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Dynamics at crystal/melt interface during solidification of multicrystalline silicon

  • Kozo Fujiwara EMAIL logo , Lu-Chung Chuang and Kensaku Maeda
Published/Copyright: February 23, 2022
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High Temperature Materials and Processes
From the journal High Temperature Materials and Processes Volume 41 Issue 1

Abstract

A fundamental understanding of crystal growth dynamics during directional solidification of multicrystalline Si (mc-Si) is crucial for the development of crystal growth technology for mc-Si ingots for use in solar cells. In situ observation of the crystal/melt interface is a way to obtain direct evidence of phenomena that occur at a moving crystal/melt interface during growth. In this review, some of the phenomena occurring in the solidification processes of mc-Si are introduced based on our in situ observation experiments, after a brief introduction of the history of the development of crystal growth technologies to obtain mc-Si ingots for solar cells.

Keywords: solidification; crystal/melt interface; semiconductor; grain boundary

1 Introduction

To solve the problem of global warming, decarbonization policies are being promoted all over the world, and it is expected that the use of solar power generation will further expand in the future. Recently, solar cells using various materials such as perovskites are being actively researched; but in practice, crystalline Si solar cells accounted for about 95% of the total solar cell production in 2019 [1]. Considering manufacturing cost, safety, reliability, and abundance of resources, crystalline Si solar cells are expected to continue to be the main product in the future. Single-crystal Si (mono-Si) and multicrystalline Si (mc-Si) are used as substrate materials for crystalline Si solar cells, and recently the production of mono-Si solar cells has been increasing owing to a decrease in the production cost of mono-Si ingots grown by the Czochralski (CZ) method [1]. However, comparing the weight of the ingot, mc-Si ingots grown by directional solidification in a crucible are four to five times larger than mono-Si ingots grown by the CZ method [1]. Therefore, in the future, if the quality of mc-Si ingots is improved further, their use may increase again. Control of the “grain structure” in mc-Si ingots, which contain not only a distribution of grain sizes and grain orientations but also a distribution in the density of crystal defects, is the key for improving their quality. For the development of crystal growth technology for mc-Si ingots, a fundamental understanding of the crystal growth mechanisms is crucial.

In this review, first, the history of the growth technology for mc-Si ingots is briefly described, and then some of the phenomena that occur during the directional solidification process will be explained based on the results of our in situ observation experiments.

2 Growth of mc-Si ingots for solar cells

The following is a brief introduction to the history of the development of the growth technology for mc-Si ingots. Research on the directional solidification of mc-Si ingots for solar cells began in earnest in the late 1970s. Carbon (graphite) or silica crucibles were used for the directional solidification of mc-Si ingots [2,3,4,5,6,7,8,9,10]. Because a silicon melt is very reactive toward the crucible materials, silicon nitride powders were used to coat the inside wall of the crucible as a mold release agent to prevent sticking and cracking of the ingot [3]. Silicon nitride-coated crucibles are commonly used for the growth of mc-Si ingots at present. In earlier research, the purity of the Si feedstock was not high, so the conversion efficiency of solar cells based on mc-Si substrates was around 15% in the 1980s [11]. The purity of Si feedstock has been improved [12,13], and a stable supply of high-purity feedstock is available for the growth of mc-Si; thus, the energy conversion efficiency of mc-Si solar cells has been improved.

