Demonstration of single crystal growth via solid-solid transformation of a glass

Many advanced technologies have relied on the availability of single crystals of appropriate material such as silicon for microelectronics or superalloys for turbine blades. Similarly, many promising materials could unleash their full potential if they were available in a single crystal form. However, the current methods are unsuitable for growing single crystals of these oftentimes incongruently melting, unstable or metastable materials. Here we demonstrate a strategy to overcome this hurdle by avoiding the gaseous or liquid phase, and directly converting glass into a single crystal. Specifically, Sb2S3 single crystals are grown in Sb-S-I glasses as an example of this approach. In this first unambiguous demonstration of an all-solid-state glass → crystal transformation, extraneous nucleation is avoided relative to crystal growth via spatially localized laser heating and inclusion of a suitable glass former in the composition. The ability to fabricate patterned single-crystal architecture on a glass surface is demonstrated, providing a new class of micro-structured substrate for low cost epitaxial growth, active planar devices, etc.

solid-state transformation of glass → single crystal, and very much resembles the traditional floating zone crystal growth from the melt 11 .
Although epitaxial conversion of solid amorphized surface film of semiconductors (such as from ion implantation) back to single crystal 12 , and growth within a polycrystalline solid through seeded conversion have been reported 13 , there is no evidence in the literature showing all solid-state conversion of bulk solid glass to a single crystal. In contrast to these works, only the single crystal growth that occurs directly from solid glass offers the possibility of SCAG for crystal compositions that melt incongruently, decompose on heating to the melting temperature (T m ), or for which the desired crystalline phase is unstable at temperatures between T x and T m . Moreover, the underlying science and mechanism of the phase transformation from melt-to-crystal vis-à-vis directly from glass → crystal are fundamentally different.
So, how can a glass → single crystal transformation be achieved? The basic premise of fabricating a single crystal is simple: establish only one nucleus and then help it grow to the desired dimensions. It is implicit that for this to happen the experimental conditions should inhibit the formation of any other competing nuclei while the initially nucleated crystal grows. This is most readily accomplished by destabilizing nucleation in the vicinity of the growing crystal by maintaining the temperature slightly < T m , in the metastable Ostwald-Miers supercooled zone 1 . In this temperature range no nucleation occurs (see Fig. 1a), and an external seed crystal is utilized such as in Czochralski method 3 .
On the other hand, when one relies on spontaneous nucleation such as in the case of glass devitrification, multiple crystals grow simultaneously resulting in a polycrystalline ceramic. Since the temperature of nucleation onset (T n ) is always lower than T x 1,2 , unwanted nuclei are always likely to form and remain stable around the heated region 14 as shown schematically in Fig. 1. Notwithstanding, we have devised a strategy that allows us to grow a single crystal using direct crystallization of glass, which involves heating it from ambient to T x (see Fig. 1). Nucleation is a stochastic process so that its overall probability depends on the volume of the heated region and the time. Heating with a focused laser can limit the volume of glass so that only one nucleus is allowed to form, which is then grown quickly into a single crystal. We show that unwanted additional nucleation can be avoided by decreasing the volume of the heated region and growing the crystal by moving the laser beam at a sufficiently fast rate such that there is no time for forming extraneous crystals.
To validate our strategy and demonstrate proof-of-concept, it is most appropriate to begin with a composition that is within the glass-forming region but not too far from the boundary where crystallization is unavoidable. If the glass is highly stable, the probability of nucleation, especially homogeneous nucleation, and hence controlled laser crystallization is too low to test the hypothesis in a reasonable time. On the other hand, if the composition crystallizes too easily, precise observation of the crystallization process, especially single-crystal formation would become difficult. Further, for experimental convenience the glass should be able to absorb readily available laser light in a sufficiently deep region of the sample. A laser that is strongly absorbed just in the very top surface layer (<1 μm) is not desirable, as the nucleation becomes relatively improbable and the crystal growth is not as well controlled. The bandgap of most chalcogenide glasses falls into the visible to near-infrared spectral region, so that light from red lasers is absorbed efficiently and no additional dopants are required in contrast to oxide glasses 9,15 . Changing the wavelength of the laser diode allows altering the corresponding absorption cross-section conveniently, which would facilitate modification of the temperature profile within the sample, providing a useful tool for optimizing crystal nucleation/growth dynamics.
