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Reduction of carbon contamination during the melting process of Czochralski silicon crystal growth
Journal of Crystal Growth (xxxx) xxxx–xxxx
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Reduction of carbon contamination during the melting process of Czochralski silicon crystal growth ⁎
Xin Liu , Bing Gao, Satoshi Nakano, Koichi Kakimoto Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasuga-Koen, Kasuga 816-8580, Japan
A R T I C L E I N F O
A BS T RAC T
Communicated by Francois Dupret
Generation, incorporation, and accumulation of carbon (C) were investigated by transient global simulations of heat and mass transport during the melting process of Czochralski silicon (CZ-Si) crystal growth. Contact reaction between the quartz crucible and graphite susceptor was introduced as an extra origin of C contamination. The contribution of the contact reaction on C accumulation is affected by the back diffusion of C monoxide (CO) from the gap between the gas-guide and the crucible. The effect of the gas-guide coating on C reduction was elucidated by taking the reaction between the silicon carbide (SiC) coating and gaseous Si monoxide (SiO) into account. Application of the SiC coating on the gas-guide could effectively reduce the C contamination because of its higher thermochemical stability relative to that of graphite. Gas flow control on the back diffusion of the generated CO was examined by the parametric study of argon gas flow rate. Generation and back diffusion of CO were both effectively suppressed by the increase in the gas flow rate because of the high Péclet number of species transport. Strategies for C content reduction were discussed by analyzing the mechanisms of C accumulation process. According to the elucidated mechanisms of C accumulation, the final C content depends on the growth duration and contamination flux at the gas/melt interface.
Keywords: A1. Computer simulation A1. Impurities A1. Mass transfer A2. Czochralski method
1. Introduction Carbon (C) contamination in single crystalline silicon (Si) is detrimental for the minority carrier lifetime, which is a critical parameter of the wafers used for power devices [1]. Reduction of C contamination in the Czochralski (CZ) crystal growth is critical for the production of high-performance Si wafers. Incorporation of C from gas/melt interface occurs prior to the growth stage and sustains until the tailing stage of the crystal [2]. Accumulation of C in Si feedstock depends on the back diffusion of CO that is continuously generated from the furnace elements at high temperature [3]. To effectively reduce the C contamination, it is essential to control the generation, incorporation and accumulation of C in the CZ-Si growth process. The origins of CO generation and the relevant chemical reactions at high temperature must be identified for the development of approaches for the effective reduction of C content. In addition to CO generation by the reaction between graphite and SiO, the reaction between the quartz crucible and graphite susceptor should be considered as another CO source [4]. Silicon carbide (SiC) coating can be applied conventionally to the gas-guide above the melt surface to suppress the CO generation. Generally, the reaction between SiO and SiC has been ignored because of its low reaction rate [5]. However, C contamination in the Si
⁎
feedstock occurs even when the SiC coating is applied. Despite the lower reactivity of SiC relative to graphite, the reaction between SiC and gaseous SiO should be considered because of the short distance between the gas-guide and the Si melt. Transport phenomena of C and CO in the CZ-Si process have been studied extensively in the last decades [1–3,6–12], and it was found that Si melt and argon (Ar) gas act as impurity carriers of C, O, and related compounds such as CO and SiO. In a numerical study, Bornside et al. [8] derived the chemical model of coupled CO and SiO from the thermodynamic analysis of their reactions in the high temperature range. Based on this chemical model, Gao et al. [9] developed the coupled transport model for SiO and CO in Ar gas and for C and O in a Si melt. Recently, Vorob’ev et al. [10] reviewed the chemical models and impurity transport for global modeling of the CZ-Si crystal growth. However, the C content predicted under the quasi-static assumption does not account for C accumulation during the CZ-Si crystal growth [2]. Therefore, transient global simulations of heat and mass transport should be conducted for C accumulation in the CZ-Si crystal growth [11,12]. The present study focuses on the evolution of C contamination during the melting process of CZ-Si crystal growth. C transport during generation, incorporation, and accumulation of C during growth were
Corresponding author. E-mail address: [email protected] (X. Liu).
http://dx.doi.org/10.1016/j.jcrysgro.2016.12.013
0022-0248/ © 2016 Elsevier B.V. All rights reserved.
Please cite this article as: Liu, X., Journal of Crystal Growth (2016), http://dx.doi.org/10.1016/j.jcrysgro.2016.12.013
