Optical and mechanical properties of ion-beam-sputtered MgF2 thin filmsfor gravitational-wave interferometers

M. Granata∗ and D. ForestLaboratoire des Materiaux Avances - IP2I, CNRS, Universite de Lyon,

Universite Claude Bernard Lyon 1, F-69622 Villeurbanne, France

A. Amato and G. CagnoliUniversite de Lyon, Universite Claude Bernard Lyon 1,

CNRS, Institut Lumiere Matiere, F-69622 Villeurbanne, France

M. Bischi,† F. Piergiovanni, F. Martelli, M. Montani, and G. M. GuidiUniversita degli Studi di Urbino Carlo Bo, Dipartimento di Scienze Pure e Applicate, I-61029 Urbino, Italy and

INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Firenze, Italy

M. Bazzan, G. Favaro, and G. MaggioniUniversita di Padova, I-35131, Padova, Italy

F. Schiettekatte and M. ChicoineUniversite de Montreal, Montreal, Quebec, Canada

M. MenottaUniversita degli Studi di Urbino Carlo Bo, Dipartimento di Scienze Biomolecolari, I-61029 Urbino, Italy

A. Di MicheleUniversita degli Studi di Perugia, Dipartimento di Fisica e Geologia, Via Pascoli, 06123 Perugia, Italy

M. CanepaOPTMATLAB, Dipartimento di Fisica, Universita di Genova, Via Dodecaneso 33, 16146 Genova, Italy and

INFN, Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy(Dated: November 3, 2021)

Brownian thermal noise associated with highly reflective coatings is a fundamental limit for severalprecision experiments, including gravitational-wave detectors. Research is currently ongoing to findcoatings with low thermal noise that also fulfill strict optical requirements such as low absorptionand scatter. We report on the optical and mechanical properties of ion-beam-sputtered magnesiumfluoride thin films, and we discuss the application of such coatings in current and future gravitational-wave detectors.

Brownian thermal noise in highly reflective coatings [1,2] is a fundamental limitation for precision experimentssuch as interferometric gravitational-wave detectors [3],optomechanical resonators [4], and frequency standards[5]. As measured with a laser beam, its power spectraldensity can be written in a simplified form [6],

SCTN ∝kBT

2πf

d

w2ϕc , (1)

where kB is the Boltzmann constant, f is the frequency,T is the temperature, d is the coating thickness, w is thelaser beam radius where intensity drops by 1/e2, and ϕcis the coating loss angle. The latter quantifies the dissipa-tion of mechanical energy in the coating and is in turn afunction of frequency and temperature, ϕc(f, T ). Ther-mally induced fluctuations of coated surfaces can thus

∗ m.granata@lma.in2p3.fr† matteobischi92@gmail.com

be reduced by increasing the beam radius, by decreasingthe temperature, or by choosing coating materials whichminimize the dϕc term in Eq.(1).

High-reflection coatings are usually Bragg reflectors ofalternating layers of high and low refractive indices nH

and nL, respectively, where the number of layer pairsdetermines the coating transmissivity. However, for thesame transmissivity, the number of pairs can vary de-pending on the refractive index contrast C = nH/nL.Thus, the higher the contrast C, the lower the coatingthickness d and hence the coating thermal noise.

The high-reflection coatings of the Advanced LIGO [7],Advanced Virgo [8] and KAGRA [9] gravitational-wavedetectors are thickness-optimized stacks [10] of ion-beam-sputtered (IBS) layers of tantalum pentoxide (Ta2O5,also known as tantala, high index) and silicon dioxide(SiO2, silica, low index), produced by the Laboratoiredes Materiaux Avances (LMA) [11, 12]. Following a pro-cedure developed by the LMA to reduce their opticalabsorption and loss angle [13], the high-index layers of

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Advanced LIGO and Advanced Virgo also contain a sig-nificant amount of titanium dioxide (TiO2, titania) [15].Despite the superb optical and mechanical properties oftheir current coatings [12, 14, 15], coating thermal noiseremains a severe limitation for further sensitivity im-provement in current gravitational-wave detectors. Thus,in the last two decades, a considerable research effort hasbeen committed to find alternative coating materials fea-turing extremely low mechanical and optical losses (ab-sorption, scatter) at the same time [16].

