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. 2025 Aug 11;10(35):40492–40500. doi: 10.1021/acsomega.5c05911

Thermal Field Simulation and Optimization for 8 in. SiC Crystal Growth via Novel Resistance Furnace Design

Dan Liu †, ShaoYi Jiang ‡, WeiTian Li †, Song Yang §,*, XueChao Liu ∥,*, JingXuan Sun †, MinGao Ding ‡, YunZhou Xue ⊥, ShaoLong He ⊥, RongBing Li †, Ying Wang †,*, Pan Gao †,*
PMCID: PMC12423845  PMID: 40949241

Abstract

Silicon carbide (SiC), a wide-band gap semiconductor, is essential for applications in electric vehicles, 5G communications, and aerospace due to its outstanding physical properties. However, their high production costs limit their widespread industrial applications. The growth of larger diameter and thicker crystals, particularly 8 in. crystals, offers the potential to reduce these costs. Therefore, large-diameter PVT crystal growth equipment with resistance heating has become a focal point of research in this field. In this paper, a novel double-flap resistance furnace design is proposed for the first time, and the thermal field is systematically studied by three-dimensional COMSOL Multiphysics modeling to optimize the growth of 8 in. 4H-SiC single crystals. It is found that the resistance heating system significantly outperforms the induction heating system by providing a lower radial temperature gradient necessary for large-diameter SiC crystals. Additionally, the influence of key parameters such as the crucible, the distance between the heater and the crucible, and the growth power on the thermal field distribution in the crucible was also systematically studied. The influence of the distance from the surface of the source material to the crystal surface and the distance from the center of the crystal to the edge on both the axial and radial temperature differences is also analyzed. Based on the simulation results, the crystal growth scheme was further optimized and an 8 in. SiC crystal with a thickness above 20 mm and resistivity uniformity was successfully obtained using the novel resistance furnace. This is of great significance for the growth of large-diameter SiC crystals.

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1. Introduction

Semiconductor materials serve as the foundation for integrated circuits, electronic devices, and optoelectronic systems, driving advancements in artificial intelligence and other emerging technologies. − Among these materials, silicon carbide (SiC), a wide-bandgap semiconductor, stands out due to its exceptional properties, including a wide bandgap (3.3 eV), high breakdown electric field (3–5 MV/cm), and superior thermal conductivity (4.9 W/(cm·K)). − These characteristics make SiC a pivotal material for next-generation applications in new energy vehicles, photovoltaics, rail transportation, smart grids, and aerospace technologies. ,

Despite its advantages, the widespread adoption of SiC remains hindered by high manufacturing costs, with substrates alone accounting for nearly 47% of total device cost. − While alternative growth methods like liquid-phase epitaxy (LPE) and high-temperature chemical vapor deposition (HTCVD) have been explored, , physical vapor transport (PVT) remains the dominant technique for mass production. , The induction-heating PVT system is suitable for crystals smaller than 6 in., but it is difficult to control the radial temperature gradient, which is crucial for growing larger and thicker SiC crystals. Therefore, the resistance-heating PVT systems have received much attention in recent years as a promising way to reduce the cost of SiC crystals. However, the conventional cylindrical resistance furnaces still present significant challenges in ensuring thermal field uniformity during the growth of large-diameter SiC crystals. ,

In this article, a novel double-flap resistance-heating PVT furnace is proposed to improve the convenience of thermal field control and equipment operation. First, the thermal field distributions of the induction heating system and resistance heating system with the same crucible structure and process conditions were compared by COMSOL Multiphysics simulation. The advantages of the latter are highlighted in favor of large-diameter SiC crystal growth. Second, the influence of key parameters such as the outer insulation layer of crucible, the distance between the heater and the crucible, and the growth power on axial temperature, radial temperature, and their corresponding temperature gradient was systematically investigated by simulation in the novel double-flap resistance furnace. Based on the above simulation results, the 8 in. 4H-SiC crystal with a thickness above 20 mm and uniform resistivity was obtained. This is the first time that this novel double-flap resistance furnace has been used to produce large-diameter, high-quality SiC crystals. This study is of great significance for the development of low-cost and high-yield SiC crystal growth technology.

