# Exploration of co-sputtered Ta2O5-ZrO2 thin films for gravitational-wave
detectors

M Abernathy1,2, A Amato3, A Ananyeva4, S Angelova5, B Baloukas6, R Bassiri7, G
Billingsley4, R Birney5,8, G Cagnoli3, M Canepa9,10, M Coulon11, J
Degallaix11, A Di Michele12, M A Fazio13, M M Fejer7, D Forest11, C Gier5, M
Granata11, A M Gretarsson14, E M Gretarsson15, E Gustafson4, E J Hough16, M
Irving17, É Lalande17, C Lévesque17, A W Lussier17, A Markosyan7, I W
Martin16, L Martinu6, B Maynard18, C S Menoni13,19, C Michel11, P G Murray16,
C Osthelder4, S Penn18, L Pinard11, K Prasai7, S Reid5, R Robie16, S Rowan16,
B Sassolas11, F Schiettekatte17, R Shink17, S Tait16, J Teillon11, G Vajente4,
M Ward17, L Yang19 1Department of Physics, American University, Washington,
DC, USA  2Johns Hopkins University Applied Physics Laboratory, Laurel, MD, USA
3Université de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière
Matière, F-69622 Villeurbanne, France  4LIGO Laboratory, California Institute
of Technology, Pasadena, CA, USA  5SUPA, Department of Biomedical Engineering,
University of Strathclyde, Glasgow, UK  6École Polytechnique de Montréal,
Montréal, Québec, Canada  7Edward L. Ginzton Laboratory, Stanford University,
Stanford, CA 94305, USA  8SUPA, Institute of Thin Films, Sensors and Imaging,
University of the West of Scotland, Paisley, UK  9OPTMATLAB, Dipartimento di
Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy  10INFN,
Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy  11Laboratoire des
Matériaux Avancés, Institut de Physique des 2 Infinis de Lyon, CNRS/IN2P3,
Université de Lyon, Université Claude Bernard Lyon 1, F-69622 Villeurbanne,
France  12Dipartimento di Fisica e Geologia, Università degli Studi di
Perugia, Via Pascoli, 06123 Perugia, Italy  13Department of Electrical and
Computer Engineering, Colorado State University, Fort Collins, CO, USA
14Embry-Riddle Aeronautical University, 3700 Willow Creek Rd., Prescott, AZ
86301, USA  15Wyant College of Optical Sciences, University of Arizona, 1630
E. University Blvd., Tucson, AZ 85721, USA  16SUPA, Institute for
Gravitational Research, University of Glasgow, Glasgow, UK  17Université de
Montréal, Montréal, Québec, Canada  18Department of Physics, Hobart and
William Smith Colleges, Geneva, NY, USA  19Department of Chemistry, Colorado
State University, Fort Collins, CO, USA<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

We report on the development and extensive characterization of co-sputtered
tantala-zirconia thin films, with the goal to decrease coating Brownian noise
in present and future gravitational-wave detectors. We tested a variety of
sputtering processes of different energies and deposition rates, and we
considered the effect of different values of cation ratio $\eta=$ Zr/(Zr+Ta)
and of post-deposition heat treatment temperature $T_{a}$ on the optical and
mechanical properties of the films. Co-sputtered zirconia proved to be an
efficient way to frustrate crystallization in tantala thin films, allowing for
a substantial increase of the maximum annealing temperature and hence for a
decrease of coating mechanical loss. The lowest average coating loss was
observed for an ion-beam sputtered sample with $\eta=0.485\pm 0.004$ annealed
at 800 ∘C, yielding $\overline{\varphi}=1.8\times 10^{-4}$. All coating
samples showed cracks after annealing. Although in principle our measurements
are sensitive to such defects, we found no evidence that our results were
affected. The issue could be solved, at least for ion-beam sputtered coatings,
by decreasing heating and cooling rates down to 7 ∘C/h. While we observed as
little optical absorption as in the coatings of current gravitational-wave
interferometers (0.5 parts per million), further development will be needed to
decrease light scattering and avoid the formation of defects upon annealing.

Keywords: xxx, yyy, zzz

##  1 Introduction

The detection of gravitational-wave (GW) signals from astrophysical systems
[13] has ushered in a new era in astronomy [2, 14], allowing the study of
systems previously invisible. The current generation of GW interferometric
detectors are sensitive enough to allow a confident candidate event about once
per week [16, 17]. Increasing the sensitivity of the detectors is important
not only to increase the detection rate but also to improve the signal to
noise ratio and sky localization of events, allowing for a more precise
probing of the properties of nuclear matter in neutron stars [15] and of the
fundamental physics of gravitation and general relativity [1].

Ironically, the sensitivity of current detectors to signals from very large
and massive astrophysical systems is limited by random noise in microscopic
systems, that is, fluctuations resulting from the internal mechanical
dissipation in the material constituting the mirrors used as test masses [48].
In the most sensitive region of the detection band of Advanced LIGO [39] and
Advanced Virgo [25], between 50 and 300 Hz, the sensitivity is limited by an
equal contribution of quantum noise [21] and thermal noise, the latter being
dominated by coating Brownian noise [60]. Indeed, all GW detectors currently
operating are laser interferometers with km-scale optical resonators [32],
where the test masses used to probe the space time metric fluctuations are
high-quality fused silica mirrors with high-reflection (HR) dielectric
coatings on the front surfaces [23, 50, 76]. Of all the sources of thermal
noise in the mirrors, the Brownian motion of particles in the coating layers
is the limiting factor and hence needs to be reduced for future sensitivity
upgrades [46, 45, 22].

The dielectric coatings used in the current generation of GW detectors are
Bragg reflectors [68] made of alternate ion-beam sputtered (IBS) thin layers
of silica (SiO2) and tantala-titania (Ta2O5-TiO2). Silica is the low
refractive index material ($n=1.45$ at 1064 nm), and the tantala-titania is
the high refractive index material ($n=2.07$ at 1064 nm) [43]. These materials
and their synthesis by various methods have been extensively investigated in
the context of optical materials in general and interferometric filters in
particular [68], including for example their mechanical properties [40, 5,
43], showing that their performance is intimately related to parameters such
as their internal stress and growth parameters [43].

The detection of GW signals is performed by monitoring the change in the
relative distance between the mirrors, measured as a change in the phase of
the laser beams [72]. Therefore, any fluctuation in the thickness or in the
optical properties of the coating materials acts like a spurious displacement
noise. Thermo-refractive and thermo-elastic fluctuations are not relevant
[24], and the dominant source of phase noise is due to the Brownian motion of
all the layers. The fluctuation dissipation theorem [3] links Brownian noise
to the rate of energy dissipation in the coating material due to internal
friction. The amount of friction is measured by the material loss angle
$\varphi$, that is the fraction of energy lost per cycle when the material is
driven by a sinusoidal external force. In the coating materials used so far,
the worst offender is tantala-titania, with measured values $(2.3-3.4)\times
10^{-4}$ [75, 43]. The silica layers have one order of magnitude lower loss
angle, $(2.3-4.0)\times 10^{-5}$ [55, 43].

The goal for the GW detector upgrades in the next 2-5 years is to roughly
double the sensitivity to GW inspiral signals [46], which translates to an
improvement of the same factor of the sensitivity in the $100$ Hz region. In
Advanced LIGO, for instance, this sets a target of $6.6\times 10^{-21}$
m$/\sqrt{\mbox{Hz}}$ at 100 Hz in terms of coating Brownian noise, to be
compared with the current estimated level of $1.3\times 10^{-20}$
m$/\sqrt{\mbox{Hz}}$ [11]. The Brownian noise amplitude spectral density
scales with the square root of the total loss angle of the HR coating [29].
Theerfore the upgrade goal translates into improving the high refractive index
material loss angle by at least of a factor 4. Marginal or no improvement is
necessary for the low refractive index material. For this reason, most of the
coating research in the Virgo and LIGO collaborations focused on finding an
alternative material to replace the tantala-titania layers [76, 44], while
keeping the same outstanding optical properties (absorption, scattering, etc.)
of the HR coatings. The main line of research explores the co-sputtering of
other oxides with tantala, following the success of co-sputtered tantala-
titania coatings [30] which allowed a reduction of the coating loss angle by
about 25% [43] with respect to tantala.

Beginning in 2012, one of the authors (S. P.) characterized a series of
zirconia-based coatings. That investigation was motivated by zirconia (ZrO2)
being a high-index material ($n\geq 2$ at 1064 nm, like tantala) possessing a
similar molecular structure and physical parameters to silica. However, unlike
silica, when treated at high temperatures, zirconia will crystallize unless
stabilized. Tewg et al. [64] showed that the addition of zirconia to tantala
thin films allowed for a higher maximum heating temperature, before the onset
of crystallization. Post-deposition heat treatment, referred to as annealing
hereafter, is a standard procedure to decrease the internal stress, the
optical absorption and the mechanical loss of coatings [43]. As a general
empirical rule, the higher the annealing peak temperature, the lower the
resulting coating mechanical loss. In the work of Tewg et al., the annealing
had a duration of 10 minutes, while typical annealing times for HR coatings
used in GW detectors are of the order of 10 hours [43]. Indeed, higher
annealing temperatures (up to 900 ∘C) and duration would be beneficial also
for the silica layers, decreasing their mechanical loss [9, 34] as a result of
structural relaxation, leading to HR coatings with overall lower loss angle
and hence lower thermal noise.

This paper focuses on a collaborative work, carried out by different groups of
the LIGO and Virgo Collaborations to produce and characterize co-sputtered
tantala-zirconia thin films, for possible use as high refractive index layers
for the new sets of mirrors of the Advanced LIGO+ and Advanced Virgo+
sensitivity upgrade projects. We considered the effect of adding various
amounts of zirconia, and measured the optical and mechanical properties of the
films as functions of their chemical composition and annealing temperature. As
coating mechanical loss depends in general on the nature of the growth
technique, we tested a variety of sputtering processes of different energies
and deposition rates. A detailed description of the coating samples is given
in Section 2. Different techniques and methodologies have been used to
characterize the optical and mechanical properties of the coating samples,
described with their results in Sections 3 and 4. In Sections 4 and 5 we show
that the main effect of co-sputtering zirconia with tantala is a significant
increase of the maximum annealing temperature $T_{a}$, hence a reduction of
coating mechanical loss. The main issues we encountered are cracking of all
annealed single-layer samples and bubble-like defects in annealed IBS HR
coatings. Later we found that cracking could be avoided by drastically slowing
down the annealing heating and cooling rates of the samples. Bubble-like
defects, however, remain a pending issue to date. In Section 6 we present the
results of Raman spectroscopy measurements, and discuss the possibility of
using Raman peaks as a probe of the state of relaxation or a predictor of the
loss angle in a material. Finally, we discuss the results and their
implications in Section 7.

