Directional Solidification Of Multicrystalline Silicon Research Articles

Analysis of the Effect of a Vertical Magnetic Field on Melt Convection and Oxygen Transport During Directional Solidification of Multi-Crystalline Silicon by Numerical Simulation

Melt convection during the directional solidification process of multi-crystalline silicon plays a critical role in the transport of impurities. The utilization of a static magnetic field is an effective way to control the melt convection pattern. Studying the effect of the Lorentz force induced by the vertical magnetic field (VMF) on the melt convection of silicon in detail is beneficial to optimize the magnetic field parameters in the production process. Based on the numerical simulation method of multi-physics coupling, this paper explores the effects of different VMF intensities on the convection of silicon melt and the transport of oxygen in the melt during the directional solidification of polycrystalline silicon. The results show that in the first 125 minutes of the crystallization stage, the melt convection velocity is affected significantly by the magnetic field intensities. When different convection circulations are present in the silicon melt, the upper circulation easily transports oxygen to the furnace atmosphere, and the subjacent circulation easily lead to the retention and accumulation of oxygen. Enhancing the VMF intensity to a certain extent can reduce the size of the oxygen retention region in the silicon melt, and the time of the first disappearance of the subjacent circulation near the sidewall of the crucible is shortened. Then the average oxygen concentration in the silicon melt can be reduced. However, a larger vertical magnetic field intensity can result in greater average oxygen concentration in the oxygen retention region.

Numerical modeling of carbon distribution and precipitation during directional solidification of photovoltaic silicon

Numerical modeling is used to investigate carbon distribution and precipitation in directional solidification of multicrystalline silicon. Computations are performed for samples of 6 cm in diameter grown in a Vertical Bridgman Freezing (VGF) system starting from silicon feedstock with different grades of contamination in carbon. The value of the unknown reaction rate coefficient governing the carbon precipitation in the silicon melt was estimated in the present work by comparing the numerically computed concentration profiles to the experimental results taken from the literature. Numerical results show that the growth rate has a significant influence on the interface deflection, melt convection and carbon precipitation. It is found that the silicon samples grown from the melts of low carbon contamination (<1018at/cm3) exhibit low content in SiC precipitates, even if they are solidified at high growth rates (1–2 cm/h). The samples with high initial carbon contamination (5·1018at/cm3) should be solidified at much lower rates (0.2 cm/h) in order to avoid the formation of SiC precipitates.

Optimizing oxygen impurities using different heater design in the directional solidification of multi-crystalline silicon

The numerical simulations of heat and mass transport have been carried out. The heater design has been modified. The melt convection and oxygen impurities have been analysed. The simulation has been made for conventional and modified heater design using directional solidification (DS) furnace. The results were compared and the better heater design was used to control the oxygen impurities in the mc-Silicon ingot. The reduced melt convection is obtained in the silicon melt due to the modified heater design. The modified heater design reduces the oxygen impurities in the melt and crystal. The modified heater design improves the melt-crystal (m-c) interface. It gives less concave interface shape in the periphery region near the crucible wall. The m-c interface is mainly affected by flow pattern and melt convection. The numerical results are very useful for better understanding of thermal effect and melt convection in the directional solidification system for reduction of oxygen impurities in the mc-Silicon ingots.

Influence of interfacial structure on propagating direction of small-angle grain boundaries during directional solidification of multicrystalline silicon

Small-angle grain boundary (SAGB) growth in multicrystalline Si was observed in situ during directional solidification, and the misorientation and boundary structure were analyzed by electron backscatter diffraction and high-resolution transmission electron microscopy. It was found that SAGBs change their orientation in order to reduce the number of grain boundary dislocations and thus the energy. This suggests that grain boundary dislocations have an influence on SAGB behavior during solidification.