Journal of Crystal Growth (xxxx) xxxx–xxxx
X. Liu et al.
The configuration of the system and the computational grids for the melting process of a CZ-Si crystal growth are shown in Fig. 1(a). The furnace was divided into a number of domains and a structured mesh was generated for the solid and Si feedstock domains, whereas an unstructured mesh was applied for the Ar gas domain. Along the melt free surface, both of the gas side and melt side were generated by fine meshing to handle the boundary layer of species transport. The furnace is described in detail in Ref. [11]. The results at two locations, in the gas domain as well as in the Si domain (marked as PAr and PSi , respectively), were monitored during the transient global simulation, as shown in Fig. 1(b). 2.1. Contact reaction between quartz crucible and graphite susceptor In addition to the CO generation because of graphite etching by gaseous SiO, the contact reaction between the quartz crucible and graphite susceptor was also introduced as a new CO source [4]. When the temperature of the quartz approaches the melting point of Si (1685 K), the quartz begins to soften and deform, and because of the load of the molten Si in the crucible, the crucible comes almost entirely into close contact with the inner shape of the susceptor supporting the crucible from the outside. The contact reactions between the crucible and the susceptor are actively involved at this high temperature, with the contact reaction process shown schematically in Fig. 2. For the first use of the susceptor, SiC was deposited on the surface because of the etching of graphite by gaseous SiO. The generated SiC layer could then react with the softened crucible during the subsequent usage. The two reactions involved in this process are given by: (1) Graphite fixture surfaces: SiO(g) + 2C (s ) ↔ CO(g) + SiC (s ); (2) Crucible/susceptor contact: 2SiO2(s ) + SiC (s ) ↔ CO(g) + 3SiO(g). The Gibbs free energy for the generation of SiO and CO in the reaction (2) was computed and was found to be [14]
ΔG0 = 1, 444, 316.8 − 682.0T [J/mol].
(1)
The reaction equilibrium constant was taken as
K=
3 aSiO (g)aCO(g) 2 aSiC (s)aSiO 2 (s )
= e−ΔG0 / RT . (2)
Assuming that sufficient amounts of SiO2(s ) and SiC (s ) are present,
Fig. 1. Geometry and dimensions used to simulate the melting process of CZ-Si crystal growth. (a) Configuration and computational grids; (b) monitor locations in the gas domain and the melt domain.
investigated by transient global simulations of heat and mass transport with fully coupled boundary conditions, and accumulation of C in Si feedstock in the melting process was predicted for different conditions. Two additional origins of C contamination because of the implantation of chemical reactions on the crucible and the gas-guide were investigated, and strategies for C reduction were devised for different stages of the CZ-Si crystal growth. 2. Modeling and formulations The methodology for transient global simulation of coupled heat and mass transport during the melting process of the CZ-Si crystal growth has been reported elsewhere [11]. A virtual proportional integral derivative (PID) controller for the temperature [13] was introduced to realize power control of the heater. The coupled boundary conditions for the transport of impurities were modeled based on the chemical reactions in a CZ-Si crystal furnace.
Fig. 2. Schematic diagram of contact reaction between quartz crucible and graphite susceptor.
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the activities of the species (a ) are expressed as
aSiO2(s) = 1, aSiC (s) = cSiC (s) / cSiO2(s), aSiO(g) = aCO(g) =
PCO(g) 101, 325 Pa
PSiO(g) 101, 325 Pa
,
,
(3)
where cSiO2(s) and cSiC (s) are the molar concentrations of SiO2(s ) and SiC (s ) as estimated by their molar masses and densities, respectively. Partial pressures of SiO(g) and CO(g) follow the molar ratio given by
PSiO(g) / PCO(g) = 3.
(4)
Finally, partial pressures of SiO(g) and CO(g) can be expressed by the following equations:
PSiO(g) = 1.5286e−43, 430/ T +20.5 [atm], PCO(g) = 0.5095e
−43, 430/ T +20.5
[atm].
(5) Fig. 3. Reaction equilibrium constants between gaseous SiO and SiC coating or graphite surfaces.
(6)
Assuming a full contact and pure diffusion, the generated CO and SiO are imposed on the contact surface. A narrow gap with three layers between the crucible and the susceptor was assumed for the diffusion of SiO and CO. The generated gas was transported from the contact into the gas domain. The outlet for the products was located on the joint corner of the crucible and the susceptor. A stagnant gas was imposed in the assumed gap as well as the in the outlet. Except for the generation and outlet boundaries, zero flux conditions were imposed for the other boundaries.
pressure and Ar gas flow rate were set to 15 Torr and 10 SLPM (standard liter per minute at 273.15 K and 760 Torr), respectively.
3.1. Effect of contact reaction on CO and C contamination To address the effect of the contact reaction between the crucible and the susceptor, the melting process of the CZ-Si growth with and without the contact reaction was investigated. CO generation on the gas-guide was eliminated in order to examine the case with only contact contribution. Comparison of CO in the gas and C in the melt is shown in Fig. 4. For the case with contact reaction, the maximum CO concentration in the gas is located at the corner of the crucible and the susceptor and is 5×10−8 mol/cm3. This is an order of magnitude larger than the value obtained for the case without the contact reaction. Therefore, it is found that the contact reaction markedly increases the species (CO and SiO) concentrations in the gas. Furthermore, the generated SiO could enhance the etching of graphite elements and CO generation. These results indicate that the levels of SiO and CO in Ar gas were underestimated when the contact reaction was not considered. Back diffusion of the generated CO affects the C contamination in Si feedstock. Therefore, the final C concentration in Si melt also shows an order of magnitude increase because of the contact reaction with the maximum C concentration reaching 6×1014 atoms/cm3. This indicates that the contribution of the contact reaction to C contamination is because of the back diffusion of the generated CO. Since the entire
2.2. Reaction between SiC coating and gaseous SiO on gas-guide Because of its thermochemical stability, SiC is introduced as the coating material on the graphite elements used in CZ-Si growth. A coating with a thickness of approximately 80–100 µm can be applied on graphite surfaces by a chemical vapor deposition process. It is believed that the SiC coating acts as a diffusion and reaction barrier and helps reduce the C contamination. According to the thermochemical data, SiO in the gas domain can also react with the coated graphite according to the following equation:
SiC coating surfaces: SiO(g) + SiC (s ) ↔ CO(g) + 2Si(s ). The reaction rate could be obtained using the reaction equilibrium constant
K = PCO(g) / PSiO(g) = e−ΔG0 / RT .
