Investigating methods and materials which can more accurately model and reduce a gravitational wave detector's coating thermal noise

Gravitational waves were predicted by Einstein’s General Theory of Relativity which described gravity as arising from the curvature of space-time due to the presence of mass. Gravitational waves are caused by the acceleration of an asymmetrical mass distribution which perturbs space-time causing a ripple-like effect that travels at the speed of light. These ripples are known as gravitational waves. The first directly detected gravitational waves were observed on the 14th of September 2015. These waves were formed from the inspiral and merger of two black holes. Since that day, gravitational waves have been observed (from four more binary black hole systems and from a binary neutron star system). These detections have demonstrated the power and potential of gravitational wave astronomy as they have provided vast new information regarding the binary systems which produce them (e.g. the mass of black holes, that merging neutron stars are a source of short gamma-ray bursts etc). These detections were made using ground-based interferometric detectors in which a laser beam is split and passed along two perpendicular arms. At the end of these arms, the laser light is reflected back towards the beam splitter by test masses coated with a highly reflective mirror coating. At the beam splitter, the two laser beams recombine and the intensity of the signal is monitored. Differential changes in the arm-length result in changes to the interference pattern. Since gravitational waves are only expected to change a 1 km arm length detector by approximately 1 × 10−19 m, it is essential for all sources of noise to be exceedingly low. Coating thermal noise - arising from thermally induced motion in the interferometer mirror coatings - forms a major limit to sensitivity of current gravitational wave detectors at their most sensitive frequencies. The magnitude of this noise source is proportional to the detector’s operation temperature, laser beam radius and coating mechanical loss (also known as internal friction). The research presented in this thesis focuses upon improving the processes currently used to determine the coating thermal noise in a detector as well as identifying materials which can reduce coating thermal noise. Chapter 1 contains an introduction to the theory of gravitational waves, describes the sources used to produce them, the experimental methods used to detect them and summarises all of the signals already observed. Chapter 2 presents a detailed description of thermal noise and outlines how the thermal noise of a highly reflective coating in a gravitational wave detector has been historically calculated. Chapter 3 introduces the theory of a new and more accurate approach to determining the thermal noise of a gravitational wave detector coating by using the coating’s bulk and shear mechanical losses. Two methods to determine the bulk and shear losses of a coating are developed and applied to a range of coatings (ECR IBD amorphous silicon and RLVIP amorphous silicon) that were deposited upon silicon cantilevers. It was found that, the bulk and shear losses of a coating could be significantly different to each other. The ECR IBD amorphous silicon coating had a bulk loss of (3.4 ± 0.8) × 10−4 and shear loss of (1.4 ± 0.2) × 10−4. Whilst the room temperature deposited RLVIP amorphous silicon coating had a bulk loss of 0 ± 1 × 10−9 and a shear loss of (1.53 ± 0.09) × 10−4.This thesis is believed to present the first analysis which shows that the bulk and shear losses of a coating can indeed be significantly different from each other. Furthermore, the results also showed that it is possible for the loss of a coating to be purely shear loss. Since the thermal noise of a gravitational wave detector is less sensitive to shear loss than bulk loss, this result indicates the possibility of being able to further reduce coating thermal noise by using materials which are dominated by shear loss. Shear loss is explained in this chapter to have less effect than bulk loss upon the thermal noise of a gravitational wave detector, as a result of the shear motion of the coating changing the arm length of the detector much less than the coating’s bulk motion. Chapter 3 lastly investigated whether the same coating deposited upon two different substrate geometries can be determined to have the same bulk and shear losses. This was an interesting test as it would help to illustrate the robustness of the methods developed to determine bulk and shear loss. A tantala coating was deposited upon a cantilever and disc substrate. The coating’s bulk and shear losses were determined to be (1.90 ± 0.30) × 10−3 and (6.7 ± 0.5) × 10−4 upon the cantilever and (1.28 ± 0.22) × 10−3 and (7.8 ± 0.5) × 10−4 upon the disc. Whilst good qualitative agreement can be observed between the results (the bulk losses for the two geometries are greater than their shear loss), the different substrate’s bulk losses are significantly different from one another. It is expected that this could be due to limited experimental data. To determine the thermal noise of a coating in a gravitational wave detector, the mechanical loss of the coating must first be known. Typically, the coating’s mechanical loss is obtained using a combination of ring down experiments and mathematical equations. However, recent research and observations have called into question the accuracy of coating losses which have been determined using