Formation mechanism and properties of twinned structures in (111) seeded directionally solidified solar grade silicon

Acta Materialia 121 (2016) 24e36

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Formation mechanism and properties of twinned structures in (111) seeded directionally solidified solar grade silicon V.A. Oliveira a, b, c, *, B. Marie a, b, C. Cayron d, M. Marinova d, M.G. Tsoutsouva e, H.C. Sio f, T.A. Lafford e, J. Baruchel e, G. Audoit g, h, A. Grenier g, h, T.N. Tran Thi e, D. Camel a, b a

Univ. Grenoble Alpes, INES, F-73375 Le Bourget du Lac, France CEA, LITEN, Department of Solar Technologies, F-73375 Le Bourget du Lac, France ECM Greentech, 109 rue Hilaire du Chardonnet, 38100 Grenoble, France d CEA, LITEN, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France e European Synchrotron Radiation Facility, CS 40220, 38043 Grenoble Cedex 9, France f Research School of Engineering, Australian National University (ANU), Canberra ACT0200, Australia g Univ. Grenoble Alpes, F-38000 Grenoble, France h CEA, LETI, MINATEC Campus, F-38054 Grenoble, France b c

a r t i c l e i n f o

a b s t r a c t

Article history: Received 1 July 2016 Received in revised form 20 August 2016 Accepted 23 August 2016

The growth structure of photovoltaic multicrystalline silicon formed by directional solidification presents a high fraction of S3 and higher order twins. Previous studies proposed that these complex structures are formed by a succession of 2D nucleation events of S3 twins on {111} growth facets at the triple line formed by their intersection with the crucible wall, another crystal, or the surface. In this work, we report the reproducible formation of multiple twinned domains inside solar grade Si single crystals grown by directional solidification above a (111) seed. These domains start on a S3 twin nucleated inside the crystal bulk, and systematically develop into similar twinned structures characterized by a ternary arrangement of grains in S3, S9, and S27 relationship. The mechanism of formation of the initial twin nucleus is discussed, and a scenario is proposed for the processes of subsequent multiple twinning. The growth competition between twin grains is shown to promote the appearance of incoherent twin boundaries, and dislocations near grain boundaries and in the twin grains themselves. The electrical activity of S-boundaries is measured, and the correlation between the structure of the defects and the resulting detrimental electrical activity is then discussed. © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Twinning Monolike silicon Defects Crystal growth Electrical properties

1. Introduction A large fraction of the grain boundaries present in photovoltaic multicrystalline silicon (mc-Si) grown by directional solidification from the melt are twin boundaries, especially S3 [1,2]. The unique property of the perfect S3 (111) coherent boundary is its very low boundary energy [3], with which is associated a negligible electrical activity [4]. Perfect S3 (111) boundaries are thus acceptable defects in mc-Si growth as they are less harmful to the photovoltaic properties of the material than random boundaries. However, successive twinning events result in higher-order S9 and S27 boundaries that are more recombination active, and may act as sites


man, 73375 Le Bourget-du-Lac, * Corresponding author. 50, Avenue du Lac Le France. E-mail address: [email protected] (V.A. Oliveira). http://dx.doi.org/10.1016/j.actamat.2016.08.063 1359-6454/© 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

for dislocation nucleation [5,6]. These twinning phenomena also play a major role on the overall mechanism of selection of the grain structure of multi-crystalline silicon [7]. A way to improve the control of the grain structure consists in using heterogeneous nucleation sites at the bottom of the ingot. The material obtained by this technique, known as High Performance multicrystalline silicon (HP-Si), shows a reduction in the area occupied by grains in S3n relationship and much lower intra-grain dislocation densities [6]. Indeed, the random boundaries nucleated at the bottom of the ingot can better accommodate the thermo-mechanical stress in the ingot, thus improving the material quality [6]. With the aim of further improving the material quality to approach that of single crystals, another route has been recently developed which consists in growing quasi-monocrystalline (“monolike”) ingots by directional solidification starting on a pavement of monocrystalline seeds that are placed in the bottom of the crucible [8]. This creates a

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single crystal or, more often, large crystals separated by grain boundaries parallel to the growth direction, the characteristics of which are determined by the relative misorientations between seeds [9]. The possibility of choosing the growth direction in this process allows a better control of the optical reflectivity, the <100> direction giving the lowest reflectivity with the standard basic surface texturing etch. However, this requires elimination of the twins which have be reported to be able to propagate from junctions between seeds or at crucible walls (see for instance [10]). For all the above reasons, there is a strong interest in understanding the processes of formation of the different twin boundaries and their associated electrical activity. The possibility of choosing the arrangements of the seeds makes monolike growth ideal for this. An example is the work of Trempa et al. [10], where nucleation of twins near the crucible wall was studied for different growth orientations. Another example was recently published by Autruffe et al. [11], who investigated dislocation generation from artificially created S3n grain boundaries. It is well accepted that, thanks to their very low energy, S3 (111) boundaries are formed by two dimensional nucleation on the (111) growth facet [12e14]. However, thermodynamic considerations indicate that the probability of forming such a twinned nucleus on the facet at the typical undercoolings at which these facets grow (1
Ce10
C according to the data compiled in Ref. [14]) remains very low, except at particular favourable sites such as the triple line (TPL) formed at the intersection of the facet with the crystal surface or another grain [13,14]. Using the criterion developed by Voronkov [15] for the anchoring of facets at the solid-liquid-vapor triple junction during Czochraski growth, Hurle [13] showed that nucleation at this site could explain the high twinning frequency in III-V compounds; Duffar and Nadri [14] subsequently extended the approach to the case of directional solidification of multicrystalline silicon. More specifically, these last authors developed criteria for the occurrence of facets at grain boundary triple lines, and found, for particular facet orientations, nucleation probabilities in qualitative agreement with observed twinning frequencies. The mechanism was recently confirmed by Tandjaoui et al. [16] who, thanks to in situ synchrotron X-Ray imaging, directly observed twin nucleation at grain boundary grooves in silicon. It is also worth noticing that the same mechanism was found in molecular dynamics simulations by Pohl et al. [17]. In addition, numerous studies mention possible effects of impurities on the nucleation of S3 twins [3]. In particular, it has been argued that carbon, which is one of the main contaminants of solar grade silicon, might play a role through the formation of SiC precipitates. Such precipitates, when located at the twin boundary, causes a reduction in the grain boundary energy [18,19]. As they have much higher interface energy than the coherent S3 boundary, S9 and S27 twins are considered to result from successive events of nucleation of the coherent S3, which finally lead to complex multiple twinned structures. The elementary processes by which the formation of these multiple twinned domains occur are difficult to follow in a multi-crystalline growth structure. One such process may be the encounter of two grains previously nucleated with a S3-type relationship from the same grain as has been observed in in situ experiments on thin samples in Ref. [7]. In a post mortem study performed on bulk multi-crystalline samples [2], the different multiple twinned structures were observed and discussed in terms of the associated reduction of the grain boundary energy (for instance, the dissociation of the high energy S9 (221) boundary) but their relation with the instantaneous growth front morphology was not discussed. Other open questions concern the mechanism which control the crystallographic orientation of the twin boundary planes as well as the crystallographic distortions and dislocation densities at these boundaries, all parameters which