Three-dimensional phase field modelling of twin nucleation during directional solidification of multi-crystalline silicon

The development of grain structures during directional solidification of multi-crystalline silicon (mc-Si) plays a crucial role in the materials quality for silicon solar cells. Three dimensional (3D) modelling of the grain boundary (GB) interaction and evolution based on phase fields by considering anisotropic GB energy and mobility for mc-Si has been developed recently. Here, we further consider twin nucleation at the tri-junction groove for the simulation. To compare with the experimental results, the initial seed orientations are described by the Euler angles. With the previous developed twinning model at the three-grain tri-junction and the T matrix for twinning, the simulated grain orientation and the resulted GB types are consistent with the experiments.

Heterogeneous twinning during directional solidification of multi-crystalline silicon

Heterogeneous twinning nucleation from the wall or gas interface during directional solidification of silicon have been modelled, and further used to clarify the details of twining observed in situ in X-ray synchrotron imaging experiments (Tsoutsouva et al., 2016). It is found that the heterogeneous twinning from the wall/grains or wall/gas/grain trijunctions requires much lower undercoolings leading to much higher twinning probability. The lower attachment energy and the contact area are the key factors for the heterogeneous nucleation of twins.

Origin of small-angle grain boundaries during directional solidification in multicrystalline silicon

The formation of small-angle grain boundaries (SAGBs) during directional solidification of multicrystalline silicon was directly observed in situ. SAGBs were confirmed by preferential etching due to the aggregation of dislocations at the solid/melt interface. Dislocations self-arrange by polygonization into an energetically favorable SAGB configuration. The misorientation of the SAGBs increases during crystal growth, possibly through the continual incorporation of dislocations. The present results suggest that there is considerable dislocation motion at the solid/melt interface and polygonization can occur during solidification.

Possible Twinning Operations during Directional Solidification of Multicrystalline Silicon

Twinning is an important phenomenon during crystal growth of multicrystalline silicon. During twinning, the nucleated new grain is in twin relation with the parent grain, and the twin relation math...

Three dimensional modelling of grain boundary interaction and evolution during directional solidification of multi-crystalline silicon

The development of grain structures during directional solidification of multi-crystalline silicon (mc-Si) plays a crucial role in the materials quality for silicon solar cells. Three dimensional (3D) modelling of the grain boundary (GB) interaction and evolution based on phase fields by considering anisotropic GB energy and mobility for mc-Si is carried out for the first time to elucidate the process. The energy and mobility of GBs are allowed to depend on misorientation and the GB plane. To examine the correctness of our method, the known the coincident site lattice (CSL) combinations such as (∑a+∑b→∑a×b) or (∑a+∑b→∑a/b) are verified. We frther discuss how to use the GB normal to characterize a ∑3 twin GB into a tilt or a twist one, and show the interaction between tilt and twist ∑3 twin GBs. Two experimental scenarios are considered for comparison and the results are in good agreement with the experiments as well as the theoretical predictions.

Cellular Automaton Modeling of the Transition of Multi-Crystalline Silicon from a Planar Faceted Front to Equiaxed Growth

A modeling approach combining the lattice Boltzmann (LB) method and the cellular automaton (CA) technique are developed to simulate the faceted front to equiaxed structure transition (FET) of directional solidification of multi-crystalline silicon. The LB method is used for the coupled calculation of velocity, temperature and solute content field, while the CA method is used to compute the nucleation at the silicon-crucible interface and on SiC particles, as well as the mechanism of growth and capturing. For silicon, the interface kinetic coefficient is rather low, which means that the kinetic undercooling can be large. A strong anisotropy in the surface tension and interfacial kinetics are considered in the model. A faceted front in conjunction with a sufficiently high carbon content can lead to equiaxed growth by nucleation on SiC. The temperature gradient in Si melt at the interface is negative, which leads to the occurrence of a faceted interface. The higher the absolute value of thermal gradients, the faster the growth velocity. Due to differences in the degree of undercooling, there will be the unification of facets in front of the solid-liquid interface. Transitions from faceted front to thermal equiaxed dendrites or faceted equiaxed grains are observed with smaller or larger impurity contents, respectively.

