Influence of thermal conductivity and emissivity of heat shield surface material on the thermal field of Czochralski silicon crystal growth

doi:10.21203/rs.3.rs-3936974/v1

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Influence of thermal conductivity and emissivity of heat shield surface material on the thermal field of Czochralski silicon crystal growth

https://doi.org/10.21203/rs.3.rs-3936974/v1

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published 08 Jun, 2024

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Silicon crystal for solar cells are mainly produced by the Czochralski (CZ) method, in which the quality and production cost of silicon crystal are mainly affected by the thermal field of the crystal growth furnace. While the thermal field is significantly influenced by the heat shield material, in this study, the effect of thermal conductivity and emissivity of the heat shield material on the global thermal field was investigated by numerical simulation in Ansys Fluent software. The heat shield surface is divided into two parts, the high-temperature side part (close to the crucible and melt) and the low-temperature side part (close to the crystal), which are named as Hot-Side-Material and Cold-Side-Material, respectively. The results show that the same material can be chosen for both parts and the smaller the thermal conductivity and the emissivity of the material, the better the thermal field. As the thermal conductivity and emissivity of the heat shield surface material decrease, the melt-crystal (m-c) interface deflection decreases; the maximum thermal stress of the crystal and the required heater power are also reduced, while the crystal axial temperature gradient increases. Therefore, it is recommended to select material with low emissivity and low thermal conductivity as heat shield surface material.

Thermal conductivity

Emissivity

Heat shield

Thermal field

Numerical Simulation

Czochralski silicon

Nowadays, the Czochralski (CZ) method is the mainstream technology method for the production of silicon wafer material for solar cells [1]. To date, the main issues and challenges in this area have been to reduce production costs and improve crystal quality [2, 3].

Optimizing the structure of the thermal field, and increasing the crystal size have been carried out by many scholars to reduce the cost and improve the quality of the crystal. Liu et al. reduced the production cost and improved the crystal quality by optimizing the structure of the crystal growth furnace [4–8]. However, research in this area has been bottlenecked in terms of optimizing the crystal growth furnace and introducing water cooling due to the complexity of the crystal growth furnace structure and the small space available. Increasing the diameter of pulling crystal can significantly reduce the cost of producing [9, 10]. But the crystal diameter increase results in turbulent flow in the melt characterized by fluctuation in velocity and temperature [11], which affects the growth of large-diameter crystal. The continuous Czochralski (CCZ) method is also an important method for cost reduction, but in the presence of an inner crucible, the oxygen content in both the melt and the crystal increases, which affects the crystal quality, such as point defects, streaks, and photodegradation in solar cells [12–14]. A final way to improve crystal quality and optimize the thermal field is to introduce suitable new material into the crystal growth furnace.

As one of the most important structures in a crystal growth furnace, the main function of the heat shield is to isolate the crystal from the high-temperature melt zone to prevent the thermal conduction and the thermal radiation from the crucible and melt to the crystal, thus providing a relatively low ambient temperature favorable for crystal growth. The presence of the heat shield increases the flow of argon through the melt-crystal (m-c) interface, thus reducing the oxygen impurity content in the melt [15]. Because the thermal conduction and thermal radiation are determined by the thermal conductivity and the emissivity of the materials covered on the shield surface, we investigated the effect of these physical property parameters on the thermal field.

We divided the surface material of the heat shield into two parts, the first being the high-temperature side part near the melt and crucible, and the second part being the low-temperature side near the crystal. For the later description, we define them as the Hot-Side-Material and the Cold-Side-Material, respectively, as shown in Fig. 1 (left). We found that the specific heat and density of the material on the surface of the heat shield have almost no effect on the thermal field, which is consistent with our previous findings [16]. Therefore, we focus on the influence of the thermal conductivity and the emissivity of the Cold-Side-Material and the Hot-Side-Material of the heat shield on the thermal field. And we characterize the advantages and disadvantages of the thermal field of crystal growth by the relevant characterization parameters, such as the shape of the m-c interface, the heater power, and the thermal stress inside the crystal. This study provides theoretical guidance for the selection of surface material for future monocrystalline silicon growth furnace heat shield.

