Controlling solidification front shape and thermal stress in growing quasi-single-crystal silicon ingots: Process design for seeded directional solidification

Applied Thermal Engineering 91 (2015) 225e233

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research paper

Controlling solidification front shape and thermal stress in growing quasi-single-crystal silicon ingots: Process design for seeded directional solidification Lijun Liu a, *, Qinghua Yu a, Xiaofang Qi a, Wenhan Zhao a, Genxiang Zhong a, b a

Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China Donghai JA Solar Technology Co., Ltd., Lianyungang, Jiangsu 222300, China

b

h i g h l i g h t s
Different moving partition blocks are designed and compared for a seeded DS furnace.
Small-grain region in silicon ingots can be notably reduced via moving partition designs.
Lower thermal stress in silicon ingots can be achieved with moving partition designs.
The process with a down-up moving partition block is the most favorable.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 January 2015 Accepted 9 August 2015 Available online 20 August 2015

To control the solidification front shape and thermal stress in the growing silicon ingot and reduce the small-grain region at its periphery, a moving insulation partition block was designed in an industrial seeded directional solidification furnace for quasi-single-crystal silicon ingots. We propose several moving process designs of the partition block. A transient global model of heat transfer in which all types of heat transfer are included was established to investigate the thermal field, solidification front evolution, and thermal stress in the growing ingot. Corresponding experiments were conducted to validate the simulation results through the relationship between solidification front shape and the small-grain region. It was found that the moving process can significantly influence the thermal field, solidification front shape, and thermal stress in the growing ingot during the solidification process. The moving partition block design is feasible to control the solidification front shape and reduce the small-grain region at the periphery of the solidified ingot. A favorable moving process design of the partition block was obtained that can simultaneously achieve a small small-grain region and low thermal stress in the solidified ingot. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Quasi-single-crystal silicon Directional solidification Heat transfer Solidification front Thermal stress Photovoltaics

1. Introduction Directional solidification (DS) of quasi-single-crystal silicon (QSC-Si) ingots for high efficiency solar cells has emerged as a new technology in photovoltaic (PV) industries [1e4]. In this technology, the entire bottom of the crucible is paved with single crystalline silicon bricks as seed crystals, which have a minimum thickness of 10 mm and uniform crystal orientation, whereas no seed crystals are used in the conventional DS technology for producing multi-

* Corresponding author. Tel./fax: þ86 29 82663443. E-mail address: [email protected] (L. Liu). http://dx.doi.org/10.1016/j.applthermaleng.2015.08.023 1359-4311/© 2015 Elsevier Ltd. All rights reserved.

crystalline silicon (mc-Si) ingots. The seeds prevent random nucleation at the crucible bottom, and lead to subsequent crystal growth with the same crystal orientation as the seeds [1]; thus, the seeds need to be well preserved during the melting process [4e6]. This seeded DS technology is theoretically beneficial for singlecrystal growth. However, experimental results have shown that nucleation always occurs along the crucible wall, and the generated silicon grains move into the interior of the ingot, eventually forming a small-grain region at the periphery of the solidified ingot [7,8]. The small-grain region should be as small as possible to improve the average efficiency of solar cells made from wafers of the ingot. To obtain this goal, it is crucially important to control the axial

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temperature gradient and the melting front shape during the melting process of feedstock, preserve the seeds and the solidification front shape during the solidification process, prevent nucleation from the crucible sidewalls, and reduce the thermal stress in the growing ingot. To obtain a large axial temperature gradient and a favorable seed-melt interface shape during the seed preservation process, an insulation partition block (labeled 8 in Fig. 1) has been designed to control the temperature distribution in the hot zone of the seeded DS furnace [8]. The partition block is installed in the space between the heat exchange block and the heater. Li and Liu et al. [6] investigated the melting process in a seeded DS furnace for seed preservation. Their results showed that the melting process progresses from the periphery, top, and bottom to the center of the silicon region without a partition block, while it progresses from the top to the bottom of the silicon region with the partition block. Some other studies [8e11] have investigated the effect of the partition block on the solidification front shape, thermal stress, growth rate, and power consumption during the solidification process in DS furnaces. These studies showed that the design of the partition block is effective to preserve the seeds during the melting process, and it is also beneficial for increasing the growth rate and reducing power consumption. However, it is unfavorable for obtaining a flat or slightly convex solidification front shape and reducing thermal stress in the growing ingot during the solidification process. It is difficult to design a fixed partition block to maintain a favorable melting/solidification front shape through the whole process (both the melting and solidification processes). Considering that a fixed partition block can effectively maintain a favorable seed-melt interface shape during the seed preservation process [6], an appropriate design of the moving insulation partition block might be effective to maintain a favorable melting/solidification front shape through the whole process. That is, to establish a sufficiently large upward axial temperature gradient during the melting process and a flat or slightly convex solidification front during the solidification process. In our previous studies [6,8], we installed a partition block at a favorable position in the DS furnace and successfully controlled the seed-melt interface shape, and thus preserved the seeds during the melting process. In this study, based on the above idea, a few moving processes of this partition block are proposed to control the solidification front shape and thermal stress in the growing ingot during the solidification process. A transient global model of heat transfer was developed to investigate the evolution of the thermal field during

