ARTICLE pubs.acs.org/crystal
Dependence of Si-Faceted Dendrite Growth Orientation on Twin Spacing and Undercooling Xinbo Yang,*,† K. Fujiwara,†,‡ K. Maeda,† J. Nozawa,† H. Koizumi,† and S. Uda† † ‡
Institute for Materials Research (IMR), Tohoku University, Katahira 2-1-1, Aoba-ku, Sendai 980-8577, Japan PRESTO, Japan Science and Technology Agency (JST), 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan ABSTRACT: Si-faceted dendrites growth orientation as a function of twin spacing and undercooling were investigated by in situ observation, and the mechanisms of the growth behaviors were discussed and clarified. The growth orientation of Si-faceted dendrites strongly depends on the twin spacing and undercooling. For a given undercooling, a dendrite with twin spacing narrower than the critical twin spacing preferentially grows in the Æ110æ direction, whereas growth in the Æ112æ direction preferentially occurs for a dendrite with twin spacing wider than the critical twin spacing. The critical twin spacing for stable faceted dendrite growth increases as the undercooling increases. In the case of low undercooling (∼10 K < ΔT j 15 K), dendrites dominantly grow in the Æ112æ direction. For high undercooling (∼25 K< ΔT j 100 K), dendrites preferentially grow in the Æ110æ direction. Æ110æ and Æ112æ growth directions occur with equal frequency for intermediate values of undercooling (∼15 K < ΔT e 25 K).
1. INTRODUCTION Solar cells with high conversion efficiency and low cost are expected to be in strong demand in the future because of the shortage of fossil fuels as well as the problem of global warming. At present, multicrystalline silicon (mc-Si)-based solar cells dominate the solar-cell market because of their low cost using the directional casting technique. However, the conversion efficiency of mc-Si solar cells is still unsatisfactory. This can be attributed to the impurities (oxides, metals, and inclusions) and crystal defects (dislocations, grain boundaries, and subgrain boundaries) in mc-Si, which act as recombination centers for light-generated photocarriers.1-5 Additionally, the random orientation on an mc-Si wafer surface, which leads to the difficulty of forming a uniform textured structure on the surface because of differences in the etching rate and morphology between grains, is also a big problem. The increasing share of mc-Si solar cells in the solar-cell market has stimulated demand for higher-quality mc-Si wafers. Therefore, extensive research is being carried out to develop new mc-Si crystal growth techniques that may overcome the above-mentioned problems and enhance the conversion efficiency of mc-Si solar cells. Recently, an mc-Si crystal growth technique based on faceted dendrite growth, called the dendritic casting method,6,7 has attracted considerable attention. The most important characteristic of this technique is that dendrite growth is induced at the bottom of a quartz crucible at the initial stage of casting by controlling the undercooling and the subsequent directional solidification in the usual way. As a result, mc-Si ingots with large crystal grain size and controlled crystallographic orientation have been obtained, and the conversion efficiency of solar cells based on mc-Si grown by this method has proven to be much higher than that of cells based on conventional mc-Si, and even approaches the efficiency of Si single-crystalbased solar cells.8 In addition to silicon, germanium also exhibits special faceted dendrite growth during crystal growth from the undercooled melt, which was first reported in the 1950s.9 Since then, faceted dendrites have attracted great interest from both scientific r 2011 American Chemical Society
research and technological viewpoints. Three types of dendrites, twin-related Æ112æ, twin-related Æ110æ and twin-free Æ100æ dendrites, have so far been found in silicon melts at different amount of undercooling.10 Here, a Æuvwæ dendrite denotes a dendrite growing in the Æuvwæ direction. The surfaces of twin-related Æ112æ and Æ110æ dendrites are bounded by smooth {111} habit planes, and at least two parallel twins can be found at the center of each dendrite, which is quite different from the dendrites of HgS,11 CdS,12 Ag,13 Cu,14 and so on. The Æ100æ dendrite, which is bounded by rough {110} and {100} planes, does not contain any twin planes.10,15 The re-entrant corner growth mechanism of twin-related dendrites was proposed by Hamilton and Seidensticher (H-model) in the 1960s,16,17 and recently modified by Fujiwara et al. on the basis of in situ observation (F-model).18 If a crystal contains two or more parallel twins, re-entrant corners are formed on the growth surface, and successive nucleation and rapid growth easily occur there. So far, three methods, flux method,15,19 electromagnetic levitation (EML) method,20-22 and in situ observation method,18,23-25 have been developed to study the faceted dendrites in Si and Ge crystals. Regarding practical applications, faceted dendrites have been used for growing thin Si ribbon crystals for solar cells for a few decades.26,27 Generally, twin-related Æ110æ and Æ112æ dendrites appear at the undercooling ΔT < 100 K, and the twin-free Æ100æ dendrite only appears at ΔT > 100 K.10 Dendrites predominantly grow in the Æ110æ and Æ112æ directions parallel to the crucible bottom in the dendritic casting method, forming upper planes of {112} and {110}, respectively, consistent with the results of electron backscattering diffraction patterns (EBSPs).6,28 Usually, no Æ100æ dendrites appear because the undercooling is insufficient. It would be ideal if only Æ110æ or Æ112æ dendrites could be induced at the initial stage by controlling the undercooling at a suitable Received: December 28, 2010 Revised: January 19, 2011 Published: February 22, 2011 1402
dx.doi.org/10.1021/cg101721v | Cryst. Growth Des. 2011, 11, 1402–1410
Crystal Growth & Design
Figure 1. (a) Experimental procedure for observing the dendrite growth of silicon crystal.32 (b) Experimental procedure for observing the dendrite growth at different amount of undercooling using the same sample.
