Directional Solidification Of Silicon Research Articles

In situ observation and numerical analysis of temperature gradient effects on growth velocity during directional solidification of silicon

AbstractThe < 110 > directional solidification of silicon under varying overall temperature gradients was investigated using an in situ observation system. The growth velocity of an atomically rough interface was found to decrease with increasing temperature gradient. A theoretical model of the thermal field taking undercooling into account was developed to describe this phenomenon and was demonstrated to be valid. The results of this work indicate that the reported linear relationship between growth velocity (V) and undercooling (ΔT), given by V (mm s−1) = 120ΔT (K), is most accurate in the case of a rough interface. In the case that the overall temperature gradient is small, the melting point isotherm moves rapidly such that it becomes more difficult for the interface to keep pace with the isotherm compared with a large temperature gradient. This effect leads to increased undercooling at the interface and consequently a rapid growth velocity. Thermal field calculations confirm that a rapid increase in the ratio of the temperature gradient in the crystal to that in the melt should increase the latent heat release, again providing a more rapid growth velocity.

Misorientation increase of small-angle grain boundaries during directional solidification of silicon

In situ observation of the solidification process of Si combined with ex situ characterization revealed that small-angle grain boundaries (SAGBs) increase misorientation through two paths. First, coalescence with other SAGBs leads to a boost in misorientation and SAGBs tend to coalesce during solidification. Second, the absorption of individual lattice dislocations also increases the misorientation of an SAGB. Three possible mechanisms behind dislocation absorption by SAGBs have been proposed and are discussed in this paper. Among these mechanisms, the incorporation of same-sign lattice dislocations is regarded as the prominent mechanism when misorientation increases during solidification.

Interplay between facetting and confinement in directional solidification of silicon: A direct comparison between experiments and phase-field simulations

We combine the analysis of experiments based on in situ X-ray imaging and phase-field simulations to get insight into the interplay between faceting and confinement effects in thin silicon samples during directional solidification from a monocrystalline seed. The phase-field model is parametrized by available experimental results, especially regarding the anisotropy functions for the surface energy and for the kinetic attachment coefficient. In the present work, a method is proposed to extrapolate 2D fully quantitative simulations results to 3D thin sample geometry. Two simple seed orientations along the 〈110〉 and 〈100〉 crystal directions are considered. For 〈110〉 direction, it is shown that confinement effects are weak so 2D simulations can be readily compared to the experiments. For 〈100〉 direction, much stronger confinement effects are identified and characterized by a confinement factor that is estimated from phase-field simulations of thin 3D systems. For both directions, the length of the side facets is shown to increase with the solidification velocity and an analytical expression including the confinement factor is obtained for the law relating both quantities. A very quantitative experiment-simulation agreement is obtained in each case.

Adjustment of resistivity for phosphorus-doped n-type multicrystalline silicon

In this work we present a novel approach to reduce inhomogeneity of resistivity for n-type phosphorus-doped directionally solidified silicon ingots by using complex arrangements on influencing dopant transport during growth process, which involves adjustments of melt flow and gas transport. In order to obtain more uniform resistivity profile over ingot's height, different process conditions were tested on G1-sized (22 × 22 × 12 cm 3 ) n-type directionally solidified ingots, including altering of ambient gas pressure, enhanced melt mixing with travelling magnetic fields and variations of argon flow above the melt. The quality of ingots was characterised in terms of electrical resistivity and minority carrier lifetime, as well as the presence of impurities and inclusions. The influence of process parameters on material quality will be discussed. It will be shown that a complex approach to melt stirring and gas transport is an effective way to control resistivity distribution along the height of phosphorus-doped multicrystalline ingots, which makes it possible to provide n-type ingots with resistivity profiles comparable to p-type boron-doped ones. • The mechanisms of phosphorus transport during directional solidification of silicon is investigated. • Process parameters influencing phosphorus transport in G1-size system are defined. • An optimized growth recipe, which ensures more uniform resistivity distribution along the ingot length, is developed. • A multicrystalline ingot showing 45% narrower resistivity variation and high material quality is grown.

