Diffusion and mass transfer of boron in molten silicon during slag

Diffusion and mass transfer of boron in molten silicon during slag re ?ning process of metallurgical grade silicon

Jijun Wu a ,b ,*,Fanmao Wang b ,Zhengjie Chen b ,Wenhui Ma a ,b ,*,Yanlong Li b ,Bin Yang a ,Yongnian Dai a ,b

a

State Key Laboratory of Complex Nonferrous Metal Resources Cleaning Utilization in Yunnan Province/The National Engineering Laboratory for Vacuum Metallurgy,Kunming University of Science and Technology,Kunming 650093,China b

Engineering Research Center for Silicon Metallurgy and Silicon Materials of Yunnan Provincial Universities/Faculty of Metallurgical and Energy Engineering,Kunming University of Science and Technology,Kunming 650093,China

A R T I C L E I N F O

Article history:

Received 10April 2015

Received in revised form 24June 2015Accepted 25June 2015

Available online 2July 2015

Keywords:

Solar-grade polysilicon Boron removal Kinetics

Diffusion coef ?cient

Mass transfer coef ?cient Boundary layer

A B S T R A C T

In this paper,the formulas of diffusion coef ?cient (D )and mass transfer coef ?cient (b )of boron in molten silicon were deduced.The diffusion coef ?cient of boron was determined to be 1.46?10à8m 2s à1by the diffusion experiment at 1823K in the resistance furnace.The mass transfer process of boron between silicon and slag was described using the two-?lm theory and the mass transfer coef ?cient (b )of boron was measured to be 1.7?10à4m s à1while using the binary CaO –SiO 2slag re ?ning at 1823K.It was calculated by the relation between diffusion coef ?cient and mass transfer coef ?cient that the effective boundary layer thickness (d )close to molten silicon side was 0.086mm.

?2015Elsevier B.V.All rights reserved.

1.Introduction

The solar-grade polysilicon used as solar cell materials is mainly produced by the chemical methods including the Siemens process and the Fluidized Bed Reactor [1–3].As a result of some disadvantages such as high cost and heavy environmental pollution,the chemical route is being substituted by some other techniques [4,5].The metallurgical route for a low cost solar-grade polysilicon production has gradually become a hot topic of research.In this route,the slag re ?ning can effectively remove impurity boron from metallurgical grade silicon and most of current researches have focused on the thermodynamics of boron removal by this method [6–9].Wu et al.[10]found that boron in metallurgical grade silicon could be removed from 18ppmw to 1.4ppmw using a re ?ning technique of high basic slag.Also,the thermodynamic relation between distribution coef ?cient of boron (L B )and slag activity parameter was established and con ?rmed.Li et al.[11]described that boron can be removed by increasing the

basicity and the oxygen potential of slag.Fang et al.[12]found that the boron concentration in silicon can be decreased from 10.6ppmw to 0.65ppmw by Na 2O –SiO 2slag re ?ning treatment and it is bene ?cial for boron removal while increasing re ?ning time under the condition of a small mass ratio of slag to silicon.

Some studies [13,14]show that the kinetic factors such as the diffusions of boron in molten silicon and borate in slag play the important roles to boron removal during the process of slag re ?ning.The diffusion coef ?cient of boron in silicon melt was calculated to be 2.7?10à4cm 2s à1by Tang et al.[15]and it was also experimentally determined to be (2.4?0.7)?10à4cm 2s à1by Kodera [16].Based on the work of Kodera [16],Garandet [17]propose new determinations of the diffusion coef ?cients of various dopants in liquid silicon,and a diffusion coef ?cient of 1.2?10à8m 2s à1for boron in silicon melt was gotten.It has been reported that the rate controlling step of boron removal from metallurgical grade silicon is the mass transfer process of borate in slag.Nishimoto et al.[18]found that the boron removal rate was controlled by mass transport in the calcium silicate slag with a mass-transfer coef ?cient (k S )of 1.4?10à6m/s.Krystad et al.[19]had also reported the larger values for the same slag and temperature in the range of 1.7?10à6–3.5?10à6m/s and a relatively larger value of 4.3?10à6m/s has also been obtained using the CaO –MgO –SiO 2slag.Zhang et al.[20]calculated the total mass transfer coef ?cient of boron to be 6.85?10à4cm/s for the 10%CaF 2–10%Al 2O 3–20%CaO –60%SiO 2slag at 2073K.

