112-

Oxide layer(~100nm)

0.15mm* Pt-15%Rh wire

0.15mm* Ft wire

Chart Recorder

@ 3.1.3-4 Schematic diagram of the experimental apparatus for measurements of solid silicon.

-113-

Oneway valve

Emfaft

Thermocouple

0.15mm<|) Mo

Silica insulator

0 3.1.3-6 Schematic diagram of experimental probe and crucible.-115-

Ther

mal

Con

duct

ivity

X /W

• m

"1 • 293K

Current,//A

HI 3.1.3-10 Relation between the thermal conductivity for mercury and the current supplied to the wire.

-119-

/t/W

-m

60F

40b

20b

Temperature /°C500 1000

Sn

H O&OvOv&r OO

500

M.P.«S0SK 1

1000Temperature ZK

1500

• This study □ Pashaev o Konno et al O Yurchak et al a Brown —Nikolskii et alv Filippov

— Wiedemann-Franz law

0 3.1.3-11 Thermal conductivity for tin as a function of temperature.

-120-

A/W

m

^ 30-

20-

10-

M.P, = 600.5K

500

Temperature /°C

500 1000

Pb

.» »»»»■# m......

1000Temperature /K

• This study o Berman et al.o Fillipov O Yurchak et al.a Dutchak et al. @ Nakamura et al.v Powell et al. 0 Duggin

— Wiedemann-Franz law

0 3.1.3-12 Thermal conductivity for lead as a function of temperature.

150'0Temperature /°C

500 1000

a ioo£

50

0 J---------L

500

r------- 1------- 1------- 1------- 1------- j------- 1——i------- 1------- 1------- 1------- 1--------r------ 1—

9 A Boboneetal.v Beers et al.

o ° Glassbrenner et al.: fc> D Fulkerson et al.r ® Kimura et al.

rift ® Yamamoto et al.• This study

TXcpqp gD

J t 1 L J t:i i i............... t.1000

Temperature ZK1500

0 3.1.3-13 Thermal conductivity of solid silicon compared with reported values.

-122-

A,.<H IA V

0.9 T T

U G1737K

mm 350Iim

y=a + b In xa=6.125717e-01b=7.230423e-022.622845e-03|r|=9.967875e-01

Tl sec

HI 3.1.3-14 Effect of gravity on A V vs In t profile.

-123-

A,.O

I / A

T /sec

0 3.1.3-15 Effect of coating thickness on A V vs In t profile.

-124-

Temperature/^

W - F Law

Temperature/K

0 3.1.3-16 Temperature dependence of thermal conductivity of liquid silicon.

-125-

Focusing lensSpectroscope

Short cut filterChart recorderWindow Prism

Diaphragm

• V Detector MonochromatorSample

Cold crucibleCamera

WindowBN plate

Induction coilsGraphite plate

yGraphite crucible

Zr sponge

Alumina crucible

Alumina tube

Air-tight chamberPositioning rod

0 3.1.3-17 Instrumental setup to record the normal spectral radiation from sample.

-126-

Nor

mal

Spec

tral

Em

issiv

ity

Wavelength/nm

Jellison and LowndesLiquid

+Solid

Aoyamaetal.Liquid♦

Solid

Allen B Linde et al. B

Lange et al. B Krishnan et al. +

Li and Fauchet * Takasukaet al.

Shvarev 0 Present study " # ' -o-Lamport B □

0 3.1.3-18 Comparison of the reported values of the normal spectral emissivity of liquid and solid Si at and near the melting temperature.

-127-

Tota

l Hem

isph

eric

al Em

issi

vity

Measured Values • 78 Qcm Sia 0.012 Qcm Si

Calculated Values j o From Sato :D From Vandenabeele-^

and Maex :

200 .300 400 500 600 700 800 .900Temperature (°C)

@ 3.1.3-19 The total hemispherical emissivity of the lightly(78 Q cm) and heavily (0.012Qcm) doped silicon specimens as a function of temperature. The solid curves are fits to the data point. (Reprinted from the Journal of Applied Physics,74,6353(1993).)

3. i. 4 u3

auc*# >?-

#□ ##

Equilibrium of Liquid Silicon and Segregation Coefficient of Oxygen in Silicon.

Yasutaka Iguchi

New Industrial Creation Hatchery Center,

Tohoku University

3. 1. 4. 1 Si yUk h/Si02$fctt Si3N4, SiC lifl © iS JR ¥ W

(1) S8

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Stc$©-> V 3

h41'x©B#C#'5ffiiFB6x*;|y*-$rt;:£:BtBUA:. S 6>fc, -> V 3

Equilibrium between Liquid Silicon and Si02, Si3N4 or SiC,

Abstract:

The solubilities of oxygen, nitrogen and carbon in liquid silicon equilibrated with silica,

silicon nitride and silicon carbide, respectively, were measured. The melting and analytical

methods were developed and accurate data on the solubilities were obtained. The standard Gibbs

free energy changes for dissolution of oxygen, nitrogen and carbon in liquid silicon were

-129-

determined. The effect of alloying elements on oxygen and carbon solubilities was clarified.

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eQSb = -0.02

e0B = -0.03

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(U)

(12)

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3Si(l) + 2N2(g) = Si3N4( & ,s)

AG18° = -9.252x10s + 450T (J)

(18)

(19)

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AG20° = -4.45xl04 + 66.4T (J) (21)

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C(s) = C(lmass%, in liquid silicon) (25)

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-136-

( 6)

( a) 85C5B8

1) K.Yanaba, M.Akasaka, M.Takeuchi, M.Watanabe, T.Narushima and Y.Iguch, “Gabon Solubility

in Liquid Silicon Equilibrated with Silicon Carbide,” Mater.Trans.JIM, 38 (1997), 990.

2) K.Yanaba, Y.Matsumura, T.Narushima and Y.Iguch, “Effect of Alloying Elements on Gabon

Solubility in Liquid Silicon Equilibrated with Silicon Carbide,” Mater.Trans.JIM, 39 (1998),

819.

(b)

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(7)

1) Oxygen, Carbon, Hydrogen and Nitrogen in Crystalline Silicon, Ed. By J.C.Mikkelsen, Jr.,

S.J.Pearton, J.W.Corbett and S.J.Pennycook, Materials Research Society, PA, (1986).

2) F.Shimura, Semiconductor Silicon Crystal Technology, Academic Press, (1989), p.307.

3) T.Abe, K.Kikuchi, S.Shirai and S.Muraoka, Semiconductor Silicon 1981, Ed. By H.R.Huff,

R.K.Kriegler and Y.Takeishi, Electrochem.Soc., Pennington, (1981), p.54.

4) F.Shimura and R.S.Hockett, Appl.Phys.Lett., 48 (1986), 224.

5) H.J.Stein, P.P.Peercy and C.R.Hills, J.Mat.Res., 4 (1989), 616.

6) Y.Shimanuki, H.Furuya and I.Suzuki, J.Electrochem.Soc., 136 (1984), 2058.

-137-

7) S.Kishino, Y.Matsushita and M.Kanamori, Appl.Phys.Lett., 35 (1979), 213.

8) F.Shimura, J.Appl.Phys., 59 (1986), 3251.

9) T.Narushima, K.Matsuzawa, Y.Mukai and Y.Iguchi, Mater.Trans.JIM, 35 (1994), 522.

10) T.Narushima, N.Ueda, M.Takeuchi, F.Ishii and Y.Iguchi, Mater.Trans.JIM, 35 (1994), 821.

11) K.Yanaba, M.Akasaka, M.Takeuchi, M.Watanabe, T.Narushima and Y.Iguchi, Mater.Trans.

JIM, 38 (1997), 990.

12) T.Narushima, K.Matsuzawa, M.Mamiya and Y.Iguchi, Mater.Trans.JIM, 35 (1994), 763

13) K.Yanaba, Y.Matsumura, T.Narushima and Y.Iguchi, Mater.Trans.JIM, 39 (1998), 819.

14) O.Kubaschewski and C.B.Alcock, Metallurgical Thermochemistry 5th ed., Pergamon Press,

New York, (1979).

15) T.Carlberg, T.B.King and A.F.Witt, J.Electrochem.Soc., 129 (1982), 189.

16) W.Kaiser and P.H.Keck, J.Appl.Phys., 28 (1957), 882.

17) W.Kaiser and J.Breslin, J.Appl.Phys., 29 (1958), 1292.

18) Y.Yatsurugi, N.Akiyama, Y.Endo and T.Nozaki, J.Electrochem.Soc., 120 (1973), 975.

19) H.Hirata and K.Hoshikawa, J.Crystal Growth, 106 (1990), 657.

20) X.Huang, K.Terashima, H.Sasaki, E.Tokizaki and S.Kimura, Jpn.J.Appl.Phys., 32 (1993),

3671.

21) L.Ottem, private communication.

22) S.Otsuka and Z.Kozuka, Trans.JIM, 22 (1981), 558.

23) A.E.Organ and N.Riley, J.Crystal Growth, 82 (1987), 465.

24) A.Seidl and G.Muller, J.Electrochem.Soc., 144 (1997), 3243.

25) S.W.Tu and D.Yanke, Z.Metallld., 85 (1994), 701.

26) H.Nafe, J.Electrochem.Soc., 146 (1999), 1130.

27) W.Kaiser and C.D.Thurmond, J.Appl.Phys., 30 (1959), 427.