3D numerical simulation with experimental validation of a traveling magnetic field stirring generated by a Bitter coil for silicon directional solidification process

Silicon is the most widely used raw material in photovoltaic industry; however, the quality of the silicon photovoltaic solar cells depends on the quality of the raw material (i.e. metallurgical silicon or poly-silicon) and the solidification methods used for the production of the silicon ingot from which the solar cells are produced. This study is related to how improve the quality of the final ingot in the directional solidification process; it is necessary to control the impurity segregation of silicon raw material during the processing. This control can be accomplished by adding an electromagnetic Bitter coil which can generate an external traveling magnetic field (TMF) stirring to control the hydrodynamic flow of silicon melt during the solidification process without contaminating it. To carry out this study, we used a Bridgman vertical directional solidification furnace, equipped with a cylindrical Bitter coil stirrer used in order to have the control of the silicon melt convection on the principal parameters of the solidification process, such as the growth rate, the thermal gradient and the natural convection of silicon melt. For the electromagnetic, heat exchange and silicon melt flow modelling, we used 3D numerical Multiphysics coupled models. Parallel to the numerical results we carried out experimental investigations relating to the characterization of the electromagnetic parameters. This study shows a promising effect of the applied traveling magnetic field on the final ingot quality; indeed, we have the ability to control the silicon melt flow which can affect the thermal configuration, the solidification interface shape and the segregation of impurities by changing the electric current input configuration of the Bitter coil stirrer.

Propagation of Crystal Defects during Directional Solidification of Silicon via Induction of Functional Defects

The introduction of directional solidified cast mono silicon promised a combination of the cheaper production via a casting process with monocrystalline material quality, but has been struggling with high concentration of structural defects. The SMART approach uses functional defects to maintain the monocrystalline structure with low dislocation densities. In this work, the feasibility of the SMART approach is shown for larger ingots. A G2 sized crystal with SMART and cast mono silicon parts has been analyzed regarding the structural defects via optical analysis, crystal orientation, and etch pit measurements. Photoluminescence measurements on passivated and processed samples were used for characterization of the electrical material quality. The SMART approach has successfully resulted in a crystal with mono area share over 90% and a confinement of dislocation structures in the functional defect region over the whole ingot height compared to a mono area share of down to 50% and extending dislocation tangles in the standard cast mono Si. Cellular structures in photoluminescence measurements could be attributed to cellular dislocation patterns. The SMART Si material showed very high and most homogeneous lifetime values enabling solar cell efficiencies up to 23.3%.

Numerical Study of the Upgraded Hot Zone in Silicon Directional Solidification Process

Abstract2D global transient model for generation‐six (G6) GT‐style furnace and upgraded generation‐seven (G7) ALD‐style furnace in which all types of heat transfer and flow are included is established to investigate the thermal field, melt convection, melt–crystal (m–c) interface shape, thermal stress, growth rate, and Voronkov ratios in the growing silicon ingot. The modeling is verified by the heater power and temperature experiment. Simulation results show that the melt flow is relatively stronger as the furnace upgrades. For G7, a relatively higher thermal stress and growth rate are found due to the higher temperature gradient both in the horizontal and axial directions. Furthermore, unlike the optimized G6, G7 shows the overly convex m–c interface in the initial stage and edge nucleation throughout crystal growth stage.

Effect of calcium addition on the silicon purification in the presence of low concentration of iron

In this research, the efficiency of Si-Ca system for B and P removal from the silicon was initially evaluated during furnace cooling. In the second step, 5 to 25 wt% Ca was added to Si-5 wt.% Fe system and the removal of boron and phosphorus from the solidified silicon were studied. Results showed that the removal of B and P increased by adding more Ca. For 25 wt% Ca, ∼89% of P alongside ∼48% B were removed. These removal rates were about 75% for P and 30% for B better than those that could be obtained by directional solidification of silicon. P removal was not increased to more than 88–90% by increasing the phosphorus concentration of the initial mixture. However, higher boron concentration of the initial mixture caused higher B removal as a result of a new Ca-B compound formation. Presence of about 5 wt% Fe was slightly effective in gathering calcium and decreased its content in the purified silicon. Furthermore, a slight improvement in boron removal just in samples with lower amounts of calcium was observed. Among the samples in this study, the least concentration of iron in the purified silicon was obtained when the overall composition of the initial mixture was nearest the ternary eutectic point of the Si-Fe-Ca system.

