Twinning in Solar Cells.pdf

Twinning in multicrystalline silicon for solar cells

G. Stokkan n,1

SINTEF Materials and Chemistry, Sector for Sustainable Energy Technology, Department of Solar Cell Silicon, Alfred Getz Getz vei 2, Trondheim 7465, Norway

a r t i c l e i n f o

Article history:Received 16 August 2013Accepted 9 September 2013Communicated by Chung wen LanAvailable online 18 September 2013

Keywords:A1 DefectsA1 TwinsA2 Growth from meltA2 Industrial crystallizationB2 Semiconducting siliconB3 Solar cells

a b s t r a c t

Twinning in multicrystalline silicon was studied by observing the surface of as-cut wafers and by EBSD.By tracing twin structures downwards to their first point of origin, the conditions at the point ofgeneration were identified. Twins covering the whole width of a grain predominantly originates atjunctions between three grain boundaries. Twins also originate at straight grain boundary segments ofalternating direction, indicative of faceted grain boundaries. The phenomena are proposed to occurbecause they reduce grain boundary energy, which is substantiated by pole figure analysis. In addition tothe CSL relationship, the orientation of the grain boundary in low energy configurations turned out to beessential.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Multicrystalline silicon formed by directional solidification isthe dominant technology for producing cost efficient solar cells [1]because of the industrial robustness, and because of the lowertechnological entry level compared to monocrystalline siliconproduced by the Czochralski crystal pulling method. The materialcontains numerous crystal defects and a higher contaminationlevel than monocrystalline silicon. Twins are important defects,not because of their impact on electrical performance, which isvery low due to their high degree of reconstruction, but because oftheir abundance. The majority of grain boundaries are twins, asshown by several reports, e.g. [2]; the actual fraction of the totaldepends on the resolution of the measurement method, but morethan 60% is a common number.

Twins are also often, but not always, associated with very lowdislocation density [3]. Such highly twinned regions may often bealmost devoid of dislocations. Twins are therefore regularlyconsidered as benign defects and the twinning process a favorableprocess because it is believed it may cause reduced generation ofdislocations. On the other hand, dislocation density is often seen tobe very high in areas where dislocation generating grain boundaries[4] operate close to twins or stacking faults [5]. Moreover successivetwinning during growth by rotation around different axes willcreate Σ9, Σ27 and random angle grain boundaries, which are much

more recombination active than twins [6], and may also act asdislocation nucleation sites [4,5,7]. Understanding twin formation istherefore an important part of the knowledge necessary to optimizecrystal growth of multicrystalline silicon and minimize the contentof performance limiting crystal defects.

Twinning during crystal growth is closely linked to a facetedsolid liquid interface. Fujiwara et al. [8] showed how emergence ofa twin nucleus on a faceted interface results in formation of twoparallel, stable (1 1 1) twins during subsequent growth in a twodimensional system. Stokkan [3] noted that ingots with a hightwin density and correspondingly low dislocation density had apredominance of grains in which the ⟨1 1 0⟩ direction (whichcorresponds to two crossing (1 1 1) facets) lies parallel to thewafer surface, such that long facet rims are possible. Duffar andNadri [9] used the theory for twin formation in Czochralskimonocrystalline silicon developed by Voronkov [10] and Hurle[11] and modified it to describe the situation of directionalsolidification. They showed that not only a faceted interface isnecessary, but also the presence of a grain boundary of a veryspecific angle to the melt. The necessity of a grain boundary wasalso shown by Pohl et al. by molecular dynamics simulations [12].

The theoretical and simulation works of Duffar and Nadri [9]and Pohl et al. [12] were however not compared to experimentalobservations. Such experimental observations are reported in thiswork. Very simple visual observations are compared to measure-ments of crystal orientation and grain boundary misorienta-tion, and the nature of the twin generating grain boundaries iselucidated.

Note that in this paper, the denotation “twins” is used for Σ3twins only.

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Journal of Crystal Growth

0022-0248/$ - see front matter & 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.jcrysgro.2013.09.008

n Corresponding author at: P.O.Box 4760 Sluppen, 7465 Trondheim, Norway.Tel.: þ47 41 559 851.