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play a determining role in their electrical activity [20]. In the present paper, a very reproducible process of formation of multiple twinned domains observed during monolike growth of solar grade silicon in the <111> direction is reported. These multiple twinned domains were observed several times in two distinct ingots grown with the same seed orientation, feedstock, and cooling rate. The possible mechanisms of initiation of these domains are discussed on the basis of the characterization of the initial interface by HRTEM and Atom Probe Tomography. The subsequent steps of multiple twinning are thoroughly investigated by EBSD on successive horizontal cross sections. Synchrotron X-ray White beam Topography and Rocking Curve Imaging are then used to characterize the dislocation network and lattice distortions associated with the formation of these twinned domains. Lastly, the electrical activities of the different twin boundaries are measured using Light Beam Induced Current (LBIC) and calibrated Photoluminescence imaging, and the correlations between the structural characteristics of the defects and the resulting detrimental electrical activity are discussed. 2. Experimental procedure 2.1. Crystal growth A <111> monolike Si ingot with a diameter of 158 mm and a height of 100 mm was grown by directional solidification in a laboratory furnace devised for seeded growth [21]. For this, a circular (111)-monocrystalline seed (154 mm in diameter and 20 mm thick) was extracted from a Czochraslki ingot and placed in the bottom of a cylindrical Si3N4-coated silica crucible so as to cover the crucible base. The crucible was then filled with Solar Grade (SoG) silicon feedstock previously characterized by Glow Discharge Mass Spectrometry (GDMS): dopant concentrations were 0.65 ppm wt B and 1.4 ppm wt P; the only metallic element detected apart from Ge was Al at a level of 0.02 ppm wt, the other metallic elements being below detection limits of 1 ppm for Ta, 0.05 ppm wt for Fe, and lower than 0.01 ppm wt for the other elements. As for the concentrations of the light elements O and C, which depend on the growth environment, these were directly measured in the solidified ingot by FTIR. The O content, which results from the balance between the inward O flux from the oxidised crucible coating and the outward flux from the melt surface into the argon flow, was around 3  1017 at/cm3. The C concentration profile, which mainly results from the contamination by the CO vapours present in the furnace atmosphere, and the segregation due to rejection by the advancing front, was found to vary from 1  1017 at/cm3 at the top of the ingot to 4  1017 at/cm3 at the bottom of the ingot, which means that the liquid remained under-saturated in C during most of the crystallisation, the saturation value being in the range 4  1017 at/cm3 to 6  1017 at/cm3. In contrast, it is known that, due to the contact of the Si melt with the Si3N4 crucible coating, the liquid ahead the front is slightly super-saturated in N during the whole crystallisation process, and that, depending on growth conditions, Si3N4 particles may precipitate inside the liquid or at the growth front [22]. The ingot was grown from the bottom (where the seed crystal was located) towards the top. Here, seeding is controlled thanks to a system for tuning heat extraction from the bottom of the crucible. The heating arrangement simultaneously provides top and lateral heating, which causes a change in the shape of the isotherms from concave towards the melt in the lower part to convex in the upper part of the ingot. This change in curvature occurs at around 25% of the height of the ingot, as revealed by the shape of iso-resistivity curves viewed on a peripheral vertical section of the ingot (Fig. 1) (Iso-resistivity curves represent instantaneous shapes of the

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CCD camera developed at the ESRF [25], with optics giving a 1.87 mm image pixel size (see Ref. [26] for more details). To complement these analyses, the microstructure of the defect was revealed by etch-pits using Wright etching for 2 min. Lastly, the electrical activity of different S-boundaries was measured using two complementary techniques: calibrated Photoluminescence (PL) imaging and Light Beam Induced Current (LBIC). PL imaging was performed on a single-side passivated wafer containing the twinned structure, and the recombination rates of charge carriers at the S-boundaries were extracted according to the method defined in Ref. [27]. For LBIC mapping, a mechanically polished wafer was used in order to avoid the influence of crystallographic orientation-dependent reflections on the LBIC measurement. The wafer was processed into a conventional solar cell by applying phosphorus diffusion and a SiN anti-reflection coating followed by screen printing of contacts and firing at 800
C. The recombination velocities at the S-boundaries were derived from the corresponding contrast profiles on LBIC maps using Donolato's model [28]. Fig. 1. Resistivity map of a vertical half-section of the ingot taken at the border of the brick which was subsequently sliced horizontally into the wafers shown on Fig. 2 (the overall size of the ingot is indicated by dashed lines).

