Journal of The Electrochemical Society, 151 ~6! G408-G427~2004!0013-4651/2004/151~6!/G408/20/$7.00 © The Electrochemical Society, Inc.

G408

Alkaline Etching for Reflectance Reduction in MulticrystallineSilicon Solar CellsJ. D. Hylton,z A. R. Burgers, and W. C. Sinke

Energy Research Centre of The Netherlands, 1755 ZG Petten, The Netherlands

The reflection reducing properties of alkaline-etched multicrystalline wafers are investigated experimentally for high concentrationsaw-damage etching and low concentration texture etching. Saw-damage etch textures are too flat for multiple bounce reflectancein air, with only 1.6% of the multicrystalline wafer surface calculated to have facet tilt angles above 45° whereby double-bouncereflectance is guaranteed. Texture etching yields 3% lower reflectance in air, due to high angled~up to 54.7°! pyramidal structureson near~100! orientations, whereby 13% of the multicrystalline etch surface has tilt angles above 45°. However, under encapsu-lation, light is coupled more effectively into the silicon; reflectances for the saw-damage and texture-etched wafers compare only7 and 5.5% higher, respectively, than upright pyramid textures on monocrystalline silicon~100!, compared to 18 and 15% higherin air. This is because a far larger proportion of the multicrystalline wafer~around 40% for the two etches! has tilt angles above20.9° whereby escaping light is totally internally reflected at the glass-air interface. For texture etching, not only$111% planes arestable to etching but the whole range of$XXY % crystallographic planes between these and$110% orientations, contrary to theaccepted texture etching theory.© 2004 The Electrochemical Society.@DOI: 10.1149/1.1738137# All rights reserved.

Manuscript received June 30, 2003. Available electronically May 4, 2004.

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Alkaline etchants for solar cell processing.—As a standard pratice alkaline etchants are employed in solar cell processing.temperatures~above 100°C! and concentrations~around 10 M omore! of alkali are used for the removal of sawing damage for assilicon wafers. These etching conditions are chosen in ordermove the required depth of saw-damaged silicon as quickly assible. In contrast, low temperatures~below 100°C! and concentrations ~,0.5 M! of alkali are used in the processing of~100!-orientedmonocrystalline wafers. In this case, the anisotropic action oalkaline etchant is exploited, whereby slow etching planes, aently of $111% orientation, are exposed and intersect to form uprfour-sided pyramids with square bases up to 103 10mm2. Thesepyramidal textures have geometries which allow sunlight to beeasily coupled into the silicon, and thus to allow as much lighpossible to be absorbed and converted to electrical current isolar cell.

Reflectance reduction through geometrical texturization.—Figure1 uses two-dimensional groove textures to demonstrate howmetrical texturization can reduce the amount of light lost by frsurface reflectance for silicon in air, without the use of an antiretion coating. Light which is reflected away from a groove facet afirst point of incidence@e.g., at ~i! in Fig. 1# may be redirectetoward the silicon via a neighboring texture facet, for a secchance of transmission into the silicon@e.g., at ~ii ! in Fig. 1# therebylowering reflectance at the front surface. The probability with wlight will receive such double-bounce incidence or still higher orof multiple incidence depends upon the facet tilt angles of themetrical textures with respect to the surface of the wafer, as rsented bya in the figure. For normally incident light falling upoperiodic textures, angles ofa . 45° ensure double-bounce refltances will occur; angles ofa . 60° yield triple-bounce reflectances at least. As facet tilt angles decrease belowa , 45°, less anless light will receive double-bounce incidence, closer to the bathe grooves, until at angles below 30°, no light will receive multbounce incidence in air, and reflectance levels are equivalent tof polished silicon. For the upright pyramid textures formed~100! oriented wafers, the$111% facets are angled at 54.7° to the bso that double-bounce reflectances are predominant. As a resuturing of the silicon~100!, leads to an absolute reflection reductof approximately 20% compared to a flat polished wafer in air.

Also important in the assessment of textures is their opticalformance under encapsulation, as is the situation for the finsilicon solar cells in a module. Figure 2 shows how light esca

z E-mail: hylton@ecn.nl

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on the initial incidence at the silicon front surface may be confiat the glass-air interface and redirected towards the siliconsecond chance of incidence, thus reducing front surface refleclosses. From Snell’s laws of refraction~e.g., Ref. 1!, light approaching the glass-air interface at angles greater than the critical angac

will receive total internal reflectance~TIR!, where ac

5 arcsin(nair /nglass), n being the refractive index. Settingnair 5 1and nglass5 1.5, thenac for the glass-air interface is 41.8°. Thwhile facet tilt angles of 30° or more are required for double-boincidence of light on the bare silicon, texture angles of only 2are sufficient for glass-encapsulated wafers to confine light reflaway from the silicon at the glass-air boundary@e.g., at ~iii ! in Fig.2#. This light will fall reincident upon the surface for a secochance of incidence whereby reflection reduction is also achie

Geometrical surface morphologies for multicrystallwafers.—The surface reflection of periodic geometrical structurrelatively easily explained using basic ray-tracing, as demonsin Fig. 1 and 2. The accuracy of ray-tracing depends on howpletely the etch surface geometry is quantified. However formasked alkaline etched wafers, quantification of the etch sumorphology is more complex. Etch structures are nonperiodic,dimensions are nonuniform, and the homogeneity of the strucvaries over the wafer.

For a multicrystalline wafer,i.e., with crystal grains of betweenmm2 and 10 cm2,2 the situation is further complicated. Anisotroetching will lead to a surface morphology which will vary overwafer according to the orientation of the crystals present. The sof the surface texture and correspondingly the reflecting propper crystal, are dependent upon the angular proximity of theetching crystallographic planes with respect to the wafer surHowever, many different crystal orientations are present; indeedistribution of crystal orientations in multicrystalline Solsix~for-merly Baysix! wafers for example has been found to be essenrandom, with no preferential orientation being present.3-5 Thus anumber of different surface geometries will determine the intetion of incident light with the surface and will contribute tooverall reflectance of the multicrystalline wafer.

Effect of etch composition upon surface texture geotries.—Furthermore, the action of the alkaline etch depends stroupon its composition, which affects the effectiveness of texturizand consequently the level of front-surface reflection. Figushows the measured total reflectances of two bare neighboringticrystalline wafers~i.e., sawn adjacently from the ingot so that thare essentially identical as-cut!, which have received either a sadamage or a texture etch. The differences between the two me

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Journal of The Electrochemical Society, 151 ~6! G408-G427~2004! G409

reflectances suggest a difference in surface morphology betweneighboring wafers. The two etch compositions apparently athe silicon surface differently, suggesting that lower facet angleexposed after the saw-damage etch~due to its relatively high reflectance! than for the texture etch.

In order to explain such differences, the surface geometriesbe fully quantified on a per orientation basis for the etch comptions used and related to the measured reflectances for the mrystalline wafers. However, perhaps as a consequence of thementioned complexities, relatively little attention has been pathe quantification and optimization of alkaline etching for multictalline wafers. High concentration saw-damage etches are empindustrially purely for their high and relatively well controlled erates~typically a few tens of micrometers per minute!, and withouknowledge or understanding of the resulting optical propertieshigh measured reflectance of saw-damage etched waferswould initially suggest that such surface textures will not contrito reflectance reduction, and these surface geometries are gepoorly investigated. Indeed, there has so far been no attemptin the literature~except by these authors, see Ref. 3 and 6! to

Figure 1. Possible paths for light incident upon geometrically texturedcon in air. Ray 1 experiences double-bounce incidence at a facet tilanglea1 . 30°. Light which is not coupled into the silicon for absorption~i! falls reincident for a second chance of transmission into the silicon a~ii !,thereby reducing front surface reflection. Ray 2 falls incident on tewhose facet tilt anglea2 , 30° and is reflected directly away withousecond chance of incidence. However, for values ofa2 between 20.9, a2 , 30°, ray 2 experiences multiple incidence from this facet uencapsulation, as shown in Fig. 2.

Figure 2. Possible paths for light incident upon the geometrically textsilicon surface shown in Fig. 1 for the silicon under encapsulation. Lreflected away at first or second incidence at~ii ! and ~iii ! ~where facet tilanglesa1 and a2 . 20.9°) is trapped at the glass-air interface by TIRthat light is redirected towards the silicon for a second or third chanabsorption.

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describe these surfaces geometrically for either mono- or multtalline wafers.

Low concentration texture etches, being optimized for theition on $100% orientations,i.e., pyramidal textures, are rarely invetigated for their effect on other crystal orientations. It is assuthat $111% facets will be exposed exclusively by etching, regardof the base crystal orientation. This would imply that for goodture etching~i.e., under conditions whereby a mono-~100! orientedwafer is completely covered by pyramids!, the shape of the etcstructures for any crystal will be defined by the positions of$111% planes closest to the surface orientation.7 According to thistheory, ~tilted! pyramid structures will form on~near! ~100! orien-tated crystals. For the extremes of the~111! and~110! crystal orientations, the exposure of$111% etch facets would lead to three-sidpyramids and two-dimensional V-shaped grooves~with respectivefacet tilt angles 70.5° and 35.3° to the surface!, respectively. However for the~111!, shallower triangular structures or even polisstructures may possibly be expected since the surface orienitself is, of course, a stable~111! plane. Thus potentially, textuetching would lead to extremes in reflectance over the bare mrystalline wafer, on varying from pyramidal textures to essentpolished silicon.