For all the above-mentioned reasons, we selected Sb 2 S 3 composition as a test example. This simple binary composition belongs to technologically important A 2 B 3 type chalcogenides (A = As, Sb, Bi; B = S, Se, Te), which have been investigated due to their attractive physical and chemical properties [16][17][18][19] . Consequently, their basic physical, thermodynamic and chemical properties have been determined and are readily available in the literature. Among possible choices, antimony trisulfide (Sb 2 S 3 ) is particularly attractive because of its interesting ferroelectric properties 20 and potential practical applications in solar cells, microwave devices, switching sensors, thermoelectric and optoelectronic devices [21][22][23][24][25] . To exemplify the impact of the proposed new strategy of single crystal fabrication, we note that this material burns in air at ~300 °C, and loses sulfur preferentially upon heating to high temperature in an inert atmosphere [26][27][28] . Therefore, it is practically impossible to obtain its stoichiometric single crystal by starting from melt using conventional methods.

1-D single crystal fabrication.
The success of the space selective laser-induced heating for transforming glass into single crystal is evident from the results shown in Fig. 2, using the example of Sb 2 S 3 glass. We employed a diode laser with wavelength (λ ) of 639 nm, which is focused to a few μm on the surface, and its intensity is gradually increased from 0 to 50 μW/μm 2 in 5 s and then maintained at this value. The first sign of a crystal is observed 2 s thereafter. Within 20 s it reaches the equilibrium dimensions as seen in Fig. 2. The uniform color of inverse pole figure (IPF) maps obtained from electron backscatter diffraction (EBSD) analysis confirms that the Sb 2 S 3 glass transformed into a single crystal dot by laser heating (see Supplementary video SV1 for the details).
As the laser beam is subsequently moved laterally across the surface at a rate of 1 μm/s, the growth of the initial dot follows the laser, forming a single crystal line of Sb 2 S 3 as seen in Fig. 2. The orientation IPF maps for both the dot and line exhibit the same color, which confirms that the whole structure is a single crystal of Sb 2 S 3 (Fig. 2c,d).
In order to extend our approach to other materials systems, we further suppressed unwanted nucleation by adding a glass-forming component. This additional strategy can have broad applicability through appropriate choice of glass composition. For its validation, we repeated the above experiments on homogeneous 16SbI 3 -84Sb 2 S 3 glass A laser-induced dot created on the surface of Sb 2 S 3 glass by slowly ramping the laser power density from 0 to 50 μW/μm 2 in 5 s, followed by steady exposure for 60 s, and its extension into a straight line by moving the laser spot at the speed of 1 μm/s. Scale bar corresponds to 5 μm. (a) SEM image, (b) colored IQ map, and orientation IPF maps with reference vector along surface normal (c) and along in-plane direction (d), respectively. EBSD mapping is collected using 70 o -inclined geometry, which in the case of rough sample surface results in a "shadow" region inaccessible to the probe electron beam. The white-colored regions on IPF maps inside of the dot correspond to such "shadow" regions.
wherein the addition of 16% SbI 3 makes glass formation easier and nucleation more difficult relative to Sb 2 S 3 29 . Nevertheless,when heated with a laser beam only Sb 2 S 3 crystalline phase precipitates out either through the evaporation of SbI 3 in the heated zone or enrichment of the region around the growing crystal with iodine and antimony. In either case, nucleation in front of the growing crystal is suppressed relative to crystal growth. Figure 3a shows typical morphology of the initial dot (D1), which was induced by laser beam above a minimum threshold intensity of 65 μW/μm 2 . The energy dispersive spectroscopy (EDS) analysis maps (Fig. 3e) for this region show deficiency of iodine, which indicates SbI 3 evaporation under sustained heating by the laser beam. This change in composition increases the concentration of Sb 2 S 3 and stimulates the formation of its crystal in shallow crater.
