# Studies of the mechanical dissipation of thin films for mirrors in interferometric gravitational wave detectors

Craig, Kieran (2015) Studies of the mechanical dissipation of thin films for mirrors in interferometric gravitational wave detectors. PhD thesis, University of Glasgow.

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Printed Thesis Information: https://eleanor.lib.gla.ac.uk/record=b3115020

## Abstract

Einstein's General Theory of Relativity predicts the existence of gravitational waves, which are fluctuations in the curvature of space-time, which propagate at the speed of light. Gravitational waves arise from the asymmetric acceleration of mass. While these waves have not been directly detected, studies of the inspiral of a binary pulsar system provide strong evidence for their existence. The detection of gravitational waves would enable a new form of astronomical observations which would provide great insight into bodies such as black holes.

In order to detect gravitational waves, a world wide network of first generation interferometric detectors was built. These detector projects aim to measure the fluctuating tidal strains in space produced by gravitational waves using laser interferometry to measure fluctuations in the relative positions of highly reflective mirrors which are separated by kilometre scale distances. The second generation detector era will be formed by the American Advanced LIGO project, the French/Italian Advanced Virgo detector, the German/British GEO 600 detector and the Japanese KAGRA detector project.

The change of interferometer arm length due to a gravitational wave is expected to be very small, at the order of $\sim10^{-20}$m for a kilometre scale long interferometer arm. This magnitude of displacement is small enough such that the thermal motion of the mirrors and their suspensions is expected to form an important limit to detector sensitivity. The magnitude of thermal noise is related to the mechanical loss of the materials used in the mirror substrates, the suspension elements and the mirror coatings.

The research presented focuses on the charaterisation of the optical mirror coatings, with the aim of reducing the magnitude of thermal noise in future gravitational wave detectors. In Chapter 1, an introduction to gravitational waves is given, along with the sources of gravitational waves. An introduction to interferometric detectors and the techniques commonly employed within these detectors to improve upon the basic Michelson interferometer is also given in Chapter 1. Chapter 2 discusses coating thermal noise, one of the major limits to detector sensitivity in interferometric gravitational wave detectors. The different types of coating thermal noise are discussed, along with the relationship between coating Brownian noise and the mechanical loss of coating materials.

The mirror coatings used in current gravitational wave detectors are dielectric thin films composed of alternating layers of high and low refractive index materials. The predominant source of coating thermal noise is Brownian noise, which is dependent upon the mechanical loss of the coating materials. In Chapter 3, several methods used to deposit thin films are discussed. A general method of measuring mechanical loss is described, and the application of the technique to cantilever samples and disk samples is detailed. A description of the apparatus used to measure the mechanical loss in each case is given. The methods described in this chapter are used throughout the thesis.

In Chapter 4, the mechanical losses of titania-doped tantala thin films are characterised at low temperature. The doping concentration within the films is varied in order to investigate the effects of doping cation concentration on the mechanical loss. Here, tantala doped with titania to a cation concentration of 25\% and 55\% is studied. Additionally, different post-deposition heat-treatments are applied to investigate the effect of the types of heat-treatment regime typically used to reduce stress and optical absorption in optical coatings. The temperature dependent mechanical losses of the coatings exhibit relatively broad cryogenic loss peaks. Analysis of these peaks allows insight into the possible dissipation mechanisms in the coatings. The activation energies responsible for the loss peaks of the as-deposited 25\% doped, as-deposited 55\% doped and 600\,$\si{\degreeCelsius}$ heat-treated 55\% doped coatings were calculated to be $(25.3\pm5.4)$\,meV, $(13.6\pm1.6)$\,meV and $(35.8\pm5)$\,meV respectively. The rate constants calculated for these coatings were $(2.2\pm3.8)\times10^{-8}$\,s, $(13.6\pm1.6)\times10^{-7}$\,s, and $(35.8\pm5)\times10^{-13}$\,s respectively. The width of the loss peaks suggests that there is a broad distribution of barrier heights, which have been calculated and compared to the barrier height distribution previously calculated for pure tantala heat-treated at 600\,$\si{\degreeCelsius}$. These comparisons suggest that an increase in doping concentration acts to decrease the number of barriers at each barrier energy. The calculated barrier height distributions will aid computational molecular models of tantala thin films, and will also aid investigations of the molecular structure of the material. Tantala films deposited by different processes are expected to have radically different molecular structures. As such, the mechanical loss of a tantala film deposited by atomic layer deposition was measured, and a cryogenic loss peak was found. The associated activation energy and rate constant were calculated to be $E_a=(91\pm22)$\,meV and $(0.02\pm1)\times10^{-11}$\,s respectively.

