Journal of Crystal Growth 352 (2012) 53–58

Contents lists available at SciVerse ScienceDirect

Journal of Crystal Growth

0022-02

doi:10.1

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Laborat

USA. Te

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journal homepage: www.elsevier.com/locate/jcrysgro

The influence of core geometry on the crystallography of silicon optical fiber

Stephanie Morris a, Colin McMillen a, Thomas Hawkins a, Paul Foy a, Roger Stolen a,John Ballato a,n, Robert Rice b

a The Center for Optical Materials Science and Engineering Technologies (COMSET) and the School of Materials Science and Engineering, Clemson University,

Clemson, SC 29634, USAb Dreamcatchers Consulting, Simi Valley, CA 93065, USA

a r t i c l e i n f o

Available online 16 December 2011

Keywords:

A1: X-ray diffraction

A2: Growth from melt

B2: Semiconducting silicon

B3: Optical fiber devices

48/$ - see front matter & 2011 Elsevier B.V. A

016/j.jcrysgro.2011.12.009

espondence to: 91 Technology Drive, Ad

ory, Clemson University Advanced Materials

l.: þ1 864 656 1035; fax: þ1 864 656 1099.

ail address: jballat@clemson.edu (J. Ballato).

a b s t r a c t

Crystalline semiconductor core optical fibers have received growing attention as greater understanding

of the underlying materials science, coupled with advances in fiber processing and fabrication, have

expanded the quality and portfolio of available materials. In a continued effort to better understand the

nature of the crystal formation this work studies the role of the cross-sectional geometry on the

resultant core crystallography with respect to the fiber axis. More specifically, a molten-core approach

was used to fabricate silicon optical fibers clad in silica tubes of either circular or square inner cross-

sections. In both geometric cases, the silicon core was found to possess regions of single crystallinity

where specific crystal orientations persisted along a fiber length of about 4–5 mm prior to transitioning

through polycrystalline regions. However, the rotation and tilting angular combination needed to align

a given crystallographic axis with the fiber axis was more constant over the single crystalline region in

the case of the square-core fiber while more significant variations were observed in the round-core

case. This work begins to elucidate some of the microstructural features, not present in conventional

glass optical fibers, that could be important for future low-loss single crystalline semiconductor optical

fibers.

& 2011 Elsevier B.V. All rights reserved.

1. Introduction

Optical fibers possessing crystalline semiconductor cores havebecome a topic of recent interest internationally. Though mostfocus to-date has been paid to silicon [1,2], germanium [3–5],indium antimonide [6], and, more recently, zinc selenide [7,8],fibers have been realized using a variety of fabrication methods.While much work remains to further optimize their performance,interest in such fibers abounds for their consideration in non-linear optical, biomedical, and defense, sensing, and securityapplications [9].

In addition to this potential for technological impact, thecrystalline semiconductor optical fibers offer fundamentalinsights into various aspects of materials science that conven-tional glass optical fibers do not, including, for example, solidifi-cation under highly non-equilibrium and confined conditions, theinterplay between thermodynamics and kinetics, and phaseequilibria to name just a few [10].

ll rights reserved.

vanced Materials Research

Center, Anderson, SC 29625,

This work focuses on the role that the geometry of the core canplay on the crystallinity and crystallography of crystalline semi-conductor core optical fibers. Glass (i.e., silica) optical fibersgenerally possess cores of circular cross-section which are naturalbyproducts of the various chemical vapor deposition processesused in their fabrication. Additionally, cores of circular cross-section facilitate low-loss splicing and connectorization and themodal properties of cylindrical waveguides have been well-established for many years [11]. While extensive modeling ofheat flow, stress and strain, and applied external electromagneticfields has been reported in the past for fiber cores of circularcross-section, relatively little work has been devoted to fibercores of rectangular symmetry. With the successful demonstra-tion of optical fibers having square silicon cores, interestingdevice applications in nonlinear optics, image relay, or integrationwith planar optoelectronic circuits may be enabled.