##  2 Deposition methods and film composition

The co-sputtered tantala-zirconia coating samples used for this work were
produced by one industrial manufacturer and several academic research groups,
using different growth techniques:

  * •

ion-beam sputtering (IBS), at MLD Technologies (MLD) and Laboratoire des
Matériaux Avancés (LMA)

  * •

electron-cyclotron-resonance ion-beam deposition (ECR-IBD), at University of
Strathclyde (UoS)

  * •

reactive biased-target deposition (RBTD), at Colorado State University (CSU),
Fort Collins

  * •

high-power impulse (HiPI) and radio-frequency (RF) magnetron sputtering (MS),
at Université de Montréal and Polytechnique Montréal (UMP).

Acronyms of growth techniques and groups are used throughout this paper to
identify the samples. The measured atomic cation ratio $\eta$ = Zr/(Zr+Ta) and
density $\rho$ of all samples considered in this work are summarized in Table
1 and plotted and discussed in Section 3.5. Details on the different growth
processes, sample specifications and characterizations follow below.

Sample | Process |  $\eta$ [at.%] |  $\rho$ [g/cm3]
---|---|---|---
MLD2014 | IBS | $48.5\pm 0.4$ |
MLD2018 | IBS | $50.2\pm 0.6$ |
LMA | IBS | 19 $\pm$ 1 | 6.9 $\pm$ 0.1
UoS | ECR-IBD | $34.0\pm 0.5$ |
UMP 551 | RF-MS | 41 $\pm$ 3 | 6.1 $\pm$ 0.2
UMP 554 | RF-MS | 43 $\pm$ 3 | 5.9 $\pm$ 0.2
UMP 658 | HiPIMS | 24 $\pm$ 3 | 7.0 $\pm$ 0.2
UMP 659 | HiPIMS | 24 $\pm$ 2 | 7.1 $\pm$ 0.2
UMP 542 | HiPIMS | 7 $\pm$ 2 | 7.3 $\pm$ 0.2
UMP 664 | HiPIMS | 7 $\pm$ 2 | 7.1 $\pm$ 0.2
UMP 678 | HiPIMS | 47 $\pm$ 2 | 6.6 $\pm$ 0.2
UMP 680 | HiPIMS | 47 $\pm$ 2 | 6.5 $\pm$ 0.2
CSU II | RBTD | 23 $\pm$ 1 | 7.1(∗)
CSU III | RBTD | 54 $\pm$ 3 | 7.1(∗)
Table 1: Measured atomic cation ratio $\eta$ = Zr/(Zr+Ta) and density $\rho$
of co-sputtered Ta2O5-ZrO2 thin films. RF-MS samples had Ta deposited by RF-MS
and Zr deposited by DC-MS, HiPIMS samples had Ta deposited by HiPIMS and Zr
deposited by RF-MS. Density values are plotted and discussed in Section 3.5,
where correlation between oxygen concentration, density and refractive index
are considered. (∗)Estimated from component values and concentration.

###  2.1 IBS

Ion-beam-sputtered films where produced by MLD Technologies and by the LMA
group. Details are described below.

####  2.1.1 MLD Technologies –

The provider is a manufacturer of high performance and specialty optical
coatings located in Mountain View, CA, with coating facilities in Eugene, OR.
The company deposited the coatings using standard IBS, where a beam of Ar ions
is directed at a metal target and the sputtered metal atoms are oxidized in a
low density O2 atmosphere before striking the substrate. For all deposition
runs, MLD coated: (i) thin super-polished disk substrates of Corning 7980
fused silica that were 76.2 mm in diameter and 2.5-mm thick; (ii) a
$\sim$100-$\mu$m thick fused-silica cantilever welded to a 10 mm $\times$ 10
mm $\times$ 3 mm clamping block; (iii) and a number of 35 mm $\times$ 5 mm
$\times$ $\sim$65 $\mu$m silicon cantilevers with a 10 mm $\times$ 5 mm
$\times$ $\sim$550 $\mu$m clamping block. As is standard practice, each run
included fused-silica witness samples with 25.4 mm in diameter that were used
to test the coating composition and thickness.

MLD conducted 2 runs, whose samples are referenced as MLD2014 and MLD2018, of
identical specifications: the design goal was a single 500-nm thick tantala-
zirconia coating with atomic cation ratio
$\eta=\mathrm{Zr}/\left(\mathrm{Zr}+\mathrm{Ta}\right)\sim 36$%, as specified
by Tewg et al. [64] for achieving amorphous coatings stable to peak annealing
temperatures of 800 ∘C, where the ratio was intended to denote atomic number
density. MLD performed post-deposition energy-dispersive X-ray spectroscopy
(EDX) measurements that reported cation ratios in agreement with that goal.
However, while Tewg et al. reported atomic number densities, MLD reported
ratios were later learned to be molecular number densities. Moreover, a
reanalysis of the EDX data showed that the $\eta$ was $48.5\pm 0.4$% for
MLD2014 and $50.2\pm 0.6$% for MLD2018. Thus the actual molecular number
densities were $\mathrm{ZrO_{2}}=65.3\pm 0.4\%$ and
$\mathrm{Ta_{2}O_{5}}=34.7\pm 0.4\%$ for MLD2014 and $\mathrm{ZrO_{2}}=66.8\pm
0.6\%$ and $\mathrm{Ta_{2}O_{5}}=33.2\pm 0.6\%$ for MLD2018. MLD also reported
coating thicknesses of 590 nm for MLD2014 and 483 nm for MLD2018.

After coating deposition, to test the effect of annealing on coating
mechanical loss, the fused-silica disk and the silicon cantilevers were
progressively annealed with steps of increasingly high temperatures: 400, 600
and 700 ∘C for one set of samples; 300, 400, 600, 700, and 800∘C for a second
set of samples.

####  2.1.2 LMA –

Co-sputtered Ta2O5-ZrO2 coatings were produced with the custom-developed so-
called Grand Coater (with a volume of 10 m3) used to coat the mirrors of the
Advanced LIGO, Advanced Virgo and KAGRA detectors [50, 23, 43]. Prior to
deposition, the base pressure was less than 10-7 mbar. Ar gas was fed into the
sputtering source while O2 gas was fed directly into the vacuum chamber, for a
total working pressure of $2\times 10^{-4}$ mbar. Energy and current of the
sputtering Ar ions were of the order of 1 keV and 0.1 A, respectively. During
deposition, the co-sputtered Ta2O5 and ZrO2 particles impinged on substrates
heated up to about 120 ∘C.

Single layers with a thickness between 500 and 650 nm have been grown on
various substrates for different purposes: (i) on fused-silica witness samples
(50 mm in diameter, 6-mm thick) for transmission spectrophotometry; (ii) on
silicon wafers (75 mm in diameter, 0.5-mm thick) for reflection spectroscopic
ellipsometry and EDX analyses; (iii) and on a Corning 7980 fused-silica disk-
shaped mechanical resonator of 75 mm in diameter and 1-mm thick for measuring
coating mechanical loss, Young modulus, Poisson ratio and density.
Additionally, Ta2O5-ZrO2/SiO2 HR coatings with the same design of those of
Advanced LIGO and Advanced Virgo [43] have been deposited on micro-polished
fused-silica witness samples for optical absorption and scattering
measurements.

Prior to coating deposition, to release the internal stress due to
manufacturing and induce relaxation, the fused-silica disk was annealed in air
at 900 ∘C for 10 hours. After deposition, all coating samples were annealed in
air for 10 hours: optical samples were annealed at 500 ∘C, the disk underwent
consecutive annealing treatments of increasing peak temperature (500, 600 and
700 ∘C) and the mechanical loss of its coating was measured after each
annealing step.

We used an analytical balance to measure the mass of the disk before and after
the coating deposition, as well as after the 500-∘C annealing. To estimate the
surface area coated in the deposition process, we measured its diameter with a
Vernier caliper. As the coating thickness was known with high accuracy from
the optical characterization (see Section 3.1.2), the coating density
$\rho=6.9\pm 0.1$ g/cm3 was straightforwardly estimated as the mass-to-volume
ratio.

We used a Zeiss LEO 1525 field-emission scanning electron microscope (SEM) and
a Bruker Quantax system equipped with a Peltier-cooled XFlash 410-M silicon
drift detector to analyze the surface and elemental composition of the single-
layer coatings. The SEM beam was set to 15 keV for the survey. We performed
multiple energy-dispersive X-ray (EDX) analyses on different coating sample
spots and with different magnifications (from $100\times$ to $5000\times$).
Semi-quantitative (standardless) results were based on a peak-to-background
evaluation method of atomic number, self-absorption and fluorescence effects
(P/B-ZAF correction) and a series fit deconvolution model provided by the
Bruker Esprit 1.9 software. Using the self-calibrating P/B-ZAF standard-based
analysis, no system calibration had to be performed. According to our EDX
analyses, our thin films had an average atomic cation ratio $\eta=$ Zr/(Zr+Ta)
= 19 $\pm$ 1 %. We also found that they incorporated 2.9 $\pm$ 0.6 at.% of Ar.

###  2.2 ECR-IBD

Coatings were deposited using a custom-built ion beam deposition system that
utilized three ECR ion sources for sputtering [52]. The ion beams are
generated by injection of Ar gas into a resonance microwave cavity, with
$\sim$3 W injected power at 2.45 GHz. The confinement of the plasma permits
the extraction of ions through a single aperture, enabling a larger range of
stable extraction potentials to be explored, with low ion current. The
extraction potential was 10 kV and ion currents ranged between $0.2-0.6$ mA
per source, resulting in a deposition rate of 0.001 nm/s. Base pressure was
below $1\times 10^{-5}$ mbar prior to deposition, with pressure rising to
$8\times 10^{-5}$ mbar with Ar injected through the ion sources, and
increasing to $1.2\times 10^{-4}$ mbar with reactive O2 gas fed into the
chamber. The targets used during the deposition process are two circular
152.4-mm diameter targets of pure tantala and zirconia provided by Scotech,
UK, both with $99.99\%$ purity. During the deposition process, two ion beams
were directed onto the tantala target and one beam on the zirconia target,
with the aim for cation ratio $\eta=$ Zr/(Zr+Ta) of $\sim$33%. Fused-silica
witness samples and cantilevers were placed on a rotating substrate holder to
ensure coating uniformity.

The cantilevers, used for coating mechanical loss measurements [31], were
fabricated from 45 mm $\times$ 5 mm $\times$ $(175\pm 3)$ $\mu$m strips of
fused silica, flame welded to 10 mm $\times$ 10 mm $\times$ 3.1 mm clamping
blocks [31]. They were cleaned in boiling H2O2 (30% w/w in H2O) with 1 mol/l
KOH dissolved, in order to remove the majority of particulates associated with
the welding process, then annealed in air for 5 hours at 950 ∘C prior to
measurement and deposition.