However, the validity of this theory has not been tested exmentally for multicrystalline textures. Indeed, the exposure of$111%facets has even been questioned for monocrystalline~100! waferswith suggestions that the pyramid facets may not be$111% planes buin fact be split into two facets of near$111% orientation.8

Reflection reduction in air vs. light confinement unencapsulation.—Until now, the reflection reducing propertiesalkaline-etched multicrystalline wafers, have usually been quanby somewhat disappointing values of short-circuit current deJsc or efficiencyh ~for example, compared to mono wafers! of thefully processed solar cells.9-11 As a result, isotropic texturizatiomethods, such as mechanical grooving or acidic etching, havceived more attention in recent years. However, the measuredtrical output parameters of the complete cell can only give ancation of the optical properties resulting from texturization, sother processing parameters~such as emitter quality, etc.! and material qualities will also contribute to these values. Also, whereencapsulated wafers are used for assessment of reflection red~e.g., Ref. 9! results do not indicate the possible benefits attainthrough light confinement at the glass-air interface on encapsuas in the module. The number of surface textures yielding mureflectance could be greatly increased under encapsulation.

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Figure 3. Measured reflectances of saw-damage and texture-etchedwafers in air.

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Journal of The Electrochemical Society, 151 ~6! G408-G427~2004!G410

light of the random distribution of wafer orientations in the silica potentially far larger proportion of crystals will have etch faallowing reflectance reduction through light confinement on ensulation, than will give multiple incidence of light in air.

Reflectance reduction in alkaline-etched multicrystallinecon.—In this paper, it is aimed to establish experimentally whealkaline etching methods can provide levels of reflection reduapproaching those of pyramidally textured monocrystalline sil~100!. Investigations concentrate purely upon the reflection retion achieved due to the physical geometry of the etch surface,out the aid of an antireflection coating, and in particular by exping the benefits of light confinement under encapsulationdetermine this, the etch surface morphology for multicrystallinefers are quantified using existing and specially developed technand related to the measured reflectances. A secondary aiminvestigate and test the validity of the accepted texture etch th

Experimental

Wafers used in experimentation.—Monocrystalline wafers oseven different orientations~see Fig. 4d! as well as neighborinmulticrystalline Bayer wafers were used in our experimentation.orientations of the monocrystalline wafers are distributed evover the triangle joining the normals to the principal~100!, ~110!,and ~111! crystallographic planes. Figure 4 below shows the worientations represented spatially in a spherical polar coordinat

Figure 4. ~a! The polar coordinate system defining wafer and crystal otations.~b! The positions of the principal~100!, ~110!, and ~111! crystallo-graphic planes with respect to the coordinate system, with arrows repring surface normals.~c! The position of the triangle of principal orientatioThis is represented by joining between the points of intersection of theface normals to the~100!, ~110!, and ~111! with a sphere centered at torigin of the polar coordinate system.~d! 2D representation of the principtriangle of orientations in~c! showing the positions of the seven monoctalline orientations used in experimentation.

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tem by the tilt~Q! and azimuth~F! angles of their surface normaAngles in this coordinate system are described with respect tsurface normal to the~100! plane, with coordinates (Q,F)5 (0,0).

The orientations contained within the principal triangle canused to represent all the different possible crystal orientapresent within a multicrystalline wafer. This includes all relaplanes @for example, the~110! orientation also represents~011!,

~101!, (1̄10), etc., from the$110% set of planes#, since their crystalography and resulting etch surface textures are analogous.

Sample preparation.—The monowafers were initially polishelapped; the surfaces were therefore sandblasted with Al2O3 powderfollowed by thorough rinsing and a cleaning step to give a stasurface equivalent to the as-cut multicrystalline wafers.Wafers received either a low concentration texture etch, or aconcentration saw-damage etch in NaOH. Mono- and multicryline wafers were etched together, so that both had received prethe same etch treatments for comparison. The etch times usechosen to correspond with a total etch depth of 25mm by weight onthe as-cut multicrystalline silicon for both etches. For the effecencapsulation upon the reflecting properties, wafers were enclated under glass and ethyl vinyl acetate~EVA! in the order of glassEVA-silicon-EVA-white module backing foil. The glass at the frsurface is 1 mm thick window glass, and the white backing fofrom Icosolar, no. 2116.

Coordinate system used for the quantification of the etch sumorphology.—In all cases the resulting etch surface morpholowere observed by optical or scanning electron~SEM! microscopyand total hemispherical reflectance measurements were perfusing an integrating sphere and spectroradiometer setup. In adfor the quantification of the etch surface geometries, a numbtechniques were developed, as are discussed below.

The surface morphology of the alkaline-etched wafers is qufied using a spherical polar coordinate system, as was the cadescribing the relationship between different wafer or crystal otations. However in this case, the tilt~u! and azimuth~f! anglesrefer to the positions of the normals to a particular facet oftextured surface exposed by the etch. These angles are merelative to a particular crystal or wafer orientation, whose surfaparallel to theXYplane in the coordinate system and whose sunormal is parallel to theZ axis ~see Fig. 5!. The positions of the etcfacets formed on a particular crystal or wafer orientation aredescribed in terms of their anglesu andf with respect to the baorientation.

Atomic force microscopy (AFM).—A Nanoscope III AFM waspecially adapted for the accurate scanning of textures with hein the micrometer~as opposed nanometer to submicrometer! rangeA scanner with an 8mm height range (2003 200mm maximumscan area! was used, accommodating for the height variations insurface textures found in experimentation. The silicon needlelow tip angle of;34° and an asymmetrical shape from front-to-balong the length of the lever~i.e., in the trace direction! as shown inFig. 6. Maximum slope angles of 70°-80° could thus be measurthe trace direction, and troughs were better accessible to the nIn the lateral directions the probe is symmetric, with tip half anof 17°, each giving maximum lateral scanning angles of 73°. Almeasuring tips are examined prior to use using the SEM to ethere were no artefacts in shape, and the tips were regularly renprior to abrasion.

Calibration of the scanner was performed with a~100! orientedmonocrystalline silicon wafer with a photolithographically etchperiodic inverted pyramid texture~Fig. 7!. The facets of the fousided pyramids are composed of intersecting$111% oriented planes54.7° to the base orientation. This calibration sample allows coon three aspects of dimension, laterally, through the periodici

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Journal of The Electrochemical Society, 151 ~6! G408-G427~2004! G411

the pyramidal grid; vertically, through the depth of the invepeaks; and angularly, since the tilt and azimuthal angles of four

Figure 5. The polar coordinate system defining the positions of expetch facets in geometrical alkaline etch structures, with respect to thewafer or crystal orientation.

Figure 6. ~a! Schematic side view of the AFM tip and cantilever showthe 10° mounting angle of the cantilever with respect to the sample dscanning.~b! SEM image showing the typical shape of the actual AFM

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directions must be determined. These details can be mostrepresented through plotting the height data from the scan inof an AFM facet transform.

AFM facet transforms.—The AFM facet transform analysmethod was developed by Burgerset al.;3 an equivalent procedurthe radial-histogram transform was reported later in Ref. 12.technique enables the three-dimensional height maps to beverted into angular data, describing the tilt and azimuthal anglfacets on the textured surface as scanned.

The AFM gives heightszij on a square grid consisting of 23 256 data points. The AFM facet transform procedure uses acially developed computer program for the computation of thesity of facet normals from the height maps~see Ref. 3 for detailemathematical analysis!. The AFM scan is approximated locallyeverypoint with a plane. The normal vectors to the fitted planesexpressed in terms of the angular components of tiltu and azimuthf in the spherical coordinate system of Fig. 5, and the densitytion of normal vectors, which is equal to the number of norvectors per solid united angle, is determined.

Localized laser scatter recordings.—He-Ne laser light of 0.5 mmbeam diameter is incident perpendicular to the textured surfacehole in a semitransparent projection screen. Light is reflectedfrom the crystal in preferential directions according to the surtexture resulting from the etch type used and the orientation eined. The reflected light impinges upon and is diffused by thejection screen giving a pattern characteristic of the surface morogy. Light transmitted through the screen is recorded with a chcoupled device~CCD! camera. These laser scatter patterns canbe recorded using photogoniometry,13 whereby a photodetectmounted on a rotatable arm is used to make a hemispherical sthe reflected light, whereby a mercator projection~projection of asphere on a flat surface! yields the laser scatter pattern. Laser scpatterns may also be checked against the AFM facet transform~forlow-angled facets yielding direct light reflectance spots! as an extrcontrol of measurement accuracy.

Determination of facet orientations.—Scatter measurementsused in combination with Laue photography6 to determine the orentations of the exposed etch facets in terms of their Miller indeThere are parallels between the Laue and scatter methods. FLaue technique, the reflection of X-rays from crystal planes icorded giving crystallographic information, while for the scatechnique, light reflected from the surface gives information athe surface morphology. The wafer to projection screen distancset at 4 cm for both Laue and scatter experiments, and it is enthat the position of the wafer with respect to the incident lightthe projection screen is the same in both cases. Then the~mirrorimage! of the scatter reflection patterns are superimposed upoLaue photograph, laser light reflection spots will correspondthe Laue reflection spot for the crystal plane with the same sunormal, yielding the orientation of the exposed etch facet, provreflectance spots result from direct reflectances from the etchwithout multiple reflectance from adjacent surfaces.

Modeling

Modeling of texture-etched surfaces using the ray-traprogram Sunrays.—Theoretical surface morphologies and refltances, whereby the etch surface is composed exclusively of$111%facets, could be modeled on a per orientation basis using thetracing program Sunrays.14 This program calculates the optical prerties of geometrically textured silicon cell structures, these texbeing described in terms of a geometrically defined unit cell sture. Theoretical texture etch geometries are described geometfor a particular base wafer orientation using the matrix transfotion described in Ref. 15. Modeling with Sunrays leads to an idized view of the texture-etched surface, since only texture feaof identical size can be modelled, with no flat areas betweenfeatures.