The motivation to find alternative coating materialsis even stronger for cryogenic gravitational-wave detec-tors, either present or future, such as KAGRA, EinsteinTelescope [17], and Cosmic Explorer [18]. Although thelow-temperature behavior of the loss angles of tantalaand titania-tantala coatings is still matter of debate todate [19–22], the coating loss angle of silica has beenconclusively shown to considerably increase below 30 K[23, 24].

Because of their low refractive index [25–37] and po-tentially low mechanical loss at low temperature [38],fluorides could be a valid option for use in cryogenicgravitational-wave detectors. In this paper we reporton the measured optical and mechanical properties ofIBS magnesium fluoride (MgF2) thin films, and we dis-cuss their use in gravitational-wave detectors in place oftheir current low-index silica layers. As post-depositionannealing is a standard procedure to decrease coatingloss angle and optical absorption, we took special care tocharacterize its effect on the coating properties.

I. METHODS

A. Samples

∼200-nm thick layers of IBS MgF2 have been depositedon different substrates: (i) silicon wafers (∅ 75 mm)for optical characterization, ion beam analysis and x-raydiffraction measurements, and (ii) fused-silica disks (∅ 50mm, t = 1 mm) for mechanical characterization. Priorto deposition, the disks have been annealed in air at 900◦C for 10 hours to release the internal stress due to man-ufacturing and induce relaxation.

Coatings were deposited by Laser Zentrum Hannover1

via IBS. Prior to deposition, the base pressure inside thecoater vacuum chamber was 5 × 10−6 mbar. The totalpressure during the coating process was 2 × 10−4 mbar,with 54 sccm of noble gases (mainly Xe) and gases con-taining fluorine injected into the chamber. Energy andcurrent of the sputtering ions were 0.9 keV and 0.2 A,respectively, for an average coating deposition rate of 0.1nm/s. The angle between the main axis of the ion beamsource (main propagation direction of the ion beam) and

1 www.lzh.de

TABLE I. Soaking temperature Ta and time ∆ta of annealingtreatments applied to disk A. Heating and cooling ramps of100 ◦C/hour were used.

#1 #2 #3 #4 #5Ta [◦C] 120 200 285 311 373∆ta [h] 10 10 10 10 10

TABLE II. Soaking temperature Ta and time ∆ta of anneal-ing treatments applied to disk B. Heating and cooling rampsof 100 ◦C/hour were used.

#1 #2 #3 #4Ta [◦C] 285 285 285 285∆ta [h] 10 20 30 64cumulative time [h] 10 30 60 124

the rotation axis of the substrate holder, parallel to thesubstrate normal, was 90◦. The angle between the sourceand the target was set to 38◦.

All samples were treated together in a first coatingrun. Then, in order to cancel out the coating-inducedcurvature that would affect their mode frequencies, thedisks underwent a second coating run on their other side,under identical conditions.

In order to minimize coating mechanical loss ϕc andoptical absorption α, coated samples were thermallytreated. The annealing treatments were performed inAr atmosphere, at overpressure with respect to the envi-ronment, to avoid surface oxidation. We tested differentsoaking temperatures Ta and, with the disks only, alsodifferent times ∆ta. More specifically, a disk A under-went a series of treatments of increasing soaking tem-perature, each one of the same duration, while a diskB underwent a series of treatments of increasing time,each one performed at the same soaking temperature.Parameters used for the annealing runs of the disks aresummarized in Tables I and II.

In between measurements, all samples were stored un-der primary vacuum (10−2 − 10−1 mbar) to mitigate ox-idation from air exposure.

B. Structure and chemical composition

In order to determine the microscopic structure of thecoating samples, as well as its change upon annealing, weperformed a series of grazing-incidence X-ray diffraction(GI-XRD) measurements with a Philips MRD diffrac-tometer, equipped with a Cu tube operated at 40 kVand 40 mA. The probe beam was collimated and par-tially monochromatized by a parabolic multilayer mirror,whereas the detector was equipped with a parallel platecollimator to define the angular acceptance.

