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Dislocation generation at near-coincidence site lattice grain boundaries during silicon directional solidification
Journal of Crystal Growth 411 (2015) 12–18
Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Dislocation generation at near-coincidence site lattice grain boundaries during silicon directional solidification Antoine Autruffe a,n, Vegard Stenhjem Hagen b, Lars Arnberg a, Marisa Di Sabatino a a b
NTNU, Department of Materials Science and Engineering, Trondheim, Norway NTNU, Department of Physics, Trondheim, Norway
art ic l e i nf o
a b s t r a c t
Article history: Received 16 September 2014 Received in revised form 28 October 2014 Accepted 29 October 2014 Communicated by: K.W. Benz Available online 6 November 2014
Bi-crystal silicon ingots separated by near-coincident site lattice (near-CSL) grain boundaries (GBs), namely Σ9 and Σ27a, have been grown in a small scale Bridgman-type furnace at 3 mm/s. Surface observations show different microstructure developments, depending on the nature of the seed GB and initial deviation from the low energy configuration. Grain boundary structure evolution and dislocation emission sources have been assessed for both types of GBs. Topological imperfections forming at the near – Σ9 and Σ27 GBs during the growth have been found to be the major source of defect generation. These imperfections are the result of the re-arrangement of the GBs during the growth due to the seed GBs deviation from low energy configurations – i.e. Σ9{221}1/{221}2 and Σ27a{511}1/{511}2. & 2014 Elsevier B.V. All rights reserved.
Keywords: A1. Defects A1. Solidification A2. Seeded growth B1. Multicrystalline silicon
1. Introduction Multicrystalline silicon (mc-Si) contains a wide range of structural defects that contribute to deteriorate the material quality. Dislocations have been identified as a major obstacle to obtain high performance mc-Si based solar cells. A drastic decrease of solar cell efficiency has been observed for densities higher than 104 cm 2 [1,2], while local dislocation densities up to 108 cm 2 are measured in industrial mc-Si [3]. It is therefore crucial to limit dislocation emission during mc-Si growth. Dislocations are generated and multiplied in the silicon ingot at high temperature, during growth and cooling. Grain boundaries (GBs) have been identified to be a major source of dislocations [4–6]. When a multi-crystal is strained, the GB surfaces are concentrating stresses in order to preserve the grains compatibility at the GB interface region. Dislocation emission can therefore be activated at GB, even at relatively low applied stress. Varin et al. showed that shear stresses as low as G/1000 to G/400 applied at grain boundaries where G is the shear modulus of the material, can start local plastic deformation responsible for dislocation generation [7]. Silicon has anisotropic mechanical properties depending on the crystal orientation [8,9] and it has been shown that under applied strain, stresses arise preferentially in certain grains [4,10]. Takahashi et al. investigated dislocation generation mechanisms during
n
Corresponding author. Tel.: þ 47 73597093. E-mail address: [email protected] (A. Autruffe).
http://dx.doi.org/10.1016/j.jcrysgro.2014.10.054 0022-0248/& 2014 Elsevier B.V. All rights reserved.
directional solidification of mc-Si and observed unilateral emission of dislocations at GBs, in the grains where the resolved shear stresses developing in the {111} planes appear to be the highest [4]. The resolved shear stress, τ, is related to the applied load, σ, by the Schmid factor, m, of the slip system, relatively to the load direction:
τ ¼ mσ
ð1Þ
The Schmid factor is expressed as follows: m ¼ cos φ cos ϕ
ð2Þ
with φ the angle between the applied load direction and the slip plane normal – i.e. o111 4 and ϕ the angle between the applied load direction and the slip direction – i.e. o110 4. Twelve slip systems are available for dislocation in silicon. When the main load direction is known, the maximum Schmid factor M of each grain can be calculated. The grain with the higher maximum Schmid factor M is the one where dislocations are expected to be first generated. Dislocation generation at a GB is also closely related to the GB nature as the interfacial energy of a GB is depending on grain misorientation [11]. Recent improvements in the process showed that by increasing the fraction of random GBs in mc-Si ingots, the density of defects can be decreased [12]. On the other hand, semicoherent GBs have proven to have a peculiar potential to emit defects [13]. Local topology is important to consider as GB imperfections such as steps are well known to be stress concentrators where dislocations tend to be emitted [6]. Coincident site
A. Autruffe et al. / Journal of Crystal Growth 411 (2015) 12–18
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Fig. 1. (a) Vertical cross section of Σ27a bi-crystal. The two seeds used and the GB are indicated. (b) Sketch of the top view of an indexed monocrystalline cylinder drilled out of a Czochralski ingot, as prepared for manufacturing the bi-crystal seeds. Cutting angles α and β are calculated to define the GB natures and planes. Σ27a{511}1/{511}2 GB planes were controlled while Σ9 GB planes were not. Only the misorientation was.
lattice (CSL) boundaries are the most common GBs found in mc-Si [14–16]. The aim of the present work is to investigate the structure evolution and dislocation emission at selected near-CSL GBs – i.e. Σ9 and Σ27a. Bi-crystal silicon ingots have been solidified for this purpose, in order to isolate the central GBs from the other potential dislocation sources. The dislocation emission mechanisms are described in detail in the following.