A 300 mm crystal growth furnace structure is selected for this work [17]. Figure. 1 shows the basic structure of the two-dimensional (2D) crystal growth furnace (left) A quasi-steady-state 2D rotational axisymmetric model of the 300 mm crystal growth furnace was established using the ANSYS Fluent software to simulate the global heat transfer of the whole crystal growth furnace in terms of thermal radiation, convection, and conduction. And the Von Mises thermal stress inside the crystal were also solved using the Comsol software. The results of the study are validated by the mesh-independent solution method. The initial and boundary conditions, discretization method, and physical property parameters of the material can be found in our previous report [16].

The heat shield surface material is divided into two parts: Cold-Side-Material (blue color) and the Hot-Side-Material (red color), as shown in Fig. 1 (left). As shown in Table 1, the physical property parameters are divided as Cold-Side-Material A-I and Hot-Side-Material A-I. A-E refer to five groups of materials with different emissivity (0.1, 0.3, 0.5, 0.7, 0.9), and E-I refer to those with different thermal conductivity (10, 20, 30, 40, 50 W/m·K). And the specific heat and density are set at 1600 J/kg·K and 1000 \(\text{k}\text{g}/{\text{c}\text{m}}^{3}\), respectively. Figure. 1 (right) and Fig. 2 is the global temperature field and the Von Mises equivalent thermal stress in the crystal of Hot-Side-Material E, respectively. The other material physical property parameters of the crystal growth furnace are the same as those in [16]. The physical property parameters of the two parts of the material were investigated using the control variable method, where the thermal conductivity and the emissivity of the Cold-Side-Material analyzed for their effect on the thermal field, defaulting to the physical property parameters of the graphite material being utilized for the Hot-Side-Material and vice versa.

Since changes in the physical property parameters of the material affect the temperature gradients of the crystal and the melt at the same time, it is necessary to compare the temperature gradients of the crystal and the melt to perform subsequent analyses. According to the calculation results, the minimum axis temperature gradient of crystal difference of the crystal is 0.84 K/m and the maximum axis temperature gradient of melt difference of the melt is 0.05 K/m. Therefore, the predominance of crystal temperature gradient changes is considered reasonable, which will be utilized in the subsequent discussion of the results.

3.1 Influence of the thermal conductivity of the Cold-Side-Material and ot-Side-Material on the thermal field

The thermal conductivity are 10, 20, 30, 40, and 50 W/m·K for the Cold-Side-Material and Hot-Side-Material with emissivity, specific heat, and density of 0.1, 1600 J/kg·K, and 1000 \(\text{k}\text{g}/{\text{m}}^{3}\), respectively, as shown in Table 1 numbered as E-I.

In this case, the effect of the thermal conductivity of the two parts of the material on the thermal field is investigated. Figure. 3(a) and (b) show the relationship between the thermal conductivity of the two parts of the material and the deflection, respectively. As the thermal conductivity of Cold-Side-Material and Hot-Side-Material decreases, the m-c interface deflection also decreases and the maximum thermal stress on the side wall of the crystal decreases as well as shown in Fig. 3(c). In addition, from Fig. 3(d) and (e), we find that with the decrease of thermal conductivity, the heater power required to maintain the triple point temperature also decreases, and the axial temperature gradient inside the crystal increases conversely.

During the pulling of the crystal, the latent heat of crystallization is released at the m-c interface, and the heat flux at the m-c interface satisfies Eq. (1) [16, 18]

\(\begin{array}{c} \rho \varDelta H{V}_{pull}+{\left(\lambda \frac{\partial T}{\partial n}\right)}_{melt}={\left(\lambda \frac{\partial T}{\partial n}\right)}_{crystal } \left(1\right)\end{array}\)

where \(\rho\) is the density of the crystal at the melting point, \(\varDelta H\) is the latent heat of crystallization of the crystal, which was set to 1.8e6 J/kg, \({V}_{pull}\) is the pulling rate of the crystal, which was set to 1.0 mm/min, \(\lambda\) is the thermal conductivity, and \(\frac{\partial T}{\partial n}\) is the vector component of the temperature gradient in the pulling direction [19].