2. Materials and Methods

The SiC single crystals are grown in quasi-sealed graphite crucibles via the PVT method at temperatures exceeding 2100 °C, which makes real-time process monitoring extremely challenging. Therefore, the Finite Element Method (FEM) COMSOL Multiphysics software is usually used to study the thermal field of SiC crystal growth, considering the heat transfer via conduction, convection, and radiation. − Figure presents the model of the 2D axisymmetric thermal field structure of the innovative double-flap resistance PVT furnace. The model consists of resistance heaters, graphite felts, graphite crucible, SiC source materials, and seed crystal. The key innovation is the use of a symmetric double-flap resistive heater, whose inner diameter varies with height. The design provides precise thermal field control through adjustable heater geometry while facilitating automated operation. This is particularly suitable for mass production of SiC crystals.

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Thermal field structure of a novel double-flap resistance furnace.

It is well-known that the control of the thermal gradients is essential for growing large-diameter, high-quality SiC crystals, requiring uniform radial gradients and large axial gradients. , First, the thermal field distribution of the induction and novel resistance heating systems under the same 8 in. crucible structure was compared through simulation. Further, the influence of key parameters such as the outer insulation layer of the crucible, the distance between the heater and the crucible, and the growth power on the axial temperature, radial temperature, and their corresponding temperature gradient in the novel double-flap resistance furnace was studied. Meanwhile, the variation of the thermal field related to the growth stability was analyzed in detail. The growth duration was set to 20 h for all experimental conditions. These simulation results reveal the optimal conditions for the stable growth of 8 in. SiC crystals. The accuracy of the material parameters is critical to the reliability of the simulation, so the specific material properties used are summarized in Table .

1. Physical Parameters of the Resistance Furnace.

parameter graphite felt graphite SiC
conductivity (S/m) 909 5.69 × 104 400
heat capacity (J/(kg·K)) 1000 710 1200
density (kg/m3) 180 1850 3220
thermal conductivity (W/(m·K)) kGF(T) 100 450
surface emissivity 0.7 0.8 0.85
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Based on the simulation results, the novel double-flap resistance PVT furnace was constructed for 8 in. SiC crystal growth, as shown in Figure (from Shenzhen Himachines Microelectronic Equipment Technology Co., Ltd.). This novel furnace has a simple thermal field structure and low cost, mainly composed of a double-flap heater, insulation felt, and graphite crucible. This innovative heater enables precise thermal field control and automated operation. The detailed SiC crystal growth process is as follows: an 8 in. 4H-SiC seed crystal (C-face, 4° off-axis) was placed 106 mm above high-purity SiC source material in the crucible. In the experiment, the crystal growth pressure was controlled at 1–10 mbar. Ar was used as the atmosphere gas, N2 was used as the dopant gas, and the flow ratio of Ar to N2 was 100:5 sccm. The heating power was 45 kW, and the growth time was lasting for 120 h, while the crucible rotated at a speed of 5 rpm to improve thermal uniformity. The obtained SiC crystal was processed into wafers via standard cutting, grinding, polishing, and cleaning procedures. The doping uniformity and thermal field stability of the novel double-flap resistance furnaces were characterized through the mapping of wafer resistivity characterized by an RP-1000 tester. This provides an important basis for this novel resistance furnace suitable for large-diameter SiC crystal growth.

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Novel double-flap resistance PVT furnace.