More specifically, silicon optical fibers are drawn using silicacladding tubes that possess either a (conventional) circular cross-section or square cross-section. The underlying question positedhere is whether or not the cross-sectional geometry of the coreinfluences the crystallographic orientation of the crystallineSi core (with respect to the fiber axis). The elemental profiles,crystallinity, and crystallography of said round and square-corefibers are evaluated and discussed. Hypercircles are employed as

S. Morris et al. / Journal of Crystal Growth 352 (2012) 53–5854

a convenient and simple approach to quantifying the degree towhich the square-core preform maintains its geometry duringsubsequent fiber fabrication. While it is found that the square-core fiber is more similar mathematically to a round fiber than apure square cross-section, the impact on crystallinity and crystal-lography is discernable.

2. Experimental section

2.1. Fiber fabrication

High purity silica cladding tubes (VitroCom, Inc., MountainLakes, NJ) with an outer diameter of 30 mm and inner diameterof either 3.270.2 mm (round-core) or 3.270.2 mm flat-to-flat(square-core) were employed in this work. Silicon rods that wereabout 3 mm in diameter and 40 mm in length were placed into thesilica cladding tubes and drawn into fiber at 1925 1C using a carbonresistance furnace purged with argon (Clemson University, Clem-son, SC). The target fiber diameter was 1 mm, yielding a core size ofabout 100 mm, and the draw speed was 1 m/min. This molten coreapproach yields a fluent melt that fills and accommodates thevolume and geometry of the core tube [12] hence the use of a roundsilicon rod inside the square-core preform is of little consequence.

2.2. Electron microscopy and compositional determination

Electron microscopy was performed using a Hitachi SU-6600scanning electron microscope (SEM). Images were obtained undervariable pressure at 20 kV and a working distance of approxi-mately 10 mm. Elemental analysis was conducted under highvacuum, in secondary electron (SE) mode, using energy dispersivex-ray (EDX) spectroscopy in order to determine the elementalcomposition across the core and core/clad interface. Prior to anymicroscopy, the samples were polished to a 0.5 micrometer finish.

2.3. Crystallographic orientation measurement and analysis

The crystallography of the silicon core in the as-drawn fiberswas measured and analyzed in an equivalent manner to thatreported previously on germanium core optical fibers [13]. Briefly,samples of approximately 2 cm in length were affixed to agoniometer and first aligned vertically (within 21 of the long-itudinal axis) in the x-ray beam. A Rigaku AFC8S diffractometerequipped with MoKa radiation and a Mercury CCD area detectorwas used. The x-ray beam was collimated to a diameter of0.5 mm. Upon centering, images were collected and a preliminarycubic unit cell was determined [14]. The crystallinity of the siliconcore was determined using axial photographs with the fiber in itsvertical orientation and, subsequently, in specific crystallographicorientations: [1 0 0], [0 1 0], [0 0 1], [1 1 0], [1 0 1], [0 1 1], [1 1 1],and [2 1 0]. The process of centering, screening, cell determina-tion and axial orientation was repeated in 1 mm steps along thelength of both the round- and square-core optical fiber.

Tilt (w) and rotation (f) angles relative to the original verticalfiber orientation required to match the above crystallographicorientations were recorded for each position along the length[13]. In order to ensure consistency in the determination ofcrystallographic orientation, only the angular combination withthe lowest positive w angle for each direction was determined ateach consecutive position along the fiber.

2.4. Optical attenuation measurements

Transmission measurements were made at 1.3 mm in a man-ner equivalent to that described in Ref. 2. The output beam was

imaged under 20�magnification using an optical microscope andviewed with an IR viewer (Find-R-Scope 84499(A)-5) to ensurethat the measured light was propagating in the core.

3. Results and discussion

Fig. 1 provides electron micrographs of the as-drawn round-(Fig. 1a) and square-core (Fig. 1c) silicon optical fibers. Clearly,some rounding of the edges has occurred during the drawing ofthe square-core optical fiber.