value. So that the upper surface would be dominated by only {112} or {110} planes, which would improve the surface texture of wafers. However, it is still unknown how the undercooling affects the growth orientation of faceted dendrites, thus further research on the growth orientation behavior of Æ110æ and Æ112æ dendrites is required. In this work, the effects of the spacing between two parallel twin planes, called the twin spacing, and undercooling on the dendrite growth orientation were investigated by in situ observation, which has been proven to be a powerful technique for studying the dendrite growth behaviors in silicon.18,29-31
2. EXPERIMENTAL PROCEDURES An in situ observation system consisting of a furnace and a microscope was used to observe the dendrite growth behaviors of silicon.23-25 The experimental procedure is shown in Figure 1a.32 Silicon wafers (7 N, 20 10 mm) with the required orientations were prepared and then dipped in HF:H2O (2.5:97.5) solution for 2 min to remove the oxide layer from the surface before placing them in a quartz crucible. After pumping to a low vacuum, the furnace was filled with high-purity argon gas and then heated. Using the microscope lens, we melted the sample in such a way that an unmelted part remained, which served as a seed crystal. The furnace was then cooled at different cooling rates. Generally, crystal growth began at the solid-liquid interface and the dendrite growth could be induced with sufficient undercooling. Images of samples during melting and crystallization were monitored and recorded on videotape. According to our previous work, the growth velocity of the solid-liquid interface (V) as a function of undercooling can be expressed as V (μm/s) = 7.5ΔT (K).30 We used the same in situ observation furnace in this study, and ΔT was determined by using this equation. The crystal orientation and twin spacing were measured using EBSPs.
3. RESULTS AND DISCUSSION 3.1. Effect of Twin Spacing on the Faceted Dendrite Growth Orientation under the Same Undercooling. It is
well-known that at least two parallel twins exist at the center of Si Æ110æ and Æ112æ faceted dendrites, and that twins form on the
ARTICLE
solid-liquid surface before dendrite growth.29 However, the question of which growth direction is preferred, Æ110æ or Æ112æ, once the parallel twins are formed still remains. We observed both Æ110æ and Æ112æ dendrites that grew at the same interface, and the twin spacings in the dendrites were measured using EBSPs. To directly measure the twin spacing using EBSPs, the sample with the Æ112æ upper surface was used. A typical example of dendrite growth is shown in Figure 2a. Two Æ110æ dendrites (d1 and d2) and one Æ112æ dendrite (d3) with different growth velocities were observed. The dendrite growth orientation in this sample must be related to the twin spacing, because dendrites grew at the same interface in a small area, which can be considered to be subjected to the same undercooling. Figure 2b shows the parallel twins observed at the center of d1, d2, and d3 by EBSP analysis. All the dendrites contain two parallel {111} twin planes, and the twin spacings of d1, d2, and d3 are 9 μm, 11.5 μm, and 31 μm, respectively. Under the same undercooling, the Æ112æ dendrite contains a wider twin spacing than the Æ110æ dendrite. In other words, dendrites with narrower twin spacing preferentially grow in the Æ110æ direction. To investigate whether this phenomenon is universal or depends on the sample orientation, samples with different orientations were used for in situ dendrite growth observation. Figure 3 shows two other typical examples of dendrite growth. One Æ110æ dendrite and one Æ112æ dendrite with different growth velocities were observed in both samples. The Æ110æ and Æ112æ dendrite growth velocities in panels a and b in Figure 3 are 723 μm/s and 191 μm/s, and 426 μm/s and 255 μm/s, respectively. The Æ110æ dendrite has a higher growth velocity than the Æ112æ dendrite in both samples. However, we did not measure the twin spacing directly by EBSP analysis this time. According to our previous work, the growth velocity of a faceted dendrite is inversely proportional to the twin spacing at the same undercooling.33 We can conclude that the Æ110æ dendrite contains a narrower twin spacing than the Æ112æ dendrite in both samples. In fact, in most cases, we observed that the Æ110æ dendrite grows faster than the Æ112æ dendrite at the same undercooling, independent of the sample orientation. Even we melt the entire sample, the dendrites that grow from the crucible wall exhibit the same phenomenon. Therefore, we concluded that the growth orientation of faceted dendrite depends on the twin spacing under a given undercooling. The Æ110æ growth direction is the preferential direction for a narrow twin spacing, and for a wide twin spacing, the Æ112æ direction is the preferential direction. 