Laser recrystallization and inscription of compositional microstructures in crystalline SiGe-core fibres

Glass fibres with silicon cores have emerged as a versatile platform for all-optical processing, sensing and microscale optoelectronic devices. Using SiGe in the core extends the accessible wavelength range and potential optical functionality because the bandgap and optical properties can be tuned by changing the composition. However, silicon and germanium segregate unevenly during non-equilibrium solidification, presenting new fabrication challenges, and requiring detailed studies of the alloy crystallization dynamics in the fibre geometry. We report the fabrication of SiGe-core optical fibres, and the use of CO2 laser irradiation to heat the glass cladding and recrystallize the core, improving optical transmission. We observe the ramifications of the classic models of solidification at the microscale, and demonstrate suppression of constitutional undercooling at high solidification velocities. Tailoring the recrystallization conditions allows formation of long single crystals with uniform composition, as well as fabrication of compositional microstructures, such as gratings, within the fibre core.


Supplementary Figure 2
As-drawn fibre crystallinity. Representative electron backscattered diffraction pattern from an as-drawn 6 at% Ge fibre; the entire fibre cross section showed the same pattern (see Fig. 6 in the main text for a map of the orientation). Brightness and contrast were each increased by 40% over the original image. Emission profile at 514nm. Image of fibre melt zone using a 514 nm narrow band filter (a) and a greyscale value plot from the red line (b). A sharp decrease in greyscale value in seen at the solid-liquid interface due to a difference in emissivity of the two phases. Noise in the central region is due to emission from particles in the interface layer.

Supplementary Figure 9
Diffraction patterns integrated over a range of projection angles φ a) Pure Ge microwire, overlaid with the calculated powder diffraction rings for Ge. The Bragg peaks are sharp, with the radial width dominated by the instrumental resolution. b) Recrystallized SiGe (6 at% Ge) microwire, overlaid with the calculated powder diffraction rings for Si. In this case, the Bragg reflections in (b) are radially broadened, as expected for an inhomogeneous Si-Ge blend. The strong isotropic scattering at low q can be ascribed to the glass surrounding the semiconductor core. The Ge content of the melt is higher than the fibre average due to migration of Ge-rich material to the melt zone (as shown in Supplementary Video 3) and due to the preferential segregation of silicon into the solid phase, as indicated by the phase diagram. A concentration of approximately 9 at% Ge was estimated using the width over which Ge was gathered, giving a melting temperature of 1673K. By considering the ratio between the highest intensity value in the melt and the value at the interface (~1.3), assuming a constant emissivity in the melt and linear response in the detector, the temperature difference can be estimated using the Planck distribution: where is the emissivity, h the Planck constant, c the speed of light, the wavelength, T the temperature and k B the Boltzmann constant. Taking the intensity value in Supplementary Fig. 3 at the melting point B(514 nm, 1673 K) and solving for T at an intensity 1.3 times as great gives a maximum temperature of 1983 K.
Dividing by the distance from the interface to the maximum yields an upper bound of 1.4×10 4 K cm -1 for the temperature gradient .
The same procedure was performed using a 633 nm narrow band filter. A greyscale value ratio of ~1.24 is observed for the frame presented in Supplementary   Fig. 4. Solving for T max gives a thermal gradient of 1.5×10 4 K cm -1 , in reasonable agreement given the noise levels in the images.