crystallisation front, because the dopant concentration is homogeneous in the liquid at any time thanks to the good mixing achieved under these experimental conditions). A silica rod was dipped into the melt at regular time intervals in order to check the position of the solid-liquid interface during melt-back and growth. The measured growth rate was 1.2 cm/h, and the temperature gradient in the solid Si, derived from the measurement of the extracted heat flux, was around 25 K/cm [21]. 2.1.1. Characterization After crystallisation, the ingot was sliced horizontally into parallel 200 mm thick-wafers (dimensions: 100  100 mm2). In order to study the initiation and development of the multiple twinned domains, macroscopic images of the wafers were first made using an optical scanner. Then, parts of wafers containing twinning defects at different stages in their development from bottom to top were selected and etched to remove the surface saw damage. Grain orientations and S3n multiple twinning boundaries were determined by EBSD on a LEO1530 (Zeiss) Field Emission Gun Scanning Electron Microscope FEG-SEM equipped with Oxford Instruments HKL Channel 5 EBSD software. Atomic scale analyses of the twins and defects were carried out by HRTEM on a 300 kV FEI Titan transmission electron microscope. Defects and the strain fields around them were analysed from the HRTEM images by using the Geometric Phase Analysis (GPA) method [23]. In order to analyse the potential influence of carbon impurities present in solar grade silicon on twin nucleation, local analyses of the carbon content were performed inside the twinned domain, on its border and outside by Secondary Ion Mass Spectroscopy (SIMS). These measurements were made at a sensitivity of 5  1015 atoms/ cm3 with a CAMECA IMS4F, using a Cs þ primary ion beam detecting negative secondary ions. Then 3D chemical mapping was carried out across the initial twin boundary by Atom Probe Tomography (APT) [24] with a FLEXTAP CAMECA instrument. The dislocation network and lattice distortions associated with the formation of the twinned structure were imaged and quantified using synchrotron X-ray White Beam Topography (WBT) and Rocking Curve Imaging (RCI) at 20 keV at beamline BM05 at the European Synchrotron Radiation Facility (ESRF). For Rocking Curve Imaging, the sample was positioned to diffract the Si (220) reflection vertically and the diffracted beam image was recorded using a

3. Results 3.1. Sequences of development of multi-twinned domains inside the crystal Macroscopic examination of the wafers reveals peculiar defects, which all present the same structure and steps of development, but appear at different times and positions during growth (Fig. 2). The defect localized in the middle of every wafer is caused by an indentation of the dipping rod on the solid silicon surface during crystallisation and is not related to the occurrence of the twinned structures. Fig. 2 shows that all these characteristic twinned structures develop from a circular defect of diameter around 3 mm (yellow arrows). EBSD was applied in two selected zones (delimitated by red squares in Fig. 2 and magnified in Fig. 3a) showing: I) the initial cylindrical defect and II) an intermediate state of evolution of the twinned structure. The crystallographic maps and corresponding pole figures are shown in Fig. 3b and c. The initial defect is a cylindrical twinned crystal S3 (denoted A, in green in Fig. 3b) rotated by 60
around the [111] growth direction relative to the matrix denoted O (in yellow in Fig. 3b). At the periphery of A, which presents a corrugated shape, small crystals nucleate which are identified to be in S3 relationship with A and S9 relationship with the matrix O. Two millimeters higher in the crystal, the surrounding grains are arranged into three grains (denoted Bi, with i ¼ 1, 2, 3) that present a ternary symmetry around crystal A. The three Bi orientations together with the matrix O constitute the four S3 twin variants related to the initial twinned domain A. Thus Bi are in S9 relationship with each other and with the matrix O. Successive sections such as that of Fig. 3c show that the structure develops with the growth of Bi crystals over crystal A, with an angle of 19.5
relative to the normal of the solidification front as confirmed on the vertical section presented below in Fig. 4. Simultaneously, crystals Bi grow at the expense of the matrix O. Between Bi and O, new crystals, called Ci (in blue), are finally nucleated. EBSD analysis of the misorientation through the boundaries between Bi and Cj crystals (in black in Fig. 3b) shows a misorientation of 31
around <110> which corresponds to a S27a multiple twin. S27a is a chain of three twins denoted 111 by Cayron [29]; it can be seen as the result of three 70.5
rotations around the same <110> axis. However, these Cj crystals are in S3 relationship with the matrix O. In summary, the crystallographic orientations of the crystals

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Fig. 2. Wafers showing several twinned defects with similar structural evolution. These structures start always with a circular defect as source (marked with yellow arrows). The defect in a red square is characterized by EBSD in Figs. 3 and 4. The distances in millimeters correspond to the distance between the correspondent wafer and the bottom of the ingot. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

constituting the twin-related domains are as schematically illustrated in Fig. 3d, and the twinning scheme of the growth defect is as follows: O/A/Bi and O/Cj, where the arrow / is a S3 relationship. From this twinning chain, the orientation relationship between Bi and Cj results from the composition of S9 with S3, resulting in S27. Thus, the different twin boundaries formed during the crystal growth are: O-A ¼ S3, A-Bi ¼ S3, O-Bi ¼ S9, Bi1-Bi2 ¼ S9, O-Cj ¼ S3 and Bi-Cj ¼ S27. Higher in the ingot, due to the orientations of the A-Bi boundaries, crystal A is gradually engulfed. During this process, the grain boundaries between the Bi grains adopt a low energy orientation. Concurrently, the coherent S3 boundaries between Bi and A begin to depart from the {111}-plane as seen later in Fig. 8. The final structure observed in the upper part of the ingot is composed of the three Bi crystals in S9 relationship with each other surrounded by Cj crystals with similar grain dimensions to the Bi crystals.

systematically observed. This feature is shown in more detail by HRTEM (Fig. 5). Here, a portion of vertical ð112Þ boundary formed between A and O is observed. Due to the appearance of a B twin, this boundary is dissociated into ð111Þ and ð221Þ planes (Fig. 5a and b). Some dislocations are revealed by the GPA deformation field (Fig. 5c and d). The expansion strain field in the coherent twin interface along the (111) plane in the vicinity of the step relaxes in the region where dislocation density increases inside crystal A (left zone in Fig. 5d). Following the S9 ð221Þ boundary, it appears that it
alternates coherent segments with distorted zones (Fig. 5e). Moire patterns, with a fringe periodicity of 1 nm, which is equal to three times the d111 distance, are often visible at the edge of horizontal (111) and vertical ð112Þ boundaries, as shown in Fig. 6. Such patterns are artefacts produced by the superposition along the electron beam direction of two crystals related by a twin relationship [30]. This confirms the perfection of the twinning relation between A and O.

