Control of Oxygen Impurities in a Continuous-Feeding Czochralski-Silicon Crystal Growth by the Double-Crucible Method

: The continuous-feeding Czochralski method is a cost-effective method to grow single silicon crystals. An inner crucible is used to prevent the un-melted silicon feedstock from transferring to the melt-crystal interface in this method. A series of global simulations were carried out to investigate the impact of the inner crucible on the oxygen impurity distributions at the melt-crystal interface. The results indicate that, the inner crucible plays a more important role in affecting the O concentration at the melt-crystal interface than the outer crucible. It can prevent the oxygen impurities from being transported from the outer crucible wall effectively. Meanwhile, it also introduces as a new source of oxygen impurity in the melt, likely resulting in a high oxygen concentration zone under the melt-crystal interface. We proposed to enlarge the inner crucible diameter so that the oxygen concentration at the melt-crystal interface can be controlled at low levels.


Introduction
The continuous-feeding Czochralski method (CCZ) is an effective method to produce single crystals, especially for crystalline silicon (Si) [1,2]. Compared with the standard Czochralski (CZ) method, it has many advantages. For example, since silicon melt can be replenished continuously during a CCZ crystal growth process, the melt volume can remain limited and unchanged in the crucible so that the melt flow becomes stable and the unsteady kinetics of the melt will be suppressed. In addition, continuous recharging of the melt allows for stable control of dopant [3], impurities, and resistivity distribution in a growing crystal, which helps to improve the crystal quality [4,5]. Therefore, it is a very promising technology to produce high-quality crystals at a low cost. However, the CCZ grown crystal exhibits special defects, which are considered to be related to the relatively high hydrogen content of the recharged Si granules [6]. These defects lead to serious challenges in the application of CCZ single crystals of silicon in electronic devices. Fortunately, with respect to the solar application, they are considered unlikely to have an adverse effect on solar cell performance [7]. In recent years, with a strong demand for producing n-type crystals for high-efficiency solar cells, the CCZ method has become very promising [8][9][10]. It is predicted that the CCZ method will make significant gains in the market share over conventional CZ in the next 3-5 years [11].
The growth of crystalline silicon is invariably accompanied by impurities transport, such as oxygen (O), carbon (C), and other related products, from reactions [12]. Special attention has been paid to, and, therefore, many researches [13][14][15][16][17][18][19][20][21][22] have been contributed, the control O concentration in the melt and growing crystals. In the growth process of some conventional methods, it affects the formation of micro-defects in the growing crystal in a complex manner [13]. In the CCZ process, to prevent the unmelted silicon feedstock from transferring to the melt-crystal (m-c) interface, an inner quartz crucible is usually placed on the bottom of the outer quartz crucible [23]. Since O impurities are dissolved from the quartz crucible wall, a new source of O impurity is thus introduced. Therefore, it is important to investigate the impact of the inner crucible on the O distributions in the melt, especially at the m-c interface, because O impurities will enter the crystal through the m-c interface. If the initial O concentration of n-type CCZ wafers is too high, the solar cell efficiency will be reduced [24]. Previous research indicates that the inner crucible is the main reason for this phenomenon, and the O concentration at the m-c interface will increase in the double-crucible CCZ method [25]. Providing an electromagnetic stirring of the melt is an effective way to decrease the O concentration at the m-c interface [26]. However, the complexity of the crystal growth systems and the cost will be increased by this method.
This study aims to find an effective way to reduce the O concentration by the doublecrucible CCZ method. The impact of the inner crucible was investigated by global simulations, including coupled O and C transport, which have been widely used to study the O distributions in a crystal growth process [16,20,[27][28][29][30][31][32][33]. The influence mechanism of the inner crucible on the O concentration in the melt was analyzed. Based on this research, an effective method to decrease the O distribution in the double-crucible CCZ method was proposed.