Owing to numerous studies, it has been recognized that various types of crystal defects in mc-Si ingots, such as metallic impurities, dislocation clusters, and grain boundaries, degrade the properties of solar cells [14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42] because they act as recombination centers for photo-carriers. Therefore, a decrease in the defect density of mc-Si ingots has been demanded, and new growth methods for controlling the “grain structure” of mc-Si ingots have been proposed and developed. Here, a few of them are introduced. Commonly, in the growth of mc-Si ingots, nucleation of crystal grains occurs on the bottom wall of the crucible. The impingement of grains forms the initial grain structure of the mc-Si ingot, and then the ingot is directionally grown toward the upper side, as schematically shown in Figure 1(a). In 2006, the “dendritic casting method” was proposed where dendrite growth is promoted along the bottom wall of the crucible in the early stage of directional solidification, as shown in Figure 1(b) [43,44]. Because the growth rate of the dendrite grains is much faster than that of normal crystal grains [43,45,46], a grain structure with larger crystal grains is formed at the bottom of the ingot. This structure formed on the bottom wall of the crucible will act as a “seed” for the following directional solidification. Around the same time, BP Solar developed the “mono casting method” where a single crystal seed is placed on the bottom of the crucible in advance; thus, a mono-Si ingot would be grown by directional solidification from the seed, as shown in Figure 1(c) [47]. Methods that use several seed set on the bottom of the crucible have been developed [48,49,50,51], which were derived from the mono casting method. Also, a method that involves seeding from the top of the melt in the crucible has been studied to promote crystallization inside the melt [52,53,54]. In the dendritic-casting and seed-assisted growth methods, the aim is to obtain a grain structure with larger crystal grains to reduce the grain boundary density. However, Lan’s group proposed mc-Si ingots with smaller crystal grains and showed that the minority carrier lifetime was improved compared with that of mc-Si with larger grains [55,56]. This was mainly due to the reduction of dislocation clusters in the grains; the large number of random grain boundaries may have served as sinks for dislocation clusters in the solidification of these mc-Si ingots. The mc-Si ingots with smaller crystal grains are referred to as “high performance (HP) mc-Si.” In the growth of HP mc-Si ingots, tiny beads (Si, SiO2, or other materials) are set on the bottom of the crucible to increase the nucleation sites at the beginning of solidification, which leads to the formation of a grain structure with smaller grains, as shown in Figure 1(d). At present, HP mc-Si is widely used commercially. The energy conversion efficiency of solar cells based on HP mc-Si has reached more than 19% [57,58,59]. The development efforts for each growth method, especially regarding the recent development of seed-assisted growth, are reviewed well in ref. [60].

Figure 1 Directional solidification processes in various methods for producing mc-Si ingots for solar cells: (a) conventional directional solidification method, (b) dendritic casting method, where dendrite growth is promoted along the bottom wall of the crucible to create a grain structure with large grains, (c) mono casting method, where a single crystal is preset on the bottom wall of the crucible to grow a single crystal ingot in the crucible, and (d) HP mc-Si growth, where tiny beads are preset on the bottom wall of the crucible to enhance nucleation to obtain a grain structure with small grains.
Figure 1

Directional solidification processes in various methods for producing mc-Si ingots for solar cells: (a) conventional directional solidification method, (b) dendritic casting method, where dendrite growth is promoted along the bottom wall of the crucible to create a grain structure with large grains, (c) mono casting method, where a single crystal is preset on the bottom wall of the crucible to grow a single crystal ingot in the crucible, and (d) HP mc-Si growth, where tiny beads are preset on the bottom wall of the crucible to enhance nucleation to obtain a grain structure with small grains.

As outlined above, control of the grain structure in the solidification process of mc-Si is the key for obtaining high quality ingots. Usually, the bottom structure will not be maintained at the top of the ingot, because the microstructure continuously changes during directional solidification. To control the microstructure during directional solidification, it is crucial to understand the fundamental phenomena that occur during the solidification processes. In the next section, some of these phenomena will be explained.

3 Crystal growth dynamics in solidification processes of mc-Si ingots

3.1 In situ observation system

In our earliest study on observing the solidification processes of Si [61], we used a confocal scanning laser microscope with an infrared image furnace, which had been established for observing solidification processes in iron/steel materials [62,63]. In that system, the available sample size was limited in a few millimeters and a ceramic crucible was used. So that we can observe various phenomena that occur in the solidification processes of Si, we developed an in situ observation system which consists of an optical digital microscope and a growth furnace, as shown in Figure 2 [64,65]. In this system, we usually use a silica crucible with a size of 22 mm × 12 mm × 11 mm. The upper surface of the sample is observed through a silica window on the upper part of the furnace. The temperature inside the furnace is controlled by two carbon heaters, and the temperature gradient can be controlled by controlling the power output of the heaters. When we would like to observe a crystal/melt interface during directional solidification, crystal growth can be initiated from one side of the crucible by controlling the temperatures of the two carbon heaters.