2. Experimental set up and method Small silicon bi-crystals (55 mm height, 32 mm diameter, and 100 g weight) have been grown in a Bridgman furnace, using seed growth process. This method has been chosen in order to isolate one GB, and to control the orientation of the two grains as well as the GB planes. The solidification method is described in Refs. [17,18]. Si3N4 coated alumina crucibles have been used and the pulling rate was 3 mm/s. A vertical cross section of the ingot with a Σ27a grain boundary is shown in Fig. 1a. The seeds have been prepared from a Czochralski monocrystalline ingot solidified in the o100 4 direction. Two half cylinders oriented in the o1104 direction have been drilled out and a controlled tilt misorientation was introduced between them, as explained in Ref. [17]. In the present work, seeds have been prepared in order to grow near-CSL GBs. Fig. 1b shows the seed manufacturing process. During the following study, please note that a distinction is made between the seed GB – i.e. the GB between the seeds, and the grown GB – observed above the seeds. Σ9 and Σ27a seed GBs have been manufactured by introducing a tilt misoriention angle around the o1104 axis of 38.91 and 31.61 respectively between the seeds [19]. In the case of the Σ27a GB, the cutting angles α and β have been adjusted to select the GB planes. The Σ9 seed GB planes have not been controlled. The seed GB natures have been confirmed by electron back scattered diffraction mappings (EBSD) on vertical cross sections and, in the case of the Σ27a seeds, the GB planes have been identified by the same technique. The Σ27a seed GB is close to the Σ27a{511}1/{511}2 configuration. The Σ9 and Σ27a seed GB additional misorientations with respect to the CSL misorientation values given by Cunningham et al. [19] are less than the selected tolerance factor values of the EBSD analysis software (10/√Σ – i.e. 31 for Σ9 and 21 for Σ27a).
Vertical cross sections of 2 mm thick have been polished with diamond slurry down to 1 mm size, as well as horizontal cuts taken above the seeds. All samples have been etched with Sopori etchant [20] and observations of the defect patterns have been performed by light microscopy (LM) and scanning electron microscopy (SEM). GB identification and plane orientation have been performed by EBSD. Residual strains have been measured in the vertical cuts of the bi-crystal ingots by the near infrared Mueller matrix imaging method (MMI), described in Ref. [21]. Residual strain in the material is proportional to the birefringence, which again is proportional to the retardance. Using MMI, the retardance is found by analyzing the measured Mueller matrix image. The selected light source was a collimated 160 mW light emitting diode array with center wavelength 1300 nm and the detector a Xeva indiumgallium-arsenide 2D array.
3. Results and discussion 3.1. Surface observations on vertical cuts Fig. 2 shows GB growth and dislocation pattern developments, as observed on vertical cross sections made perpendicularly to the central GBs. High densities of dislocations are observed close to the central GBs. As mentioned in the introduction, these GBs are isolated from the other dislocation sources. Arrays of dislocations aligning along {111} planes are visible in Fig. 2a, close to the Σ9 GB. These are deformation structures which suggest, together with the high strain values locally observed close to the GBs (Fig. 2b), that the dislocations have been emitted at the GBs. It is then assumed that the observed dislocations have been emitted at the GBs. As observed previously by Takahashi et al. [4], dislocations tend to generate preferentially in one grain. By assuming similar dislocation mobility in both grains, this observation is the consequence of the anisotropic mechanical properties of silicon. The {111} planes are the most densely packed planes in the silicon diamond cubic structure. Dislocations glide in those planes. At GBs, dislocations are generated in the grain where the shear stresses developing in the {111} planes are the highest. Fig. 2b shows dislocation patterns compared with qualitative residual strain maps made on the same area of vertical cuts, around both
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Assumption (1) is made: considering the cylindrical geometry of the furnace and the crucible, the stresses developing in the ingot are considered to be independent of λ. Under such assumption the identification of the grain where the dislocations are first generated is made by calculating, for a given γ, the maximum Schmid factor, Mλ, over λ. M λ ¼ f γ ¼ maxλ M λ; γ ð3Þ
Fig. 2. (a) LM image of Sopori etched vertical cuts. The etchant revealed the structure development during Σ9 (left) and Σ27a (right) bi-crystals growth. (b) Comparison of dislocation development patterns revealed by Sopori etchant and qualitative residual strain maps performed by MMI around the Σ9 (left) and Σ27a (right) GB, on vertical cuts. Note the different scale between the two strain maps.
Mλ values have been calculated for all γ, for both Σ9 and Σ27a bi-crystals, and the results are displayed in Fig. 3b. In both cases, Grain#1 is the grain where dislocations are emitted in Fig. 2. In the case of a pure axial load (γ ¼ π/2), the maximum Schmid factors Mλ of Grain#1 and Grain#2 are similar, for both bi-crystals. This is not surprising, as all the seeds are axially oriented in the same o110 4 direction, and all the central grains should then present the same potential to activate slip planes when γ ¼ π/2. Therefore a pure axial load cannot be responsible for the asymmetric dislocation development shown in Fig. 2. The ingots have been pulled slowly and the radial temperature gradients in the ingot can be neglected. Thus, asymmetric dislocation emissions shown in Fig. 2 cannot be attributed to thermal stresses only. The Mλ calculations displayed in Fig. 3b show that under assumption (1), slip planes are expected to be first activated in Grain#2 for 0 o γ o π/24 in the case of the Σ9 bi-crystal, and for π/4 o γ o π/2 in the case of the Σ27a bi-crystal. For all other values of γ, Grain#1 and Grain#2 have similar Mλ, and slip planes are not expected to be activated preferentially in one of the grains. These calculations are then in contradiction with the observations made on the bi-crystals and shown in Fig. 2, where dislocations are emitted unilaterally in Grain#1. Assumption (1) is therefore invalidated, and dislocations are then emitted as a consequence of stress discontinuities over λ. Fig. 3c shows thereby an example of Schmid factor calculations for a given γ value (γ ¼ 0 in this case), for λ varying from 0 to π/2. In this case, slip planes are expected to be activated first in Grain#1 for particular λ values (e.g. π/5o λ o π/ 3 in the case of the Σ9 bi-crystal, and for π/4o λ o2π/5 in the case of the Σ27a bi-crystal). It is believed that the stress discontinuities are introduced by the grain boundaries. This is supported by observations made on horizontal cuts and presented in the Section 3.2. 3.2. Surface observations on horizontal cuts
Σ9 and Σ27a GB. It is also observed that the strain develops preferentially in one grain, in both Σ9 and Σ27a cases. The strained grains are the ones where lattice dislocations are emitted. Relatively higher strain values are reached in one side of the GB due to lower activation energy of the {111} plane leading to plastic deformation by dislocation generation and migration. Fig. 3a represents a cylindrical bi-crystal ingot during solidification. Ryningen et al. have demonstrated that dislocations are emitted at grain boundaries by phenomena occurring during solidification, close to the solid–liquid interface, as the crystals are subjected to stresses during the process [5]. However, the main load direction is unknown. In the following discussion, the origin of the stresses responsible for dislocation emission at the GBs is assessed by considering all possible load directions. Schmid factors of all slip systems of both grains have been evaluated for both Σ9 and Σ27a bi-crystals under different load direction assumptions. Two angles, λ and γ, are defined. The angle λ corresponds to a rotation of the normal to the GB plane around z-axis. γ corresponds to a rotation around r-axis, where the r is being defined as the result of the cross product of z and the applied load vector σ. The Schmid factors M of each grain have been calculated for both Σ9 and Σ27a bi-crystals, for all possible load directions – i.e. for 0 o γ, λ o π/2. Grain orientations are determined by EBSD.