(7)
According to Ref. [14], it is found that, for the uncoated graphite surfaces, ΔG0 = 79, 224 − 1.297T Jmol−1, while for the SiC coating surfaces, ΔG0 = 71, 128 − 20.92T Jmol−1. The equilibrium reaction constants of uncoated and coated graphite are plotted in Fig. 3. Boundary conditions for CO generation on the SiC coating or the uncoated graphite surfaces can be implemented according to their different textures. Except for the above specifications, the other boundary conditions in the Ar gas and Si feedstock were as follows. A zero flux boundary condition was used for C on the crucible wall. For non-C walls and the symmetry axis in gas, zero fluxes of SiO and CO were used; for the gas inlet, the concentrations of SiO and CO were set to zero; for the gas outlet, zero gradients of SiO and CO were used. 3. Results and discussion The final C concentration in the growing CZ-Si crystal is determined by complex mechanisms. To elucidate the mechanisms of CO and C transport, transient global simulations were performed for the melting process of CZ-Si crystal growth. Thermal field, melt and gas flow, and impurity transport were predicted with fully coupled boundary conditions of heat, flow, and impurities. The reference values of furnace
Fig. 4. Effect of contact reaction on CO in gas and C in Si feedstock. Concentrations of CO and C without contact reaction (left) and concentrations of CO and C with contact reaction (right).
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Fig. 5. Effect of gap width on C incorporation for the cases without contact reaction (black) or with contact reaction (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
growth process can last more than 50 h, the contact reaction may introduce remarkable C incorporation in the Si melt and the growing crystal. Therefore, the contact between the silica crucible and the graphite susceptor is a crucial source of C contamination in the Si crystal. It is believed that back diffusion can be suppressed by a welldefined gas flow. Therefore, C incorporation because of the contact reaction can also be affected by the width of the gap between the crucible and the gas-guide. Three widths of 20 mm, 40 mm and 60 mm were investigated to determine the dependence of the contact reaction contribution on the width of the gap. Contact reaction contributions were compared for different gap widths in Fig. 5. Examination of Fig. 5 shows that the contact reaction contribution increased dramatically with increasing width of the gap. The differences between the results obtained with and without the contact reaction indicate the contributions of the back diffusion of CO for different gap widths. Since the gas velocity decreases with an increasing gap width, a narrow gap is favorable for the reduction of CO back diffusion and C incorporation caused by the contact reaction. Fig. 6. Effect of SiC coating on C incorporation. (a) Evolutions of CO concentration at the monitored location in gas during the melting process and (b) concentrations of CO and C without SiC coating (left) and with SiC coating (right).
3.2. Effect of coating reaction on CO and C contamination 3.3. Discussion of the strategies of C reduction To elucidate the effect of the SiC coating on C reduction, three cases were investigated: the case of zero generation, with SiC coating and without SiC coating. The CO concentrations above the melt surface (monitor point) for these cases were compared as a function of time, as shown in Fig. 6(a). When the coating reaction was not considered, the CO concentration at the monitor point was lower than 10−16 mol/cm3, indicating that hardly any CO could be incorporated into the Si melt as C contamination. Nevertheless, C contamination still exists at remarkable levels in the practical process with SiC coating application. Even though the reactivity of SiC is lower than that of graphite, the reaction between SiC and gaseous SiO must be taken into account because of the short distance between the gas-guide and Si feedstock. Comparison with the results for the uncoated case shows that the presence of a SiC coating can reduce the CO concentration at the monitor point by an order of magnitude, as shown in Fig. 6(a). Even slight generation of CO can be incorporated into the Si melt as C contamination. Accumulation of C in the Si melt was also investigated for the cases with and without SiC coating, as shown in Fig. 6(b). After the end of the melting process, the maximum C concentrations for the uncoated and coated cases are 9.4×1015 atoms/cm3 and 7.1×1014 atoms/cm3, respectively. Thus, the C concentration in CZ-Si growth can be effectively reduced by the application of the SiC coating.
In addition to the C found in the original feedstock, C contamination arises mainly from the gaseous CO generation in the furnace. The CO generation rate depends on the reactivity of the furnace elements, which are functions of temperature. Because of the lack of kinetic data on this heterogeneous chemical reaction, the origins of CO require further detailed examination taking the entire thermal history of the crystal growth process into account. The contact reaction between the quartz crucible and graphite susceptor obviously increases the CO content in Ar gas and the C contamination in the Si feedstock. Coatings of SiC or other substitute materials with high thermo-chemical stability could reduce the CO generation from this source. If we choose the diameter of the crucible as the characteristic length, the Péclet number for CO transport in Ar gas is generally in the range of 200–2000. This indicates that control of the gas flow control can efficiently suppress the back diffusion of CO, as discussed in Ref. [11]. Convective transport of SiO and CO becomes dominant with the increase of the gas flow rate. Much more of the generated CO in the chamber can then be pumped out together with the SiO that is also a reactant for CO generation. Because of the combination of these two positive effects, an increased flow rate can effectively reduce the C flux
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adjustment of the width of the gap between the crucible and the gasguide can affect the back diffusion of the generated CO. The reaction between the SiC coating and gaseous SiO was taken into account in order to describe the reduction of C contamination because of the application of the coating. The presence of the coating on the gas-guide has tangible benefits for the generation of CO and C incorporation into the Si feedstock. Strategies for reduction of C generation, incorporation and accumulation were summarized according to the accumulation mechanisms of C contamination. For accurate prediction of C accumulation in Si feedstock, a transient global simulation that involves the entire crystal growth process must be performed. The increase of the gas flow rate and the application of a coating with high thermochemical stability are suggested to be efficient strategies for the reduction of C contamination. Acknowledgments Fig. 7. C concentration and flux at the monitored location in the melt as functions of Ar gas flow rate.