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Journal of The Electrochemical Society, 151 ~6! G408-G427~2004!G412

Results of Saw-Damage Etching

Surface morphology.—Figures 8 and 9 show the saw-dametched surfaces for the seven orientations from SEM and AFMcroscopy. The surface morphologies of the saw-damage etchefers are generally relatively flat, in terms of their optical reflecproperties in air. The majority of exposed etch facets have sunormals with tilt angles of less than 30°,i.e., lower than is requirefor even minimal double-bounce incidence of light in air~see TableI!. This flatness arises due to the large number of crystallogrplanes which are stable to the etch, these being predominant$100%, $111%, $110%, $311%, and $211% sets of planes, as found

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investigations with Laue photography/scatter patterns. With soplanes being stable to the etch, the angle of intersection of aplane to any miscellaneous base orientation is relatively low, reing in generally flat but nevertheless often complex geomestructures.

The $100% and $111% planes are particularly stable to the eThis is exhibited on etching the~100! and ~111! wafer orientationssince they etch down toward the base orientations giving palarly flat etch surface morphologies. Correspondingly, their Afacet transforms show that facets are angled normally to thesurface, and laser light is reflected back upon itself yielding a

Figure 7. ~a! SEM photograph of thinverted pyramid texture used for cabration.~b! Corresponding AFM sca

Figure 8. SEM micrographs of surface morphologies for saw-dametched wafers as viewed~a! from above and~b! in cross section

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tinct reflectance spot centered around the wafer surface no$111% planes are exposed as polygonal stepped crater-like etchseveral tens of micrometers in dimension, with steps expandinfrom the pit centers. In contrast, the square-shaped plateaus of$100%planes are smooth, with no steps visible. Both$100% and/or $111%planes are found exposed on all the wafer orientations to a grealesser extent.

Crystals oriented away from the$100% and$111% yield more complex etch surfaces, with structures composed from several ostable etch facets, as is summarized in Table I. The exposedare not always distinct, with some facets merging into other~inparticular, neighboring$211% and $311% facets which are separatspatially by a tilt angle of only 10°! or being somewhat roundedeven broken up whereby facet normals are spread up to sdegrees around the central exposed facet normal.

The most complex etch structures are found on the~110! waferorientation, which has etch facets exposed in no less thandirections. The majority of facet normals are oriented within adiffuse spot~620°! centered around the normal to the wafer surfHowever, the remaining facets have tilt angles around 30° or mLimited double-bounce reflectance is possible between azimuopposite~100! and ~010! exposed etch facet pairs, which haveangles of 45°. This leads to the slightly lower reflectance of the~110! wafer with respect to the other saw-damage etched wafeentations.

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Reflectance measurements of bare saw-damage etchures.—The wide variation in texturization with orientation conquently yields differences between the individual reflectancessured. Figure 10 shows that reflectances lie between 0-4%than that for the polished silicon, with the~100! and~110! being thehighest and lowest reflecting orientations, respectively. Forlower reflecting orientations this indicates that a low level ofentry of light is present, although generally the majority of faceangles are too low for double-bounce reflectance in air. The retances at wavelengths above 1.2mm ~i.e., where the silicon is fulltransmitting so that the rear surface reflectance is visible in thesured total reflectance! also give an initial indication of the variatioin facet tilt angles between the textures. These vary by appmately 7% for the monocrystalline wafers suggesting that signifilevels of ~internal! light scattering occur for some textures. Tpoint will be further discussed in a forthcoming paper.16 ~The peakin reflectance atl 5 0.36mm corresponds with the position of tdirect bandgap of silicon at 3.4 eV.!

As discussed previously, the dominant etch facets exposedthe crystal orientations~represented in the AFM facet transformsFig. 9 by the spots or facet clusters with the highest densisurface normals! have tilt angles less than the 30° required for indouble-bounce reflectances~see also Table I!. This explains the higtotal reflectances approaching those of polished silicon, as mea

Figure 9. ~a! AFM height mappings of saw-damage etch surface morpgies as viewed from above. The adjacent height scale applies for aAFM scans shown.~b! Resulting AFM facet transforms of saw-dametched wafers.d 5 position of etch facet as calculated from theory. Fangles are calculated from thex,y coordinates of the axes of the facet traforms by solving the simultaneous equationsx 5 u cosf, y 5 u sinf.

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Journal of The Electrochemical Society, 151 ~6! G408-G427~2004!G414

for the individual wafer/crystal orientations. Where facets haveangles above 30° relative to the wafer surface, there are generaazimuthally opposing facets with high enough tilt angles onto wthe light can be reflected for a second incidence@except for near~110! oriented crystals#. Thus light is still reflected away from thsilicon after its first point of incidence, and reflectance remainsIn summary, the bare saw-damage etched wafers have reflecin air equivalent to polished silicon. This is because the tilt angl

Figure 10. Reflectances for the saw-damage etched monocrystalline w~starting thickness;525 mm! and a double-polished 100mm thick siliconwafer. The order of front surface reflectance for the seven orientatioR . R . R . R . R . R . R .

Table I. Quantification of the surface morphology for saw-damageexposed etch facets, and optical properties in terms of the probabcorresponding, respectively, with „ i … guaranteed multiple incidencpossible multiple incidence of light„30° Ë u Ë 45° in air…, and „ ilation…. Italic type indicates calculated results.

Orientations in termsof Miller indexes

Facet angles~°!~calcul

Wafer Etch facet Tiltu

~100! ~100! 1.5 ~0.0!

~311! ~211! 10.0 ~10.0!~100! 30.1 ~25.2!~311! 0.0 ~0.0!~110! 31.8 ~31.5!~101! 26.9 ~31.5!

~210! ~311! 14.1 ~19.3!

(311̄) 18.4 ~19.3!

~111! 31.6 ~39.2!

(111̄) 42.4 ~39.2!

~321! ~110! 19.0 ~19.1!~111! 23.4 ~22.2!~101! 36.5 ~40.9!

~110! ~110! 0.0 ~0.0!~100! 37.8 ~45.0!~010! 38.2 ~45.0!~311! 26.4 ~31.5!

(311̄) 25.6 ~31.5!

~131! 27.3 ~31.5!

(311̄) 28.3 ~31.5!

~221! ~111! 13.1 ~15.8!

~111! ~111! 1.5 ~0.0!

100 210 311 321 111 221 110

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the dominant etch facets exposed are lower than the 30° requirdouble bounce reflection.

Reflectances of saw-damage etched wafers under encation.—There is a larger spread in reflectances of 7% for thesewafer orientations under encapsulation compared to the caseFigure 11 shows that the reflectances of the different orientationseparated into three groups, with the~100!, ~210!, and~111! havingthe highest reflectances, the second group including the~311! and~221! having intermediate reflectance, and the third group inclu~110! and ~321! having the lowest reflectances.

Considering the first group, reflectances are almost identicthe ~100!, ~210!, and ~111! orientations below a wavelengthl5 1 mm, lying approximately 1-2% lower than for the polishsilicon under encapsulation. This emphasizes the flatness ofparticular textures, with most of the incident light reflected bnormally to escape out through the glass encapsulation. On~210! has a lower reflectance abovel 5 1 mm, indicating the effecof the greater faceting of the etch surface~with two clusters oopposing facets around 16° to the normal! compared to the particlarly flat ~100! and ~111!. Although this facet angle is too low flight confinement at the glass encapsulant by total internal retance~minimal facet angle5 20.9°), the difference in reflectancehigher wavelengths suggests that the level of texturization mayan eventual effect on internal scattering of light within the silico16

For the~311! and~221! wafer orientations, reflectance is appromately 6% lower than the polished silicon case. This is causethe higher facet angles of the texture, whereby in both casesexist with tilt angles greater than the 20.9° required for total intereflectance at the glass-air interface. In the case of the~311!, three o

ed wafers, in terms of Miller indexes, tilt, and azimuth angles of thef multiple incidence of light. YÄ yes, N Ä no, and P Ä possible,angles u Ì 45° in air or u Ì 20.9° under encapsulation…, „ i i …multiple incidence „u Ë 30° in air or u Ë 20.9° under encapsu-

easuredMultiple incidence~Y/N/P! dueto facet tilt angleu as measured

~calculated!

Azimuth f In air Encapsulated

0.0 ~0.0! N ~N! N ~N!

180.0 ~180.0! N ~N! N ~N!23.8 ~20.0! P ~N! Y ~Y!

0.0 ~0.0! N ~N! N ~N!118.2 ~106.8! P ~P! Y ~Y!116.9~2106.8! N ~P! Y ~Y!

112.9 ~114.1! N ~N! N ~N!119.4~2114.1! N ~N! N ~N!

53.0 ~65.9! P ~P! Y ~Y!272.9 ~265.9! P ~P! Y ~Y!

15.0 ~15.0! N ~N! N ~N!129.8 ~133.1! N ~N! Y ~Y!170.5~2165.0! P ~P! Y ~Y!

0.0 ~0.0! N ~N! N ~N!24.6 ~20.0! P ~Y! Y ~Y!174.0 ~180.0! P ~Y! Y ~Y!40.7 ~35.3! N ~P! Y ~Y!

251.3 ~235.3! N ~P! Y ~Y!

144.3 ~144.7! N ~P! Y ~Y!138.7~2144.7! N ~P! Y ~Y!

0.0 ~0.0! N ~N! N ~N!

0.0 ~0.0! N ~N! N ~N!