Since the focus of this work is to determine if non-circularityof the core can enhance the single crystallinity of (cubic) crystal-line core optical fibers, then a means is needed to quantify thedegree to which the core is round or square. For this purpose,Lame curves (also known as hypercircles) are employed; see theAppendix A for more detail. Based on the measured dimensionsusing the electron microscope, the hypercurve exponent, n, wasfound to be 3 for the square-core optical fiber. While this value ismathematically closer to a circle (n¼2) than to a true square(n¼N), the core shown in Fig. 1d is more reminiscent of a square-than the round-core optical fiber of Fig. 1b; see the Appendix A formore of a comparison of this feature.

It is worth noting that fibers could be fabricated that wouldincrease the hypercurve exponent (i.e., possess a more square-core), which could be beneficial both from the perspective ofsingle-crystallinity and from the perspective of modal behavior. Inthe latter case, square-cores are somewhat analogous to round-cores in that they possess two degenerate orthogonal modes withno cut-off for the lowest order mode [15]. However, as thedimensions deviate into either rectilinear or elliptical geometries,the modal properties can be quite different [16,17] and poten-tially advantageous in these fibers where strong nonlinearities areexpected. To the best of our knowledge, no one has studied indetail the modal behavior of a fiber as a function of such ageometric continuum; i.e., mode curves as a function of hyper-circle parameter, nor in such strongly guided fibers.

The round-core silicon fiber exhibited local single-crystallinity(at individual 1 mm positions) over about 70% of the lengthexamined whereas this was closer to 90% in the case of thesquare-core fiber (see Fig. 2). In both cases, the longest singlecrystalline length was found to be between 4–5 mm. The longestsingle crystal length in the square-core fiber (relative positions3–7 mm) extended to the end of the fiber accessible for analysisso it is unclear exactly how long this grain was in its entirety. Theresults from the round-core fiber are consistent with thosemeasured (not reported) on previous silica-clad crystalline siliconcore optical fibers indicating that a more square cross-sectionpromotes higher single-crystallinity.

The change in orientation between the two primary crystalgrains observed in the square-core fiber appears to occur over adistinct grain boundary between the grains (at a relative positionbetween 2–3 mm). Alternatively, in the round-core fiber thereexists a longer region of polycrystallinity between 0–3 mmrelative positions where many polycrystals coexist. A distinctgrain boundary between two crystal grains also is observedbetween relative positions 7–8 mm in the round-core fiber.

There is also an observed misorientation in the longest singlecrystal grains of both fibers studied where the orientationgradually changes in small increments along the fibers’ lengths.For the square-core fiber the maximum tilting misorientation was1.21, observed for the [0 0 1] and [1 1 1] directions, and themaximum rotational misorientation was 5.31, observed for the[2 1 0] orientation. Average misorientation values for all direc-tions were 0.91 in tilt angle and 2.81 in rotational angle. In thelongest single crystal grain of the round-core fiber more extensive

Fig. 1. Electron micrographs of round-core silicon optical fiber (a) with core region further magnified (b) and square-core silicon optical fiber (c) with core region further

magnified (d).

S. Morris et al. / Journal of Crystal Growth 352 (2012) 53–58 55

misorientation was observed. A maximum tilting misorientationof 5.61 (for [0 0 1]) and a maximum rotational misorientation of7.31 (for [0 1 0]) were observed. Average tilting and rotationalmisorientation values for all directions were 2.91 and 3.81,respectively. Thus not only does the square-core fiber exhibitmore single crystalline behavior on the local scale than the round-core fiber, its longest single-crystal grain also shows less variationin its orientation over the fiber’s length than a grain of compar-able length in the round-core fiber.

As also was observed for a crystalline germanium (round) coreoptical fiber [13], at no point in either the square or the round-core silicon fiber did a specific crystallographic direction corre-spond to the longitudinal direction of the fiber. Some combinationof tilting and rotation was always required to move the crystal-lographic direction of interest into the reference (longitudinal)position. For the round-core germanium and silicon as well as thesquare-core silicon the closest orientations of interest were mostoften offset from the longitudinal direction by a tilting angle of5–151 (though sometimes up to 351, as in the round-core fiberlength shown in Fig. 2b). Fig. 3 summarizes, as a percentage of thefiber, which families of crystallographic directions were closest intilting orientation to the longitudinal dimension of the fiber.While the sampling size is admittedly small for this preliminarystudy of the square-core fiber, the initial results could suggest aninteresting feature of this core geometry.