3.2. Initial stages of twinning 3.3. Local carbon distribution To get a better understanding of the initial stages of formation of the defect, a cross-section of the wafer shown in Fig. 3b where the defect first appears was cut roughly along a <110> direction (parallel to the A/B interface, Fig. 3c), and first inspected using EBSD and SEM (Fig. 4). EBSD maps and SEM images show that the bottom of the defect is constituted of planar segments of S3 (111) boundary parallel to the (111) growth plane. These planar horizontal segments are separated by vertical steps, at the upper end of which interrupted Bi twin bands penetrating into the A twinned domain are

In order to characterize the carbon composition in the vicinity of the first twin nucleus and at the twin boundary itself, Secondary Ion Mass Spectroscopy (SIMS) and Atom Probe Tomography (APT) were carried out. SIMS results showed a homogeneous carbon distribution inside the twinned domains, across their common border and outside, with concentrations of 2.0  1017 atoms/cm3, 2.3  1017 atoms/cm3 and 2.2  1017 atoms/cm3, respectively. These values are significantly below the saturation value of 5  1017 atoms/cm3.

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milling in a Ga Focused Ion Beam (FIB). Fig. 7a presents a TEM image of the tip showing that the tip contained the twin. Fig. 7b presents the 3D elemental map of the Si tip, where the reconstructed volume was obtained using the tip profile method. The Ga ions are mainly located on the edge of the tip and come from FIB milling. Fig. 7c presents the mass spectrum of the selected inset in the Si tip, giving access to the chemical nature of the ions. The contribution of carbon ions, indicated by arrows, is not detected and is limited by the background noise in the mass spectra, which has been estimated around 3  1018 atoms/cm3. By comparison, the average C concentration which would result in this volume if one SiC atomic plane was present at the twin boundary is estimated to be in the range of 1  1020 atoms/cm3 to 2  1020 atoms/cm3 depending on the precise surface area of twin boundary contained in the selected volume. Thus we can infer that the concentration of C atoms actually present in the boundary plane is much lower than the SiC stoichiometric composition. 3.4. Associated defects

Fig. 3. Evolution of the twinned structure. a) Scan images of the twinned structure taken at differents heights in the ingot. b) EBSD map of the cylindrical defect source of the twinned structure seen in c). c) EBSD map of the twinned structure. Red lines represent S3 boundaries, yellow lines represent S9 boundaries, and black lines represent S27a boundaries. d) Schematic representation of the twinning chains that link the grains observed on the EBSD map on c) (the details of this type of representation are given in Ref. [29]). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

However, each SIMS spot has a surface of approximately 0.01 mm2, thus a higher spatial resolution is required to determine the presence of a layer of SiC at the twin interface. For this, APT measurements were performed on tip-shaped samples prepared using the standard lift-out technique followed by an annular

Dislocation networks and lattice distortions revealed inside and outside the twinned domain by White Beam Topography and Rocking Curve Imaging are illustrated in Fig. 8 for the case of a twinned structure taken 7 mm above its first nucleus, and whose EBSD map is shown in Fig. 8a. Here are presented partial views showing an X-ray topography image (Fig. 8b), integrated intensity maps that are sensitive to the lattice distortion (Fig. 8d, f, and g), a peak position map sensitive to the crystal mosaicity (Fig. 8c), and an image of the etch-pits (Fig. 8e) of the central part of the twinned structure. Integrated intensity maps (Fig. 8 d, f, g) reveal different levels of distortion among the different twin boundaries, particularly the central S3 boundaries A-Bi seen in Fig. 8d. These distortions cannot be attributed to the angular departures from the perfect twinning relationship, which, as shown for instance by the peak position map of Fig. 8c, remain very low, with a maximum smaller than 102 degree. However, while the boundary A-B3 is still a coherent S3 (111) and appears as a perfect line between both grains in Fig. 8e, the boundary plane A-B1 deviates by 35
towards crystal A from the coherent S3 position, and the boundary plane A-B2 presents a deviation of 6
and an irregular zigzag shape. In relation to this, a high lattice deformation is revealed by the integrated intensity map of Fig. 8d near the boundaries A-B1 and A-B2, in contrast to the absence of distortion shown by the coherent S3 boundary A-B3. Fig. 8e and g shows that S27 boundaries also have a high lattice deformation (marked by black arrows) compared to S9 boundaries (marked by white arrows). Some of the S-boundaries are sources of dislocations that spread inside the twinned crystal. In Fig. 8d we observe that the edge of the incoherent boundary A-B1 is a source of dislocations that spread inside crystal A and are blocked by the other incoherent boundary A-B2. A similar phenomenon is also observed in Fig. 8g, where dislocations originating at the edges of the two S27 boundaries formed between B1 and Cj can be seen propagating towards the interior of B1. Two highly distorted bands expand inside the grains in Fig. 8b and g. These bands are related to the existence of sharp edges of the boundary B2-C (Fig. 8b) and B3-C (Fig. 8f), identified by yellow arrows. Also, the zone separating the incoherent boundary A-B2 and the highly distorted band inside B2 presents a peak shift of q ¼ 5  103 degrees (red zone in the peak position map of Fig. 8c). By contrast, the integrated intensity map of Fig. 8g shows a domain with coherent micro-twins and free of dislocations inside grain B1. These micro-twins start when the lateral boundary of grain B1 changes its character from S27 (B1-C1 boundary) to S9 (B1O boundary).

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Fig. 4. First twin nucleation. a) EBSD map of the first twin, same as Fig. 3b. The dotted line corresponds to the zone where a cut was performed to perform EBSD mapping on a crosssection of the first nucleus, seen in b). c) SEM image of the corresponding selected zone in the EBSD map showing the nucleation of crystals B on the {111} facets of crystal A.