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Journal of The Electrochemical Society, 151 ~6! G408-G427~2004! G415

the four exposed etch facets have facet angles high enough tothe confinement of light within the glass. However, the most prnent facet present, the~211!, at only 10° to the surface normal, wreflect equivalently to polished silicon, so that the reflectance ireduced further than shown. For the~221! wafer orientation, thexposed facets have surface normals spread around the~111! ori-ented etch facet. Since some facets are thereby angled abovesome light is confined at the glass-air interface leading to limreflectance reduction.The ~110! and ~321! wafer orientations have such a high levefaceting that a large proportion of the incident light is confined aglass surface, resulting in the lowest reflectances for the seveentations. For the~110! wafer orientation, six of the seven etfacets exposed have tilt angles permitting total internal reflecas well as double-bounce reflectances, but unfortunately, reflecreduction is restricted by the large proportion of facets angledmally to the base orientation. Similarly for the~321! orientation, thefacets all have theoretical orientations large enough to giveinternal reflection at the glass-air interface. However, sincenormals around the exposed~111! facet are spread by approximat610° around the measured angle of 23.4° for this latter waferentation, a proportion of the etch surface is tilted below the criangle for light confinement.In summary, the number of crystals experiencing multiple entrlight is significantly increased for the saw-damaged etched won encapsulation, compared to the bare silicon. This is bemany exposed etch facets have tilt angles high enough forconfinement by total internal reflectance at the glass-air inte~i.e., .20.9°!, but too low for even minimum multiple-bounce indence in air~i.e., ,30°!.

Results of Texture Etching

Surface morphology.—Figures 12 and 13 show the textuetched surfaces for the seven representative orientations fromand AFM microscopy. While for the saw-damage etch, all worientations commonly exhibited relatively flat surface textularge variations in roughness exist between the roughest and fltexture etch surfaces for the different wafer orientations. AFM ftransforms~Fig. 13! of the various wafers show that for orientatioclosest to the~100!, for example~311!, ~210!, etc., one or more othe dominant exposed etch facets have tilt angles large enoudouble-bounce interactions with light, as summarized in TablThe remaining orientations yield far flatter textures with tilt antoo low for double-bounce reflectance in air. In addition, etch texfeatures are nonuniform in size and distribution over the waferface, and are sometimes separated by nontextured~flat! regions.

Figure 11. Encapsulated reflectances for saw-damage etched monocline wafers~as-cut starting thickness;525 mm! and a double-polished 10mm wafer. The drop in reflectances aroundl 5 1 mm and also forl, 0.4mm results from absorption in the EVA encapsulation.

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Laue-scatter investigations of the wafer surface morpholoshow that the set of$111% crystallographic planes is particulastable to the low concentration alkaline texture etch~see also Ref.for further details!. Laser scatter patterns for the majority of textuetched crystal orientations exhibit direct reflectance spots in threction of one or more exposed$111% etch facets. In the case of t~100! wafer/crystal orientation, four orthogonal laser light spotsobserved due to the double-bounce reflectances originatingeach facet on the pyramidal texture. AFM facet transforms in ation to Laue-scatter investigations confirm the correspondingfacets to be of$111% orientation, with tilt angles of approximate655°.

The stability of the$111% planes to the etch is in agreement wthe generally accepted texture etch theory. Indeed, the shapetextures on the different wafer orientations, as viewed by SEMcroscopy, varies visually from upright pyramids on~100! wafers, totilted pyramids on near~100! wafer orientations@e.g., ~311! and~210!, angled at 25.2° and 26.6° to the~100! plane#, to flat triangulaplateaus on the~111! as predicted by Sopori7 and the matrix transformations described by Campbellet al.15 It should, however, bnoted that the exposed$111% facets are not perfect crystallograpcally. Closer inspection of the~tilted! pyramid morphology reveathat the exposed$111% texture facets may be slightly roundedeven split, consisting apparently of two facets slightly tilted wrespect to one another, in agreement with the observations of RThis can be seen, for example, in the AFM facet transform fopyramidally textured~100! orientation in Fig. 13, where the clustof exposed facets around the individual^111& directions are seenbe split into two groups angled within a few degrees of each o

In addition, the further away the wafer is oriented angularly fthe ~100! orientation toward the~110!, the less the tilt angles of thexposed etch facets agree with those calculated for the$111% planesexpected from theory~see Table II!. Indeed, both laser scatter aAFM facet transforms indicate that the~111! facet is not exclusivelexposed by the etch. In fact the whole range of$XXY % facets@ori-entations lying on the line between$111% and $110%, e.g., $221%,$331%, $556%, etc.# are exposed by texture etching. This is seen inlaser scatter and AFM facet transforms: lines of reflected lighexposed etch facet normals are found extending between$111% and$110% facets, as opposed to direct spots of light or facet clusterdistinct direction. In fact, in the case of the~110! wafer orientationwhere theory dictates the formation of V-shaped grooves consof intersecting$111% planes at 35° to the surfaces, far flatter surfaare obtained with somewhat rounded grooves with tilt angle;15°, these facets being closer in orientation to the$221% than the$111%. While the theoretical structure would allow a low leveldouble-bounce interaction at the base of the grooves in air, tnot possible for the actual texture formed.

In summary, the geometry of the multicrystalline surface forture etching depends upon the angular proximity of crystals from~100! orientation. Etch structures close to the~100! and ~110! haveshapes which correspond with those expected from theory, witramidal and flat triangular textures forming, respectively. Howenone of the wafer orientations yield exclusively perfect$111% facetsas expected theoretically. In fact a range of orientations@the $XXY %#are exposed so that, particularly near the$110% orientation, mucflatter surfaces may be yielded than expected.

Reflectance measurements of bare texture ewafers.—Figure 14 shows reflectances for the texture-etched wrevealing a far larger spread in the bare wafer reflectances ththe saw-damage etch. Reflectances are related to the angularation between the particular wafer orientation and that of the~100!plane, in correspondence with the facet tilt angles of the textudescribed above. The wafers oriented furthest away from the~100!,i.e., the ~111!, ~221!, and~110! wafers in this case, have the highreflectances, equivalent to that of polished silicon~front surface reflectanceR ; 31% atl 5 1 mm). This compares to front-surfareflectance values for the~100! wafer as low as 13% due toupright pyramid texture. The tilt angles of etched facets expose

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Journal of The Electrochemical Society, 151 ~6! G408-G427~2004!G416

these orientations are too low for multiple reflectance in air~i.e.,,30°!, so that reflectances approach that of polished siliconcrystals tend closer in orientation to the$100%, tilted pyramids arexposed with facets angled at increasing tilt angles with respethe wafer surface. When etch facet tilt angles begin to exceeddouble-bounce reflectance becomes more likely, so that the rtance in air decreases for crystals closest to the$100% orientations.

In summary, the reflectances of bare multicrystalline wafeair are dependent upon the angular proximity of the constituenttals with respect to the~100!. Near ~100! orientations have lowreflectances in air due to the~tilted! pyramid textures which enabdouble-bounce reflectance. Further away from the~100!, the increasing flatness of texture yields still higher reflectances towards~111!and ~110!, and other~XXY ! orientations.

Reflectances of texture-etched wafers under encaption.—Figure 15 shows the encapsulated reflectances for thetexture-etched monocrystalline wafers. The reflectances of the~111!,~110!, and~221! orientations@i.e., the$XXY % orientations# are high-est, as was the case for the bare wafers, equivalent to the en

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lated polished wafer due to the flatness of these textures. Thepyramid textures on the~210! and ~311! wafer orientations havconsiderably lower reflectances, comparable to those of the esulated upright pyramids formed on the~100! orientation. The dramatic reduction in reflectance for these tilted pyramid textures iresult of the internal confinement of light reflected away fromsilicon at first incidence at the front glass encapsulant. The meatilt angles of 36° and 27.5° for the predominantly exposedfacets~see Table II! on the~210! and ~311! wafer orientations, respectively, are large enough to ensure total internal reflectanlight at the glass-air interface. For the upright pyramid texturethe ~100!, however, encapsulation has a minimal effect uponlevel of light coupled into the cell, since most light enters the silthrough the initial double-bounce reflectance at the pyramid faas is the case in air, prior to approaching the glass-air interfac

In summary, reflectance of texture-etched multicrystalline waunder encapsulation depends upon the angular proximity of conent crystals to the$100% orientations, as is the case for the waferair. However, a far larger range of crystals further away from

Figure 12. SEM micrographs of surface morphologies for texture etwafers as viewed~a! from above and~b! in cross section~2000 times magnification, scaling line5 13mm).

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Journal of The Electrochemical Society, 151 ~6! G408-G427~2004! G417

~100! with tilted pyramid textures now experience multiple-bouincidence of light~and thus low reflectances!, since facet tilt angleof only 20.9° satisfy the condition for total internal reflectance aglass-air interface.

Comparison of measured and theoretical reflectances for teetched wafers in air.—Table III shows the value ofR at 630 nm@arbitrary nontransmitting wavelength for silicon, approximaequal to that of the laser light used for~Laue!-scatter recordings adescribed in the section on localized laser scatter recordings# for thedifferent texture-etched orientations. Reflectance in air is seincrease with the increase in angular separation between the plar crystal orientation and that of the~100!, in agreement with thtrend found for the measured reflectances. However, the theoreflectances as calculated by Sunrays are approximately 2-5%than those measured in practice, with the~110! wafer orientationhaving the poorest agreement. The exposed etch facets havetilt angles than those expected theoretically for the correspon$111% planes, and nontextured regions will reflect normally tosurface. The actual reflectances are therefore higher than extheoretically since less multiple incidence of light will occur in prtice. The lower facet tilt angles are primarily due to the stabilitthe $XXY % range of planes leading to a reduction in sharpnestexture features with rounding or splitting of etch facets ratherdistinct $111% planes as expected.