From the above equation, it can be seen that if the thermal conductivity in the melt is approximately constant, the pulling velocity of the crystal can be increased by increasing the axial temperature gradient of the crystal in the pulling direction, while the crystal pulling speed increase with the decrease of thermal conductivity of both sides, as shown in Fig. 3 (d) and (e). So it is clear that the crystal pulling speed can increase by decreasing the thermal conductivity of the Cold-Side-Material and Hot-Side-Material. The heat-retaining capacity and heat insulation performance of the heat shield increase significantly as the thermal conductivity of the two parts of the heat shield surface decreases. The former makes the heat dissipation in the high-temperature region at the melt weaker, resulting in lower heater power. The latter makes the environment temperature near the top of the crystal cooler, which increases the heat dissipation capacity of the crystal, thus the m-c interface deflection decreases. The temperature at the m-c interface remains near the melting point and is essentially unchanged, thus increasing the temperature gradient in the axial direction of the crystal. The decrease in the m-c interface deflection leads to a decrease in the thermal stress inside the crystal, resulting in a higher crystal quality.

Therefore, the smaller the thermal conductivity of the heat shield surface material is, the more favorable the crystal quality will be, and the lower power consumption in the process of pulling the crystal as well.

3.2 Influence of the emissivity of ot-Side-Material on the thermal field

We divided the ot-Side-Material into five groups according to the emissivity, as shown in Table 1 as ot-Side-Material A-E.

On the surface of ot-Side-Material, the main heat flux calculated by using the ANSYS Fluent software is shown in Fig. 4 and Table 2. The incoming heat on the wall is Q1, which is mainly the net radiation from the melt and crucible to this wall, as shown in Table 2. The heat dissipation channel in this wall is the heat conduction Q2 inside the heat shield; The heat conduction and heat convection exchange with the argon gas on the wall of the Hot-Side-Material is Q3. Q3 is very small compared to the other types heat flux values according to the results shown in the Table 2, which can be negligible. From Table 2, it can be noticed that the temperature T1 of the Hot-Side-Material wall decreases as the emissivity decreases, which is mainly due to the reduction of the thermal radiation Q1 absorbed through this wall. The heat Q2 transferred to the top of the crystal decreases accordingly, making the ambient temperature in the region around the crystal lower, which is more favorable for the heat dissipation and growth of the crystal. When the heat dissipation capacity of the crystal increases, the deflection of the m-c interface decreases and the maximum thermal stress inside the crystal decreases as well. This conclusion are conformed by the calculated results shown in Fig. 5 (a) and (b).

Figure. 5 (c) shows the crystal axial temperature gradient of Hot-Side-Material as a function of the emissivity of the Hot-Side-Material. As the emissivity decreases, the crystal axial temperature gradient increases, because the m-c interface temperature remains essentially constant at the melting point, and the temperature above the crystal decreases with the emissivity of the Hot-side-material. Figure. 5 (c) also shows the heater power versus the emissivity, and it is clear that the heater power decrease with the thermal conductivity. Due to the model being based on the quasi-steady state assumption [18], all wall temperatures no longer change. It is assumed that all radiation wall of the model is diffuse gray wall, so it satisfies Kirchhoff's law, i.e., the surface emissivity is equal to the absorptivity. For the opaque surface, absorption plus reflectance is equal to 1, i.e., low emissivity means high reflectance. Therefore, the total heat radiation from the high-temperature melt and crucible to the wall surface due to its high reflectivity makes most of the energy reflected back, i.e., the proportion of the heat radiation absorbed by the wall surface is reduced, so the heat shield has a better insulation performance, and the same conclusion can be drawn from the net radiation heat in Table 2. Therefore, when the emissivity decreases, the reflectivity of the material increases when the insulation performance of the heat shield increases, so the heater power required is lower.