This work was partially supported by the New Energy and Industrial Technology Development Organization (NEDO) under the Ministry of Economy, Trade and Industry (METI), Japan.
at the gas/melt interface and the final C concentration in Si feedstock, as shown in Fig. 7. Incorporation of C from the gas/melt interface proceeds from the melting stage to the tailing stage. The duration (Δt ) of the C accumulation process is about 50 h for a typical 100 kg charge in the volume (V ). The final C contamination is given by the time integration of the accumulation rate (∂cC /∂t ), which is proportional to the incorporation flux (DC ∂cC /∂x ) and the total area (S ) of the gas/melt interface. The C incorporation flux depends on the CO concentration along the gas/melt interface, which is proportional to the generation rate of CO (cCO ) and the inverse of the Péclet number (1/ Pe ). According to the definition of Pe , a higher gas flow rate results in a higher Pe value. These relationships could be expressed as
∫Δt ∫V
∂cC dVdt ∝ ∂t
∂c
∫Δt ∫S DC ∂xC dSdt ∝ ∫Δt ∫S Pe1
cCO dsdt. δ
References [1] Y. Nagai, S. Nakagawa, K. Kashima, Crystal growth of MCZ silicon with ultralow carbon concentration, J. Cryst. Growth 401 (2014) 737–739. [2] R.W. Series, K.G. Barraclough, Control of carbon in Czochralski silicon crystals, J. Cryst. Growth 63 (1983) 219–221. [3] T. Fukuda, M. Koizuka, A. Ohsawa, A Czochralski silicon growth technique which reduces carbon to the order of 1014 per cubic centimeter, J. Electrochem. Soc. 141 (1994) 2216–2220. [4] B. Gao, S. Nakano, K. Kakimoto, Influence of reaction between silica crucible and graphite susceptor on impurities of multicrystalline silicon in a unidirectional solidification furnace, J. Cryst. Growth 314 (2011) 239–245. [5] F. Schmid, C.P. Khattak, T.G. Digges, L. Kaufman, Origin of SiC impurities in silicon crystals grown from the melt in vacuum, J. Electrochem. Soc. 126 (1979) 935–938. [6] H.M. Liaw, Oxygen and carbon in Czochralski-grown silicon, Microelectron. J. 12 (1981) 33–36. [7] B.O. Kolbesen, A. Mühlbauer, Carbon in silicon: properties and impact on devices, Solid-State Electron. 25 (1982) 759–775. [8] D.E. Bornside, R.A. Brown, T. Fujiwara, H. Fujiwara, T. Kubo, The effects of gasphase convection on carbon contamination of Czochralski-grown silicon, J. Electrochem. Soc. 142 (1995) 2790–2804. [9] B. Gao, K. Kakimoto, Global simulation of coupled carbon and oxygen transport in a Czochralski furnace for silicon crystal growth, J. Cryst. Growth 312 (2010) 2972–2976. [10] A.N. Vorob’ev, A.P. Sid’ko, V.V. Kalaev, Advanced chemical model for analysis of Cz and DS Si-crystal growth, J. Cryst. Growth 386 (2014) 226–234. [11] X. Liu, B. Gao, K. Kakimoto, Numerical investigation of carbon contamination during the melting process of Czochralski silicon crystal growth, J. Cryst. Growth 417 (2015) 58–64. [12] X. Liu, B. Gao, S. Nakano, K. Kakimoto, Numerical investigation of carbon and silicon carbide contamination during the melting process of the Czochralski silicon crystal growth, Cryst. Res. Technol. 50 (2015) 458–463. [13] Y. Lee, J. Lee, S. Park, PID controller tuning for integrating and unstable processes with time delay, Chem. Eng. Sci. 55 (2000) 3481–3493. [14] M. Chase, NIST-JANAF Thermochemical Tables, 4th Edition, Journal of Physical and Chemical Reference Data Monographs, No. 9, 1998.