3. Results and Discussion

3.1. Thermal Field Simulation of Induction and Resistance Furnaces

It is well-known that a large axial temperature gradient and uniform radial temperature distribution are crucial for growing large-diameter, high-quality SiC single crystals by the PVT method. The two most common furnace configurations for PVT growth are induction heating (IH) and resistance heating (RH), which require the design of matching thermal fields. However, there is still a significant research gap in systematic comparative studies of the thermal field characteristics between induction heating and resistance heating systems. Therefore, two optimized insulation configurations including RH-20 and IH-20 were developed, and subsequently, thermal field simulations were carried out. For systematic comparison, cross-comparison cases IH-40 and RH-40 were also created, where the numbers denote the outer insulation layer thickness of 20 and 40 mm, respectively. The cylindrical outer insulation layer surrounds the outside of the crucible. This study mainly compares the thickness of the outer insulation layer.

The simulation results show that there is a significant difference in the thermal field distribution between the two heating methods. Figure presents a comparative analysis of the thermal fields of axial and radial temperature distribution and corresponding temperature gradients for all four configurations, with the numerical results of key parameters quantified in Table . Figure a,b shows the thermal field simulation results for the same crucible configuration with an insulation layer thickness of 20 mm under induction heating (IH-20) and resistance heating (RH-20), respectively. Due to the electromagnetic skin effect combined with the thin insulation layer, the induction heating system shows significant heat dissipation around the crucible. This results in an uneven temperature distribution and an excessively large thermal gradient. Specifically, the radial temperature difference reaches 96.5 °C, and the axial temperature difference is as high as 270.6 °C. The drastic temperature fluctuations are extremely unfavorable to the growth of large-diameter SiC single crystals. Meanwhile, this indicates that the induction furnace requires thicker insulation layers to mitigate temperature gradients caused by heat dissipation. In contrast, for the RH-20 resistance heating scheme with the same structure, the radial and axial temperature differences are only 12 and 41.9 °C, respectively. The smaller radial temperature difference is more favorable for the formation of an ideal interface for microconvex crystal growth. Figure f,h further shows the variation of the axial and radial temperature gradients. It can be found that they are smoother in the resistance furnace than in the induction furnace, indicating that the resistance furnace has an advantage in thermal field stability. Due to the relatively thin insulation layer thickness of 20 mm, it is unsuitable for the conditions of SiC crystal growth in an induction furnace. Therefore, this study further designed a comparative scheme with a 40 mm thick insulation layer for a more comprehensive analysis. Figure c,d shows the simulation results after increasing the thickness of the outer insulation layer; it was found that the overall temperature in both heating systems increased by approximately 200 °C, which can be attributed to the enhanced heat storage performance of the crucible. Due to reduced edge heat dissipation, Figure e,g shows that the radial and axial temperature difference formed by induction and resistance heating under the same structure was effectively reduced to 9 °C, 4.3 °C, 30.9 °C, and 21.9 °C, respectively. This indicates that the thickening of the outer insulation layer can effectively adjust the temperature differences and temperature gradients. Notably, it reveals a smoother radial temperature difference and temperature gradient in resistive heating compared with Figure f–h. It is worth noting that the simulation results of RH-20 and RH-40 indicate that by adjusting the thickness of the outer insulation layer of the graphite crucible, the axial temperature difference can be effectively controlled within the range of 21.9 to 41.9 °C and the radial temperature difference within the range of 4.3 to 12 °C. In fact, this is particularly beneficial for the growth of thicker SiC crystals.

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Thermal field distribution inside the crucible under induction and resistance heating conditions with different thicknesses of the insulation layer: (a–d) Temperature field distribution in the growth chamber; (e,f) radial temperature and its gradient; (g,h) axial temperature and its gradient.