For the round-core silicon fiber (about 60 mm analyzed in1 mm increments) 30% was found to be polycrystalline, whereas35% was a member of the /1 1 0S family of directions closest tothe longitudinal direction of the fiber, 20% had the /1 0 0S familyclosest to the fiber axis, and 15% favored the /2 1 0S family ofplanes. This distribution differs only somewhat from what weobserved in round-core germanium fiber. Alternatively, thesquare-core Si fiber exhibited just about 10% polycrystallinitywith the remaining 90% having the /1 1 0S family of directionsclosest to the longitudinal direction of the fiber. This strikingpreference for the /1 1 0S orientations occurring closest to thelongitudinal direction is a significant departure from what isobserved in round silicon and germanium fibers, though we

emphasize that further studies should be performed to examinethese initial results in a broader context. For completeness it isworth noting that the core sizes, i.e., solidification cross-sections,were quite different in the case of the round-core silicon treatedhere and the round-core germanium fiber treated previously [13].However, as noted above, the distribution of crystallographicorientations most closely aligned with the fiber axis was reason-ably similar.

The total attenuation, measured at 1.3 mm, was 7.4 dB/cm forthe square core fiber and 7.8 dB/cm for the round core fiber aftersubtracting Fresnel reflections. While difficult to ascribe thesenominal attenuation differences to the core geometry or resultantreduction in polycrystallinity, they are consistent with publishedlosses in silicon optical fibers [18,19], at a similar wavelength.

It is worth noting that the fibers treated here do still possesspolycrystallinity, albeit reduced in the square core case withrespect to the conventional round core optical fibers. It is knownthat grain boundaries, inevitably present in polycrystalline mate-rials, induce gap-states that contribute significantly to attenua-tion [20]. Interestingly, Ref. 20 also teaches that amorphoussemiconductors possess even higher losses than polycrystallineanalogs suggesting that such fibers are not the best route to lowloss semiconductor core optical fibers.

Sub-bandgap radiation also is attenuated by free carrierabsorption, which depends quadratically on wavelength anddirectly on carrier concentration and other semiconductor para-meters [21,22]. In addition to intrinsic band-to-band absorption,which requires photons more energetic than the bandgap, non-linear two-photon absorption, which requires photons with morethan half the bandgap energy, directly promotes carriers to theconduction band where they produce even further attenuationthrough free carrier absorption. There are various strategies formitigating free carrier absorption which include operating thefibers at reduced or cryogenic temperatures and doping for semi-insulating conditions. Free carrier absorption has even beensuppress by an applied bias to sweep free carriers from the centerof the beam in a silicon rib waveguide [23], though complexelectrode structures might be difficult to implement in fibers.

Fig. 2. (a) Representative drawing defining the tilt angle, w, and the rotation angle, f, necessary to orient a given (hkl) crystallographic plane for obtaining the axial

photographs (reproduced with permission from Reference [13]). Tilt angle required to align the given crystallographic orientation with the fiber axis: round (b) and square

(c) core. Rotational angle required to align the given crystallographic orientation with the fiber axis: round (d) and square (e) core. Yellow boxes denote regions of

polycrystallinity where a single orientation could not be uniquely determined. Black lines connecting equivalent crystallographic orientations across regions of

polycrystallinity are intended only as a guide to the eye. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this

article.)

S. Morris et al. / Journal of Crystal Growth 352 (2012) 53–5856

Fig. 3. A comparison of the percentage occurrence of crystallographic axes closest

in orientation to the fiber longitudinal axis for a crystalline germanium core

optical fiber [4] and the round and square crystalline silicon core optical fibers

treated in this work.