Hence, when selecting material for the Hot-Side-Material, low emissivity material has a significant optimizing effect on the heat field, which not only improves the crystal quality but also reduces the energy consumption.

3.3 Influence of the emissivity of Cold-Side-Material on the thermal field

We divided the emissivity of the Cold-Side-Material into five groups from A-E as shown in Table 1. On the wall of Cold-Side-Material, the main heat flux is shown in Fig. 6. The heat source and the heat dissipation from the wall are divided into four parts. The first part is heat conduction inside the heat shield Q1. The second part is heat radiation from the crystal to the heat shield Q2. The third part is the heat loss by radiation from the heat shield to the surrounding area Q3. The last part is the conduction of argon gas to the wall Q4. We have calculated Q2 by conservation of energy due to the difficulty of calculating the heat radiation through the crystal to the surface, other different forms of heat flux was calculated using the ANSYS Fluent software. The results are shown in Table 3.

It is easy to find that as the emissivity of the heat shield surface decreases, the net radiation heat Q2 from the crystal to the heat shield increases. Therefore, the average temperature of the wall of Cold-Side-Material, T1, increases and the average temperature of the crystal wall T2 decrease as shown in Table 3. Q5 is the heat dissipated by radiation from the crystal to the surroundings, which increases when the emissivity of Cold-Side-Material decreases. The lower the average temperature of the crystal wall, the more favorable for crystal growth. This can be illustrated in Fig. 7(a) and (b), the m-c interface deflection decreases with decreasing emissivity of the Cold-Side-Material and the thermal stress also satisfies this trend. Similarly, the crystal axial temperature gradient increases as shown in Fig. 7(c).

When the emissivity of Cold-Side-Material decreases, the ability of the material to heat dissipation by radiation to the surrounding area decreases, so the insulation performance of the material is excellent. Conversely, when the emissivity increases, the ability of the material to heat dissipation by radiate increases, which means that the heat transfer Q1 required to satisfy the thermal equilibrium in Cold-Side-Material is also increased. High emissivity implies a high heat loss, the increase in emissivity of Cold-Side-Material instead of weakening the insulation performance of the heat shield, which also can be found in Q1, in Table 3. This also proves the results in Fig. 7(c) why the heater power reduces with the decrease of the emissivity of the material.

Consequently, the smaller the emissivity of the Cold-Side-Material, the higher the quality of the crystal and the lower the heater power required.

In this study, we divide the surface material of the heat shield into two parts, the Cold-Side-Material, and the Hot-Side-Material, and investigate the effects of the physical property parameters such as thermal conductivity and emissivity of these two parts on the global thermal field during crystal growth. It is shown that the material in both parts can be the same material and the thermal conductivity and emissivity of the material can significantly affect the shape of the m-c interface. And the maximum thermal stress increases with the increase of the interface deflection. The axial temperature gradient inside the crystal increases with the decrease of thermal conductivity and emissivity, meanwhile, the temperature distribution in the melt does not change significantly and the heater power decreases with the decrease of thermal conductivity and emissivity.

Therefore, when choosing the surface material of the heat shield, it is necessary to choose one with low thermal conductivity and low emissivity, which not only improves the quality of the crystal but also reduces the production cost.

Authors' Contributions: Xuekang Lv: Conceptualization, Formal analysis, Methodology, Software, Visualization, Writing-original draft. Rongrong Hu: Data Curation, Formal analysis, Methodology, Visualization, Writing - Review & Editing. Jiacheng Li: Investigation, Data curation. Salamat Ali: Data curation, Writing – review & editing. Gengjin Li: Investigation. Jing Qi: Supervision, Writing - Review & Editing.

Funding: The authors are grateful for financial support from the Natural Science Foundation of Gansu Province (Grant No. 20JR5RA240) and Lanzhou University Supercomputing Center.

Data Availability The authors declare that this data and material have not been published in whole or in part elsewhere.

Competing interests: The authors declare no competing interests.

Conflict of Interest: The authors declare no conflict of interest.

Ethics Approval: The authors declare that the manuscript is not currently being considered for publication in another journal.