1 Visit address: Alfred Getz vei 2, Trondheim, Norway.E-mail address: [email protected]

Journal of Crystal Growth 384 (2013) 107–113

2. Experimental work

A stack of as-cut multicrystalline silicon wafers from a pilotfurnace (12 kg ingot, boron doped to a resistivity of 1.2 o cm) werephotographed by a regular digital camera, using side illumination.Sharp contrast appears between grains of different orientation due todifferent surface reflection; no sample preparation such as polishingor etching is necessary to achieve this effect. While not all grainorientation differences can be separated by this method, twins are soabundant in multicrystalline silicon that enough interesting twinconfigurations were found for the subsequent analysis.

The images were arranged sequentially, and established twinnedregions were traced down to their first appearance. The waferthickness is 280 mm, and if the kerf width is taken to be 170 mm, thelateral resolution is 450 mm. Assuming, as is normally accepted [13],that twins in multicrystalline silicon are growth twins, not defor-mation twins, this point is taken as the point of origin of the twins.These areas were imaged in greater detail, and some were selectedfor polishing and Sopori etching [14] to delineate dislocations andgrain boundaries, and the grain orientation was investigated byelectron backscatter diffraction (EBSD). The orientation of crystal-lographic planes was investigated by pole figure analysis, and bycomparing the pole figures of adjacent grains, possible common lowenergy planes were identified.

3. Results

3.1. Twin shapes

Twinned regions appear to take one of three forms.

1. Continuous ribbons across the entire width of the grain. Thistype of twins is common in areas where the orientation shifts

rapidly between the two different twin orientations, and in thistext they will be named ribbon twins.

2. Polygons which are constituted of at least three Σ3 boundariesinside the grain (forming �901 angles to each other) and oneboundary to an adjacent grain. These will be named polygontwins.

3. Thin lamellae that are attached to a grain boundary in one endand protruding into the grain look like needles on the surface ofa wafer. Here they will be called needle twins.

3.2. Origin of twins

Ribbon twins appear to predominately originate from grainboundary junctions, i.e. triple lines between the grain in which thetwinning occurs and two other grains. Such configurations werenot discussed by Duffar and Nadri [9] and Pohl et al. [12].An example of ribbon twin formation is shown in Fig. 1(a). It canbe seen that the upper grain boundary forming the junctionappears rather straight while the other one is curved, and this isa general feature observed for many ribbon twin formation sites.

Formation of polygon twins occurs at grain boundaries, andthis may happen in the same region as ribbon twins form, as isseen in Fig. 1. They first appear as small triangles where two of thefaces are formed by straight segments on the grain boundary andthe other two form a (1 1 1) twin boundary inside the grain. Later,as the triangles grow larger and transform into polygons, the(1 1 1) twin and one of the grain boundary segments becomesconnected by a twin boundary orthogonal to the first one, which isthus likely a (2 1 1) twin boundary. This process can be seen inimage 4–6 in Fig. 1(a), where two triangles (barely visible in 4)develop into a polygon in 6, magnified in Fig. 1(b). Note that thedirection of the straight grain boundary segments are the same for

Fig. 1. (a) Development of ribbon twins from a junction (red arrows) between two grain boundaries. The numbers refer to the sequence, starting from the bottommost of thewafers, and the lateral distance between the views is 450 mm. (b) Magnification of the formation of polygon twins at straight grain boundary segments (marked with greenarrow in a). (c) Schematic representation of a grain boundary junction. (For interpretation of the references to color in this figure legend, the reader is referred to the webversion of this article.)

G. Stokkan / Journal of Crystal Growth 384 (2013) 107–113108

the two triangles, and are thus indicative of low energy config-urations, i.e. high degree of reconstruction, possibly atomically flatfacets.

The short faces of the polygon twins tend to vary their orienta-tion, as can be seen in Fig. 2. As function of height they tend toremain in the same position when they have a reasonably flatappearance (possibly a (2 1 1) configuration), but they may alsomove rapidly, increasing or decreasing the area of the polygon;during rapid change in position the twins deviate from straightappearance and may be both convex and concave towards thedirection of movement.

Needle twins appear to have a different growth behavior thanribbon and polygon twins, as they appear to shoot out from a pointin a grain boundary, forming two parallel (1 1 1) twin boundariesin the process. Their first point of appearance is at a point where agrain boundary changes character, such as the point in Fig. 3,image 2, which is actually a grain boundary junction, or triple line,as can be seen by the changing shade of grey. However, thesituation is distinctly different than for formation of ribbon twins,where only one twin boundary is formed at a time, while here twoparallel (1 1 1) twins are formed in addition to a small segment ofhigher energy twin configuration (likely (2 1 1)). Also other grainboundary character changes were observed to be connected toformation of a needle twin, such as a grain boundary step.