Fig. 4a shows the near-Σ9 GB structure development observed by SEM on a horizontal cross section taken 10 mm above the seeds, perpendicular to the GB. The detailed GB structure is sketched with respect to EBSD maps performed on the cross section. The Σ9 seed GB is strongly deviating from the preferred low energy configuration Σ9{221}1/{221}2, as the GB planes have not been controlled. The grown Σ9 GB re-arrangement is therefore pronounced. The Σ9 GB re-arranges during the growth, in order to reach low energy configurations. Segments with clear preferred directions appear, deviating from the direction of the seed GB. The preferred configurations observed in Fig. 4 corresponds to the symmetric Σ9 {221}1/{221}2 and asymmetric Σ9{115}1/{111}2 configurations, as GB segments shown in Fig. 4a align to (115) and (221) planes in grain 1, and (111) and (221) planes in grain 2. It should be noted here, that these GB planes are perpendicular to the growth direction, i.e. [ 110]. The local GB geometry is affected by this mechanism as steps tend to develop. Fig. 4b shows the development of a step, as observed on two horizontal samples taken at different heights of the Σ9 bi-crystal. The resulting step introduces stress concentrating points where dislocations tend to generate, as shown in Fig. 4a and b. The grown Σ9 GB is observed to be locally unstable and can eventually split into two Σ3 GBs, as shown in
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Fig. 3. (a) Sketch of the bi-crystal ingot during solidification. The outer surface of the cylinder describes the outer bi-crystal shape in contact with the crucible. The crystals are subjected to stresses. The main load direction is defined by two angles γ and λ. r vector is defined as the result of the cross product of z and the applied load vector σ. (b) Grain#1 and Grain#2 maximum Schmid factors Mλ over λ, as calculated for γ varying from 0 to π/2, for both Σ9 and Σ27a bi-crystal. Grain#1 corresponds to the grain where dislocations are emitted (see Fig. 2). (c) Grain#1 and Grain#2 Schmid factors M for γ ¼ 0, as calculated for λ varying from 0 to π/2, for both Σ9 and Σ27a bi-crystal.
Fig. 4a and c. This is observed especially for the Σ9{115}1/{111}2 asymmetric segments which have higher interfacial energy than the symmetric Σ9{221}1/{221}2 segments. It has been shown previously that Σ27 and Σ9 GB can dissociate into lower Σ3n boundaries in order to decrease their energy [22,23]. In particular, the asymmetric Σ9 dissociation mechanism has been discussed in previous work [23]. The authors observed the dissociation of asymmetric Σ9 into nanometer-scale triangular grains bounded by three Σ3 GB. Similar grains have been identified and are visible on micro-meter scale in Fig. 4a and c. This dissociation forms sharp GB edges which tend to concentrate stresses. Fig. 4c shows that there is a strong correlation between Σ9 GB dissociation and dislocation generation. It is argued that the defect generation at the grown Σ9 GB is closely related to the Σ9 seed GB deviation from the Σ9{221}1/{221}2 low energy configuration. This deviation is responsible for the re-arrangement of the GB during the growth and the introduction of topological imperfections, which act as stress concentrators and are consequently associated with high densities of dislocations. The dislocation structures predominantly align along the {110} traces (see Fig. 4b), suggesting that the defect clusters observed close to the GB are dominated by recovered structures: during the cooling of the solidified ingot, dislocations originally aligning along {111} slip planes rearrange in sub-boundaries to lower the crystal energy [24–26]. It can be noted that local emissions at coarse straight GB segments are also visible, for instance on the right hand micrograph of Fig. 4c. This observation is later discussed. Fig. 5a shows the Σ27a GB structure development observed by SEM on a horizontal cross section taken 10 mm above the seeds, perpendicularly to the GB. The Σ27a seed GB deviation from the low energy configuration Σ27a{511}1/{511}2 is relatively low, and its re-arrangement is not as pronounced as it is for the Σ9 GB (see Figs. 4a and 5a). The seed GB slight deviation from the low energy configuration Σ27a{511}1/{511}2 causes however the grown GB to form coarse steps. The steps consist of two long GB segments close to the Σ27a
{511}1/{511}2 configuration, and one asymmetric GB segment, as described on the sketch in Fig. 5a. Fig. 5b shows images of one coarse step and its associated dislocations, at different heights of the ingot. It should be noted here that the later appearance of the step does not signify that the dislocations are emitted prior to the step formation, as dislocations can move down in the ingot, after having been first emitted by the GB. It is clear that the dislocation generation occurring at the grown Σ27a GB is closely related to the appearance of coarse GB steps. As for the Σ9 GB, the defect cluster formed close to the step is mainly composed of recovered structure, aligning along the {110} plane traces. In addition, dislocations aligning along {111} slip planes are also visible close the GB. They attest the occurrence of local plastic deformation during the solidification process, close to the GB. Local emissions at coarse straight segments which align close to the Σ27a{511}1/{511}2 configuration are also visible. An example is highlighted with a dashed square in Fig. 5a. Kutsukake et al. have previously investigated the structure evolution of a near-Σ5 {310}1/{310}2 GB by using the seeded growth method and transmission electron microscopy [27]. The authors observed that the GB dislocation structure becomes more organized as growth proceeds, to become only composed of edge dislocations with a Burgers vector of a/10 o310 4, high in the ingot (20 mm above the seed). This change in GB dislocation structure is accompanied by dislocation emission towards the bulk, as some GB dislocations are believed to combine to become glissile in the bulk (i.e. Burgers vector a/2 o110 4) and able to escape the GB interface. The only remaining GB dislocations (edge dislocations of Burgers vector a/10 o3104 ), cannot glide in the GB planes and are sessile in the bulk. In the present work, local observations of etched horizontal cross sections show structure changes along the Σ27a GB. Fig. 5c shows that the dislocation emissions observed at coarse straight GB segments are associated with finer GB steps. These steps are composed of GB segments very close to the Σ27a{511}1/{511}2 symmetric configuration – with a low density of GB dislocation, and therefore shallow etch – and segments which deviate more
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Fig. 4. SEM observations made on Sopori etched horizontal cross sections taken 5–6 mm above the seeds of the Σ9 bi-crystal. (a) Σ9 GB structure and geometry. A schematic view of the grown GB, deviating from the seed GB, and some {115}, {111} and {221} plane traces are added, with respect to EBSD maps performed on the sample. Σ9{221}1/{221}2 and Σ9{115}1/{111}2 GB traces are added in the left corner. These planes are perpendicular to the sample plane. (b) Observations made on cross sections taken at different heights of the Σ9 bi-crystal. The circled region shows the formation of a step composed of near-Σ9{115}1/{112}2 and Σ9{221}1/{221}2 segments. (c) Observation of Σ9 GB dissociations leading to dislocation emission. Local GB structures are sketched, with respect to EBSD maps performed on the sample.