EDX was used to quantify the cation ratio $\eta=$ Zr/(Zr+Ta), found to be
$34.0\pm 0.5$%.

###  2.3 RBTD

Coatings were deposited using in a LANS system by 4Wave, Inc [58], where a low
energy Ar ion plume is produced using an End-Hall ion source operated at 60 V
and 5.8 A, with an Ar flow of 27 sccm. For neutralization, a hollow cathode
electron source is employed at an emission current of 6.2 A with an Ar flow of
25 sccm. The Ar ions are attracted to a biased metallic target, leading to
sputtering of the target material. For oxide coatings, O2 is introduced into
the chamber during the process. Substrates are placed in a sample holder
facing the ion source, and rotating at 20 rpm during deposition to ensure
uniformity of the film. The chamber base pressure is below $1\times 10^{-7}$
mbar, while the process pressure is about $9\times 10^{-4}$ mbar.

The LANS system has the ability to simultaneously bias up to three targets to
produce mixed oxide coatings. An asymmetric, bipolar DC pulse is used to bias
the targets with a negative voltage of -800 V and a positive voltage of 10 V
and a period of 100 $\mu$s. For a binary oxide mixture, two targets are
simultaneously biased and different mixture proportions of the materials are
achieved by controlling the individual pulse duration of each target. Ta and
Zr targets were employed to deposit tantala-zirconia thin films, and the
corresponding deposition conditions are presented in Table 2. Deposition rates
for RBTD are typically an order of magnitude lower than with a gridded IBS
system, ranging from 0.0212 nm/s for tantala to 0.0116 nm/s for zirconia.
Films with a thickness between 200 - 300 nm were grown on: (i) 25.4-mm
diameter and 6.35-mm thick UV grade fused silica substrates; (ii) 75-mm
diameter and 1-mm thick fused silica substrates; and (iii) (111) Si wafer
substrates.

Film | O2 flow [sccm] | Target | Pulse width [$\mu$s] | Deposition rate [nm/s]
---|---|---|---|---
CSU I | 12 | Ta | 2 | 0.0212 $\pm$ 0.0001
CSU II | 12 | Ta - Zr | 2 - 54 | 0.0294 $\pm$ 0.0001
CSU III | 12 | Ta - Zr | 47 - 2 | 0.0217 $\pm$ 0.0001
CSU IV | 12 | Zr | 2 | 0.0116 $\pm$ 0.0001
Table 2: Deposition conditions for Ta2O5-ZrO2 thin films grown via RBTD. Pure
Ta2O5 and ZrO2 samples (I and IV, respectively) are included for reference.

X-ray photoelectron spectroscopy (XPS) measurements were performed on as-
deposited coatings using a Physical Electronics PE 5800 ESCA/ASE system with a
monochromatic Al K$\alpha$ x-ray source. The photoelectron take-off angle was
set at $45^{\circ}$ and a charge neutralizer with a current of 10 $\mu$A was
employed. The chamber base pressure was around $1\times 10^{-9}$ mbar. High
resolution scans were recorded for the main peaks of the detected elements: C
1s, O 1s, Zr 3d and Ta 4f. No Ar can be detected by XPS in this case, because
the peak associated with this element is superimposed with a Ta peak. Presence
of carbon is due to normal surface contamination of samples exposed to the
atmosphere. In the case of insulating samples the carbon is not removed but
instead used for calibration of the binding energy scale, by employing the
position of the adventitious carbon peak. CasaXPS software (version 2.3.19)
was used to fit the high-resolution spectra [59].

Film | Elemental concentration [at.%] | Cation ratio
---|---|---
C | O | Zr | Ta | Zr/(Zr+Ta)
CSU II | 38 $\pm$ 1 | 44 $\pm$ 1 | 4.3 $\pm$ 0.1 | 14.1 $\pm$ 0.1 | 0.23 $\pm$ 0.01
CSU III | 39 $\pm$ 1 | 42 $\pm$ 1 | 10.4 $\pm$ 0.4 | 8.7 $\pm$ 0.1 | 0.54 $\pm$ 0.03
Table 3: Atomic concentrations obtained from XPS analysis at the surface of
as-deposited Ta2O5-ZrO2 thin films grown via RBTD.

Table 3 shows the atomic concentrations obtained from XPS for the thin films
as deposited. The atomic percentage cation ratio, $\eta=$ Zr/(Zr+Ta), resulted
in 0.23 $\pm$ 0.01 for sample II and 0.54 $\pm$ 0.03 for sample III.

(a)

(b)

(c)

(d)

Figure 1:  Typical fit of XPS peaks for an as-deposited Ta2O5-ZrO2 thin film
grown via RBTD with a cation ratio of 0.54: (a) C 1s, (b) O 1s, (c) Zr 3d and
(d) Ta 4f.

Fig. 1 presents typical fits of the main XPS peaks. The C 1s peak was composed
mainly of adventitious carbon, and up to 5% of carbon was found to be linked
to an alcohol and/or esther functionality. This further confirmed that the
presence of carbon was due to surface contamination. The O 1s peak had two
components: lattice O, determined as such based on the tabulated position of O
1s for zirconia and tantala (around 530 eV), and non-lattice oxygen. In all
cases, 1 to 3% of the oxygen was associated with hydroxide species based on
the analysis of the C 1s peak, so the non-lattice peak could be attributed
mainly to oxygen in defective sites. In the case of the Zr 3d peak, the
doublet energy separation was found to be (2.39 $\pm$ 0.01) eV and the Zr
3d5/2 peak position was (182.1 $\pm$ 0.1) eV for both films. These values are
in agreement with the tabulated values for zirconia [69]. For the Ta 4f
doublet in both films, the energy separation was determined as (1.89 $\pm$
0.01) eV and the Ta 4f7/2 peak position as (26.0 $\pm$ 0.2) eV, which is in
agreement with reported values for tantala [69]. Therefore, for the evaluated
zirconia-doped tantala films as deposited, there was no noticeable
modification of the chemical environment of either Ta or Zr, compared to their
corresponding oxides.

###  2.4 HiPIMS/RF-MS

Layers of approximately 700 nm in thickness were synthesized in a Kurt J.
Lesker CMS-18 system, equipped with two 76-mm diameter metallic targets of Zr
and Ta of 99.95% purity located $\sim$25 cm beneath the substrate holder.
Prior to deposition, the base pressure in the system was less than $10^{-7}$
mbar. Depositions were carried out on different samples: (i) the $75$-mm
diameter fused-silica disks were placed face down, one at the time, on a
rotating substrate holder featuring a wedged hole in the middle, such that
they were supported by a $1$ mm ledge; (ii) silica and (iii) silicon
substrates were placed next to the disks as witness samples. During
deposition, the pressure was 9 mbar with a 20% O2:Ar gas ratio.

For six samples, Ta was sputtered by HiPIMS [36, 35] using a Huttinger power
supply, while the Zr was sputtered using a power supply (13.56 MHz) [27]. Two
additional samples had their Ta deposited by RF-MS while the Zr was deposited
by DC-MS, for comparison. The nominal duty cycle of the HiPIMS process was set
at a voltage of 700 V, with a pulse duration of $80$ Hz. The nominal RF
voltage applied to the Zr target varied between $200$ V and $400$ V, in order
to achieve different doping levels. Both magnetrons were pre-sputtered for 12
minutes prior to deposition, in order to reach steady-state conditions before
opening the main shutter. Depositions typically lasted 2 to 6 hours.

Rutherford back scattering (RBS) measurements [65] were performed on the Si
witness samples to measure the composition and areal atomic density of the
films. Two ion beam configurations were implemented: a 2 MeV He ion beam to
obtain the classical Rutherford cross section of O, and a 3.9 MeV He ion beam
in order to separate the different peaks of Ta, Zr and Ar. The latter allowed
for a higher precision of the concentration of these elements but with less
precision on the O content, given the non-Rutherford cross-section and
charging effects. The incidence angle was set at $7^{\circ}$ and the
scattering angle at $170^{\circ}$ to maximize mass resolution. SIMNRA
simulations [67] were compared to the experimental spectra in order to extract
the composition and the areal atomic density of the deposited layers.
Uncertainties were estimated by varying the concentrations until the
simulation no longer fit the data. The resulting cation ratios $\eta=$
Zr/(Ta+Zr) are reported in Table 1, while the O content is discussed below.
The coatings contain $\sim$1.5% Ar, as expected for samples deposited in Ar
ambient. Elastic recoil detection analysis in other coatings usually also
reveals the presence of 1.5 to 3.0% of hydrogen. We expect this to be the case
in these films as well. No concentration gradients were identified within the
sensitivity of our measurements.

The mass density of the films was calculated by the following two methods. The
first one relies on the areal atomic density (at./cm2) and composition found
by RBS. Knowing the atomic mass, it was possible to compute the areal mass
density (g/cm2). The second method consisted in measuring the substrate mass
before and after deposition using a micro-balance, and dividing it by the
coated area. The latter was measured from a photograph, in order to account
for the area of the uncoated region near the edges of the sample. For both
methods, the areal density was divided by the thickness found by ellipsometry
(see Section 3.4). We note that for the density calculation based on RBS, due
to the presence of thickness gradients, both measurements needed to be carried
out at the same location to avoid discrepancies. Likewise, in the case of the
weighing method, it was important to consider an average thickness deduced
from the thickness mapping obtained by ellipsometry.

Figure 2: Areal mass density of Ta2O5-ZrO2 thin films grown via MS: values
measured by sample weighing are presented as a function of those measured by
RBS, for comparison. The black line shows the 1:1 relationship.

Figure 2 compares the areal mass density deduced from RBS measurements and by
weighing the samples, that is, without considering the thickness. We can
observe that both data sets closely follow a 1:1 relationship. Given the
independence of both methods, we can assume that the measured values are
accurate. Densities reported in Table 1 are average values between the two
methods.

##  3 Optical properties

The optical properties of the coating samples were characterized using
different techniques. Table 4 presents the measured values for the refractive
index $n$ at the wavelengths of interest (1064 and 1550 nm) for current and
future GW interferometers [39, 25, 45, 22]. Optical absorption at 1064 nm was
measured on RBTD single-layer samples and IBS multi-layer HR stacks. Light
scattering at 1064 nm was measured on IBS multi-layer HR stacks. At 1550 nm,
where only ellipsometric and photometric measurements were available,
extinction values were smaller than the sensitivity of the instruments
($k<10^{-3}$). Measurements and their analyses are described below. A
comparative summary is presented in Section 3.5, where correlations between
oxygen concentration, density and refractive index are discussed.