3.2. Faceted Dendrite Growth Orientation As a Function of Undercooling. The experimental procedure for investigating the effect of the undercooling on the dendrite growth orientation is shown in Figure 1b. A Si crystal sample was partly melted several times and then different undercooling were applied to induce dendrite growth. As discovered in our previous work,30 if the parallel twins formed during the previous experiment are not removed, dendrites can grow from the parallel twins again. To avoid the impact of the previously formed parallel twins, more portions of the crystal were melted in every experiment. As shown in Figure 1b, the sample was first melted to (a) place, then dendrite growth was induced from interface (a) by undercooling. In the next two experiments, the sample was melted to (b) and (c) place, and dendrite growth was induced from interfaces (b) and (c) by applying different undercooling. Figure 4 shows the faceted dendrite growth of a Si crystal sample with decreasing undercooling. All the dendrites were grown from different 1403
dx.doi.org/10.1021/cg101721v |Cryst. Growth Des. 2011, 11, 1402–1410
Crystal Growth & Design
ARTICLE
Figure 2. (a) Faceted dendrite growth of Si crystal sample with the Æ112æ upper surface and Æ110æ growth direction. Two Æ110æ dendrites (d1 and d2) and one Æ112æ dendrite (d3) were observed. (b) Parallel twins observed at the center of the three dendrites by EBSP analysis.
Figure 3. Faceted dendrite growth of Si crystal samples with different orientations: (a) Æ110æ upper surface and Æ110æ growth direction; (b) Æ111æ upper surface and Æ112æ growth direction.
locations on the interface, which indicates that the twins formed in the previous experiment were completely removed. Three Æ110æ dendrites with high growth velocity were observed at an undercooling of ΔT = 28.6 K (Figure 4a). When the undercooling was decreased to 14.3 K, only two Æ112æ dendrites with low growth velocity were observed (Figure 4c). However, both Æ110æ and Æ112æ dendrites were observed at an undercooling of 21.4 K (Figure 4b). The growth velocity of the Æ110æ dendrite is higher than that of the Æ112æ dendrite, which is consistent with the results in section 3.1. The Æ110æ growth direction is the preferential direction for the dendrites at a high undercooling. As the undercooling decreases, Æ112æ dendrites become dominant. To obtain precise information on the critical undercooling of the transition from Æ112æ to Æ110æ, more in situ observation experiments were performed using samples with different orientations. Figure 5 shows another sample with a Æ112æ direction, obtained by the experimental procedure in Figure 1b. At a low undercooling (ΔT = 12.6 K), only one Æ112æ dendrite with low
growth velocity was observed (Figure 5a). As the undercooling increased to 24.1 K, two Æ110æ dendrites with high growth velocity as well as two Æ112æ dendrites were observed (Figure 5b). For a higher undercooling (ΔT = 30.2 K), only Æ110æ dendrites were observed (Figure 5c). The observed results are similar to those in Figure 4. The undercooling in the samples in Figures 2, 3a, and 3b, which have both Æ110æ and Æ112æ dendrites, are 17.6, 25.1, and 19.3 K, respectively. In fact, after investigating the dendrite growth under different undercooling for numerous samples, we found that dendrite growth in the Æ112æ direction is dominant when the undercooling ΔT is lower than ∼15 K and that dendrites preferentially grow in the Æ110æ direction at a high undercooling (ΔT j 25 K). In the case of undercooling between ∼15 and ∼25 K, Æ112æ and Æ110æ dendrites appear with equal frequency. Considering that the minimum undercooling for the initialization faceted dendrite growth is ∼10 K,30 Æ112æ dendrites are dominant at a narrow undercooling range from ∼10 to 15 K. 1404
dx.doi.org/10.1021/cg101721v |Cryst. Growth Des. 2011, 11, 1402–1410
Crystal Growth & Design
ARTICLE
Figure 4. Faceted dendrite growth of Si crystal sample under different undercooling: (a) ΔT = 28.6 K, three Æ110æ dendrites; (b) ΔT = 21.4 K, one Æ110æ dendrite and one Æ112æ dendrite; (c) ΔT = 14.3 K, two Æ112æ dendrites.