from the symmetric configuration – with higher density of GB dislocation, and therefore deeper etch. The appearance of these GB segments of low energy and high degree of coherency goes along with the migration of GB dislocations originally present at the seed GB, either along the GB or towards the bulk, if they are glissile in silicon lattice. In the case where dislocations are only mobile in the GB plane, they can be expected to pile-up and generate local stresses that can be responsible for plastic deformation leading to dislocation generation. In the case where dislocations can combine to become glissile in silicon lattice, they can be emitted towards the bulk to facilitate the re-organization of the GB to a configuration of lower energy – i.e. higher coherency. In any case, local structure changes of near-CSL GB leading to the appearance of GB segments with high degree of coherency involves dislocation emission in the bulk, which then have the potential to multiply and form clusters as described by Ryningen et al. [5]. The presence of a stress concentrator at the GB can be expected to help GB dislocations to escape the GB interface.
4. Conclusions Bi-crystal silicon ingots separated by near – Σ9 and Σ27a GBs have been grown by directional solidification. Unilateral emission of dislocations from the central GBs have been observed, as a result of shear stresses arising asymmetrically in {111} planes. It has been shown that these dislocation emissions cannot be only attributed to thermal stresses, and are related to stress irregularities introduced by GB topological imperfections. Thus, during Σ9 and Σ27a bi-crystal ingots growth, dislocations are emitted as a result of the seed GBs deviation from the symmetric low energy configurations – i.e. Σ9 {221}1/{221}2 and Σ27a{511}1/{511}2. In the case of the bi-crystal separated by Σ27a GB, this deviation introduces topological imperfections at the grown Σ27a GB – i.e. steps. These are stress concentrators and represent the main source of dislocations while Σ27a{511}1/{511}2 straight segments seem to emit very few dislocations. In the case of the Σ9 GB, the seed GB deviation also introduces steps. Concurrently, a second dislocation emission mechanism has been identified at the
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Fig. 5. (a) SEM image of a Sopori etched horizontal cut of the Σ27a bi-crystal ingot. Steps tend to form, with GB segments of particular directions, corresponding to the preferred configurations. A GB structure sketch is added, including some {511} and {111} plane traces, with respect to EBSD maps performed on the sample. (b) LM images of horizontal cuts, at different heights. Appearance of a coarse grain boundary step, associated with dislocation emission towards the bulk. Some {111} and {110} plane traces are added. (c) SEM image of straight GB segment emitting dislocations. GB segments with high degree of coherency appear – i.e. low GB dislocation density and shallow etch.
grown Σ9 GB: asymmetric Σ9{115}1/{112}2 segments were observed to dissociate and form micrometer scale grains forming sharp GB edges which also tend to concentrate stresses and lead to dislocation generation. These results suggest that during multi-crystalline silicon solidification, semi-coherent grain boundaries tend to generate dislocations as a consequence of their re-arrangement.
Acknowledgment The authors want to acknowledge Prof. Morten Kildemo, Dr. Gaute Stokkan, Prof. Otto Lohne, Dr. Torunn Ervik, Kai Erik Ekstrøm and Dr. Lars Martin Sandvik Aas for useful discussions. References [1] G. Stokkan, et al., Spatially resolved modeling of the combined effect of dislocations and grain boundaries on minority carrier lifetime in multicrystalline silicon, J. Appl. Phys. 101 (5) (2007) 053515-1–053515-9. [2] C. Donolato, Modeling the effect of dislocations on the minority carrier diffusion length of a semiconductor, J. Appl. Phys. 84 (5) (1998) 2656–2664. [3] H.J. Möller, et al., Multicrystalline silicon for solar cells, Thin Solid Films 487 (1–2) (2005) 179–187. [4] I. Takahashi, et al., Generation mechanism of dislocations during directional solidification of multicrystalline silicon using artificially designed seed, J. Cryst. Growth 312 (7) (2010) 897–901.
