Effect of different parameters on solidification structure of multi-crystalline silicon produced by continuous casting
Introduction
Multi-crystalline silicon (mc-Si) is a major raw material of solar cells because of its relatively low cost of manufacture and high production output [1]. Currently, mc-Si is usually produced by casting based on a conventional directional growth method [2]. In this method, massive ingots can be cast in large crucibles and solidified under carefully controlled conditions. However, the solidification rate is usually low and the crucible consumption is obvious. Furthermore, segregation in ingots leads to the difference in quality of solar cells. Therefore, the first few centimeters of the ingot bottom which contacts the crucible and few centimeters of the ingot top must be given up [3].
In order to overcome these disadvantages, in 1985, T.F. Ciszek performed a vertical continuous casting of a 25 × 25 mm2 cross sectional billet at a casting speed of 2.5 mm/min using a technology of continuous melting and casting of cold crucible [4]. Photovoltaic mc-Si billets were produced by K. Kyojiro’s group using the technology. A round cross sectional billet of 30 mm diameter was firstly produced. Then the square cross sectional billets with the dimensions of 220 mm side and of 350 mm side were produced. The billets were withdrawn at a casting speed from 1 to 3 mm/min [5]. Dour et al. applied the technology to photovoltaic silicon billets. The billets with different cross sections were obtained: initially the round ones, 100 and 120 mm diameters, then the square ones, 60 × 60 and 130 × 130 mm2. The casting speed was usually 1 mm/min, up to 3 mm/min [6]. Huang et al. initially produced a mc-Si billet with round cross section of 30 mm diameter. Then they improved their experimental apparatus and produced a mc-Si billet with square cross section of 60 × 60 mm2 [7], [8]. The casting speed was from 0.5 to 1.5 mm/min [9]. Kim et al. also applied the technology to produce a mc-Si billet with round cross section of 50 mm diameter at a casting speed of approximately 1.5 mm/min [10]. Although a mc-Si billet can be cast continuously with reducing crucible consumption and improving the material utilization by the technology, the casting speed is still low. The grain sizes of the vertically grown grains used to make cells are about 1–5 mm in diameter by this technology. They are sufficiently large for the purpose of use [11], [12]. However, the conversion efficiency of silicon billet obtained by this technology is lower than that of conventional ingot silicon (grain sizes are about 5–20 mm in diameter) [13]. Therefore, it is necessary to develop a manufacturing process of solar mc-Si billets, to reduce manufacturing cost of solar cells and increase the grain sizes of vertically grown grains. In order to improve the situation, a continuous casting apparatus of mc-Si has been designed firstly in our research.
Conversion efficiency of solar cells is mainly determined by minority carrier lifetime [14]. The increase of the lifetime can improve the conversion efficiency, and vice versa. Grain boundary may become recombination center of the minority carrier, leading to the decrease of the minority carrier lifetime. However, the grain boundary has little effect on the conversion efficiency when it is perpendicular to growth interface [15]. Therefore, the conversion efficiency of solar cells is significantly affected by grain size and orientation, and then the grain evolution is an important factor to consider during solidification of mc-Si continuous casting [16]. It is thus important to understand how the parameters affect solidification structure of a billet. However, it is very expensive to do experimental research on mc-Si solidification, especially on a large scale. Therefore, a simulation method was used to study the solidification structure of a mc-Si billet produced with different parameters.
In order to improve the casting speed and control the grain evolution, this paper presents a continuous casting experimental apparatus and numerical simulation based on the commercial software ProCAST, aiming to compute the solidification structure of a mc-Si billet with different parameters.
Section snippets
Mathematical model
A mathematical model combining the cellular automaton method with the heat transfer calculation was used to simulate solidification structure. The model mainly includes macroscopic and microscopic models.
Initial condition
Initial condition is supposed to be the pouring or casting temperature (Tcast) of mc-Si, as shown in Eq. (9).where T0 is a temperature constant (K) at t = 0 s.
Boundary conditions
Boundary conditions of mc-Si in the mold and on the bottom block are expressed by Eqs. (9), (10), respectively.where n is the heat flux direction, hm is the interfacial heat transfer coefficient between the mc-Si and the mold (W/m2/K), and Tm is the mold temperature (K).where hb is the interfacial heat
Experimental procedure
In this experiment, a continuous casting apparatus devised by ourselves was used, as shown in Fig. 1. The apparatus was composed of heating system, driving system, copper mold, copper bottom block and holder. Mc-Si was melted in a graphite crucible by induction heating (heating system). It was poured into the copper mold when the temperature was 1500 °C. Since the copper mold and the copper bottom block were both water-cooled, the melt was solidified soon. Then the driving system was started,
Mathematical model validation
In order to validate the mathematical model, the solidification structure of longitudinal section of mc-Si billet was etched by 20% NaOH at 80 °C for 20 min [8]. In addition to the diameter (0.1 m) of billet, the entire dimension of the computational domain of solidification structure in casting direction is 0.1 m. In order to simplify the numerical model, some assumptions are made as follows. Without consideration of the effect of flow, casting is filled with molten mc-Si instantaneously.
Results and discussion
In order to study the effect of different parameters on the solidification structure easily, constant heat transfer coefficients for boundary condition are assumed during the simulation. The heat transfer coefficient at mc-Si/mold interface is 1000 W/m2/K, the heat transfer coefficient at mc-Si/bottom block interface is 3000 W/m2/K and the convective heat transfer coefficient in the air cooling zone is 100 W/m2/K.
Conclusions
A mathematical model combining the cellular automaton method with the heat transfer calculation has been developed to understand the solidification structure of a mc-Si billet produced by continuous casting. The simulation results were validated by the experimental results. In order to obtain the evolution of the solidification structure with different parameters, a series of simulations were carried out by the model. From the present study, the following conclusions can be obtained:
- (1)
The
Acknowledgements
The authors are grateful to the financial support of the National Key Research and Development Program of China (2016YFB0701204), the National High-tech Research and Development Program of China (2015AA042502), and the technical support of the Key Laboratory for Solar Energy Photovoltaic System of Liaoning Province.
Conflict of interest
The authors declare there is no conflict of interest.
References (35)
- et al.
Continuous solidification of photovoltaic multicrystalline silicon from an inductive cold crucible
J. Cryst. Growth
(1998) - et al.
Hydrogen passivation of newly developed EMC-multi-crystalline silicon
Mater. Sci. Eng. B
(1999) - et al.
Experimental study on surface quality of silicon ingots prepared by electromagnetic continuous casting
Mat. Sci. Semicon. Proc.
(2012) - et al.
Feasibility of directional solidification of silicon ingot by electromagnetic casting
Mat. Sci. Semicon. Proc.
(2012) Electromagnetic continuous pulling process compared to current casting processes with respect to solidification characteristics
Sol. Energy Mat. Sol. C
(2002)- et al.
Multicrystalline silicon for solar cells
Thin Solid Films
(2005) - et al.
Grain growth of silicon
Acta Mater.
(2012) - et al.
Probabilistic modeling of microstructure formation in solidification processes
Acta Metal. Mater.
(1993) - et al.
Theory of microstructural development during rapid solidification
Acta Metall.
(1986) - et al.
Solidification structure of continuous casting large round billets under mold electromagnetic stirring
J. Iron Steel Res. Int.
(2016)