28) A.Hendry, p.183 in Nitrogen Ceramics, ed. by F.L.Riley, Noordhoff International Publishing,

Netherlands, (1977).

29) S.Suhara, N.Yuge, M.Fukai and F.Aratani, CAMP-ISIJ, 2 (1989), 1341.

30) L.L.Oden and R.A.McCune, Metall.Trans.A, 18A (1987), 2005.

31) R.N.Hall, J.Appl.Phys., 29 (1958), 914.

32) R.I.Scace and G.A.Slack, J.Chem.Phys., 30 (1959), 1551.

-138-

33) F.Newmann and H.Schenck, Arch.Eisenhutt., 30 (1959), 477.

34) litl, 12 (1966), 97

-139

3. 1. 4. 2 SiO

( 1 ) S©

'> U n >^;i/ 5 ©JKIft *»#!£« jib Tfigfc&ffl* SiO ftl±£'> V 31 y %)]/ v

(a) >u n >e

A (1685K) 13 ^3 If 6 # ± SiO O.Olatm T & -5 C fco 1685-1800K

13331** sio ft&tmftmmm&oMm&fe&it-rz t&izm&itLrzo

Relationship between SiO Partial Pressure in Gas Phase and Oxygen in Silicon Melt.

Abstract:

The relationship between SiO partial pressure in gas phase and oxygen contents in liquid

silicon was discussed thermodynamically, which is an important factor for removing of the

dissolved oxygen from liquid silicon. The maximum SiO partial pressure was calculated to be

around 0.01 atm at 1685 K. The SiO partial pressure was graphically shown as a function of the

dissolved oxygen contents.

(2) #081:

v u 31 y* )v h s #xi sio ©fit fctfe nJiSflTHJ. a^T, CZ 7,n-irX->5al/-->3 SiO #K

^SffE*SS®$eB9¥«IS«6^£>BT'*5. tit. CZ&\Z

-140

(3)

(a) SiO

SiO $ £ b T® fcSig&®*Fg te, Kubaschewski

and Alcock1^ JANAF2)4d =k ZS Knacke et al .3)Of—^ # ck D # 6 tl -5 « ■?■ tl ^tl (D x “ ^

^<k 0 $ n%> Si(i)-Si02(s)-Si0(g)¥ît ((i)it) (DS^FS — (Ag/ )

Si(l) + Si02(s) = 2SiO(g) (1)

A GUiefA ° = 658980 + 53.9736TlogT - 489.946T (J)^ (2)

A Gj.^f.2 ° = 618618 - 290.61T (J)2) (3)

A Gx.ref.3 ° = 622254 - 289.94T (J)3> (4)

(2)''w,(4)j£ (D & it % U T E3 3.1.4.2-1 tC Trt't* o Kubaschewski and Alcock £ JANAF

(DAG/ ££&£>&%, Knacke et al.(D#####(D 2 ^XDbCDtit

^ # T Wx x — Kubaschewski and

Alcock (DS@E> ^(2)^:& SiO(g)^ — ##(D(^

Cm W-5 C a a Ltz c

(b) '> u n >>;i/ SiO

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SiO(g)> Si(g)> Si02(g)T$>5o volatility

diagram ^ ^ T & & » volatility diagram Z> 33 X 7" 2/ is -Y )]/ \Z%t fo't' <5 fl! ;k

4)o Si(l)£fc«

Si02(s)/^#S L. e> <D^£S^&(5)& <£t£(6)^Tl&Wt‘'5

—141 —

Si(l) + 02(g) = Si02(s) (5)

AG/ = -952697 + 203.76T (J)^

= RTln(Po2) (6)

'> U 3 > E & (1685K) £43 HTte. (6)^:^ 6st#$4l6?###Ê^ 1.28x10'âtm

T&6. lot, 1.28xl019atm <D m M ft E ^ T £ 43 V> T tt ^ t L T Si(l)^£)£T.

6#X$£ Si(g)43£tf SiO(g). 1.28xl0-19atm &±T& Si02(s)^^ÊEffiT

SiO(g)> Si02(g)^#ET6^4X#T$)6o 3 1685K

£ $) It 6 volatility diagram £E 3.1.4.2-2 C^to T~ ^ £ LT&E£

Kubaschewski and Alcock <D SBfS 1}£ <A £: <, £ ® £ Y) . 1685K £43tt6 SiO (DMXftR

\%fcJ O.Olatm T & D . -ZrtUZ Si(l)43£££ SiG2(s)v^5£ # T 6 IE £ # 6 4l6<> T> £ D > (1)43

zitwztiz sio ft& ((7)^mm)

PSiG = exp (-AG^./ /(2RT)) (7)

10-27^10-4atm 3;T(7)K(Am##E#£43(AT. SiO

$6 C <h^4D^6o

(c) sio ftj£t'>v z

volatility diagram tt. SiO Ê-SrBISiÊOlSEIIfc^: L'T@7KL/c!fc>(DT$>6o (D CZ

& £ J; 6 '> U 3 SiO Ê^rSE^mSÊd: V

miE<o cz yotxc^^Tii.

Z'VIZfc h W3##T#$&^4l6. -

<£>£:£>'> U 3 >*;i/ hS@£43rt6 Sio

4l6 6#A6(D^#^T^6. ##6(D Si02(s)£ ¥«T 6 feM zs U 3

5)j;o. (8)ô#mgH(9)^:Tm$4i6.

—142 —

Si(l) + 2Q (mass%, in liquid silicon) = Si02(s) (8)

(9)AG8° = -177000 + 12.7T (J)

(l), (2)^&£EX(8)> (9)5t<£ 0 SiO(g)£ m M <D ¥■&£(10)£ £ ^ <D & ti x^;i/

Si(l) + Q (mass % , in liquid silicon) = SiO(g) (10)

AG10 ° = 240990 + 26.9868TlogT - 238.623T (J) (11)

(10), (11)^4: 0 SiO # EE £ [mass %£]<£> HI £ LTggt^. H *tt£(12)

1685K, 1750K, 1800K \Z 43 % 1*1 B# \Z

Psio = [mass%Q]exp(-AG10° / (RT)) (12)

= 2.789x[mass % Q.] at 1685 K

= 5.008x[mass% Q] at 1750 K

= 7.625x[mass % QJ at 1800 K

(12)atf*ffi3ft® SiO -Jtfi

sio t,

^>o e 3.1.4.2-3 £(i2)^6<z)tt-sss^£^t*o a*,

Si02(s)£¥«f DISKS' U 3

Si02(s)<h Si(l)^##f SiO ((7)S fc J: 0 WrW- £

fia SiO #E)

(4) ̂ a A

Sio frE^SSv U 3 Sio t;i

*t* @ A % 4V1/ 4r — <h L T kt Kubasche wski and Alcock

sio ftj££®&mmmm(Dm&&mn'?z> £&\z, fneoi

—143 —

1685K~ 1800K 1C & 1A T 0 W IZ St £ JIMS L „

(5)

1) O.Kubaschewski and C.B.AIcock, Metallurgical Thermochemistry 5th ed., Pergamon Press,

NY, (1979).

2) JANAF Thermochemical Tables, 3rd ed., ed. by M.W.Chase,Jr et al., ACS and AIP for NBS,

NY, (1985).

3) Thermodynamic Properties of Inorganic Substances, ed. by O.Knacke et al., Springer-Verlag,

Germany, (1991).

4) A.H.Heuer and V.L.K.Lou, “Volatility Diagram for Silica, Silicon Nitride and Silicon Carbide

and Their Application to High-Temperature Decomposition and Oxidation”, J.Am.Ceram.Soc.,

73 (1990), 2785.

5) T.Narushima, K.Matsuzawa, Y.Mukai and Y.Iguchi, “Oxygen Solubility in Liquid Silicon”,

Mater.Trans.JIM, 35(1994), 522.

—144 —

3. i. 4. 3 '> u 3

(1)5©

Si02 (Cs) #&

##v =z(cL>

'> U n '> U n >%#:.$/ V 3 >*§#18 0##

o@i¥IÊit k=cs/cL) £ 0.7-0.9 <hStti Lfc„

Equilibrium Distribution Coefficient of Oxygen between Solid and Liquid Silicon.

Abstract:

Oxygen solubility in solid silicon at the melting point of silicon (Cs) was measured by a

chemical equilibrium method. The value of oxygen equilibrium distribution coefficient

(segregation coefficient, Cs / CL) was evaluated to be from 0.7 to 0.9 by using Cs and oxygen

solubility in liquid silicon at the melting point (CL) which has been reported by the authors.

(2) #C&I:

f0K##* (c,„ ,oMa) k-c,. ,lquld T#

-fc c c-r k c,„ tt -> v 3 > * in- f ©E**«

T&-5. 3> W 9 , v 9 3 >#ieSct>®**#aE->3 a. v-'y a > 0 » It B, -> U 3 > ;*

«£#, ->'J 3

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V1t. if, Si02 a:¥Ef-S>B#:Û3>0KS®®$^

—145 —

8J56L, •> V 3 >6$S|-

* tt S K * ID B S ¥ ffi & E « » Sr S titi f 5.