[5] B. Ryningen, et al., Growth of dislocation clusters during directional solidification of multicrystalline silicon ingots, Acta Mater. 59 (20) (2011) 7703–7710. [6] Ervik T., et al., Dislocation formation at Σ ¼ 27a boundaries, in: proceedings of the 26th EUPVSEC multicrystalline silicon for solar cells. 2011. [7] R.A. Varin, et al., Analytical treatment of grain boundary sources for dislocations, Mater. Sci. Eng. 85 (1987) 115–126. [8] J. Turley, et al., The anisotropy of Young's modulus, shear modulus and Poisson's ratio in cubic materials, J. Phys. D: Appl. Phys. 4 (2) (1971) 264–271. [9] J.J. Wortman, et al., Young's modulus, Shear modulus, and Poisson's ratio in silicon and germanium, J. Appl. Phys. 36 (1) (1965) 153–156. [10] I. Takahashi, et al., Computational investigation of relationship between shear stress and multicrystalline structure in silicon, Jpn. J. Appl. Phys. 49 (2010) 4. [11] M. Kohyama, et al., Structures and energies of symmetrical o 011 4 tilt grain boundaries in silicon, Phys. Status Solidi (b) 137 (1) (1986) 11–20. [12] Y.M. Yang, et al., Development of high-performance multicrystalline silicon for photovoltaic industry, Prog. Photovolt.: Res. Appl. http://dx.doi.org/10.1002/ pip.2437, in press. [13] T. Hoshikawa, et al., Si multicrystals grown by the Czochralski method with multi-seeds, J. Cryst. Growth 307 (2) (2007) 466–471. [14] A. Voigt, et al., Grain orientation and grain boundaries in cast multicrystalline silicon, Mater. Sci. Eng. B B54 (3) (1998) 202–206. [15] B. Gallien, et al., Analysis of grain orientation in cold crucible continuous casting of photovoltaic Si, J. Cryst. Growth 318 (1) (2011) 208–211. [16] A. Autruffe, et al., Influence of pulling rate on multicrystalline silicon ingots' properties, J. Cryst. Growth 386 (2014) 199–203. [17] A. Autruffe, et al., Impact of growth rate on impurities segregation at grain boundaries in silicon during Bridgman growth, J. Cryst. Growth 372 (2013) 180–188. [18] I. Brynjulfsen, et al., Nucleation in small scale multicrystalline silicon ingots, J. Cryst. Growth 361 (2012) 206–211. [19] B. Cunningham, et al., High resolution electron microscopy of grain boundaries in silicon, MRS Proc. 5 (1981) 21.
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Contents lists available at ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Dislocation generation at near-coincidence site lattice grain boundaries during silicon directional solidification Antoine Autruffe a,n, Vegard Stenhjem Hagen b, Lars Arnberg a, Marisa Di Sabatino a a b
NTNU, Department of Materials Science and Engineering, Trondheim, Norway NTNU, Department of Physics, Trondheim, Norway
art ic l e i nf o
a b s t r a c t
Article history: Received 16 September 2014 Received in revised form 28 October 2014 Accepted 29 October 2014 Communicated by: K.W. Benz Available online 6 November 2014
Bi-crystal silicon ingots separated by near-coincident site lattice (near-CSL) grain boundaries (GBs), namely Σ9 and Σ27a, have been grown in a small scale Bridgman-type furnace at 3 mm/s. Surface observations show different microstructure developments, depending on the nature of the seed GB and initial deviation from the low energy configuration. Grain boundary structure evolution and dislocation emission sources have been assessed for both types of GBs. Topological imperfections forming at the near – Σ9 and Σ27 GBs during the growth have been found to be the major source of defect generation. These imperfections are the result of the re-arrangement of the GBs during the growth due to the seed GBs deviation from low energy configurations – i.e. Σ9{221}1/{221}2 and Σ27a{511}1/{511}2. & 2014 Elsevier B.V. All rights reserved.
Keywords: A1. Defects A1. Solidification A2. Seeded growth B1. Multicrystalline silicon
1. Introduction Multicrystalline silicon (mc-Si) contains a wide range of structural defects that contribute to deteriorate the material quality. Dislocations have been identified as a major obstacle to obtain high performance mc-Si based solar cells. A drastic decrease of solar cell efficiency has been observed for densities higher than 104 cm 2 [1,2], while local dislocation densities up to 108 cm 2 are measured in industrial mc-Si [3]. It is therefore crucial to limit dislocation emission during mc-Si growth. Dislocations are generated and multiplied in the silicon ingot at high temperature, during growth and cooling. Grain boundaries (GBs) have been identified to be a major source of dislocations [4–6]. When a multi-crystal is strained, the GB surfaces are concentrating stresses in order to preserve the grains compatibility at the GB interface region. Dislocation emission can therefore be activated at GB, even at relatively low applied stress. Varin et al. showed that shear stresses as low as G/1000 to G/400 applied at grain boundaries where G is the shear modulus of the material, can start local plastic deformation responsible for dislocation generation [7]. Silicon has anisotropic mechanical properties depending on the crystal orientation [8,9] and it has been shown that under applied strain, stresses arise preferentially in certain grains [4,10]. Takahashi et al. investigated dislocation generation mechanisms during
n
Corresponding author. Tel.: þ 47 73597093. E-mail address: [email protected] (A. Autruffe).
http://dx.doi.org/10.1016/j.jcrysgro.2014.10.054 0022-0248/& 2014 Elsevier B.V. All rights reserved.
directional solidification of mc-Si and observed unilateral emission of dislocations at GBs, in the grains where the resolved shear stresses developing in the {111} planes appear to be the highest [4]. The resolved shear stress, τ, is related to the applied load, σ, by the Schmid factor, m, of the slip system, relatively to the load direction:
τ ¼ mσ
ð1Þ
The Schmid factor is expressed as follows: m ¼ cos φ cos ϕ
ð2Þ
with φ the angle between the applied load direction and the slip plane normal – i.e. o111 4 and ϕ the angle between the applied load direction and the slip direction – i.e. o110 4. Twelve slip systems are available for dislocation in silicon. When the main load direction is known, the maximum Schmid factor M of each grain can be calculated. The grain with the higher maximum Schmid factor M is the one where dislocations are expected to be first generated. Dislocation generation at a GB is also closely related to the GB nature as the interfacial energy of a GB is depending on grain misorientation [11]. Recent improvements in the process showed that by increasing the fraction of random GBs in mc-Si ingots, the density of defects can be decreased [12]. On the other hand, semicoherent GBs have proven to have a peculiar potential to emit defects [13]. Local topology is important to consider as GB imperfections such as steps are well known to be stress concentrators where dislocations tend to be emitted [6]. Coincident site
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Fig. 1. (a) Vertical cross section of Σ27a bi-crystal. The two seeds used and the GB are indicated. (b) Sketch of the top view of an indexed monocrystalline cylinder drilled out of a Czochralski ingot, as prepared for manufacturing the bi-crystal seeds. Cutting angles α and β are calculated to define the GB natures and planes. Σ27a{511}1/{511}2 GB planes were controlled while Σ9 GB planes were not. Only the misorientation was.
lattice (CSL) boundaries are the most common GBs found in mc-Si [14–16]. The aim of the present work is to investigate the structure evolution and dislocation emission at selected near-CSL GBs – i.e. Σ9 and Σ27a. Bi-crystal silicon ingots have been solidified for this purpose, in order to isolate the central GBs from the other potential dislocation sources. The dislocation emission mechanisms are described in detail in the following.