(8)
In summary, C contamination can be suppressed by the decreases in the CO generation rate and the process duration, as well as by the increase of the gas flow rate. These findings can also be extended to the entire CZ-Si growth process. It is also demonstrated that the C contamination accumulation process in CZ-Si crystal growth can only be predicted by transient global simulation. 4. Conclusions To elucidate the C contamination and the strategies of its reduction in CZ-Si crystal growth, transient global simulations were performed with fully coupled boundary conditions of heat, flow and impurities, as well as with the introduction of two extra reactions. The contact reaction between the crucible and the susceptor is revealed as an extra source of CO generation and C contamination. It is found that
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Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Reduction of carbon contamination during the melting process of Czochralski silicon crystal growth ⁎
Xin Liu , Bing Gao, Satoshi Nakano, Koichi Kakimoto Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasuga-Koen, Kasuga 816-8580, Japan
A R T I C L E I N F O
A BS T RAC T
Communicated by Francois Dupret
Generation, incorporation, and accumulation of carbon (C) were investigated by transient global simulations of heat and mass transport during the melting process of Czochralski silicon (CZ-Si) crystal growth. Contact reaction between the quartz crucible and graphite susceptor was introduced as an extra origin of C contamination. The contribution of the contact reaction on C accumulation is affected by the back diffusion of C monoxide (CO) from the gap between the gas-guide and the crucible. The effect of the gas-guide coating on C reduction was elucidated by taking the reaction between the silicon carbide (SiC) coating and gaseous Si monoxide (SiO) into account. Application of the SiC coating on the gas-guide could effectively reduce the C contamination because of its higher thermochemical stability relative to that of graphite. Gas flow control on the back diffusion of the generated CO was examined by the parametric study of argon gas flow rate. Generation and back diffusion of CO were both effectively suppressed by the increase in the gas flow rate because of the high Péclet number of species transport. Strategies for C content reduction were discussed by analyzing the mechanisms of C accumulation process. According to the elucidated mechanisms of C accumulation, the final C content depends on the growth duration and contamination flux at the gas/melt interface.
Keywords: A1. Computer simulation A1. Impurities A1. Mass transfer A2. Czochralski method
1. Introduction Carbon (C) contamination in single crystalline silicon (Si) is detrimental for the minority carrier lifetime, which is a critical parameter of the wafers used for power devices [1]. Reduction of C contamination in the Czochralski (CZ) crystal growth is critical for the production of high-performance Si wafers. Incorporation of C from gas/melt interface occurs prior to the growth stage and sustains until the tailing stage of the crystal [2]. Accumulation of C in Si feedstock depends on the back diffusion of CO that is continuously generated from the furnace elements at high temperature [3]. To effectively reduce the C contamination, it is essential to control the generation, incorporation and accumulation of C in the CZ-Si growth process. The origins of CO generation and the relevant chemical reactions at high temperature must be identified for the development of approaches for the effective reduction of C content. In addition to CO generation by the reaction between graphite and SiO, the reaction between the quartz crucible and graphite susceptor should be considered as another CO source [4]. Silicon carbide (SiC) coating can be applied conventionally to the gas-guide above the melt surface to suppress the CO generation. Generally, the reaction between SiO and SiC has been ignored because of its low reaction rate [5]. However, C contamination in the Si
⁎
feedstock occurs even when the SiC coating is applied. Despite the lower reactivity of SiC relative to graphite, the reaction between SiC and gaseous SiO should be considered because of the short distance between the gas-guide and the Si melt. Transport phenomena of C and CO in the CZ-Si process have been studied extensively in the last decades [1–3,6–12], and it was found that Si melt and argon (Ar) gas act as impurity carriers of C, O, and related compounds such as CO and SiO. In a numerical study, Bornside et al. [8] derived the chemical model of coupled CO and SiO from the thermodynamic analysis of their reactions in the high temperature range. Based on this chemical model, Gao et al. [9] developed the coupled transport model for SiO and CO in Ar gas and for C and O in a Si melt. Recently, Vorob’ev et al. [10] reviewed the chemical models and impurity transport for global modeling of the CZ-Si crystal growth. However, the C content predicted under the quasi-static assumption does not account for C accumulation during the CZ-Si crystal growth [2]. Therefore, transient global simulations of heat and mass transport should be conducted for C accumulation in the CZ-Si crystal growth [11,12]. The present study focuses on the evolution of C contamination during the melting process of CZ-Si crystal growth. C transport during generation, incorporation, and accumulation of C during growth were
Corresponding author. E-mail address: [email protected] (X. Liu).
http://dx.doi.org/10.1016/j.jcrysgro.2016.12.013
0022-0248/ © 2016 Elsevier B.V. All rights reserved.
Please cite this article as: Liu, X., Journal of Crystal Growth (2016), http://dx.doi.org/10.1016/j.jcrysgro.2016.12.013
Journal of Crystal Growth (xxxx) xxxx–xxxx
X. Liu et al.
The configuration of the system and the computational grids for the melting process of a CZ-Si crystal growth are shown in Fig. 1(a). The furnace was divided into a number of domains and a structured mesh was generated for the solid and Si feedstock domains, whereas an unstructured mesh was applied for the Ar gas domain. Along the melt free surface, both of the gas side and melt side were generated by fine meshing to handle the boundary layer of species transport. The furnace is described in detail in Ref. [11]. The results at two locations, in the gas domain as well as in the Si domain (marked as PAr and PSi , respectively), were monitored during the transient global simulation, as shown in Fig. 1(b). 2.1. Contact reaction between quartz crucible and graphite susceptor In addition to the CO generation because of graphite etching by gaseous SiO, the contact reaction between the quartz crucible and graphite susceptor was also introduced as a new CO source [4]. When the temperature of the quartz approaches the melting point of Si (1685 K), the quartz begins to soften and deform, and because of the load of the molten Si in the crucible, the crucible comes almost entirely into close contact with the inner shape of the susceptor supporting the crucible from the outside. The contact reactions between the crucible and the susceptor are actively involved at this high temperature, with the contact reaction process shown schematically in Fig. 2. For the first use of the susceptor, SiC was deposited on the surface because of the etching of graphite by gaseous SiO. The generated SiC layer could then react with the softened crucible during the subsequent usage. The two reactions involved in this process are given by: (1) Graphite fixture surfaces: SiO(g) + 2C (s ) ↔ CO(g) + SiC (s ); (2) Crucible/susceptor contact: 2SiO2(s ) + SiC (s ) ↔ CO(g) + 3SiO(g). The Gibbs free energy for the generation of SiO and CO in the reaction (2) was computed and was found to be [14]
ΔG0 = 1, 444, 316.8 − 682.0T [J/mol].