( 3 ) SiSS

Si02 U 3 >08 SSSSese^teSScf. ttfttttt FZ y'J3>*8

S*e.fflyitiLy5:$t)i->U3> (lOmm X 15 mm x 1.5mm) SrfflVifc. CZ v U 3 > T- tt &

< fz ->u3¥*»«

©M*£BWtt, itfiitssii tti Ufc. C®KS6KSfliSittF. 1673K l=*®TR#

L, *S®¥E$r + ti-afi8Sti--5 (H 3.1.4.3-1 #E).

Si(s) + 2Q.(in solid silicon) = Si02(s) (1)

ttfiSSCfa. »*#7. tOKJ&lcJ: OffiBtt Si02 ftliiif < S^Sti5.®T,

WSB®*Kfl:-> U 3 >S®ES#$tt(i)Slc =fc DftSSiU. -> U 3>4-©K*»lfTtt

S#->U3>©**»**ffc#Sl/ft#^ "6R#. *EIC®f$$nfcK'fb6IKS:E«l»

ibfca, J: 0 it* Vfc.

(4)

(a) ¥#em®#w

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efT^Dfc. ffl-*Ltt-*5cTff»n, sesiic±ogtseufcBtF*sx8ES#« 5PPm, ?

30PPm. H*->U 3 >4>®KSi6E«$IC 3.5xlO-9cm2/s,0>-l2>$«-S®B

I:#rn Fick ®#c&mj&±B®#:#®T?#<**6#»&

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lc«k 0 S-*UfcK**flEtt6< -StLTHS C 4:* j:tFAerSa6*«t"ti« 500 BEGS

-146-

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C*5tt5ESSl@*li 26~36mass ppm (2.3~ 3.1xlOl8/cm3) b Itl t> -5 C b¥*T" £ i>.

1673K 7»>6 1685K C 43 tt S B # S'U 3 C©«&

S' U 3 >Bt 'J 3 /®8ISi# (Cs) -> U

3 >8t,&C43tt5SSi'> U 3 >©g£$i§JW6 (CL) CBLttt 39mass ppm (3.4xl018/cm3)

iOItfli S lc«t 0 l&sntus ”©T, -> 'J 3 >8l!,'±U;:43tt3K*©0*¥*#K

(k0 =cs/cL) a. o.7~o.9itftti.. *e%©s«e«-

J: 0 Wtti Ufc Cs43cL£tefll LT k & HW- l-Tc Z b I:

&&. ctxttftSEWiisajss&ifiifflUfcT&fttfiattofciwmsat?****.

entikii, *e, 1 htt***< 0.8 a«i ^ 3 Kakimoto and Ozoe7>¥ Huang et al.8)©^ A — Ht U T V1 5 »

(5) iti6

(t4f¥*SI:i!) 1673K (2* BfcS' 'J 3 > © & * ig* S £ M it L£ i £ 5 26 ~

36mass ppm (2.3~3.1xl018/cm3) b !-> tlfco £©x— ^7

»» v u 3 d tc j: o u 3 ><t»#*©¥*s»E«*£

o.7~o.9 <hfl,at)3fc„ c©ma. -mu

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1999 ¥ 5 fl 20 B

—147 —

(7) rnmicm

1) F.A.Trumbore, Bell.Syst.Tech.J., 39 (1960), 205.

2) Y.Yatsurugi, N.Akiyama, Y.Endo and T.Nozaki, J.Electrochem.Soc., 120 (1973), 975.

3) A.Murgai, H.C.Gatos and W.A.Westdrop, J.Electrochem.Soc., 120 (1979), 2240.

4) W.Lin and W.Hill, J.Appl.Phys., 54 (1983), 1082.

5) W.Lin and M.Stavola, J.Electrochem.Soc., 132 (1985), 1412.

6) — , S56JIIS, B 20 (1993), 37.

7) K.Kakimoto and H.Ozoe, J.Electrochem.Soc., 145 (1998), 1692

8) X.Huang, T.Nakazawa, K.Terashima and K.Hoshikawa, Jpn.J.Appl.Phys., 37 (1998), L1504.

9) T.Narushima, K.Matsuzawa, Y.Mukai and Y.Iguchi, Mater.Trans.JIM, 35 (1994), 522.

10) S.T.Lee and D.Nichols, Appl.Phys.Lett., 47 (1985), 1001.

11) R.A.Logan and A.J.Peters, J.Appl.Phys., 30 (1959), 1627.

12) M.J.Binns, C.A.Londos, S.A.McQuaid, R.C.Newman, N.G.Semaltianos and J.H.Tucker, JMS,

Materials in Electronics 7 (1996), 347.

-148-

3.i.4.i-i

Elements Temperature / K Atmosphere Holding time / ks Crucible Solid phase equilibrated

with liquid silicon

Oxygen 1693-1823 o2 7.2 Si02 0 -cristobaliteNitrogen 1723-1873 N2: H2 = 4 : 1 20 Si3N4

(sintered)

(3 -Si3N4

Carbon 1723-1873 CO : Ar = 1 :19 15 SiC(sintered)

g-SiC

3.1.4.1-2

Elements Oxygen Nitrogen CarbonAnalytical method Inert gas fusion-IR absorption

(TC436E, LECO)

Sn 4- Fe as metal bath

3500W for furnace power

Kjeldahl method

Dissolution in the mixture

of hydrofluoric acid and

chromic acidNessler’s reagent as color

indicator

Measurement of absorption

Combustion-IR absorption

(IR212, LECO)

Combustion-coulometric

titration

(VK-1C, Kokusai Electric)

Fe 4- Cu as metal bath

Calibration Fe standard sample

Si 4- Si02Ammonium chloride solution Fe standard sample

Si 4- SiC

OXY

GEN

CO

NTE

NT,

Cnl m

ass% M.P. of Si

0 3.1.4.l-i -> V * iTitSy V 3 >8t#*©E*Sg

59(/)(/)ci 10"2 E

HII-zoO

m 10"3O

£O

Temperature, 7/ K 1800;1700

M.P. of Si

o Kaiser et al.A Yatsurugi et al.O Caiiberg et al.

■ — ■ ■ * Hirata and Hoshikawaffl Huang et al.

----- — - Ottem---- - - - - Otsuka and Kozuka

Organ and Riley— — - Seidl and Muller

Present works Tu and Janke

— — - Nafe

40 ppm

20 ppm

5.4 5.6 5.8T"1 /10" K"1

0 3.1.4.1-2 '>'J

-150-

fr-r

rv£ H

„.oi

. / t.l

INTERACTION PARAMETER, 6q

o o o oco Kd Ll o

D» 0

• > □ o

▻ # □ o

OXYGEN CONTENT, Co / mass%

w oo

ri

9%4-4

m8%#

m5

30)(Z)%

r2.2

0 3.1.4.1-6 ->'J 3

NITROGEN CONTENT,/ mass%

cn ^ m

(D O

OO CP' o o o

0 ° oo o 03 CO

o OO

T'1 /10 K

0 3.1.4.1-5

OXYGEN CONTENT, CQ / mass%

• > □ o

00 CO 00 GO

> "0 oo co

CA

RB

ON

CO

NTE

NT,

Cr /

mas

s%

NIT

RO

GEN

CO

NTE

NT,

C., / m

ass%

: Kaiser and Thurmond : Yatsurugi et al.: Present work

M.P. of Si

m 3.1.4.1-7

M.P. of Si

m 3.1.4.1-8 V U 3

-153-

: Sahara et al.

: Yatsurugi et al.

: Oden and McCune

-: Hall

-: Scace and Slack

-: Ottem

M.P. of Si: Present work

r1/io4K1

I3.U1-9 v'j n

<o

-2.0 1--------------------------------------- 1--------------------------------------- 1--------------------------------------- 1----------------------------------------0 2 4 6 8

ELEMENT CONTENT, Cx / mass%H 3.1.4.1-10 ->'J 3

—154 —

20

U)

DC111I—ill

<DC<CLZOI—

%DCLU

10

0

-10

-20

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——----------- 1

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su

e Ni•>

B* >

we

Al i *Ca

______ _______

1

_______

*p_______i_______

10 15 20ATOMIC NUMBER

25 30

3.1.4.1-n

—155 —

: Kubaschewski and Alcock

- : JANAF

-: Knacke et al.

MR of Si

v 1700 1800 1900 20Temperature, T / K

m 3.1.4.2-1 (1)^0^*P6

$iO' (s) stablb

SiO(g)

-J -8

-35 —30 —25 “20 —15 —10Log(Po2 / atm)

m 3.1.4.2-2 Si-02 % , 1685K \Z & £ Volatility diagram

-156-

/ atm

Co / 1018 cm"3

0 1 2 3 4 5 6

1800 K

Oxygen solubility in silicon meltiequilibrated with silica

1685 K

Co / mass ppm

m 3.i.4.2-3 sio

-157-

3.1.4.3-1 Previous studies on equilibrium

distribution coefficient of oxygen in silicon.Reference No. Investigators k

1) Trumbore 0.52) Yatsurugi et al. 1.253) Mrugai et al. >14) Lin and Hill 0.255) Lin and Stavola 0.36) 0.2-0.47) Kakimoto and Ozoe 0.35-0.88) Huang et al. 0.5—0.8

Heating element

O2 gas

Alumina / reaction tube

U1to

4Û)w

H*ON

u>KM&

d«sSFK

UV

$m2gOr%#m#B»

OXYGEN CONTENT, Co/ ppm00O

00o 6

io

8

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m ooL 8

I

CJ18

0.05 0.1

0.15PO

SITION

, 1 / mm

0 3.1.4.3-2 500

OXYGEN CONTENT, Cy ppm

—^ ^ ro ro co coocnooi ocnocn

3. i. 5 yu3

Mil

# # B

Theoretical Estimation of Diffusion Coefficients of Impurities in Silicon Melt.