3.3. EBSD analysis of twin generation at a junction

The area shown in Fig. 1, image 5 and 6 was selected for EBSDanalysis. Particular attention was paid to the orientation of thegrain boundaries, since the visual analysis of the images indicatedthat properties of the grain boundaries influenced the formation oftwins. The orientation image micrographs (OIM) and selected polefigures are shown in Fig. 4. The pole figures are used to analyzedirections in the OIMs. The normal direction of the sample (ND)points out of the plane, as in the OIM. The rolling direction (RD)and transverse direction (TD), which is a terminology derived for

study of plastically deformed samples, generally align with themacroscopic directions of the sample (RD should be vertical andTD should be horizontal in the OIM), however due to a specialsetup of this particular SEM, these directions do not coincide, andthe pole figures have to be rotated in order for the directions to becorrect. The Miller indices given for each pole figure are thecrystallographic directions that are projected from the unit spheredown to the equatorial plane. The vector from the origin to a givenpole, indicates the crystallographic direction, however projecteddown into the sample surface plane. If a tangent is drawn wherethis vector intersects the unit circle, this always represents thetrace between the respective crystallographic plane and thesample surface, e.g. a (1 1 1) plane trace for a 1 1 1 pole figure.

4. Discussion

4.1. Ribbon twins

A schematic representation of a junction between three grainboundaries is shown in Fig. 1(c). When twins form in such a grainboundary junction and extend across the grain from one grainboundary to another, only a (1 1 1) twin boundary needs to form,not the higher energy (2 1 1) twin boundary [15]. This process canbe very sensitive to small changes in energetic properties of thethree grain boundaries forming the junction. A sudden smallincrease in the grain boundary energy may be reversed by atwinning operation if the very small increase in total Gibbs freeenergy caused by the formation of the new twin boundary iscompensated by the reduction of grain boundary energy. This canbe formulated as twinning being favorable if:

ΔGGB1; beforeþΔGGB2; before4ΔGGB1; afterþΔGGB2; afterþΔGTwin ð1Þ

Grain boundary 1 and 2 (GB1 and GB2) are here the two grainboundaries towards the grain in which the twins are formed. Thethird grain boundary (GB3) does not change coincidence site

Fig. 2. The face orthogonal to the dominating twin direction may take irregular shapes for polygon twins.

G. Stokkan / Journal of Crystal Growth 384 (2013) 107–113 109

lattice by the twinning process, and if it is assumed that the grainboundary orientation also remains unchanged, the energy is equalon the two sides of the inequality sign and is therefore neglectedfrom Eq. (1). Which changes in grain boundary configuration couldcause such a sudden change in grain boundary free energy toinitiate a twinning event? A possibility is when one of the adjacentgrains is twinned (for instance the upper grain in Fig. 1(c), and thetwin boundaries are not parallel to the growth direction. The grainboundary configuration along the grain boundary will alternatebetween two types, and the configuration in the junction will as aresult change as function of the height. If for instance the grainboundary (e.g. GB1 in Fig. 1(c) changes from a Σ9 to a Σ27coincidence site lattice (CSL) boundary, it will be energeticallyfavorable to perform a twinning operation in the grain junction inorder to shift the CSL back to the Σ9 type, since Σ27 has muchhigher grain boundary energy than Σ915. For this mechanism tooperate, it is essential that the twin boundaries in the adjacentgrain are not exactly vertical, in order to change the configurationin the junction. Such tilting of grain boundaries is generallyobserved.

Another example is illustrated in Fig. 4 where twins form in theRED/BLUE twinned grain. The formation occurs in the junctionformed towards the LIGHT BLUE grain on the right and theYELLOW/PURPLE grain on the left.

It can be seen that there is a Σ3 relationship between the REDtwin type and the LIGHT BLUE grain and a Σ9 relationship betweenthe BLUE twin type and the LIGHT BLUE grain. The RED twin typehas a Σ27 relationship to the YELLOW twin type and the BLUE twintype has a Σ27 relationship to the PURPLE twin type on the left.No CSL was observed between the other configurations on the left.The Σ27 CSL is a high energy configuration, and a shifting betweenthis and a random configuration may not influence the grainboundary energy enough to cause a twinning event; the analysisthus focused on the grain boundary on the right, towards theLIGHT BLUE grain.