Supplementary Note 2 Critical Velocity
The breakdown of a planar solid-liquid growth interface during unidirectional The slope of the liquidus can then be determined by differentiating equation (2).
Solving equation (2) and (3)  The problems in realising homogeneous growth of SiGe are typically ascribed to constitutional undercooling due to the large miscibility gap (see Fig. 1a, main text).
The severity of the constitutional undercooling depends on the composition of the melt, but also the growth velocity of the phase front, as a higher growth velocity will suppress solute diffusion into the liquid. The Tiller criterion for inhomogeneous growth during unidirectional solidification is still being used today to predict critical growth rates. However, Mullins and Sekerka 8 presented a model that also considers the effect of the difference in thermal conductivity between the phases, the temperature gradients in the phases, the latent heat released, the curvature effects on equilibrium concentration at the interface and capillarity (solid-liquid interface energy) and thus the lateral dimensions of the interface.
In their model, capillarity and high temperature gradients stabilize the phase front.
Thus, higher growth velocities can be used while still suppressing inhomogeneous growth in small dimensions and with large temperature gradients. Additionally, Yim and Dismukes 9 have pointed out that strong thermal gradients will enhance thermal diffusion and further stabilize the phase front.
Experiments were performed with fibre cores of ~130 µm and ~15 µm to see whether a difference in the critical velocity could be measured as a function of radius.
The compositional uniformity across the polished fibre cross-sections indicated whether the critical velocity had been exceeded. The Ge content in electron micrographs of polished cross-sections gives greyscale contrast in backscattered electron (BSE) imaging, and automated analysis of these images was performed using a MATLAB® script. Images were taken with identical microscope settings and were not processed prior to analysis. Polishing minimized topological contrast in the BSE signal, leaving only atomic number contrast. Edge detection was performed to determine the core/cladding interface, the radius, R, and the position of the core centre. Greyscale values were integrated in evenly spaced annuli of width R/100 and were normalized by the average greyscale value for the image to provide a quantitative metric of the fibre inhomogeneity, as seen in Supplementary Fig. 5a. A similar procedure with angular slices of size 2π/40 was performed to visualize the angular distribution, as seen in Supplementary Fig.5 b. The sum of least squares (SLS) for the radial and angular distributions gives a single-value indication of the homogeneity of a fiber, with a compositionally uniform fiber having a SLS of 0.
Plotting the resulting SLS for fibres recrystallized at different velocities, the critical value for the onset of inhomogeneous growth can be determined. Supplementary Fig.   5c presents the radial SLS, and Supplementary Fig. 5d shows the angular SLS for all tested growth velocities of the 6 at% Ge fibers with core diameters of 120 µm. There is a very distinct step between 200 and 1000 µm s -1 .
Manual investigation of SEM images of an untreated sample and a sample treated at 1000 µm s -1 reveals a very similar compositional distribution, as seen in Supplementary Fig. 6. This suggests that either the critical growth rate was reached and inhomogeneous growth occurs, or possibly, insufficient power was available for melting the cores at these high rates.

Experimental details
The text description of the experimental details is presented in the main manuscript and Supplementary Fig. 8 shows the geometry used.

X-ray diffraction analysis
The microwires were measured still encased in glass. X-ray diffraction patterns were collected i) as function of axial position along the microwire length for a chosen angle φ, and, ii) as a function of angle φ for rotations about the microwire long axis at selected axial positions.

Phase identification
The diffraction patterns acquired at selected axial positions with 1° steps in φ were summed to obtain rotationally integrated diffraction patterns, thus being similar to the classical so-called "rotating crystal method". The summed diffraction patterns were compared with the calculated powder diffraction rings of the well-known diamond cubic unit cells for Ge and Si. Examples of integrated diffraction patterns are shown in Supplementary Fig. 9 for a pure Ge microwire and for a recrystallized (100 µm s -1 scan rate) SiGe (6 at% Ge) microwire.
The diffraction patterns for the pure Ge microwire were, as expected, in agreement with the diamond cubic unit cell of Ge with a = 5.66 Å. The diffraction data for recrystallized SiGe exhibited radial broadening centred near the diamond cubic unit cell of Si having a = 5.43 Å.

Axial scans
With a beam spot size of 200 µm the spatial resolution was sufficient to observe single or polycrystalline regions along the length of the microwire. XRD measurements on the recrystallized SiGe microwire (100 µm s -1 scan rate) at different axial positions, obtained for the same sample orientation angle φ, are shown in Supplementary Fig. 10. Diffraction patterns obtained millimetres apart exhibit the same diffraction peaks, revealing longitudinal uniformity of the crystal structure and hence crystallographic coherence over several millimetres. Other samples did not exhibit this coherency, signifying that those samples were polycrystalline with crystalline domains smaller than the volume probed by the X-ray beam.

Rotation scans and 3D reciprocal space analysis
Having obtained diffraction data for a wide range of projection angles φ, threedimensional reconstructions of reciprocal space were calculated. The symmetries of different Bragg reflections were studied, as shown in Supplementary Fig. 11 for the {311} family of reflections, which has q = 3.84 Å -1 and a multiplicity of 24.
Supplementary Fig. 11a and 11b show the ideal reciprocal space structure and the acquired experimental data at approximately the same sample orientation. While the nucleating crystallite is likely to be randomly oriented, the XCT images also indicate that in some cases (cf. Fig. 3a in the main text), the fibre geometry guides and reorients the subsequent crystal growth.