Rutherford back-scattering spectrometry (RBS) andelastic recoil detection with time-of-flight detection(ERD-TOF) [39] were used to determine the composi-

3

tion of the coating samples, after deposition and afterthe different annealing steps. RBS measurements werecarried out using 4He beams: at 2 MeV in order to relyon the Rutherford cross section of O and F, and at 3.7MeV to better resolve the different elements. The beamwas incident at an angle of 7◦ from the normal, and thedetector was placed at a scattering angle of 170◦. ForERD-TOF, a 50 MeV Cu beam was incident at 15◦ fromthe sample surface and the TOF camera was at 30◦ fromthe beam axis.

C. Optical properties

We used two J. A. Woollam spectroscopic ellipsometersto measure the coating optical properties and thickness,covering complementary spectral regions from ultravio-let to infrared: a VASE for the 0.73-6.53 eV photon en-ergy range (corresponding to a 190-1700 nm wavelengthrange) and a M-2000 for the 0.74-5.06 eV range (245-1680nm). The coated wafers were measured in reflection, theircomplex reflectance ratio was characterized by measur-ing its amplitude component Ψ and phase difference ∆[40]. To maximize the response of the instruments, (Ψ,∆) spectra were acquired at different incidence angles(θ = 50◦, 55◦, 60◦) close to the coating Brewster angle.Coating refractive index and thickness were derived byfitting the spectra with realistic optical models [40]. Theoptical response of the bare wafers had been character-ized with prior dedicated measurements. Further detailsabout our ellipsometric analysis are available elsewhere[14].

We used photo-thermal deflection [41] to measure thecoating optical absorption at λ = 1064 nm with an accu-racy of less than 1 part per million (ppm).

D. Mechanical properties

Two nominally identical disks, named A and B, wereused for the characterization of the coating mechanicalproperties. We measured their mass with an analyticalbalance, before and after each treatment (coating deposi-tion, annealing runs), and their diameter with a caliper.We then used the measured coated area, coating thick-ness from ellipsometric measurements and mass values tocalculate the coating density ρ.

We used the ring-down method [42] to measure thefrequency f and ring-down time τ of the first vibrationalmodes of each disk, before and after the coating deposi-tion, and calculated the coating loss angle

ϕc =ϕ+ (D − 1)ϕ0

D, (2)

where ϕ0 = (πf0τ0)−1 is the measured loss angle of thebare substrate, ϕ = (πfτ)−1 is the measured loss angle ofthe coated disk. D is the frequency-dependent measured

FIG. 1. GeNS systems used at Universita degli Studi diUrbino Carlo Bo (top) and at Laboratoire des MateriauxAvances (bottom) to measure the mechanical properties ofthin films.

dilution factor [43],

D = 1− m0

m

(f0f

)2

, (3)

where m0, m is the disk mass as measured before andafter the coating deposition, respectively.

We measured modes from ∼2.5 to ∼39 kHz for eachdisk, in a frequency band which partially overlaps withthe detection band of ground-based gravitational-wavedetectors (10 − 104 Hz). In order to avoid system-atic damping from suspension and ambient pressure, weused two clamp-free in-vacuum Gentle Nodal Suspension(GeNS) systems [44], shown in Fig. 1. This kind ofsystem is currently the preferred solution of the Virgoand LIGO Collaborations for performing internal frictionmeasurements [15, 45].

The disks were first measured at LMA before and aftercoating deposition, then measured, annealed and mea-sured again at Universita degli Studi di Urbino CarloBo (UniUrb). After deposition, coating Young modulusY and Poisson ratio ν were estimated by fitting finite-element simulations to the measured dilution factor vialeast-squares numerical regression [15]. Further detailsabout our GeNS systems, finite-element simulations anddata analysis are available elsewhere [15, 46].