Sample | Process |  $\eta$ [at.%] | $n_{1064}$ | $n_{1550}$ |
---|---|---|---|---|---
MLD2014 | IBS | $48.5\pm 0.4$ |  |  |
MLD2018 | IBS | $50.2\pm 0.6$ | $2.08\pm 0.01$ |  |
LMA | IBS | 19 $\pm$ 1 | 2.09 $\pm$ 0.01 | 2.07 $\pm$ 0.01 |
UoS | ECR-IBD | $34.0\pm 0.5$ | 1.96 $\pm$ 0.01 | 1.95 $\pm$ 0.01 |
UMP 551 | RF-MS | 41 $\pm$ 3 | 2.01 $\pm$ 0.01 | 1.99 $\pm$ 0.01 |
UMP 554 | RF-MS | 43 $\pm$ 3 | 1.99 $\pm$ 0.01 | 1.97 $\pm$ 0.01 |
UMP 658 | HiPIMS | 24 $\pm$ 3 | 2.13 $\pm$ 0.01 | 2.11 $\pm$ 0.01 |
UMP 659 | HiPIMS | 24 $\pm$ 2 | 2.11 $\pm$ 0.01 | 2.10 $\pm$ 0.01 |
UMP 542 | HiPIMS | 7 $\pm$ 2 | 2.12 $\pm$ 0.01 | 2.11 $\pm$ 0.01 |
UMP 664 | HiPIMS | 7 $\pm$ 2 | 2.11 $\pm$ 0.01 | 2.10 $\pm$ 0.01 |
UMP 678 | HiPIMS | 47 $\pm$ 2 | 2.11 $\pm$ 0.01 | 2.10 $\pm$ 0.01 |
UMP 680 | HiPIMS | 47 $\pm$ 2 | 2.11 $\pm$ 0.01 | 2.10 $\pm$ 0.01 |
CSU II | RBTD | 23 $\pm$ 1 | 2.07 $\pm$ 0.01 | 2.06 $\pm$ 0.01 |
CSU III | RBTD | 54 $\pm$ 3 | 2.10 $\pm$ 0.01 | 2.09 $\pm$ 0.01 |
Table 4: Measured refractive index $n$ at 1064 and 1550 nm of co-sputtered
Ta2O5-ZrO2 thin films. RF-MS samples had Ta deposited by RF-MS and Zr
deposited by DC-MS, HiPIMS samples had Ta deposited by HiPIMS and Zr deposited
by RF-MS. Index values are plotted and discussed in Section 3.5.

###  3.1 IBS

####  3.1.1 MLD –

The manufacturer reported a refractive index of $n=2.08\pm 0.01$ at 1064 nm
for sample MLD2018. We measured the optical thickness dependence on
temperature for sample MLD2014 by monitoring the wavelength dependence of its
transmission spectrum extrema as a function of temperature [66], in the range
$\mathrm{89-411}$ ∘C. Typical fits to the extrema locations are shown in
Figure 3a. The measured coating optical thickness as a function of
temperature, shown in Figure 3b, is linear. Note that, due to uncertainty in
the physical thickness of the coating layer, optical thickness is not used
here to estimate the absolute value of the index, only the change with
temperature. The fractional optical thickness change as a function of
temperature was found to be

$\frac{1}{L}\frac{\mathrm{d}L}{\mathrm{d}T}=\alpha+\beta/n=(18.6\pm 1)\times
10^{-6}\,\mathrm{K^{-1}}\ ,$ (1)

where $\alpha$ is the thermal expansion coefficient and $\beta$ is the thermo-
optic coefficient.

(a)

(b)

Figure 3: Characterization of optical thickness dependence on temperature of
IBS Ta2O5-ZrO2 thin film MLD2014. (a) Transmission spectrum extrema with
parabolic fits to determine the extrema locations as a function of
temperature. Higher temperatures shifts the extrema to longer wavelengths,
indicating an increasing optical thickness with temperature. (b) Optical
thickness of the coating as a function of temperature.

####  3.1.2 LMA –

Refractive index and thickness of as-deposited coating samples were determined
by spectroscopic ellipsometry, via coupled analysis of data sets acquired with
two different J. A. Woollam commercial instruments covering complementary
spectral regions: a VASE for the 190-1100 nm range and a rotating-compensator
M-2000 for the 245-1700 nm range. The wide range swept with both instruments
allowed us to extend the analysis from ultraviolet to near infrared (0.7 - 6.5
eV). Consistent results were obtained in the overlapping range, within the
uncertainty of the models used to fit the data. Analysis was carried out
independently for VASE and M-2000 data, and eventually the information was
combined in order to obtain the final results.

The optical constants were obtained by measuring the amplitude ratio $\Psi$
and phase difference $\Delta$ of the p- and s-polarized light [61] reflected
by the samples at different incidence angles $\theta=55$°, $60$°, $65$°, close
to the coating Brewster angle. The optical response of the substrates (silicon
wafers with a thin native oxide layer and unpolished rear surface in order to
avoid backside spurious reflections) was characterized with prior dedicated
measurements and analyses [19]. As in previous works on similar systems [19,
51], we analyzed the data through a three-layer model consisting of substrate,
thin film and surface layer. The latter, accounting for surface roughness, was
defined via a Bruggeman effective medium approximation. The resulting coating
roughness was less than 1 nm, a value comparable with those measured with an
atomic-force microscope on similar samples [51]. Being less than 1% of the
coating thickness, the surface layer did not affect substantially the data
fit, especially in the near-infrared region.

The dielectric functions were reconstructed by using Kramers-Kronig-consistent
Tauc-Lorentz [8] and Cody-Lorentz [74] models. Both models fit the data with
comparable mean squared error, and yielded consistent results. We then
obtained the complex refractive index of the as-deposited thin films from the
best-fit dielectric functions. The Cody-Lorentz model provided a slightly
better fit in the region of the absorption edge and included also the Urbach
tail absorption, which may be correlated to coating mechanical loss [10].
However, data quality for energies higher than the energy gap ($E>4$ eV) was
degraded and resulted in a large uncertainty for the Urbach energy
$E_{U}=130\pm 30$ eV.

All measured spectra were fit with the same accuracy. Figure 4 shows exemplary
spectra acquired at $\theta=55^{\circ}$ and their best fits with a Cody-
Lorentz model. Figure 5a shows the reconstructed coating optical constants,
and Figure 5b is a Cody plot highlighting the coating energy gap,
$E_{g}=4.1\pm 0.1$ eV, which is consistent with that of pure tantala coatings
produced under strictly identical conditions [19].

Figure 4: Measured ellipsometric spectra of an as-deposited IBS Ta2O5-ZrO2
thin film (LMA), acquired at an incidence angle $\theta$ = 60∘. The best-fit
Cody-Lorentz model is shown (dashed line).

(a)

(b)

Figure 5: Measured optical properties of as-deposited IBS Ta2O5-ZrO2 thin
films (LMA): (a) refractive index $n$ and extinction coefficient $k$ as
function of photon energy $E$, the region of interest for present GW detectors
is around $E=1.2$ eV (corresponding to a wavelength of 1064 nm); (b) Cody plot
highlighting the energy gap $E_{g}$.

After annealing at 500 ∘C in air for 10 hours, single-layer coating samples
were characterized in their transparent region (400-1400 nm) with a Perkin
Elmer Lambda 1050 spectrophotometer, at normal incidence. The annealing
reduced the refractive index in the near-infrared region by about 3%. Samples
of HR stacks, also annealed at 500 ∘C in air for 10 hours, were characterized
for optical absorption and light scattering with a custom-developed setup
based on the photo-thermal deflection principle [12] and a commercial CASI
scatterometer, respectively. We measured an optical absorption of 0.5 parts
per million (ppm), and 45 ppm of scattered light.

###  3.2 ECR-IBD

Optical-transmission spectra of as-deposited films, shown in Figure 6, were
measured in the 250-2100 nm range using a Varian 5000 spectrophotometer and
fit to transmission simulations using SCOUT software by WTheiss. At 1064 nm
and 1550 nm, the refractive index $n$ was found to be $1.96\pm 0.01$ and
$1.95\pm 0.01$, respectively, and the extinction coefficient $k<10^{-3}$.

Figure 6:  Refractive index $n$ and extinction coefficient $k$ as function of
photon energy for as-deposited ECR-IBD Ta2O5-ZrO2 thin films with cation ratio
of 0.34.

###  3.3 RBTD

Refractive index and extinction coefficient for the films were determined by
spectroscopic ellipsometry using a Horiba UVISEL ellipsometer. Measurements
were taken at an angle of $60^{\circ}$, for a spectral range of 0.59 - 6.5 eV.
The films were evaluated as deposited and after annealing at the maximum
temperature for which no crystallization was detected and mechanical loss
minimized. A reduction of the refractive index was found after annealing,
which could be due to oxygen incorporation during the process or due to
formation of Ar bubbles [42]. Films previously grown by our group were found
to contain 3 to 5 % of Ar. When Ar bubbles are formed and coalesce upon
annealing, the films usually feature a reduction in the refractive index that
is accompanied by an increase in thickness. In our case, however, the
thickness did not increase after annealing within the resolution of the
instrument, indicating no significant presence of Ar bubbles in the coatings.

The dispersion of refractive index $n$ and extinction coefficient $k$ are
presented in Figure 7. The refractive index for both annealed films is
presented in Table 4. The film with the largest cation ratio featured the
highest refractive index, as expected, given that the refractive index of
zirconia is higher than that of tantala.

(a)

(b)

Figure 7:  Refractive index $n$ and extinction coefficient $k$ as function of
photon energy for RBTD Ta2O5-ZrO2 thin films: (a) cation ratio $\eta=0.23$,
annealed at 800 ∘C for 10 hours; (b) cation ratio $\eta=0.54$, annealed at 600
∘C for 10 hours.

Optical absorption at $\lambda$ = 1064 nm was determined by photothermal
common-path interferometry [18]. We define the absorption normalized to a
quarter wave thickness as

$\alpha_{\textrm{\tiny{QWT}}}=\frac{\alpha}{d}\frac{\lambda}{4n}\ ,$ (2)

with $\alpha$ being the absorption as measured ppm, $n$ the refractive index,
$d$ the coating thickness and $\lambda=1064$ nm.
$\alpha_{\textrm{\tiny{QWT}}}$ was 4.4 $\pm$ 0.8 for the film with cation
ratio $\eta=0.54$ and 1.85 $\pm$ 0.05 for the film with cation ratio
$\eta=0.23$. These results are summarized in Table 5.