*Corresponding authors at:State Key Laboratory of Complex Nonferrous Metal Resources Cleaning Utilization in Yunnan Province/The National Engineering Laboratory for Vacuum Metallurgy,Kunming University of Science and Technology,Kunming 650093,China.Fax:+8687165161583.

E-mail addresses:dragon_wu213@https://www.360docs.net/doc/431520039.html, (J.Wu),mwhsilicon@https://www.360docs.net/doc/431520039.html, (W.Ma).

https://www.360docs.net/doc/431520039.html,/10.1016/j.?uid.2015.06.040

0378-3812/?2015Elsevier B.V.All rights reserved.

Fluid Phase Equilibria 404(2015)70–74

Contents lists available at ScienceDirect

Fluid Phase Equilibria

j o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /?u i

d

In this paper,the diffusion coef ?cient of boron in molten silicon was determined by experiments.The mass transfer coef ?cient of boron removal using the binary CaO –SiO 2slag re ?ning was also measured and calculated.The functional relationship between boron concentration in silicon and re ?ning time was established and con ?rmed.Simultaneously,the effective boundary layer thickness close to silicon side was derived from the relationship between mass transfer coef ?cient and diffusion coef ?cient of boron.

2.Theoretical formulations

The boron atoms will diffuse from solid boron toward liquid silicon when the solid boron and the liquid silicon are placed together.The concentration gradient of boron in molten silicon will be formed and distributed from the solid –liquid interface of B –Si with a high boron concentration to the molten silicon with a low boron concentration.Finally,the boron concentration in whole liquid silicon will be saturated.The schematic diagram of boron diffusion from B –Si interface to liquid silicon is shown in Fig.1.According to Fick ’s second law,the diffusion rate of boron in molten silicon can be described as Eq.(1).

@c @t ?D @2c @x !

(1)The initial and boundary conditions of differential Eq.(1)are shown in Eqs.(2)and (3).

c ex ;0T

?g S

d ex T(2)

@c e0;t T

@x

?0(3)

where g and S are the total quantity and the sectional area of diffusible substance,respectively.d ex Tis the Dirac function at x 0?0.The property of Dirac function d ex Tcan be expressed as Eqs.(4)and (5).

d ex àx 0T?0;x ?x 0t1;x ?x 0

(4)

Z

t1à1

d ex àx 0Td x ?1

(5)

Then,the integral result of Eq.(1)at the initial and boundary conditions for Eqs.(2)and (3)is shown in Eq.(6).

c ex ;t T?g S ??????????p D t

p exp à

x 2

4D t

(6)

In the form of logarithm for Eqs.(6)and (7)can be gotten.

lg c ex ;t T?lg g S ??????????p D t p à

x 2

2:3e4D t T

(7)

By drawing to data,the curve of lg c ex ;t Tàx 2and its slope (k )can be gotten and represented as Eq.(8).

k ?

19:2D t

(8)

And lastly,the diffusion coef ?cient of boron in molten silicon (D )can be calculated and gotten according to Eq.(8).

During the slag re ?ning process of boron removal,there must be a silicon boundary layer (d )and a slag boundary layer (d 0),respectively.According to the two-?lm theory,the oxidation and removal process of boron in silicon by the binary CaO –SiO 2slag re ?ning can be shown in Fig.2.

According to the boundary-layer theory of convective mass transfer,the convective mass transfer rate is zero (u xc =0)at the verticality of phase interface,where the characteristics of mass transfer is an unsteady state diffusion.So the mass transfer rate of boron can be explained as Eq.(9):

J ?àD

@c @ x ?0?V ?d c

(9)Meanwhile,it can also be described as Eq.(10)

J ?b c àc ?eT

(10)

Then,Eq.(11)can be obtained by Eq.(9)=Eq.(10).d c d t ?àb ?A

V

?ec àc ?T(11)

where b is the mass transfer coef ?cient of boron in molten silicon.A and V are the interface area of between silicon and slag and the volume of molten silicon,respectively.c and c *are the boron concentrations in the molten silicon and at the interface of silicon-slag,respectively.