Fig. 5. a) TEM image of the cross-section of the first twin nucleus. The selected zones (I, II, and III) were analysed by HR-TEM. b) Scheme identifying the twin and twin boundary planes relation shown in a). c) HR-TEM image and GPA deformation field of a dislocation along the (111) plane. d) HR-TEM image and GPA deformation field showing strain field in the vicinity of the small step S3 (112). The expansion strain field along the coherent (111) twin relaxes in the region of high dislocation density in crystal A. e) S9 (221) seen in detail by HR-TEM. Along the S9 interface the highly distorted regions were followed by coherent (221) interfaces as the one shown on the HR-TEM magnification.

Finally, the White Beam Topograph (Fig. 8b) shows the presence of background dislocations in a cellular arrangement homogeneously distributed in the matrix. The density of the dislocations that form the cell walls is estimated to be 104 cm2 from the full

width half maximum RCI map, while the cell interior, remarkably, contains only a few dislocations or is even dislocation-free. The average dislocation density inside the twinned domain is estimated to be three times higher than in the matrix. The cellular

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S27 (Bi-Cj) boundaries. These S27 (Bi-Cj) boundaries are also electrically active in the diffusion length map. This means that the main difference between the measurements is the activity of S9 Bi-O boundaries, as confirmed by the values in Table 1. The coherent S3 boundaries formed between Cj and O show no contrast by either technique. The two incoherent S3 boundaries A-B1 and A-B2 are only seen in the diffusion length map since A is completely engulfed at the slightly later stage of growth corresponding to the PL wafer. These incoherent boundaries show quite high recombination rates, of the order of 2000 cm/s. Nonetheless, the higher order S27 boundaries show an even higher activity (>3500 cm/s), with similar values extracted from both the PL and LBIC models. 4. Discussion


patterns (interference fringes) formed at the edge of a (111) and ð112Þ S3 Fig. 6. Moire interface. A/O is the region where A and O superimpose due to the fact that the S3 ð112Þ boundary is not strictly perpendicular to the plane of the sample.

The multiple twinned domains observed start from the nucleation of an initial S3 twin inside the O single crystal. Possible physical causes for this initial twinning are discussed below, and the mechanisms controlling the subsequent steps of growth of these domains are analysed. Finally, the influence of these processes on the structural imperfections and resulting electrical properties of the different twins formed is examined.

Fig. 7. Atomic Probe Tomography (APT) analysis of the initial twin boundary: a) TEM imaging of the FIB milled tip before APT analysis, revealing the presence of the twin, b) 3D APT reconstruction of the Si tip (left image), which was previously imaged by TEM. Each dot is one atom. The mass spectrum calculated in the selected inset of the Si atom map is shown on the right.

arrangement of dislocations is, however, not achieved everywhere: in particular, in grain B2, dislocations tend to align in a favourable crystallographic direction. 3.5. Electrical properties The electrical activity of the different S-boundaries in the twinned structure was measured by calibrated PL imaging before solar cell processing, and after by LBIC, using wafers 4 mm apart in the ingot. Fig. 9a shows the calibrated PL image of the twinned structure on a single-side passivated wafer and Fig. 9b shows the minority carrier diffusion length map extracted from LBIC mapping on a solar cell. An example of a LBIC contrast profile across a S27 boundary is shown in Fig. 9d. Table 1 gives the recombination rates derived from these curves using Sio's model for PL data [27] and Donolato's model for LBIC data [28]. Comparing the PL image (Fig. 9a) and the diffusion length map (Fig. 9b), the most remarkable difference is the lack of contrast in the contour of the twinned structure in the diffusion length map whereas this is not the case for the PL image. The black contour in the PL image is mainly formed by S9 (O-Bi) boundaries and a few

4.1. Initial twinning From the above observations relative to the formation of the twinned domain, it can be stated that twin A appeared at the growth front, and subsequently grew along the [111] crystallisation direction. The shape of the bottom interface between twin A and the O matrix (planar and parallel to the (111) plane) strongly suggests that the defect was formed by nucleation and growth of a two-dimensional twinned nucleus on the (111) facetted growth plane. Although it could not be directly revealed here in the absence of growth striations, the (111) facet is expected to develop at the growth front as soon as the corresponding isotherm becomes convex towards the liquid, which, as discussed in Section 2.1 (Fig. 1), occurs at around 25% of the ingot height, i.e. 20 mm above the bottom wafer. Concerning the probability of nucleation of the twin on the (111) facet, Hurle [13] and Duffar [14] discussed the case of nucleation at the triple line forming the intersection of the facet with, respectively, the crystal surface and another grain. They showed that twins with very low energy such as the coherent S3 {111} could nucleate at these favourable sites. Our results indicate that this

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Fig. 8. Analyses of crystalline defects associated with the evolution of the twinned structure. a) EBSD map of the twinned domain. The dark-blue boundaries are S3 boundaries. b) White beam topography image of part of the twinned structure (<110> diffraction vector). The dotted white line limits the zone showed in c and d). c) Peak position map of A, part of B2, and C. d) Integrated Intensity map of the same zone shown in c. e) Etch-pits image of crystal A incoherent and coherent boundaries. f) Integrated Intensity map of B3. g) Integrated Intensity map of B1. Micro-twins can be seen in B1 in the zone limited by the red brace. Black arrows show the distorted S27 boundaries, and white arrow shows the nondistorted S9 boundary in d) and g). The yellow arrows seen in b) and f) identify distorted bands. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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Fig. 9. Electrical activity of different S-boundaries. a) Calibrated PL imaging of the twinned structure. b) Minority carrier diffusion length map of the same twinned structure, 4 mm lower in the ingot. c) Scan image of the twinned structure to help localizing the boundaries. d) (I0I)/I0 profile extracted from the LBIC measurement across a S27 boundary.