(1)
The reaction equilibrium constant was taken as
K=
3 aSiO (g)aCO(g) 2 aSiC (s)aSiO 2 (s )
= e−ΔG0 / RT . (2)
Assuming that sufficient amounts of SiO2(s ) and SiC (s ) are present,
Fig. 1. Geometry and dimensions used to simulate the melting process of CZ-Si crystal growth. (a) Configuration and computational grids; (b) monitor locations in the gas domain and the melt domain.
investigated by transient global simulations of heat and mass transport with fully coupled boundary conditions, and accumulation of C in Si feedstock in the melting process was predicted for different conditions. Two additional origins of C contamination because of the implantation of chemical reactions on the crucible and the gas-guide were investigated, and strategies for C reduction were devised for different stages of the CZ-Si crystal growth. 2. Modeling and formulations The methodology for transient global simulation of coupled heat and mass transport during the melting process of the CZ-Si crystal growth has been reported elsewhere [11]. A virtual proportional integral derivative (PID) controller for the temperature [13] was introduced to realize power control of the heater. The coupled boundary conditions for the transport of impurities were modeled based on the chemical reactions in a CZ-Si crystal furnace.
Fig. 2. Schematic diagram of contact reaction between quartz crucible and graphite susceptor.
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the activities of the species (a ) are expressed as
aSiO2(s) = 1, aSiC (s) = cSiC (s) / cSiO2(s), aSiO(g) = aCO(g) =
PCO(g) 101, 325 Pa
PSiO(g) 101, 325 Pa
,
,
(3)
where cSiO2(s) and cSiC (s) are the molar concentrations of SiO2(s ) and SiC (s ) as estimated by their molar masses and densities, respectively. Partial pressures of SiO(g) and CO(g) follow the molar ratio given by
PSiO(g) / PCO(g) = 3.
(4)
Finally, partial pressures of SiO(g) and CO(g) can be expressed by the following equations:
PSiO(g) = 1.5286e−43, 430/ T +20.5 [atm], PCO(g) = 0.5095e
−43, 430/ T +20.5
[atm].
(5) Fig. 3. Reaction equilibrium constants between gaseous SiO and SiC coating or graphite surfaces.
(6)
Assuming a full contact and pure diffusion, the generated CO and SiO are imposed on the contact surface. A narrow gap with three layers between the crucible and the susceptor was assumed for the diffusion of SiO and CO. The generated gas was transported from the contact into the gas domain. The outlet for the products was located on the joint corner of the crucible and the susceptor. A stagnant gas was imposed in the assumed gap as well as the in the outlet. Except for the generation and outlet boundaries, zero flux conditions were imposed for the other boundaries.
pressure and Ar gas flow rate were set to 15 Torr and 10 SLPM (standard liter per minute at 273.15 K and 760 Torr), respectively.
3.1. Effect of contact reaction on CO and C contamination To address the effect of the contact reaction between the crucible and the susceptor, the melting process of the CZ-Si growth with and without the contact reaction was investigated. CO generation on the gas-guide was eliminated in order to examine the case with only contact contribution. Comparison of CO in the gas and C in the melt is shown in Fig. 4. For the case with contact reaction, the maximum CO concentration in the gas is located at the corner of the crucible and the susceptor and is 5×10−8 mol/cm3. This is an order of magnitude larger than the value obtained for the case without the contact reaction. Therefore, it is found that the contact reaction markedly increases the species (CO and SiO) concentrations in the gas. Furthermore, the generated SiO could enhance the etching of graphite elements and CO generation. These results indicate that the levels of SiO and CO in Ar gas were underestimated when the contact reaction was not considered. Back diffusion of the generated CO affects the C contamination in Si feedstock. Therefore, the final C concentration in Si melt also shows an order of magnitude increase because of the contact reaction with the maximum C concentration reaching 6×1014 atoms/cm3. This indicates that the contribution of the contact reaction to C contamination is because of the back diffusion of the generated CO. Since the entire
2.2. Reaction between SiC coating and gaseous SiO on gas-guide Because of its thermochemical stability, SiC is introduced as the coating material on the graphite elements used in CZ-Si growth. A coating with a thickness of approximately 80–100 µm can be applied on graphite surfaces by a chemical vapor deposition process. It is believed that the SiC coating acts as a diffusion and reaction barrier and helps reduce the C contamination. According to the thermochemical data, SiO in the gas domain can also react with the coated graphite according to the following equation:
SiC coating surfaces: SiO(g) + SiC (s ) ↔ CO(g) + 2Si(s ). The reaction rate could be obtained using the reaction equilibrium constant
K = PCO(g) / PSiO(g) = e−ΔG0 / RT .