The interface concentration (c *)can be replaced by the equilibrium concentration of boron in silicon (c e )for a very fast reaction rate of boron oxidation at the interface of silicon-slag.After substituting the molar concentration (c )with the weight percent concentration (w [B]),Eq.(12)can be obtained by integrating Eq.(11).The value of mass transfer coef ?cient (b )can be described as the slope of curve.

ln

w ?B àw ?B e w ?B 0àw ?B e

?àb ?r m A

M m ?t (12)

where w [B]is the mass concentration of boron in silicon after the

re ?ning time (t ).w [B]0and w [B]e are the initial and the equilibrium mass concentrations of boron in molten silicon,respectively.r m and M m are the density and the mass of molten silicon,

respectively.

Fig.1.Schematic diagram of boron diffusion in molten

silicon.

Fig.2.Schematic diagram of boron oxidation and removal by CaO –SiO 2slag.

J.Wu et al./Fluid Phase Equilibria 404(2015)70–74

71

3.Experimental

The boron powder of 5g with a purity of 4N was ?rstly pressed into a slice with a diameter of 20mm and a thickness of 5mm.The electronic grade silicon powder of 50g with a purity of 9N was put into a high purity graphite crucible (F 40mm ?60mm)and the upper surface of silicon powder was smoothed.Then the boron slice was placed on the surface of silicon powder.Subsequently,the graphite crucible was put into a resistance furnace and carried out for the diffusion experiment under the protection of argon gas.After it was kept at 1873K for 180min,the sample was cooled to room temperature and removed out from furnace.Finally,the sample was lengthways cut into half and the boron concentrations of different sampling positions at a distance of every 3mm away from the B –Si interface were analyzed by the Inductively Coupled Plasma Atomic Emission Spectrometry (ICP-AES).The schematic diagram of diffusion experiment and the appearance picture of sampling are shown in Fig.3.

The raw material of re ?ning experiment for boron removal was the metallurgical grade silicon with a boron concentration of 22ppmw.The slag re ?ning agent was composed of 50%CaO –50%SiO 2.Firstly,the metallurgical grade silicon of 20g and the calcium silicate slag of 20g were loaded into a high purity graphite crucible with an inner diameter of 40mm and a height of 60mm.The slag was laid the upside of silicon.Then,the crucible was put into the heating zone of resistance furnace for re ?ning at 1823K with

different holding times of 30–180min,respectively,under the protection of argon gas.The experimental sample is shown in Fig.4.It can be seen that the Si –B interface obviously exist between molten silicon and molten https://www.360docs.net/doc/431520039.html,stly,the boron concentration in re ?ned silicon was analyzed by the Inductively Coupled Plasma Mass Spectrometry (ICP-MS).

4.Results and discussion

The B –Si interface between solid boron and molten silicon is considered as the initial position (“0”mm).The boron concen-trations with 3mm,6mm,9mm,12mm and 15mm,respectively,away from the B –Si interface as shown in Fig.3(b)are analyzed and the results were shown in Fig.5.It is found that the boron concentration of sampling point gradually reduces with the increase of diffusion distance away from the B –Si interface.A non-linear decreasing trend displays that the boron diffusion in molten silicon is an unsteady state diffusion process,which con ?rms the deduced result ahead.

According to the binary Si –B phase diagram,the maximal concentration of boron in liquid phase (on the liquidus)reaches 7.4%at 1823K.On account of the use of a solid boron powder slice in the diffusion experiment,it is consequently considered that the dissolution of boron in molten silicon has reached a saturated state at the B –Si interface and the boron concentration at the B –Si interface can be replaced by the saturated solubility.Therefore,

the

Fig.3.Schematic diagram of diffusion experiment (a)and appearance picture of sampling

(b).

Fig.4.Schematic (a)and appearance (b)diagrams of slag re ?ning using the binary CaO –SiO 2slag.

72

J.Wu et al./Fluid Phase Equilibria 404(2015)70–74

linear ?tting results for the diffusion coef ?cient of boron in molten silicon (D )at 1823K are obtained and shown in Fig.6according to ?ve sampling points by Eqs.(7)and (8).It is gotten as D =1.46?10à8m 2s à1and shown in Table 1.

Due to the large diameter/height size of crucible and the experimental factor such as convection,the result is a little lower than the value of 2.7?10à4cm 2s à1estimated by Tang et al.[15]using the Arrhenius equation but higher than the value of 1.2?10à8m 2s à1posed d by Garandet [17].The boron concentra-tion in re ?ned silicon using the binary CaO –SiO 2slag re ?ning with different time of 30–180min shown in Table 1.In the process of boron removal by slag re ?ning,the mass conservation of boron between molten silicon and molten slag can be shown in Eq.(13).