the solidification process for each moving process of the partition block. Experiments were conducted to validate the simulation results through the relationship between the solidification front shape and the small-grain region. 2. Experimental methods 2.1. Directional solidification process The configuration of the industrial seeded DS furnace for growing QSC-Si ingots is shown in Fig. 1. In the industrial production process, the dimensions of the square crucible were 84  84  42 cm3 with a silicon feedstock capacity of approximately 430 kg. Twenty-five pieces of single crystals with a cross section of 156  156 mm2 and a thickness of about 10 mm were used as crystal seeds. Thermocouple 1 (TC1) was installed near the outer wall of the graphite resistance heater to monitor the temperature, which was used to control the heater power during the whole process. The bottom insulation (labeled 6 in Fig. 1) gradually moved down when the solidification process began. The evolution of the temperature of TC1 and the moving velocity of the bottom insulation were prescribed and kept the same for all of the designed DS processes. The histories of the TC1 temperature and bottom insulation position are shown in Fig. 2(a). 2.2. Moving processes of the partition block To preserve the seed crystal, the initial position of the partition block (labeled 8 in all designed moving processes) was kept the same, as shown in Fig. 1. This position is referred to as 0 mm. Fig. 2(b) shows the four moving processes of the partition block: stationary, slow-down, fast-down, and down-up processes. Fig. 2(c) shows the position of the insulation partition block versus solidification time. In the case of stationary process, the position of the partition block was fixed in space all the time as that it is in the feedstock melting process [6]. In the slow-down process, the partition block was moved downwards along with the bottom insulation at a slow rate. In the fast-down process, the partition block was moved downwards at a fast rate. When it moved downwards by 80 mm, the partition block was keep stationary for both the slow-down and fast-down processes. In the down-up process, the partition block was moved downwards by 80 mm at the same rate as that in the fast-down process, and then moved upwards by 120 mm at a slow rate. The movement of the partition block does not cause disturbances on the melt since the partition block does not contact with the crucible and the fastest moving speed is as small as 8.0 cm per hour. Experiments were conducted in the industrial DS furnace (Fig. 1) for the stationary, slow-down, and down-up processes after linking the partition block to the transmission mechanism. The grown silicon ingots were cut into bricks with a square cross-section by wire sawing. The grain morphology of the brick side was highlighted by an infrared detector (IRB-30, Semilab). 3. Numerical models

Fig. 1. Configuration and computational grids of the seed-assisted industrial DS furnace.

The DS process under consideration in this research for growing quasi-single-crystal silicon ingots indeed is in 3D. However, the thermal field in the silicon domain, the solidification front shape and the quality of the finally grown ingot are dominated by the radial interaction between the silicon melt/crystal and the quartz crucible through the crucible inner wall rather than its asymmetry in the circumferential direction because of the huge difference in thermal properties of the silicon material and quartz crucible as well as the possibility of nucleation on the crucible inner wall

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Fig. 2. Four process designs of solidification: (a) TC1 temperature and bottom insulation position versus time. (b) Schematic diagram of the moving partition block in the different designs. (c) Position of the partition block versus time.

during solidification. As a result, the main differences in the thermal field of silicon domain and the finally grown ingot are between the central sub-region of silicon domain and the sub-region close to the crucible inner wall. The differences in the circumferential direction is minor. Therefore, to save computational resources, twodimensional models are widely used to study the characteristics of heat and mass transfer in the DS system instead of threedimensional models. In the two-dimensional models, the square crucible was equivalently simplified to a cylindrical shape under the condition that the thermal resistance remained unchanged in the DS system. This simplification is widely used in the literature [9e11] and has been validated by experiments [8]. To describe the DS process accurately, transient global models of heat transfer

including melt convection, gas flow, thermal conduction, thermal radiation and phase change were established. The main assumptions of the model are as follows: (1) the silicon melt flow is incompressible and the Boussinesq assumption is applied; (2) the low Mach approximation and the ideal gas law are applied to the argon gas; (3) all radiative surfaces are diffuse-gray. An enthalpy method based on fixed grids was used to model the evolution of the solidification front surface during the DS process [12,13]. The governing equations for the silicon domain are expressed in the following forms: .