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According to Ref. [14], it is found that, for the uncoated graphite surfaces, ΔG0 = 79, 224 − 1.297T Jmol−1, while for the SiC coating surfaces, ΔG0 = 71, 128 − 20.92T Jmol−1. The equilibrium reaction constants of uncoated and coated graphite are plotted in Fig. 3. Boundary conditions for CO generation on the SiC coating or the uncoated graphite surfaces can be implemented according to their different textures. Except for the above specifications, the other boundary conditions in the Ar gas and Si feedstock were as follows. A zero flux boundary condition was used for C on the crucible wall. For non-C walls and the symmetry axis in gas, zero fluxes of SiO and CO were used; for the gas inlet, the concentrations of SiO and CO were set to zero; for the gas outlet, zero gradients of SiO and CO were used. 3. Results and discussion The final C concentration in the growing CZ-Si crystal is determined by complex mechanisms. To elucidate the mechanisms of CO and C transport, transient global simulations were performed for the melting process of CZ-Si crystal growth. Thermal field, melt and gas flow, and impurity transport were predicted with fully coupled boundary conditions of heat, flow, and impurities. The reference values of furnace
Fig. 4. Effect of contact reaction on CO in gas and C in Si feedstock. Concentrations of CO and C without contact reaction (left) and concentrations of CO and C with contact reaction (right).
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Fig. 5. Effect of gap width on C incorporation for the cases without contact reaction (black) or with contact reaction (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
growth process can last more than 50 h, the contact reaction may introduce remarkable C incorporation in the Si melt and the growing crystal. Therefore, the contact between the silica crucible and the graphite susceptor is a crucial source of C contamination in the Si crystal. It is believed that back diffusion can be suppressed by a welldefined gas flow. Therefore, C incorporation because of the contact reaction can also be affected by the width of the gap between the crucible and the gas-guide. Three widths of 20 mm, 40 mm and 60 mm were investigated to determine the dependence of the contact reaction contribution on the width of the gap. Contact reaction contributions were compared for different gap widths in Fig. 5. Examination of Fig. 5 shows that the contact reaction contribution increased dramatically with increasing width of the gap. The differences between the results obtained with and without the contact reaction indicate the contributions of the back diffusion of CO for different gap widths. Since the gas velocity decreases with an increasing gap width, a narrow gap is favorable for the reduction of CO back diffusion and C incorporation caused by the contact reaction. Fig. 6. Effect of SiC coating on C incorporation. (a) Evolutions of CO concentration at the monitored location in gas during the melting process and (b) concentrations of CO and C without SiC coating (left) and with SiC coating (right).
3.2. Effect of coating reaction on CO and C contamination 3.3. Discussion of the strategies of C reduction To elucidate the effect of the SiC coating on C reduction, three cases were investigated: the case of zero generation, with SiC coating and without SiC coating. The CO concentrations above the melt surface (monitor point) for these cases were compared as a function of time, as shown in Fig. 6(a). When the coating reaction was not considered, the CO concentration at the monitor point was lower than 10−16 mol/cm3, indicating that hardly any CO could be incorporated into the Si melt as C contamination. Nevertheless, C contamination still exists at remarkable levels in the practical process with SiC coating application. Even though the reactivity of SiC is lower than that of graphite, the reaction between SiC and gaseous SiO must be taken into account because of the short distance between the gas-guide and Si feedstock. Comparison with the results for the uncoated case shows that the presence of a SiC coating can reduce the CO concentration at the monitor point by an order of magnitude, as shown in Fig. 6(a). Even slight generation of CO can be incorporated into the Si melt as C contamination. Accumulation of C in the Si melt was also investigated for the cases with and without SiC coating, as shown in Fig. 6(b). After the end of the melting process, the maximum C concentrations for the uncoated and coated cases are 9.4×1015 atoms/cm3 and 7.1×1014 atoms/cm3, respectively. Thus, the C concentration in CZ-Si growth can be effectively reduced by the application of the SiC coating.
In addition to the C found in the original feedstock, C contamination arises mainly from the gaseous CO generation in the furnace. The CO generation rate depends on the reactivity of the furnace elements, which are functions of temperature. Because of the lack of kinetic data on this heterogeneous chemical reaction, the origins of CO require further detailed examination taking the entire thermal history of the crystal growth process into account. The contact reaction between the quartz crucible and graphite susceptor obviously increases the CO content in Ar gas and the C contamination in the Si feedstock. Coatings of SiC or other substitute materials with high thermo-chemical stability could reduce the CO generation from this source. If we choose the diameter of the crucible as the characteristic length, the Péclet number for CO transport in Ar gas is generally in the range of 200–2000. This indicates that control of the gas flow control can efficiently suppress the back diffusion of CO, as discussed in Ref. [11]. Convective transport of SiO and CO becomes dominant with the increase of the gas flow rate. Much more of the generated CO in the chamber can then be pumped out together with the SiO that is also a reactant for CO generation. Because of the combination of these two positive effects, an increased flow rate can effectively reduce the C flux
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adjustment of the width of the gap between the crucible and the gasguide can affect the back diffusion of the generated CO. The reaction between the SiC coating and gaseous SiO was taken into account in order to describe the reduction of C contamination because of the application of the coating. The presence of the coating on the gas-guide has tangible benefits for the generation of CO and C incorporation into the Si feedstock. Strategies for reduction of C generation, incorporation and accumulation were summarized according to the accumulation mechanisms of C contamination. For accurate prediction of C accumulation in Si feedstock, a transient global simulation that involves the entire crystal growth process must be performed. The increase of the gas flow rate and the application of a coating with high thermochemical stability are suggested to be efficient strategies for the reduction of C contamination. Acknowledgments Fig. 7. C concentration and flux at the monitored location in the melt as functions of Ar gas flow rate.