Furnace Configuration
A schematic diagram of the CCZ furnace for industrial manufacture is given in Figure 1. The diameter of the crystal was 200 mm. The crystal length was 600 mm. The inner and outer crucible diameters were 300 mm and 540 mm, respectively. To prevent the un-melted silicon feedstock from transferring to the m-c interface, an inner quartz crucible was placed on the bottom of the outer quartz crucible. The main dimensions of the CCZ furnace are listed in Table 1.
some conventional methods, it affects the formation of micro-defects in the growing crystal in a complex manner [13]. In the CCZ process, to prevent the unmelted silicon feedstock from transferring to the melt-crystal (m-c) interface, an inner quartz crucible is usually placed on the bottom of the outer quartz crucible [23]. Since O impurities are dissolved from the quartz crucible wall, a new source of O impurity is thus introduced. Therefore, it is important to investigate the impact of the inner crucible on the O distributions in the melt, especially at the m-c interface, because O impurities will enter the crystal through the m-c interface. If the initial O concentration of n-type CCZ wafers is too high, the solar cell efficiency will be reduced [24]. Previous research indicates that the inner crucible is the main reason for this phenomenon, and the O concentration at the m-c interface will increase in the double-crucible CCZ method [25]. Providing an electromagnetic stirring of the melt is an effective way to decrease the O concentration at the m-c interface [26]. However, the complexity of the crystal growth systems and the cost will be increased by this method.
This study aims to find an effective way to reduce the O concentration by the doublecrucible CCZ method. The impact of the inner crucible was investigated by global simulations, including coupled O and C transport, which have been widely used to study the O distributions in a crystal growth process [16,20,[27][28][29][30][31][32][33]. The influence mechanism of the inner crucible on the O concentration in the melt was analyzed. Based on this research, an effective method to decrease the O distribution in the double-crucible CCZ method was proposed.

Furnace Configuration
A schematic diagram of the CCZ furnace for industrial manufacture is given in Figure 1. The diameter of the crystal was 200 mm. The crystal length was 600 mm. The inner and outer crucible diameters were 300 mm and 540 mm, respectively. To prevent the un-melted silicon feedstock from transferring to the m-c interface, an inner quartz crucible was placed on the bottom of the outer quartz crucible. The main dimensions of the CCZ furnace are listed in Table 1.
In our investigation, we compared the case of the conventional CZ method with a single crucible (the single-crucible case) and the proposed CCZ method with two crucibles (the double-crucible case). For the single-crucible case, the crystal and crucible rotation rates were set as 12 rpm and −6 rpm, respectively. For the double-crucible case, the rotation rates of crystal and crucible were set as 12 rpm and −4 rpm, respectively.    In our investigation, we compared the case of the conventional CZ method with a single crucible (the single-crucible case) and the proposed CCZ method with two crucibles (the double-crucible case). For the single-crucible case, the crystal and crucible rotation rates were set as 12 rpm and −6 rpm, respectively. For the double-crucible case, the rotation rates of crystal and crucible were set as 12 rpm and −4 rpm, respectively.

Numerical Modeling
A series of global simulations were carried out in this study. An in-house software (CGeMoS) which has been developed and used in our researches [16,27,28,[34][35][36] for more than 18 years (see http://cgsolar.xjtu.edu.cn/, accessed on 29 January 2021), was applied in our investigation. A grid independence test was carried out for our simulations, and the total grid number was about 60,000. The latent heat released at the m-c interface was taken into account. A dynamic meshing technique was employed to get the m-c interface position that coincides with the isotherm of 1685 K.
For O calculation, a well-developed global model of coupled O and C transport in the whole furnace was employed to study the impurities transportation in the furnace [29,30]. For the governing equations and boundary conditions of the O and C transport model, please refer to [30]. The global model has been validated in previous researches [16,18].

