Quasi-monocrystalline silicon for low-noise end mirrors in cryogenic gravitational-wave detectors

Mirrors made of silicon have been proposed for use in future cryogenic gravitational-wave detectors, which will be significantly more sensitive than current room-temperature detectors. These mirrors are planned to have diameters of $\approx 50$ cm and a mass of $\approx 200$ kg. While single-crystalline float-zone silicon meets the requirements of low optical absorption and low mechanical loss, the production of this type of material is restricted to sizes much smaller than required. Here we present studies of silicon produced by directional solidification. This material can be grown as quasi-monocrystalline ingots in sizes larger than currently required. We present measurements of a low room-temperature and cryogenic mechanical loss comparable with float-zone silicon. While the optical absorption of our test sample is significantly higher than required, the low mechanical loss motivates research into further absorption reduction in the future. While it is unclear if material pure enough for the transmissive detector input mirrors can be achieved, an absorption level suitable for the highly reflective coated end mirrors seems realistic. Together with the potential to produce samples much larger than $\approx 50$ cm, this material may be of great benefit for realizing silicon-based gravitational-wave detectors.

Figure 1

Photo of the sandblasted G2 1/4 ingot sized $195\times 195\times 220$ ${\mathrm{mm}}^3$. The drawing illustrates the position of the block in relation to the two seed plates (bottom plane). W-N-E-S are typically used markers to identify the position of the ingot to possible thermal asymmetries of the furnace, which might influence the growth process.

Figure 2

(left) Sample position marked on a photo of the {100} vertical cut of a G2 1/4 ingot. (right) Drawing of the final $ø50.8\times 5$-mm-thick disk (gray: QM disk) inside the bigger single crystalline cuboid, and the position of the smaller sample (small QM cuboid) for absorption measurements.

Figure 3

Image of the $\langle 100\rangle$-oriented QM disk balanced on top of a rounded silicon lens inside the $10\times 10$ ${\mathrm{cm}}^2$ experimental chamber of the Montana Instruments s100 Cryostation.

Figure 4

Total surface deformation of the resonance modes of the $\langle 100\rangle$-orientated QM disk, calculated using finite-element analysis. The blue corresponds to regions of least motion and the red to regions of greatest motion.

Figure 5

Mechanical loss as a function of temperature, from 4 to 300 K, of the 50.8-mm-diameter $\times$ 5-mm-thick QM disk (left) and FZ disk (right) samples.

Figure 6

(a) Optical absorption along the $\approx 40$-mm-long small QM cuboid for entering the sample at three different positions indicated by the different colors and line styles. The dotted vertical lines indicate the surface positions for the measurements shown by the green, dashed line (the position of the sample front surface slightly varied between measurements). (b) Optical absorption scans through the sample at two different positions after turning the sample back surface to the front. Panels (c) and (d) show the corresponding phase signals of those measurements. Outside the sample, the signal is meaningless: while the absorption signal becomes approximately zero, the phase shows large oscillations.

Figure 7

Typical light microscopic image of SiC inclusions near the surface in the range of 0–10 mm of the sample (top), while almost no superficial features can be seen on the rest of the sample (bottom).

Figure 8

FTIR measurement of [${\mathrm{C}}_{\mathrm{S}}$] in longitudinal direction with different apertures: red 3.5 mm and black curve 2 mm.

Figure 9

FTIR measurement of [${\mathrm{O}}_{\mathrm{i}}$] in longitudinal direction with different apertures: red 3.5 mm and black curve 2 mm.

Figure 10

Measurements of minority-carrier lifetime on the now thinned $\approx 40$-mm-small QM cuboid (used previously for absorption measurements). The low values at the marked edge (here position $-5$ on the vertical axis) correspond to the high-absorption end.