2. Simulation Results for Different Schemes.

scheme power (kW) insulation thickness (mm) heater distance (mm) radial temperature difference (°C) axial temperature difference (°C) source surface temperature (°C)
IH-20 14 20 94 96.5 270.6 2312
RH-20 45 20 55 12 41.9 2103
IH-40 14 40 94 9 30.9 2235
RH-40 45 40 55 4.3 21.9 2309
RH-20 45 20 55 14 44.3 2125
RH-0   0   3.9 9.9 2069
RH-20/50 45 20 50 15 54.5 2165
RH-20/55     55 12.9 43.1 2103
RH-20/65     65 13.9 42.4 2006
RH-20 42 20 55 15.4 52 1967
RH-20 45     12.98 44 2104
RH-20 46.5     8.5 36 2285
RH-20 48     7 34 2597
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In summary, the novel double-flap resistance furnace has significant advantages in controlling the temperature field, with a small radial temperature gradient and a large adjustable range of the axial temperature gradient. This is more suitable for producing high-quality and thicker SiC crystals with a diameter of 8 in. and larger. The RH-20 scheme has the best axial temperature gradient and a uniform radial temperature distribution. From a thermodynamic point of view, the heat transfer of the resistance furnaces is primarily through radiation, and its efficiency determines the thermal field characteristics and overall system performance. The thickness of the insulation layer affects the heat loss from the system, while the heater–crucible distance significantly affects the radiation view factor. In addition, the heating power determines the intensity of the radiant flux. In order to deeply study the thermal field characteristics of the novel double-flap resistance furnace and obtain suitable process parameters, this paper further conducts a comprehensive analysis of the above three key parameters through COMSOL Multiphysics simulation.

3.2. Influence of Key Process Parameters on the Thermal Field

It is well-established that resistance heating is mainly achieved through direct heat radiation and conduction. The insulation material outside the crucible is one of the factors affecting heat transfer efficiency. Therefore, we focus on the simulation to compare the thermal field characteristics inside the crucible with and without an insulation layer on the outside of the crucible based on the RH-20 scheme. As shown in Figure a,b, the center temperature of the top of the source material surface drops from 2125 to 2069 °C when the thickness of the external insulation layer of the crucible changes from 20 mm (RH-20) to 0 mm (RH-0). This shows that the rapid dissipation of the thermal energy leads to a sharp drop in the temperature of the entire system. Figure c–f indicates that the axial temperature difference inside the crucible decreases from 44.3 to 9.9 °C, while the radial temperature difference decreases from 14 to 3.9 °C. The corresponding temperature gradient also tends to be smooth, but the excessively small axial temperature gradient makes it very difficult to form an effective transportation of the gas phase components. This phenomenon occurs because when there is no insulation material outside the crucible, it will radiate heat to the surroundings. This causes the crucible to dissipate heat too quickly, which has an adverse effect on the heating efficiency and thermal insulation effect. In the RH-20 scheme, the radial temperature gradient increases significantly with the increase of radius and reaches the maximum value at 80–90 mm. Subsequently, the temperature gradient in the edge area of 90–100 mm gradually decreases due to the inhibition of the top insulation layer. The smaller edge temperature gradient can prevent the formation of polycrystals, thus reducing the cracks caused by edge polycrystals. The lower mass transfer rate at the edge periphery leads to a slightly convex growth interface at the edge. Therefore, it is crucial to adjust the temperature field by designing a suitable insulating layer around the periphery and the top of the graphite crucible. This not only achieves a stable thermal field but also improves energy efficiency.

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Thermal field distribution inside the crucible with and without an insulation layer outside the crucible during resistance heating: (a,b) Temperature field distribution in the growth chamber; (c,d) radial temperature and its gradient; (e,f) axial temperature and its gradient.