Figure 2 In situ observation system consisting of a crystal growth furnace and a digital optical microscope: (left) picture of the system and (right) schematic image of the inside of the furnace.
Figure 2

In situ observation system consisting of a crystal growth furnace and a digital optical microscope: (left) picture of the system and (right) schematic image of the inside of the furnace.

Another method for observing the crystal/melt interface of Si has been developed, the X-ray imaging method, which is also a powerful tool for fundamental studies on mc-Si [66,67,68,69,70].

3.2 Growth shape of crystal grains

At the beginning of directional solidification without any seed crystals, nucleation and growth of the crystal grains occur on the bottom wall of the crucible, as shown in Figure 1(a). During grain growth of the nuclei, the shape of the crystal is determined by the anisotropy of the growth rate among crystallographic planes; that shape is called the “growth shape,” whereas the “equilibrium shape” of a crystal grain is determined by minimization of the crystal/melt interfacial energy under constant volume [71,72]. Observation of the equilibrium shape of Si in the melt was attempted experimentally [73], and it has been investigated using simulations [74,75,76]. Figure 3 shows the typical growth shapes of Si crystal grains with different upper orientations [73,77]. Because the growth rate of {111} planes is the lowest, the growth shape is bounded by {111} planes, as schematically shown in Figure 3. Therefore, the observed shape of the crystals on the crucible wall is determined by the crystallographic orientation in the upper direction, as seen in Figure 3.

Figure 3 Growth shape for a normal Si crystal with different upper orientations. The shape is bounded by {111} planes because they have the lowest growth rate [73,77].
Figure 3

Growth shape for a normal Si crystal with different upper orientations. The shape is bounded by {111} planes because they have the lowest growth rate [73,77].

However, the dendritic growth often appears in Si melts even at low undercooling [45,78]. When a Si crystal (or nucleus) contains parallel twin boundaries [79], the crystal grows in a dendritic shape, as shown in Figure 4. This is a so-called “faceted dendrite.” The growth shape and the growth mechanism of a faceted dendrite are very different from the dendrites of metallic alloys. The Si-faceted dendrite contains at least two parallel twin boundaries at the center and, preferentially, grows in the <112> or <110> direction, which is determined by the growth mechanism related to the formation of reentrant corners at the growth front of the faceted dendrite. The details of the growth mechanism of a faceted dendrite are given in earlier studies [80,81].

Figure 4 Dendrites growing in the Si melt.
Figure 4

Dendrites growing in the Si melt.

Such faceted dendrite growth was also directly observed for the compound semiconductor GaSb, and it was found that its growth mechanism is similar to that of Si [82]. The growth rate of the faceted dendrites is much higher than that of normal crystal grains, and thus the grain size becomes larger when dendrite growth is promoted along the bottom wall of the crucible in the early stage of directional solidification, which is the basic idea behind the dendritic casting method [43]. However, in HP mc-Si, the grain size must be kept small and homogeneous. To realize that grain structure, the nucleation frequency in the early stage of solidification must be increased. To enhance the number of nucleation events, tiny Si (or other materials) beads are preset on the bottom wall of the crucible [55,56,57,58,59], as show in Figure 1(d).

3.3 Morphology of crystal/melt interface

During the directional growth process of the mc-Si ingot, it is significant to control the entire interface shape, as shown in Figure 5(a), because it influences on the distribution of thermal stress and the defect density in an entire ingot. To control the entire interface shape macroscopically, not only the temperature gradient in the furnace and the growth rate but also the shape of the crucible and the furnace design should be considered. One can refer to other literature for details on control of the macroscopic crystal/melt interface shape [83–89].

Figure 5 Schematic images of crystal/melt interface shapes on various scales: (a) macroscopic images of concave, flat, and convex-shaped crystal/melt interfaces during directional solidification, (b) microscopic images of flat and zigzag-shaped crystal/melt interfaces, and (c) atomic images of rough and smooth crystal/melt interfaces.
Figure 5

Schematic images of crystal/melt interface shapes on various scales: (a) macroscopic images of concave, flat, and convex-shaped crystal/melt interfaces during directional solidification, (b) microscopic images of flat and zigzag-shaped crystal/melt interfaces, and (c) atomic images of rough and smooth crystal/melt interfaces.