2. Experimental set up and method Small silicon bi-crystals (55 mm height, 32 mm diameter, and 100 g weight) have been grown in a Bridgman furnace, using seed growth process. This method has been chosen in order to isolate one GB, and to control the orientation of the two grains as well as the GB planes. The solidification method is described in Refs. [17,18]. Si3N4 coated alumina crucibles have been used and the pulling rate was 3 mm/s. A vertical cross section of the ingot with a Σ27a grain boundary is shown in Fig. 1a. The seeds have been prepared from a Czochralski monocrystalline ingot solidified in the o100 4 direction. Two half cylinders oriented in the o1104 direction have been drilled out and a controlled tilt misorientation was introduced between them, as explained in Ref. [17]. In the present work, seeds have been prepared in order to grow near-CSL GBs. Fig. 1b shows the seed manufacturing process. During the following study, please note that a distinction is made between the seed GB – i.e. the GB between the seeds, and the grown GB – observed above the seeds. Σ9 and Σ27a seed GBs have been manufactured by introducing a tilt misoriention angle around the o1104 axis of 38.91 and 31.61 respectively between the seeds [19]. In the case of the Σ27a GB, the cutting angles α and β have been adjusted to select the GB planes. The Σ9 seed GB planes have not been controlled. The seed GB natures have been confirmed by electron back scattered diffraction mappings (EBSD) on vertical cross sections and, in the case of the Σ27a seeds, the GB planes have been identified by the same technique. The Σ27a seed GB is close to the Σ27a{511}1/{511}2 configuration. The Σ9 and Σ27a seed GB additional misorientations with respect to the CSL misorientation values given by Cunningham et al. [19] are less than the selected tolerance factor values of the EBSD analysis software (10/√Σ – i.e. 31 for Σ9 and 21 for Σ27a).
Vertical cross sections of 2 mm thick have been polished with diamond slurry down to 1 mm size, as well as horizontal cuts taken above the seeds. All samples have been etched with Sopori etchant [20] and observations of the defect patterns have been performed by light microscopy (LM) and scanning electron microscopy (SEM). GB identification and plane orientation have been performed by EBSD. Residual strains have been measured in the vertical cuts of the bi-crystal ingots by the near infrared Mueller matrix imaging method (MMI), described in Ref. [21]. Residual strain in the material is proportional to the birefringence, which again is proportional to the retardance. Using MMI, the retardance is found by analyzing the measured Mueller matrix image. The selected light source was a collimated 160 mW light emitting diode array with center wavelength 1300 nm and the detector a Xeva indiumgallium-arsenide 2D array.
3. Results and discussion 3.1. Surface observations on vertical cuts Fig. 2 shows GB growth and dislocation pattern developments, as observed on vertical cross sections made perpendicularly to the central GBs. High densities of dislocations are observed close to the central GBs. As mentioned in the introduction, these GBs are isolated from the other dislocation sources. Arrays of dislocations aligning along {111} planes are visible in Fig. 2a, close to the Σ9 GB. These are deformation structures which suggest, together with the high strain values locally observed close to the GBs (Fig. 2b), that the dislocations have been emitted at the GBs. It is then assumed that the observed dislocations have been emitted at the GBs. As observed previously by Takahashi et al. [4], dislocations tend to generate preferentially in one grain. By assuming similar dislocation mobility in both grains, this observation is the consequence of the anisotropic mechanical properties of silicon. The {111} planes are the most densely packed planes in the silicon diamond cubic structure. Dislocations glide in those planes. At GBs, dislocations are generated in the grain where the shear stresses developing in the {111} planes are the highest. Fig. 2b shows dislocation patterns compared with qualitative residual strain maps made on the same area of vertical cuts, around both
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Assumption (1) is made: considering the cylindrical geometry of the furnace and the crucible, the stresses developing in the ingot are considered to be independent of λ. Under such assumption the identification of the grain where the dislocations are first generated is made by calculating, for a given γ, the maximum Schmid factor, Mλ, over λ. M λ ¼ f γ ¼ maxλ M λ; γ ð3Þ
Fig. 2. (a) LM image of Sopori etched vertical cuts. The etchant revealed the structure development during Σ9 (left) and Σ27a (right) bi-crystals growth. (b) Comparison of dislocation development patterns revealed by Sopori etchant and qualitative residual strain maps performed by MMI around the Σ9 (left) and Σ27a (right) GB, on vertical cuts. Note the different scale between the two strain maps.