As is well-known, radiant heating is the main heat transfer method in resistance furnaces. The distance between the heater and the crucible is one of the key factors that determines the radiation heating and the thermal field. The simulation experiments were conducted based on the RH-20 scheme with a growth power of 45 kW, where the distances between the heater and the outside of the crucible were set to 50, 55, and 65 mm, respectively. As shown in Figure a–g, the center temperature at the top of the source material is found to increase with the decrease of the distance mentioned above, from 2006 to 2165 °C, which is caused by the increase of heating efficiency. This further leads to an increase in the axial temperature difference, reaching 42.4 °C, 43.1 °C, and 54.5 °C, respectively. The axial temperature gradient also becomes steeper with a decrease in the distance. This indicates that it is possible to effectively increase the axial temperature difference and axial temperature gradient by reducing the distance between the heater and the crucible. In fact, the heat transfer efficiency decreases significantly when the crucible is moved away from the heater, which will result in a decrease in the temperature of the source material. It is worth noting that it is found that the radial temperature difference exhibits a nonlinear relationship with distance in Figure d,e. For a distance of 50 mm (RH-20/50), since the crucible is only 8 mm away from the inner side of the top of the heater, the heat transfer efficiency is relatively high and the radial temperature difference reaches 15 °C. This phenomenon is related to the efficiency of the dominant radiative heat transfer. As the distance increases, the radial temperature difference changes to 12.9 and 13.9 °C, respectively. And the change is not linearly reduced. In addition, the radial temperature gradient increases first and then decreases with the increase of radius. The decrease of the gradient in the edge area is beneficial to inhibit the growth of polycrystals. This confirms that it can produce a more gradual temperature distribution in the RH-20/55 scheme by a comparison of the thermal fields. This shows that radiation, conduction, and convection have mutually coupled effects on the heat transfer process during resistance heating. Therefore, there will be an optimal radiation distance for a certain heater and graphite crucible structure. The appropriate radiation distance of this novel double-flap heater is about 55 mm (RH-20/55) for the growth of 8 in. SiC crystals. It achieves appropriate axial and radial temperature fields, as well as a suitable temperature control range for the source material. The nonlinear influence mechanism of the distance between the heater and the crucible on the temperature field inside the crucible will be described in another paper.

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Thermal field distribution inside the crucible under different distances between the heater and the crucible: (a–c) Temperature field distribution in the growth chamber; (d,e) radial temperature and its gradient; (f,g) axial temperature and its gradient.

The heating power is another key factor in determining the thermal field during crystal growth by resistance heating. It is directly proportional to the generation of thermal energy in the system. The simulation experiments are based on the RH-20 scheme, and the crystal growth power is set to 42 kW, 45 kW, 46.5 kW, and 48 kW, respectively. Of course, the design for a thermal field structure with lower crystal growth power is in progress. As shown in Figure a–d, the temperature in the crucible increases significantly from 1967 to 2597 °C with increasing power. Figure e–h illustrates that the axial and radial temperature difference decreases gradually with increasing power, from 52 to 34 °C and from 15.4 to 7 °C, respectively. This phenomenon is mainly attributed to the higher heat transfer efficiency within the thermal field as the power increases. This results in more uniform heat transfer and reduced temperature differences. As the heating power increases, both heat radiation and conduction become more efficient, which results in a reduction in the radial temperature gradient. However, it was also found that the low power resulted in insufficient heating efficiency, causing the source material temperature to be as low as 1967 °C. In addition, a new phenomenon was discovered in Figure h, where the axial temperature gradient changes differently with height at different powers. It can be found that the axial temperature gradient increases with height under the lower growth power conditions of 42 and 45 kW. It rises from 0.2 °C/mm to 0.9 °C/mm and 0.6 °C/mm, respectively, which indicates that the temperature change is more obvious. However, the axial temperature gradient decreases with height at higher growth power conditions of 46.5 and 48 kW. It decreases from 0.4 to 0.3 and 0.2 °C/mm, respectively. The decrease in the temperature gradient weakens the driving force for the transport of gas phase molecules to the seed surface, which is unfavorable for the growth of thicker SiC crystals. This new phenomenon is related to the change in the heat transfer mechanism directly affected by the heating power. At the same time, it helps to guide the growth rate of SiC crystals in resistance furnaces by regulating the growth power. Based on the above analysis, it is believed that the 45 kW growth power is the best process parameter under the current conditions. Not only does it form a suitable axial and radial temperature difference, but also its axial temperature gradient gradually increases with height. This will be very beneficial to the continuous supply of the source material during crystal growth. Most importantly, the above simulation results show that it has a good ability to adjust the axial and radial temperature fields for this novel double-flap resistance furnace. This is a key requirement for the growth of larger and thicker SiC crystals.