M m B w ?B 0?M m B w ?B e tM s

BO 1:5

w eBO 1:5Te (13)

The mass distribution coef ?cient (L B )of boron between slag and silicon in equilibrium is represented in Eq.(14).

L B ?

w eBO 1:5Te w ?B e

(14)

Lastly,the boron concentration can be described as Eq.(15)when it reaches equilibrium.

w ?B e ?

w ?B 0?M BO 1:5=M B

L B ?M s =M m tM BO 1:5=M B

(15)

where L B is the mass distribution coef ?cient of boron between slag and silicon in equilibrium.M s and M m are the mass of molten slag and molten silicon,respectively.M BO 1:5and M B are the molar mass of boron oxide and boron,respectively.

It is calculated that the equilibrium boron concentration in molten silicon (w ?B e )is about 2.6ppmw with a L B value of 1.8by Eq.(15).Then,the equilibrium boron concentration is substituted into Eq.(14)and the relationship between re ?ning time (t )and Y ln X is obtained and shown in Eq.(16).X and Y are represented by Eqs.(17)and (18).

Y ln X ?àb ?t

(16)

X ?

w ?B àw ?B e w ?B 0àw ?B e

(17)

Y ?

M m r m A

(18)

Lastly,the curve derived by Eq.(16)is gotten in experiment and drawn in Fig.7.Obviously,the slope of straight line is just the mass transfer coef ?cient (b )of boron in molten silicon and it is calculated to be 1.7?10à4m s à1.

It exists a difference of ?uidity between the immiscible molten silicon and molten slag at 1823K.Therefore,a boundary layer between molten silicon and molten slag is generated.It is de ?ned that the distance of intersection point between the tangent of boron concentration distribution curve at x =0and the extension line of concentration curve (c )away from silicon-slag interface is the effective boundary layer close to silicon side.The schematic diagram of boundary layer is described in Fig.8.d can be calculated by Eq.(19).

d ?

c àc ?@c =@x eTx ?0

(19)

where @c =@x eTx ?0is the concentration gradient of boron nearby the interface of molten silicon and molten slag.c *is the boron concentration at the silicon-slag interface.In the meantime,Eq.(20)can be obtained by Eqs.(9)and (11),which displays the relationship between D and b .

D ?b ?d

(20)

Finally,the effective boundary layer thickness (d )can be calculate.

As it has been found by Nishimoto et al.[18]that the

mass

Fig.5.Boron concentration of sampling point in silicon with different distance away from B –Si

interface.

Fig.6.Linear ?tting results by experimental data.

Table 1

Experimental results of diffusion coef ?cient (D )and mass transfer coef ?cient (b ).

Sampling points

x i /mm w [B]/%D ?10à8/m 2s à1

Re ?ning time/min

w [B]/ppmw b ?10à4/m s à1

1#30.75222#60.723014.83#90.68 1.46

609.5 1.7

4#120.62120 4.75#

15

0.53

180

3.7

J.Wu et al./Fluid Phase Equilibria 404(2015)70–74

73

transport in the slag phase is the rate-controlling step,and hence the boundary layer thickness is 0.086mm when this is the case.

5.Conclusions

The diffusion coef ?cient (D )of boron in molten silicon at 1823K was determined,D =1.46?10à8m 2s à1,by the diffusion experi-ment in the resistance furnace and the mass transfer coef ?cient (b )of boron was also measured and calculated b =1.7?10à4m s à1using the binary CaO –SiO 2slag re ?ning.It was calculated by the relation between diffusion coef ?cient and mass transfer coef ?cient

that the effective boundary layer thickness (d )close to molten silicon side was d =0.086mm.

Acknowledgements

The authors wish to acknowledge the ?nancial support on this research from National Natural Science Foundation of China (51104080and 51334002)and the Natural Science Foundation of Yunnan Province (2014FB124).

References

[1]W.O.Filtvedt,A.Holt,P.A.Ramachandran,M.C.Melaaen,Chemical vapor

deposition of silicon from silane:review of growth mechanisms and modeling/scaleup of ?uidized bed reactors,Solar Energy Mater.Solar Cells 107(2012)188–200.

[2]S.Richter,M.Werner,M.Schley,F.Schaaff,H.Riemann,H.J.Rost,F.Zobel,R.