Mλ values have been calculated for all γ, for both Σ9 and Σ27a bi-crystals, and the results are displayed in Fig. 3b. In both cases, Grain#1 is the grain where dislocations are emitted in Fig. 2. In the case of a pure axial load (γ ¼ π/2), the maximum Schmid factors Mλ of Grain#1 and Grain#2 are similar, for both bi-crystals. This is not surprising, as all the seeds are axially oriented in the same o110 4 direction, and all the central grains should then present the same potential to activate slip planes when γ ¼ π/2. Therefore a pure axial load cannot be responsible for the asymmetric dislocation development shown in Fig. 2. The ingots have been pulled slowly and the radial temperature gradients in the ingot can be neglected. Thus, asymmetric dislocation emissions shown in Fig. 2 cannot be attributed to thermal stresses only. The Mλ calculations displayed in Fig. 3b show that under assumption (1), slip planes are expected to be first activated in Grain#2 for 0 o γ o π/24 in the case of the Σ9 bi-crystal, and for π/4 o γ o π/2 in the case of the Σ27a bi-crystal. For all other values of γ, Grain#1 and Grain#2 have similar Mλ, and slip planes are not expected to be activated preferentially in one of the grains. These calculations are then in contradiction with the observations made on the bi-crystals and shown in Fig. 2, where dislocations are emitted unilaterally in Grain#1. Assumption (1) is therefore invalidated, and dislocations are then emitted as a consequence of stress discontinuities over λ. Fig. 3c shows thereby an example of Schmid factor calculations for a given γ value (γ ¼ 0 in this case), for λ varying from 0 to π/2. In this case, slip planes are expected to be activated first in Grain#1 for particular λ values (e.g. π/5o λ o π/ 3 in the case of the Σ9 bi-crystal, and for π/4o λ o2π/5 in the case of the Σ27a bi-crystal). It is believed that the stress discontinuities are introduced by the grain boundaries. This is supported by observations made on horizontal cuts and presented in the Section 3.2. 3.2. Surface observations on horizontal cuts
Σ9 and Σ27a GB. It is also observed that the strain develops preferentially in one grain, in both Σ9 and Σ27a cases. The strained grains are the ones where lattice dislocations are emitted. Relatively higher strain values are reached in one side of the GB due to lower activation energy of the {111} plane leading to plastic deformation by dislocation generation and migration. Fig. 3a represents a cylindrical bi-crystal ingot during solidification. Ryningen et al. have demonstrated that dislocations are emitted at grain boundaries by phenomena occurring during solidification, close to the solid–liquid interface, as the crystals are subjected to stresses during the process [5]. However, the main load direction is unknown. In the following discussion, the origin of the stresses responsible for dislocation emission at the GBs is assessed by considering all possible load directions. Schmid factors of all slip systems of both grains have been evaluated for both Σ9 and Σ27a bi-crystals under different load direction assumptions. Two angles, λ and γ, are defined. The angle λ corresponds to a rotation of the normal to the GB plane around z-axis. γ corresponds to a rotation around r-axis, where the r is being defined as the result of the cross product of z and the applied load vector σ. The Schmid factors M of each grain have been calculated for both Σ9 and Σ27a bi-crystals, for all possible load directions – i.e. for 0 o γ, λ o π/2. Grain orientations are determined by EBSD.
Fig. 4a shows the near-Σ9 GB structure development observed by SEM on a horizontal cross section taken 10 mm above the seeds, perpendicular to the GB. The detailed GB structure is sketched with respect to EBSD maps performed on the cross section. The Σ9 seed GB is strongly deviating from the preferred low energy configuration Σ9{221}1/{221}2, as the GB planes have not been controlled. The grown Σ9 GB re-arrangement is therefore pronounced. The Σ9 GB re-arranges during the growth, in order to reach low energy configurations. Segments with clear preferred directions appear, deviating from the direction of the seed GB. The preferred configurations observed in Fig. 4 corresponds to the symmetric Σ9 {221}1/{221}2 and asymmetric Σ9{115}1/{111}2 configurations, as GB segments shown in Fig. 4a align to (115) and (221) planes in grain 1, and (111) and (221) planes in grain 2. It should be noted here, that these GB planes are perpendicular to the growth direction, i.e. [ 110]. The local GB geometry is affected by this mechanism as steps tend to develop. Fig. 4b shows the development of a step, as observed on two horizontal samples taken at different heights of the Σ9 bi-crystal. The resulting step introduces stress concentrating points where dislocations tend to generate, as shown in Fig. 4a and b. The grown Σ9 GB is observed to be locally unstable and can eventually split into two Σ3 GBs, as shown in
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Fig. 3. (a) Sketch of the bi-crystal ingot during solidification. The outer surface of the cylinder describes the outer bi-crystal shape in contact with the crucible. The crystals are subjected to stresses. The main load direction is defined by two angles γ and λ. r vector is defined as the result of the cross product of z and the applied load vector σ. (b) Grain#1 and Grain#2 maximum Schmid factors Mλ over λ, as calculated for γ varying from 0 to π/2, for both Σ9 and Σ27a bi-crystal. Grain#1 corresponds to the grain where dislocations are emitted (see Fig. 2). (c) Grain#1 and Grain#2 Schmid factors M for γ ¼ 0, as calculated for λ varying from 0 to π/2, for both Σ9 and Σ27a bi-crystal.