II. RESULTS

A. Structure and chemical composition

The GI-XRD spectra of the coating samples are shownon Fig. 2, where it can be seen that diffraction peaksat about 27◦, 40◦, 44◦ and 68◦ are already present inthe as-deposited coating. Those peaks fairly match the2θ values expected for a crystalline tetragonal structure(JCPDS 70-2269) [30, 32, 35]. Other peaks between

4

20 40 60 80 100 120

2θ [deg]

Cou

nts

[a.u.]

as dep.200 ◦C300 ◦C400 ◦C500 ◦C

FIG. 2. GI-XRD spectra of IBS MgF2 thin films on siliconwafers, acquired before and after annealing at different soak-ing temperatures Ta. Diffraction peaks at about 27◦, 40◦, 44◦

and 68◦ fairly match the 2θ values expected for a crystallinetetragonal structure (JCPDS 70-2269, vertical dashed lines)[30, 32, 35], peaks between 50◦ and 60◦ are mainly due to thebackground signal of the silicon substrate.

50◦ and 60◦ are mainly due to the background signalof the silicon substrate. The change of coating peaks wasminimal for the annealed samples, as they became justslightly higher and narrower.

Results of the RBS measurements are listed in TableIII. Relative atomic concentrations and density ρ werededuced from SIMNRA simulations [47] of the RBS spec-trum acquired on each sample. The Mg/F concentrationratio is compatible with 0.5 for all samples, before andafter annealing, within the measurement uncertainty. Inaddition, all samples contain 3-5% O and 0.4-0.5% H,and are contaminated by the sputtering gas (0.5-0.8%Xe) and by Mo from the sputtering source grids. TheMo content increases from about 0.4% at the substrateinterface to 0.7% near the surface. All the samples alsocontain traces of Cu, Ar and Ta (< 0.1%). The arealatomic density found with RBS can be divided by thelayer thickness measured via spectroscopic ellipsometry(206 nm), to find a coating density ρ close to 3.0 g/cm3

for all samples. According to our analisys, the sampleannealed at Ta = 500 ◦C also featured a 3.7 nm thicktop layer of MgO, assuming an MgO bulk density of 3.85g/cm3; hence, this sample apparently suffered from somesurface degradation due to oxidation.

B. Optical properties

By way of example, figure 3 shows (Ψ,∆) spectra ofthe as-deposited coatings, acquired at an incidence angleθ = 60◦. As the band gap of crystalline magnesium fluo-ride is 10.8 eV [48], we initially expected MgF2 coatingsto be transparent in the energy region probed by our el-lipsometers. Instead, preliminary measurements showedthat some optical absorption in the ultraviolet region had

to be taken into account, in order to explain the observeddegradation of data quality above 5.7 eV, where the sig-nal to noise ratio was drastically reduced, and to correctlyfit our data. Such absorption could be explained by thepresence of color centers [30, 31], as well as by the ob-served 0.5-0.7% Mo contamination or the O-related cen-ters due to the 5% O in the samples. We then used atwo-pole function and a Tauc-Lorentz oscillator for theoptical model of the thin films, which better reproducedthe data and simultaneously fitted all the measured spec-tra with the same accuracy. In particular, the pole in theultraviolet region takes into account absorption at higherphoton energy which affects the real part of the dielec-tric function in the measurement region, and the pole inthe infrared region allows the refractive index to have aninflection point. The Tauc-Lorentz model describes theoptical absorption, but the exact position of the oscilla-tor could not be accurately determined, due to the poordata quality in the ultraviolet region. However, for thesame reason, data for E > 5.7 eV had a negligible influ-ence on the fit algorithm, and the results were compatiblewith those obtained by fitting the data up to 5.5 eV andextrapolating the values to higher photon energies.