In summary, the same trends in reflectance are found fo

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individual bare-texture-etched wafer orientations for measuredcalculated reflectances based on texture etch theory. Both meand theoretical reflectances increase with the angular separatitween the particular crystal orientation and that of the~100!. Reflec-

Figure 13. ~a! AFM height mappings of texture etch surface morpholoas viewed from above. The adjacent height scale applies for all thescans shown.~b! Resulting AFM facet transforms of texture etched wafd 5 position of etch facet as calculated from theory. Facet angles arculated from thex,y co-ordinates of the axes of the facet transformssolving the simultaneous equationsx 5 u cosf, y 5 u sinf. Where anarbitrary$XXY % orientation is exposed, the theoretical position of the cest $111% or other$XXY % orientations is also shown.

Figure 14. Reflectance in air for the texture-etched wafers~initial thickness;525mm! compared to polished 100mm silicon.~a! ~111!, ~221!, and~110!,~b! ~311! and ~210! orientations.

afersr

eme facets

theoretical position of the closest$111% or other$XXY % orientations is also shown.

Journal of The Electrochemical Society, 151 ~6! G408-G427~2004!G418

Figure 15. Encapsulated reflectances for the texture etched mono-w~starting thickness;525mm! and a double-polished 100mm thick wafer.~a!~111!, ~221!, and~110!, ~b! ~311!, ~210!, ~100! orientations.

Table III. Measured and calculated reflectances atl Ä 630 nmfor the seven-texture-etched wafer orientations.

Wafer orientation

Reflectances at 630 nm

In air Under encapsulation

MeasuredCalculated~Sunrays! Measured

Calculated~Sunrays!

~100! 15.0 10.3 8.1 6.5~311! 26.6 22.4 8.7 5.1~210! 26.1 21.1 7.5 4.3~321! 31.8 26.8 16.9 4.7~110! 34.1 28.8 20.6 8.4~221! 34.1 31.8 20.8 14.7~111!a 34.1 34.9 21.6 22.1Polished 34.4 34.9 21.5 22.1

a Sunrays crashes during ray-tracing for the~111! orientation; the cal-culated values shown are for polished silicon, since the triangulastructure modeled by the program is seen to be completely flat.

Table II. Quantification of the surface morphology for texture-etched wafers, in terms of Miller indexes, tilt, and azimuth angles of the exposedetch facets, and optical properties in terms of the probability of multiple incidence of light. Y Ä yes, N Ä no, and P Ä possible, corre-sponding, respectively, with„ i … guaranteed multiple incidence„tilt angles u Ì 45° in air or u Ì 20.9° under encapsulation…, „ i i … possiblemultiple incidence of light „30° Ë u Ë 45° in air…, and „ i i i … no multiple incidence „u Ë 30° in air or u Ë 20.9° under encapsulation….Italic type indicated calculated results.

Orientations in terms ofMiller indexes

Facet angles~°! as measured~calculated!

Multiple incidence~Y/N/P! due to facet tilt

angleu as measured~calculated!

Wafer Etch faceta Tilt u Azimuth f In air Encapsulated

~100! ~111! 57.5 ~54.7! 95.5 ~90.0! Y ~Y! Y ~Y!

(111̄) 57.5 ~54.7! 1.9 ~0.0! Y ~Y! Y ~Y!

(11̄1̄) 55.5 ~54.7! 291.5 ~290.0! Y ~Y! Y ~Y!

(11̄1) 57.4 ~54.7! 178.5 ~180.0! Y ~Y! Y ~Y!

~100! 5.0 ~0.0! 0.0 ~0.0! N ~N! N ~N!

~311! ~111! 30.6 ~29.5! 172.5 ~180.0! P ~P! Y ~Y!

(111̄) 58.4 ~58.5! 77.7 ~73.2! Y ~Y! Y ~Y!

(11̄1) 55.8 ~58.5! 280.2 ~273.2! Y ~Y! Y ~Y!

~110! 30.3 ~31.5! 98.5 ~106.8! P ~P! Y ~Y!~101! 28.0 ~31.5! 2101.3 ~2106.8! N ~P! Y ~Y!

~210! From ~111! 39.5 ~39.2! 124.7 ~114.1! P ~P! Y ~Y!Via ~110! 16.7 ~18.4! 2171.4 ~2180.0! N ~N! N ~N!

To (111̄) 39.1 ~39.2! 2116.6 ~2114.1! P ~P! Y ~Y!

~321! ~111! 11.2 ~22.2! 2137.0 ~136.9! N ~N! N ~Y!

~110! ~110! 0.0 ~0.0! 0.0 ~0.0! N ~N! N ~N!~XXY !, ~111! 19.5 ~35.3! 25.1 ~0.0! N ~N! N ~N!

~XX-Y !, (111̄) 20.1 ~35.3! 176.2 ~180.0! N ~N! N ~N!

~221! ~221! 0.0 ~0.0! 0.0 ~0.0! N ~N! N ~N!

~111! From ~111! 0.0 ~0.0! 0.0 ~0.0! N ~N! N ~N!To: ~a! ~XXY !, ~110!, 19.8 ~35.3! 3.8 ~0.0! N ~N! N ~Y!

(111̄) ~70.5! ~0.0! ~Y! ~Y!

~b! ~XYX !, ~101!, 16.1 ~35.3! 2120.0 ~2120.0! N ~N! N ~Y!

(11̄1) ~70.5! ~2120.0! ~Y! ~Y!

~c! ~YXX !, ~011!, 11.4 ~35.3! 127.9 ~120.0! N ~N! N ~Y!

(1̄11) ~70.5! ~120.0! ~Y! ~Y!

a Where facet normals are exposed over a range of orientations as opposed to a distinct crystal plane, the range is described by the most extrexposed~from...to! and/or the most central orientation through which the range passes~...via...!. Where an arbritrary$XXY % orientation is exposed, the

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Journal of The Electrochemical Society, 151 ~6! G408-G427~2004! G419

tances are somewhat higher than predicted by theory since etcets are not perfectly$111% oriented and generally have lowerangles than predicted.

Comparison of measured and theoretical reflectances for teetched wafers under encapsulation.—Table III shows measured apredicted reflectances~as calculated by Sunrays! for the representative orientations on encapsulation. For the majority of orientatclosest to~100! and around the stable~111!, any discrepancy between measured facet tilt angles and those predicted by theoryminimal effect on the reflectance reduction expected on encaption. The high reflectances measured on the~111! orientationequivalent to polished silicon, and the low reflectances on upand tilted pyramids@e.g., on ~100! and~210! and~311! orientations#through initial multiple bounce incidence and light confinementheglass-air interface, respectively, are both predicted and measupractice.

However for wafers oriented closer to the~110!, the measureand predicted reflectances on encapsulation differ considerablthe very shallow tilted pyramid texture on the~321! orientation forexample, angled closer to the~110! than to the~100!, measured ancalculated encapsulated reflectances differ by 12.2%. The meaangle for the primary facet exposed is approximately 11°, so thbenefits are gained by light confinement. However, if the~321! tiltedpyramid texture was composed of perfect$111% facets, then the theoretical 22.2° tilt angle of the~111! facet would be high enoughensure total internal reflection at the glass-air interface. The situfor the encapsulated~110! orientation itself is also extreme. Whfor the other orientations investigated, predicted reflectances atween 1-5% below those measured, the predicted reflectances~110! wafer orientation are approximately 11% lower than is msured. This is because the facet angles of the actual texturelower than 20.9°, as required for total internal reflectance of ligthe glass-air interface. In contrast according to theory, V-sh

grooves would be formed through intersecting~111! and (1̄1̄1)planes with 35° facet tilt angle with respect to the base~110! orien-tation. This angle is large enough to allow total light confinemthe glass-air interface, whereby double incidence and thus greflection reduction would occur as predicted.

In summary, the theoretical model of texture etching predictsfor the majority of wafer/crystal orientations, except those closethe ~111! orientation, etch facet tilt angles will be large enoughachieve reflection reduction under encapsulation. This would rfrom multiple-bounce incidence either primarily at highly facetextures~for example, for upright pyramids! or in any case via totainternal reflectance of escaping light at the glass-air interfacetowards the silicon. However the stability of all the$XXY % orienta-tions, in particular the~110!, limits the proportion of wafer/crystorientations whose etch facets have tilt angles above 20.9° forconfinement at the glass-air interface. As a result, not only~111! orientations but also wafers close to the~110! yield highlyreflecting etch surfaces.

Discussion

Comparison of saw-damage and texture etchingmonocrystalline wafers.—The differences in surface morphologysulting from saw-damage and texture etching result in contrareflectances on a per orientation basis. The crystallographic pexposed by etching are entirely different for the two etches, leato textures with relatively low facet angles~generally less than 30!for the majority of saw-damage etched surfaces, compared tofaces with facet tilt angles up to 55° for texture etching.

Figure 16 summarizes the resulting reflecting properties fodifferent orientations, using the principal triangle of orientationsscribed in Fig. 4. The differences in surface morphology for theetches mean that completely different regions of the principaangle of orientations yield high or low reflectances. For examwhile texture etching of the~100! orientation yields highly facete

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pyramids with low reflectance in air, saw-damage etching osame orientation yields microscopically flat textures with retances equivalent to polished silicon.