To check if the above results is valid in dendritic casting process, we performed a simple experiment using in situ observation furnace. In the experiment as shown in Figure 1a, we melt all the sample instead of partial melted this time, then different undercooling was applied to induce the dendrite growth from the melts. Although we can not determine the dendrite growth orientation from the video directly this time, the dendrite growth orientation can be deduced from the upper surface orientation. As we know, faceted dendrites grow in the Æ110æ or Æ112æ directions parallel to the crucible bottom, forming upper planes of {112} and {110}, respectively.28 Figure 6 shows the EBSP measurement results of the upper surface of the samples applied with different undercooling. At a low undercooling (ΔT = 12.2 K), the upper surface is occupied with random orientations (Figure 6a). Small areas (right side) are covered by {110} planes with parallel twins, and it can be attributed to the Æ112æ dendrites grew along the crucible bottom. When the undercooling increased to 25.1 K, the upper surface is mainly occupied with the orientations close to {112} and {110} (Figure 6b), which indicates that both Æ110æ and Æ112æ faceted dendrites were induced at this undercooling. The upper surface is dominated by orientation close to {112} for the sample prepared at the undercooling of 33.4 K [Figure 6c], which indicates that Æ110æ faceted dendrites are dominant. As-obtained results from the all melted samples are consistent with the results we got from the partial melted samples. In most case, the areas occupied by {110} and {112} planes contains parallel twins, which were marked by the arrows in Figure 6. The twin spacings in {112} planes are
narrower than that in {110} planes, which indicates that the Æ112æ dendrite contains a wider twin spacing than the Æ110æ dendrite, which is consistent with results described in section 3.1. 3.3. Discussion. On the basis of the above results, the distribution map of the faceted dendrite growth orientation in terms of the undercooling (ΔT) and twin spacing (d) is summarized in Figure 7. We assumed that there are two critical twin spacings (d1 and d2), where d1 is the maximal twin spacing for stable Æ110æ dendrite growth and d2 is the minimum twin spacing for stable Æ112æ dendrite growth. Dendrites preferentially grow in the Æ110æ direction at a high undercooling (∼25 K < ΔT j 100 K) and a narrow twin spacing (d < d1), whereas growth in the Æ112æ direction preferentially occurs at a low undercooling (∼10 K < ΔT j15 K) and a wide twin spacing (d > d2). For intermediate region of undercooling (∼15 K < ΔT j 25 K) and twin spacing (d1 < d < d2), the Æ110æ and Æ112æ growth directions occur with equal frequency. However, the critical twin spacings d1 and d2 have not been determined yet. Albon and Owen reported that the faceted dendrite growth orientation in indium antimonide also depends on the twin spacing for a given undercooling.34 They found that the critical twin spacings d1 and d2 are 5 and 10 μm, respectively, in indium antimonide on the basis of numerous observations. According to our observations, the critical twin spacings d1 and d2 in silicon may change with the undercooling rather than be invariant. An in situ observation experiment was designed to investigate this hypothesis. First, a Æ112æ dendrite was induced at an interface with a low undercooling (ΔT = 14.8 K) (Figure 8a). 1405
dx.doi.org/10.1021/cg101721v |Cryst. Growth Des. 2011, 11, 1402–1410
Crystal Growth & Design
ARTICLE
Figure 5. Faceted dendrite growth of Si crystal sample under different undercooling: (a) ΔT = 12.6 K, only one Æ112æ dendrite; (b) ΔT = 24.1 K, two Æ110æ dendrites and two Æ112æ dendrites; (c) ΔT = 30.2 K, three Æ110æ dendrites.