Here, we would prefer to consider the microscopic (submillimeter scale) shape of the crystal/melt interface for Si.

First, we consider the case of a crystal that does not contain grain boundaries (single crystal) [81,90–92]. Even if the interface looks macroscopically flat, it can have a flat or zigzag shape on the microscopic scale, as schematically shown in Figure 5(b). Also, it should be noted that even if the interface shape looks microscopically flat, it may have a rough interface or a smooth interface at the atomic level, as schematically shown in Figure 5(c). In the case of Si, according to Jackson’s criteria [93,94], planes other than {111} planes are atomically rough, and only the {111} plane is an atomically smooth “facet plane.”

When the plane of the crystal/melt interface is a rough plane, the microscopic interface shape is kept flat under the condition that the degree of undercooling of the melt in front of the crystal/melt interface is smaller than that at the crystal/melt interface. Generally, in the directional solidification process of mc-Si ingots, the temperature gradient in the furnace is positive to the direction of the solidification and the growth rate is low enough, and thus a flat interface would be kept microscopically. If the growth rate increases and the degree of undercooling of the melt becomes larger than that at the crystal/melt interface, the interface shape transforms from flat to zigzag, as schematically shown in Figure 6(a). However, in the case of a facet plane, the microscopic interface shape remains flat even as the growth rate is increased, as shown in Figure 6(b).

Figure 6 Transformation of microscopic interface shape for atomically rough and smooth planes [90]: (a) the case of a rough plane. The flat interface is transformed to a zigzag interface with increasing growth rate due to the interface instability and (b) the case of a smooth plane (facet plane). The flat interface is maintained even at a higher growth rate.
Figure 6

Transformation of microscopic interface shape for atomically rough and smooth planes [90]: (a) the case of a rough plane. The flat interface is transformed to a zigzag interface with increasing growth rate due to the interface instability and (b) the case of a smooth plane (facet plane). The flat interface is maintained even at a higher growth rate.

The transformation of a flat interface to a zigzag one in a rough plane is known as the Mullins–Sekerka interface instability [95]. This is explained as interface instability that occurs when the temperature gradient in the melt at the crystal/melt interface is negative in the growth direction, as shown in Figure 7. It can be considered that the flat interface is often perturbed during growth, and when perturbation is introduced to a planar interface, the degree of undercooling at the top of the perturbed part is larger than that at the bottom part under a negative temperature gradient, as schematically shown in Figure 7(a). Therefore, the growth rate at the top part is higher than that at the bottom part, which leads to amplification of the perturbation. The amplified perturbed part will be bounded by {111} planes finally in the case of Si because these planes have the lowest growth rate, which is similar to the evolution of the growth shape of crystal grains (see Figure 3). Actually, this transformation from a flat to a perturbed to a zigzag shape has been directly observed, as shown in Figure 7(b). However, when the temperature gradient is positive, the growth rate at the top part of the perturbation is lower than that at the bottom part; therefore, the bottom part will catch up with the top part, and a flat interface is maintained. In the case that the crystal/melt interface is a facet plane, which is the {111} plane of Si, the flat interface is already bounded by the plane with the lowest growth rate, and thus a change of the interface shape does not occur even for a negative temperature gradient, as shown in Figure 6(b).

Figure 7 Process of interface instability: (a) schematic image of the interface at the instability with a temperature gradient at the interface. Under a negative temperature gradient, the perturbation introduced into the flat interface is amplified, and a zigzag interface is formed finally and (b) actual images of the interface at the point of interface instability for a Si single crystal.
Figure 7

Process of interface instability: (a) schematic image of the interface at the instability with a temperature gradient at the interface. Under a negative temperature gradient, the perturbation introduced into the flat interface is amplified, and a zigzag interface is formed finally and (b) actual images of the interface at the point of interface instability for a Si single crystal.