Comparison of O Distributions in the Melt between Single-Crucible and Double-Crucible Cases
Since the O is dissolved from the quartz crucible wall, an extra O source is introduced when an inner crucible is placed in the outer crucible. This may lead to the increase in O concentration in the melt. However, it is the O concentration at the m-c interface that affects the O concentration in the growing crystal. Therefore, we needed to investigate the impact of the inner crucible on the O concentration at the m-c interface. For this purpose, we first carried out a series of simulations to compare the O concentration at the m-c interface between the case with a single-crucible and the case with a double-crucible.
Temperature distributions in the silicon melt using the single-crucible and doublecrucible methods are shown in Figure 2. It was found that the highest melt temperature increased by about 14 K in the double-crucible case. This is because that the thermal conductivity of the inner quartz crucible is much smaller than that of the silicon melt. The introduction of the inner crucible in the melt makes the heat transferred more difficult from the outer crucible to the m-c interface, and more oxygen is released from the crucible wall with a higher temperature.

Numerical Modeling
A series of global simulations were carried out in this study. An in-house software (CGeMoS) which has been developed and used in our researches [16,27,28,[34][35][36] for more than 18 years (see http://cgsolar.xjtu.edu.cn/, accessed on 29 January 2021), was applied in our investigation. A grid independence test was carried out for our simulations, and the total grid number was about 60,000. The latent heat released at the m-c interface was taken into account. A dynamic meshing technique was employed to get the m-c interface position that coincides with the isotherm of 1685 K.
For O calculation, a well-developed global model of coupled O and C transport in the whole furnace was employed to study the impurities transportation in the furnace [29,30]. For the governing equations and boundary conditions of the O and C transport model, please refer to [30]. The global model has been validated in previous researches [16,18].

Comparison of O Distributions in the Melt between Single-Crucible and Double-Crucible Cases
Since the O is dissolved from the quartz crucible wall, an extra O source is introduced when an inner crucible is placed in the outer crucible. This may lead to the increase in O concentration in the melt. However, it is the O concentration at the m-c interface that affects the O concentration in the growing crystal. Therefore, we needed to investigate the impact of the inner crucible on the O concentration at the m-c interface. For this purpose, we first carried out a series of simulations to compare the O concentration at the m-c interface between the case with a single-crucible and the case with a double-crucible.
Temperature distributions in the silicon melt using the single-crucible and doublecrucible methods are shown in Figure 2. It was found that the highest melt temperature increased by about 14 K in the double-crucible case. This is because that the thermal conductivity of the inner quartz crucible is much smaller than that of the silicon melt. The introduction of the inner crucible in the melt makes the heat transferred more difficult from the outer crucible to the m-c interface, and more oxygen is released from the crucible wall with a higher temperature.
To clarify if this is a general conclusion for the CCZ method with double-crucible, we compared the O distributions at the crucible walls, as shown in Figure 4, for both cases with a single crucible and with double crucibles, which act as the origins of oxygen impurities. From the results shown in Figure 4, we can see that the oxygen concentration at the outer crucible walls was higher and the oxygen concentration at the inner crucible walls was lower in the double-crucible case than that in the single crucible case. Since O impurities dissolve from both the inner and outer crucible walls, it is essential to make clear which crucible is the dominant source of oxygen impurities transported to the m-c interface.   To clarify if this is a general conclusion for the CCZ method with double-crucible, we compared the O distributions at the crucible walls, as shown in Figure 4, for both cases with a single crucible and with double crucibles, which act as the origins of oxygen impurities. From the results shown in Figure 4, we can see that the oxygen concentration at the outer Crystals 2021, 11, 264 5 of 9 crucible walls was higher and the oxygen concentration at the inner crucible walls was lower in the double-crucible case than that in the single crucible case. Since O impurities dissolve from both the inner and outer crucible walls, it is essential to make clear which crucible is the dominant source of oxygen impurities transported to the m-c interface.