The effect of the variation in facet tilt angles with orientatiobest appreciated for the two etches by observing the changeflectance in air compared to encapsulation. This is quantifieTables IV and V below, whereby reflectances are related to theportion of the etch surface yielding facets with tilt angles satisfthe conditions for multiple reflectance in air or under encapsulaThe majority of test orientations for both the etches give reflectain air approaching or equivalent to polished silicon. This is becawith the exception of texture etched~tilted! pyramid textures on th~100!, ~311!, and ~210! orientations, the test orientations yield ttures whereby more than 60% of etch facets have tilt angles b30° so that no multiple incidence of light is possible. For the sdamage etch in air, for example, near~110! orientations have facewhereby multiple incidence of light may be possible, but its retance values are still only 4% lower than for polished silicon duthe large number of facets angled below 30°. In comparisontexture etching the upright pyramid textures formed on the~100!orientation have reflectances approximately 20% lower than foished silicon, through double-bounce incidence of all light falupon pyramid facets. Moving away from the~100!, pyramid structures correspondingly tilt so that dominant etch facets have atending below 45°, whereby multiple-bounce incidence decrea

However under encapsulation, many orientations whose etcface geometries allowed only minimal, or even no reflectance retion in air, have structures whose dominant facets have angles20.9° required for light confinement at the glass-air interface~seealso Tables I and II!. This is the case for both the texture etch~forthe aforementioned tilted pyramid textures! and the saw-damaetch, for the central orientations in between the flat etching~100!and ~111!. Therefore under encapsulation, the number of optiuseful orientations is significantly increased as compared to thewhen bare.

The results from Table IV and V are summarized graphicalFig. 17, which shows the relationship between the measured rtance and the percentage of the silicon surface having facet ayielding guaranteed multiple incidence of light, fitted linearly forwafers in air and under encapsulation. The measured reflectancseen to decrease as the percentage of the surface yielding guamultiple incidence of light increases.

For the bare wafers, the decrease in reflectance is greatesvalues of 34% as equivalent to polished silicon in air, to vaaround 2% for the surface where 100% of light will experiemultiple reflectance~experimental etch textures with optical propties in this latter regime have surface morphologies equivalevertical columnar structures, such as those obtainable using reion etching.17 For the saw-damage etch textures, with generallythan 5% of the surface yielding guaranteed multiple incidenceflectances are equivalent to polished silicon, while for the texetched wafers, the differences in facet angles between flat e$XXY % orientations and~tilted! pyramid textures yields a far greaspread in measured reflectances.

For the encapsulated wafers, the decrease in reflectance isgradual, from values of;22% reflectance equivalent to polishsilicon under encapsulation, decreasing to values of;6% wheremultiple-bounce incidence is guaranteed, this value resultingtirely from reflectance from the glass. The reflectance distributimore evenly spread for the encapsulated saw-damage etchedcompared to the texture etched wafers. The differences in etcface geometries between the orientations now become visible fsaw-damage etch texture depending upon the percentage oftilted above 20.9°, whereas these differences were barely visi

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Journal of The Electrochemical Society, 151 ~6! G408-G427~2004!G420

air due to the small proportion of facets above 45° yielding guateed multiple incidence. The increase in facet tilt angles with otation for the saw-damage etched samples, from the flattest e~100! and ~111! orientations to the highest facet tilt angles oncentral~110! and~321! orientations, is far more gradual than fortexture etched wafers, where textures contrast over the printriangle of orientations from polished textures on the$XXY % orien-tations and to the pyramidal textures.

Table IV. Relationship between measured reflectances and facet t

Waferorientation

Percentage of surface with mangleu greater th

45°A 30°B

~100! 0.0 1.0

~311! 1.5 24.8

~210! 1.1 12.4

~321! 1.8 22.1

~110! 0.2 24.6

~221! 1.7 14.8

~111! 4.7 8.9

Polished 0.0 0.0

a Facet tilt angles are grouped as a function of the probability of muanglesu . 45° both in air and under encapsulation, B5 as A with addiis possible in air but guaranteed under encapsulation, and C5 as B wioccurs in air but is guaranteed under encapsulation. This also app

g

l

Algorithm linking monocrystalline and multicrystallireflectances.—In order to relate the results on monocrystallinefers to the situation for multicrystalline wafers, an algorithmdeveloped by Burgers18 whereby a weighted average is calculafor the quantitative data acquired for the individual wafer orietions. This weighted average accounts for the random orientatiocrystals in the wafer, whereby, for example, the reflectance prties of a multicrystalline wafer may be calculated from the equa

Figure 16. Sketches indicating the rflectances of alkaline-etched wafers afunction of orientation, using the princpal triangle of orientations as describin Fig. 4. Reflecting properties are dscribed on the basis of measured refltance values in the visible by~a! reflec-tances equivalent to polished silicon,~b!some multiple incidence of light,~c! ma-jority of incident light experiences mutiple bounce incidence.@Reflectanceequivalent to upright pyramids omonocrystalline~100! silicon.#

les for saw-damage etched monocrystalline wafers.a

red facet tilt Measured reflectance atl 5 630 nm

20.9°C In air Encapsulated

9.2 33.7 19.3

44.1 32.4 15.4

30.5 32.7 18.4

59.3 31.9 11.9

51.1 30.2 11.9

28.2 31.2 14.7

10.9 31.5 19.0

0.0 34.4 21.5

incidence of light whereby A5 guaranteed multiple incidence for facet tiltfacets with angles 30°, u , 45°, for which multiple incidence of light

ditional facets angled 20.9°, u , 30°, whereby no multiple incidenceTables V and VI.

ilt ang

easuan

ltipletionalth adlies to

onpalthe

d isanceanceeflec-tallinthane wa

thebe-

the

licon

h,

evene for

Journal of The Electrochemical Society, 151 ~6! G408-G427~2004! G421

Rt 5

EF50

p/2 EQ50

tan21~sin F!R~F,Q!cosQdFdQ

EF50

p/2 EQ50

tan21~sin F!cosQdFdQ

5weighted sum of reflectances

area

whereF andQ are defined as in Fig. 4. This weighting is basedthe projection of the areas of all 48 families of princi$100%:$110%:$111% triangles upon a sphere encompassing allpossible crystal coordinates. The accuracy of this methodemonstrated in Fig. 18, where the weighted average of reflectfor texture-etched wafers is compared to the mean of reflectmeasured for eighteen multicrystalline wafers. The absolute rtances derived from weighted averages on the seven monocryswafers average 1 and 1.5% lower, respectively, in the visiblethose measured for the bare and encapsulated multicrystallin

Figure 17. Relationship between reflectance and the proportion of sisurface yielding multiple incidence, fitted linearly for the bare wafers~solidline! and the wafers under encapsulation~dashed line!. SD saw-damage etc

Table V. Relationship between measured reflectances and facet til

Waferorientation

Percentage of surface with mangleu greater th

45°A 30°B

~100! 59.8 70.3~311! 21.6 57.3~210! 14.1 47.8~321! 2.1 6.8~110! 0.0 0.1~221! 0.0 0.0~111! 0.0 0.0Polished 0.0 0.0

a See footnote a to Table IV.

ss

e

-

fers. However, the weighted averages lie within the limits ofstandard deviation for the eighteen multicrystalline wafers, thising 61.9 and61.75% in absolute reflectance in the visible forbare and encapsulated wafers, respectively.

Figure 18. Comparison of the weighted average reflectance for the smonocrystalline wafer orientations with the actual average reflectancmulticrystalline wafers etched under the same conditions for~a, top! bare and~b, bottom! encapsulated wafers.

les for texture etched monocrystalline wafers.a

red facet tilt Measured reflectance atl 5 630 nm

20.9°C In air Encapsulated

81.2 15.0 8.182.1 26.6 8.774.6 26.1 7.518.1 31.8 16.913.7 34.1 20.62.5 34.1 20.80.1 34.1 21.60.0 34.4 21.5

TE texture etch.

t ang

easuan

ysi-tionince

ibleenta-age

in ori-roach-yncesrved

n twoen-

nally,rs tooverrithm

lline

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re-t ofsaw-ly 7%-ue toir in-into

r thee hasflec-ultiplethe

mageoringce ofamidy vir-eres

aw-ocryla-

Journal of The Electrochemical Society, 151 ~6! G408-G427~2004!G422

Application to multicrystalline wafers.—The absence of anpreferential orientation~s! dominating the crystallographic compotion of the multicrystalline wafer renders it essential that reflecreduction be applicable to as many orientations as possible. S

Figure 19. Reflectances for multicrystalline wafers with alkaline sdamage and texture etches as compared to a pyramidally textured montalline ~100! wafer. ~a! Reflectances in air,~b! reflectances under encapsution.

Table VI. Relationship between measured reflectances and facepolished silicon and pyramid texture on monocrystalline„100…. Facethe seven saw-damage and texture etched monocrystalline wafer

Etch type

Percentage of surangleu

45°A

Saw-damage 1.6Texture 13.0Polished 0.0Mono ~100! with texture etch 59.8

a See footnote a to Table II.

a

proportion of crystals invariably yield flat surfaces, it is impossto give reflectance reduction by geometrical means on all oritions. However, Tables IV and V show that both the saw-damand texture etches yield geometrical surface textures on certaentations which under encapsulation can give reflectances apping that of pyramidal texture on the~100! orientation. With so manorientations present in a multicrystalline wafer, will the reflectaof the alkaline-etched wafers be significantly improved if obseencapsulated rather than bare?

Figure 19 shows the average of measured reflectances oneighboring sets of 18 multicrystalline wafers in air and undercapsulation, one set for each of the etches investigated. AdditioTable VI relates the reflectances of the multicrystalline wafetheir surface morphologies as a function of etch facet tilt anglesthe wafer, as calculated using the weighted average algodescribed previously.

Unsurprisingly, the absolute reflectances of the multicrystawafers in air are far higher than for the pyramidally textured~100!monowafer, approximately 14 and 17% higher for the texturesaw-damage etches, respectively, in the visible. For the saw-daetch, this high multicrystalline reflectance highlights the flatnesthe etch surface, whereby approximately 80% of the surfacefacet tilt angles too low to give double-bounce reflectance in air~i.e.,tilt anglesu , 30°). For the texture etch, the slightly lower mucrystalline reflectance results from multiple incidence of light~tilted! pyramids. However the number of near~100! crystals yielding pyramidal textures is too low in proportion with other orientions in the wafer to bring the overall wafer reflectance in air tolevel of the monocrystalline wafer.