The critical growth rate where the temperature gradient in the melt changes from positive to negative is dependent on the temperature gradient in the furnace. Here, it should be noted that when the temperature gradient in the furnace is set to be positive, the temperature gradient in the melt can be negative at a higher growth rate due to release of the latent heat of crystallization. In our experimental set-up, the one-dimensional thermal field in the crystal and melt along the crystal growth direction, T c,m, can be calculated by equation (1a–c) [90],

(1a) T c,m ( x ) = A c,m exp − x l c,m + G x + ρ c,m C p c,m G V l q l Si k q + T i ,

(1b) l c = 2 ρ c C Pc V / k c − ( ρ c C Pc V / k c ) 2 + 8 k q / k c l q l Si ,

(1c) l m = 2 ρ m C Pm V / k m + ( ρ m C Pm V / k m ) 2 + 8 k q / k m l q l Si ,

where ρ c,m, C Pc,m, k c,m, k q, l q, l Si, and V are the heat capacity of the Si crystal and melt, the thermal conductivity of the Si crystal and melt, the thermal conductivity of the quartz plate, the thickness of the quartz plate, the thickness of the Si crystal, and the growth velocity, respectively. G is the temperature gradient in the furnace, and T i is the furnace temperature at the interface position. A c,m is a constant determined by the boundary conditions: these are energy conservation at the crystal-melt interface described as ∆HV = k c(∂T c/∂x) x=0 – k m(∂T m/∂x) x=0, where ∆H is the latent heat of Si, and temperature continuity at the crystal-melt interface, which is considered to be at the melting temperature T mp, and thus is described as (T c) x=0 = (T m) x=0 = T mp. In the calculations, the values of l q, l Si, and G are based on our experimental values, and the other physical properties of Si used are based on those reported in an earlier study [96]. The temperature gradient at the crystal/melt interface (x = 0), G 0, is defined as follows:

(2) G 0 = ∂ T c,m ∂ x x = 0 = − A c,m l c,m + G .

The critical growth rate V cri is defined as the growth rate where the temperature gradient in the melt at the interface changes from positive to negative, which can be calculated from the condition G 0 = 0 using equation (2). Figure 8 shows the calculated temperature field for various growth rates [90]. It is shown that when the growth rate is low, the temperature gradient in the melt remains positive, whereas it becomes negative at a high growth rate. The calculated critical growth rate is V c = 109 µm·s−1 [90], and the V c obtained by our in situ observations was 100 µm·s−1 < V c < 150 µm·s−1 [90,92].

Figure 8 Calculated thermal field in the growth direction at various growth rates [90]. When the growth rate is low, the temperature gradient in the melt at the interface is positive, whereas it becomes negative at a high growth rate. The calculated critical growth rate where the temperature gradient changes from positive to negative is 109 µm·s−1 under our experimental conditions.
Figure 8

Calculated thermal field in the growth direction at various growth rates [90]. When the growth rate is low, the temperature gradient in the melt at the interface is positive, whereas it becomes negative at a high growth rate. The calculated critical growth rate where the temperature gradient changes from positive to negative is 109 µm·s−1 under our experimental conditions.

Next, we consider the interface instability for a crystal containing grain boundaries. Figure 9 shows a crystal/melt interface containing (a) a small-angle grain boundary and (b) a Σ3 twin boundary [97]. It is clearly observed that the instability started at portions of the grain boundary in both cases, whereas the instability began over the entire interface at the same time in the case of single-crystal Si, as shown in Figure 7(b). The critical growth rate for initiation of instability at the grain boundary was found to be smaller than that in the case of a single crystal [97]. It was also shown that the critical growth rate was different depending on the characteristics of the grain boundary, such that V R < V SAG < V Σ3, where V R, V SAG, and V Σ3 are the critical growth rates at a random grain boundary, small-angle grain boundary, and Σ3 twin boundary, respectively [97].

Figure 9 In situ observations of interface instability for Si crystals containing grain boundaries [97]: (a) crystal with a small-angle grain boundary and (b) crystal with Σ3 twin boundaries. In both cases, the interface instability was initiated at the grain boundary position.
Figure 9

In situ observations of interface instability for Si crystals containing grain boundaries [97]: (a) crystal with a small-angle grain boundary and (b) crystal with Σ3 twin boundaries. In both cases, the interface instability was initiated at the grain boundary position.