Figure 6. EBSP measurement of the upper surface of the samples applied with different undercooling: (a) ΔT = 12.2 K; (b) 25.1 K; (c) 33.4 K.
The Æ112æ dendrite growth was stable under this undercooling, and we assumed the twin spacing in this dendrite to be d0. Then the sample was heated carefully to melt the crystal in such a way that an unmelted part remains, leaving parallel twins in the
unmelted crystal. After that, a higher undercooling (ΔT = 21.3 K) was applied to induce dendrite growth from the parallel twins again. We observed the interesting phenomenon that the dendrite initially grew in the Æ112æ direction, then changed to the 1406
dx.doi.org/10.1021/cg101721v |Cryst. Growth Des. 2011, 11, 1402–1410
Crystal Growth & Design Æ110æ direction [Figure 8b]. The dendrite grew from the same parallel twins with the twin spacing d0. This result indicates that the dendrite with twin spacing d0 that grew in the Æ112æ direction was unstable at the higher undercooling. In other words, stable dendrite growth in the Æ112æ direction at a higher undercooling requires parallel twins with a wider twin spacing d > d0. Therefore, we concluded that the critical twin spacing d2 for stable Æ112æ dendrite growth increases as the undercooling increases. As shown in Figure 8b, we found that after changing the growth direction to the Æ110æ direction, the dendrite growth velocity became greater than that in the Æ112æ direction. This is consistent with the result that the theoretical growth velocity of a Æ110æ dendrite is higher than that of a Æ112æ dendrite with the same twin spacing.33 Similarly, we can imagine that the critical twin spacing d1 for stable Æ110æ dendrite growth also increases as the undercooling increases. In summary, both the critical twin spacings d1 and d2 increase with increasing undercooling. We next discuss the effect of the twin spacing on the dendrite growth orientation under a given undercooling. Figure 9 shows
Figure 7. Distribution of faceted dendrite growth orientation in terms of the undercooling ΔT and twin spacing. d1 is the maximal twin spacing for stable Æ110æ dendrite growth and d2 is the minimum twin spacing for stable Æ112æ dendrite growth. As the undercooling increases, d1 and d2 increase.
ARTICLE
the three-dimensional and two-dimensional growth processes of Æ110æ and Æ112æ faceted dendrites according to the F-model.18,31 It is supposed that two parallel twins (twin 1 and twin 2) are contained in the equilibrium form of the silicon crystals (Figure 9a) and that the twin spacing d is narrower than the critical twin spacing d1 (d < d1). The crystal was bounded by {111} habit planes, and the potential growth directions of the dendrite were Æ110æ and Æ112æ. The main growth process of Æ110æ and Æ112æ dendrites includes rapid growth at the re-entrant corner and continuous growth at the {111} plane surface. The different-colored triangles in the two-dimensional images indicate the transition of the location of the re-entrant corner at twin 1 and twin 2. The gray indicates that the location of the re-entrant corner is at twin 1, and pink indicates that the re-entrant corner is at twin 2. The detailed growth process is not described here instead we focus on the final shape of Æ110æ and Æ112æ dendrites. Æ110æ dendrites grow without any change in the shape of the dendrite tip (Figure 9b4). For Æ112æ dendrites, the dendrite tip becomes wider as the dendrite grows (Figure 9c4). Langer et al.35-37 reported that the stability criterion for dendritic crystal growth is νF2 = constant, where ν is the dendrite growth velocity and F is the tip radius of the dendrite. For stable dendrite growth in any given direction, the growth process must preserve the tip morphology. The tip morphology remains constant for the Æ110æ faceted dendrite, which indicates that dendrite growth in the Æ110æ direction is stable. However, the tip radius F of the Æ112æ faceted dendrite becomes wider during the growth process, which indicates that dendrite growth in Æ112æ direction by the F-model is unstable. That is the reason why dendrites preferentially grow in the Æ110æ direction when the twin spacing is narrow (d < d1). Now we consider dendrite growth in the Æ112æ direction with a wide twin spacing (d > d2). Although Fujiwara et al.18 proposed the growth mechanism of Æ112æ dendrites shown in Figure 9c, which is consistent with their experimental observations, the Æ112æ dendrite growth in this model is unstable according to the stability criterion for dendritic crystal growth. Albon and Owen reported that for a wide twin spacing, the reentrant corner may be separated by curved regions, and that dendrites growing in the Æ112æ direction in accordance with the H-model are stable, because the dendrite tip morphology can be maintained by the layers originate at the re-entrant
Figure 8. Faceted dendrite growth from the same parallel twins under different undercooling: (a) ΔT = 14.8 K, one stable Æ112æ dendrite; (b) ΔT = 21.3 K, initial dendrite growth in Æ112æ direction that changed to Æ110æ direction. 1407