Film |  $T_{a}$ [∘] | Cation ratio $\eta$ |  $\alpha_{\textrm{\tiny{QWT}}}$ @ 1064 nm ppm)
---|---|---|---
CSU II | 800 | 0.23 | 1.85 $\pm$ 0.05
CSU III | 600 | 0.54 | 4.4 $\pm$ 0.8
Table 5: Absorption loss normalized to a quarter wave thickness
$\alpha_{\textrm{\tiny{QWT}}}$ at 1064 nm for RBTD Ta2O5-ZrO2 thin films
annealed at the maximum temperature $T_{a}$ before crystallization (see
Sections 5. See Eq. (2) for more details.

###  3.4 HiPIMS/RF-MS

Similarly to what is described in Sections 3.1.2 and 3.3, spectroscopic
ellipsometry was carried out between wavelengths of 210 nm and 2500 nm with a
J. A. Woollam Co., Inc. RC2-XI ellipsometer. Data analysis to obtain the
complex refractive index and thickness mappings were carried out using the J.
A. Woollam CompleteEASE software, with the optical properties being
represented by a general oscillator model consisting of a Tauc-Lorentz and
Gaussian oscillators for the UV absorption. The model parameters were first
fit for each sample from a series of measurements at four different incidence
angles, $45^{\circ}$, $55^{\circ}$, $65^{\circ}$ and $75^{\circ}$, carried out
at the center of the sample. The average thickness of the samples was then
established through a mapping of 48 points, measured at $70^{\circ}$ where
only the thickness and surface roughness (Bruggeman effective medium
approximation) were fit while keeping the optical model constant. The measured
refractive index at 1064 and 1550 nm of all HiPIMS/RF-MS samples is presented
in Table 4.

###  3.5 Comparative summary

Figure 8a shows the refractive index values at 1064 nm and 1550 nm reported in
Table 4 as a function of the cation ratio $\eta=$ Zr/(Zr+Ta). The solid line
corresponds to the rule of mixtures, assuming bulk values for pure oxides. The
low dependence on $\eta$ is expected, since tantala and zirconia have a
similar refractive index at these wavelengths. Samples deposited by HiPIMS,
IBS and RBTD feature values close to the rule of mixture. For samples where
tantala is deposited by RF-MS or when the coating is deposited by ECR-IBD, the
refractive index is significantly lower.

Figure 8: Correlation between oxygen concentration, density and refractive
index of co-sputtered Ta2O5-ZrO2 thin films, as a function of cation ratio
$\eta=$ Zr/(Ta+Zr): (a) refractive index at 1064 nm (filled markers) and 1550
nm (empty markers), the black solid line is the value expected from the rule
of mixtures at 1064 nm when considering the refractive index found in Ref.
[80] for bulk zirconia and Ref. [77] for that of bulk tantala; (b) oxygen
concentration; (c) density. The solid lines in (b) and (c) are the expected
oxygen content and density, respectively, according to the rule of mixture and
assuming stoichiometric tantala and zirconia for the oxygen content, and
density values for Ta2O5 and ZrO2 taken from the literature [31, 7]. Red
pentagons and blue triangles denote HiPIMS and RF-MS samples, respectively,
while yellow circle, orange squares and green diamonds denote ECR-IBD, IBS
(LMA) and RBTD samples, respectively.

In Figure 8b, we find that the oxygen content in the layers where tantala is
deposited by HiPIMS follows the rule of mixture between stoichiometric tantala
and zirconia, while there is an excess of oxygen in the films where tantala
was deposited by RF-MS. Accordingly, as shown by Figure 8c, the density of
films where tantala is deposited by HiPIMS or IBS follow the rule of mixture
considering bulk densities of tantala and zirconia [31, 7], while those where
tantala was deposited by RF-MS show a significantly lower density. Hence, the
excess of oxygen leads to films with lower density and correspondingly lower
refractive index. The explanation partly lies in the fact that atoms, when
deposited by HiPIMS, have a higher kinetic energy than in RF-MS, which
produces more compact films with less chances to have, for example, two oxygen
atoms on the same bond. It is worth noting that we did not attempt to grow
stoichiometric RF-MS layers, for example by changing the O2:Ar ratio during
deposition, as we wanted to compare HiPIMS and RF-MS under the same
conditions.

Our results show the correlation between the oxygen concentration, the
density, and the refractive index. Techniques such as HiPIMS and IBS feature
atomic fluxes with higher kinetic energy, leading to higher dissociation rates
of oxygen. This means that less oxygen may be used in the Ar/O2 mixture to
obtain stoichiometry. Also, the higher energy of species impinging on the
growing film surface leads to coatings of higher density. Conversely, RF-MS
films are generally less dense and have a lower refractive index. However,
pores are frequently filled with water vapour that adds oxygen and hydrogen,
leading to apparent oxygen over-stoichiometry. The former may therefore have
more desirable properties for optical components. We will see in Section 4 how
that affects the loss angle.

##  4 Mechanical properties

The mechanical loss $\varphi_{c}$, Young modulus $Y_{c}$ and Poisson ratio
$\nu_{c}$ of the coating materials were measured using different setups, all
based on the ring-down technique [70]: the mechanical resonances (modes) of a
suspended coated resonator are excited using an actuator, and the amplitude of
their ring-down oscillations is monitored using an optical transducer. For a
resonating mode of frequency $f$ and ring-down time $\tau$, the measured
mechanical loss angle is $\varphi=(\pi f\tau)^{-1}$. The coating loss angle
$\varphi_{c}$ can be calculated as

$\varphi_{c}=\frac{\varphi+(D-1)\varphi_{s}}{D}\ ,$ (3)

where $\varphi_{s}$ is the measured loss angle of the substrate, $\varphi$ is
the measured loss angle of the coated sample and $D$ is a so-called dilution
factor, defined as the ratio of the coating elastic energy to the total
elastic energy of the coated sample.

Coated samples were suspended under vacuum, in order to prevent systematic
damping from ambient pressure. We used different suspension systems, each one
specifically adapted to the different geometries of the substrates used as
resonators. Because of the different suspension systems and samples, we used
also different methods to estimate the dilution factor and the coating Young
modulus and Poisson ratio. Specific measurements and their analyses are
described in the following.

Results are summarized in Table 6, where an average coating loss
$\overline{\varphi}$, taken from every set of resonant modes of each sample,
is used to ease comparisons. A comparative summary is presented in Figures 17
and 18 of Section 4.5, where the effects of different cation ratios $\eta=$
Zr/(Zr+Ta) and annealing temperatures $T_{a}$ on the coating mechanical loss
are discussed.

Sample | Process |  $T_{a}$ [∘C] |  $\eta$ [at.%] |  $\overline{\varphi}$ [$10^{-4}$ rad] |  $Y_{c}$ [GPa] | $\nu_{c}$
---|---|---|---|---|---|---
MLD2014 | IBS | 800 | $48.5\pm 0.4$ | $4.26\pm 0.11$ | $130.5\pm 2$ |
MLD2018 | IBS | 700 | $50.2\pm 0.6$ | $1.82\pm 0.04$ |  |
LMA | IBS | 700 | 19 $\pm$ 1 | 4.41 $\pm$ 0.68 | 120 $\pm$ 3 | 0.32 $\pm$ 0.01
UoS | ECR IBD | 750 | $34.0\pm 0.5$ | 3.64 $\pm$ 0.45 | $176\pm 8$ |
UMP 551 | RF-MS | 800 | 41 $\pm$ 3 | 2.36 $\pm$ 0.85 | 125 $\pm$ 2 | 0.21 $\pm$ 0.05
UMP 554 | RF-MS | 800 | 43 $\pm$ 3 | 2.52 $\pm$ 0.82 | 114 $\pm$ 2 | 0.36 $\pm$ 0.03
UMP 658 | HiPIMS | 700 | 24 $\pm$ 3 | 5.59 $\pm$ 0.90 | 110.6 $\pm$ 1.2 | 0.31 $\pm$ 0.02
UMP 659 | HiPIMS | 700 | 24 $\pm$ 2 | 5.04 $\pm$ 1.53 | 108 $\pm$ 5 | 0.35 $\pm$ 0.05
UMP 542 | HiPIMS | 600 | 7 $\pm$ 2 | 5.69 $\pm$ 0.37 | 100.6 $\pm$ 1.1 | 0.34 $\pm$ 0.02
UMP 664 | HiPIMS | 650 | 7 $\pm$ 2 | 4.45 $\pm$ 0.38 | 116.5 $\pm$ 1.3 | 0.33 $\pm$ 0.02
UMP 678 | HiPIMS | 800 | 47 $\pm$ 2 | 4.38 $\pm$ 0.63 | 111 $\pm$ 4 | 0.28 $\pm$ 0.09
UMP 680 | HiPIMS | 800 | 47 $\pm$ 2 | 4.87 $\pm$ 0.92 | 110 $\pm$ 4 | 0.28 $\pm$ 0.09
CSU II | RBTD | 800 | 23 $\pm$ 1 | 3.22 $\pm$ 0.53 | 145 $\pm$ 6 | 0.30 $\pm$ 0.09
CSU III | RBTD | 600 | 54 $\pm$ 3 | 2.67 $\pm$ 0.15 | 143 $\pm$ 5 | 0.37 $\pm$ 0.05
Table 6: Measured mechanical properties of co-sputtered Ta2O5-ZrO2 thin films:
frequency-averaged mechanical loss $\overline{\varphi}$ of samples annealed at
the highest peak temperature $T_{a}$ before the onset of crystallization,
Young modulus $Y$, Poisson ratio $\nu$. RF-MS samples had Ta deposited by RF-
MS and Zr deposited by DC-MS, HiPIMS samples had Ta deposited by HiPIMS and Zr
deposited by RF-MS. RF-MS, HiPIMS and IBS (LMA) samples have been annealed for
10 hours, ECR-IBD samples for 5 hours. Average coating loss values are plotted
in Figures 17 and 18 and discussed in Section 4.5.

###  4.1 IBS

####  4.1.1 MLD –

The coating samples used to measure coating mechanical loss, Young modulus and
Poisson ratio were grown on fused-silica disks and cantilevers and on silicon
cantilevers (see Section 2.1.1). Samples grown on fused-silica substrates were
used for measurements at ambient temperature, those on silicon cantilevers to
perform cryogenic measurements.

Disks – The mechanical loss measurements were performed at Hobart and William
Smith Colleges, where the disks were welded to monolithic fused-silica fibers
and suspended. The mechanical loss of the lowest eight vibrational modes of
the disks, which span the frequencies from 2.5 to 18 kHz, were measured by
resonating the samples using an electrostatic comb exciter and then measuring
the ring-down using an ellipsometry readout [30]. Each mode was measured
several times with both weighted and unweighted averages retained.