As noted, there is a Σ3 relationship between RED and LIGHTBLUE, and if the grain boundary between them were a (1 1 1) Σ3twin, which has a particularly low energy, there would be nodriving force towards changing to the BLUE orientation. However,when analyzing the 1 1 1 pole figures of RED and LIGHT BLUE, it is

clear that the common (1 1 1) plane between the two grains (thegreen pole in the two pole figures) is not parallel to the grainboundary. Also the higher energy (2 1 1) Σ3 twin is ruled out forthe same reason (again common poles are marked green).

The LIGHT BLUE grain is heavily twinned, although it does notappear such in Fig. 4, except for a WHITE blade-shaped grain in thelower right corner of the lower picture. The RED grain has a Σ9relation to this orientation. The low energy grain boundary config-uration parallel to a (2 2 1) plane is not present here, as can be seenfrom the common green poles in the pole figures. However, anasymmetric grain boundary type has also been reported for Σ9grain boundaries, where the (1 1 1) plane in one grain coincideswith a (5 1 1) plane in the other. The (1 1 1) pole figure of theWHITE grain and the (5 1 1) pole figure of the RED twinned graindo have one common pole (marked in red), which gives a grainboundary plane parallel to the observed grain boundary. Thus if thedirection of this grain boundary in the junction is parallel to thisdirection, and a thin WHITE twin lamella separates the RED andLIGHT BLUE grains, a low energy configuration can be achieved forthe Σ9 orientation, although an asymmetric one.

What is the driving force for switching back to the BLUEorientation? Fig. 5 shows a magnified view of the junction afterformation of the BLUE grain. BLUE and LIGHT BLUE have Σ9relation. The grain boundary between the two grains alternatesbetween two types of straight boundary segments; either parallelto the black areas, which are probably very thin WHITE areas notdetected by the EBSD system, or parallel to one of the commonlow energy (2 2 1) plane of the two grains, as seen from the greenpoles in the pole figure.

Thus, if the grain boundary in the junction, after having beenparallel to the (5 1 1)||(1 1 1) plane, attains a different direction,and the grain in the junction changes from WHITE to LIGHT BLUE,the grain boundary energy will be reduced if twinning occurs,shifting the relation back to Σ9, with a (2 2 1) grain boundaryorientation.

This example shows that the grain boundary energy configura-tion in the junction may be influenced by the orientation of thegrain boundary as well as the CSL.

It is also possible that the two grain boundaries forming thejunction have competing low energy configurations as function of

Fig. 3. Development of a needle twin. First appearance of the twin is in image 2, in the upper right corner.

G. Stokkan / Journal of Crystal Growth 384 (2013) 107–113110

the twinning. Such an unstable system could be very sensitive tofluctuations in the heat flux driving the growth. Consider a facetedsolid liquid interface bounded by two different grain boundaries,

where one grain boundary has a low energy configuration and theother a high energy configuration, e.g. a Σ9 and a Σ33 grainboundary. If the growth isotherm is such that nucleation of a new

Fig. 4. Orientation image micrograph of area in Fig. 1 (rotated approximately 901), image 5 (a) and image 6 (b). Σ3 boundaries are black, Σ9 boundaries are red and Σ27boundaries are green. (c) Overview of pole figures. The colors in the rectangles indicate which grain the pole figures belong to. The miller indices show which crystaldirections have been projected from the unit sphere to the equatorial plane, and RD, TD normally corresponds to the edges of the sample. However here, the pole figures aretilted due to the setup of the equipment.

G. Stokkan / Journal of Crystal Growth 384 (2013) 107–113 111

atomic layer on the (1 1 1) facet always starts from the Σ9boundary, this will remain stable. However, if the isothermchanges and the nucleation starts from the Σ33 side, the grainboundary can reduce its energy by a twinning operation andtransform into a Σ11 boundary. However, this will transform theother grain boundary, possibly into a Σ27 state. If the temperaturefield fluctuates and the favorable piling direction alternates, arapid fluctuation between twinned states may result for suchspecial configurations. Such densely twinned areas are seen fromtime to time in multicrystalline silicon.

Grain boundary energies at temperature close to the meltingpoint are not known. The discussion above assumes implicitlythat similar differences in grain boundary energy exist at thistemperature level as are generally acknowledged (from modelingand experiments) at lower temperature. In a review of grainboundary modeling in Si Bristowe [16] argues that symmetric tiltboundaries are reconstructed also at elevated temperature, whichsupports the assumption in the analysis above.