dx.doi.org/10.1021/cg101721v |Cryst. Growth Des. 2011, 11, 1402–1410
Crystal Growth & Design
ARTICLE
Figure 9. (a) Equilibrium form of silicon crystal that contains two parallel twins (twin 1 and twin 2); three-dimensional and two-dimensional images of (b) Si Æ110æ and (c) Æ112æ dendrite growth process. The different-colored triangles in the two-dimensional images indicate the transition of the location of the re-entrant corner at twin 1 and twin 2. The gray indicates that the location of the re-entrant corner is at twin 1, and pink indicates that the re-entrant corner is at twin 2.
grooves and advance over the curved interface to the adjacent.34 To grow stably, in fact, Æ112æ dendrite has three different growth models according to our in situ observation. One model is that Æ112æ dendrite initially grew rapidly then the growth velocity decreased, and finally ceased with a triangular tips. The growth process follows the F-model. Hmodel is also possible for Æ112æ dendrite growth with a wide twin spacing. Another growth model is that the dendrite initially grew in the Æ112æ direction then changed to the Æ110æ direction. All the three growth models, which depend on the twin spacing and undercooling, can meet the stability criterion for dendritic crystal growth. Detailed experimental and discussion of the Æ112æ dendrite growth models will be presented in a later publication. Finally, we discuss the relationship between the dendrite growth orientation and the undercooling. Nagashio and Kuribayashi10 discussed this relationship from the viewpoint of the Berg effect38 that the concentration is not constant over the entire rectangular crystal surface, but is highest at the corners. They concluded that with increasing undercooling, the edges become regions with more efficient heat dissipation, which leads to the transition of the growth direction from Æ112æ to Æ110æ. According to the results of section 3.1, the dendrite growth orientation is related to the twin spacing, and we consider the above relationship from the viewpoint of parallel twin formation in the crystal. At present, the location where the parallel twins form in silicon is still disputed. Fujiwara et al. reported that the parallel twins may form at a faceted interface, and that the formation mechanism of parallel twins involves the formation of a twin boundary at the {111} facet plane at the growth interface followed by the formation of another twin parallel to
Figure 10. Location of formation of parallel twins in Si crystal under different undercooling.
the first one, and then a faceted dendrite grows parallel to the facet plane.29 Pohl et al. suggested, on the basis of the results of simulations, that parallel twins may form at grain boundaries, and they gave an explanation of this from a thermodynamic point of view.39 We observed the location of twin formation directly by EBSP measurement. Figure 10 shows the location of parallel twins formation in the crystal under different undercooling. The results indicate that the parallel twins were formed at grain boundaries, which is consistent with the simulation results of 1408
dx.doi.org/10.1021/cg101721v |Cryst. Growth Des. 2011, 11, 1402–1410
Crystal Growth & Design Pohl et al.39 In Figure 6, we also can observe similar result. As can be seen from the EBSP results, after one twin boundary is formed, another twin boundary is formed parallel to the first one rather than forming simultaneously, which is consistent with the formation process proposed by Fujiwara et al..29 Once the first twin boundary is formed, the twin spacing depends on when another twin boundary is formed. Hurle reported that a twinned nucleus is thermodynamically favored if the undercooling exceeds a critical value.40 The higher the undercooling, the easier the generation of twins. Thus, when the undercooling was increased, the second twin boundary formed easily, which indicates that a narrow twin spacing is predominantly formed at a high undercooling. For a low undercooling, a wide twin spacing is formed. According to the simulation results of Pohl et al.,39 a high twin density appears at a high undercooling, which is consistent with the results in Figure 10. As the undercooling increases, a higher twin density and parallel twins with a narrow twin spacing appear. According to the results in section 3.1, dendrites preferentially grow in the Æ110æ direction with a narrow twin spacing. That is the reason why the Æ110æ dendrite is dominant at a high undercooling and the Æ112æ dendrite usually appears at a low undercooling. In EML experiments, hardly any Æ112æ dendrites were found for pure silicon,21,22 which may be attributed to the fact that the undercooling in the EML experiments (ΔT > 30 K) was too high to form the wide twin spacing required for stable Æ112æ dendrite growth (ΔT < 25 K).