To assess the tendency of nucleation relative to the growth of Sb 2 S 3 crystal in 16SbI 3 -84Sb 2 S 3 glass, the laser was turned off after forming the single crystal line L1. It took less than 1 s to form a new dot next to the previously formed line L1, compared to ~43 s needed to form the initial dot D1. Therefore, the crystal line can be grown indefinitely using the previously created crystal as a seed.

2-D single crystal fabrication.
Having demonstrated the feasibility of solid glass → single crystal transformation and the ability to fabricate single crystal lines by eliminating extraneous nucleation, we turned our attention to the realization of 2D crystals, further enhancing the usefulness of solid state crystal growth as a SCAG. Based on Fig. 4, which shows a 2D crystal of Sb 2 S 3 grown on the surface of 16SbI 3 -84Sb 2 S 3 glass, it is indeed possible to 'stitch' successive lines together to form a 2D crystal. In this approach 30 , the laser is moved from the initial dot D1 in X-direction at 20 μm/s, and the first Sb 2 S 3 single crystal, L1, grows without introducing additional nuclei. To obtain the second line, the end of first line is used as the seed. Laser exposure for the second and subsequent dots (D2-D7) was reduced to 15 s compared to 60 s for D1. Then the second line was written anti-parallel to and overlapping the first line. The subsequent laser-written crystal lines were written similarly, overlapping with the previous line by slightly more than half the width of the previous line. The result is a 2D planar single-crystal structure made via solid-solid transformation, with c-axis orientation normal to the laser scanning direction for the whole area as shown by the EBSD maps in Fig. 4. Each crystal in these dots (D2-D7) and subsequent lines maintains the same orientation. The neighboring lines merge and form the 2D single crystal structure.
The reproducibility of the observations reported here is excellent as established from experiments on a few tens of dots and lines, and several 2D structures using optimal laser irradiation parameters (power, focus position relative to surface, scanning rate, etc.).

Discussion
Previous attempts of crystallization of amorphous Sb 2 S 3 films, which did not follow the strategy developed in the present work, produced only polycrystalline structures 31,32 . The authors of these investigations used argon laser with a spot size of 400 μm diameter, and no attempt was made to maintain the temperature below the melting temperature. Sb 2 S 3 does not form glass easily; it requires very rapid cooling of the melt to form bulk glass, as in this study, or vacuum deposition of its vapor phase to form thin amorphous films prepared by Arun et al. 31,32 . Therefore, in their work the probability of extraneous nucleation was too high to yield a single-crystal upon heating. This challenge of unwanted nucleation could be successfully overcome by decreasing significantly the heated volume with a finely focused laser beam, and addition of SbI 3 as a glass stabilizer. There are two independent key observations pertaining to the premise of this Report, which prove that the glass → single crystal transformation occurs here entirely in the solid state. First, scratches that were present on the glass surface before laser irradiation (seen in Fig. 2c,d, most clearly in the region of the line) persist through the crystallization process, indicating that the nucleation and growth processes occur without forming a melt that would have altered the surface morphology. Second, the in situ observation of the crystal growth process (see Supplementary video SV1) demonstrates that the crystallization occurs at the leading, not the trailing edge of the laser beam. The former region represents the region being heated from ambient to crystallization temperature, while the latter represents the region cooled to ambient from the crystallization temperature. This is a direct indication that the glass transforms into single crystal upon its heating, and not during the cooling of the melt that would have happened at the trailing edge of the laser spot 14 . Thus, these results provide the first unequivocal proof-of-principle that it is possible to transform a glass into single-crystal by heating to crystallization onset temperature (T X ), rather than by the usual crystal growth processes via cooling to the crystallization temperature from above the melting point (Fig. 1).