Study of the O Source at the Melt-Crystal Interface with Double-Crucible Method
To make clear which crucible is the dominant source of oxygen impurities transported to the m-c interface in the double-crucible CCZ method, we investigated the impact of the inner crucible and the outer crucible, respectively, on the O concentration at the mc interface. For the sake of convenience in our numerical investigation, we introduced a concept of a virtual coating layer that is of no thickness and no oxygen dissolution. For example, when the inner crucible walls are covered with the virtual coating layer, there is no oxygen dissolved into the melt from the inner crucible. Therefore, the outer crucible becomes the unique source of oxygen impurities.
In Figure 5a, we show the O distribution in the melt for the case in which the outer crucible was covered by this virtual coating layer, which means that the inner crucible was the unique source of oxygen impurities in the melt. Compared with the results in Figure 3b, we found that the O concentration under the m-c interface only slightly decreased. Correspondingly, in Figure 5b, we show the O distribution in the melt for the case in which the inner crucible was covered by this virtual coating layer, which means that the outer crucible was the unique source of oxygen impurities in the melt. It is obviously found in this case that the O concentration under the m-c interface was remarkably reduced as compared to the results shown in Figures 3b and 5a. In Figure 6

Study of the O Source at the Melt-Crystal Interface with Double-Crucible Method
To make clear which crucible is the dominant source of oxygen impurities transported to the m-c interface in the double-crucible CCZ method, we investigated the impact of the inner crucible and the outer crucible, respectively, on the O concentration at the m-c interface. For the sake of convenience in our numerical investigation, we introduced a concept of a virtual coating layer that is of no thickness and no oxygen dissolution. For example, when the inner crucible walls are covered with the virtual coating layer, there is no oxygen dissolved into the melt from the inner crucible. Therefore, the outer crucible becomes the unique source of oxygen impurities.
In Figure 5a, we show the O distribution in the melt for the case in which the outer crucible was covered by this virtual coating layer, which means that the inner crucible was the unique source of oxygen impurities in the melt. Compared with the results in Figure 3b, we found that the O concentration under the m-c interface only slightly decreased. Correspondingly, in Figure 5b, we show the O distribution in the melt for the case in which the inner crucible was covered by this virtual coating layer, which means that the outer crucible was the unique source of oxygen impurities in the melt. It is obviously found in this case that the O concentration under the m-c interface was remarkably reduced as compared to the results shown in Figures 3b and 5a. In Figure 6, we compared the impact of the inner crucible and outer crucible on the oxygen distribution at the m-c interface. The results verified that the inner crucible can effectively prevent the O impurities dissolved from the outer crucible walls from being transported to the m-c interface, but the inner crucible itself acts as the dominant source of O impurities transported to the m-c interface. Therefore, the design of the inner crucible and control of the melt flow in the inner crucible are the key factors to reduce the O concentration at the m-c interface in the CCZ double-crucible method.
interface. The results verified that the inner crucible can effectively prevent the O impurities dissolved from the outer crucible walls from being transported to the m-c interface, but the inner crucible itself acts as the dominant source of O impurities transported to the m-c interface. Therefore, the design of the inner crucible and control of the melt flow in the inner crucible are the key factors to reduce the O concentration at the m-c interface in the CCZ double-crucible method.
(a) oxygen only from the inner crucible walls (b) oxygen only from the outer crucible walls

Approach to Decrease O Distributions at the m-c Interface by Double-Crucible Method
Based on our research, the inner crucible was the dominant source of oxygen impurities transported to the m-c interface, and the melt flow inside the inner crucible plays a key role in transporting the oxygen dissolved from the crucible walls to the m-c interface. Therefore, we proposed an approach with a larger inner crucible in the CCZ method to reduce the oxygen content in the growing crystals. We carried out numerical simulations to verify our proposed approach. interface. The results verified that the inner crucible can effectively prevent the O impurities dissolved from the outer crucible walls from being transported to the m-c interface, but the inner crucible itself acts as the dominant source of O impurities transported to the m-c interface. Therefore, the design of the inner crucible and control of the melt flow in the inner crucible are the key factors to reduce the O concentration at the m-c interface in the CCZ double-crucible method.
(a) oxygen only from the inner crucible walls (b) oxygen only from the outer crucible walls

Approach to Decrease O Distributions at the m-c Interface by Double-Crucible Method
Based on our research, the inner crucible was the dominant source of oxygen impurities transported to the m-c interface, and the melt flow inside the inner crucible plays a key role in transporting the oxygen dissolved from the crucible walls to the m-c interface. Therefore, we proposed an approach with a larger inner crucible in the CCZ method to reduce the oxygen content in the growing crystals. We carried out numerical simulations to verify our proposed approach.