Figure 4 shows the dispersion law and the extinctioncurve derived from our analysis of the as-deposited coat-ing data, and Table IV lists our results against thosewe found in the literature concerning IBS MgF2 thinfilms [25, 29, 30, 33, 34]. Values at E = 1.17 eV and E= 0.80 eV are particularly relevant, since those photonenergies correspond to 1064 and 1550 nm, respectively,which are the operational laser wavelenghts of currentand future gravitational-wave detectors [7–9, 17]. Re-fractive index values are n = 1.405 ± 0.005 at 1064 nmand n = 1.401± 0.005 at 1550 nm. For comparison, therefractive index at 1064 nm of the IBS silica coatingsof present detectors is n = 1.47 ± 0.01 before annealing[15]. Extinction at 6.4 eV (193 nm) is considerably higherthan the one reported in the literature [33, 34], due tothe high absorption we observed in the ultraviolet regionof the spectra.

Figure 5 shows the extinction coeffient k obtained fromthe photo-thermal deflection measurements of optical ab-sorption, as a function of the annealing temperature Ta.We assumed that loss by light scatter was negligible. Weobtained k = 1.1× 10−4 before treatment. The first an-nealing step at Ta = 200 ◦C decreased the extinction by27%, but subsequent treatments at higher temperatureconsiderably increased it. Thus, the annealing tempera-ture for minimum extinction due to optical absorption isbetween 200 and 300 ◦C.

C. Mechanical properties

The main features of disks A and B used for the mea-surements are presented in Table V.

Beside the fact of providing a cross-check of the results,the use of two independent GeNS systems allowed us to

5

TABLE III. Relative atomic concentrations (%) and density ρ of IBS MgF2 thin films, before and after annealing at differentsoaking temperatures Ta, deduced from SIMNRA simulations [47] of the RBS spectrum acquired on each sample. The Mg/Fratio is in at./at, the density was calculated by assuming a layer thickness of 206 nm for all samples, as measured via spectroscopicellipsometry on as-deposited samples. (∗)Mo concentration decreases with depth in all samples, from about 0.7% at the surfaceto about 0.45% at the substrate interface; average values are shown. (∗∗)The sample annealed at Ta = 500 ◦C features an MgOsurface layer ∼4 nm thick.

Mg F O H Ar Cu Mo(∗) Xe Ta Al Mg/F ρ [g/cm3]as deposited 32.2 63 3 0.4 0.04 0.05 0.53 0.52 0.01 0.6 0.51 2.96200 ◦C 31.5 62 5 0.5 0.04 0.05 0.53 0.71 0.01 0.51 2.97300 ◦C 31.1 62 5 0.5 0.04 0.05 0.60 0.69 0.01 0.5 0.50 3.00400 ◦C 30.8 62 5 0.5 0.08 0.05 0.56 0.60 0.01 0.49 2.98500 ◦C (∗∗) 30.4 63 5 0.4 0.04 0.05 0.61 0.84 0.01 0.48 2.83

2 4 6

20

40

60

80

Photon energy [eV]

Ψ[d

eg]

data fitextrapolation

2 4 6

100

150

200

250

Photon energy [eV]

∆[d

eg]

data fitextrapolation

FIG. 3. Measured ellipsometric spectra of IBS MgF2 thin films, acquired at an incidence angle θ = 60◦.

1 2 3 4 5 6

1.4

1.45

1.5

Photon energy [eV]

n

0

0.5

1

1.5

2

2.5

k[10−

2]

nk

FIG. 4. Refractive index n and extinction coefficient k of as-deposited IBS MgF2 thin films as a function of photon energy,derived from ellipsometric measurements. Relevant values forpresent and future gravitational-wave detectors are 0.80 and1.17 eV, corresponding to a laser wavelength of 1550 and 1064nm, respectively. For energy values smaller than ∼3.5 eV, theextinction is smaller than the sensitivity of the ellipsometers(k < 10−3).

identify and correct for a systematic effect due to thesample temperature, as described in the following.