Here, we consider the reason why the interface instability is initiated at a position on a grain boundary. As explained above, the formation of a negative temperature gradient in the melt at the interface causes interface instability. In case of a single crystal, the instability occurs over the entire interface at the same time due to the homogeneous thermal field. However, when a grain boundary exists on the interface, it is considered that the thermal field is locally different around the position of the grain boundary. Factors that affect the thermal field at the crystal/melt interface are the latent heat of crystallization, and diffusion of the generated latent heat from the crystal/melt interface into the crystal and the melt when the temperature gradient in the furnace is fixed. As considered that the crystal imperfections such as grain boundaries affect the electric conduction [98], we can imagine that the thermal conductivity at a grain boundary is lower than that within the grain due to the disordered atomic structure at the grain boundary, as schematically shown in Figure 10. However, the thermal conductivity in the melt would not be changed even when the crystal contains grain boundaries.

Figure 10 Schematic image of thermal diffusivity at a crystal/melt interface with a grain boundary [97]. The thermal conductivity at the grain boundary is lower than that within the grain due to the disordered atomic configuration.
Figure 10

Schematic image of thermal diffusivity at a crystal/melt interface with a grain boundary [97]. The thermal conductivity at the grain boundary is lower than that within the grain due to the disordered atomic configuration.

However, to our knowledge, the thermal conductivity at grain boundaries at the melting temperature has not been reported yet. Therefore, we estimated the thermal conductivities at grain boundaries from our in situ experiments [97]. As explained above, we can estimate the critical growth rate from equation (2) when all of the physical properties in equation (1a–c) are known. Conversely, when one physical value in equation (1a–c) is unknown and the critical growth rate is obtained by experiment, the unknown value can be calculated. Here, the thermal conductivity at grain boundaries at the melting temperature is unknown, but we can directly measure the critical growth rate at the instability at the grain boundary position [97]. Therefore, it was possible to calculate the thermal conductivity at each grain boundary. However, it should be noted that the width of the “grain boundary area” that affects the thermal field is not known. Therefore, the obtained thermal conductivity might be an “effective” thermal conductivity in the area including a grain boundary. From the in situ observations, the critical growth rates of a small-angle grain boundary, Σ3 twin boundary, and random grain boundary were found to be 110, 119, and 37 µm·s−1, respectively [97]. In the case of a single crystal with no grain boundaries, the critical growth rate was 139 µm·s−1 [97]. The temperature gradient at the interface G 0 must be zero at the critical growth rate. Therefore, the effective thermal conductivity at each grain boundary is determined so that the G 0 = 0 at the critical growth rates by using equation (2). The obtained effective thermal conductivities at the melting temperature were 1.6 × 10−2, 1.9 × 10−2, and 2.7 × 10−3 W·K−1·mm−1 for small-angle, Σ3, and random grain boundaries, respectively. The thermal conductivity of a single crystal was obtained as 2.2 × 10−2 W·K−1·mm−1. This shows that a negative temperature gradient is locally formed at a portion of the grain boundary due to the lower thermal conductivity, which promotes the instability at the grain boundary position on the crystal/melt interface.

3.4 Twin boundary formation at the grain boundary groove

In a solidified mc-Si ingot, it is often observed that Σ3{111} twin boundaries are generated from a large-angle grain boundary. Here, we consider the underlying mechanism of twin boundary formation at a grain boundary at a crystal/melt interface. Duffar and Nadri theoretically determined that a {111} facet may appear at the grain boundary groove on the crystal/melt interface, and twin nucleation occurs on the {111} facet at the groove [99]. The shape of the grain boundary groove was observed directly, and a faceted groove was confirmed at grain boundaries other than the Σ3{111} twin boundary, as shown in Figure 11 [100].

Figure 11 Shape of crystal/melt interfaces for various grain boundary characteristics [100]: (a) an interface with Σ3 twin boundaries. A grain boundary groove is not observed, (b) an interface with a Σ27 grain boundary. A faceted grain boundary groove is observed, and (c) an interface with a random grain boundary. A faceted groove is observed, similar to (b).
Figure 11

Shape of crystal/melt interfaces for various grain boundary characteristics [100]: (a) an interface with Σ3 twin boundaries. A grain boundary groove is not observed, (b) an interface with a Σ27 grain boundary. A faceted grain boundary groove is observed, and (c) an interface with a random grain boundary. A faceted groove is observed, similar to (b).