Yoshio Waseda

Institute for Advanced Materials Processing,

Tohoku University

Abstract:

The self-diffusion coefficient in pure silicon melt and diffusion coefficients of O, Al,

B and P impurities in silicon melt have been calculated on the basis of the Enskog theory

implemented with a pair-correlation function at contact between dissimilar atoms. The

activation energies for diffusion were also estimated by taking in account the temperature

dependence of packing fraction of silicon melt. Although only limited experimental data

are available for comparison, the present theoretical approach appears to work well and to

be useful for predicting diffusion coefficients of impurities in silicon melts.

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iEH?!i C„(0) = 1.1, C1(A1) = C1(P) = 1.2. C„(B) = 0.9 iLfc. E 3.1.5-1

t£E«* Da(l©a*JEfl:SSS»:««* ©s cesi*£if. Sfc. * 3.1.5-1 12, m

,6 it Jt 12 25(2-5 onP«*±OJ»ttftx^;u^-S* i»fc*S*t?*4. J8tA5 gôsi

l:<tot3HMSSIC*4ftll>BBe6nS:H. Al i B P ©a * ifi« t fc It 5

DaP©S6^<*iiS3^$fi'S tlTVi-5»l. ■5-n6©eit*ECii63UTV^fcte. *6f

%©8»69r yn-ytoBStt&BStoCMEfS.C ^ tiEUH, L&L. SfiStiTHS

%^#I2 Al : 0.2~7.0xl0'8m2/s, B : 1.8-3.3x10 8m2/s. P : 2.3-5 .lxlO'8m2/s12,T <6 <0 .

n m m * * if © s h ^ # it t s t s « t 12+# - » -r -s is * t m * s « « ®r u r t- »s.

(4) asrfsa

1) D.Mitev, M.Saito and Y.Waseda, “Theoretical Estimation of Diffusion Coefficients

of Impurities in Silicon Melt”, High Temp. Mater. Proc., 19 (2000), EP R(j f.

(5)

1) S.Chapman and T.G.Cowling, The Mathematical Theory of Non-Uniform Gases,

Cambridge University Press , London, (1970).

2) P.Protopapas and N.A.D.Parlee, High Temp. Sci., 8 (1976), 141.

3) B.J.Alder, W.E.Alley and J.H.Dymond, J.Chem. Phys., 61 (1974), 1415.

4) N.F.Carnahan and K.E.Starling, Phys. Rev., Al (1970), 1672.

5) T.L.Lebowitz, Phys. Rev., A133 (1964), 895.

6) X.Huang, K.Terashima, K.Izunome, and S.Kimura, Jpn. J. Appl. Phys., 33 (1994),

136.

-163-

7) P.D.Mitev, M.Saito and Y.Waseda, High Temp. Mater. Proc., 19 (2000), in press.

8) I.Stich, Phys. Rev., A44 (1991), 1401.

9) T.Iida and R.I.L.Guthrie, The Physical Properties of Liquid Metals, Clarendon

Press, Oxford, 1988.

10) Y.Waseda, The Structure of Non-Crystalline Materials, McGraw-Hill, New York,

1980.

11) Y.Waseda, K.T.Jacob, Y.Iguchi, T.Narushima, J. Crystal Growth, 139 (1994), 357.

12) K.H.Hellwege and O.Madelung (eds.), Numerical Data and Functional Relationship

in Science and Technology, Landolt-Bornstein Vol.17, Springer-Verlag, Berlin,

1984.

—164 —

T /K1840 1800 1760 1720 1680

— - cs

1 IT / 10 V

W 3.1.5-1 Temperature dependence of diffusion coefficients of several impurities insilicon melts, together with results for self-diffusion coefficient in pure silicon melt.

-165-

Diff

usio

n co

effic

ient

s / 10

" m s

20

HI 3.1.5-2 Comparison for self-diffusivities of liquid metals at their melting points as a function of (Tm/M)l/2Vml/3. The diamond denotes the present result for silicon melt. Points linked by a vertical line represent the range of different experimental values for a single metal.

—166 —

Act

ivat

ion E

nerg

y / eV Normal metals

Semi-metals

T / 10 K

- M 3.1.5-3 Comparison for activation energies of self-diffusivity in liquid metals at their melting points. A diamond denotes the present result for silicon melt.

-167-

3.1.5-1 Self-diffusion coefficient in pure silicon melt and impurity diffusion coefficients of O, Al, B and P in silicon melt at the melting point. Pre-exponential factors and activation energies for diffusion are also given.

Si melt - self-diffusionDs (-10V/S) at T„ D0 (*10'8m2/s) G(eV)

1.9 11.9 0.27O in Si melt

B„„(-10V/s)atTm D0 (‘10"8m2/s) G(eV)L 4.4 21.0 0.23

PP 4.1 21.5 0.24CS 4.2 21.4 0.24

Al in Si meltL 1.9 9.4 0.23

PP 1.7 9.6 0.25CS 1.7 9.5 0.25

B in Si meltL 3.7 17.9 0.23

PP 3.4 18.2 0.24CS 3.5 18.1 0.24

P in Si meltL 2.5 12.5 0.23

PP 2.3 12.8 0.25CS 2.4 12.7 0.24

—168 —

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O $, 6.

Computer Simulations

Nobuyuki Imaishi

Inst. Advanced Material Study

Kyushu University

Abstract:

In order to realize a large-scale numerical simulation code, the members of the research

project have developed a large set of numerical codes. The global analysis code is composed of

four element simulation codes each of which treats the transport phenomena in the gas phase, the

melt phase, conductive heat transport in various solid parts and radiative heat transfer between

partially specular diffuse gray surfaces. These four element codes share the global analysis of a

Cz furnace through interactions by exchanging the values and/or fluxes at phase boundaries. At

the end of the research project, we have developed a global simulation code and confirmed its

validity for a small scale Cz furnace. This global analysis code remains some problems.

Extraordinary long CPU time requirement for the 3-D unsteady simulations of melt phase

transport phenomena makes the iterative calculation almost impossible on a conventional

computer. The alternative candidate must be the introduction of a turbulence model for melt flow.

We have developed numerical code that can adopt a turbulent model. However, we could not pick

up a reliable turbulent model applicable to such a weak turbulence accompanied by rotating flow.

Beside these macro-scale simulations, Molecular Dynamics (MD) simulation and Monte

Carlo (MC) simulation have investigated fundamental aspect of crystal growth from atomistic

viewpoints. Some members searched a scaling law to connect the results of these micro-scale

-170-

simulations and the realistic crystal growth phenomena. The MD simulations have been applied

for studying diffusion coefficients of point defect in silicon crystal and diffusion coefficient of

oxygen atoms in silicon melt.

-171

3. 2. 2

4-5 m±

( 1 ) BB

^ 3 2 7 llX^r— (Cz) ftlCj3tt-5^fXffll*lfSibS®lRyt SiO fflftf l*SlS«ft5 t

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©SttSffSfT ofc, IPi»!0l*tt»it}»£ST»li *>©£<R£t.

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e©K*6@ATA*t:-&L,. JFFSIcSSiSSrESt"-E. C i:T.

###»»**< A 0 , SiO <DMm&&mT£ 5 £ ££SL£. L, fflUftC/Rh*

miC*e%-&A,*A&Rtgf t A, x;l- h®S«lA 5'->ÊS©S«J#tt$E'(bS1jr-5

c ££*!* Lfc. C©7,D^7Atti®6#6r©itIt*E*a$tiTH3>„

Numerical Analysis of Transport Phenomena in Gas Phase in a Cz furnace.

Nobuyuki Imaishi

Inst. Advanced Material Study, Kyushu University

Abstract:

A finite element code was developed for analysis of flow, convective heat transfer and mass

transfer of SiO in the gas phase in a Cz furnace. The code was run in stand-alone mode, by

assigning the boundary temperature and velocity values independently. The results suggest that a

gas guide duct significantly increase the mass transfer coefficient at the melt surface, i.e. the

increase of evaporation rate of SiO from the melt surface and reduction of oxygen concentration

in the melt. But at the same time, the increased gas flow velocity would cause an increase of drug

force to the melt surface and may change flow pattern and oxygen transport characteristics in the

-172-

melt.

The over-all effect of the gas-guide duct will be clarified by the global analysis.

This program has been successfully combined into the global analysis code.

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W. C @ *§ $ 13 Brown S> t U tb X &$? 1C-gt U T S . 21 © © * ;H- SB _hT © SiO

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1) Bornside, D.E., and Brown, R.A.; J.Electrochem. Soc., vol. 142, 2790 (1995)

-175-

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-177-

tou>

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0=0.57m/s

<D

Evaporation coefficient [cm/s]

Stress on the melt surface [N/m2]

Stress on the rpelt surface

Evaporation coefficient [cm/s]

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Numerical Simulation of Melt Convection and Heat Transfer in Czochralski Single Crystal

Growth Processes

Kenjiro SUZUKI

Department of Mechanical Engineering

Graduate School of Engineering

Kyoto University

-179-

Abstract:

Two-dimensional and three-dimensional unsteady numerical computations have been made

for the melt convection and related heat transfer in Czochralski single crystal growth processes.