Numerical Simulation on Design of Temperature Control for Side Heater in Directional Solidification System of Multi-Crystalline Silicon

In this paper, the transient numerical simulation was used to study the effects of temperature variation in three ways (the open downward parabola, the straight line and the open upward parabola) of side heater in multi-crystalline silicon directional solidification system during solidification period. The melt-crystal (m/c) interface, thermal field and thermal stress during directional solidification of polysilicon have been simulated. The results show that in the process of solidification, compared with the open downward parabola and straight line temperature variation, the temperature change of the side heater depends on the open upward parabola can better control the horizontal and vertical temperature difference in polysilicon, making the deflection of m/c interfaces smaller. Smaller thermal stress distribution can be obtained from the middle stage to the end of solidification while temperature change of side heater according to upward parabola, which is beneficial to improve the quality of polysilicon ingots.

Strain building and correlation with grain nucleation during silicon growth

This work is dedicated to the grain structure formation in silicon ingots with a particular focus on the crystal structure strain building and its implication in new grain nucleation process. The implied mechanisms are investigated by advanced in situ X-ray imaging techniques during silicon directional solidification. It is shown that the grain structure formation is mainly driven by Σ3 <111> twin nucleation. Grain competition phenomena occurring during the growth process lead to the creation of higher order twin boundaries, localised strained areas and associated crystal structure deformation. On the one hand, it is demonstrated that local strain building can be directly related to the characteristics of the twin boundaries created during silicon growth due to grain competition. On the other hand, space restriction due to competition during growth can be at the origin of local strain building as well. Finally, the accumulation of all these factors generating strain is responsible for spontaneous new grain nucleation. When occurring, both grain nucleation and subsequent grain structure reorganisation contribute to lower the strain in the growing ingot. It is demonstrated as well that the local distribution of the strained areas created during silicon growth is retrieved after cooling down, from melting temperature to room temperature, on top of an additional larger scale deformation of the sample due to the cooling down only.

Simulation of grain evolution in solidification of silicon on meso-scopic scale

We present a cellular automata model for computing the grain evolution during directional solidification of silicon on a meso-scopic scale. Firstly, the method is applied to test cases with different shapes of the melt/crystal interface. In a second step we compute the case of an experiment with in-situ observation of the interface shape evolution (Tandjaoui et al., 2012). Here we also include the effect of twinning. The interchanging appearance of two twins could be revisited by our calculations. The probabilities used correspond to those which were analytically derived for an undercooling of ΔT=0.6K (Lin and Lan, 2017). This undercooling is a typical value for a groove with 〈111〉 facets (Miller and Popescu, 2017).

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.

Mathematical Modeling of Solid-Liquid Interface Morphology in The Process of Polycrystalline Silicon Directional Solidification

Mathematical Modeling of Solid-Liquid Interface Morphology in The Process of Polycrystalline Silicon Directional Solidification

Modelling analysis and experiments of polycrystalline silicon directional solidification in an annular heating field

Abstract As a solution to the low convection strength of the Bridgman method and the convection control difficulties of the electromagnetic induction melting method, a novel, large directional solidification device with annular heaters arranged above the crucible is designed. The inhomogeneous heating field causes differences in melt density, intensifies controllable natural convection and accelerates the moving of impurities from the solid–liquid interface to the surface of the melt, thereby improving purification efficiency and reducing energy consumption. Although the temperature field is inhomogeneous, vertical crystal growth can still be achieved. Mathematical analytic modelling is used to explain the principle, and the feasibility is verified by experiments. The results show that high-quality and large bulk silicon ingot (1 m × 1 m × 0.45 m) can be produced at an average solidification rate of 3.68 μm s−1.