Fig. 4a and c. This is observed especially for the Σ9{115}1/{111}2 asymmetric segments which have higher interfacial energy than the symmetric Σ9{221}1/{221}2 segments. It has been shown previously that Σ27 and Σ9 GB can dissociate into lower Σ3n boundaries in order to decrease their energy [22,23]. In particular, the asymmetric Σ9 dissociation mechanism has been discussed in previous work [23]. The authors observed the dissociation of asymmetric Σ9 into nanometer-scale triangular grains bounded by three Σ3 GB. Similar grains have been identified and are visible on micro-meter scale in Fig. 4a and c. This dissociation forms sharp GB edges which tend to concentrate stresses. Fig. 4c shows that there is a strong correlation between Σ9 GB dissociation and dislocation generation. It is argued that the defect generation at the grown Σ9 GB is closely related to the Σ9 seed GB deviation from the Σ9{221}1/{221}2 low energy configuration. This deviation is responsible for the re-arrangement of the GB during the growth and the introduction of topological imperfections, which act as stress concentrators and are consequently associated with high densities of dislocations. The dislocation structures predominantly align along the {110} traces (see Fig. 4b), suggesting that the defect clusters observed close to the GB are dominated by recovered structures: during the cooling of the solidified ingot, dislocations originally aligning along {111} slip planes rearrange in sub-boundaries to lower the crystal energy [24–26]. It can be noted that local emissions at coarse straight GB segments are also visible, for instance on the right hand micrograph of Fig. 4c. This observation is later discussed. Fig. 5a shows the Σ27a GB structure development observed by SEM on a horizontal cross section taken 10 mm above the seeds, perpendicularly to the GB. The Σ27a seed GB deviation from the low energy configuration Σ27a{511}1/{511}2 is relatively low, and its re-arrangement is not as pronounced as it is for the Σ9 GB (see Figs. 4a and 5a). The seed GB slight deviation from the low energy configuration Σ27a{511}1/{511}2 causes however the grown GB to form coarse steps. The steps consist of two long GB segments close to the Σ27a
{511}1/{511}2 configuration, and one asymmetric GB segment, as described on the sketch in Fig. 5a. Fig. 5b shows images of one coarse step and its associated dislocations, at different heights of the ingot. It should be noted here that the later appearance of the step does not signify that the dislocations are emitted prior to the step formation, as dislocations can move down in the ingot, after having been first emitted by the GB. It is clear that the dislocation generation occurring at the grown Σ27a GB is closely related to the appearance of coarse GB steps. As for the Σ9 GB, the defect cluster formed close to the step is mainly composed of recovered structure, aligning along the {110} plane traces. In addition, dislocations aligning along {111} slip planes are also visible close the GB. They attest the occurrence of local plastic deformation during the solidification process, close to the GB. Local emissions at coarse straight segments which align close to the Σ27a{511}1/{511}2 configuration are also visible. An example is highlighted with a dashed square in Fig. 5a. Kutsukake et al. have previously investigated the structure evolution of a near-Σ5 {310}1/{310}2 GB by using the seeded growth method and transmission electron microscopy [27]. The authors observed that the GB dislocation structure becomes more organized as growth proceeds, to become only composed of edge dislocations with a Burgers vector of a/10 o310 4, high in the ingot (20 mm above the seed). This change in GB dislocation structure is accompanied by dislocation emission towards the bulk, as some GB dislocations are believed to combine to become glissile in the bulk (i.e. Burgers vector a/2 o110 4) and able to escape the GB interface. The only remaining GB dislocations (edge dislocations of Burgers vector a/10 o3104 ), cannot glide in the GB planes and are sessile in the bulk. In the present work, local observations of etched horizontal cross sections show structure changes along the Σ27a GB. Fig. 5c shows that the dislocation emissions observed at coarse straight GB segments are associated with finer GB steps. These steps are composed of GB segments very close to the Σ27a{511}1/{511}2 symmetric configuration – with a low density of GB dislocation, and therefore shallow etch – and segments which deviate more
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Fig. 4. SEM observations made on Sopori etched horizontal cross sections taken 5–6 mm above the seeds of the Σ9 bi-crystal. (a) Σ9 GB structure and geometry. A schematic view of the grown GB, deviating from the seed GB, and some {115}, {111} and {221} plane traces are added, with respect to EBSD maps performed on the sample. Σ9{221}1/{221}2 and Σ9{115}1/{111}2 GB traces are added in the left corner. These planes are perpendicular to the sample plane. (b) Observations made on cross sections taken at different heights of the Σ9 bi-crystal. The circled region shows the formation of a step composed of near-Σ9{115}1/{112}2 and Σ9{221}1/{221}2 segments. (c) Observation of Σ9 GB dissociations leading to dislocation emission. Local GB structures are sketched, with respect to EBSD maps performed on the sample.
from the symmetric configuration – with higher density of GB dislocation, and therefore deeper etch. The appearance of these GB segments of low energy and high degree of coherency goes along with the migration of GB dislocations originally present at the seed GB, either along the GB or towards the bulk, if they are glissile in silicon lattice. In the case where dislocations are only mobile in the GB plane, they can be expected to pile-up and generate local stresses that can be responsible for plastic deformation leading to dislocation generation. In the case where dislocations can combine to become glissile in silicon lattice, they can be emitted towards the bulk to facilitate the re-organization of the GB to a configuration of lower energy – i.e. higher coherency. In any case, local structure changes of near-CSL GB leading to the appearance of GB segments with high degree of coherency involves dislocation emission in the bulk, which then have the potential to multiply and form clusters as described by Ryningen et al. [5]. The presence of a stress concentrator at the GB can be expected to help GB dislocations to escape the GB interface.
4. Conclusions Bi-crystal silicon ingots separated by near – Σ9 and Σ27a GBs have been grown by directional solidification. Unilateral emission of dislocations from the central GBs have been observed, as a result of shear stresses arising asymmetrically in {111} planes. It has been shown that these dislocation emissions cannot be only attributed to thermal stresses, and are related to stress irregularities introduced by GB topological imperfections. Thus, during Σ9 and Σ27a bi-crystal ingots growth, dislocations are emitted as a result of the seed GBs deviation from the symmetric low energy configurations – i.e. Σ9 {221}1/{221}2 and Σ27a{511}1/{511}2. In the case of the bi-crystal separated by Σ27a GB, this deviation introduces topological imperfections at the grown Σ27a GB – i.e. steps. These are stress concentrators and represent the main source of dislocations while Σ27a{511}1/{511}2 straight segments seem to emit very few dislocations. In the case of the Σ9 GB, the seed GB deviation also introduces steps. Concurrently, a second dislocation emission mechanism has been identified at the
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Fig. 5. (a) SEM image of a Sopori etched horizontal cut of the Σ27a bi-crystal ingot. Steps tend to form, with GB segments of particular directions, corresponding to the preferred configurations. A GB structure sketch is added, including some {511} and {111} plane traces, with respect to EBSD maps performed on the sample. (b) LM images of horizontal cuts, at different heights. Appearance of a coarse grain boundary step, associated with dislocation emission towards the bulk. Some {111} and {110} plane traces are added. (c) SEM image of straight GB segment emitting dislocations. GB segments with high degree of coherency appear – i.e. low GB dislocation density and shallow etch.
grown Σ9 GB: asymmetric Σ9{115}1/{112}2 segments were observed to dissociate and form micrometer scale grains forming sharp GB edges which also tend to concentrate stresses and lead to dislocation generation. These results suggest that during multi-crystalline silicon solidification, semi-coherent grain boundaries tend to generate dislocations as a consequence of their re-arrangement.
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