title: Properties of bonded silicon for future generations of gravitational wave observatories
Creators: name: Masso Herrera, Mariela C.
Publisher: name: University of Glasgow
Year: 2019
Subjects: subject: Gravitational waves, silicon, silicon bonded material, thermal conductivity, crystalline silicon, hydroxide catalysis bonds, hydroxide catalysis bonded silicon, strength of silicon bonded samples, hydroxide catalysis bonding, future generations of GW detectors, gravitational wave detectors.

description: In September 2015, the Advanced LIGO gravitational wave (GW) interferometers detected the first signals, associated with the merger of two black holes, heralding the opening of an entirely new window on the Universe. Einstein predicted the existence of GWs in 1916, as a consequence of his Theory of General Relativity. GWs can be considered as fluctuations in the curvature of space-time, produc- ing orthogonal stretching and squeezing (i.e. strains) in space. The predicted strains, even from the largest and most violent astrophysical events, are expected to be very small when observed at the Earth - in the order of 10−21 or lower in the audio frequency band. Many decades of research were required to realise instruments able to achieve these sensitivities. The detections thus far have been made using long-baseline Michelson interferometers, utilising optical cavities with mirrors separated by 3 to 4 km. An international team of researchers were involved in developing the myriad of advanced technologies contained in these instruments, and the UK has played (and continues to play) a leading role in devel- oping many of the core technologies. To date, the Advanced LIGO interferometers have carried out two observing runs. These operated from September 2015 to January 2016, where three binary black hole mergers were observed, then from November 2016 to August 2017, where one binary neutron star merger and seven additional binary black hole mergers were reported. The binary neutron star merger was the first astrophysical event to be observed simultaneously in gravitational waves and light, and allowed a new, independent estimate of the expansion of the Universe to be calculated (Hubble’s constant) in addition to explaining how many of the heavier elements are created. The black hole binaries are the most energetic events known to exist in the Universe, converting up to five solar masses into gravitational radiation in a fraction of a second during their merger. Improved detector sensitivities are required to fully open this new window on the Universe, to precisely survey the range of astrophysical events emitting GWs, and to better extract the astrophysical source parameters (e.g. neutron star equations of state, or mapping of space-time curvature around supermassive black holes). This is particularly challenging, as a variety of fundamental noise sources limit the current detector sensitivities, such as quantum noise (photon shot noise and radiation pressure noise) and thermally driven dis- placements (Brownian thermal noise). Further improvements will thus require significant changes in the interferometer configuration and operation, such as the use of cryogenics to mitigate the effects of thermal noise. However, many of the proposed detector upgrades present opposing challenges, such as the increased laser power to decrease the photon shot noise, which in turn increases the radiation pressure noise in addition to creating additional heating which may be incompatible with cooling the mirrors to cryogenic temperatures. The work presented within this thesis describes a series of experiments to characterise bonded silicon samples, relevant to the possible construction of cooled, quasi-monolithic silicon mirror suspensions, for use in future gravitational wave detectors. The next major upgrade to Advanced LIGO (LIGO Voyager) proposes to use silicon mirror suspensions at a temperature of around 124 ± 2 K, and the third generation detector in Europe, the Einstein Telescope, proposes to use silicon mirror suspensions at 20 K. An overview of gravitational waves, the sources that are expected to provide the largest signals, and details the development of the detectors, is detailed in Chapter 1. The various fundamental noise sources relevant to interferometric detectors are reviewed. Chapter 2 describes the nature of thermal noise, which remains one of the most significant challenges for future detectors, and provides much of the motivation for the work carried out in this thesis. Chapter 3 details the plans for GW detector upgrades and the third generation detec- tors in the global network, providing further relevance and context for realising cryogenic mirror suspensions systems for the reduction of thermal noise. For cooling the mirror suspensions in future GW detectors, heat must be extracted through conduction through the suspension