By definition, the measured dilution factor D is verysensitive to variations of frequencies and masses. Asshown by Fig. 6, ∆D/D can be as high as ∼15% if ∆f/f

0 100 200 300 400

1

2

3

Ta [◦C]

k1064[10−

4]

FIG. 5. Extinction coefficient k1064 of IBS MgF2 thin filmsas a function of the annealing temperature Ta, obtained fromphoto-thermal deflection measurements of optical absorptionperformed at 1064 nm (Ta = 0 ◦C denotes as-deposited coat-ings).

and ∆m/m are both of the order of 0.01%. Indeed, thefrequency ratio in Eq.(3) depends on the Young modulusof the sample, which is in turn temperature dependent.The relative variation of the sample Young modulus withtemperature is a constant, η = 1

YdYdT , whereas the sample

mode frequencies are proportional to the square root of

6

TABLE IV. Refractive index n, extinction coefficient k and density ρ of as-deposited IBS MgF2 thin films. n and k valuespresented in this work were measured in the 190-1680 nm wavelength range via spectroscopic ellipsometry. The k value at1064 nm was deduced from photo-thermal deflection measurements of optical absorption, by assuming negligible scatter loss.(∗)Extrapolations.

E [eV] / λ [nm] This work Allen et al. [25] Bosch et al. [29] Quesnel et al. [30] Gunster et al. [33] Yoshida et al. [34]

0.80 / 1550n 1.401 ± 0.005 1.380 (∗)

k < 10−3 1.5× 10−5 (∗)

0.94 / 1320n 1.403 ± 0.005 1.380 (∗)

k < 10−3 7× 10−4 1.7× 10−5 (∗)

1.17 / 1064n 1.405 ± 0.005 1.380 (∗)

k (1.062± 0.004)× 10−4 5× 10−4 2.0× 10−5 (∗)

1.96 / 633n 1.411 ± 0.005 1.453 ± 0.023 1.383

k < 10−3 4.2× 10−5

3.53 / 351n 1.426 ± 0.005 1.391 1.390− 1.41

k < 10−3 1.7× 10−4 8× 10−6 − 3.3× 10−2

6.42 / 193n 1.46 (∗) 1.44− 1.45 1.44

k 0.024 (∗) 2− 5× 10−3 2× 10−4

ρ [g/cm3] 2.7 ± 0.2 3.18

TABLE V. Disks used to characterize the coating mechanicalproperties: diameter ∅, mass m0 before coating, mass m aftercoating, coating thickness d on each side.

A B∅ [mm] 49.77 ± 0.03 49.92 ± 0.01m0 [g] 4.6158 ± 0.0001 4.6348 ± 0.0001m [g] 4.6180 ± 0.0001 4.6369 ± 0.0004d [nm] 206 ± 2 206 ± 2

FIG. 6. Relative error ∆D/D on dilution factor as a functionof relative errors ∆f/f and ∆m/m on frequency and mass,respectively, for disk B (f0 = 2681.062 Hz, f = 2682.759 Hz).See Eq. (3) and Table V for more details.

the Young modulus, f ∝√Y . Thus we expect that

logf(T )

f(T0)=η

2(T − T0) , (4)

where f(T ) is the mode frequency at temperature T . OurGeNS system at LMA is installed in a clean room wherethe temperature is stabilized to (21.9 ± 0.5) ◦C, while ourGeNS system at UniUrb is in a room without tempera-ture control. Each setup has a temperature probe in itsvacuum tank: right under the GeNS copper base plate at

30 40 50 60

0

1

2

·10−3

T [◦C]

log[f

(T)/f

(T0)]

substrate

coated (B)fit

FIG. 7. Variation of mode frequency f(T ) as a function ofsample temperature T , for a bare disk and coated disk B.

LMA, on a twin suspended sample2 at UniUrb (visible inthe foreground of Fig. 1). In order to measure the changeof resonant frequencies with temperature, we installedheating strips around the vacuum tank of the GeNS sys-tem at UniUrb and slowly heated a bare disk, monitor-ing the frequency of its first mode. That bare disk wasnominally identical to disks A and B, from their samebatch. Afterward, we applied the same procedure alsoto the coated disk B. Figure 7 shows the results of thosemeasurements. We obtained η = (1.50 ± 0.01) × 10−4◦C−1 for the bare disk and η = (1.58±0.01)×10−4 ◦C−1

for coated disk B, by linearly fitting the data in a semi-logaritmic scale. We then used these values to perform a

2 We found no experimental evidence that the laser of the opticallever used to measure the ring-down amplitude of the main sam-ple induced a temperature variation, therefore we assumed thatthe temperature measured on the twin sample is equal to that ofthe main sample.