Characteristics of flow and thermal fields have been analyzed for two cases of different Prandtl

number; namely Silicon Oil of Pr=4,580, which is popularly used for melt flow simulation

experiments, and Si of Pr=0.0133. Two- and three-dimensional computations with Launder-

Sharma turbulence model have also been conducted for the larger crucible size and mass transfer

of Oxygen in the melt has been discussed. In the case of Silicon Oil, the flow pattern in the melt

obtained from the three-dimensional computation was found to remain axi-symmetric, and good

agreement was confirmed to exist between present computations and experiment. In the case of Si,

the melt convection could not hold axi-symmetry and no agreement was observed between two-

dimensional computation and three-dimensional computation. It was found that the crucible

rotation could affect the melt flow to keep the axi-symmetric flow structure in laminar case,

contrary to the turbulent case where the crucible rotation may result in the asymmetric flow field.

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( 6)

1) U.Bueckle, M.Osumi, K.Suzuki and T.Yamamoto, Flow and Temperature Field in a Model

Czochralski Low-Prandtl Number Melt, The 2"1 International Symposium on Heat and Mass

Transfer.(1997)

2) J.S.Szmyd, T.Yamamoto, K.Suzuki and U.Bueckle, An Analysis of the Melt Convection for

Superconductor YBa2Cu307.x Single Crystal Growth by a Modified Czochralski Method, The

10th International Symposium on Transport Phenomena. (1997)

3) lilF*U, M.Jaszczur, 41 §15, $u A, Three-dimensional Simulation of Melt Flow and its Thermal

Characteristics in Cz Crucible, B 4-tilto^TSH!M5j£§1S$S 73 (1998)

4) J.S.Szmyd, G.Mika, M.Jaszczur and K.Suzuki, Osillatory Convection in InSb Single Crystal

Growth, Fifth International Conference on Advanced Computational Methods in Heat Transfer

(1998).

-191-

5) ill F*9 , G.Mika, $p /fc, Three-dimensional Numerical Simulation of Melt Flow and Its Thermal

Characteristics in Cz Crucible (Further Report), HI 36 HI E Wk is ^ ^ V ^ A 1 (1999)

P?5




Validation. (1999)

( 7 )

1) H.Ozoe, K.Toh, T.Inoue, J.Crystal Growth, 110 (1991), p472.

2) S.Nakamura, M.Eguchi, T.Azami, T.Hibiya, J.Crystal Growth, 207 (1999), p55.

3) H.Tomonari, M.Iwamoto, K.Kakimoto, H.Ozoe, K.Suzuki, T.Fukuda, Chemical Engineering

Journal 71 (1998), pl91.

4) Hyung-Tae Chung, Seung-Cheol Lee, Jong-Kyu Yoon, J.Crystal Growth, 163 (1996), p249.

5) A.Lipchin, R.A.Brown, J.Crystal Growth, 205 (1999), p71.

6) T.A.Kinney ,R.A.Brown, J.Crystal Growth, 132 (1993), p551.

7) B.E.Launder, B.I.Shama, Letters in Heat and Mass Transfer 1 (1974), pl31.

8) G.H.Hoffmann, Phys. Fluids 18 (1975), p309.

9) A.A.Mohamad, R.Viskanta, Funadmentals of Mixed Convection ASME 213 (1992), p43.

10) S.Hassid, M.Porch, J.Fluid Engng 100 (1978), pl07.

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CaseC3 2.0 0.0 5.0 55 x 55 x 56 radiative

CaseC4 0.0 -0.1 5.0 55 x 55 x 56 radiative


CaseCO 2.0 -0.1 5.0 55 x 55 x 56 radiative


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CaseCO 2.0 -0.5 5.0 55 x 55 x 56 radiative

-204-

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Numerical simulation of heat and mass transfer in CZ melt

Hiroshi Kawamura

Faculty of Science & Technology,

Science University of Tokyo

Abstract:

Numerical analyses with two dimensional boundary fitted and three dimensional cylindrical

coordinates have been performed to analyze the heat and mass transfer during the silicon crystal

growth by the Czochralski method.

The developed numerical methods were compared with two experiments and found to give

-207-

good agreements.

As a result of calculation, the crucible rotation was found to cause an internal recirculating

flow with the same rotational direction as the one caused by the buoyancy. An azimuthal

instability was captured through the simulation. The mode number was found to decrease as the

crystal Reynolds number increased. With the increase of the crucible rotation speed, the

azimuthal modal structure was observed more clearly.

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Numerical analyses of conductive heat transfer in the solid and radiative heat transfer between

the solid surfaces

Shigenao Maruyama* and Takao Tsukada"

* Institute of Fluid Science, Tohoku University

** Institute for Chemical Reaction Science,

Tohoku University

-223-

Abstract:

To understand accurately the transport phenomena during the silicon crystal growth by the

Czochralski (CZ) method, the computer simulation code for a global analysis of heat transfer in

the CZ furnace was developed, in which the radiative heat transfer between the surfaces that

possess both specular and/or diffuse reflectance components was taken into account, and the

effect of the radiative characteristic of crystal and melt surfaces on the silicon CZ crystal growth

process was theoretically investigated. As a result, it was found that the puling rate of the crystal

with a purely specular surfaces becomes faster than that with a diffuse surface to maintain the

crystal diameter constant for a given heater power. Also, the effect of the radiative characteristic

of the melt surface on the crystal growth strongly depends on the surface shape. In addition, in

order to improve the computational accuracy and to speed up the calculation, the simulation code

for the radiative heat transfer was modified.

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1) fitiUSS, #E$j# : j;&^< *g#m (REM2) £ fflV'fcff*®

we*r, 0*itt»6»x# (bH), $62#- 595

#, pp.1091-1097, 1996.

2) S.Maruyama and T.Aihara: “Radiation Heat Transfer of Arbitrary 3-D Absorbing, Emitting and

Scattering Media and Specular and Diffuse Surfaces”, ASME Journal of Heat Transfer, Vol.119,

No.l, pp.129-136, 1997.

3) S.Maruyama and M.Higano : “Radiative Heat Transfer of Torus Plasma, in Large Helical

Device by Generalized Numerical Method REM2”, Journal of Energy Conversion and

Management, Vol.38, No.10-13, pp.1187-1195, 1997.

4) Z.Guo, S.Maruyama and T.Tsukada : “Radiative Heat Transfer in Curved Specular Surfaces in

Czochralski Crystal Growth Furnace”, Numerical Heat Transfer, Part A, Vol.32, pp.595-611,

1997.

5) S.Maruyama : “Radiative Heat Transfer in Anistoropic Scattering Media with Specular Boundary

Subjected to Collimated Irradiation”, International Journal of Heat and Mass Transfer, Vol.41,

pp.2847-2856, 1998.

6) Z.Guo, S.Maruyama and S.Togawa : “Radiative Heat Transfer in Silicon Floating Zone Furnace

with Specular Reflection on Concave Surfaces”, JSME International Journal, Vol.41, No.4,

-230-

pp.888-894, 1998.

7) M.Higano, S.Maruyama and T.Takagi, “Numerical Analysis of Radiative Heat Flux on Large

Helical Device”, Fusion Engineering and Design, Vol.39, No.40, pp.341-346, 1998.

8) Z.Guo, S.Maruyama and S.Togawa : “Combined Heat Transfer in Floating Zone Growth of

Large Silicon Crystals With Radiation on Diffuse and Specular Surfaces”, Journal of Crystal

Growth, Vol.194, pp.321-330, 1998.

9) S.H.Hahn, T.Tsukada, M.Hozawa, S.Maruyama, N.Imaishi, and S.Kitagawa, “Global Analysis

of Heat Transfer in Si CZ Furnance With Specular and Diffuse Surfaces”, Journal of Crystal

Growth, Vol.191, pp.413-420, 1998.

10) Z.Guo, S.Maruyama, A.Komiya, “Rapid yet accurate measurement of mass diffusion coefficients

by phase shifting interferometer”, Journal of Physics. D, Applied Physics, Vol.32, pp.995-999,

1999.


Silicon Furnace with Radiation on Curved Specular Surfaces”, Heat and Mass Transfer, Vol.35,

pp.185-190, 1999.

b. tgoanEiiix

12) noise, : -a> x• »

S 32 Vol. 2, PP.591-

592, 1995.

13) B |p]ff = e, ROlSe, iS*8cfr

15S\ PP.211-213, 1996.

14) MOlSe • BlfllWHS • Jean Taine : KtxASSUfe C02 £ H20 ©

PP.467-470, 1996.

15) noise • B |6]»Ett • Jean Taine : C02-H20-N2 S

s 34 0B*eiss->>#>!')A»sss:i, m 1 #, PP.i33-134, 1997.

16) M.Hihano, S.Maruyama and T.Takagi : “Numerical Analysis of Radiative Heat Flux on Large

Helical Device”, Abstract of the Fourth International Symposium on Fusion Nuclear

Technology, p.69, 1997.

-231-

17) RlJUSS : REM2 #6# ( — 'A

”, m34m i#, pp.m-m,

1997.

18) S.H.Hahn, T.Tsukada, M.Hozawa, S.Maruyama, N.Imaishi and S.Kitagawa : “Global Analysis

of Heat Transfer in Si CZ Furnace with Specular and Diffuse Surfaces”, {b#ZC#^^ 62

m2^#, p.27, 1997.