wires and/or through radiative cooling. Radiative cool- ing may be considered for higher operating temperatures e.g. 124 ± 2 K, however conduc- tion is essential to reach lower temperatures e.g. 20 K. For the proposed mirror suspensions in future GW detectors, this would require heat conduction through the test mass, the sus- pensions fibres, in addition to the material that forms the bond interface between these components. The nature of heat flow in solids is reviewed in Chapter 4, along with the various meth- ods by which thermal conductivity can be measured. An overview of the factors that in- fluence the thermal conductivity in crystalline silicon is given. The experimental set up developed here for measuring the thermal conductivity of silicon and jointed silicon com- ponents, from room temperature to 10 K, is presented. The evolution of various aspects of the experimental set up, in order to improve the quality and accuracy of the obtained data, is highlighted. The thermal conductivity of crystalline silicon here was measured to be around 155 Wm−1K−1 at 300 K, rising to around 1300 Wm−1K−1 at 30 K. At the pro- pose operating temperature of the Einstein Telescope (20 K), the thermal conductivity is observed to be 1100 Wm−1K−1. These values are in very close agreement with literature values for similar purities of silicon. In Chapter 5, the silicon samples that have been hydroxide catalysis bonded are described; such a bonding technique is used to join test masses to suspension elements. An overview of the bonding process, and experimental procedure for oxidising and jointing silicon sam- ples, is presented. A recommended set of values for the thermal conductivity from 10 to 300 K as well as a detailed analysis of the errors is provided for the hydroxide catalysis bonds. The values are attributed to the total bond structure, which includes the thermal oxide layers on the surfaces of the silicon substrates, in addition to the hydroxide catalysis bond interface. The thermal conductivity of the bonds were found to be 0.05 Wm−1K−1 at 20 K, and 0.15 Wm−1K−1 at 120 K. These values obtained are compatible with the cooling requirements for the Einstein Telescope, as discussed within the chapter, and provide a ro- bust proof-of-principle that quasi-monolithic silicon suspensions, jointed using hydroxide catalysis bonds, are an attractive route for realising future GW detector upgrades. The strength of silicon samples, jointed using hydroxide catalysis bonding, using a four point bending set up, is presented in Chapter 6. This includes the measured strength as a function of curing time. In addition, since silicon in not transparent in the visible, both thermal imaging and infrared (IR) transmission mapping are employed to assess the quality of the bonds prior to breaking. The thermal images were capable of identifying bonds where the bonding solution had not filled the entire interface between samples, and therefore provided a method to identify poor quality bonds (strongly evidenced in the samples cured for 6 months). The IR maps often exhibited strong (high contrast) interference fringes for samples with good (strong) bonds. This is consistent with the hypothesis that good bonds are highly transmissive, and suitably thinner than the wavelength of the light being used to probe the bond, resulting in a “clean” transmission. The fringes therefore result from “clean” reflections of the IR light between the faces and the interfaces of composite silicon samples. This is the first time that a non-destructive technique was used to study the quality of the bonds between silicon substrates prior to strength testing. A weak exponential trend is observed at the early stages of the curing time with an increased strength of the bonds. A lower limit is set for the strength of hydroxide catalysis bonds between silicon substrates of 4.8 MPa with a mean strength observed as 30.2 ± 4.6 MPa. The expected bond stress in an ET-LF style mirror is shown to be around 0.85 MPa, and therefore the presented strengths of hydroxide catalysis bonds are highly favourable for using this technique for the construction of future mirror suspensions. In Chapter 7, a computational finite element analysis (FEA) model is presented for simulat- ing the cool-down rate of an ET-LF style mirror suspension using the thermal conductivity values obtained in Chapter 5. Including heat transfer from both radiation and conduction, and assuming the penultimate test mass and the surroundings to be held constant at 5 K, it will take 35.5 days to cool from 300 to 20 K, the proposed operating temperature of ET-LF. In Chapter 8, a summary of the results relevant for future generations of GW detectors is presented. Supplementary information is provided in the appendices regarding sample fabrication, thermal conductivity data, error analysis and IR transmission images for all samples.