Fig. 4. (a) Schematic representations of selected hypercurves: n¼2 (ideal circle), n¼3 (s

square-core fiber was drawn), and n¼100 (an approximation to an idealized square, n

square-core fiber was drawn with overlay of n¼10 hypercircle. (c) Electron micrograp

(d) Electron micrograph of square-core silicon optical fiber with overlay of n¼3 hyper

S. Morris et al. / Journal of Crystal Growth 352 (2012) 53–58 57

It is not the intent of this work to assert that core geometry is thesingular solution to enhanced crystallinity and, therefore, reduce theloss in these crystalline core optical fibers. Recent work [24] hasshown that annealing of silicon fibers also can greatly enhancesingle crystallinity. Accordingly, the continued optimization of thesefibers will almost certainly rely on multiple factors that include, butare likely not limited to the influences of core geometry, annealing,and controlled doping. However, polycrystallinity and defects willalmost certainly be reduced. Ultimately, though, the application willdetermine the requisite level of acceptable attenuation, which couldrequire single crystallinity over centimeter length-scales (e.g.,Raman amplifiers) or some polycrystallinity over meter length-scales (e.g., IR power transmission).

The results presented here suggest strongly that fiber cross-section can facilitate greater single crystallinity in these crystal-line core semiconductors. For the future, analogous studies overlonger lengths and with higher n values (hypercircle exponents;see Appendix A) are planned. Additionally, core geometry design,coupled with post-annealing [24] or tailored time, temperatureprofiles/gradients, akin to zone-refining [25] but potentiallyperformed in-situ during the fiber draw, may prove to be valuabletools to the continued evolution of crystalline semiconductor

quare-core fiber treated in this work), n¼10 (square-core preform from which the

¼N. (b) Optical micrograph of initial square-core silica preform from which the

h of round-core silicon optical fiber with overlay of n¼2 (ideal circle) hypercircle.

circle.

S. Morris et al. / Journal of Crystal Growth 352 (2012) 53–5858

fibers into practical photonic and optoelectronic devices andapplications.

4. Conclusion

Silica-clad, crystalline silicon optical fibers with a core ofeither round or square cross-section were fabricated and theinfluence of this geometric factor on the resultant crystallographywas investigated. Fibers of both cross-sections exhibited regionsof single crystallinity where the orientation of a given (silicon)crystallographic plane persisted along the length of the fiber.However, it was found that the square-core fibers maintainedmore precisely the specific angle that a given crystallographicorientation makes with respect to the fiber axis. The results notedhere suggest that, unlike all-glass analogs, greater control of thefiber geometry may significantly impact the properties of crystal-line core optical fibers.

Acknowledgments

The authors also wish to acknowledge financial support fromClemson University, the Northrop Grumman Corporation, and theRaytheon Company.

Appendix A. A refresher on hypercircles

Hyperellipses, or sometimes called superellipses or Lame curves[26,27] represent a general class of curves defined by the followingrelationship: xnþan

Uyn ¼ 1, where n is any positive real numberand a is a constant. ‘‘Hypercircles’’ occur when a¼1 and the x and y

intercepts are equal such that xnþyn¼1 or y¼ ð1�xnÞ

1=n. Wheny¼x, the radius vector makes a 451 angle with both axes such that2xn¼1 and x¼ y¼ ð1=2Þ1=n. At this 451 point, the radius vector, R

(a measured quantity, in this case measured using the SEM), haslength: R¼

ffiffiffi

2p

Ux, so R¼ffiffiffi

2p

Uð1=2Þ1=n, from which followslogðR=

ffiffiffi

2pÞ¼ ð1=nÞUlogð1=2Þ and n¼ logð2Þ=logð

ffiffiffi

2p

=RÞ. So a directmicroscopic (or micrographic) measure of the radius vector yieldsthe exponential factor that defines the hypercurve. Fig. 4 providesseveral representative hypercircles for given values of n, whichdepend only on the measured value of R, as well as overlays ofhypercircles that best fit the initial square-core silica glass preformand resultant round and square silicon core optical fiber.

As noted in the main body of the paper, the radius, R, for thesquare-core optical fiber was measured from the SEM micro-graphs. The resulting exponential term, n, was computed to beabout 3, which may seem is more like a circle (n¼2) than a square(n¼N). However, it bears noting that the initial square preformhad a n-value of 10, which very much looks like a square for allintents and purposes. Regardless, the x-ray crystallographyresults indicate that not much asymmetry is necessary to mark-edly improve the continuity of crystallographic orientation.

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