7

correction of measured mode frequencies by an amount

∆f =η

2(T − T0) f(T0) (5)

for data of both disks A and B. This correction is criti-cal, whenever mode frequencies are measured in a systemwhere temperature may drift.

Figure 8 shows the dilution factor and loss angles ofdisks A and B, as measured at LMA. In the 2.5–39 kHzfrequency band, the mechanical loss of the as-depositedIBS MgF2 coatings ranges from about 5.5 to 7.5× 10−4

rad, that is, 20 to 30 times higher than that of the as-deposited silica layers of current gravitational-wave de-tectors [15]. This excess loss might be partly explainedby the poly-crystalline phase of the MgF2 coatings.

For comparison, Kinbara et al. measured a coatingloss angle of 3.5 to 5 × 10−4 rad at 30 Hz on thermallyevaporated MgF2 thin films [49, 50]. Such different valuescould be explained by the different frequency of theirmeasurement, and possibly also by the different natureof their thin films, grown with a different technique.

In order to describe the observed frequency-dependentbehavior of the coating loss angle, we fit a power-lawmodel [51–53]

ϕc(f) = a

(f

10 kHz

)b(6)

to our data via least-squares linear regression. Table VIlists the best-fit parameters (a, b) for each measured disk,together with the best-fit estimations of coating Youngmodulus Y and Poisson ratio ν obtained via the dilutionfactor fitting procedure described in Section I D. By tak-ing the average of the results of the two disks, we obtainY = 115 GPa and ν = 0.27. Kinbara et al. [49, 50] ob-tained Y = 70 GPa and Y = 150 GPa by applying theresonant method to two different substrates, but couldnot identify the reason for such discrepancy. Our resultsfall within that range.

For the as-deposited samples, we obtained a density ρof 2.7 ± 0.2 g/cm3 from coating mass and thickness el-lipsometric measurements, a value fairly close but lowerthan that of 2.96 g/cm3 obtained via RBS. Similarlyto the coating sample annealed at 500 ◦C, which hasthe lowest density as measured through RBS (ρ = 2.83g/cm3), this might be explained by the fact that the sam-ples used for the characterization of the coating mechan-ical properties suffered from some surface oxidation, de-spite their storage under primary vaccum.

Figure 9 shows the effect of the post-deposition an-nealing treatments on the average coating loss angle ofdisks A and B, calculated from several exemplary modesat different frequencies. As we increased the annealingtemperature up to Ta = 311 ◦C, the average coating lossof disk A monotonically decreased from the initial valueof (5.9± 0.7)× 10−4 rad to (2.0± 1.3)× 10−4 rad. Aftertreatment at Ta = 373 ◦C, however, its average coatingloss increased to (8.4± 3.6)× 10−4 rad. Such substantial

TABLE VI. Measured mechanical properties of as-depositedIBS MgF2 thin films: Young modulus Y , Poisson ratio ν andbest-fit parameters of the power-law model of Eq.(6) used todescribe the observed frequency-dependent behavior of thecoating loss angle.

Y [GPa] ν a [10−4 rad] bdisk A 115 ± 3 0.28 ± 0.02 6.4 ± 0.1 0.09 ± 0.02disk B 115 ± 3 0.26 ± 0.02 5.9 ± 0.2 0.10 ± 0.03

increase might be explained by the appearence of crackson the coating surface, observed on disk A with an opti-cal microscope and shown on Fig. 10, likely due to thefact that the SiO2 substrate and the MgF2 coatings havedifferent thermal expansion coefficients. Similar crackswere previously observed by Kinbara et al., and ascribedto the relaxation of accumulated stress [49, 50]. Regard-less, the annealing temperature for minimum coating lossangle ϕc is around Ta = 311 ◦C.