4. CONCLUSIONS The effects of twin spacing and undercooling on the growth orientation of Si-faceted dendrites were thoroughly elucidated by in situ observation. The results indicate that the growth orientation of Si-faceted dendrites greatly depends on the twin spacing and undercooling. The Æ112æ growth orientation occurs preferentially for a wide twin spacing and low undercooling (∼10 K < ΔT j 15 K). Æ110æ dendrites were found to dominate in the case of a narrow twin spacing and high undercooling (∼25 K < ΔT j 100 K). Æ110æ and Æ112æ growth directions occur with equal frequency for intermediate value of undercooling (∼15 K < ΔT j 25 K). The critical twin spacing for stable Æ112æ growth increases as the undercooling increases, which means that a wider twin spacing is required for stable Æ112æ dendrite growth at a high undercooling. However, at a high undercooling, twin formation becomes easier, which indicates that a narrow twin spacing is predominantly formed, which is why Æ110æ dendrites dominated at a high undercooling. To improve the quality of mc-Si ingots produced by dendritic casting, it is preferable to induce Æ110æ dendrites growth at a high undercooling (ΔT J 25 K) because Æ110æ dendrites with a high growth velocity will occupy the crucible bottom, enabling the production of high-quality mc-Si ingots with {112} planes dominating the upper surface. At present, large-sized mc-Si ingots are being prepared in our group by dendritic casting method by applying as-obtained results, and the ingots’ properties are being evaluated. ’ AUTHOR INFORMATION Corresponding Author
*Tel: þ 81 22 215 2103. Fax: þ 81 22 215 2101. E-mail: louis.
[email protected].
ARTICLE
’ ACKNOWLEDGMENT This work was partially supported financially by a Grant-inAid for Scientific Research (21686001) from the Ministry of Education, Culture, Sports, Science and Technology of Japan. X.Y. gratefully acknowledges the Japan Society for the Promotion of Science (JSPS) for financial support. Dr. K. Kobayashi is acknowledged for performing the EBSP measurements.
’ REFERENCES (1) Donolato, C. Semicond. Sci. Technol. 1998, 13 (7), 781–787. (2) Donolato, C. J. Appl. Phys. 1998, 84 (5), 2656–2664. (3) Card, H. C.; Yang, E. S. IEEE Trans. Electron. Devices 1977, 24 (4), 397–402. (4) Donolato, C. Solid State Phenom. 1999, 67-68, 75–80. (5) Hoshikawa, T.; Taishi, T.; Huang, X.; Uda, S.; Yamatani, M.; Shirasawa, K.; Hoshikawa, K. J. Cryst. Growth 2007, 307 (2), 466–471. (6) Fujiwara, K.; Pan, W.; Usami, N.; Sawada, K.; Tokairin, M.; Nose, Y.; Nomura, A.; Shishido, T.; Nakajima, K. Acta Mater. 2006, 54 (12), 3191–3197. (7) Fujiwara, K.; Nakajima., K. U.S. Patent 20090000536, 2009. (8) Wang, H. Y.; Usami, N.; Fujiwara, K.; Kutsukake, K.; Nakajima, K. Acta Mater. 2009, 57 (11), 3268–3276. (9) Billig E. Proc. R. Soc. 1955, A229 (1178), 346–361. (10) Nagashio, K.; Kuribayashi, K. Acta Mater. 