V$ u ¼ 0;

(1)

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. i h  . vu . . .T þ r u $V u ¼ Vp þ V m V u þ V u r vt .  . . Cp þ S m ;  r g b h  href

r

rCp (2)

  vh l . þ r u $Vh ¼ V$ Vh þ Sh ; vt Cp

(3)

.

where u is the fluid velocity, r is the density, p is the pressure, m is .

the dynamic viscosity, g is the gravity acceleration, b is the thermal expansion coefficient of fluid, h is the sensible enthalpy, href is the reference sensible enthalpy, Cp is the heat capacity and l is the heat conductivity. Instead of tracking the solidification front surface explicitly, a concept of liquid fraction gl in each volume cell is introduced in this fixed-grid technique. For pure silicon with a fixed melting point, the relationship between the liquid fraction and temperature is described as

 gl ¼

1; 0;

T  Tm ; T < Tm

(4)

where T is the temperature and Tm is the melting point of silicon. .

.

.

The source term S m in Eq. (2) is defined as S m ¼ A u , where A increases from zero to a large value as the liquid fraction gl of a grid cell decreases from 1 at full liquid state to 0 at full solid state. In the liquid (silicon melt) region, it takes a zero value and the momentum equation is in terms of the actual fluid velocities. In the solid (silicon crystal) region, the source term dominates all other terms in the momentum equation and the predicted superficial velocity of the .

cell approaches to zero. In this way, the source term S m in Eq. (2) is used to drop the velocity to zero when the melt has fully solidified in a grid cell during the DS process. The source term Sh in Eq. (3) represents the change rate of volumetric latent heat during the DS process, which can be written as

Sh ¼ r

vðDHÞ ; vt

(5)

where DH is the latent heat content for solidification. The latent heat content can be defined as DH ¼ glL, where L is the latent heat of solidification. The governing equations for the argon gas flow are expressed as

 . vr þ V$ r u ¼ 0; vt  . v ru vt

(6)

   ..   2 . . þV$ r u u ¼VpþV  mV$ u þV$ 2mS_ þðrr0 Þ g ; 3 (7)

    v rCp T . þ V$ rCp u T ¼ V$ðlVTÞ; vt

(8)

vT _ ¼ V$ðlVTÞ þ q; vt

(10)

where q_ is the heat generation rate per unit volume, which equals zero for all solid components except the heater. In view of the strong nonlinear interactions among the melt convection, the gas flow and all solid components in the furnace, all domains in the furnace were fully coupled in the calculation. Temperature continuity and heat flux conservation were maintained at all interior boundaries between any two different domains. No-slip and non-penetration conditions for both the gas and the melt were applied for all walls in the gas and the melt domains. Along the meltegas interface, the normal velocity components were set to zero. The tangential velocity components and the shear stresses were equal on both sides of the meltegas interface. The temperature of the chamber outer wall was 300 K. The argon flow rate was 30 L/min. The furnace pressure was 0.6 bar. The initial thermal field must ensure that the crystal seeds have a minimum thickness of 10 mm. The time step for the transient calculations was 10 s. The algorithms for the global modeling of heat transfer in a DS furnace have been published elsewhere [14,15]. The global model was validated by experiments in our previous study [8]. To improve computational efficiency, a structured/unstructured mixed mesh scheme was used. As shown in Fig. 1, all of the domains in the entire furnace were subdivided into block regions. Each region was discretized by structured or unstructured grids. The structured grid was applied to the block regions with regular geometrical boundaries, while the unstructured grid was employed for the gas flow region where the geometrical boundaries were highly irregular. The grids in the melt and gas regions near the solid walls were refined. The displacement-based thermo-elastic stress model was adopted to analyze the thermal stress distribution in the growing silicon ingot [16]. The resulting thermal field in the growing silicon ingot was used as an input to calculate the thermal stress at discrete time steps. The Von Mises stress was used to represent the thermal stress components. 4. Results and analysis 4.1. Evolution of the thermal field in the hot zone Fig. 3 shows the thermal fields in the hot zone for the four moving processes 70 min and 10 h after the start of the solidification process. The partition block separates the heating and cooling zones in space. The moving processes have a slight effect on the global temperature distribution. However, the heat flux directions at the gap between the crucible wall and the partition block are quite different for the four processes. This indicates that the direction of the heat flux (marked with arrows) is significantly different because of the process design of the moving partition block. This can be easily explained by the fact that the timedependent position of the partition block results in a timedependent thermal radiating pathway near the partition block. It is evident that different moving processes can result in different solidification front shape and thermal field evolution. 4.2. Solidification front shape and evolution