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Thermal field distribution inside the crucible under different heating powers: (a–d) Temperature field distribution in the growth chamber; (e,f) radial temperature and its gradient; (g,h) axial temperature and its gradient.

3.3. Experiments of Crystal Growth

In order to further verify the thermal field characteristics of this novel double-flap resistance furnace, crystal growth experiments were carried out. Based on the above simulation results, the following important growth conditions were determined. The thickness of the outer insulation layer of the crucible was 20 mm. The distance between the heater and the crucible was 55 mm, and the crystal growth power was 45 kW. As shown in Figure a,b, an 8 in. SiC ingot with a thickness of more than 20 mm was obtained after 120 h of growth. Its surface shape was slightly convex, and the surface was smooth. The surface of the crystal was irradiated by an UV lamp and showed a uniform brownish yellow color, which indicated that the 4H polytype was consistent. As shown in Figure c,d, the resistivity of the crystals was in the range of 0.0225–0.0245 Ω·cm, with most of the region below 0.0240 Ω·cm. This again demonstrates the excellent thermal field uniformity of this novel resistance furnace. The higher resistivity values are limited to a narrow region at the edge of the ingot, which can be solved by using slightly larger-diameter seed crystals for growth. The above results show that the thermal field of this novel double-flap resistance furnace based on the thermal field simulation has been successfully verified. It not only enables temperature field regulation and the growth of larger and thicker SiC single crystals but also provides an important new method for the industrial production of low-cost SiC crystals. The study on the preparation of 30 mm thick SIC crystals by extending the time to 200 h will be described in detail in another paper.

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(a) As-grown 8 in. SiC ingot. (b) Ingot surface irradiated by an UV lamp. (c) Resistivity distribution of the substrate. (d) Resistivity scalar contour distribution.

4. Conclusion

In this paper, the thermal field distribution characteristics of the novel double-flap resistance furnace for 8 in. SiC crystal growth were systematically analyzed using COMSOL Multiphysics simulations and it was compared with the conventional induction furnace. The results show that this novel resistance furnace can greatly improve the thermal field uniformity and temperature gradient control. The radial temperature gradient and corresponding thermal stress on the seed crystal surface were also significantly reduced. Further, the thermal field simulations were carried out by optimizing the key parameters, including maintaining a suitable insulation thickness of 20 mm, a suitable heater–crucible distance of 55 mm, and a matched heating power of 45 kW. It was found that the novel resistance furnace could achieve excellent radial temperature uniformity (ΔT r = 12.98 °C/100 mm) and a sufficient axial temperature gradient (ΔT a = 44 °C/105 mm). This is very beneficial for the stable growth of larger-diameter high-quality SiC crystals. Finally, the 4H-SiC ingot with a thickness of more than 20 mm was successfully obtained for the first time by using this novel double-flap resistance furnace by simulating and optimizing the growth process. The resistivity of the wafers ranges from 0.025 to 0.045 Ω·cm. The above results not only verify the feasibility of this novel double-flap resistance furnace in the growth of large-diameter SiC crystals but also have a positive guiding significance for its thermal field design and process optimization. At the same time, it also provides a new way to achieve efficient and low-cost industrialization of 8 in. and above SiC crystals.

Acknowledgments

This work was supported by the National Key R&D Program of China (2024YFB3816700), the Ningbo Youth Science and Technology Innovation Leading Talent Program (2024QL018), and the Key R&D Program of Zhejiang (2024SSYS0052).

The article was written through contributions of all authors. All authors have given approval to the final version of the article.

The authors declare no competing financial interest.

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