Concerning the annealing time, in order to avoid theformation of cracks, we used a soaking temperatureTa = 285 ◦C for our tests. The average coating loss angleof disk B decreased after each step until the cumulativetime of treatment amounted to 30 hours, when it was(3.5 ± 1.4) × 10−4 rad. However, the change in coatingloss between the step of 10 hours and those of longer cu-mulative soaking time is negligible, when compared to themeasurement uncertainty. Thus, in summary, we foundthat a soaking time longer than 10 hours has no effect onthe average coating loss angle value, for Ta = 285 ◦C.

III. CONCLUSIONS

In the framework of a research activity devoted to findlow-noise coating materials for present and future grav-itational wave detectors [16], we characterized the opti-cal and mechanical properties of a set of IBS MgF2 thinfilms. We chose fluoride coatings because of their lowrefractive index, with the aim of minimizing the coat-ing thickness d in Eq.(1). Furthermore, because of theirpotentially low mechanical loss at low temperature [38],fluorides could be a valid option for use in cryogenic de-tectors.

Indeed, the IBS MgF2 thin films featured a 4% lowerrefractive index than that of IBS silica layers of currentdetectors [15]. However, their optical absorption andambient-temperature loss angle turned out to be con-siderably higher, likely because they were partially poly-crystalline. In order to minimize such losses, the coatingsamples were thermally treated with increasing soakingtemperature and time. The lowest loss values obtainedwere then compared against the very stringent require-ments of current detectors. It then appeared evidentthat, in order to be used in gravitational-wave detectors,both the optical and mechanical loss of IBS MgF2 thinfilms will have to be further reduced. This could be pos-

8

10−8

10−7

10−6

ϕ0,ϕ

[rad

]

A

ϕ0ϕ

B

ϕ0ϕ

1.6

1.7

1.8

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D[1

0−3]

datafit

datafit

10 20 30 40

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Frequency [kHz]

ϕc

[10−

4ra

d]

datafit

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Frequency [kHz]

datafit

FIG. 8. Characterization of loss angles of disks A (left column) and B (right column), as a function of frequency. Top row:measured loss angles before and after deposition of IBS MgF2 thin films (ϕ0 and ϕ, respectively). Middle row: comparisonbetween measured and least-squares best-fit simulated dilution factor D. Bottom row: coating loss angle ϕc of as-depositedIBS MgF2 thin films; the best-fit power-law model of Eq.(6) is also shown (dashed line). See Eq.(2) for more details.

sibly achieved by changing the coating growth conditions[15], as well as by reducing the amount of impurities. Asshown in Table IV, for instance, Bosch et al. and Ques-nel et al. demonstrated that IBS MgF2 thin films ofsignificantly lower extinction and refractive index can beproduced [29, 30].

The optimization of the growth parameters and themeasurement of the low-temperature mechanical loss an-gle of IBS MgF2 thin films will be the object of futurestudies.

ACKNOWLEDGMENTS

This work has been promoted by the Laboratoire desMateriaux Avances and partially supported by the VirgoCoating Research and Development (VCR&D) Collabo-ration. The work carried out at U. Montreal is supportedby the FRQNT through the RQMP on equipment ob-tained in part thanks to the CFI and NSERC. The au-thors would like to thank M. Gauch, F. Carstens and H.Ehlers of the Laser Zentrum Hannover for the production

9

0 100 200 300 400

2

4

6

8

10

12

Ta [◦C]

ϕc[10−

4rad]

0 30 60 90 120

Cumulative time [h]

FIG. 9. Coating loss angle ϕc of IBS MgF2 thin films, as a function of annealing temperature Ta for a soaking time ∆ta = 10h (left) and of cumulative soaking time at temperature Ta = 285 ◦C (right), see Tables I and II for more details (Ta = 0 ◦Cdenotes as-deposited coatings).

FIG. 10. Cracks at the surface of the IBS MgF2 thin films ondisk A, observed after annealing at Ta = 373 ◦C.

of the MgF2 thin films and for the fruitful discussions, aswell as M. Fazio for the first review of the manuscript.This work has document numbers LIGO-P2100113 andVIR-0314C-21.

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