Table 1 Grain boundary recombination velocities measured by LBIC and PL. The accuracy of the measurement is up to 200 cm/s. Grain boundary Coherent S3 boundaries Incoherent S3 A-B1 Incoherent S3 A-B2 S9 B1-B2 S9 B1-O S27 B1-C left S27 B2-C S27 B1-C right

Vs LBIC (cm/s)

Vs PL (cm/s)

2800 1000 100 2700 12400 5500 4800

3600

event might even occur in the middle of the horizontal facetted growth plane. In view of the energy of a 2D nucleus, the probability of this event would be very low. Kutsukake et al. [31] showed that twins formation is favoured by changes in the growth rate. However, local fluctuations due to convective instabilities are not expected in the present case where the vertical temperature gradient is stable, and the thermocouple measurements did not reveal any disturbance in the programmed temperature cycle. Thus, triggering of this process requires in the present case either a further lowering of the twin energy, or the presence of a local nucleating defect. Previous studies [18,19] indicate that a layer of SiC could be the source of twin nucleation by lowering the stacking fault energy. But such is not the case in our experiment, as atom probe analysis does not show carbon adsorption at the first twin nucleus boundary. This may be related to the fact that the local SIMS measurements show that the carbon concentration inside and near the 2D twin is significantly below the saturation value. As previously discussed in the literature [32,33], stacking faults can be formed in silicon by condensation of vacancies. But it is generally accepted that such condensation occurs below the crystallisation front, while vacanices are near equilibrium at

concentrations in the range of 1  1015 cm3 at the melting point [34]. Molecular dynamics simulations suggest, however, that vacancy clusters may be directly incorporated at the facetted solidliquid growth interface in silicon [35], thus possibly impacting on the formation of twins. However, foreign particles are known to favour twinning in Czochralski growth [3]. As mentioned above, during directional solidification of Si, the melt is saturated in nitrogen due to the contact with the Si3N4 coating covering the inner walls of the crucible. Micrometric particles of Si3N4 may thus come into contact with the growth front, as attested by the incorporation of Si3N4 particles in solid silicon under certain growth conditions [22]. Contact between such a particle and the growth front can favour twin nucleation. Indeed, the potency of these particles for nucleating silicon has been demonstrated [36]. However, no incorporated Si3N4 particle could be evidenced here by infrared microscopy. 4.2. Steps of multiple twinning Initially, the twinned 2D nucleus A extends laterally in all directions on the presumably (111) facet plane, which gives its characteristic circular shape when viewed from above. However, as illustrated in Fig. 10a, step-by-step growth simultaneously continues on the surrounding growth facet of matrix O. Thus, the lateral growth of the A steps is finally stopped by the opposite motion of steps growing on the surrounding matrix O. This gives rise to the formation of a vertical boundary between A and O (shown on the vertical sections of Figs. 4e6, and a corresponding triple line (TPL) on the solidification front. The competition between the lateral expansion of A and the growth of O gives the very corrugated shape of this TPL as viewed in the horizontal plane. The evolution of the morphology of the growth interface at this TPL will determine the possibility of nucleating new twins

V.A. Oliveira et al. / Acta Materialia 121 (2016) 24e36

33

Fig. 10. Sketch of the inferred local configurations and mechanisms of twin nucleation at the successive stages of formation of the multiply twinned domain: a) Formation of facets on A and O sides. b) Nucleation of crystals Bi on the {111} facets of crystal A. c) Nucleation of crystals Cj, on the {111} facets of the matrix, O.

according to the mechanism proposed in the literature (twodimensional nucleation on a (111) growth facet anchored at a triple line). To analyse this possibility, we use the energetic criterion proposed by Voronkov [15], which states that a facet can remain anchored to the TPL only if a negative free energy change (per unit length of TPL) results when the growth step moving on the facet merges into the TPL and the TPL correspondingly advances by one interplanar spacing. In the present case, considering the strong possibility of a (111) growth facet, the O matrix and the A nucleus present the same (111) facet in the direction of crystallisation. A first question is thus whether this facet can remain anchored to the TPL on both sides of it (Configuration I in Fig. 10a). The Voronkov criterion transposed to this situation is written:

ðge  2gÞh < 0

(1)

where gh is the free energy of unit length of the steps of height h formed on each of the two facets, and geh is the free energy change per unit length associated with the change in geometric configuration upon merging of these two steps. In Configuration I, merging of the steps leads to a corresponding increase of the grain boundary area without change of the facet area, so that ge is simply given by:

ge ¼ sGB and condition 1 becomes:

sGB < 2g

(2)

Considering the value of g ¼ 0.09 J m-2 proposed by Hurle [13], condition 2 would be satisfied for the S3 (111) twin boundary

which has a very low energy (sS3 (111) ¼ 0.03 J m-2 to 0.06 J m-2 according to the literature data compiled in Ref. [3]). Indeed, it has been observed in in situ experiments that no grooving occurs at such a triple line [37]. By contrast, criterion (2) is definitely no longer satisfied for the other S3 twin planes realised at the present vertical boundaries, for instance the S3 (211) boundary evidenced in Fig. 5, for which, according to theoretical estimations [38,39], the interfacial energy is about 30% lower than for a high angle grain boundary (smax GB ), i.e. much higher than 2g. Thus, at least on one side, the facet cannot remain anchored to the TPL. On this side, the piling-up steps will then form a locally inclined front. At the points where the TPL is locally parallel to one of the three horizontal <110> directions, an inclined {111} facet will then appear, leading to Configuration II of Fig. 10a, or Configuration III of the same Figure if this occurs on both sides. In view of the corrugated shape adopted by the advancing A front, this condition may occur at many points around the lateral A/O interface. Application of Voronkov's criterion for these two configurations, which is developed in the Annex, indicates that anchoring of the facets at the TPL is possible in both. The occurrence of Bi twins, as observed at the bottom of the defect in vertical section (Fig. 4), is consistent with the formation of an inclined {111} facet on the A side of the A-O triple-line. But it is important to notice also on the same sections that these first twinnings are followed by a new sequence of growth of A in the horizontal direction, leaving a Bi twin band in A. Such a new sequence of lateral growth of A can even occur without an apparent intermediate formation of Bi, which gives the characteristic steplike shape of the bottom of the defect. These last events can only be explained by considering that, at least at the beginning, Configuration II is achieved so that new A nuclei can expand on the assumed growth facet of O. This configuration also explains that, at