For the wafers under encapsulation, the same overall rankireflectances are found for the saw-damage and texture etchetiwafers and the monowafer, from highest to lowest reflectarespectively. However, the level of reflectance is dramaticallyduced for the multicrystalline wafers, and lies far closer to thathe ~100!-oriented wafer than was the case when bare. Thedamage etched wafers have an average reflectance level onhigher than for the encapsulated~100! wafer in the visible, compared to the 17% difference between them when in air. This is dthe benefits obtained through light confinement at the glass-aterface, which significantly improves the level of light coupledthe silicon for the alkaline-etched wafers.

The improvement under encapsulation is most marked fosaw-damage etched wafers. In this case, 38% of the surfacfacet tilt angles above the 20.9° threshold for total internal retance at the glass-air interface and thereby the guaranteed mincidence of light. This compares to a maximum of 17% ofwafer surface for which multiple incidence is possible in air~angles.30°!. The visible reflectance value for encapsulated saw-daetched wafers lies only around 1.5% above that of its neighbtexture-etched multicrystalline wafers, compared to a differen3% when bare. This is because a large proportion of tilted pyrstructures already facilitate multiple-bounce reflectance in air btue of facets angled above 30°~amounting to 29% of the wafsurface according to Table VI!, compared to the far flatter textur

s-

angles for texture-etched multicrystalline wafers,6 in comparison tongles are derived from the weighted average of facet angle data forations as in Tables IV and V previously.

ith measured facet tiltter than

Measured reflectance atl 5 630 nm

20.9°C In air Encapsulated

3 38.3 32.0 15.344.2 29.0 13.80.0 34.4 21.581.2 15.0 8.1

t tiltt tilt aorient

face wgrea

30°B

17.28.80.0

70.3

ctionss.ents

cting

alsoshedfinal

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or. A

frac-

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age

Journal of The Electrochemical Society, 151 ~6! G408-G427~2004! G423

for the saw-damage etch. As a result the reflection reduachieved by light confinement on encapsulation is relatively le

The fact remains, however, that both alkaline etch treatmcompare much more favorably in terms of their surface refleproperties with respect to monocrystalline~100! oriented siliconwhen observed under encapsulation than when bare. This ismuch more practical and realistic comparison, since the finisilicon cells will always be placed under encapsulation in themodule.

Employment of antireflection coatings.—Although antireflectioncoatings~ARCs! are not investigated explicitly in this paper, itinteresting to discuss their effect upon the surface-reflecting prties of ~textured! silicon solar cells. So-called quarter wavelenpredominantly single-layered ARCs are generally employed intrially, applied directly upon the silicon, which for a coating thinessd1 and refractive indexn1 satisfy the relationship

d1 5l0

4n1

whereby light of incident wavelengthl0 which is reflected awaythe silicon-ARC interface initially, will destructively interfere wilight reflected directly away from the ARC encapsulant~e.g., air orglass! interface with which it will be 180° out of phase, thereideally cancelling out reflection~see,e.g., Ref. 1!. ARCs for siliconsolar cells are usually optimized for a maximum current outputhe terrestrial solar spectrum~AM 1.5 G!. This is achieved for coaings with a reflectance minimum at wavelengths of around 600these ARCs giving the finished cells their characteristic blue colreflectance minimum of zero can be achieved forl0 if the refractiveindex of the ARC corresponds to the geometric mean of the retive indexes of the adjacent media, whereby

n1 5 An0n2

where the subscripts 0, 1, and 2 correspond to the encapsulan~e.g., air or glass/pottant!, the ARC, and the silicon, respectiveTaking refractive index values ofnair 5 1.0, nglass5 1.5, andnSi

5 3.8, then optimal refractive index values for the ARC will beand 2.3, respectively, for the silicon cell in air and under encalation. Typical coating materials are SiNx deposited by remoplasma enhanced chemical vapor deposition~RPECVD!, or TiOx .These materials have high transparency, can be depositedlarge range of refractive indexes, and, in the former case, canvide electronic passivation of the silicon wafer surfaces.

When used in addition to geometrical texturization, an antiretion coating further reduces front surface reflection losses fromfinished solar cell. However, the optimization of an ARCalkaline-etched multicrystalline wafers presents extra complexThe optimal thickness of an ARC has been shown to vary withfacet tilt angles of surface texture for the examples of randommidal and periodically microgrooved textures.19,20 The large differences in facet tilt angles between crystals of different orientafound for both the etches investigated here, pose potential profor the optimization of the ARC. Coating thicknesses whichappropriate for a particular crystal and surface morphologythereby be less optimal for other crystals in the wafer. The posity also exists, depending upon the deposition techniques usedthe ARC may not coat the textured surfaces uniformly,i.e., for ex-ample, for a pyramidal texture, that the coating is thicker attroughs between pyramids than at the peaks.

The geometrical texturization of the surface also leads to acrease in the front surface area of the wafers. Electronic passiof the front surface is thereby of particular importance in ordeprevent recombination losses, so that the use of a passivatinging such as SiNx is more important. However, SiNx films becomemore absorbing as their refractive index is increased,21 which is aproblem when coatings are to be optimized for the wafers u

a

-

r

a-

s

t

n

t-

glass encapsulation where higher refractive indexes are requiraddition, surface recombination velocities have been shownorientation-dependent on p-type silicon.22 Although for n-type silicon ~and thus the emitter at the top side of the cell! such a relationship was not found, this may potentially cause problems forwith open rear metallization where rear-side passivation ofp-type bulk is required. Since particular crystallographic planeexposed by etching, it may be found that passivation is more etive on some crystal orientations than others, and certainly betthe two alkaline etch concentrations examined in this work.

Validity of Texture Etch Theory

Comparison of theory and experiment for monocrystawafers.—The results of texture etching showed that in additio$111% crystallographic planes the whole range of$XXY % planes lyingbetween~110! and ~111! orientations are also exposed by etchThis contrasts with what is expected from theory, whereby$111% planes are predicted to be stable to the etch. For the ortions investigated, the stability of this range of planes leads to lfacet tilt angles than expected, resulting in higher measured rtances in practice, particularly under encapsulation.

Development of etch texture as a function of etch depthorientation.—It is also observed that, with the exception of the~111!orientation itself, the discrepancy between the measured facangles and those calculated by theory increases for orientangled further away from the~100!. From Fig. 20 we see thatsimilar relationship holds for etch rates on the seven represenorientations. Large variations in etch rate are observed, withfastest etching orientations having the lowest angular sepafrom the ~100!. Since all the orientations were etched for the sduration~as is inherently the case for differently oriented crystaa texture-etched multicrystalline wafer!, it may thus be possible ththe exposure of non-$111% oriented facets is simply a consequenca lesser stage of development of the geometrical surface textuthe slow etching orientations. In order to investigate this hypoththe seven wafer orientations were etched to various etch depobserve the development of the texture etch facets as a functtime.

The resulting surface morphologies can be discussed asously in terms of the distance of the wafer orientation from

Figure 20. Total etch depths as a function of orientation for saw-damand texture etches~etch times used give an etch depth of 25mm on multi-crystalline silicon!.

y

2 for

preapr thees a

timeewend thts de

ilted

rnal

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ceteddl.

Journal of The Electrochemical Society, 151 ~6! G408-G427~2004!G424

~100!, whereby tilted pyramids closer to the~100! behave differentlto wafers with the$XXY % orientations~110!, ~221!, and~111! usedin experimentation. The results are summarized in Fig. 21 and 2the examples of the tilted pyramid structure formed on the~321!orientation and the~110! orientation, respectively.

In all cases, the shorter the etch duration, the greater the sin exposed facet angles, with ranges of$XXY % facets extending uto 10° or more from around the major etch facet orientation. Fo~tilted! pyramidal textures, an increase in the etch duration sestrong tendency of the etch facets towards the$111% orientationspredicted by theory. Etch facets become less rounded withwith increasingly sharp edges bounding the pyramid faces. Fflat untextured regions are present between texture features, aetch structures become larger. Most importantly, as these facevelop with time their tilt angles increase. Consequentially, tpyramid structures on those orientations furthest from the~100! nowhave facet angles which may satisfy the conditions for total intereflectance~i.e., greater than 20.9°!. For the ~321! orientation, forexample, the tendency of the facets towards the$111% facet withtime sees more facets allowing for light confinement at the glasinterface, whereby its reflectance value under encapsulatiocreases from 15.9 to 12.3% atl 5 630 nm.

However, for orientations close to the~110!, the etch facets exposed continue to tend towards$XXY % orientations, as opposedthe $111% orientations exclusively. Rather than etch facets becosteeper, the surface morphology becomes flatter with etch deptthe wafers investigated, it is observed that while$111% facets areindeed exposed on the~111! orientation, the~221! and the~110! bothalso etch down to their base orientation yielding flat surfaces. Tof particular importance for the measured reflectances, whichconsequence are equivalent to polished silicon, both bare andencapsulation. It also demonstrates a paradox in the etching prwhile increasing the etch depth leads to higher facet angleslower reflectances for~tilted! pyramid textures, it also results in tincreased flatness and higher reflectances of textures on orienfurthest removed from the~100!.

d

,re-

-

r

rs;

s

Stability of the (110) orientation.—The stability of the$XXY %orientations are particularly significant for the reflectance leachieved for the~110! orientation. Theoretically, this orientatiwould yield two-dimensional V-shaped grooves consisting of insecting$111% facets angled at 35° to the base orientation. Althoin air, only a minimum of multiple incidence would be achievafor this theoretical etch structure at the base of the groovesreflection levels achievable under encapsulation would be aequal to that of an upright pyramid texture. Although a grootexture is achieved for the shorter etch time shown in Fig. 22, itfacet tilt angles are too low for multiple-bounce reflectance, eithair or under encapsulation. Shorter etch durations barely remoinitial sawing damage, and prolonged etching causes the surfpolish down flat to the stable~110! base orientation rather than teing towards the expected$111% facets, so that the majority of lightreflected normally to the surface.