Tsoutsouva et al. directly observed twin boundary formation at a faceted grain boundary groove by using an in situ X-ray imaging method [101], and we also observed this phenomenon directly by our in situ observation system [102]. Figure 12 shows the process of twin boundary formation. It is seen that the grain boundary groove indicated by a red circle (t = 5.7 s) was gradually deepened with crystal growth, and the melt inside the groove was rapidly crystallized when the depth of the groove became large enough (between t = 30 and t = 40 s). During this rapid growth to fill the groove, twin nucleation occured on the {111} facet in the groove.

Figure 12 Process of twin boundary formation at a grain boundary groove. When the groove becomes deep enough, rapid growth occurs at the groove, and then twin nucleation occurs on the {111} facet that formed the groove [102].
Figure 12

Process of twin boundary formation at a grain boundary groove. When the groove becomes deep enough, rapid growth occurs at the groove, and then twin nucleation occurs on the {111} facet that formed the groove [102].

The degree of the driving force (undercooling) for twin nucleation has not been directly obtained experimentally. Theoretical models indicate the probability of twin nucleation as a function of the degree of undercooling, but the value is dependent on the model [99,103,104]. Therefore, further studies are expected in the future.

3.5 Interaction of grain boundaries at the crystal/melt interface

In order to understand the formation of the grain structure of mc-Si during directional solidification, the dynamics of grain boundaries at the crystal/melt interface should be clarified.

In earlier works on grain growth at the crystal/melt interface during directional solidification, the grain growth behavior was discussed on the basis of the difference in the crystal/melt interfacial energy between two adjacent grains [65]. However, recent studies indicated that grain growth at a crystal/melt interface is affected by the kinetics at a grain boundary groove. The direction of extension for the grain boundary has been investigated theoretically [105] and by experiment [106,107], focusing on the shape and growth rate at a grain boundary groove. Those studies showed that the direction of extension for a grain boundary is determined by the difference in the growth rates of two facet planes forming a grain boundary groove. When two facet planes grow with the same growth rate, the grain boundary extends along the bisector line of the groove, and when the growth rates of two facet planes are different, the grain boundary extends in the direction of the sum of the growth rate vectors [107].

Also, the formation of small-angle grain boundaries (SAGB) was directly observed at a moving crystal/melt interface due to the aggregation of dislocations during directional solidification [108,109].

Further, in the directional solidification of mc-Si, two-grain boundaries are often encountered at a crystal/melt interface, as schematically shown in Figure 13.

Figure 13 Schematic image of the impingement of two-grain boundaries at a crystal/melt interface.
Figure 13

Schematic image of the impingement of two-grain boundaries at a crystal/melt interface.

Here, we introduce the interactions of grain boundaries at a crystal/melt interface. The mechanisms behind the phenomena are not well understood yet, but we think it is meaningful to show the observed phenomena for future study. Figure 14(a) and (b) show snapshots of the impingement of two-grain boundaries at the crystal/melt interface during directional solidification. In both cases, after the impingement of two large-angle grain boundaries (LAGB), one new LAGB was formed and extended with crystal growth. Such interactions of two-grain boundaries are often observed in mc-Si ingots [110,111]. Similarly, it was shown that the impingement of two SAGB produces one new SAGB [112]. On the contrary, cases in which one grain boundary decomposes into two-grain boundaries during growth were also observed [110,111,113].

Figure 14 Observations of grain boundary impingement: (a) two Σ3 grain boundaries impinge at the interface, and a Σ9 grain boundary is formed and (b) a Σ27 grain boundary and a Σ3 grain boundary produce a random grain boundary after the impingement, and a random grain boundary and a Σ3 grain boundary produce a Σ27 grain boundary after the impingement.
Figure 14

Observations of grain boundary impingement: (a) two Σ3 grain boundaries impinge at the interface, and a Σ9 grain boundary is formed and (b) a Σ27 grain boundary and a Σ3 grain boundary produce a random grain boundary after the impingement, and a random grain boundary and a Σ3 grain boundary produce a Σ27 grain boundary after the impingement.