34

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this stage of development of the twinned domain, twinnings occur only on A and not on O. The achievement of this configuration requires the growth facet of A to be a little in advance of that of O, meaning that the growth undercooling is slightly lower on the A facet than on the O facet. A possible reason for this may be a difference in the evacuation of the solutes (particularly C and N present in solar grade silicon) rejected ahead the front: lateral evacuation of the solutes is easier ahead the steps growing radially outward on A, than ahead the steps growing radially inward on O. Nucleation of the corresponding Bi variant on the inclined facet of A in Configuration II of the triple line is energetically favoured in the presence of a step on the (111) facet of O (Fig. 10b). The interface energy between this step on O and the twinned nucleus is minimized if it adopts the orientation of the S9 (221) plane (bisector of the angle formed by the two (111) planes), whose structure has been studied experimentally [40] and for which the theoretically estimated energy is sS9(221) ¼ 0.66 J m-2[37,38]. Here appears the main difference between the situation discussed here, where the interface is facetted on both sides of the triple line so that there is an interaction between both sides during nucleation and growth of the twin, and the situation described by Duffar in Ref. [14], where the interface is facetted on one side only so that there is no such interaction. The consequence is that in the present case, when the Bi twin develops in three dimensions, its interface with crystal O is not bound to stay along the vertical plane of the original S3 (211) boundary but can adopt the optimum coherent S9 (221) boundary, which in addition is consistent with an equality of the growth rate of the facets on both sides (Fig. 10b). This translates into the dissociation:

      S3 112 /S3 111 þ S9 221 Thus, this dissociation, which can be seen in the vertical section of Fig. 5, appears to be the result of a twinning nucleation occurring at a triple line junction facetted on both sides. The boundary energy is reduced in this transformation, in accordance with the criterion put forward in Ref. [2] to explain boundary dissociations observed in multi-crystalline Si growth. The numerous Bi domains nucleated around A (see Fig. 3a) expand at the expense of both O and A, and finally merge into one crystal of each of the Bi variants (see Fig. 3b). This expansion is favoured by the fact that, since the Bi crystals have no (111) facet plane parallel to the growth front, they grow ahead the average front until they adopt a polyhedral shape limited by their {111} facets. The interfaces developing between these crystals as they grow adopt S9 boundaries perpendicular to the growth face, which minimize the boundary energy per unit area. However, the expansion of the interfaces between Bi crystals resulting from their growth at the expense of A finally causes the interfaces between A and Bi to leave the coherent S3 {111} planes and to become incoherent, as illustrated in Fig. 8f. Finally, at the triple lines between Bi and O, a new generation Cj of twins is seen to nucleate, these being the other three variants of S3 on O. Similarly to the previous scenario of nucleation of Bi on A, twin nucleation of Cj on O suggests that inclined (111) facets formed on the O side of the triple line. This configuration can be obtained if the rate of advance of the horizontal (111) facet of O along the crystallisation direction is larger than that of the {111} facet of Bi, which will cause the boundary between B and O to leave the S9 (221) orientation and become vertical. The geometrical configuration of the new groove thus formed is similar to the previous Configuration III, with inclined facets anchored on both sides of the TPL. Thus, a twin nucleation phenomenon similar to the one described above for Bi on A can now occur but for Cj on O (Fig. 10c), this leading to the new dissociation:

S9/S3 þ S27 As a conclusion, the two successive scenarios described above of twinning at triple lines facetted on both sides allow the main features of the characteristic geometry of the multi-twinned domain to be described.

4.3. Structural defects and their effect on electrical properties The results of synchrotron X-ray imaging presented in section 3.4 evidence the following main mechanisms of formation of structural defects associated with the multiple twinning process described above: - A partial loss of coherency of the S3 boundaries between and A and Bi crystals is due the expansion of the interfaces between Bi crystals that causes an engulfment of crystal A by crystals Bi as growth proceeds. - A local lattice deformation results from this loss of coherency. Consistently, S27 boundaries show higher lattice deformation than S9 boundaries as they are less coherent. - These highly incoherent boundaries are sources of dislocations that spread into the bulk of adjacent crystals: this is the case for the A/B1 boundary from which dislocations spread into A (Fig. 8e), and the B1/Ci boundary from which dislocations spread into A (Fig. 8c). - In addition, sharp angles present along some boundaries cause a local concentration of stress, and are thus the source of highly distorted bands propagating inside the adjacent crystals (Fig. 8b and g). - In contrast, in particular regions where micro-twin bands have been formed, the propagation of dislocations has been blocked. - Apart from the particular regions above, dislocations tend to adopt a cellular arrangement which is similar to the one described by P. Rudolph [41] in the case of Czochralski growth of III-V compounds. These cells are formed by cross-slip, climb and short-range interactions between dislocations in a way which minimizes the system energy by achieving a more stable configuration [42]. The resulting structural characteristics which may play a role in the electrical activity of the different twin boundaries formed can be classified in the following way: 1) their twinning order (S3, S9, S27); 2) the coherency or non-coherency of the boundary (related to the interface plane); 3) possible additional dislocations due to the stress imposed by the non-coherent boundaries; and 4) possible misorientations relative to perfect twinning and the associated geometrically necessary dislocations. Concerning the effect of twinning order, Table 1 shows that the recombination rates (VS) measured for the S27 boundaries are the highest, while non-measurable values are obtained for the low energy coherent S3 {111} boundaries, in accordance with literature data [43,44]. For S9 boundaries, measurements on the same boundary by PL and LBIC give very different results: an intermediate value of VS (lower than those of S27) is obtained by PL, while it is at the sensitivity limit in LBIC. This difference in VS values is mainly explained by sample preparation before each measurement, which is different for PL and LBIC. For this latter, the application of P diffusion and hydrogenation steps during solar cell processing may give rise to a gettering and/or passivation effect. It is known that the electrical activity of structural defects is mainly due to their interaction with impurities [44], and thus can be modified by the treatments applied during the preparation of the wafers [45]. The influence of a non-coherency can best be seen in the case of