p r¼ 0; RT

(9)

where S_ is the strain tensor, r0 is the reference density, p0 is the reference pressure and R is the specific gas constant. The heat transfer in the solid components is governed by

The solidification front can be represented by the isothermal of the melting point (1685 K). The height at the center of the solidification front represents the height of the solidification front. In Fig. 4(a) and (b), we compare the shape of the solidification front among the four processes when the front height is 10 and 20 cm,

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Fig. 3. Temporal thermal fields in the hot zone for the four moving processes of the partition block: (a) stationary, (b) slow-down, (c) fast-down, and (d) down-up. The right side of each figure is the crucible centerline.

respectively. When the front height is 10 cm, the solidification front in the stationary process is concave to the melt side while the fronts in the other processes are all convex to the melt side. Among these fronts, the front in the fast-down process is most convex and the front in the down-up process is least convex. When the front height is 20 cm, the fronts in the four processes are all convex to the melt side. The front in the stationary process changes from concave to convex, and the fronts in the other three processes become more convex when the front height changes from 10 to 20 cm. The heat flux is in the opposite direction to the temperature gradient, and the temperature gradient is perpendicular to the isothermals. Therefore, the heat flux is perpendicular to the solidification front and the front shape is determined by the direction of heat flux at the solidification front. The axial heat flux, or axial temperature gradient, at the front is similar for the four processes. Thus, the direction of heat flux at the solidification front is mainly determined by the lateral heat flux. For example, the lateral heat flux when the solidification front height is 10 cm was checked to analyze its influence on the solidification front shape. Fig. 5(a) shows the lateral heat flux profiles along the inner sidewall of the crucible when the solidification front height is 10 cm. A negative value of the heat flux is defined as outgoing heat flux through the sidewall from the silicon region. The heat flux near the solidification front is only outgoing from the silicon region in the stationary process. Therefore, the direction of the heat flux at the solidification front tilts toward the outside, resulting in a concave solidification front shape (see Fig. 4). Similarly, in the other three processes, because of the ingoing heat flux near the solidification front through the sidewall into the silicon region, the direction of the heat flux at the solidification front tilts toward the inside, resulting

in a convex solidification front shape (see Fig. 4). Because of the near-zero heat flux near the solidification front, it is nearly flat when the front height is 10 cm in the down-up process (see Fig. 4). It should be noted the heat flux has an extreme value at the solidification front, which is caused by the release of the solidification latent heat. The release of the latent heat increases the outgoing heat flux in the stationary process and reduces the ingoing heat flux in the other processes through the sidewall of the crucible. The heat flux through the crucible sidewall is partly determined by the heat flux through the susceptor sidewall. Fig. 5(b) shows the lateral heat flux profiles along the outer sidewall of the susceptor when the solidification front height is 10 cm. The positions of the partition block in the stationary, slow-down, fast-down, and downup processes are 0, 7.7, 8, and 2.8 cm, respectively. A negative value of the heat flux is defined as outgoing heat flux through the sidewall of the susceptor. For the stationary process, the heat flux is ingoing through the upper susceptor sidewall and outgoing through the lower susceptor sidewall. This is because when the partition block is at a higher position it partially obstructs heat radiation from the heaters to the lower susceptor sidewall and creates a passage for heat radiation from the lower susceptor sidewall to the cooling zone. For the slow-down and fast-down processes, the partition block is located at the lowest position when the front height is 10 cm. The conditions for heat radiation near the lower susceptor sidewall completely change. Thus, the heat flux is ingoing through the whole susceptor sidewall and gradually increasing from top to bottom along the sidewall in the two processes. For the down-up process, the partition block is located between those in the stationary and fast-down processes when the front height is 10 cm. Thus, the heat flux profile is

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25

Stationary Slow-down Fast-down Down-up

11

10

9

8 50

40

30

20

10

0

10

20

30

40

Stationary Slow-down Fast-down Down-up

20

Height (cm)