Kunert,P.Dold, C.Hagendorf,Structural and chemical investigations of adapted Siemens feed rods for an optimized ?oat zone process,Energy Procedia 38(2013)604–610.

[3]H.Ni,S.Lu,C.Chen,Modeling and simulation of silicon epitaxial growth in

Siemens CVD reactor,J.Cryst.Growth 404(2014)89–99.

[4]H.A.Aulich,F.W.Schulze,Crystalline silicon feedstock for solar cell,Prog.

Photovoltaics:Res.Appl.10(2002)141–147.

[5]L.Cai,X.Ren,B.Fan,J.Zheng,C.Chen,Effect of temperature on crystalline

silicon solar cells processed from chemical and metallurgical route,Optik 125(2014)3918–3921.

[6]Y.Li,J.Wu,W.Ma,Kinetics of boron removal from metallurgical grade silicon

using a slag re ?ning technique based on CaO –SiO 2binary system,Sep.Sci.Technol.49(2014)1946–1952.

[7]J.Wu,Y.Li,W.Ma,K.Wei, B.Yang,Y.Dai,Boron removal in purifying

metallurgical grade silicon by a CaO –SiO 2slag re ?ning,Trans.Nonferrous Met.Soc.China 24(2014)1231–1236.

[8]K.Morita,T.Miki,Thermodynamics of solar-grade-silicon re ?ning,

Intermetallics 11(2003)1111–1117.

[9]L.A.V.Teixeira,K.Morita,Removal of boron from molten silicon using CaO –

SiO 2based slags,ISIJ Int.49(2009)783–787.

[10]J.Wu,M.Xu,K.Liu,W.Ma,B.Yang,Y.Dai,Removing boron from metallurgical

grade silicon by a high basic slag re ?ning technique,J.Min.Metall.B 50(2014)83–86.

[11]M.Li,T.Utigard,M.Barati,Removal of boron and phosphorus from silicon

using CaO –SiO 2–Na 2O –Al 2O 3?ux,Metall.Mater.Trans.B 45(2014)221–228.[12]M.Fang,C.Lu,L.Huang,https://www.360docs.net/doc/431520039.html,i,J.Chen,X.Yang,J.Li,W.Ma,P.Xing,X.Luo,

Multiple Slag operation on boron removal from metallurgical-grade silicon using Na 2O –SiO 2Slags,Ind.Eng.Chem.Res.53(2014)12054–12062.

[13]J.Safarian,G.Tranell,M.Tangstad,Thermodynamic and kinetic behavior of B

and Na through the contact of B-doped silicon with Na 2O –SiO 2slags,Metall.Mater.Trans.B 44(2013)571–583.

[14]J.F.White,D.Sichen,Mass transfer in slag re ?ning of silicon with mechanical

stirring:transient kinetics of Ca and B transfer,Metall.Mater.Trans.B 46(2015)135–144.

[15]K.Tang,E.J.?vrelid,G.Tranell,M.Tangstad,Critical assessment of the impurity

diffusivities in solid and liquid silicon,JOM 61(2009)49–55.

[16]H.Kodera,Diffusion coef ?cients of impurities in silicon melt,Jpn.J.Appl.Phys.

2(1963)212–219.

[17]J.P.Garandet,New determinations of diffusion coef ?cients for various dopants

in liquid silicon,Int.J.Thermophys.28(2007)1285–1305.

[18]H.Nishimoto,Y.Kang,T.Yoshikawa,K.Morita,The rate of boron removal from

molten silicon by CaO –SiO 2slag and Cl2treatment,High Temp.Mater.Processes 31(2012)471–477.

[19]E.Krystad,S.Zhang,G.Tranell,The kinetics of boron removal during slag

re ?ning in the production of solar-grade silicon,in:L.F.Zhang,J.A.Pomykala,A.Ciftja (Eds.),EPD Congress 2012(TMS),FL,USA,2012,pp.471–480.

[20]L.Zhang,Y.Tan,J.Y.Li,Y.Liu,D.K.Wang,J.Y.Li,Study of boron removal from

molten silicon by slag re ?ning under atmosphere,Mater.Sci.Semicond.Process.16(2013)1645–1649

.

Fig.7.Relationship between Y ln X and re ?ning time (t

).

Fig.8.Schematic diagram of boundary layer close to silicon side.

74

J.Wu et al./Fluid Phase Equilibria 404(2015)70–74