Twinning mechanism at three-grain tri-junction during directional solidification of multi-crystalline silicon

We propose a model to explain the formation mechanism of twin grains at the three-grain tri-junction (3GTJ) on the growth interface during directional solidification of multi-crystalline silicon. We also attempt to confirm its validity by comparing with the experimental results. This model is an extension of the previous model for the two-dimensional (2D) nucleation at the grain boundaries (GBs). It is found that the energy barriers for faceting and twinning nucleus at the 3GTJ are much smaller than that at GBs. As a result, a higher twinning probability can be obtained at a much lower undercooling. Two types of tri-junctions are considered according to the experiments and the dominant factors which decide the twinning probability on each facet at the 3GTJ are further discussed.

A multilayer nucleation model for twinning during directional solidification of multi-crystalline silicon

Twin nucleation is an important phenomenon in the directional solidification of photovoltaic multi-crystalline silicon. Unfortunately, the models proposed so far were not sufficient to explain the small undercooling (<1K) for twinning observed in the experiments. In this paper, we propose a multilayer nucleation mechanism for twinning during silicon directional solidification. When the nucleus contains more than one layer, the free energy of formation for the nucleus can be reduced. Asa result, the critical radius decreases and the twinning probability increases. The required undercooling for twinning based on the present model could be reduced to around 0.4–0.6K, which is much more consistent with the experimental observations.

Investigation of dislocation cluster evolution during directional solidification of multicrystalline silicon

Dislocation clusters are the main crystal defects in multicrystalline silicon and are detrimental for solar cell efficiency. They were formed during the silicon ingot casting due to the relaxation of strain energy. The evolution of the dislocation clusters was studied by means of automated analysing tools of the standard wafer and cell production giving information about the cluster development as a function of the ingot height. Due to the observation of the whole wafer surface the point of view is of macroscopic nature. It was found that the dislocations tend to build clusters of high density which usually expand in diameter as a function of ingot height. According to their structure the dislocation clusters can be divided into light and dense clusters. The appearance of both types shows a clear dependence on the orientation of the grain growth direction. Additionally, a process of annihilation of dislocation clusters during the crystallization has been observed. To complement the macroscopic description, the dislocation clusters were also investigates by TEM. It is shown that the dislocations within the subgrain boundaries are closely arranged. Distances of 40–30nm were found. These results lead to the conclusion that the dislocation density within the cluster structure is impossible to quantify by means of etch pit counting.

A thermodynamic model for the formation of bubble defects in multicrystalline silicon ingot

Preparation of multicrystalline silicon for solar cells is significant to photovoltaic industry. Up to now, the formation of bubble defects during directional solidification of multicrystalline silicon has not been explored clearly. In the present experiment, spherical bubble defects distributed randomly at ingot top, and the surface of bubble defects was covered with SiC or Si3N4 particle. A thermodynamic model was proposed to illustrate the formation of bubble defects. Bubble defects were caused by gaseous SiO in silicon melt. SiO was the reaction product of melt silicon and oxygen. Oxygen was dissolved by quartz crucible, diffusing through broken Si3N4 coatings into silicon melt. Gaseous SiO in the silicon melt nucleated and grew into bubbles against insoluble particles, such as SiC and Si3N4, and finally enveloped in solid silicon, producing bubble defects. According to the principle of thermodynamics, the formation process was discussed in detail.

The effect of holding time on the size distribution of β‐Si3N4 particles and nucleation undercooling in multicrystalline silicon

AbstractThe nucleation mechanism for directional solidification of multicrystalline silicon (mc‐Si) in silicon nitride (Si3N4) coated crucibles has been investigated. A combination of thermal and particle size analysis was used to show that the nucleation undercooling was inversely proportional to the particles size. The particle size was increased by keeping the silicon melted for increasing time periods and the growing particles were identified as β‐Si3N4. The results from the particle analysis were verified by topographical studies using scanning electron microscopy (SEM). These results indicate that β‐Si3N4 particles are the dominant nucleation substrates for mc‐Si in Si3N4 coated crucibles. (© 2016 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

The effect of heating power on impurity formation and transport during the holding phase in a Bridgman furnace for directional solidification of multi-crystalline silicon