Approach to Decrease O Distributions at the m-c Interface by Double-Crucible Method
Based on our research, the inner crucible was the dominant source of oxygen impurities transported to the m-c interface, and the melt flow inside the inner crucible plays a key role in transporting the oxygen dissolved from the crucible walls to the m-c interface. Therefore, we proposed an approach with a larger inner crucible in the CCZ method to reduce the oxygen content in the growing crystals. We carried out numerical simulations to verify our proposed approach.
Except for the case with an inner crucible diameter of 300 mm, as we have investigated in detail, global simulations of the thermal field and oxygen transport in the whole furnace were carried out for two cases with larger inner crucible diameters of 360 mm and 420 mm, respectively. The melt flow pattern and oxygen distributions in the melt for the two cases are shown in Figure 7. Comparing the results shown in Figures 7 and 3b, we can see that when the diameter of the inner crucible was enlarged, the melt flow patterns in the crucibles were similar. However, the O concentration in the melt between the two crucibles increased while it decreased inside the inner crucible. As a result, the O concentration at the m-c interface decreased accordingly, as shown in Figure 8, where a comparison is shown for O distributions at the m-c interface for cases with different inner crucible diameters and the case with a single crucible. The oxygen concentration at the m-c interface in the case with the inner crucible diameter of 420 mm was reduced by nearly 40% from about 20 ppma to about 12 ppma when compared to the case with the inner crucible diameter of 300 mm, and reduced by 25% from 16 ppma to about 12 ppma when compared to the case of conventional method with a single crucible. This finding is exciting to us because it is very useful to reduce the oxygen impurities in the silicon crystals grown by a CCZ method. Our proposed approach is, therefore, verified as effective.
furnace were carried out for two cases with larger inner crucible diameters of 360 mm and 420 mm, respectively. The melt flow pattern and oxygen distributions in the melt for the two cases are shown in Figure 7. Comparing the results shown in Figures 7 and 3b, we can see that when the diameter of the inner crucible was enlarged, the melt flow patterns in the crucibles were similar. However, the O concentration in the melt between the two crucibles increased while it decreased inside the inner crucible. As a result, the O concentration at the m-c interface decreased accordingly, as shown in Figure 8, where a comparison is shown for O distributions at the m-c interface for cases with different inner crucible diameters and the case with a single crucible. The oxygen concentration at the m-c interface in the case with the inner crucible diameter of 420 mm was reduced by nearly 40% from about 20 ppma to about 12 ppma when compared to the case with the inner crucible diameter of 300 mm, and reduced by 25% from 16 ppma to about 12 ppma when compared to the case of conventional method with a single crucible. This finding is exciting to us because it is very useful to reduce the oxygen impurities in the silicon crystals grown by a CCZ method. Our proposed approach is, therefore, verified as effective.

Conclusions
In this research, a series of global simulations were carried out for a double-crucible CCZ furnace. The impact of the inner crucible on the O distribution at the m-c interface was investigated. On the one hand, the inner crucible can prevent the O impurities dis-

Conclusions
In this research, a series of global simulations were carried out for a double-crucible CCZ furnace. The impact of the inner crucible on the O distribution at the m-c interface was investigated. On the one hand, the inner crucible can prevent the O impurities dissolved from the outer crucible from transporting to the m-c interface effectively. On the other hand, the inner crucible itself is the main source of O impurities transported to the m-c interface in the melt. We proposed an improved approach with a larger inner crucible diameter to reduce the O concentration at the m-c interface in a double-crucible CCZ method. The numerical investigation results verified the proposed approach as effective. The O concentration at the m-c interface can be reduced by 25% compared to the conventional CZ method with a single crucible.