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.

Engulfment and pushing of Si3N4 and SiC particles during directional solidification of silicon under microgravity conditions

In this work, crystal growth experiments concerning particle incorporation behavior of SiC and Si3N4 particles in silicon melt growth were carried out on earth as well as under microgravity conditions. The experimental results are compared to calculations based on very simple theoretical models. It can be concluded that the critical growth velocity for the capture of particles with given size differs between SiC and Si3N4 particles because the thermal conductivity and interfacial energy of SiC and Si3N4 are different. Furthermore it seems that the lift force which pushes the particles away from the solid-liquid interface due to melt flow, might act only on larger particles. This could result in higher critical growth velocities under convective conditions.

Determination of impurity distributions in ingots of solar grade silicon by neutron activation analysis

AbstractIn a series of crystallization experiments, the directional solidification of silicon was investigated as a low cost path for the production of silicon wafers for solar cells. Instrumental neutron activation analysis was employed to measure the influence of different crystallization parameters on the distribution of 3d-metal impurities of the produced ingots. A theoretical model describing the involved diffusion and segregation processes during the solidification and cooling of the ingots could be verified by the experimental results. By successive etching of the samples after the irradiation, it could be shown that a layer of at least 60 μm of the samples has to be removed to get real bulk concentrations.

Numerical study of the influence of forced melt convection on the impurities transport in a silicon directional solidification process

Time dependent three-dimensional numerical simulations were carried out in order to understand the effects of forced convection induced by electromagnetic stirring of the melt, on the crucible dissolution rate and on the impurity distribution in multicrystalline silicon (mc-Si) melt for different values of the diffusion coefficient and electric and magnetic field parameters.Once the electromagnetic stirring is switched on, in a relative short period of time approx. 400s the impurities are almost homogenized in the whole melt. 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 the electromagnetic stirring leads to a moderate increase of the dissolution rate and also to a uniform distribution of impurities in the melt.

Interaction of SiC particles with moving solid–liquid interface during directional solidification of silicon

In this work, the interaction of SiC particles, having sizes of 7µm to 300µm, with the moving solid–liquid interface during directional solidification of silicon was experimentally and theoretically investigated. This included both convective and nearly diffusive conditions. In the nearly diffusive regime under microgravity, the particles were incorporated at a lower growth velocity than in the convective regime under 1g conditions. The experimental data were compared to simple theoretical models allowing the calculation of the critical growth velocity for the incorporation of spherical particles in dependence of the particle size. It was found that the theoretical results could qualitatively explain the experimental observations when a proper set of equations for the forces acting on the particle and of the material constants are chosen. It can be concluded that sedimentation of the particles due to gravity seems to play a role only for large particles. On the other hand, melt flow might cause a lift force which would push the particles away from the solid–liquid interface, and thus would result in higher critical growth velocities under convective conditions, e.g. due to buoyancy convection. Therefore, a contribution of the missing lift force under µg conditions could lead to the smaller critical growth velocity for particle incorporation that is observed under microgravity.

Phase-field simulations of particle capture during the directional solidification of silicon

We present a phase-field model for particle capture during directional solidification. Its predictions for critical growth velocities for particles of different sizes are compared with experimental results for capture of silicon carbide (SiC) particles during directional solidification of silicon. The phase-field model allows us to systematically test the influence of different assumptions about attractive and repulsive forces and the capture mechanisms, including the effects of particle shape and of partial engulfment of the particle by the interface. We identify common properties of models that show agreement with experiments, trying to determine the underlying physical effects by abductive inference. We find that predictions vary only slightly between models with different repulsive forces and that the shape of the particle can have a larger effect on the critical growth velocity than the exact nature of the repulsive force or the capture process. We assess to what extent a good description of experimental critical growth velocities implies that the model accurately describes the actual physical processes and propose additional ways to test the validity of models.