2005, 53 (10), 3021–3029. (11) Chen, X. Y; Wang, X.; Wang, Z. H.; Yang, X. G.; Qian, Y. T. Cryst. Growth Des. 2005, 5 (1), 347–350. (12) Wang, Q. Q.; Xu, G.; Han, G. R. Cryst. Growth Des. 2006, 6 (8), 1776–1780. (13) Fang, J. X.; You, H. J.; Kong, P.; Yi, Y.; Song, X. P.; Ding, B. J. Cryst. Growth Des. 2007, 7 (5), 864–867. (14) Zhang, X. J.; Wang, G. F.; Liu, X. W.; Wu, H. Q.; Fang, B. Cryst. Growth Des. 2008, 8 (4), 1430–1434. (15) Devaud, G.; Turnbull, D. Acta Metall. 1987, 35 (3), 765–769. (16) Hamilton, D. R.; Seidensticker, R. G. J. Appl. Phys. 1960, 31 (7), 1165–1168. (17) Wagner, R. S. Acta Metall. 1960, 8 (1), 57–60. (18) Fujiwara, K.; Maeda, K.; Usami, N.; Nakajima, K. Phys. Rev. Lett. 2008, 101 (5), 055503. (19) Lau, C. F.; Kui, H. W. Acta Metall. Mater. 1991, 39 (3), 323–327. (20) Li, D.; Herlach, D. M. Phys. Rev. Lett. 1996, 77 (9), 1801–1084. (21) Aoyama, T.; Kuribayashi, K. Acta Mater. 2000, 48 (14), 3739–3744. (22) Liu, R. P.; Volkmann, T.; Herlach, D. M. Acta Mater. 2001, 49 (3), 439–444. (23) Fujiwara, K.; Nakajima, K.; Ujihara, T.; Usami, N.; Sazaki, G.; Hasegawa, H.; Mizuguchi, H.; Nakajima, K. J. Cryst. Growth 2002, 243 (3), 275–282. (24) Fujiwara, K.; Obinata, Y.; Ujihara, T.; Usami, N.; Sazaki, G.; Nakajima, K. J. Cryst. Growth 2004, 266 (4), 441–448. (25) Fujiwara, K.; Pan, W.; Sawada, K.; Tokairin, M.; Usami, N.; Nose, Y; Nomura, A.; Shishido, T.; Nakajima, K. J. Cryst. Growth 2006, 292 (2), 282–285. (26) Ohara, S.; Bennett, A. I. J. Appl. Phys. 1964, 35 (3), 686–693. (27) Barrett, D. L.; Myers, E. H.; Hamilton, D. R.; Bennett, A. I. J. Electrochem. Soc. 1971, 118 (6), 952–957. (28) Stokkan, G. Acta Mater. 2010, 58 (9), 3223–3229. (29) Fujiwara, K.; Maeda, K.; Usami, N.; Sazaki, G.; Nose, Y.; Nakajima, K. Script. Mater. 2007, 57 (2), 81–84. (30) Fujiwara, K.; Maeda, K.; Usami, N.; Sazaki, G.; Nose, Y.; Nomura, A.; Shishido, T.; Nakajima, K. Acta Mater. 2008, 56 (11), 2663–2668. (31) Fujiwara, K.; Fukuda, H.; Usami, N.; Nakajima, K.; Uda, S. Phys. Rev. B 2010, 81 (22), 224106. 1409
dx.doi.org/10.1021/cg101721v |Cryst. Growth Des. 2011, 11, 1402–1410
Crystal Growth & Design
ARTICLE
(32) Yang, X. B.; Fujiwara, K.; Maeda, K.; Nozawa, J.; Koizumi, H.; Uda, S. Appl. Phys. Lett. 2011, 98 (1), 012113. (33) Yang, X. B.; Fujiwara, K.; Gotoh, R.; Maeda, K.; Nozawa, J.; Koizumi, H.; Uda, S. Appl. Phys. Lett. 2010, 97 (17), 172104. (34) Albon, N.; Owen, A. E. J. Phys. Chem. Solids 1963, 24 (7), 899–907. (35) Langer, J. S.; Mullern, H. Acta Metal. 1978, 26 (11), 1681–1687. (36) Langer, J. S. Suppl. Prog. Theor. Phys. 1978, 64, 463–476. (37) Langer, J. S.; Sekerka, R. F.; Fujioka, T. J. Cryst. Growth 1978, 44 (4), 414–418. (38) Berg, W. F. Proc. R. Soc. London, Ser. A 1938, 164 (A916), 79–95. (39) Pohl, J.; Muller, M.; Seidl, A.; Albe, K. J. Cryst. Growth 2010, 312 (8), 1411–1415. (40) Hurle, D. T. J. J. Cryst. Growth 1995, 147 (3-4), 239–250.
1410
dx.doi.org/10.1021/cg101721v |Cryst. Growth Des. 2011, 11, 1402–1410