this approach when silicon cantilever substrates are used to deposit the coating on. It is speculated that the inaccuracy of these losses could be due to the effect of the coating causing the coated cantilever to curve and stress which in turn changes the silicon cantilever’s thermoelastic loss. Chapter 4 presents an investigation into the effect of stress and curvature upon a silicon cantilever’s thermoelastic loss. The results from finite element analysis (FEA) indicated that the thermoelastic loss of a silicon cantilever (which has been coated) is unaffected by stress but is affected by curvature. Experimental evidence appears to confirm these conclusions and further imply that either the FEA does not fully account for the effect of curvature upon thermoelastic loss or an unmodelled effect is also affecting a silicon cantilever’s thermoelastic loss. FEA was also used to investigate the effect of stress and curvature upon a silicon disc’s thermoelastic loss. A disc geometry was also investigated as discs along with cantilevers are the two most commonly used substrates in mechanical loss experiments due to their low substrate loss. It was observed that the magnitude of stress and curvature caused by depositing a coating onto a silicon disc in the lab had no effect upon the substrate’s thermoelastic loss. Some future gravitational wave detectors, such as the Einstein Telescope (ET), are being designed to operate at cryogenic temperatures. To achieve these detector’s thermal noise requirements, new mirror coatings with low mechanical loss and low absorption (to ensure the mirror coating remains cool) at cryogenic temperatures will have to be found. One possible material which could be potentially used in a highly reflective coating is silicon nitride. Silicon nitride has already been shown to have a low mechanical loss which decreases as its stress increases. However, its absorption is currently too high to meet the ET’s design requirements if it is to be used as one of two materials in a simple coating bilayer structure. Chapter 5 outlines an investigation into whether the absorption of a silicon nitride membrane can be reduced by changing its stress. Due to experimental limitations, the direct effect of stress upon absorption could not be quantified, instead the effect of stress upon the product of the membrane’s absorption and its thermo-refractive coefficient was determined. The product of the membrane’s absorption and its thermo-refractive index was found to be independent of stress. Whilst this result implies that absorption is independent of stress, this should be explicitly checked. It was also determined from this experiment that the thermal conductivity and thermal expansion of a Norcada fabricated low stress silicon nitride membrane is (23 ± 3) W/mK and (1.4 ± 0.2) × 10−6 1/K respectively. The Institute for Gravitational Research (IGR) has recently gained access to an operational coating chamber. The usual substrate geometries which coatings are deposited upon for mechanical loss experiments are not compatible with the coating chamber due to their size. In this chapter, the possibility of using a thin, low loss silicon nitride membrane as a substrate for this chamber is presented. If silicon nitride membranes can be successfully used as substrates it will enable full control over the deposition process, meaning that the effect of individual deposition parameters upon a coating’s mechanical loss can be investigated. Chapter 6 presents an investigation into whether silicon nitride membranes can be used as substrates in mechanical loss experiments and compares their performance to other commonly used substrates (silica cantilevers, silicon cantilevers and silica discs). Out of these substrates, membranes were shown to be the second most sensitive substrate to clamping effects, exhibit the second least variation of loss for nominally identical substrates and have the second lowest mechanical loss. Whilst none of these results excludes silicon nitride membranes being used in mechanical loss experiments, they indicate a preference should be shown in selecting silica discs before membranes. However, it was also observed that the bulk and shear losses of the same coating deposited upon a membrane and cantilever had significantly different values. Further work is required to fully understand these differences in coating loss before membranes can be reliably used for these experiments. The effect of heat-treatment upon a silicon nitride membrane’s absorption was investigated at both 1064 and 1550 nm wavelengths. No degradation in performance was observed for annealing temperatures up to 900 °C, indicating that silicon nitride could be used as a partner material for amorphous silicon (which requires heat-treatment at 450 °C to reduce it’s absorption to a usable level). The effect of using a silicon nitride and amorphous silicon coating in the (ET) was investigated. It was shown that such a coating can significantly reduce the low-temperature coating thermal noise when compared to an Advanced LIGO (silica/ titania doped tantala) coating. However, this coating does not have a suitably low optical absorption and so “multi-material” coating designs were investigated and a coating design proposed which meets the ET’s absorption requirement. Whilst this “multi-material” coating would still not enable the ET to meet thermal noise design requirements, it represents the best coating which can currently be made from silica, titania doped tantala, silicon nitride and amorphous silicon materials