After each set of measurements, the samples have been annealed and remeasured.
The annealing temperatures were 300, 600, 650, 700, 750 and 800 ∘C for MLD2014
and 400, 600 and 700 ∘C for MLD2018. For these experiments, the fused silica
substrate is typically annealed to high temperature before being coated. The
MLD2018 disk was properly annealed at 950 ∘C, whereas the MLD2014 disk was not
annealed prior to coating. For the latter sample, the substrate loss was
determined from the data using the frequency dependence of the loss as
determined by finite-element modeling. The model, created using COMSOL, was
used to calculate the dilution factor for the total coating loss and for the
decomposition of the coating loss into bulk and shear loss [78].

As shown in Figure 9, the coating loss for both samples decreased with
increasing annealing temperature, until reaching a minimum at 700 ∘C. A linear
fit of the frequency-dependent coating loss after annealing at 700 ∘C gave:

$\varphi_{c}\left(f\right)=\left(9.29\pm 0.09\right)\times
10^{-9}\,\mathrm{Hz}^{-1}\,\,f+\left(2.907\pm 0.007\right)\times 10^{-4}$ for
MLD2014

$\varphi_{c}\left(f\right)=\left(5.7\pm 0.2\right)\times
10^{-9}\,\mathrm{Hz}^{-1}\,\,f+\left(3.87\pm 0.02\right)\times 10^{-4}$ for
MLD2018.

(a)  (b)

Figure 9: Coating loss as a function of frequency for IBS Ta2O5-ZrO2 thin
films, as measured on suspended disks: (a) sample MLD2014, (b) sample MLD2018.
The loss is steadily reduced with increased annealing temperature $T_{a}$,
until reaching a minimum near 700 ∘C. A linear fit is shown (black line) for
the data sets of the 700-∘C annealing.

(a)  (b)

Figure 10: Comparison of analysis methods, as applied to coating loss data of
IBS Ta2O5-ZrO2 thin films (MLD) measured on suspended disks: (a) fit with
single loss angle, (b) fit with bulk and shear loss angles. The need for
separate analysis of bulk and shear coating loss angle is pointed out by the
improved fit of panel (b).

The variation in the ratio of bulk and shear energy with mode shape, which in
turn depends on frequency, introduces a scatter of the data about any function
of a single coating loss angle. Instead, a decomposition of the coating loss
into shear and bulk components allows a more precise fit to the data, as shown
in Figure 10. A fit of each data set to bulk and shear coating loss resulted
in the dependence of these values with annealing temperature $T_{a}$ shown in
Figure 11: the shear loss steadily decreased for increasing $T_{a}$, whereas
the bulk loss showed no clear dependence.

(a)  (b)

Figure 11: Bulk and shear coating loss as function of annealing temperature
for IBS Ta2O5-ZrO2 thin films, as measured on suspended disks: (a) sample
MLD2014, (b) sample MLD2018. The shear loss is steadily reduced with increased
annealing temperature, while the bulk loss shows no clear dependence.

The coating Young modulus was measured after annealing at two different
temperatures, using a nano-indentation facility at the California Institute of
Technology. The results, $Y=130\pm 2$ GPa for MLD2018 annealed at 800 ∘C and
$Y=131\pm 2$ GPa for MLD2014 annealed at 600 ∘C, assume a coating Poisson
ratio of 0.298 determined by molecular dynamics models [63].

Cantilevers – The mechanical loss of the MLD2018 coating was measured also on
a fused-silica cantilever at ambient temperature, and on silicon cantilevers
at cryogenic temperatures. Measurements were performed at the Institute for
Gravitational Research of the University of Glasgow.

The cantilevers were mounted in a clamp, under vacuum, and their bending modes
were excited using an electrostatic actuator. The amplitude of the ring-down
motion was monitored using an optical shadow sensor. The coating mechanical
loss was then calculated using Eq. (3) and

$D=\frac{3Yd}{Y_{s}d_{s}}\ ,$ (4)

where $Y$ and $d$ are the coating Young modulus and thickness, respectively,
and $Y_{s}$ and $d_{s}$ are the substrate Young modulus and thickness,
respectively.

After each set of measurements, the coated fused-silica cantilever was
progressively annealed at increasing peak temperatures, up to 500 ∘C. Figure
12 shows the effect of annealing on the coating mechanical loss as a function
of frequency, and that the coating mechanical loss at $1$ kHz decreased by
over a factor of three upon annealing, from $\overline{\varphi}=1.1\times
10^{-3}$ in its as-deposited state to $\overline{\varphi}=3.2\times 10^{-4}$
after a 500∘C annealing.

Figure 12: Coating loss of IBS Ta2O5-ZrO2 thin film MLD2018, as measured on a
clamped $\sim$100-$\mu$m thick fused-silica cantilever at ambient temperature:
(a) the loss was measured as a function of frequency on the as-deposited
sample, then re-measured after progressive annealings at 300, 400 and 500 ∘C;
(b) frequency-averaged coating loss $\overline{\varphi}$ as a function of
annealing temperature. The coating loss decreased after each annealing
treatment.

The coated silicon cantilevers were measured in a temperature-controlled,
liquid-helium-cooled cryostat [73]. The coating mechanical loss was calculated
using Eqs. (3) and (4) for a large number of resonant modes, from $\sim$1 to
30 kHz, as extensively detailed in [73]. Here, for sake of conciseness, we
present in Figure 13 only the coating loss of the third- and fourth-order
bending modes, at $\sim$1.4 kHz and $\sim$2.7 kHz respectively.

Figure 13: Cryogenic mechanical loss of IBS Ta2O5-ZrO2 coatings as a function
of sample temperature, as measured on clamped $\sim$65-$\mu$m thick silicon
cantilevers: (a) results for the third-order bending mode at $\sim$1.4 kHz,
(b) results for the fourth-order bending mode at $\sim$2.7 kHz. The coating
loss of sample MLD2018 as deposited and after a 300-∘C annealing and of sample
MLD2014 after 600-∘C and 800-∘C annealing are shown, and compared to data of
IBS amorphous Ta2O5 and poly-crystalline Ta2O5-TiO2 samples annealed to 600 ∘C
[38, 47]. Finite-element representations of the measured resonant mode are
visible at the bottom of each plot.

Figure 13 shows that IBS Ta2O5-ZrO2 coating in its as-deposited state has a
very small and broad loss peak of $\sim$6$\times 10^{-4}$ at $\sim$30 K. This
peak narrowed to $1\times 10^{-3}$ after annealing at 300 and 400 ∘C, and
further increased to $1.2\times 10^{-3}$ after an 800 ∘C anneal. Below 100 K,
the coating loss temperature-dependent trend of the annealed Ta2O5-ZrO2
samples is similar to that of pure IBS Ta2O5 films annealed at 600 ∘C [38].
After annealing at 800 ∘C, the coating loss of Ta2O5-ZrO2 does not show the
large and broad loss peak observed at 80 K for IBS poly-crystalline Ta2O5 thin
films annealed to the same temperature [38]. This is a clear indication that
co-sputtering ZrO2 with Ta2O5 prevented the onset of crystallization for
annealing at 800 ∘C.

As shown in Figure 12, annealing reduced the coating loss at ambient
temperature. At the same time, Figure 13 suggests that annealing increased the
coating loss at low temperatures, which is the opposite of what has been
observed on IBS poly-crystalline Ta2O5-TiO2 [47]. This is of interest for
further understanding of coating loss and structure and modelling, and
suggests that different values of the cation ratio $\eta=$ Zr/(Zr+Ta) need to
be investigated at low temperatures.

####  4.1.2 LMA –

We used a Gentle Nodal Suspension (GeNS) system [20] to measure coating
mechanical loss, Young modulus and Poisson ratio via the direct measurement of
the disk dilution factor [43]. As a matter of fact, the dilution factor $D$ in
Eq. (3) can be written as a function of the resonator mode frequency ($f_{0}$,
$f$) and mass ($m_{0}$, $m$) before and after coating deposition, respectively
[41]:

$D=1-\left(\frac{f_{0}}{f}\right)^{2}\ \frac{m_{0}}{m}\ .$ (5)

The advantage of measuring the dilution factor is that the ensuing coating
loss estimation is then exclusively based on measured quantities: sample loss
angle, mode frequency and mass. Therefore, unlike other experimental setups
based on the ring-down method, our method does not require prior knowledge of
coating Young modulus and thickness. Furthermore, one can estimate coating
Young modulus $Y$ and Poisson ratio $\nu$ by fitting the results of finite-
element simulations to measured values of $D$ estimated via Eq. (5). Compared
to nano-indentation, such method does not rely on the prior knowledge of
$\nu$, and does not depend on the nature of the substrate used nor on the
model chosen for data analysis [43]. Figure 14a shows best-fit results for
three mode families of different shapes and frequency [43], giving $Y=120\pm
3$ GPa and $\nu=0.32\pm 0.01$. Details about our fitting method and finite-
element simulations can be found elsewhere [43, 33].

Figure 14b shows the coating loss angle before and after consecutive annealing
treatments at 500, 600 and 700 ∘C for 10 hours, in air. As expected, the
annealing reduced the coating loss. However, the coating showed cracks after
the 700 ∘C annealing. This issue is further discussed in Section 5.

(a)

(b)

Figure 14: Measured mechanical properties of IBS Ta2O5-ZrO2 thin films (LMA)
as a function of frequency, as measured on a disk suspended with a GeNS
system: (a) measured and best-fit simulated dilution factor $D$, for the first
three families of disk mode shapes [43]; (b) coating loss angle $\varphi_{c}$,
as measured after deposition and after annealing treatments at 500, 600 and
700 ∘C for 10 hours, in air. Data of the annealed Ta2O5-TiO2 layers of
Advanced LIGO and Advanced Virgo is also shown, for comparison [43]. Dashed
lines are least-squares fits using a power-law model $\varphi_{c}(f)=af^{b}$,
best-fit parameters $a$ and $b$ are presented in Table 7. Values at $f<1$ kHz
are model extrapolations.

We used a power-law model $\varphi_{c}(f)=af^{b}$ to describe the observed
frequency-dependent behavior of the coating internal friction [62, 26, 28],
and applied least-squares linear regression in order to fit the data. Best-fit
parameters are presented in Table 7. It is worth noting that the $b$ parameter
increased after each annealing step, implying lower loss values in the most
sensitive region (50-300 Hz) of GW detectors. Thus, by extrapolating our
results to lower frequency, we obtain a loss angle of $1.8\times 10^{-4}$ at
100 Hz for the Ta2O5-ZrO2 annealed at 700 ∘C. This value has to be compared to
$2.4\times 10^{-4}$ for the Ta2O5-TiO2 layers of GW detectors [43].