Consent to Participate: The consent was obtained from individual or guardian participants.

Consent for Publication: All authors have checked the manuscript and have agreed to the submission.

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Table 1

Material Properties in Simulations
Components	Density	Heat capacity	Thermal conductivity	Emissivity
	(\(\mathbf{k}\mathbf{g}/{\varvec{m}}^{3}\))	(J/(kg·K))	(W/(m·K))
Graphite	2300	2019	90	0.8
Hot-Side-Material A	1000	1600	10	0.9
Hot-Side-Material B	1000	1600	10	0.7
Hot-Side-Material C	1000	1600	10	0.5
Hot-Side-Material D	1000	1600	10	0.3
Hot-Side-Material E	1000	1600	10	0.1
Hot-Side-Material F	1000	1600	20	0.1
Hot-Side-Material G	1000	1600	30	0.1
Hot-Side-Material H	1000	1600	40	0.1
Hot-Side-Material I	1000	1600	50	0.1
Cold-Side-Material A	1000	1600	10	0.9
Cold-Side-Material B	1000	1600	10	0.7
Cold-Side-Material C	1000	1600	10	0.5
Cold-Side-Material D	1000	1600	10	0.3
Cold-Side-Material E	1000	1600	10	0.1
Cold-Side-Material F	1000	1600	20	0.1
Cold-Side-Material G	1000	1600	30	0.1
Cold-Side-Material H	1000	1600	40	0.1
Cold-Side-Material I	1000	1600	50	0.1

Table 2

The relationship between emissivity and various types of heat transfer and average wall temperature of Hot-Side-Material. Q1 is the net radiation heat of melt and crucible to the wall; Q2 is the conduction heat from the wall to the top of the crystal direction; Q3 is conduction and convection heat between the wall and argon gas; T1 is the temperature of the wall
Emissivity	Q1	Q2	Q3	T1
	(W)	(W)	(W)	(K)
0.1	4391.9	-4391.1	-0.8	1215.2
0.3	5901.6	-5899.8	-1.8	1222.2
0.5	6643.2	-6642.5	-0.7	1225.0
0.7	7143.1	-7142.1	-1.0	1227.6
0.9	7503.5	-7502.1	-1.4	1228.4

Table 3

The relationship between the emissivity of Cold-Side-Material and various types of heat transfer and average wall temperature. Q1 is the heat transferred to Cold-Side-Material wall; Q2 is the net radiation heat of crystal to Cold-Side-Material wall; Q3 is the net radiation heat dissipation of Cold-Side-Material to the surrounding; Q4 is net conduction and convection heat between the wall and argon gas; Q5 is the net radiation of the crystal to the surrounding environment dissipates heat; T1 is the average temperature of Cold-Side-Material wall near the crystal direction; T2 is the average temperature of crystal wall
Emissivity	Q1	Q2	Q3	Q4	Q5	T1	T2
	(W)	(W)	(W)	(W)	(W)	(K)	(K)
0.1	4056	242.5	-4290	-8.5	3184	1282.9	1255
0.3	6138	223.0	-6354	-7.0	3135	1233.5	1261
0.5	7206	214.5	-7414	-6.5	3117	1218.6	1263
0.7	7928	209.2	-8131	-6.2	3106	1210.3	1265
0.9	8472	205.1	-8671	-6.1	3099	1205.2	1266

No competing interests reported.

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Journal Publication

published 08 Jun, 2024

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Editorial decision: Revision requested
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You are reading this latest preprint version

Influence of thermal conductivity and emissivity of heat shield surface material on the thermal field of Czochralski silicon crystal growth

Status:

Journal Publication

Version 1

Abstract

Figures

1. Introduction

2. Model Description

3. Results and Discussion

3.1 Influence of the thermal conductivity of the Cold-Side-Material and ot-Side-Material on the thermal field

3.2 Influence of the emissivity of ot-Side-Material on the thermal field

3.3 Influence of the emissivity of Cold-Side-Material on the thermal field

4. Conclusion

Declarations

References

Tables

Additional Declarations

Status:

Journal Publication

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