Oxygen and carbon are the most common impurities in multi-crystalline silicon. The general mechanism for formation and transport of O and C in the solidification furnace is as follows: oxygen from the silica crucible comes into the melt and combines with a silicon atom and evaporates at the gas/melt interface in the form of silicon oxide (SiO). Argon inert gas, injected into the furnace chamber, carries the SiO to the hot graphite fixtures, where it reacts with carbon to form carbon monoxide (CO) and silicon carbide (SiC). CO is carried by the gas to the melt free surface, where it dissociates into carbon and oxygen. Finally, during solidification oxygen and carbon are incorporated into the crystal. A global furnace model accounting for heat transfer, melt flow, gas flow and impurity transport has been applied to investigate the oxygen and carbon formation and transport in a vertical Bridgman furnace during the holding phase when the furnace is at its hottest. A case study is performed to investigate the effect of the applied heating power on the carbon and oxygen concentrations in the melt prior to solidification.

Influence of Mechanical Stirring on the Crucible Dissolution Rate and Impurities Distribution in Directional Solidification of Multicrystalline Silicon

Abstract In this study, time dependent three-dimensional numerical simulations were carried out using the STHAMAS3D software in order to understand the effects of forced convection induced by mechanical stirring of the melt, on the crucible dissolution rate and on the impurities distribution in multicrystalline silicon (mc-Si) melt for different values of the diffusion coefficient. Numerical simulations were performed on a pilot scale furnace with crucible dimensions of 38x38x40cm3. The computational domain used for the local 3D-simulations consists of melt and crystal. The dissolution rate was estimated from the total mass of impurities that was found in the silicon melt after a certain period of time. The obtained results show that enhanced convection produced by a mechanical stirrer leads to a significant increase of the dissolution rate and also to a uniform distribution of impurities in the melt.

A novel method for gas flow and impurity control in directional solidification of multi-crystalline silicon

In this paper the potential of a specially designed argon gas injector for controlling the gas flow and transport of impurities in directional solidification of multi-crystalline silicon is evaluated. The gas injector which consists of a valve allows one to control the flow direction independently in the vertical and horizontal directions. Based on a gas flow model derived from a semi-industrial crystallization furnace the impact of different gas injection combinations on the gas flow pattern and impurity transport is studied. Special focus is given to the SiO evacuation from the melt-free surface, the CO formation at graphite surfaces and the CO evacuation from the furnace interior. It is found that for gas flow pattern formed through horizontal rather than vertical gas injection, SiO and CO are evacuated most effectively from the furnace interior and the formation of CO is inhibited. Such a type of gas injector presents a versatile tool for controlling the flow and impurity transport in the gas phase and possibly improving the material properties of crystalline silicon.

Improvement of multi-crystalline silicon ingot growth by using diffusion barriers

The control of impurity is crucial to the ingot quality and yield in the directional solidification of multi-crystalline silicon for solar cells. The major impurities, such as metals, are mainly from the quartz crucible and the silicon nitride coating. The use of high-purity materials mitigates the problem, but it also increases the cost. Another way is to use diffusion barriers between silicon and these materials to reduce the incorporation of impurities. In this study, polysilazane and barium oxide coatings with different layer configurations were considered. With the diffusion barrier layer, the lifetime of the ingot was improved and the red zone was reduced. The wetting behaviors of these diffusion barriers in contact with silicon were also discussed.

Numerical parameter studies of 3D melt flow and interface shape for directional solidification of silicon in a traveling magnetic field

The role of various growth and process conditions (Lorentz force, temperature gradients in the melt and the crystal, steady-state crystallization velocity) in directional solidification of multicrystalline silicon in a traveling magnetic field is analyzed for a research-scale furnace (melt size of 22×22×11cm3). The influence on the melt flow pattern, the typical melt flow velocity, the oscillation amplitude of the velocity and the temperature, the shape of the crystallization interface is determined using three-dimensional (3D) numerical calculations with the STHAMAS3D software and a local quasi steady-state model. It was found that both the interface shape and the melt flow are sensitive to the variation of the considered growth and process parameters.