As for the lines fabricated in Sb 2 S 3 glass, the crystallization also occurs at the leading edge of the laser-heated region (see Supplementary video SV2), which confirms the growth of single-crystal Sb 2 S 3 line by the solid state transformation of 16SbI 3 -84Sb 2 S 3 glass during heating. The relatively small volume contraction of the line compared to the initial dot in Fig. 3 suggests that the crystal growth occurs by the redistribution of Sb, S and I atoms during growth rather than evaporation of SbI 3 . The same is also indicated by the depletion of S and enrichment of I just outside the line (arrows in Fig. 3e).
In conclusion, we have demonstrated that indeed it is feasible to fabricate SCAG via a completely solid-state transformation. As proof-of-principle, successful examples of 1D and 2D Sb 2 S 3 single-crystal structures are produced on the surface of xSbI 3 -(1 − x)Sb 2 S 3 glass by employing a strategy, which relies on eliminating extraneous nucleation relative to crystal growth via space localized laser heating below T m , and adding suitable glass former. The new method offers the opportunity to obtain single crystals that may decompose, melt incongruently or undergo phase transformation between the crystallization and melting temperature of the glass.

Methods
Glass preparation. The glasses were made following the ampule quenching method previously developed for the Sb-S-I system 33 . To make Sb 2 S 3 samples, which does not form glass easily, the melt cooling rate was increased by limiting quartz ampules to 1 mm inside diameter (ID) and 10 μm wall thickness. 16SbI 3 -84Sb 2 S 3 glass was prepared using ampules with 11 mm ID and wall thickness 1 mm. X-ray diffraction analysis of the as-quenched samples confirmed their amorphous state. For details of glass fabrication and its characterization, please see Supplementary Information, Figs S1-S3. The samples for laser-induced treatments were polished using metallographic techniques.
Laser-induced crystallization. The intensity of the fiber-coupled 639 nm diode laser (LP639-SF70, ThorLabs) used for crystallization, was modulated by an analog voltage (ILX Lightwave LDX-3545 Precision Current Source). The beam was focused onto the sample by a 50x, 0.75NA microscope objective. The sample was placed in a flowing nitrogen environment on a custom-built stage, which could be translated independently in the x-, y-, and z-directions. Flow of nitrogen eliminated oxidation of Sb 2 S 3 crystals, which was observed in air environment. A CCD camera monitored the sample in-situ, while LabView software controlled the laser intensity, and the movement of the stage. A detailed description of laser crystallization system is presented in Supplementary Information, Fig. S4. First, a seed dot D1 and line L1 were created on the surface of 16SbI 3 -84Sb 2 S 3 glass, as in Fig. 3. New seed dots (D2-D7) were formed from previous lines, and then used to grow new lines (L2-L7), correspondingly. To form dots D2-D7 the beam was shifted laterally in the y-direction by 3 μm and the exposure was reduced to 15 s. (a) Plan-view; SEM images (b) before and (c) after repolishing; and orientation IPF maps with reference vectors (d) along surface normal and (e) the in-plane direction, respectively. Scale bar corresponds to 10 μm.
Scientific RepoRts | 6:23324 | DOI: 10.1038/srep23324 Materials characterization. The laser-irradiated regions were analyzed by a scanning electron microscope (SEM, Hitachi 4300 SE) in water vapor environment to eliminate charging effects. The chemical compositions were determined at multiple locations on each sample by EDS detector attached to SEM, using the EDAX-Genesis software. Local crystallinity and orientation were determined by EBSD with Kikuchi patterns collected by a Hikari detector within the SEM column. EBSD pattern scans were collected and indexed using TSL OIM Data Collection software, whereas Orientation Imaging Microscopy Analysis software yielded image quality, pole figure and inverse pole figure maps 34 .