In Chapter 5, the mechanical losses of nominally identical coatings to those for use in Advanced LIGO are studied. The coatings to be used on the end mirrors of Advanced LIGO exhibit a broad low-temperature loss peak at approximately 23-28\,K with a peak magnitude of 0.9-1$\times10^{-3}$. The loss exhibited by the coatings at room temperature is found to be 3$\times10^{-4}$. The room temperature mechanical loss of the coatings intended for use on the input mirrors of Advanced LIGO was found to be in the range 1-1.4$\times10^{-4}$. The mechanical loss of this coating is lower than predicted from previous measurements of silica and titania-doped tantala coatings.

The mechanical loss of tantala is known to be significantly higher than that of silica. As such, the mechanical loss of multilayer coating may be improved by finding a lower loss high refractive index coating than tantala. Previous studies found that ion beam sputtered hafnia has a lower mechanical loss at cryogenic temperatures than tantala despite the coatings being partially crystalline, a property which is usually associated with increased loss. Since silica-doping is known to stabilise hafnia against crystallisation, the temperature-dependent mechanical loss of a hafnia film doped with silica to a cation concentration of 30\% as a function of post-deposition heat-treatment is presented in Chapter 6. At room temperature, the mechanical loss of the coating is shown to be approximately 1$\times10^{-3}$, which may be reduced to 3$\times10^{-4}$ by hear-treating the coating at 600\,$\si{\degreeCelsius}$. However, this is a higher loss than current titania-doped tantala films. At cryogenic temperatures, the coating heat-treated at 400\,$\si{\degreeCelsius}$ is shown to exhibit a lower loss than comparable tantala films. The thermal noise of a silica/silica-doped hafnia coating on a silicon substrate at cryogenic temperatures is calculated to be lower than that of the Advanced LIGO end mirror coating for comparable design parameters. At 20\,K, a silica/silica-doped hafnia coating offers a factor of 2.5 improvement in Brownian noise over the Advanced LIGO ETM coating at room temperature, and a factor of 1.14 improvement in Brownian noise over the Advanced LIGO ETM coating at 20\,K.

In previous studies, a multilayer coatings composed of GaAs/AlGaAs exhibited a lower mechanical loss than the best silica/tantala coatings. However, these studies used either free-standing structures made from the material, or were based on calculations following thermal noise measurements. Hence, Chapter 7 presents direct room temperature mechanical loss measurements of a GaAs/AlGaAs multilayer coating bonded to a silica disk. The lowest coating loss exhibited in these measurements was $2.0\pm0.7\times{-5}$, which is consistent with the loss found in previous investigations by other methods. The Brownian thermal noise arising from an AlGaAs coating bonded to a silica substrate would be a factor of 2.9 lower than that of the Advanced LIGO end mirrors operating under similar conditions. Investigations of an AlGaAs coating bonded to a silicon disk found that the coating delaminated after cooling to cryogenic temperatures. The mechanical loss of a crystalline GaP/AlGaP coating grown directly onto a silicon wafer is presented in Chapter 7. The coating loss was measured to be as low as 1.4$\times10^{-5}$. The Brownian thermal noise of such a coating would be a factor of 8-13.3 lower than the Brownian noise arising from the Advanced LIGO coatings at room temperature, and a factor of 3.7-6 lower than the Brownian noise arising from the Advanced LIGO coatings operating at 20\,K.

Item Type: Thesis (PhD) Doctoral Optics, thin films, optical coatings, dielectric materials, mechanical loss, mechanical dissipation, crystalline coatings, gravitational waves Q Science > QC Physics College of Science and Engineering > School of Physics and Astronomy Rowan, Prof. Sheila and Martin, Dr. Iain W. 2015 Mr Kieran Craig glathesis:2015-6582 Copyright of this thesis is held by the author. 24 Jul 2015 08:25 08 Apr 2019 10:41 http://theses.gla.ac.uk/id/eprint/6582