19) S.H.Hahn, ROlSfi, : “SiCz

B Vol.24, p.13, 1997.

20) S.H.Hahn, W ^2R%E, RlilME : “CZ&C

t^Sly^^ya/”, rx-Z't-n >Ha.-

5^^ <h SCFS ’97, pp.33-39, 1997.

21) rojss, % : “LBL

^”, m 35 Avoi.i, PP.ii5-ii6, 1998.

22) S.Togawa, Z.Guo and S.Maruyama, “Effect of Thermal Radiation on Heat Transfer in

Floating Zone Growth of Large Silicon Crystals”, I" X —

A ——f-xT a # ##%#:## J SCFS'98, pp.95-102, 1998.

23) S.Maruyama, Z.Guo, and S.Togawa, “Coupled Radiative and Conductive Heat Transfer in Si

Floating Zone Furnace with Diffuse and Specular Surfaces”, B

~%M, No.98-7, pp.44-50, 1998.

24) Z.Guo, S.Maruyama and S.Togawa : “Radiative Heat Transfer in Needle-eye Floating Zone

Crystal Growth Furnace”, Proc. 75th JSME Spring Annual Meeting, Vol.5, No.98-1, pp.98-

101,1998.

25) Z.Guo and S.Maruyama : “Numerical Prediction of Radiation Transfer in a Boiler with Non-

isothermal, Non-gray Gases and Anisotropic Particles”, 35th National Heat Transfer

Symposium of Japan, Vol.2, pp.481-482, 1998.

26) Z.Guo, S.H.Hahn, S.Maruyama and T.Tsukada: “Heat Transfer in Czochralski Crystal Growth

Furnace With Radiation on Curved Specular Surfaces”, The 75th JSME Spring Annual

Meeting, Vol.3, No.98-1, pp.389-390, 1998.

27) RUlSfi:”:iS'a^^'>5n.l/-i/3 > £Eigifi£:E”, B Vol.25, p.13,

1998.

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28) mii

Vol.II, pp.467-468, 1999.

29) 4"5g±, S.H.Hahn, ROjSS, #,

— S, ttJH j|S : “SiCz B Vol.26, p.18, 1999.



pp.000-000, 1999.

c. mm, mm, ##

31) miima : m36# 141 40-52, 1997.

d .

32) S.Maruyama and T.Aihara : "Radiation Heat Transfer of Arbitrary 3-D Participating Media

and Surfaces Using Radiation Element Method by Ray Emission Model (REM2)", Proc.

ASME/JSME Thermal Engineering Conference, Vol.3, pp.235-242, 1995.

33) S.Maruyama, and M.Higano : “Radiative Heat Transfer of Torous Plasma in Large Helical

Device by Generalized Numerical Method REM2”, Proc. International Symposium on

Advanced Energy Conversion System and Related Technology, pp.387-394, 1995.

34) S.Maruyama and T.Aihara : “Radiation Heat Transfer of Arbitrary 3-D Participating Media

and Surfaces with Non-Participating Media by a Generalized Numerical Method REM2”,

Radiative Transfer- I , Proc. International Symposium on Radiative Transfer, Ed. M.P.

Menguc, Begel House, Inc., pp.153-168, 1996.

35) S.Maruyama,: “Radiative Heat Transfer in a Layer of Anisotropic Scattering Fog Subjected to

Collimated Irradiation”, Radiative Transfer- II, Proc. International Symposium on Radiative

Transfer, Ed. M.P. Menguc, Begel House, Inc., pp.157-172, 1998.

36) S.Maruyama : “Radiative Heat Transfer of Arbitrary Three-dimensional, Nongray And

Anisotropically Scattering Media And Surfaces”, Heat Transfer 1998, Proc. of 11th

International Heat Transfer Conference, Vol.7, pp.457-462, 1998.

37) S.H.Hahn, T.Tsukada, M.Hozawa, S.Maruyama and N.Imaishi : “Global Analysis of Heat

Transfer in Si CZ Furnace with Specular and Diffuse Surfaces”, Proc. The 14th KACG Tech.

-233-

Meeting and 5th Korean-Japan EMGS, pp.45-47, 1998.

e.

38) ROiSit : =

No.49, pp.19-24, 1996

39) S.Maruyama and M.Higano, Radiative Heat Transfer of Torus Plasma in Large Helical Device

by Generalized Numerical Method REM2, B *6##==, M U X ^ )V ^

(1997-3), pp.259-266.

40) prnss • b[6]Shs • mm^j# : rem2 r • e$l •

fttfcf&om-mtir, ms#,

pp.107-117, 1997.

1) F.Dupret, P.Nicodeme, Y.Ryckmans, P.Wouters and M.J.Crochet : Int. J. Heat Mass Transfer,

33 (1990) 1849.

2) mm##,

t£, 18 (1991) 431.

3) T.A.Kinney and R.A.Brown : J. Crystal Growth, 132 (1993) 551.

4) J.Baumgartl, A.Bune, K.Koai, G.Muller and A.Seidl : Mat. Sci. Eng., A173 (1993) 9.

-234-

3.2.5-1 #### j3 ^ * — 9

E 3.2.5-1

Property/parameter Value

Emissivity 0.55 (Crystal, Chamber wall)0.318 (Melt)0.50 (Quartz crucible) 0.90 (Graphite crucible, Heater, Pedestal, Radiation shield, Supporter)0.20 (Puller)0.70 (Insulator)

Thermal conductivity (W/mK) 22.0 (Crystal)64.0 (Melt)2.89 (Quartz crucible)60.0 (Graphite crucible, Heater, Pedestal, Radiation shield, Supporter,)58.94 (Puller)1.31 x 103/T (Insulator)

Melting temperature of silicon (K) 1683Density of solid silicon (kg/m3) 2.3 x 103Specific heat of solid silicon (J/kgK) 1.0 x 103Heat of fusion (J/kg) 1.8x10*Electric conductivity (1/Qm) 1.2 x 105 (Graphite)Crucible inner diameter (m) 0.0720/0.3872Crystal diameter (m) 0.0350/0.1524Chamber wall temperature (K) 300

Chamber

GraphiteCrucible

QuartzCrucible

Crystal

Heater

InsulatorPedestal

Chamber

Puller

RadiationShield

Crystal / Melt

Heater

Pedestal

E 3.2.5-2 '> U 3 > CZ @

— 235 —

□ Case 1A Case 2O Case 3

Crystal length [-]

0 3.2.5-3 CZ($&## 3.5cm

0 3.2.5-53.5cm

AT = 50K

1683K

2183K

Case 3Case 2Case 1

□ Case 1A Case 2O Case 3

0 =17.657[-]Q =18.533[-] O =17.998[-]

O □O D

Crystal length [-]

0 3.2.5-4 CZ

15.24cm (Dm a)

0 3.2.5-6 PeWLt<Dm&15.24cm (Dm&)

3.2.5-2( SSSiS : 1.0 [-]

: 12.415 [-] )

Curved Flat

Case 1 0.0643 0.0614

Case 2 0.0709 0.0693

Case 3 0.0669 0.0515

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0 3.2.5-7 CZiPrtS(teflS 15.24cm,

3.2.5-3 PeWit AztCKJf-f «W**J£iKffc©;S5#

Q/Qo Case 1 Case 2 Case 3a 1.000 Pe =8.363 XI0"2

Az=3.345X10'2Pe=1.666 X101 Az=5.479 X10'2

Pe =7.909X102 Az=3.077X10’2

b 0.856 Pe=1.364 XI O’1 Az=2-225X10"2

Pe=1.901 X10"' Az=3.714X10‘2

Pe =1.144X10' Az=1237X10"2

c 0.829 Pe=2.618X10"' Az =5.528 XI0"2

Pe =3.189 XI O'1 Az=7.368 X10'2

Pe =2.400X10"' Az=4.511 X10'2

a: without a shield, b, c: with a shield.

a b c

0 3.2.5-8 CZ 3.5cm <Z>Mn)

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Pe 0.0304 0.0351 0.0422

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Molecular dynamics simulation of vacancy and self-interstitial in silicon under constant pressure

and temperature

Koichi KAKIMOTO

Institute of Advanced Material Study,

Kyushu University

Abstract:

Molecular dynamics simulation was carried out to estimate diffusion constants and

mechanism of point defects such as a single vacancy and a self-interstitial atom under hydrostatic

pressure. Stillinger-Weber potential was used as a model potential, which is widely accepted for

modeling of silicon crystals and melts. We obtained the following results on a self-interstitial

atom from the calculation. 1) Diffusion constants of self-interstitial are almost independent of

pressure within a range from ?50 to +50 k bar. 2) A self-interstitial atom diffuses with a

-238-

formation of dumbbell structure, which is aligned in [110] direction. For single vacancy, the

followings were clarified. 1) Diffusion constants of vacancy are also independent of pressure

within a range from ?40 to +40 k bar. 2) A vacancy diffuses with a switching mechanism to

nearest neighbor atoms in lattice site.

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defects” J. Crystal Growth, in print.


near solid-liquid interface”, J. Vacuum Science, in print.

-243-

(7)

1) T.Tsukada, M.Hozawa and N.Imaishi, J. Chem. Eng. Japan, 21 (1988), 184.