Figure 23 translates this to the situation for orientations inprincipal triangle of orientations. According to theory, a perfectture etch, yielding etch surfaces bounded exclusively by$111% fac-ets, would give encapsulated reflectances equivalent to uprightmids on the majority of test orientations except those closest t~111! itself. However in practice, the stability of the~110! orienta-tion means that the conditions under which~tilted! pyramids develop ~i.e., at longer etch duration! lead to the polishing of the~110!orientation. This leads to the particularly large discrepanciestween the measured and theoretical values for the~110! orientationthat were shown in Table III. As a result the actual reflectance oencapsulated multicrystalline wafer will be less than predicted

Comparison of experiment and theory for multicrystalwafers.—The theoretical and experimentally measured reflectaof texture-etched multicrystalline wafers are compared in Figand 25, respectively, for wafers in air and under encapsulationexperimental values are the average for eighteen wafers, etchthe longest duration whereby facets on tilted pyramid structuresmost strongly to the$111%. The theoretical reflectances are calcula

Figure 21. ~i! SEM photographs and~ii !laser scatter patterns showing the etexture development on the~321! orien-tation, for ~a! 5 and~b! 25 min etch durations. Tilted pyramid etch facets tetowards the$111% with etch depth. (d)5 theoretical facet position. Laser sc

ter patterns are compared here insteaAFM facet transforms because themin etch leads to surface roughnestoo great for the AFM~i.e., .9 mm withthe special AFM scanner, see the secon wafers under encapsulation and Fiand 7!. For this reason, the axes ofpolar plot are multiplied by 2u ratherthanu as for the facet transforms, sinthe facet positions are now represenby an angle of reflection 2u as opposeto the tilt angleu of the surface norma

Sun-

measur

htafersal

-allineof the

andriesred o

ofre-eomafertry olting

dthehe

thh.n.ip-

tchedes areions.

inngles

Journal of The Electrochemical Society, 151 ~6! G408-G427~2004! G425

using the weighted average of the reflectances determined byrays, for the seven orientations used in experimentation.

For the wafers in air, the difference between theoretical andsured reflectances is relatively small, despite the differences inface morphology on$XXY %-oriented crystals, since only uprigpyramids, which are present both in theory and practice on wclosest to the~100!, allow multiple incidence of light. Theoreticreflectance values in air are indeed lower~24.7% atl 5 630 nm)due to the imperfections of the textures formed practically~for ex-ample, polished regions between texture, etc.!. However under encapsulation, the measured reflectances for the multicrystwafer are 5.4% higher than expected theoretically, as a resulthigh reflectance of the stable, flat etching crystals near the~110!orientation.

Conclusions

The surface morphologies of multicrystalline alkaline texturesaw-damage etch textures have been quantified using a seanalysis techniques, using the weighted average of data acquiseven orientations spread over the principal triangle~100!:~111!:~111! orientations. Hereby it was possible to relateflectance properties in air and under encapsulation to the etch getries obtained on a per orientation basis. By using uncoated wthe reflectance reduction observed is purely due to the geomethe wafer surface morphology formed by the etch and the resu

Figure 22. ~i! SEM photographs an~ii ! laser scatter patterns showingetch texture development on t~110! orientation, for~a! 5 and~b! 25min etch durations. The~110! orien-tation is polished by the etch witime showing its stability to the etc(d) 5 theoretical facet positioSee caption of Fig. 21 for a descrtion of the laser patterns.

--

ofn

-sf

Figure 23. Sketch indicating the encapsulated reflectances of texture-ewafers according to theoretical calculations with Sunrays. Reflectancgiven as a function of orientation, using the principal triangle of orientatIn region ~c!, the majority of light experiences multiple incidence, whileregion~a! reflectance are equivalent to polished silicon since facet tilt aare less than 20.9°.

llent

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Journal of The Electrochemical Society, 151 ~6! G408-G427~2004!G426

multiple bounce incidence of light, as is responsible for the exceoptical properties of pyramidally textured~100! monocrystallinesilicon.

The level of reflection reduction is strongly dependent uponetch composition and conditions, combined with the orientationthe crystals in the wafer. The surface morphologies of thedamage etched wafers are generally relatively flat, in terms ofoptical reflective properties in air. The majority of exposed

Figure 24. Measured reflectances of texture-etched multicrystalline win air, compared to weighted averages~WA! based on the seven orientatioas measured experimentally and as modeled theoretically using the Sray-tracing program.

Figure 25. Measured reflectance of texture-etched multicrystalline wunder encapsulation, compared to weighted averages~WA! based on thseven orientations as measured experimentally and as modeled theorusing the Sunrays ray-tracing program.

facets have normal surfaces with tilt angles of less than 30°i.e.,lower than is required for even minimal double-bounce incidenlight. This results in reflectances comparable to polished silicoair. This flatness arises due to the large number of crystallogrplanes which are stable to the etch, these being predominan$100%, $111%, $110%, $311%, and$211% sets of planes.

For the low concentration texture etch, a larger variation inface roughness arises, depending upon the angular proximityconstituent crystal orientations to that of the~100!. Near~100! ori-entations have low reflectances in air due to the~tilted! pyramidtextures with facet tilt angles up to 55° which enable double-boreflectance. Further away from the~100! toward the~XXY ! orienta-tions such as~111! and ~110! ~where X and Y are integers!, theincreasing flatness of the texture yields still higher reflectancesparable to polished silicon. As a result, reflectances of indivcrystals differ by up to 20% within a given texture-etched murystalline wafer in air.

The reflectances of neighboring saw-damage and texture-emulticrystalline wafers, etched to the same etch depth of 25mm intotal by weight, are respectively 17 and 14% higher than for pmidally textured~100! monocrystalline wafers in air. In the casethe saw-damage etched wafers, this is because the majority ofon all orientations are too low to allow more than minimal multbounce incidences of light. For the texture-etched wafers, thedom distribution of crystal orientations in multicrystalline silicmeans that the weighting of~tilted! pyramid structures on near~100!is too low compared to flat etching orientations to reduce the levreflection more significantly. In the light of such a comparison inone may be inclined to reject geometrical texturization by thesemethods as being ineffective for multicrystalline silicon.

However, the situation improves dramatically under encaption, with saw-damaged and texture-etched multicrystalline whaving reflectances only 7 and 5.5% higher than for the enclated upright pyramids on monocrystalline~100!. This is due to theffect of light confinement at the glass-air interface, wherebyreflected away initially at facets can be totally internally refleand thus redirected towards the silicon for a second chance opling into the silicon. All etch facets with angles above 20.9° sathe condition for total internal reflection, so that this methodmultiple bounce incidence is far more effective for the alkaletched multicrystalline silicon than that required between sifacets in air. Thus while for the saw-damaged etch, for exampleetch surface is practically devoid of facets with tilt angles allowfor multiple bounce incidence, many of these facets have aabove 20.9° whereby reflection reduction is achievable onmajority of crystal orientations. Similarly for the texture etch, alarger range of crystals further away from the~100! with tilted pyra-mid textures now experience multiple bounce incidence of lthus yielding low reflectances equal to those on the~100!. Howeverthe random orientation of the crystals in the multicrystalline wamean that overall reflectances for both saw-damage and teetches remain higher than for pyramidally textured monocrystasilicon ~100!, since the total reflectance is overweighted by theticularly flat etching and high reflecting orientations, these bein~100! and ~111! for the saw-damage etch, and the$XXY % orienta-tions between the~110! and ~111! for the texture etch.

Despite the reflection reduction achieved due to light conment on encapsulation, the level of reflectance measured fotexture-etched wafers was far higher than expected by theorytheory dictates that alkaline texture etching exposes exclus$111% facets, whereby~tilted! pyramids form on~near! $100% orien-tations, with textures tending to two-dimensional V-shaped groon $110%, and ~near! $111% orientations etching flat to their baorientation. Experimentation showed that the$111% facets were indeed particularly stable to etching, so that~tilted! pyramidal textureformed on~near! $100% oriented crystals. However it was determinthat in addition to the$111% crystallographic planes, the whole ranof $XXY % planes is also exposed for the etch duration used.

s

ly

par-

itselfmay

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Journal of The Electrochemical Society, 151 ~6! G408-G427~2004! G427

results in lower facet tilt angles than expected from theory, inticular for the orientations close to the$110%.

However, the speed of development of the texture was inorientation dependent. Thus while a particular etch durationlead to microscopically flat$111% etch facets on the~100! orienta-tion, for example, a longer etch duration may be required for thedevelopment of tilted pyramid structures, for example. This wimply that rounded or split facets, or an untextured backgrounobserved by microscopy of the etch surfaces are simply a signearlier stage of development of the etch structure on a slowering orientation. A longer etch duration allows a more completevelopment of the$111% facets on tilted pyramid textures. Howevetching for a longer period paradoxically leads to increasinglypolished surfaces for the~XXY ! orientations, which are detrimento reflection reduction. This is particularly important for the$110%orientations, which according to texture etch theory should yieldencapsulated reflectances comparable to pyramids on silicon~100!by virtue of V grooves at 35° to the base, but instead etches flaprolonged etching. As a result, a far larger proportion of crystathe encapsulated multicrystalline wafer reflects light away atnormal angles to the wafer surface, whereby light confinemeless effective than predicted theoretically. The theory of$111% exclu-sivity in texture etching is thus proven to be invalid in this cas

Energy Research Centre of the Netherlands, assisted in meeting thlication costs of this article.

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