V.A. Oliveira et al. / Acta Materialia 121 (2016) 24e36

the incoherent S3 A-B1 and A-B2 boundaries, for which the Vs values measured by LBIC approach those for S27. This is probably related to the very corrugated shape of the boundary, indicating a high interfacial energy. In addition, the recombination rates are certainly affected by the high density of dislocations present in the vicinity of the boundary, as indicated by the strong distortion seen in the integrated intensity maps. This high dislocation density may result from a multiplication of dislocations caused by the stress concentration at the sharp angles of the boundary. As for the angular departures from the perfect twinning relationship measured by RCI (Fig. 8d), they are very small (q  103 degrees) e much smaller than those of the artificial twin boundaries studied in Ref. [39]. So, contrary to that case, a simple order of magnitude estimate confirms that the associated geometrically necessary dislocations should make, in the present case, a negligible contribution to the recombination activity of the boundaries. Indeed, the corresponding recombination rate is classically written [20]:

V S ¼ gd n d where gd (in cm2s1) is the dislocation recombination rate, from which the dimensionless recombination strength Gd is defined (Gd ¼ gd/D where D ¼ diffusion coefficient of minority carriers), and nd (in cm1) is the number of dislocations per unit length of the boundary, which is related to the misorientation angle q by: nd ¼ q/ b*, where b* is the component of the Burgers vector of the dislocations perpendicular to the plane of the boundary. Taking typical values of b* ¼ 3  108 cm, D ¼ 30 cm2/s and an upper limit of the dislocation recombination strength Gd ¼ 102, we get VS ¼ 200 cm/s. This value of VS is at the limit of the sensitivity of our measurements, thus the other factors, i.e. twinning order, coherency and additional dislocations, have here the dominant influence on the electrical activity. 5. Conclusions Our directional solidification experiments on (111)-oriented seeds using solar grade silicon evidenced a reproducible sequence of nucleation of an initial twin inside the single crystalline region, and subsequent development into a characteristic structure formed by multiple twinning events at the triple lines between twin and matrix. These twinned structures were initiated by the formation of a S3 twinned nucleus very likely on the (111) growth facet of the matrix, away from any triple line. Atom probe analysis at the initial matrix/twin interface did not show the presence of a layer of SiC, which would have favoured twin nucleation by lowering the stacking fault energy. Other possible causes are the incorporation of vacancy clusters at the front and/or transient contact with Si3N4 particles immersed in the liquid. The following sequences of twinning occur according to the process of nucleation at the new triple line formed between the melt, the matrix and the previously-formed twin. The particularity in this case is that the triple line is presumably facetted on both sides, leading to the decomposition of the former twin boundary into two new twin boundaries. Growth competition between twin grains generates defects inside and near the twin boundaries that were quantified by Rocking Curve Imaging using synchrotron X-rays. The electrical activities of these twin boundaries have been derived from PL and LBIC mapping. In the present case, it has been found that small misorientations relative to perfect twinning have a negligible influence, and that the electrical activity increases by increasing twinning order and incoherency of the boundary, while it can be

35

reduced by external gettering or passivation, depending on boundary structure. Acknowledgements APT sample preparation and analyses were performed at the nano-characterization platform (PFNC) of the Minatec Campus. The authors would like to thank N. Enjalbert for solar cell processing. V. A. Oliveira would like to thank Prof. D. MacDonald for making possible the collaboration between ANU and INES. This work was partially funded by the CEA and the ESRF under the Project Carnot/ Solar Innovation call. V. A. Oliveira acknowledges financial support from ECM Greentech. Annex: application of Voronkov criterion to configurations II and III The Voronkov criterion can simply be applied to triple line Configuration III of Fig. 10a. The free energy change per unit length geh associated with the change in geometric configuration upon merging of the two steps coming from the facets on both sides is simply written:

 h sin q



ge h ¼ sGB  2s0SL cos q

(A1)

where s0SL is the interfacial energy of the (111) growth facet, q is the angle between grain boundary and facet as shown on Fig. 10a, and the second term corresponds to the reduction of facet area on merging of the steps. Then, condition (A1) becomes:

sGB < 2g$x sin q þ 2s0SL cos q

(A2)

or, introducing smax GB and sSL, the energy of the solid-liquid interface far from facetted orientations:

sO sGB 2sSl < A$BðC$sin q þ cos qÞ where A ¼ max ; B ¼ SL and C max sGB sGB sSL g ¼ 0 sSL (A3) According to the values proposed by Hurle [5], B y 0.94 and C y 0.34. And, as generally accepted, A should be close to one. Taking A ¼ 0.9 and q ¼ 19.6
then gives for criterion (A3) sGB/smax GB < 0.90, a condition which is largely satisfied for the S3 (211) twin boundary. For the alternative Configuration II, criterion (A3) is approximately modified to become:





sGB cos q < A$B C$sin q þ smax 2 GB

(A4)

which, taking the same values as above, gives: sGB/smax GB < 0.50. This condition would also be satisfied according to the theoretical data given in Ref. [38]. References [1] A. Voigt, E. Wolf, H.P. Strunk, Grain orientation and grain boundaries in cast multicrystalline silicon, Mater. Sci. Eng. B 54 (1998) 202e206. [2] G. Stokkan, Twinning in multicrystalline silicon for solar cells, J. Cryst. Growth 384 (2013) 107e113. [3] T. Duffar, Comprehensive review on grain and twin structures in the bulk photovoltaic silicon, Recent Res. Dev. Cryst. Growth 5 (2010) 61e111. [4] J. Chen, T. Sekiguchi, R. Xie, P. Ahmet, T. Chikyo, D. Yang, et al., Electron-beaminduced current study of grain boundaries in multicrystalline Si, Scr. Mater. 52 (2005) 1211e1215.

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