$T_{a}$ [∘C] |  $a$ [$10^{-4}$ rad Hz-b] | $b$
---|---|---
0 | 4.4 $\pm$ 0.4 | 0.05 $\pm$ 0.01
500 ℃ | 1.6 $\pm$ 0.2 | 0.13 $\pm$ 0.01
600 ℃ | 1.7 $\pm$ 0.2 | 0.12 $\pm$ 0.01
700 ℃ | 0.8 $\pm$ 0.1 | 0.18 $\pm$ 0.02
Table 7: Best-fit parameters of a power-law internal friction model
$\varphi_{c}(f)=af^{b}$ for data sets of IBS Ta2O5-ZrO2 thin films (LMA)
measured on a disk suspended with a GeNS system, as function of annealing peak
temperature $T_{a}$ (as-deposited coating samples are denoted by $T_{a}=0$
∘C), shown in Figure 14b. Each annealing treatment was performed in air and
lasted 10 hours.

###  4.2 ECR-IBD

The coating mechanical loss at ambient temperature was characterized using
fused-silica cantilevers. They were mounted in a stainless steel clamp within
a vacuum chamber with residual pressure pressure below $5\times 10^{-6}$ mbar,
and excited using an electrostatic actuator [53]. The freely-decaying
amplitude of the resonant motion was monitored using an optical shadow sensor.
We then used Eqs. (3) and (4) to calculate the coating loss for the cantilever
bending modes [4], and the results are presented in Section 4.5.

The same method was applied to perform cryogenic loss measurements of coated
silicon cantilevers, whose results are shown in Figure 15 for the the third-
and fourth-order bending modes at $\sim$1.4 kHz and $\sim$2.7 kHz,
respectively, and compared to the results obtained for the IBS sample MLD2018
(see Section 4.1.1 and Figure 13). Below $\sim$100 K, both the ECR-IBD and IBS
as-deposited Ta2O5-ZrO2 coatings have a lower coating loss than that of as-
deposited IBS Ta2O5 [38]. This shows that, prior to annealing, the addition of
ZrO2 already reduced the coating loss at low temperature. Below 30 K, the loss
of the ECR-IBD coatings is comparable to that of IBS coatings.

Figure 15 also shows the data of coating loss for an ECR-IBD Ta2O5-ZrO2
coating sample grown on a substrate held at 200 ∘C. By comparing the ECR-IBD
samples, it can be seen that heating the substrate to a higher temperature had
a considerable effect on the low-temperature coating loss, between 100 and 200
K: for instance, the coating loss of the sample grown at 200 ∘C is 1.8 times
smaller at 200 K. Finally, we found that the coating loss of the ECR-IBD
sample grown at 200 ∘C is similar to that of the IBS sample MLD2018 in its as-
deposited state.

Figure 15: Cryogenic mechanical loss of as-deposited ECR-IBD Ta2O5-ZrO2
coatings as a function of sample temperature, as measured on clamped
$\sim$65-$\mu$m thick silicon cantilevers: (a) results for the third-order
bending mode at $\sim$1.4 kHz, (b) results for the fourth-order bending mode
at $\sim$2.7 kHz. Data of an ECR-IBD sample grown through standard deposition
(blue markers) and that of an ECR-IBD grown on a substrate held at 200 ∘C
(green markers) are shown, and compared to the data of as-deposited IBS
Ta2O5-ZrO2 MLD2018 (see Figure 13) and Ta2O5 [38] coating samples. Finite-
element representations of the measured resonant mode are visible in each
plot.

Coating Young modulus $Y$ was measured using a Bruker Hysitron TriboScope
nano-indenter system, with a three-sided Berkovich pyramid diamond tip
($Y_{\textrm{\footnotesize{indenter}}}=1140$ GPa, and
$\nu_{\textrm{\footnotesize{indenter}}}=0.007$) and found to be $176\pm 8$
GPa, assuming a coating Poisson ratio of $\nu=0.297$ determined by molecular
dynamics models [63]. Measurements were taken on as-deposited thin films grown
on 1-mm thick JGS-1 fused-silica witness samples, following the Oliver–Pharr
method [79].

###  4.3 RBTD

Coating mechanical loss, Young modulus and Poisson ratio were estimated by
measuring suspended coated fused-silica disks. The disks were measured by the
LIGO Laboratory group at the California Institute of Technology, in a setup
with four independent GeNS systems [20] installed in the same vacuum chamber
to simultaneously measure all the accessible resonant modes of four samples
[56].

Prior to coating deposition, the resonant frequencies and mechanical loss of
the disks were characterized through specific measurements, which served as a
reference and for background noise estimation for the subsequent series of
measurements performed after deposition. All surfaces of the bare disks,
including the edge, were polished to a standard optical grade to reduce the
contribution of substrate surface losses [71, 28].

After coating deposition, the disks were measured again, and then repeatedly
annealed at increasing peak temperature $T_{a}$, from 300 to 800 ∘C. After
each annealing treatment, the resonant frequencies and mechanical loss of the
disks were measured. Knowing the coating thickness and density from the
previous characterizations (see Sections 2 and 3), it was possible to compute
the coating elastic properties, i.e. Young modulus $Y$ and Poisson ratio
$\nu$, with a procedure similar to what explained in [41] and in [57] and to
what was done in analyzing the LMA sample. The measured elastic properties,
with their estimation uncertainties, were then used to compute the dilution
factors $D$ and extract the coating loss angle according to Eq. (3). The
results are presented in Table 6 and Figures 17 and 18, and discussed in
Section 4.5.

###  4.4 HiPIMS/RF-MS

Coating mechanical loss, Young modulus $Y$ and Poisson ratio $\nu$ were
measured on suspended coated fused-silica disks by the LIGO Laboratory group
at the California Institute of Technology, using the same setup and analysis
methods described in Section 4.3.

HiPIMS coating samples with different cation ratios $\eta=$ Zr/(Zr+Ta) were
produced, in order to determine how ZrO2 content affects the loss angle. Also,
as mentioned in Section 3.5, RF-MS coating samples were grown with the same
Ar:O2 gas ratio, which had higher oxygen content and hence lower densities and
refractive index. Samples were then annealed at increasing peak temperature
$T_{a}$ by steps of 50 and 100 ∘C, starting from 400 ∘C, until they showed
signs of crystallization. The annealing time for each soaking temperature
$T_{a}$ was 10 hours. Depending on the cation ratio, the onset of
crystallization was observed at temperatures which ranged from $T_{a}=700$ ∘C
to $T_{a}=850$ ∘C.

Figure 16 presents the coating loss angle as a function of the cation ratio
$\eta$ at $650$ ∘C, where it can be seen that most values are overlapping.
This means that, within the uncertainties of the measurements, $\eta$ does not
considerably affect the coating loss angle. Although still within measurement
uncertainty, however, RF-MS samples feature a slightly lower coating loss
angle. Therefore, even if HiPIMS samples were shown to be denser and closer to
stoichiometry than RF-MS samples, this did not translate into a decrease of
the coating loss angle.

Figure 16: Coating loss of HiPIMS (red markers) and RF-MS (blue markers)
Ta2O5-ZrO2 thin films as a function of cation ratio $\eta=$ Zr/(Zr+Ta), as
measured on suspended fused-silica disks after annealing at 650 ∘C. The dashed
black line represents the loss angle value of the annealed Ta2O5-TiO2 layers
of Advanced LIGO and Advanced Virgo [43].

###  4.5 Comparative summary

We discuss here the effects of different cation ratios $\eta=$ Zr/(Zr+Ta) and
annealing peak temperatures $T_{a}$ on the mechanical loss of our coating
samples, limiting our analysis to the results obtained at ambient temperature
so that we can compare samples from all the growth techniques presented in
this work. To ease comparison, an average coating loss $\overline{\varphi}$
can be taken from every set of measured resonant modes of each sample.

Figure 17 shows the resulting $\overline{\varphi}$ as a function of cation
ratio $\eta=$, where it can be seen that $\eta=$ does not affect significantly
the coating mechanical loss. Furthermore, coating loss seems to be fairly
independent of the technique used to grow the samples.

Figure 17: Frequency-averaged coating loss angle $\overline{\varphi}$ of all
the Ta2O5-ZrO2 coating samples considered in this work, as a function of
cation ratio $\eta=$ Zr/(Ta+Zr). Each panel corresponds to a different
annealing temperature $T_{a}$.

The samples were progressively annealed through steps of increasingly high
peak temperature $T_{a}$ to test the effect of annealing on coating loss. For
these experiments, the fused silica substrate is typically annealed to
temperatures higher than 900 ∘C before being coated. The high temperature
annealing of the bare substrate lowers its mechanical loss
($\varphi_{s}<10^{-7}$) such that it is negligible compared to the coating
loss. In addition, the substrate loss will not change with lower temperature
annealing cycles, so that any change in the coated sample loss may be
attributed solely to the coating.

Figure 18 shows that annealing significantly reduced the coating mechanical
loss, from about 10-3 for as-deposited samples down to $(2-4)\times 10^{-4}$
for samples treated at 800 ∘C.

Figure 18: Frequency-averaged coating loss angle $\overline{\varphi}$ of all
the Ta2O5-ZrO2 coating samples considered in this work, as a function of the
annealing temperature $T_{a}$ (as-deposited samples are denoted by $T_{a}=0$
∘C). The four panels group together different samples with similar cation
ratio $\eta=$ Zr/(Ta+Zr).

##  5 Effects of annealing

As expected, co-sputtering zirconia proved to be an efficient way to frustrate
crystallization in tantala thin films, allowing for a substantial increase of
the maximum annealing temperature $T_{a}$. Figure 19 shows that higher cation
ratios $\eta=$ Zr/(Zr+Ta) allowed to increase $T_{a}$ up to 800 ∘C, without
crystallization occurring. More specifically, IBS samples have been tested up
to 800 ∘C and no sign of crystallization was observed. RBTD sample CSU II
($\eta=0.23$) was amorphous after treatment at 800 ∘C. HiPIMS/RF-MS samples
showed signs of crystallization for temperatures ranging from 700 to 850 ∘C,
depending on the cation ratio $\eta$.

Figure 19: State of IBS, RBTD and HiPIMS/RF-MS Ta2O5-ZrO2 thin films after
annealing at temperature $T_{a}$, as a function of cation ratio $\eta=$
Zr/(Ta+Zr). The blue markers denote amorphous samples, while red ones indicate
that the transition to a poly-crystalline phase was observed. The dashed curve
shows the approximate limit of the phase transition as a function of $\eta$.