Front position (cm)

12

15

10

The front position

50

Radius (cm)

5

(a) 0 -14 -12 -10 -8

Stationary Slow-down Fast-down Down-up

21

-6

-4

-2

0

2

4

Stationary Slow-down Fast-down Down-up

20

30

20

10

0

10

20

30

40

10 12

25

19

40

8

(a)

20

18 50

6

2

Heat flux (kW/m )

50

Radius (cm)

(b) Fig. 4. Solidification front shape with a solidification front height of (a) 10 and (b) 20 cm.

between those of the two processes. The results show that the change of the solidification front shape was because of the significant change of the heat flux along the susceptor sidewall with the movement of the partition block. During the DS process, the solidification front shape continuously changes and its evolution is different for the four moving processes. To characterize the evolution, we define deflection of the solidification front as the difference in the position of the solidification front at the center and the crucible wall. A negative value of deflection indicates that the solidification front is concave, and vice versa. Fig. 6 shows the deflection versus the height of the solidification front for the four processes. It indicates that the solidification fronts in the four processes gradually change from concave to convex. However, the transition heights are quite different. The transition heights in the stationary, slow-down, fast-down, and down-up processes are 11.9, 2.5, 1.3 and 1.3 cm, respectively. Because the moving down rate of the partition block in the latter two processes is higher than that in the slow-down process, the direction of heat flux through the susceptor sidewall reverses more quickly. Therefore, the solidification front shape in the latter two processes reverses more quickly from concave to convex. For seeds with a height of 1.2 cm and an ingot with a height of 25 cm, the solidified fractions with a concave front in the four cases are 42.8%, 5.2%, 0.4% and 0.4%, respectively. These results indicate that it is favorable to lower the partition block to a lower position as quickly as possible at the start of solidification process in a seeded DS process to prevent nucleation of small grains from the crucible walls during crystal growth. In this way, the small-grain region in the final solidified ingots can be reduced. It should be noted that the deflection of the solidification front is larger in the slow-down and fast-down processes than in the stationary process. This is unfavorable for reduction of thermal stress

Height (cm)

Front position (cm)

22

15

Block position: h= 0.0 cm

10 h= -2.8 cm 5

h= -8.0 cm h= -7.7 cm

0 -20

-10

0

10

20

30

40

50

2

Heat flux (kW/m )

(b) Fig. 5. Heat flux profiles along the (a) inner sidewall of crucible and (b) outer sidewall of the susceptor when the solidification front height is 10 cm.

and homogeneity of impurities in the lateral direction in the growing ingot. Therefore, the down-up process design is proposed based on the fast-down design to reduce the deflection of the solidification front during the solidification process. As shown in Fig. 6, the down-up process design has the smallest solidified friction with a concave solidification front shape and the least deflection of the solidification front during the whole solidification process. 4.3. Thermal stress in the solidified silicon ingot Dislocation generation and multiplication are closely related to thermal stress in the solidified silicon ingot. Figs. 7 and 8 show the transient temperature field and thermal stress distribution in the solidified silicon ingots at the halfway stage and the end of the solidification process for the four moving processes of the partition block. The thermal stress distribution depends on the temperature field. At the halfway stage (Fig. 7), the axial temperature gradients in the four processes are similar while the radial temperature gradients in the slow-down and fast-down processes are higher than those in the stationary and down-up processes, as evidenced by the curvature of the isotherms in the ingots. This results in lower thermal stress in the stationary and down-up processes. In the two

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25

Height (cm)

20

15

H=11.9 cm

10

H=2.5 cm Seed: H=1.2 cm

5

0

-5

0

H=1.3 cm

5

Stationary Slow-down Fast-down Down-up

10

15

Deflection (mm) Fig. 6. Deflection versus height of the solidification front.

processes, the thermal stresses are highest at the bottom center of the ingots, and the highest values are about 5.0 and 4.5 MPa for stationary and down-up processes, respectively. In the other two processes, the thermal stresses are highest at the bottom center and the lower periphery of the ingots, and the highest values are roughly 8.0 MPa. As the melt continues to solidify (see Fig. 8), the slow-down and fast-down processes maintain higher radial temperature gradients than the stationary and down-up processes, in which lower stresses are maintained. At the end of the solidification process (Fig. 8), the highest thermal stresses in the four