4.2. Polygon twins

This type of twinned structure forms at grain boundaries andincludes low energy (1 1 1) twin boundaries as well as higher energy(2 1 1) twin boundaries. In the example seen in Fig. 1 the polygontwins start as small triangular grains on a Σ9 grain boundary thatforms straight boundary segments. It is well known that the Σ9 grainboundary can, if the macroscopic orientation of the grain boundarydeviates from the low energy (2 2 1) plane, easily reduce its energyby dissociating, forming triangles that contain two (1 1 1) twins andone (2 1 1) twin. This has been observed experimentally by TEM [17]and EBSD [7]. It is very likely that Σ9 grain boundaries contain a highdensity of such twinned triangles. Fig. 6 illustrates different stages ofhow a polygon twin may be generated from such a dissociated grainboundary, (a)–(c) roughly represents the situation seen in Fig. 1(a),4–6, and magnified in Fig. 1(b). In Fig. 6(a) the dissociation hasproduced two triangles, with a short (1 1 1) twin and a long (2 1 1)twin towards the upper grain and a (1 1 1) twin towards the lowergrain. In (b) the energetically favorable (1 1 1) twin towards thelower grain have increased their length, also forming a (2 1 1) twin,while in (c) the two triangles have merged, forming a polygon twin.The situation towards the upper grain with a long (2 1 1) twin and a

short (1 1 1) twin does not appear to be stable on a macroscopic scalebut probably appears microfaceted. This structure may grow intolong polygon twins by lateral movement of the macroscopic Σ9boundary or the (2 1 1) twin boundary, as seen in Fig. 2.

4.3. Needle twins

Formation of needle twins which shoot out into the graincannot be explained solely by grain boundary energetics, sincethey involve formation of two new grain boundaries, which isthermodynamically unfavorable, even though the energy of thetwo (1 1 1) Σ3 boundaries is very low. Although it is apparent that

Fig. 5. Magnified orientation image micrograph of the junction after formation of the BLUE twinned grain. (For interpretation of the references to color in this figure legend,the reader is referred to the web version of this article.)

Σ3 (211)

Σ3 (111)Σ3 (111)

Σ9 Σ3 (111)

Σ3 (111)

Σ3 (211)

Σ3 (211)

Σ3 (211)

Σ3 (211)

Σ3 (111)

Σ3 (111)

Σ3 (111)

Σ3 (111)

Σ3 (211)

Σ3 (211)

Σ9

Σ9

Σ3microfaceted

Σ9

Fig. 6. Illustration of generation of polygon twin from dissociated Σ9 grainboundary. (a) A dissociated Σ9 grain boundary. (b) The triangles have grown andintersected. (c) Formation of a polygon twin.

G. Stokkan / Journal of Crystal Growth 384 (2013) 107–113112

the starting point at the grain boundary is linked to a local changein grain boundary energy, it is not clear why the twins shouldmigrate into the grain.

5. Conclusions

It has been shown that twins in multicrystalline silicon can betraced downwards to special features on grain boundaries and arethus likely growth twins. They can conveniently be classified intothree groups: ribbon, polygon and needle twins, according to theappearance of the twinned structure on the wafer surface. Ribbontwins were shown to originate at grain boundary junctions, whilepolygon twins appear to start as small triangles on straight boundarysegments, possibly microscopic, atomically smooth facets. In bothcases thermodynamic arguments can explain the formation of twinsas a result of reduction of total Gibbs free energy at the grainboundary. For ribbon twins this occurs as a reaction to changinggrain boundary configurations due either to changing coincidencesite lattice or to changing grain boundary orientation. Polygon twinsappear to originate by formation of low energy secondary grains on agrain boundary, which lower the energy locally upon formation. Thetriangles are stretched out as function of grain boundary movement.In both cases Σ9 boundaries were found to be involved in thetwinning operation.

Acknowledgments

The work was performed as part of the research project Defectengineering for crystalline silicon solar cells, supported by theResearch Council of Norway, ELKEM and REC, and Impurity Controlin High Performance Multicrystalline Silicon, supported by theResearch Council of Norway, ELKEM, The Quartz Corp, REC andSteuler Solar. The author wishes to acknowledge discussions withOtto Lohne, Birgit Ryningen, Maulid Kivambe and Torunn Ervik.

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