Figures 17 and 18 show that annealing significantly reduced the coating
mechanical loss, from about $\overline{\varphi}\sim 10^{-3}$ for the as-
deposited samples down to $\overline{\varphi}\sim(2-4)\times 10^{-4}$ for the
samples treated at 800 ∘C, whereas, within the measurement uncertainties, the
doping does not affect the loss angle for a given $T_{a}$.

However, cracks appeared on IBS (MLD), RBTD and HiPIMS/RF-MS samples after
annealing at 500 ∘C, and on IBS (LMA) samples after annealing at 700 ∘C.
Likely, this happened because of a mismatch between the thermal expansion
coefficients of the thin films and substrates, causing high thermal stress.
Although in principle our mechanical loss measurements are sensitive to such
defects, we found no evidence that our results were affected. At least for
some IBS samples (LMA), we found that the formation of cracks could be avoided
by decreasing the annealing heating and cooling rates down to 7 ∘C/h.

Nevertheless, starting from $T_{a}=500$ ∘C, bubble-like defects of different
number and size, detected with an optical microscope, appeared at variable
depth in the IBS HR coating samples, likely due to the presence of
incorporated argon within the layers [6, 42, 49]. We observed no trace of such
defects in the annealed IBS single-layer annealed samples deposited under
strictly identical conditions, indicating that this phenomenon only occurs
when layers are stacked. It is not clear how to avoid this issue yet, and we
are currently working to solve this problem.

At the same time, annealing at $T_{a}=500$ ∘C decreased the optical absorption
of the IBS HR samples down to 0.5 ppm.

##  6 Raman spectroscopy

Raman spectroscopy probes the vibrational modes of a material constituents. In
previous studies on amorphous silicon (a-Si), Roorda et al. found a
correlation between structural relaxation and the width of a peak in its Raman
spectrum [54]. A sharpening of the peak was interpreted as the results of a
decrease in the bond angle distribution upon annealing. Granata et al. also
found a correlation between the mechanical loss and the normalized area of a
Raman line in IBS and bulk silica [34]. Thus, it is of interest to see if
there is a correlation between the Raman spectra of Ta2O5-ZrO2 thin films and
their loss angle, via structural relaxation.

Raman spectroscopy was performed on the coated silica disks with a Renishaw
Invia Reflex microscope, with an Ar laser at a wavelength of 514 nm. The
measurement was performed three times at different locations on each sample,
then the spectra of each sample were averaged. It was carried out on all the
MS as-deposited samples and on seven MS samples after annealing at 800 ∘C.
Note that two of these annealed samples showed signs of crystallization, with
significant change in the coating Young modulus and loss angle measurements
(see Table 6 and Sections 4.4 and 4.5). Figure 20a presents an example of the
Raman spectrum measured on a crystallized sample, where the arrows identify
peaks associated with the crystal phase [37].

Tantala-zirconia has a complex structure, which translates into several peaks
in the Raman spectrum, some of them overlapping, and makes the data analysis
non-trivial. In addition, Ta2O5-ZrO2 thin films are transparent at 514 nm, so
that peaks from the underlying silica substrate also contribute to the
measured spectra. Therefore, the initial step of the analysis was to
decorrelate the contribution of the thin film from that of the substrate.
Figure 20a shows a Raman spectrum of an amorphous sample (red curve), with
superimposed a model (black) resulting from different contributions summed
together: (i) the spectrum of a bare silica substrate (blue), (ii) the
spectrum of a pure tantala thin film (green) obtained from a previous study
[31], (iii) a background contribution represented by an exponential (dashed
grey), (iv) additional contributions required so that the model correctly fit
the data (purple), which are then assumed to be due to the addition of
zirconia and which were modeled using four Lorentzian functions. Thanks to
this model, we can identify where the thin film is the main contributor to the
measured spectrum: referring to the purple curve of Figure 20a, this can be
seen to happen in the interval from 600 to 750 cm-1. An additional
contribution from the thin film is observed near 900 cm-1, but is less clearly
separated from the substrate signal and was disregarded in the following
analysis.

Next, we wanted to estimate the width of the Raman peak attributed to the thin
film. However, trying to subtract substrate contributions or using a fit model
would likely influence the shape of the peak, hence its width. To avoid this,
we rather relied directly on the experimental data: we calculated the maximum
slope of the raw signal on one side of the peak, at a location where the
coating contribution to the spectrum is dominant. Indeed, the slope of a peak
edge is a proxy for the peak width: for both Lorentzian and Gaussian
functions, the maximum slope is proportional to the inverse squared width.
Thus narrower peaks, which might be attributed to a more relaxed material,
should feature a steeper slope on each side. To this end, the raw spectra were
smoothed with a bi-cubic spline and normalized so that their maximum, in the
550 cm-1 to 750 cm-1 spectral region, where the contribution of the thin film
is at the highest, is at unity. We then computed the derivative, an example of
the result is found in Figure 20b.

Figure 20: Measured Raman spectra of HiPIMS/RF-MS Ta2O5-ZrO2 thin films and
their analysis: a) example of a spectrum obtained for an amorphous sample (red
line), with superimposed a model (black) resulting from different
contributions summed together (blue, green, dashed grey, see text for
details); b) derivative of the raw Raman spectrum, smoothed using bi-cubic
splines; c) raw, normalized spectrum of the same sample, as-deposited (blue)
and annealed (green). The slopes extracted using the derivative method shown
in b) are represented by straight lines. The vertical red line across all
panels is the position of the minimum of the first derivative of the Zr
contribution (purple curve) shown in a).

In all panels of Figure 20, the position of interest, i.e. the point where the
slope of the signal related to the Zr contribution is the steepest, is
represented by a vertical red line. In Figure 20c, we can see two raw spectra
of the same sample, acquired before and after annealing. The slope computed
using the spline fit at the Raman shift of interest is also plotted as a
straight line, for each spectrum. We can observe from the raw data that the
slope around 705 cm-1 changes upon annealing and are well represented by the
first derivative deduced from the method illustrated in Figure 20b.

Figure 21: Absolute value of the minimum of the derivative of the Raman
spectrum near 705 cm-1 as a function of the loss angle, for HiPIMS/RF-MS
Ta2O5-ZrO2 thin films. The color scale corresponds to the cation ratio $\eta=$
Zr/(Zr+Ta), circles denote spectra acquired on the as-deposited samples and
triangles denote those acquired on the annealed samples, the same sample being
linked by a black arrow. Red markers represent samples showing signs of
crystallization.

If Raman peaks sharpen with relaxation, and relaxation decreases the loss
angle, we expect a higher value of the derivative with decreasing loss angle.

Figure 21 shows the absolute value of the first derivative around 705 cm-1 as
a function of the loss angle, where the color scale represent the cation ratio
$\eta=$ Zr/(Zr+Ta). The red markers correspond to the two crystallized samples
which show characteristic peaks in their Raman spectrum, and most probably
some delamination, making their loss angle measurements unreliable. The
circles are for measurements carried out on as-deposited samples while the
triangles are for the annealed ones, and the same samples are linked by an
arrow pointing toward the annealed one.

Figure 21 clearly shows that, upon annealing, each individual sample sees its
peak slope increase and its loss angle decrease at the same time. Hence, the
Raman peak sharpens upon relaxation, similar to what is observed in a-Si [54].
However, if one considers only the subset of the as-deposited samples
(circles), it appears that the lower the loss angle, the lower the slope,
which means the Raman peaks are wider. Also, samples having the lowest loss
angle are the ones with the highest cation ratio $\eta$ (greener data points).
Hence, the shape of the Raman peak near 705 cm-1 cannot be attributed solely
to relaxation, as it is also clearly influenced by the micro-structural
modifications that large amounts of Zr induce into the thin films, which in
turn have an impact on the vibrational states distribution and hence on the
shape of the Raman spectrum.

Therefore, these results show that Raman spectroscopy could be used as a probe
to monitor the relaxation state of tantala-based alloys, and that relaxation
is linked to the loss angle. Similar conclusions were reached using X-ray
diffraction on tantala [31], where the X-ray peak of tantala sharpened with
decreasing loss angle. However, the Raman peak shape is also influenced by the
amount of doping, so that while it can be used to monitor the evolution of a
specific sample, it would be difficult to use it more generally as a probe of
the state of relaxation in a material or a predictor of the loss angle.

##  7 Summary and Conclusions

In order to decrease coating Brownian noise in current GW detectors, we
developed a set of co-sputtered tantala-zirconia thin films. We extensively
characterized these coatings for optical and mechanical properties, to test
their performances against the very stringent requirements of GW detectors.

As expected, co-sputtering zirconia proved to be an efficient way to frustrate
crystallization in tantala thin films, allowing for a substantial increase of
the maximum annealing temperature $T_{a}$, hence for a decrease of coating
mechanical loss. The lowest average loss, $\overline{\varphi_{c}}=1.8\times
10^{-4}$, was measured on IBS sample MLD2018 with cation ratio Zr/(Ta+Zr) =
48.5 $\pm$ 0.4 % annealed at 800 ∘C. This value has to be compared to
$\varphi_{c}=(2.3-3.4)\times 10^{-4}$ of tantala-titania layers in current GW
detectors [43, 75].

As measured on IBS HR samples with the same design of those of Advanced LIGO
and Advanced Virgo, we observed as little optical absorption (0.5 ppm) as in
current GW detectors [50, 23]. The same samples, however, featured an
unusually high value of scattering, 45 ppm, compared to that of present
detectors (5 ppm) [50, 23].

For some samples, we measured a refractive index at 1064 and 1550 nm higher
than that of pure tantala thin films. This implies that HR stacks containing
zirconia-doped tantala layers could be even thinner than HR coatings of
present detectors, further decreasing coating Brownian noise [44].

For use in future GW detectors, further development will be needed to decrease
scattering and to avoid the formation of bubble-like defects upon annealing.
We are currently working to find appropriate solutions to these issues.

## Acknowledgments

The research performed at the Laboratoire des Matériaux Avancés was partially
supported by the Virgo Coating Research and Development (VCR&D) Collaboration.

The work performed at U. Montréal and École Polytechnique de Montréal was
supported by the Natural Sciences and Engineering Research Council of Canada
(NSERC), the Canadian foundation for innovation (CFI) and the Fonds de
recherche Québec, Nature et technologies (FQRNT) through the Regroupement
Québécois sur les matériaux de pointe (RQMP). These authors thank S. Roorda,
M. Chicoine, L. Godbout and F. Turcot for fruitful discussions and technical
support.

The work performed at the University of Glasgow was supported by the Science
and Technology Facilities Council (STFC, ST/N005422/1 and ST/I001085/1) and
the Royal Society (UF100602 and UF150694).

The research performed at Hobart and William Smith Colleges was supported by
National Science Foundation grant awards PHY-1307423, 1611821, and 1707863.

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