231

processes all occur at the periphery of the ingots. The highest values in the slow-down and fast-down processes are about 20.0 MPa and located at a height of about 4 cm. The highest value in the stationary process is about 15.0 MPa and located at a height of about 10 cm. The highest value in the down-up process is about 11.0 MPa and located at a height of about 16 cm. Thus, it can be inferred that the highest thermal stress decreases and its position rises when the position of the partition block rises at the end of the solidification process. Note that, while the thermal stress distributions in the stationary and down-up processes are similar at the halfway stage (see Fig. 7), the thermal stress distributions in the two processes are quite different at the end (see Fig. 8). This indicates that the thermal stress and its distribution depend not only on the position of the partition block but also on the moving process. The down-up process exhibits the lowest thermal stress level in the solidified silicon ingot among the four process designs. 4.4. Experimental comparison of small-grain region in solidified silicon ingots Based on the simulation results of the seeded DS process, corresponding experiments for the stationary, slow-down, down-up processes were conducted to grow three QSC-Si ingots with a weight of 430 kg. Each 84  84  25 cm3 square ingot was cut into 25 bricks, and the numbering of these 25 bricks is shown in Fig. 9(a). Because of the concave solidification front shape, grains with various crystal orientations inevitably form from the crucible sidewall and continuously grow towards the center and the top of the ingot. A small-grain region consequently forms at the peripheral region of the ingot. Therefore, considering the geometric symmetry of the ingot, only the corner (A1) and central (B3) bricks

Fig. 7. Temperature (left, interval of 10 K) and thermal stress (right, interval of 0.5 MPa) distributions in the growing silicon ingots at the halfway stage of the solidification process for the four moving processes of the partition block: (a) stationary, (b) slow-down, (c) fast-down, and (d) down-up.

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Fig. 8. Temperature (left, interval of 10 K) and thermal stress (right, interval of 1.0 MPa) distributions in the growing silicon ingots at the end of the solidification process for the four moving processes of the partition block: (a) stationary, (b) slow-down, (c) fast-down, and (d) down-up.

in contacted with the crucible sidewall are compared in Fig. 9(b)e(d) for the three processes. The grain images of the bricks were obtained with the infrared scanning technique. The right side of each brick is the side in contact with the crucible sidewall. The bright region with a diverging shape is the small-grain region, which usually gradually increases from bottom to top. It is obvious that the small-grain region is much larger in the stationary process (Fig. 9(b)) than that in the slow-down process (Fig. 9(c)), and it is the smallest in the down-up process (Fig. 9(d)). Therefore, the small-grain region in a QSC-Si ingot can be significantly reduced with an appropriate process design of the moving insulation partition block. The experimental results are consistent with the analysis based on numerical simulations. These results clearly demonstrate that the design of a moving partition block is a feasible solution for the reduction of the small-grain region in a solidified QSC-Si ingot by effective control of the solidification front shape and thermal stress in the growing ingot during the solidification process.

5. Conclusions In this study, a technique was proposed to control the solidification front shape and thermal stress in a growing QSC-Si ingot during the solidification process through an appropriate process design of a moving insulation partition block between the crucible and insulation walls. Different moving process designs of the insulation partition block were proposed and compared. Numerical simulations and corresponding experiments were carried out to investigate their effects on the solidification front shape and the thermal stress in the growing ingot during the solidification process and the small-grain region formed in the final solidified QSC-Si ingot. The following conclusions were drawn: (1) Compared with the stationary process, the slow-down and fast-down processes reduce the solidified fraction with a concave solidification front roughly from 42.8% to 5.2% and 0.4%, respectively. However, they also increase the solidification front deflection and thermal stress in the growing ingot. (2) Compared with the stationary process, the

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Fig. 9. Comparison of the QSC-Si ingots obtained from different process designs: (a) numbering of the bricks of a QSC-Si ingot, (b) bricks of the stationary process, (c) bricks of the slow-down process, and (d) bricks of the down-up process.

down-up process reduces the solidified fraction with a concave solidification front roughly from 42.8% to 0.4%, and reduces the solidification front deflection and thermal stress as well. (3) The experimental results agree well with the analyses based on numerical simulations. Therefore, the moving partition block can effectively control the solidification front shape during the solidification process and notably reduce the small-grain region formed in the QSC-Si ingots. In the proposed processes, the process with a down-up moving partition block simultaneously achieved the smallest small-grain region and the lowest thermal stress in the QSC-Si ingot. Acknowledgements

[5]

[6]

[7]

[8]

[9]

This work was supported by the National Natural Science Foundation of China (No. 51176148) and Fundamental Research Funds for the Central Universities of China (No. 2010jdgz08).

[10]

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