This work was partially supported by the New Energy and Industrial Technology Development Organization (NEDO) under the Ministry of Economy, Trade and Industry (METI), Japan.
at the gas/melt interface and the final C concentration in Si feedstock, as shown in Fig. 7. Incorporation of C from the gas/melt interface proceeds from the melting stage to the tailing stage. The duration (Δt ) of the C accumulation process is about 50 h for a typical 100 kg charge in the volume (V ). The final C contamination is given by the time integration of the accumulation rate (∂cC /∂t ), which is proportional to the incorporation flux (DC ∂cC /∂x ) and the total area (S ) of the gas/melt interface. The C incorporation flux depends on the CO concentration along the gas/melt interface, which is proportional to the generation rate of CO (cCO ) and the inverse of the Péclet number (1/ Pe ). According to the definition of Pe , a higher gas flow rate results in a higher Pe value. These relationships could be expressed as
∫Δt ∫V
∂cC dVdt ∝ ∂t
∂c
∫Δt ∫S DC ∂xC dSdt ∝ ∫Δt ∫S Pe1
cCO dsdt. δ
References [1] Y. Nagai, S. Nakagawa, K. Kashima, Crystal growth of MCZ silicon with ultralow carbon concentration, J. Cryst. Growth 401 (2014) 737–739. [2] R.W. Series, K.G. Barraclough, Control of carbon in Czochralski silicon crystals, J. Cryst. Growth 63 (1983) 219–221. [3] T. Fukuda, M. Koizuka, A. Ohsawa, A Czochralski silicon growth technique which reduces carbon to the order of 1014 per cubic centimeter, J. Electrochem. Soc. 141 (1994) 2216–2220. [4] B. Gao, S. Nakano, K. Kakimoto, Influence of reaction between silica crucible and graphite susceptor on impurities of multicrystalline silicon in a unidirectional solidification furnace, J. Cryst. Growth 314 (2011) 239–245. [5] F. Schmid, C.P. Khattak, T.G. Digges, L. Kaufman, Origin of SiC impurities in silicon crystals grown from the melt in vacuum, J. Electrochem. Soc. 126 (1979) 935–938. [6] H.M. Liaw, Oxygen and carbon in Czochralski-grown silicon, Microelectron. J. 12 (1981) 33–36. [7] B.O. Kolbesen, A. Mühlbauer, Carbon in silicon: properties and impact on devices, Solid-State Electron. 25 (1982) 759–775. [8] D.E. Bornside, R.A. Brown, T. Fujiwara, H. Fujiwara, T. Kubo, The effects of gasphase convection on carbon contamination of Czochralski-grown silicon, J. Electrochem. Soc. 142 (1995) 2790–2804. [9] B. Gao, K. Kakimoto, Global simulation of coupled carbon and oxygen transport in a Czochralski furnace for silicon crystal growth, J. Cryst. Growth 312 (2010) 2972–2976. [10] A.N. Vorob’ev, A.P. Sid’ko, V.V. Kalaev, Advanced chemical model for analysis of Cz and DS Si-crystal growth, J. Cryst. Growth 386 (2014) 226–234. [11] X. Liu, B. Gao, K. Kakimoto, Numerical investigation of carbon contamination during the melting process of Czochralski silicon crystal growth, J. Cryst. Growth 417 (2015) 58–64. [12] X. Liu, B. Gao, S. Nakano, K. Kakimoto, Numerical investigation of carbon and silicon carbide contamination during the melting process of the Czochralski silicon crystal growth, Cryst. Res. Technol. 50 (2015) 458–463. [13] Y. Lee, J. Lee, S. Park, PID controller tuning for integrating and unstable processes with time delay, Chem. Eng. Sci. 55 (2000) 3481–3493. [14] M. Chase, NIST-JANAF Thermochemical Tables, 4th Edition, Journal of Physical and Chemical Reference Data Monographs, No. 9, 1998.
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In summary, C contamination can be suppressed by the decreases in the CO generation rate and the process duration, as well as by the increase of the gas flow rate. These findings can also be extended to the entire CZ-Si growth process. It is also demonstrated that the C contamination accumulation process in CZ-Si crystal growth can only be predicted by transient global simulation. 4. Conclusions To elucidate the C contamination and the strategies of its reduction in CZ-Si crystal growth, transient global simulations were performed with fully coupled boundary conditions of heat, flow and impurities, as well as with the introduction of two extra reactions. The contact reaction between the crucible and the susceptor is revealed as an extra source of CO generation and C contamination. It is found that
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