The interaction between a SAGB and a Σ3 twin boundary was found to be different from those mentioned above [112,114]. Figure 15 shows the impingement of a SAGB and a Σ3 twin boundary [112]. At the impingement of these two boundaries at the crystal/melt interface (middle picture in Figure 15), they penetrate each other and continued to extend as seen in the image on the right in Figure 15. Such penetration of grain boundaries was not observed in the cases of impingement of two LAGBs or two SAGBs.

Figure 15 Observations of the impingement of a small-angle grain boundary and a Σ3 twin boundary [112]. The grain boundaries penetrate each other and extend with growth.
Figure 15

Observations of the impingement of a small-angle grain boundary and a Σ3 twin boundary [112]. The grain boundaries penetrate each other and extend with growth.

It was also shown that the behavior after the impingement of a SAGB and a Σ3 twin boundary was dependent on the misorientation angle of the SAGB before the impingement [114]. The patterns of grain boundary interactions observed to date are summarized in Figure 16 [110–114].

Figure 16 Summary of the observed interactions of grain boundaries at a crystal/melt interface: (a) two-grain boundaries produce a single grain boundary, (b) one grain boundary splits into two grain boundaries, (c) two grain boundaries penetrate each other, and (d) one grain boundary is formed after the impingement of two grain boundaries, but it splits into two grain boundaries immediately.
Figure 16

Summary of the observed interactions of grain boundaries at a crystal/melt interface: (a) two-grain boundaries produce a single grain boundary, (b) one grain boundary splits into two grain boundaries, (c) two grain boundaries penetrate each other, and (d) one grain boundary is formed after the impingement of two grain boundaries, but it splits into two grain boundaries immediately.

As shown above, the interaction of grain boundaries at a crystal/melt interface is complicated, and thus further studies are required to deepen our understanding. Not only experimental evidence but also theoretical and computational studies remain limited; thus, study of the dynamics of grain boundaries at the crystal/melt interface is an open topic for future studies.

4 Summary

It has been expected that the energy conversion efficiency of solar cells using mc-Si substrate will improve. For that to happen, control of the microstructure in mc-Si ingots in the directional solidification process is indispensable. Many phenomena occur at the crystal/melt interface whose mechanisms have not been clarified completely, especially regarding the dynamics of crystal defects, including grain boundaries, dislocations, and impurities. Observation of the macrostructures and microstructures of solidified mc-Si is of significance for indicating what takes place during directional solidification processes. In addition, global simulation and numerical analysis are also important for understanding the defect distributions in an entire ingot [115–123]. Transmission electron microscope (TEM) observations and various computational simulations have clarified the local distributions of defects [124–133]. In situ observation is also a powerful tool for obtaining direct evidence revealing phenomena at the crystal/melt interface. However, for clarification of crystal growth mechanisms, research from the theoretical side is also crucial.

Acknowledgments

The authors would like to thank Dr Masatoshi Tokairin, Dr Kuan-Kan Hu, Dr Xinbo Yang, and Mr Ryoichi Maeda for their efforts in some of the experiments. Also, the authors wish to express their thanks for fruitful discussions with Dr Haruhiko Morito and Dr Keiji Shiga.

  1. Funding information: This study was funded by JSPS KAKENHI Grant numbers 16686001, 17656223, 18686060, 15KK0198, and 17H01336, and by the Cabinet Office, Government of Japan, through its “Funding Program for Next Generation World-Leading Researchers,” GR016. Now this study is funded by JSPS KAKENHI Grant numbers 21H04658 and 21K20343.

  2. Author contributions: Kozo Fujiwara: writing – original draft, writing – review and editing, methodology, formal analysis; Lu-Chung Chuang: writing – review, methodology, formal analysis; and Kensku Maeda: writing – review, methodology, formal analysis

  3. Conflict of interest: There is no conflict of interest.

  4. Data availability statement: The authors have a right to use graphics in this article.

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Received: 2021-09-24
Revised: 2021-11-08
Accepted: 2021-12-06
Published Online: 2022-02-23

© 2022 Kozo Fujiwara et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/htmp-2022-0020
Keywords for this article
solidification; crystal/melt interface; semiconductor; grain boundary
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