2) M.Itsumi and F.Kiyosumi, Appl. Phys. Lett., 40 (1982) , 496.

3) R.A.Brown, D.Maroudas and T.Sinno, J. Crystal Growth, 137 (1994), 12.

4) P.J.Ungar, T.Halicioglu and W.A.Tiller: Phys. Rev. B50 (1994), 7344.

5) H.Bracht, N.A.Stolwijk and H.Mehrer: Semicond. Silicon, ECS, Pennington N. J., p.593

(1994).

6) T.Y.Tan and U.Goesele, Appl. Phys. A37 (1985), 1.

7) H.J.Gossmann, C.R.Rafferty and H.S.Luftmann, Appl. Phys. Lett., 63 (1993), 639.

8) G.B.Bronner, J. Crystal Growth, 53 (1981), 273.

9) K.Wada and N.Inoue, Defects and Properties of Semiconductors, Defect Engineering, KTK

Scientific, p.169. (1985)

10) R.Habu, A.Tomiura and H.Harada, Semicond. Silicon, ECS, Pennington N. J., p.635 (1994).

11) B.Leroy, J. Appl. Phys., 50 (1979), 7996.

12) C.Boit, J. Crystal Growth, 53 (1981), 563.

13) T.Abe, K.Kikuchi, S.Shirai and S.Muraoka, Semiconductor Silicon 1981, ed. H.R.Huff,

R.K.Kriegler and Y.Takeishi (Electrochem. Soc., Pennnington, 1981) p.54

14) H.Zimmermann and H.Ryssel, Appl. Phys. A55 (1992), 121.

15) K.Taniguti, D.A.Antoniadis and Y.Matsushita, Apll. Phys. Lett., 42 (1983), 961.

16) M.Yoshida and K.Saito, Jpn. J. Appl. Phys., 6 (1967), 573.

17) K.Tempellhoff, Appl. Phys. Lett., 42 (1988), 961.

18) C.W.Gear, “Numerical initial value problems in ordinary differential equations”, Englewood

Cliffs, Prentice Hall, 1971.

19) F.H.Stillinger and T.A.Weber, Phys. Rev., B31 (1985), 5262.

-244-

Diff

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Interstitial

Vacancy43 (1/2,1/2,1/2)

0 3.2.6-1 Initial positions of a vacancy and an interstitial atom in silicon crystal. The initial positions of the defects are indicated by reduced units.

Vacancy

InterstitialPerfect lattice

Time [sec]

0 3.2.6-2 Mean-square displacements of silicon atoms as a function of time for cases of vacancy, interstitial and perfect crystal.

-245 —

--------PJ.Ungar '94 ---------R.Habu '94..........RA.Brown '94 —X— B.Leroy '79

A H.Bracht '94 —A— C.Boit '90—T.Y.Tan '85 □ TAbe '86—h— HJ.Gossmann '93 —■— H.Zimmermann '92 —♦— G.B.Bronner '87 —V— K.Taniguti '83

A K.Wada '81

0 3.2.6-5 Arrhenius plot of diffusion constants of an interstitial atom.

-------- R.Habu 94 ...........R.A.Browa '94--A--K.Wada '87 —•—T.Y.Tam '85

H.Zimmeraiana '89 —■—H.Ziaimeruiaun '92—ffl—M.Yoshida '67 -------- PJ.Ungar '94—B— K.Tempelhoff '82

T [K]1250 1000

E elect P attern

11X10

1/T [K~l]

0 3.2.6-6 Arrhenius plot of diffusion constants of a vacancy.

-247-

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Molecular dynamic simulation of an oxygen atom in silicon crystal

Koichi KAKIMOTO

Institute of Advanced Material Study,

Kyushu University

Abstract:

Molecular dynamic simulation of an oxygen atom in silicon crystal and the melt was carried

out to obtain diffusion constants of oxygen in the melt. The simulation using mixed potential in

the melt in which an oxygen atom and 216 silicon atoms were taken into account has been carried

out. Vibration frequencies of oxygen and vacancy-oxygen (V-O) pair in the crystal have been

calculated. Calculated frequency of oxygen and V-O pair were 1000 and 800 cm-1, respectively,

while experimental results which were obtained from Fourier transform spectra of infrared

absorption (FTIR) are 1100 and 830 cm-1, respectively. Oxygen diffusion constant was obtained

-248-

in elevated temperature of 1700 K. Calculated diffusion constant of oxygen in the melt was

2x10-4 cm2/sec.

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1) K.Kakimoto, Shin Kikuchi and H.Ozoe, ’’Molecular dynamics simulation of oxygen in silicon

melt”, J. Crystal Growth, 198/199 (1999) 114.

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Numerical simulation of drop behavior in an electromagnetic levitator

Takao Tsukada

Institute for Chemical Reaction Science,

Tohoku University

Abstract:

A mathematical model, which can predict the equilibrium shape of a molten silicon drop and

additionally the nonlinear drop oscillations, has been developed for the improvement and

determination of the optimal processing conditions in an electromagnetic levitation device

developed in Japan to accurately measure the thermophysical properties such as surface tension

and density of silicon melt. As a result, the effects of the electric current and frequency in the RF

— 256 —

coil on the equilibrium shape and the average temperature of the drop were clarified numerically,

and it was demonstrated that the present model is useful for determination of the operating

condition to make the shape of the molten drop spherical. Also, the mathematical model for the

drop oscillations revealed that the frequency decreases as the ratio of the electric current ratio

(heating coil/levitation coil) increases.

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(7)

a.

1) S.H.Hahn, Y.Sakai, T.Tsukada, M.Hozawa, N.Imaishi and S.Kitagawa: “Effect of Processing

Conditions on Drop Behavior in an Electromagnetic Levitator”, Metail. Trans. B, VoI.29B,

pp.223-228, 1998.


N.Imaishi: “Equilibrium Shape of a Molten Silicon Drop in an Electromagnetic Levitator in

Microgravity Environment”, Metail. Trans. B, in press.

b.

3) S.H.Hahn, Y.Sakai, T.Tsukada, M.Hozawa, N.Imaishi and S.Kitagawa:“Numerical Simulation

-265-

of Drop Behavior in an Electromagnetic Levitator”, fb # % # ^ 29

lilal, #—'Ê, p.305, 1996.

4) S#iA, S.H.Hahn, #5#*, tfi, ft,

^ Vol.14, pp.67-68, 1997.

5) m#m&, S.H.Hahn, tf, lUM it

m : “nmmmmffiommizmrz&mmffi”, 63

S, S-Ê, p.315, 1998.

6) ¥EStii, S.H.Hahn, ?S,

B S, B204, 1999.

(8) #*%#

1) S.Asai: “Electromagnetic Processing of Materials”, ISIJ, Nagoya, 1994.

2) M.Przyborowski, T.Hibiya, M.Eguchi and I.Egry: J. Crystal Growth, 1995, vol.151, pp.60-65.

3) E.Gorges, L.M.Racz, A.Scillings and I.Egry: Int. J. Thermophysics, 1996, vol. 17, pp.1163-

1172.

4) I.Egry, G.Jacobs, E.Schwartz and J.Szekely: Int. J. Thermophysics, 1996, vol.17, pp.1181-

1189.

5) J.H.Zong, B.Li and J.Szekely: Acta Astronautica, 1992, vol.26, pp.435-449.

6) J.H.Zong, B.Li and J.Szekely: Acta Astronautica, 1993, vol.29, pp.305-311.

7) J.H.Zong, and J.Szekely: Acta Astronautica, 1993, vol.29, pp.371-378.

8) A.Gagnoud and J.F.Brancher, IEEE Trans. Mag., 1985, vol.21, pp.2424-2427

9) O.A.Basaran, J.Fluid Mech., 1992, vol.241, pp.169-198

— 266 —

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Properties or parameters Unit ValueEmissivity - 03

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—274 —

Crystal and Interface Analysis (molecular dynamics simulation)

T. Motooka

Dept, of Materials Science and Engineering,

Kyushu University

Abstract:

We have investigated growth mechanisms and defect formation processes during

crystallization from melted Si and solid phase epitaxy (SPE) by using large-scale molecular

dynamics simulations combined with the Tersoff potential. Structural changes and energy levels

in impurity (B, P, AJ-doped Si have been also analyzed by using first-principle molecular orbital

calculations based on a cluster model. The main results are as follows: (i) Liquid Si is, in a short

time-scale, composed of the j3 -S„ and simple hexagonal structures which may give rise to an

anomaly in the density near the melting point; (ii) The solid/liquid Si interface is a rough surface

composed of {111} facets in the [001] pulling, while it is essentially a flat (111) surface in the

[111] pulling; (iii) The melt growth in the [001] direction occurs by attaching Si atoms in melt at

the kink sites associated with the {111} facets formed at the solid/liquid Si interface, while in the

[111] direction double-layered two-dimensional nucleation is first created and then followed by

double-step layer-by-layer growth; (iv) In the case of SPE, layer-by-layer crystallization along

the (111) plane can be seen at higher temperatures, while at lower temperatures layer-by-layer

crystallization occurs along the (001) plane; (v) Defect formation can be initiated by 5-membered

rings created at the interfaces which give rise to interstitials and {111} stacking faults in the melt

and SPE growth, respectively; (vi) The Si band structure and impurity levels can be well

reproduced by cluster model calculations including 38 Si atoms; (vii) The uniaxial strain induced

near the solid/liquid interface becomes smaller than equilibrium thermal expansion and it

gradually changes to compressive as the temperature gradient increases.

-275

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(6)

a.

1) "Uniaxial strain observed in solid/liquid interface during crystal growth from melted Si: A

molecular dynamics study" by Ken Nishihira, Shinji Munetoh, and Teruaki Motooka 8-th Int.






— 281 —

b . !ro 5C jx

1) M.Ishimaru and T.Motooka:"Molecular dynamics simulations of crystal growth from melted

silicon: defect formation processes" Mat. Res. Symp. Proc. Vol. 538, 247-250 (1999).

2) Ken Nishihira, Shinji Munetoh, and Teruaki Motooka:"Uniaxial Strain Observed in

Solid/Liquid Interface during Crystal Growth from Melted Si: A Molecular Dynamics Study" J.

Crystal Growth, in press (2000)

3) T.Motooka, K.Nisihira, S.Munetoh, K.Moriguchi, and A.Shintani: "Molecular dynamics

simulations of solid phase epitaxy of Si: Growth mechanisms" Phys. Rev. B, in press (2000)

4) T.Motooka, K.Nisihira, S.Munetoh, K.Moriguchi, and A.Shintani: "Molecular dynamics



( 7) ####

1) T.Motooka, Phys. Rev. B49, 16367 (1994).

2) T.Motooka, Thin Solid Films 272, 235 (1996).

3) M.Ishimaru, K.Yoshida, and T.Motooka, Phys. Rev. B53, 7176 (1996).

4) M.Ishimaru, K.Yoshida, T.Kumamoto, and T.Motooka, Phys. Rev. B54, 4638 (1996).

5) T.Motooka, S.Harada, and M.Ishimaru, Phys. Rev. Lett. 78, 2980-2981 (1997).

6) J.Tersoff, Phys. Rev. B38, 9902 (1988).

7) Gaussian 94, Revision E.2, M.J.Frisch, G.W.Trucks, H.B.Schlegel, P.M.W.Gill, B.G.Johnson,

M.A.Robb, J.R.Cheeseman, T.Keith, G.A.Petersson, J.A.Montgomery, K.Raghavachari,

M.A.Al-Laham, V.G.Zakrzewski, J.V.Ortiz, J.B.Foresman, J.Cioslowski, B.B.Stefanov,

A.Nanayakkara, M.Challacombe, C.Y.Peng, P.Y.Ayala, W.Chen, M.W.Wong, J.L.Andres,

E.S.Replogle, R.Gomperts, R.L.Martin, D.J.Fox, J.S.Binkley, D.J.Defrees, J.Baker,

J.P.Stewart, M.Head-Gordon, C.Gonzalez, and J.A.Pople, Gaussian, Inc., Pittsburgh PA, 1995.

8) ±m. sb, ±», > u 3 sVol. 25, No. 5, 412 (1998).

9) G.L.Olson and J.A.Roth, Mat. Sci. Rep. 3, 1 (1988).

10) H.C.Abrink, R.M.Broudy, and G.P.McCarthy, J.Appl. Phys. 39, 4673 (1968).

-282-

11) R.A.Joyce, R.R.Bradley, and G.R.Booker, Phil. Mag. 15, 1167 (1967).

-283-

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Global Simulation Code

Nobuyuki Imaishi Takao Tsukada Shigenao Maruyama Hiroshi Kawamura Kenjiro Suzuki

Inst. Advanced Material Study, KyushuUniv. Res. Inst. Chem. Reaction Sci., Tohoku Univ. Res. Inst. Fluid Science, Tohoku Univ.Fac. of Sci&Tech, Science Univ. of Tokyo Graduate School of Engineering, Kyoto Univ.

Abstract:

A large scale numerical code was developed for a global analysis of silicon Cz furnace to

understand transport phenomena in details. The code is composed of four major element codes

each of which analyzes transport phenomena in the gas, melt and solid phases and the radiative

heat transfer between partly specular diffuse gray surfaces. Each code has been developed by the

-299-

research project members, separately. A main program was developed to manage the exchanges of

velocity, temperature and concentration values as well as the momentum, heat and mass fluxes on

the phase boundaries in order to proceed the iterative convergence process for a pseudo steady

state. After the 5 year long project, a global simulation code has been developed. The code is able

to calculate successfully the transport phenomena and melt-crystal interface shape in a small Cz

furnace.

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1) D.E.Bornside and R.A.Brown, J.Electrochem. Soc., vol. 142,2790(1995)

2) T.Carlberg, J.Electrochem. Soc., vol.133, 1940(1986)

3) M.Watanabe, K.W.Yi, T.Hibiya and K.Kakimoto, Progress in Crystal Growth and

Characterization of Materials (1999) 215-238

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WM&a**Aaar* A&a

Experimental validation of the global simulation code

Nobuyuki Imaishi


Kyushu University

Abstract:

The validity of the developed global simulation code must be verified by comparing the

numerical results with the corresponding experimental results. Two sets of experiments have been

conducted at Shinshu Universit and NEC Corporation, respectively. The results of Shinshu

University confirmed the simulation result that a funnel shaped gas guide installed in the furnace,

between the crucible and the crystal, would provide a reduction of heater power and provide

easier temperature control. Further experiments will be provided by Shinshu University after

their installation of a power meter. A X-ray radiographic observation of the crystal-melt interface

was conducted at the Fundamental Research Laboratory of NEC Corporation. The crystal-melt

interface shape was reasonablly reproduced by the global analysis code. The global simulation

code predicted the oxygen concentration in the grown crystal. The predicted result fell very close

to the NEC’s experimental result that was reported elsewhere and the growth conditions were

slightly different from the present ones. These experimental results suggest the validity of the

developed global simulation code.

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Model Experiment of Cz Furnace

Kimihisa Itoh

Department of Science & technology,

Waseda University

Abstract:

The precise experimental data are important to develop and verify a computer simulation

program of the unsteady convection flow of molten silicon in Cz furnace. The following

experiments were conducted to establish the database of the melt flow in a cold model using

-321-

; * *=#**#*

water, silicone oil and Wood's metal as model materials.

(1) Temperature profile measurement in the Cz melt: The temperatures in Wood's metal which is a

low Pr melt as silicon were continuously measured using telemeter system. The obtained results

were arranged in a visible form and stored as a database.

(2) Velocity profile measurement in the Cz melt: The larger single crystal was employed and the

experimental furnace was modified to rotate at very low rate. This modification made the model

experiments more close to the actual operating conditions of Cz furnace. Time change of melt

flow was measured by LDV and the flow profile was measured by PIV. The obtained results were

arranged and stored as a database.

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-331-

APPENDIX-1 • SWJSt/r (t >x* 11/ n 80

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-334-

Analysis of Crystalline and Interface (Monte Carlo Method)

Toshiharu Irisawa

Computer Center, Gakushuin University

Abstract:

Monte Carlo simulation of the melt growth was performed to study the interface process. At

first, we investigated in detail the process of the solid's holding the melt. This process affects the

introducing the point defect in a crystal. We find that the point defect density in the case of the

slow growth rate is less than that in the equilibrium states, in spite of the usual knowledge that

the defect density is the increase function of the growth rate. Next, we examined the taking-in

process of the impurities for the melt growth. In the condition that the interaction of the impurity

atoms can be ignored, the impurity atoms concentration in the melt and the growth rate become

steady state. However, in the condition that the concentration of the impurity atoms becomes

super saturate in melt, the impurities nucleate the front of the interface in melt, and it is included

in the solid. Then, we fined that the concentration of the impurity atoms in the melt and the

growth rate cannot become the steady state. In the case of the diamond lattice, we found that

(111) surface is flat in the atomic level but the (100) surface is a rough surface, and the (110)

surface is surrounded by the (111) surface when the effective bond energy (|)eff =3kT. The

equilibrium and effective distribution coefficient can be evaluated by simulation. When the

growth rate is small, it was found that the impurity concentration, which is contained in the solid,

can be used the equilibrium concentration. Also, in the case where it is easy for impurities to be

taken in, and the growth rate is small, it was found that the diffusion of impurities becomes the

rate determining process but when the growth rate is large, the heat diffusion becomes the rate

determining process.

(2) #C&

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simulation” Proceedings of the Second Symposium on Atomic-scale Surface and Interface

Dynamics, 277-280 (1998).

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3) D.E.Temkin: Crystallization Process (Consultant Bureau, New York,1966) 15.

4) R.H.Swendsen: Monte Carlo studies of the interface roughening transition, Phys. Rev. B 15,

5421 (1977).

5) K.K.Mon, S.Wansleben and D.P.Landau: Monte Carlo studies of anisotropic surface tension

and interfacial roughening in the tree-dimensional Ising model, Phys. Rev. B 39, 7089 (1989).

6) K.K.Mon, D.P.Landau and D.Stauffer: Interface roughening in the tree-dimensional Ising

model, Phys. Rev. B 42, 545 (1990).

7) M. Caselle, F. Gliozzi and S. Vinti: Finite-size effects in the interface of 3D Ising model,

Rhys.Lett. B 302, 74 (1993).

8) J.A.Buruton, R.C.Prim and W.P.Slicher: J. Chem. Phys 21 (1953) 153.

$ zl !/ — '> a B Vol. 25, No. 5, 24 (1998).

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